Ion clustering in aqueous solutions probed with ... - Semantic Scholar

Ion clustering in aqueous solutions probed with vibrational energy transfer Hongtao Biana, Xiewen Wena, Jiebo Lia, Hailong Chena, Suzee Hana, Xiuquan Sunb, Jian Songb, Wei Zhuangb, and Junrong Zhenga,1 a Department of Chemistry, Rice University, Houston, TX 77005; and bState Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People’s Republic of China

Edited* by Robert F. Curl, Rice University, Houston, TX, and approved February 4, 2011 (received for review January 3, 2011)

T

he solution properties of ions in water are relevant to a wide range of systems, including electrochemistry, biological environments, and atmospheric aerosols (1, 2). For more than 100 yr, tremendous scientific efforts have been devoted to unravel the hydration structures of ions in water (1–11). However, many fundamental questions remain open, in particular concerning the existence, concentration, and structure of ion clusters in 1∶1 strong electrolyte aqueous solutions. Whether strong 1∶1 electrolytes (especially salts of Naþ and K þ ) form ion pairs or clusters in water has been considered a key issue for understanding many important problems, e.g., the excess ionic activity in 1∶1 electrolytes (12), ion dependent conformational and binding equilibria of nucleic acids (13), the concentration difference between Naþ and K þ in living cells, protein denaturation by salts (14, 15), and ion concentration dependent properties of ion channels (16). The properties of aqueous solutions of 1∶1 strong electrolytes deviate from the ideal dilute solution at extremely low concentrations (90%) form ion clusters, suggesting water/ion microphase separations. In other words, in an apparent “homogeneous” SCN− aqueous solution, both clustered and water-solvated anions simultaneously exist, as illustrated in Fig.. 1A. Even at a medium concentration (1M) with a salt/water molar ratio only 1∶50, ∼27% of anions are clustered under the ambient condition. As expected, diluting the solution shifts the dissolution equilibrium to fewer and smaller clusters, but, surprisingly, dilution makes the clusters tighter. The ion clustering is cation-size-dependent with smaller cations tending to form smaller and fewer clusters. Results and Discussion Anions in a Cluster Can Exchange Vibrational Energy. We first describe

the vibrational energy transfer method for studying ion clustering in a concentrated KSCN solution, and then present the concentration and cation dependent results. Fig. 1B is the FTIR spectrum of the CN and 13 C15 N− stretches of SCN− and S13 C15 N− in a 1∶1 KSCN∕KS13 C15 N mixed aqueous (D2 O) solution with a salt/water molar ratio 1∕2.4 (10M, which we name as solution C). The isotope labeling shifts the CN stretch frequency from 2;064 cm−1 (SCN− ) down to 1;991 cm−1 (S13 C15 N− ). Theoretical predictions for other concentrated or melt electrolyte solutions (26, 27), suggest that the probability of forming contact clusters of the general formula K n ðSCNÞm ðS13 C15 NÞp is statistically very high in solution C. In these clusters, the anions SCN− and S13 C15 N− can be considered as “ligands” to the cation K þ . The anions thus held in close proximity can exchange vibrational energy through their overlapped orbitals or via dipole-dipole interactions, in a manner similar to that observed for metal carbonyl compounds (28). Vibrational energy exchange between SCN− and S13 C15 N− in the clusters can be monitored with fast 2D IR methods (Fig.. 1C, here the solution is C, i.e., 10M). From these 2D IR measurements, not only the vibrational energy exchange rates, but also the cluster concentration and the exchange dynamics between clustered and separated anions can be obtained. The intermolecular mode-specific vibrational energy transfer 2D IR technique has been previously described in detail (22, 23). Very briefly, energy exchange 2D IR measurements allow the energy exchange between the CN and 13 C15 N stretches of SCN− and S13 C15 N− to be followed in real time through the Author contributions: J.Z. designed research; H.B., X.W., J.L., S.H., and J.Z. performed research; X.S., J.S., W.Z. did MD simulations; H.B., X.W., J.L., H.C., and J.Z. contributed new reagents/analytic tools; H.B., X.W., H.C., and J.Z. analyzed data; and J.Z. wrote the paper. The authors declare no conflict of interest. *This Direct Submission article had a prearranged editor. 1

To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/ doi:10.1073/pnas.1019565108/-/DCSupplemental.

PNAS ∣ March 22, 2011 ∣ vol. 108 ∣ no. 12 ∣ 4737–4742

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Despite prolonged scientific efforts to unravel the hydration structures of ions in water, many open questions remain, in particular concerning the existences and structures of ion clusters in 1∶1 strong electrolyte aqueous solutions. A combined ultrafast 2D IR and pump/probe study through vibrational energy transfers directly observes ion clustering in aqueous solutions of LiSCN, NaSCN, KSCN and CsSCN. In a near saturated KSCN aqueous solution (water/KSCN molar ratio ¼ 2.4∕1), 95% of the anions form ion clusters. Diluting the solution results in fewer, smaller, and tighter clusters. Cations have significant effects on cluster formation. A small cation results in smaller and fewer clusters. The vibrational energy transfer method holds promise for studying a wide variety of other fast short-range molecular interactions.

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growth of the two cross peak pairs (Peaks 5 ∼ 8) as marked in the 50-ps row of Fig.. 1C (for the 10M solution named C). The anions which have not exchanged their energy (including anions which have exchanged but received energy from reverse transfers and the resonance acceptors of the same isotope) produce the two diagonal peak pairs (Peaks 1 ∼ 4). Now we consider all six waiting-time (T w ) dependent 2D IR spectra of solution C at room temperature. The 200-fs row corresponds to a very short T w , at which negligible vibrational energy exchange has occurred. During the T w period, the initial and final energy carriers in the sample are unchanged. Therefore, the ωpump (the excitational frequency) and ωprobe (the detected frequency) values of each red peak (the 0–1 CN or 13 C15 N stretch transition) are identical, and the peaks appear only on the diagonal. The two blue peaks 2 and 4 are the 1-2 transitions, which shift to lower frequencies along the ωprobe axis because of vibrational anharmonicity. Peaks 1 and 2 represent SCN− and Peaks 3 and 4 are for S13 C15 N− . With the increase of probe delay time (T w ¼ 200 fs ∼ 20 ps), vibrational energy begins to flow between the two anions. Cross peak pairs begin to grow. After a long reaction period (T w ¼ 50 ps), vibrational energy has exchanged to a substantial degree as shown by the additional peaks (Peaks 5 ∼ 8) that have appeared on the off-diagonal. These new peaks arise from the vibrational energy exchange. The vibrational energy transfer from SCN− to S13 C15 N− produces peaks 5 and 6 at positions with ωpump ¼ 2;064 cm−1 and ωprobe ¼ 1;991 cm−1 and 1;966 cm−1 . ωpump ¼ 2;064 cm−1 is the 0–1 transition frequency of the CN stretch, representing the vibrational energy is originally from SCN− . ωprobe ¼ 1;991 cm−1 and 1;966 cm−1 are the 0–1 and 1–2 transition frequencies of the 13 C15 N− stretch, respectively, representing that at the end of T w the vibrational energy has transferred to S13 C15 N− . Likewise, peaks 7 and 8 are produced by energy transfer from S13 C15 N− to SCN− . 4738 ∣

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Fig. 1. (A) A snapshot of a 1.8M KSCN aqueous solution from a molecular dynamics simulation (Details are in SI Appendix). O (red), H (white), C (light blue), N (deep blue), K (green), and S (yellow). An ion cluster is visible at the center of the picture. Some water molecules are removed from the original file to better display the cluster structure. (B) FTIR absorption spectra of the CN and 13 C15 N stretches of SCN− and S13 C15 N− of a 10M 1∶1 KSCN∕KS13 C15 N aqueous solution (solution C). (C) The time dependence of the 2D IR spectrum of solution C. As T w increases, the off-diagonal peaks grow in because of energy exchange between SCN− and S13 C15 N− . The vibrational coupling and the heat effect (22, 23) (pump/probe data are in SI Appendix: Fig. S1) are too weak to show up in the spectra of the time range.

In contrast to the chemical exchange 2D IR methods (29–33), the cross peak intensities in the energy exchange method are not equal. The ratio of the cross peaks’ growth rates is determined by the Boltzmann distribution. The energy mismatch between the CN and 13 C15 N stretches is 2;064-1;991 ¼ 73 cm−1 , making the energy up-pumping rate constant from S13 C15 N− to SCN− ∼70% of the down-flowing rate constant from SCN− to S13 C15 N− . As in Fig.. 1C, Peaks 5 and 6 are always bigger than Peaks 7 and 8 at the same T w s. In solution C, some anions are clustered and can transfer energy efficiently. Some anions are well separated from each other and less able to exchange energy with other anions. These two types of anions are not frequency resolvable. Both produce diagonal peak pairs in 2D IR spectra in Fig.. 1C. Because the clustered anions can exchange energy much more efficiently, the cross peak pairs are mostly from the clustered anions. Therefore, simultaneous analysis of diagonal and cross peaks provides not only the rate constants for energy exchange, but also the ratio of clustered to separated anions and the rate constants for the exchange of anions from separated to clustered. In solution C, based on the liquid density, the nominal average anion distance is calculated to be 5.5 Angstrom (Å). Can the energy exchange observed in Fig. 1C be simply because of the short average distance rather than ion clustering? The speculation can be directly tested by diluting the solution. Previous experiments suggest that the intermolecular vibrational energy transfer can be described by the dipole-dipole interaction (25, 34–36):  6 1 ; [1] k∝ r where k is the energy transfer rate constant and r is the donor/ acceptor distance. According to [1], diluting solution C with a water/salt ratio from 2.4∕1 to 25∕1 will increase the average anion distance for ∼1.9 times and therefore slow down the energy transBian et al.

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very close distance in the aqueous solutions is the most probable reason for this discrepancy. (More details and supporting experiments are in the control experiment part of the SI Appendix.) The main reason for the smaller cross peaks in the spectra of a more dilute solution (Fig.. 2) is a lower concentration of clustered ions instead of a slower energy transfer rate. Quantitative analysis based on the nonresonant energy transfer data and the following kinetic model shows that only 35% of anions (Data and calculations are in SI Appendix) are clustered in the 1.8M solution while 95% of the anions form clusters in solution C. Surprisingly, diluting the solution in fact decreases rather than increases the average distance between two clustered anions, as observed from our energy transfer experiments presented in following paragraphs. 95% of Anions Form Clusters with Average Anion Distance 3.7 Å in a 10M KSCN Aqueous Solution. In solution C, some S13 C15 N− and

SCN− form clustered anions (denoted as S13 C15 N− clu and SCN− clu ), and the rest of the anions are separated (denoted as S13 C15 N− iso and SCN− iso ). These two types of anions are in dynamic equilibrium: they can exchange locations with rate constants kclu→iso and kiso→clu with a ratio equal to an equilibrium constant K ¼ kkiso→clu . The S13 C15 N− clu and SCN− clu anions can exclu→iso change vibrational energy with rate constants kS13 C15 N− →SCN− and kSCN− →S13 C15 N− with a ratio determined by detailed balance: k

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fer rate for 51 times. However, from the concentration dependent 2D IR measurements (Fig.. 2), in such a dilute solution (1.8M), the energy exchange cross peaks at 50 ps are still clearly visible, with a normalized intensity about 14 of those of solution C at the same waiting time (Fig.. 1C). This result indicates that the apparent energy transfer rate in the 1.8M solution is only about four times slower than solution C, one order of magnitude smaller than the predicted 51 times. The contradiction between experiments and the prediction based on the speculation suggests that the observed energy transfer is probably from some anions with average distance much smaller than the nominal 5.5 Å and this distance is not affected by dilution significantly. The only plausible explanation of this dilution experiment is that the anions responsible for energy transfer are in clusters. In a control experiment, no energy exchange was observed between the SCN and S13 C15 N groups in a 1∶1 C2 H5 SCN and C2 H5 S13 C15 N mixed liquid (Fig.. 3). In the control sample, the average molecular distance is 5.2 Å, and the energy mismatch (78 cm−1 ) between the two isotope-labeled CN stretches is very similar to that (73 cm−1 ) between the two anions in C. If anions in the electrolyte solutions are not clustered, based on [1] without considering other factors, the energy transfer rates in the control sample would be 67 times faster than those in the 1.8M solution, which has assuming no clustering an average anion distance of 10.5 Å. However, at T w ¼ 30 ps, the energy transfer cross peaks in the 2D IR spectrum of the 1.8M solution (Fig.. 2) are already visible, while no cross peaks are observed for the control sample, indicating that energy transfers faster in the 1.8M solution than in the control sample. Ion clustering which holds anions within a

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Fig. 3. The time dependence of the 2D IR spectrum of a 1∶1 C2 H5 SCN∕C2 H5 S13 C15 N mixed liquid. No cross peaks have grown in up to 30 ps, indicating negligible energy has exchanged between the CN and 13 C15 N stretches of the two molecules.

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Fig. 2.

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One Energy Donor has Seventeen Acceptors in a 10M KSCN Solution.

In addition to the concentration of ion clusters revealed by the nonresonant energy transfer experiments, the cluster sizes can also be evaluated by resonant energy transfer measurements. In these experiments, the resonant energy transfer from one donor to any acceptor, as well as molecular rotations, can cause the anisotropy of vibrational excitation to decay (25, 36). During resonant energy transfers, the energy can be transferred back from acceptors to the original donor. The probability of reverse transfer is inversely proportional to the number of acceptors: more acceptors resulting in statistically less likely reverse trans-

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4740 ∣

where τor is the molecular rotational time constant in a cluster, and c is the fraction of S13 C15 N− (the energy carrier) among the isotope-labeled anions in a cluster. Changing the ratio of S13 C15 N− ∕SCN− in a solution can change the number of resonant energy acceptors for one donor and therefore the resonance-energy-transfer-induced anisotropy decay rate, while the chemical properties of the cluster are unchanged. ntot is the number of anions (both S13 C15 N− and SCN− ) within an effective energy transfer unit. τ is the resonant one-donor-to-one-acceptor energy transfer time constant. In Eq. 2, only two parameters (ntot and τ) are experimentally unknown. Calculations with the two adjustable parameters simultaneously fit the experimental results of six different isotope ratios very well (Fig.. 5). The calculations show that τ ¼ 54
8 ps and ntot ¼ 18
3. The number 18 is the same as the number of first shell SCN− anions surrounding one anion in the KSCN crystals (37, 38). (More details are in SI Appendix). At this point, we don’t have any solid evidence to show that the energy acceptor number 18 − 1 ¼ 17
3 obtained from our experiments represents the number of anions surrounding one anion in the crystal. However, from the similarity of the anion distance and this acceptor number between the ion clusters and the crystal, we believe that some structural aspects of a big cluster in solution C is probably similar to those in the crystal, e.g., the shortest anion distance and the number

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fers. When a reverse transfer occurs, the anisotropy is recovered. Therefore, fewer acceptors for one donor (corresponding to a smaller cluster) will result in slower energy-transfer-induced anisotropy decay. Based on the physical picture, we derive an equation which can be used to extract the number of anions involved in the effective energy transfer (Details are in SI Appendix):   t RðtÞ 1 t ¼ e−τor 1 − e−½1þðntot −1Þ×cτ Rð0Þ 1 þ ðntot − 1Þ × c  1 ; [2] þ 1 þ ðntot − 1Þ × c

Normalized Anisotropy

transfer vibrational energy to another anion. The vibrational excitations of S13 C15 N− and SCN− decay with their own vibrational relaxation rate constants kS13 C15 N− and kSCN− (here we assume the clustered and separated ions have the same k. The assumption with different vibrational relaxation rate constants for clustered and separated ions is also tested. See SI Appendix for more details). From these considerations, we construct a kinetic model for the observations as illustrated in the following scheme 1. In these experiments, we obtained molecular-rotation-free data (22). Therefore, the model doesn’t contain any orientational component. From the model, four differential equations are derived. By solving the equations (Details are in SI Appendix), the energy transfer rate constants, the clustered/separated ion equilibrium constant, and the location exchange rate constants are obtained. Because the ratio of the rate constants for location exchange is the equilibrium constant and the ratio of the energy transfer rate constants are determined by the difference in the CN stretching energy of the isotopic species, there are only three unknown parameters to be determined. The vibrational relaxation rate constants, and the time dependent concentrations of excited species are experimentally determined. Calculations simultaneously fit the four experimental curves very well (Fig. 4 A and B) with the three parameters: 1∕kSCN− →S13 C15 N− ¼ 115
15 ps, the equilibrium constant K ¼ 19
3 (95
1% of anions are clustered), and the clustered and separated ion exchange time constant 1∕kclu→iso ¼ 12
7 ps. Based on the energy transfer rate constant, and the energy transfer equation from a previous publication (23), the experimentally determined vibrational coupling constant, and the assumption of dipoledipole interaction for vibrational energy transfer, the average distance between the C ≡ N groups of two SCN− anions in a cluster is determined to be 3.7
0.3 Å. The value is very close to the shortest C ≡ N distance 3.8 ∼ 4.0 Å in KSCN crystals (37, 38). (More details are in SI Appendix.)

www.pnas.org/cgi/doi/10.1073/pnas.1019565108

Fig. 5. The anisotropy decay data (dots) and calculations of Eq. 2 (lines) of the 13 C15 N stretch of S13 C15 N− in 10 M salt aqueous solutions with different KS13 C15 N∕KSCN ratios. Adjusting the KS13 C15 N∕KSCN ratio changes the number of resonance energy acceptors for the excited S13 C15 N− donor. The calculations yield ntot ¼ 18
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Diluted Solutions Have Fewer, Smaller, and Tighter Clusters. According to the thermodynamic principle (39), diluting solution C with water shifts the dissolution equilibrium to fewer clusters. Diluting solution C with water shifts the dissolution equilibrium to fewer clusters, this can be revealed by simple inspection of the growth of cross peaks in 2D IR spectra of solutions with different salt concentrations (Fig.. 2). At higher concentrations, the intensities of cross peaks are higher at the same T w s. As described above, the growth of cross peaks is from the energy exchange of clustered anions, while the diagonal peak pairs are from both clustered and separated anions. The cross/diagonal peak ratio represents not only how fast the energy exchange is, but also how many of the anions form clusters. A higher cross/diagonal peak ratio indicates a faster energy transfer and/or more clusters. Quantitative analyses based on the above methods show that fewer and smaller clusters form in a lower concentration (Fig. 6A. Numerical values are listed in SI Appendix: Table S1). The fraction of anions in clusters is unexpectedly large in all studied concentrations. In highly concentrated solutions (10 and 8.8M) almost all anions are in clusters (>90%). Even for a relatively dilute solution (1M) whose salt/water ratio is only ∼1∕50, there still ∼27% of anions in clusters which contain three anions on average. The results suggest microphase separation in these solutions. SCN− is one of the strongest and most frequently used protein denaturants. SCN− has been the subject of intense investigations and debates for its “salt-in” effect for many years (40). The high clustering tendency of KSCN observed in these experiments suggests another avenue for understanding SCN− ’s high effectiveness in denaturing proteins: it is conceivable that the interaction between SCN− and water is indeed not very strong so that

Salts with Bigger Cations Form More Clusters. It has long been recognized that the size and charge density of a cation have profound effects on the properties of electrolyte solutions and their biological activities (2). Theoretical calculations suggest that cations may affect the formation of ion pairs and clusters in aqueous solutions (12, 41). To explore cation specific effects, we performed energy transfer measurements on 4M (salt∕ water ratio ¼ 1∕10) aqueous solutions of LiSCN, NaSCN, KSCN, and CsSCN. These experiments show that in solution, smaller cations form smaller and fewer clusters (Fig.. 6 C and D. Numerical values are listed in SI Appendix: Table S1). In solution with the smallest cation Liþ (LiSCN), ∼50% of the anions form clusters which contain ∼4 anions on average. In solution with the biggest cation Csþ (CsSCN), ∼70% of the anions form clusters containing ∼9 anions. This trend may be qualitatively understood with the theoretical description of “matching cation and anion sizes” for some electrolyte solutions (41, 42): small-small and large-large easily associate, while small-large readily dissociate. SCN− is large and polarizable, and therefore, more readily associates with the large and polarizable Csþ than the small Liþ . The Energy Exchange Method Can Be General for Short-Range Molecular Interactions. The mode-specific vibrational energy exchange

method can be used to study many molecular interactions if the interactions are strong enough and the probe vibrational lifetimes are long enough. The energy exchange method may or may not need isotope labeling, which in general does not perturb the

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Fig. 6. (A) The concentration dependences of clustered ion percentage and the number (ntot ) of anions in an energy transfer unit of KSCN aqueous solutions. (B) The concentration dependence of the one-donor-to-one-acceptor resonant energy transfer time constant in ion clusters of KSCN aqueous solutions. (C) The cation dependences of clustered ion percentage and the number (ntot ) of anions in an energy transfer unit of 4M aqueous solutions of LiSCN, NaSCN, KSCN, and CsSCN. (D) The cation dependence of the one-donor-to-one-acceptor resonant energy transfer time constant in ion clusters of 4 M aqueous solutions of LiSCN, NaSCN, KSCN, and CsSCN.

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SCN− prefers to associate to amino acid residues of a protein over water in a protein aqueous solution. Another interesting result of the concentration dependent experiments is that the one-donor-to-one-acceptor energy transfer rate is faster at a lower concentration (Fig.. 6B). According to [1], this result suggests that a smaller cluster is tighter. The exact molecular mechanism giving rise to this phenomenon is not clear at this point. Instead, we propose a qualitative explanation. In a bigger cluster, more anions are close to each cation so that the average radius of the anion shells could be larger because of the geometry constraint and electrostatic repulsion.

of anions in the first solvation shell of an energy donor. In experiments, Kþ doesn’t produce any signal. Kþ ’s number in any cluster was therefore not determined. In highly concentrated solutions, the clusters could be large and contain many energy transfer units. Thus ntot is not the same as the number of anions in a cluster. At lower concentrations, the numbers and sizes of clusters become smaller. ntot is expected to become closer to the number of anions in a cluster.

molecular interactions. The only requirement is that the ions (or molecules) have IR active modes and the vibrational lifetimes of the modes are comparable to the energy transfer time scales (which mostly range from a few ps to a few hundred ps). Many important anions in biology or electrochemistry, e.g., CN− , SO4 2− , NO3 2− , PO4 3− , CO3 2− , BF4 − , SCN− , and ClO4 − , have strong IR active vibrational modes. These modes typically have lifetimes of a few to tens of ps, overlapping with the energy transfer time scales. In addition, high salt concentrations are not necessarily required. The method can be applied to solutions of any concentration if the percentage of the clustered ions is high enough to provide a sufficient signal/noise ratio. In principle, the requisite clustering percentage can be as low as ∼0.1%. The method is not limited to ions. The energy exchange method can be also applied to the investigation of other short-range molecular interactions, e.g., those of peptide/sugar, DNA/protein, and drug/protein complexes, as long as the complexes have vibrational active modes fulfilling the requirements.

Materials and Methods Materials. Unless specified, chemicals were purchased from Sigma-Aldrich and used without further purification. KS13 C15 N and NaS13 C15 N were purchased from Cambridge Isotope Laboratory. D2 O was from C/D/N ISOTOPES INC. LiS13 C15 N was synthesized by precipitating KClO4 out of the KS13 C15 N and LiClO4 mixed aqueous solution. CsS13 C15 N was synthesized by precipitating LiF out of the LiS13 C15 N and CsF mixed aqueous solution. Methods. A ps amplifier and a fs amplifier are synchronized with the same seed pulse. The ps amplifier pumps an optical parametric amplifier (OPA) to produce ∼1 ps mid-IR pulses with a bandwidth ∼21 cm−1 in a tunable frequency range from 900 cm−1 to 4;000 cm−1 with energy 10 ∼ 40 μJ∕pulse at 1 KHz. The fs amplifier pumps another OPA to produce ∼140 fs mid-IR pulses with a bandwidth ∼200 cm−1 in a tunable frequency range from 900 cm−1 to 4;000 cm−1 with energy 10 ∼ 40 μJ∕pulse at 1 KHz. In 2D IR and pump/probe experiments, the ps IR pulse is the pump beam (pump power is adjusted based on need). The fs IR pulse is the probe beam which is frequency resolved by a spectrograph yielding the probe axis of a 2D IR spectrum. Scanning the pump frequency yields the other axis of the spectrum. Two polarizers are added into the probe beam path to selectively measure the parallel or perpendicular polarized signal relative to the pump beam. Vibrational lifetimes are obtained from the rotation-free 1–2 transition signal P life ¼ P ∥ þ 2 × P ⊥ , where P ∥ ;P ⊥ are parallel and perpendicular data respectively. Rotational reP ∥ −P ⊥ . laxation times are acquired from τ ¼ P∥ þ2×P ⊥

Concluding Remarks The results presented here demonstrate that in the 1∶1 electrolyte aqueous solutions with medium to high concentrations, a significant portion of the ions form clusters. Diluting the solution results in fewer, smaller, and tighter clusters. Cations have significant effects on cluster formation. A small cation results in smaller and fewer clusters. The vibrational energy transfer method holds promise for studying a wide variety of other fast short-range molecular interactions.

ACKNOWLEDGMENTS. We thank Professors Anatoly Kolomeisky, Philip Brooks, Robert Curl, and James Kinsey at Rice, Xueming Yang at Dalian Institute of Chemical Physics (DICP) and Dr. Xin Chen at Harvard for insightful discussions. This work was supported by Rice University and the Welch foundation. W.Z. thanks DICP for the 100 Talents Support Grant and National Natural Science Foundation of China (NSFC) for the 2010 QingNian Grant.

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23. Bian HT, Wen XW, Li JB, Zheng JR (2010) Mode-specific intermolecular vibrational energy transfer. II. Deuterated water and potassium selenocyanate mixture. J Chem Phys 133:034505-1–034505-15. 24. Woutersen S, Bakker HJ (1999) Resonant intermolecular transfer of vibrational energy in liquid water. Nature 402:507–509. 25. Gaffney KJ, Piletic IR, Fayer MD (2003) Orientational relaxation and vibrational excitation transfer in methanol—carbon tetrachloride solutions. J Chem Phys 118:2270–2278. 26. Petrucci S (1971) Ionic Interactions from dilute solutions to fused salts (Academic Press, New York and London). 27. Hamer WJ (1959) The Structure of Electrolytic Solutions (John Wiley & Sons, Inc, New York). 28. Khalil M, Demirdoven N, Tokmakoff A (2004) Vibrational coherence transfer characterized with Fourier-transform 2D IR spectroscopy. J Chem Phys 121:362–373. 29. Zheng J, et al. (2005) Ultrafast dynamics of solute-solvent complexation observed at thermal equilibrium in real time. Science 309:1338–1343. 30. Kim YS, Hochstrasser RM (2005) Chemical exchange 2D IR of hydrogen-bond making and breaking. Proc Natl Acad Sci USA 102:11185–11190. 31. Woutersen S, Mu Y, Stock G, Hamm P (2001) Hydrogen-bond lifetime measured by time-resolved 2D-IR spectroscopy: N-methylacetamide in methanol. Chem Phys 266:137–147. 32. Zheng JR, Fayer MD (2008) Solute-solvent complex kinetics and thermodynamics probed by 2D-IR vibrational echo chemical exchange spectroscopy. J Phys Chem B 112:10221–10227. 33. Arrivo SM, Heilweil EJ (1996) Conservation of vibrational excitation during hydrogenbonding reactions. J Phys Chem 100:11975–11983. 34. Forster T (1948) *Zwischenmolekulare energiewanderung und fluoreszenz. Ann PhysBerlin 2:55–75. 35. Forster T (1965) Modern Quantum Chemistry (Academic, New York). 36. Woutersen S, Bakker HJ (1999) Resonant intermolecular transfer of vibrational energy in liquid water. Nature 402:507–509. 37. Yamada Y, Watanabe T (1963) The phase transition of crystalline potassium thiocyanate, kscn. 2. X-Ray study. Bull Chem Soc Jpn 36:1032–1037. 38. Akers C, Peterson SW, Willett RD (1968) A refinement of crystal structure of Kscn. Acta Crystall B-Stru B 24:1125–1126. 39. Atkins PW (1994) Physical Chemistry (WH Freeman, New York). 40. Mason PE, Neilson GW, Dempsey CE, Barnes AC, Cruickshank JM (2003) The hydration structure of guanidinium and thiocyanate ions: implications for protein stability in aqueous solution. Proc Natl Acad Sci USA 100:4557–4561. 41. Fennell CJ, Bizjak A, Vlachy V, Dill KA (2009) Ion pairing in molecular simulations of aqueous alkali halide solutions. J Phys Chem B 113:6782–6791. 42. Lund M, Jagoda-Cwiklik B, Woodward CE, Vacha R, Jungwirth P (2010) Dielectric interpretation of specificity of ion pairing in water. The Journal of Physical Chemistry Letters 1:300–303.

4742 ∣

www.pnas.org/cgi/doi/10.1073/pnas.1019565108

Bian et al.

300 8

(A) Delay Time (ps)

Delay Time (ps)

200

150

100

50

6 5 4 3 2 1 0 -1

0 2020

2030

2040

2050

Probe Frequency

2060

2070

(cm-1)

2080

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Probe Frequency

Heat effect

2070

(cm-1)

2080

Coupling

8

300

7

(C)

250

(D)

6

Delay Time (ps)

Delay Time (ps)

(B)

7

250

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5 4 3 2 1 0

50

-1 0

1950

1960

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1980

Probe Frequency

1990

2000

-2

2010

(cm-1)

1950

1960

1970

1980

Probe Frequency

1990

2000

2010

(cm-1)

Figure S1. Time dependent pump/probe spectra of a 10M 1:1 KSCN/KS13C15N mixed aqueous solution. (A) and (B) are the time evolutions of Peak 7 and 8 (pumped at 1991 cm-1) in Fig. 1. (C) and (D) are the time evolutions of Peaks 5 and 6 (pumped at 2064 cm1

). (B) and (D) are the early time portions of (A) and (C). The heat from vibrational

relaxations induced bleaching(1, 2) with a shift to a higher frequency at long waiting (after 100ps), clearly visible in (A) and (C). The vibrational coupling peaks are also visible in (B) and (D). Because their intensities are only ~1% of the Peaks 1 and 3 in fig. 1(C) in the main text, they don’t show up in fig. 1(C) which only displays features with intensities at least 10% of the maximum intensity of the spectrum. In kinetic analyses, the heat effect and the vibrational coupling are taken out with a method we developed previously(1, 2).

1

Data descriptions Data in Fig.3 in the main text are from the pump/probe experiments with the pumping and probing frequencies corresponding to the peaks in Fig. 1C. The data are rotation free, which are Pdata = P + 2 × P⊥ , where P , P⊥ are parallel and perpendicular polarization configuration data respectively. Data in Fig.4 in the main text are from the pump/probe experiments, which are the real time anisotropy of the system, R(t ) =

P − P⊥ P + 2 × P⊥

2

.

Experiments that support the argument that the observed energy transfer in the MSCN aqueous solutions arises mostly from transfers in ion clusters and calculations for the anion distance in the clusters The control sample: C2H5SCN and C2H5S13C15N 1:1 mixed liquid. To compare the energy transfer rates between the control sample and the MSCN aqueous solutions, we use the equation from our previous work(1, 2): kij = γ ij β

where γ ij =

2

τ c −1 , τ c −2 + ωij 2

1 1 + exp(−

ωij kT

Eq. (S1)

accounts for detailed balance. ωij is the energy mismatch.

)

β is the average coupling strength. τ c is the coupling correlation time, which is replaced by the spectral diffusion time (1.9 ps for all systems we have studied including the current ones: ~95% of the 2D IR diagonal linshape change from elongation to round (fig. 1) is done within 1.9ps). Here, β 2 is assumed to be equal to β . In Eq. S1, all 2

quantities (no fitting) were experimentally independently determined. This equation successfully described an organic mixed system (CDCl3:C6H5SeCN)(1), an aqueous solution (D2O:KSeCN), and the current MSCN/D2O systems with different coupling strength, energy mismatches and different environments (in terms of dielectric constant). D2O instead of H2O is used because deuteration can effectively remove the H2O combination band at ~ 2000 cm-1 which overlaps in frequency with the nitrile stretches of the anions. For solution C, the experimentally determined = β 13.6 ± 2.0 cm −1 , and 1/ k SCN − → S13C15= 115 ± 15 ps with an energy mismatch 73 cm-1. The vibrational coupling N−

3

β 13.6 ± 2.0 cm −1 between the nitrile stretches of SCN- and S13C15N- in the strength = solution is determined based on the experimental off-diagonal and diagonal anharmonicity values, according to the exciton model(3) and the matrix diagonalization method(1, 2). This coupling strength is between one donor and nine acceptors (see the resonant energy transfer part). The average coupling strength between one donor and one acceptor is

13.6 9

= 4.5 cm −1 .

The energy mismatch (78 cm-1) between the two isotope-labeled CN stretches of the control sample is very similar to that (73 cm-1) between the two anions in the aqueous MSCN solutions. Therefore, according to Eq.S1, β

is the only factor determining

which system has a faster energy transfer rate. Because the dipole-dipole interaction holds for intermolecular vibrational energy transfers(4, 5), β average over all angle can be described(6) as

β =

1 4πε 0

2 μD μ A 1 , 3 r 3 n2

Eq. S2

where r is the distance between the two oscillators. ε 0 is the dielectric constant. μ i is the transition dipole moment of donor or acceptor. n is the refractive index of the solution at the transferred energy frequency. The spectral diffusion of the system is done in about 2ps (the 2D IR lineshapes of the diagonal peaks in fig.1 in the main text become round at about 2ps) and the rotational time constant (95% of the anions form clusters. The vibrational lifetimes of the anions are = kSCN − fast 1/= 2.5 (ps −1 ); kSCN − slow 1/ 44.6 = (ps −1 ); kS13C15 N − fast 1/ 2.3 = (ps −1 ); kS13C15 N − slow 1/ 51.4 (ps −1 ). In a 0.5M solution, more than 80% of the anions are separated by waters. Their vibrational lifetimes are

10

k SCN − fast 1/1.8 (ps −1 ); kSCN − slow 1/ 20 (ps −1 ); k S13C15 N − fast 1/1.7 (ps −1 ); k S13C15 N − slow 1/ 28 (ps −1 ) = = = =

with similar prefactors. In general, these lifetimes determined from the two extreme cases can’t be immediately applied into solutions of other concentrations, because the liquid environments can be different at different concentrations. To test the uncertainty of our kinetic analysis induced by the lifetime issue, we use the lifetimes from the two extreme cases to fit the data for the 10M and 4M solutions, assuming the clustered anions have lifetimes as those in Solution C, and the separated anions have lifetimes as those in the 0.5M solution. The calculation results show that kSCN − → S13C15 N − = 1/115 (ps −1 ) and 98% of anions form clusters for solution C, and kSCN − → S13C15 N − = 1/145 (ps −1 ) and 63% of anions form clusters for the 4M solution. Within experimental uncertainty, both results are consistent with the results based on the assumption of same vibrational lifetimes for both clustered and separated anions. The insensitivity of the kinetic results to the change of vibrational lifetimes partially comes from the fact that the energy transfer rates and the concentrations of clusters are mainly determined by the amplitudes of the cross peaks rather than the diagonal peaks. Calculations and data are shown in fig. S2.

11

0.08 0.07

KSCN KS13C15N

0.8 0.6

0.06

Normalized Population

Normalized Population

1.0

10M

0.4

(A)

0.2

Flowing down Pumping up

0.05 0.04

10M

0.03 0.02

(B)

0.01 0.00

0.0 0

50

100

150

200

-0.01

250

0

50

Waiting Time (ps)

150

200

250

0.030

1.0

0.025

0.8

KSCN KS13C15N

0.6

Normalized Population

Normalized Population

100

Waiting Time (ps)

4M

0.4

(C)

0.2

Flowing down Pumping up

0.020

4M

0.015 0.010

(D)

0.005 0.000

0.0 0

50

100

150

200

-0.005

250

0

Waiting Time (ps)

50

100

150

200

250

Waiting Time (ps)

Figure S2. Data and calculations of energy transfers for solution C [(A) and (B)] and the 4M solution [(C) and (D)] with different vibrational lifetimes for the clustered and separated anions. Dots are data, and lines are calculations. Calculations for (A) and (B) are with input parameters: 1/= 2.5 (ps −1 ); k clu − 1/ 45.0 (ps −1 ); k clu 1/ 2.3 (ps −1 ); k clu 1/ 55.0 (ps −1 ); k clu − = = = 13 15 − 13 15 − SCN fast

SCN slow

−1

S C

−1

N fast

S C

−1

1/1.8 (ps ); k − 1/ 20.0 (ps ); k 13 15 − 1/1.7 (ps ); k 13 15 k − = = = iso

SCN fast

kclu →iso

iso

iso

SCN slow

S C

N fast

1/10.0 (ps −1 ); K=40; kSCN − → S13C15 N − 1/110 (ps −1 ); D=0.7 =

with pre-factors of the subgroups and offset of the bi-exponential clu iso clu A= A= 0.25; A= − − − SCN fast

SCN fast

iso A= 0.75; −

SCN slow

SCN slow

iso A= A= 0.25; A= A= 0.75; = offset 0 13 15 − 13 15 − 13 15 − slow 13 15 − slow clu

S C

iso

N fast

S C

clu

N fast

S C

N

S C

N

Calculations for (C) and (D) are with input parameters:

12

N slow

iso

S C

N − slow

= 1/ 28.0 (ps −1 );

= = = k clu − 1/= 2.5 (ps −1 ); k clu − 1/ 40.0 (ps −1 ); k clu 1/ 2.3 (ps −1 ); k clu 1/ 52.0 (ps −1 ); 13 15 − 13 15 − SCN fast

SCN slow

−1

S C

−1

N fast

S C

−1

k − = = = 1/1.8 (ps ); k − 1/17.0 (ps ); k 13 15 − 1/1.8 (ps ); k 13 15 iso

SCN fast

kclu →iso

iso

iso

SCN slow

S C

N fast

N slow

iso

S C

N − slow

= 1/ 23.0 (ps −1 );

= 1/10.0 (ps −1 ); K=1.7; kSCN − → S13C15 N − 1/145 (ps −1 ); D=0.7

with pre-factors of the subgroups and offset of the bi-exponential clu iso clu A= A= 0.25; A= − − − SCN fast

SCN fast

iso A= 0.75; −

SCN slow

SCN slow

iso A= A= 0.25; A= A= 0.75; = offset 0 13 15 − 13 15 − 13 15 − slow 13 15 − slow clu

S C

iso

N fast

S C

clu

N fast

S C

N

S C

N

Correlation between anisotropy decay and resonance energy transfer

kanisotropy kenergy

= 0.96

The derivation follows how FRET changes the anisotropy of a molecule.

In a vibrational resonance energy transfer process, the orientational factor for the donoracceptor pair is = κ 2 (3cos 2 θ + 1) cos 2 ω

13

where θ being the angle between the donor transition moment and the direction joining donor and acceptor and ω being the angle between the electric field of the donor at the acceptor and the acceptor transition moment (as shown in the figure above). For simplicity, the molecules are assumed to be immobile and the excited state is assumed to remain localized on the originally excited molecule. Then neglecting the effects of rotational diffusion and only considering the situation at t = 0, the probability for transfer depends on θ and ω according to W (θ , ω ) ∝ (3cos 2 θ + 1) cos 2 ω During the energy transfer, the donor transition moment is rotated by an angle ψ , so as to coincide with its own electric field at the acceptor. Then it is rotated from this new orientation by an angle ω so that it coincides finally with the acceptor transition moment. Assuming that the angular jump of ψ or ω is equally probable in all azimuths, the final anisotropy of acceptor emission for a given pair (ψ , ω ) is 1 ) rD (3cos 2 ψ − 1)(3cos 2 ω − 1) rA (ψ , ω= 4 or

1 3(3cos 2 θ − 1) 2 ( − 1)(3cos 2 ω − 1) 2 10 3cos θ + 1 Here, rA and rD are the anisotropy of the acceptor and donor, respectively. We have (θ , ω ) rA=

3cos 2 θ − 1 2 and the fact that cosψ = which can be 5 3cos 2 θ + 1 obtained from the form of the electric field of a static dipole.

made use of the result rD =

Thus, the anisotropy of a molecule can be obtained rA =

=

π

π

0

0

∫ ∫

W (θ , ω )rA (θ , ω ) sin θ dθ sin ω d ω π

π

0

0

∫ ∫ π

π

0

0

∫ ∫

W (θ , ω ) sin θ dθ sin ω d ω 1 3(3cos 2 θ − 1) 2 ( − 1)(3cos 2 ω − 1) ⋅ sin θ dθ sin ω d ω 10 3cos 2 θ + 1 π π 2 2 ∫ ∫ (3cos θ + 1) cos ω sin θ dθ sin ω dω

(3cos 2 θ + 1) cos 2 ω ⋅ 0

0

4 8 ⋅ 1 5 15 = = 0.016 = 4% × 0.4 10 2 ⋅ 4 3

14

Finally, it is shown that a single resonance energy transfer step can reduce the anisotropy to 4% of the initial value. In other words, the anisotropy decay rate constant is only 96% of the energy transfer rate constant. In practice, because 96% is very close to 100%, it is much simpler to use 100% instead of 96% in processing the data. Such an approximation only causes a very small uncertainty (~4%).

Calculations of the number of acceptors for an energy donor In experiments, the resonant energy transfer from one donor to any acceptor, as well as molecular rotations, can cause the anisotropy of vibrational excitation to decay(4, 5). During resonant energy transfers, the energy can be transferred back from acceptors to the original donor. The probability of reverse transfer is inversely proportional to the number of acceptors: more acceptors resulting in statistically less likely reverse transfers. When a reverse transfer occurs, the anisotropy is recovered. Therefore, fewer acceptors for one donor (corresponding to a smaller cluster) will result in slower energy-transferinduced anisotropy decay. In the physical picture, the anisotropy is directly proportional to the time dependent number of excited donor molecules. A new kinetic equation can therefore be derived as stated in the following (by Hailong Chen and Junrong Zheng). In an energy transfer unit, there are n chromophores. Energy can exchange among them. For an excited molecule i , the rate equation for its probability pi (t ) of being still excited at time t is

15

dpi (t ) = dt

∑k j ≠i

ij

p j (t ) − ∑ kij pi (t ) .

Eq. S(7)

j ≠i

kij is the transfer rate between molecules i and j. For resonant energy transfers, k= k= k . In Eq. S(7), we only consider the energy transfer processes which are ij ji

involved in changing anisotropy. The vibrational decay is thus not considered here. Then we have

dpi (t ) =k ∑ p j (t ) − k ∑ pi (t ) =k[1 − pi (t )] − k (n − 1) pi (t ) =k[1 − npi (t )] . dt j ≠i j ≠i

Eq. S(8)

According to the experimental condition (less than 0.2% of the anions are excited), we assume that only one molecule “1”, the donor, is excited in a cluster at time 0. We have the initial conditions = p1 (0) 1,

= pm (0) 0

(m ≠ 1) .

Eq. S(9)

Solving Eq. S(8), we obtain 1 1 1 − nt 1 p1 (t ) = (1 − )e − knt + = (1 − )e τ + , n n n n

pm (t ) = 1 − p1 (t )

(m ≠ 1) .

Eq. S(10)

Using the assumption that the anisotropy is directly proportional to the time dependent number of excited donor molecules(11), we have the anisotropy decay rate equation t

− R(t ) t 1 −n t 1 e τ or [(1 − )e τ + ] = exp(− ) p1 (t ) = R(0) n n τ or t −[1+ ( ntot −1)×c ]   1 1 τ ]e e τ or [1 − = +  1 + (ntot − 1) × c   1 + (ntot − 1) × c −

t

,

Eq. S(11)

where τ or is the rotational time constant of clustered S13C15N- which is experimentally determined by removing the contribution of the isolated anions from the overall signal. The concentration of the isolated ions is known from the non-resonant energy transfer

16

measurements. Their rotation time constants are assumed to be very close to the free anions in dilute solutions ( 3.7 ~ 4.0 ps ). c is the fraction of S13C15N- (the energy carrier) among the isotope-labeled anions in a cluster. Changing the ratio of S13C15N-/SCN- in a solution can change the number of resonant energy acceptors for one donor and therefore the resonance-energy-transfer-induced anisotropy decay rate, while the chemical properties of the cluster are unchanged. ntot is the number of anions (both S13C15N- and SCN-) in a cluster and τ =

1 is the resonance one-donor-to-one-acceptor energy transfer k

time constant. To obtain Eq. S(11), we use the equation, n =1 + (ntot − 1) × c

Eq. S(12)

The derivation of Eq. S(12) Assuming sufficient A and B molecules, the concentration of A is c. c =

[ A] . Each [ A] + [ B ]

A contributes to the signal equally. They form N clusters of size ntot (number of molecules in a cluster). They can form ntot + 1 kinds of clusters. The number of each cluster is: (0) with ntot A s in one cluster ( Nc ntot ); (1) ntot -1 A s….; ( Nntot c ntot −1 (1 − c) ) … (k) ntot -k A s….; ( NCnktot c ntot − k (1 − c) k ) … (n) 0 A in one cluster. ( N (1 − c) ntot )

17

ntot

We have

∑ NC k =0

k ntot

c ntot − k (1 − c) k= N [c + (1 − c)]ntot= N

The number of a cluster with m A s is NCnmtot c m (1 − c) ntot − m . The total number of A in all clusters ( = Nntot c , by definition) is: ntot

ntot

ntot ! c m (1 − c) ntot − m 1= m 1 ( ntot − m)!( m − 1)!

ntot − m m m = N∑ ∑ mNC ntot c (1 − c ) m

ntot

= N ∑ ntot m =1

(ntot − 1)! c m (1 − c) ntot − m [(ntot − 1) − (m − 1)]!(m − 1)!

ntot −1

= N ∑ ntot m=0

(ntot − 1)! c m +1 (1 − c) ntot − m −1 (m − 1 → m) [(ntot − 1) − m]!m !

ntot −1

= Nntot c ∑ Cnmtot −1c m (1 − c) ntot −1− m m=0

ntot −1 Nntot c = Nntot c[c + (1 − c)]=

The contribution of each cluster to the experimentally determined n (the number of A in a cluster) is m ×

n= = =

1 ntot

1 ntot

mNCnmtot c m (1 − c) ntot − m

ntot

∑ m × mC c m =1

m ntot

c m (1 − c) ntot − m

ntot

∑ [m × (m − 1)C c

1 ntot c

. Therefore,

Nntot c

m =1

m ntot

c m (1 − c) ntot − m + mCnmtot c m (1 − c) ntot − m ]

ntot

[ntot c + ∑ m × (m − 1) m=2

ntot ! c m (1 − c) ntot − m ] (ntot − m)!m !

ntot ntot ! 1 [ntot c + ∑ c m (1 − c) ntot − m ] = ( )!( 2)! ntot c n m m − − m=2 tot

=

1 ntot c 1

=

ntot c

[ntot c + ntot (ntot − 1)c 2 [ntot c + ntot (ntot − 1)c 2

ntot − 2

(ntot − 2)! c m (1 − c) ntot − 2− m ] 2 )! ! m m − − tot

∑ (n

m=0

ntot − 2

∑C

m =0

c (1 − c) ntot − 2− m ]

m m ntot − 2

1 1 + (ntot − 1)c = [ntot c + ntot (ntot − 1)c 2 ] = ntot c

18

In the model, we consider the exchange between the anions inside an energy transfer unit and anions outside this unit as a special type of molecular rotation. Its contribution to the anisotropy decay is incorporated into Eq. (S11) as part of the effective molecular rotational time constant τ or . This treatment is supported by experimental results: τ or = 10 ps in the 10M solution, which is only about three times of the time for free ions in a very dilute solution, while it contains at least nineteen anions. This observation shows that the rotation time observed in the 10M solution is not for the whole cluster. Instead, it is for the individual ion which is loosely bound to other ions. The exchange event between clustered and separated position is part of the molecular rotation mechanism. In fact, the independent measurements from the non-resonance energy transfer experiments show that the clustered and separated ions exchange time is also 7~20 ps (in the above location-energy-exchange model). This value is consistent with τ or = 10 ps . It is possible that the energy can transfer from one acceptor to another anion which is far way from the original donor and so on, so that the energy will never transfer back to the original donor. This effect is also included into the effective molecular rotational time constant, because the anion is not symmetric (the atom S is a good vibrational energy blocker(1, 2)). In order for an anion to transfer energy to another anion which is not directly associated with the original donor, the anion probably has to rotate to the right configuration before the energy can transfer away. Therefore, we consider the anisotropy loss caused by this factor as already been included in the anisotropy loss induced by the molecular rotation. Note, this effect only occurs in a very big cluster which contains more than one effective energy transfer units.

19

Another assumption we make in the model is that the non-resonance energy transfer from S13C15N- to SCN- is much slower than the resonance energy transfer among S13C15N- so that the anisotropy decay induced by the non-resonance energy transfer is negligible. This assumption is verified by experiments. In the non-resonance energy exchange experiments, we found kSCN − → S13C15 N − = 1/115 (ps −1 ) which corresponds to

kS13C15 N − → SCN − = 1/165 (ps −1 ) (required by detailed balance). kS13C15 N − → SCN − is the apparent rate constant, which is the sum of

k1−1− S13C15 N − → SCN − . In the 10M solution,

ntot one-donor-to-one-acceptor rate constants 2

ntot 1 ( ps −1 ) . The value = 9 . k1−1− S13C15 N − → SCN − = 1485 2

is more than one order of magnitude smaller than the resonance one-donor-to-oneacceptor rate constant

1

τ

=

1 ( ps −1 ) (Data are in fig. S2~10 and table S1.). Even in a 54

1:99 SCN-:S13C15N- mixed 10M solution, the total non-resonance energy transfer rate from S13C15N- to SCN- is only

(

1 ( ps −1 ) , still much slower than the molecular rotation 87

1 ( ps −1 ) ). Another issue is important to point out. In our experiments, in any cluster, at 10

most one anion can be excited. In the non-resonance energy exchange experiments, for each excited anion there are exactly

ntot acceptors (the other isotope-labeled anions). The 2

experimentally measured rate constant is the sum from all these acceptors. However, in the resonance energy exchange experiments of a pure isotope solution, for each excited anion there are exactly ntot − 1 acceptors. In processing the data, we obtain the one-donor-

20

to-one-acceptor rate constant

1

τ

instead of the apparent rate constant (the sum for the

ntot − 1 acceptors). Based on the crystalline structures of KSCN(7, 12), the first anion shell surrounding one anion has totally 26 anions (similar as simple cube): eight at the same layer of the anion, nine at the top and another nine at the bottom. If we take away the eight diagonal anions on the cube which are far away from the cube center, 18 are left. At this point, we don’t have any solid evidence to show that the energy acceptor number 18 − 1 = 17 ± 3 obtained from our experiments represents the number of anions

surrounding one anion in the crystal. However, from the similarity of the anion distance and this acceptor number between the ion clusters and the crystal, we believe that some structural aspects of a big cluster in solution C is probably similar to those in the crystal, e.g. the shortest anion distance and the number of anions in the 1st solvation shell. To develop the above model, we used the linear average of isotope distribution in a cluster which is simply determined by the experimentally set isotope ratio. However, this is not perfectly precise, because the anisotropy decay induced by resonant energy transfer is not linearly proportional to the isotope ratio in a cluster. A precise way to count for the nonlinear dependence is to calculate the anisotropy for each cluster kind and sum the signals from all clusters together. The following is the mathematical derivation (suggested and derived by Prof. Robert Curl). In anisotropy decay for a given (n, m) cluster where now let m = number of S13C15N- in a cluster of n ( n = ntot ) anions. Let the mole fraction of the normal species by X2 and of 13C15NS be X1. The anisotropy decay upon excitation of S13C15N- is given by

21

[ R(t)]m =e−t /τ (1 − m−1 ) e− mt /τ + m−1  [ R(0)]m . or

The probability that there will be a species excited in an (n, m) cluster is proportional to m. Thus the signal from a given cluster is

[ R(t)]m =e−t /τ (1 − m−1 ) e− mt /τ + m−1  m [ R(0)]1 or

and the total signal summed over the clusters will be = R(t ) n

n

n!

∑ m!( n − m )! X m =1

m 1

X 2n − m me − t /τ or (1 − m −1 ) e − mt /τ + m −1  [ R(0) ]1

This can be analyzed using the binomial moment generating function.    n  − mt / τ m n−m = + 1 [ R(0) ]1 e − t / τ or  ∑   X 1m X 2n − m ( me − mt / τ − e − mt / τ + 1)  R(t ) n [ R(0) ]1 e − t / τ or ∑  =  X 1 X 2 ( m − 1) e m 1 n   m 1= n     m m       n

The quantity inside the bracket equals zero when m = 0 because the first term vanishes and the second and third term cancel each other. Thus we can change the sum from starting with m = 1 to starting with m = 0.

R(t ) n

[ R(0)]1 e−t /τ

or

   n     X m X n − m ( me − mt /τ − e − mt /τ + 1)  1 2  m∑  =0  n        m  

The last term after summing equals 1. The middle term after summing is the binomial moment generating function and the first term is the first derivative of the moment generating function with respect to t.

Using the equations from Wolfram

Research (http://mathworld.wolfram.com/BinomialDistribution.html) and realizing that the first term is the derivative of the second by the quantity -t/τ, we have R(t ) n =

[ R(0)]1 e−t /τ

or

{n  X e 1

− t /τ

+ X 2 

n −1

n

}.

X 1e − t /τ −  X 1e − t /τ + X 2  + 1

22

When t = 0, we have = R(0) n

[ R(0)]1 {nX= [ R(0)]1 nX 1 . 1 − 1 + 1}

Thus

{

R(t ) n / R(0) n n −1 X 1−1e − t /τ or n  X 1e − t /τ + X 2  =

n −1

}.

n

X 1e − t /τ −  X 1e − t /τ + X 2  + 1

The above equation is then converted into Eq. S13 with the same symbols as in eq. S11,

{

R(t ) n / R(0) n ntot −1c −1e − t / τ or ntot ce − t / τ + 1 − c  =

ntot −1

ce − t / τ − ce − t / τ + 1 − c 

ntot

}.

+1

Eq. S(13)

Eq. S13 is not exactly the same as Eq. S11. Numerical calculations for all solutions in this work show that the difference between these two equations for anisotropy values within the 10ps delay (data after 10ps are too small and therefore much less reliable) is smaller than 10%. For solution C, the difference is smaller than 5%. The difference is small enough that both approaches are suitable for the studied systems. Generally speaking, Eq. S11 is from an assumption that the linear average doesn’t deviate much from the actual situation, which holds for our experiments, but it is not necessarily safe for other cases. Eq. S13 doesn’t have such an assumption and therefore is general for all cases.

23

Data and calculations

0.8

Normalized Population

Normalized Population

1.0

Energy down-flowing Peaks 1 and 5

0.6

(A) Energy up-pumping Peaks 3 and 7

0.4 0.2 0.0

0

40

80 120 160 Waiting Time (ps)

200

0.06 Peak 5 0.04

(B)

0.02 Peak 7 0.00

240

0

40

80 120 160 Waiting Time (ps)

200

240

1.0

KS13C15N : KSCN

Normalized Anisotropy

0.8

1:99 2:98 10:90 20:80 50:50 100:0

0.6

(C)

0.4

0.2

0.0

-0.2 0

10

20

30

40

50

60

70

Waiting Time (ps)

Figure S3. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for a 10M KSCN aqueous solution. Dots are data, and lines are calculations. Calculations for (A) and (B) are with input parameters: = kSCN − fast 1/= 2.5 (ps −1 ); kSCN − slow 1/ 44.6 = (ps −1 ); kS13C15 N − fast 1/ 2.3 = (ps −1 ); kS13C15 N − slow 1/ 51.4 (ps −1 ); kclu →iso

1/= 7.6 (ps −1 ); K=18.9; kSCN − → S13C15 N − 1/115 (ps −1 ); D=0.7

with pre-factors of the subgroups and offset of the bi-exponential

24

= ASCN − fast 0.25; = ASCN − slow 0.75;= AS13C15 N − fast 0.23; = AS13C15 N − slow 0.77; = offset 0 (C) τ or = 10 ps is experimentally determined, which is the rotation time of the clustered ions. ntot = 18 , τ = 54 ps .

0.06

1.0

Normalized Population

Normalized Population

0.05

KSCN KS13C15N

0.8

0.6

0.4

(A)

0.2

Flowing down Pumping up

0.04 0.03

(B)

0.02 0.01 0.00

0.0 -0.01 0

50

100

150

200

250

0

Waiting Time (ps)

50

100

150

200

250

Waiting Time (ps)

1.0

2:98 20:80 50:50 100:0

Normalized Anisotropy

0.8

0.6

0.4

(C)

0.2

0.0

-0.2 0

10

20

30

40

50

Waiting Time (ps)

Figure S4. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for a 8.8M KSCN aqueous solution. Dots are data, and lines are calculations. Calculations for (A) and (B) are with input parameters: = kSCN − fast 1/1.5 = = = (ps −1 ); kSCN − slow 1/ 33 (ps −1 ); kS13C15 N − fast 1/ 2.5 (ps −1 ); k S13C15 N − slow 1/ 35 (ps −1 ); kclu →iso

= 1/10 (ps −1 ); K=11; k SCN − → S13C15 N − 1/110 (ps −1 ); D=0.71

with pre-factors of the subgroups and offset of the bi-exponential = ASCN − fast 0.20; = ASCN − slow 0.80;= AS13C15 N − fast 0.20; = AS13C15 N − slow 0.80; = offset 0 .

25

(C) τ or = 6.9 ps is experimentally determined, which is the rotation time of the clustered ions. ntot = 13 , τ = 40 ps . 0.035

1.0

Normalized Population

Normalized Population

0.030

KSCN KS13C15N

0.8

0.6

(A) 0.4

0.2

Flowing down Pumping up

0.025 0.020

(B)

0.015 0.010 0.005 0.000

0.0

-0.005 0

50

100

150

200

250

300

0

50

Waiting Time (ps)

100

150

200

250

300

Waiting Time (ps)

1.0

2:98 10:90 50:50 100:0

Normalized Anisotropy

0.8

0.6

0.4

(C)

0.2

0.0

-0.2 0

10

20

30

40

50

Waiting Time (ps)

Figure S5. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for a 6.5M KSCN aqueous solution. Dots are data, and lines are calculations. Calculations for (A) and (B) are with input parameters: = kSCN − fast 1/= 2.5 (ps −1 ); kSCN − slow 1/ = 32 (ps −1 ); kS13C15 N − fast 1/ 2.9 = (ps −1 ); kS13C15 N − slow 1/ 34 (ps −1 ); kclu →iso

1/10 = (ps −1 ); K=2.3; kSCN − → S13C15 N − 1/130 (ps −1 ); D=0.70

with pre-factors of the subgroups and offset of the bi-exponential = ASCN − fast 0.24; = ASCN − slow 0.76;= AS13C15 N − fast 0.25; = AS13C15 N − slow 0.75; = offset 0 . (C) τ or = 5.7 ps is experimentally determined, which is the rotation time of the clustered ions. ntot = 9 , τ = 32 ps .

26

0.030

KSCN KS13C15N

0.8

0.025

Normalized Population

Normalized Population

1.0

0.6

(A)

0.4

0.2

Flowing down Pumping up

0.020 0.015

(B)

0.010 0.005 0.000

0.0 -0.005 0

50

100

150

200

250

0

Waiting Time (ps)

50

100

150

200

250

Waiting Time (ps)

1.0

2:98 10:90 50:50 100:0

Normalized Anisotropy

0.8

0.6

0.4

(C)

0.2

0.0

-0.2 0

10

20

30

40

50

Waiting Time (ps)

Figure S6. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for a 4M KSCN aqueous solution. Dots are data, and lines are calculations. Calculations for (A) and (B) are with input parameters: = kSCN − fast 1/1.3 = = = (ps −1 ); kSCN − slow 1/ 26 (ps −1 ); kS13C15 N − fast 1/ 2.2 (ps −1 ); kS13C15 N − slow 1/ 33 (ps −1 ); kclu →iso

= 1/10 (ps −1 ); K=2.0; kSCN − → S13C15 N − 1/140 (ps −1 ); D=0.70

with pre-factors of the subgroups and offset of the bi-exponential = ASCN − fast 0.25; = ASCN − slow 0.75; = AS13C15 N − fast 0.225;= AS13C15 N − slow 0.775; = offset 0 . (C) τ or = 4.3 ps is experimentally determined, which is the rotation time of the clustered ions. ntot = 5 , τ = 25 ps .

27

0.025

LiSCN LiS13C15N

0.8

0.6

(A)

0.4

Flowing down Pumping up

0.020

Normalized Population

Normalized Population

1.0

0.2

0.015

0.010

(B)

0.005

0.000

0.0 -0.005

0

50

100

150

200

0

Waiting Time (ps)

50

100

150

200

Waiting Time (ps)

1.2

Normalized Anisotropy

1.0

2:98 20:80 50:50 100:0

0.8 0.6 0.4

(C)

0.2 0.0 -0.2 0

10

20

30

40

50

Waiting Time (ps)

Figure S7. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for a 4M LiSCN aqueous solution. Dots are data, and lines are calculations. Calculations for (A) and (B) are with input parameters: = kSCN − fast 1/1.55 = (ps −1 ); kSCN − slow 1/16.8 = (ps −1 ); kS13C15 N − fast 1/1.58 = (ps −1 ); kS13C15 N − slow 1/ 20.7 (ps −1 ); kclu →iso

1/= 20 (ps −1 ); K=1.0; k SCN − → S13C15 N − 1/ 80 (ps −1 ); D=0.70

with pre-factors of the subgroups and offset of the bi-exponential = ASCN − fast 0.31; = ASCN − slow 0.69;= AS13C15 N − fast 0.24; = AS13C15 N − slow 0.76; = offset 0 . (C) τ or = 10.2 ps is experimentally determined, which is the rotation time of the clustered ions. ntot = 4 , τ = 10 ps .

28

0.025

NaSCN NaS13C15N

0.8

Normalized Population

Normalized Population

1.0

0.6

(A)

0.4

0.2

0.020

Flowing down Pumping up

0.015

0.010

(B)

0.005

0.000 0.0 -0.005 0

50

100

150

200

0

50

100

150

200

Waiting Time (ps)

Waiting Time (ps)

1.0

2:98 20:80 50:50 80:20 100:0

Normalized Anisotropy

0.8

0.6

0.4

(C)

0.2

0.0

-0.2 0

10

20

30

40

50

Waiting Time (ps)

Figure S8. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for a 4M NaSCN aqueous solution. Dots are data, and lines are calculations. Calculations for (A) and (B) are with input parameters: = = = = kSCN − fast 1/1.5 (ps −1 ); kSCN − slow 1/ 23.5 (ps −1 ); k S13C15 N − fast 1/ 2.6 (ps −1 ); k S13C15 N − slow 1/ 31.6 (ps −1 ); kclu →iso

1/= 20 (ps −1 ); K=1.5; k SCN − → S13C15 N − 1/120 (ps −1 ); D=0.70

with pre-factors of the subgroups and offset of the bi-exponential = ASCN − fast 0.31; = ASCN − slow 0.69;= AS13C15 N − fast 0.28; = AS13C15 N − slow 0.72; = offset 0 . (C) τ or = 8.5 ps is experimentally determined, which is the rotation time of the clustered ions. ntot = 5 , τ = 18 ps .

29

0.020

0.015

CsSCN CsS13C15N

0.8

Normalized Population

Normalized Population

1.0

0.6

(A)

0.4

0.2

Flowing down Pumping up

0.010

(B)

0.005

0.000

0.0 -0.005

0

50

100

150

200

250

300

0

Waiting Time (ps)

50

100

150

200

250

300

Waiting Time (ps)

1.0

2:98 50:50 100:0

Normalized Anisotropy

0.8

0.6

0.4

(C)

0.2

0.0

-0.2 0

10

20

30

40

50

Waiting Time (ps)

Figure S9. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for a 4M CsSCN aqueous solution. Dots are data, and lines are calculations. Calculations for (A) and (B) are with input parameters: kSCN − fast 1/= 2.1 (ps −1 ); kSCN − slow 1/ 26 (ps −1 ); kS13C15 N − fast 1/1.7 (ps −1 ); kS13C15 N − slow 1/ 27 (ps −1 ); = = = kclu →iso

1/10 (ps −1 ); K=2.3; kSCN − → S13C15 N − 1/ 200 (ps −1 ); D=0.70 =

with pre-factors of the subgroups and offset of the bi-exponential = ASCN − fast 0.24; = ASCN − slow 0.76;= AS13C15 N − fast 0.31; = AS13C15 N − slow 0.69; = offset 0 . (C) τ or = 4.9 ps is experimentally determined, which is the rotation time of the clustered ions. ntot = 9 , τ = 45 ps .

30

0.014

1.0

Normalized Population

Normalized Population

0.012

KSCN KS13C15N

0.8

0.6

(A)

0.4

0.2

0.0

Flowing down Pumping up

0.010 0.008 0.006

(B)

0.004 0.002 0.000 -0.002

0

50

100

150

200

250

0

Waiting Time (ps)

50

100

150

200

250

Waiting Time (ps)

1.2

Normalized Anisotropy

1.0

2:98 50:50 100:0

0.8 0.6 0.4

(C)

0.2 0.0 -0.2 0

10

20

30

40

50

Waiting Time (ps)

Figure S10. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for a 1.8M KSCN aqueous solution. Dots are data, and lines are calculations. Calculations for (A) and (B) are with input parameters: (ps −1 ); kSCN − slow 1/ 22 (ps −1 ); kS13C15 N − fast 1/ 2.7 (ps −1 ); kS13C15 N − slow 1/ 29 (ps −1 ); = kSCN − fast 1/1.4 = = = kclu →iso

1/10 (ps −1 ); K=0.55; kSCN − → S13C15 N − 1/160 (ps −1 ); D=0.70 =

with pre-factors of the subgroups and offset of the bi-exponential = ASCN − fast 0.16; = ASCN − slow 0.84;= AS13C15 N − fast 0.22; = AS13C15 N − slow 0.78; = offset 0 . (C) τ or = 4.5 ps is experimentally determined, which is the rotation time of the clustered ions. ntot = 4 , τ = 18 ps .

31

0.008

KSCN KS13C15N

0.8

Normalized Population

Normalized Population

1.0

0.6

(A)

0.4

0.2

Flowing down Pumping up

0.006

0.004

(B)

0.002

0.000

0.0 -0.002 0

50

100

150

200

250

0

50

100

150

200

250

Waiting Time (ps)

Waiting Time (ps)

1.0

10:90 50:50 100:0

Normalized Anisotropy

0.8

0.6

0.4

(C)

0.2

0.0

-0.2 0

10

20

30

40

50

Waiting Time (ps)

Figure S11. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for a 1M KSCN aqueous solution. Dots are data, and lines are calculations. Calculations for (A) and (B) are with input parameters: kSCN − fast 1/1.7 (ps −1 ); k SCN − slow 1/ 21 (ps −1 ); k S13C15 N − fast 1/1.6 (ps −1 ); kS13C15 N − slow 1/ 28 (ps −1 ); = = = = kclu →iso

1/10 (ps −1 ); K=0.38; kSCN − → S13C15 N − 1/180 (ps −1 ); D=0.70 =

with pre-factors of the subgroups and offset of the bi-exponential = ASCN − fast 0.25; = ASCN − slow 0.75;= AS13C15 N − fast 0.21; = AS13C15 N − slow 0.79; = offset 0 . (C) τ or = 4.3 ps is experimentally determined, which is the rotation time of the clustered ions. ntot = 3 , τ = 15 ps .

32

ωprobe (cm-1)

2120 2080

100fs

0.5ps

1ps

2ps

5ps

2040 2000 1960 1920 1900

1950

2000

2050

ωpump (cm-1)

2100

1950

2000

2050

2100

1950

2000

2050

2100

1950

2000

2050

2100

2000

2050

2100

1950

2000

2050

2100

2120

ωprobe (cm-1)

2080

20ps

10ps

30ps

50ps

2040 2000 1960 1920 1900

1950

2000

2050

ωpump (cm-1)

2100

1950

2000

2050

2100

1950

2000

2050

2100

1950

Figure S12. The time dependence of the 2D IR spectrum of 1M 1:1 KSCN/KS13C15N aqueous solutions. (water/salt molar ratio = 1:50)

33

2120

ωprobe (cm-1)

2080

100fs

0.5ps

1ps

2ps

5ps

2040 2000 1960 1920 1950

ωprobe (cm-1)

2120

2000

2050

2100

ωpump (cm-1)

1950

2000

2050

2100

20ps

10ps

1950

2000

2050

2100

30ps

1950

2000

2050

2100

2000

2050

2100

1950

2000

2050

2100

50ps

2080 2040 2000 1960 1920 1950

2000

2050

2100

1950

2000

2050

2100

1950

2000

2050

2100

1950

ωpump (cm-1)

Figure S13. The time dependence of the 2D IR spectrum of 4M 1:1 LiSCN/LiS13C15N aqueous solutions. (water/salt molar ratio = 1:10)

34

ωprobe (cm-1)

2120 2080

100fs

0.5ps

1ps

5ps

2ps

2040 2000 1960 1920 1950

2000

2050

ωpump (cm-1)

2100

1950

2000

2050

2100

1950

2000

2050

2100

1950

2000

2050

2100

2000

2050

2100

1950

2000

2050

2100

ωprobe (cm-1)

2120 2080

20ps

10ps

30ps

50ps

2040 2000 1960 1920 1950

2000

2050

2100

ωpump (cm-1)

1950

2000

2050

2100

1950

2000

2050

2100

1950

Figure S14. The time dependence of the 2D IR spectrum of 4M 1:1 NaSCN/NaS13C15N aqueous solutions. (water/salt molar ratio = 1:10)

35

ωprobe (cm-1)

2120 2080

100fs

0.5ps

1ps

2ps

1950 2000 2050 2100

1950 2000 2050 2100

1950 2000 2050 2100

5ps

2040 2000 1960 1920 1900 1950 2000 2050 2100

ωpump (cm-1)

ωprobe (cm-1)

2120

10ps

20ps

30ps

1950 2000

50ps

2080 2040 2000 1960 1920 1900 1950 2000 2050 2100

1950 2000 2050 2100

1950 2000 2050 2100

ωpump (cm-1)

1950 2000 2050 2100

Figure S15. The time dependence of the 2D IR spectrum of 4M 1:1 CsSCN/CsS13C15N aqueous solutions. (water/salt molar ratio = 1:10)

36

Table S1. Experimental cluster concentrations, the number of anions ( ntot ) in an energy transfer unit, and the resonance one-donor-to-one-acceptor energy transfer time constant ( τ ).

Percentage of

ntot

τ (ps)

clustered ions KSCN (10M)

95 ± 1%

18 ± 3

54 ± 8

KSCN (8.8M)

92 ± 1%

13 ± 2

40 ± 8

KSCN (6.5M)

70 ± 4%

9±2

32 ± 6

KSCN (4M)

67 ± 4%

5± 2

25 ± 6

KSCN (1.8M)

35 ± 5%

4 ±1

18 ± 5

KSCN (1M)

27 ± 6%

3 ±1

15 ± 4

LiSCN (4M)

50 ± 4%

4 ±1

10 ± 4

NaSCN (4M)

60 ± 4%

5 ±1

18 ± 5

CsSCN (4M)

70 ± 4%

9±2

45 ± 8

37

MD simulations The simulations were performed (by Xiuquan Sun, Jian Song, and Wei Zhuang) using the AMBER11 package(13). Models: Water molecules were modeled using the TIP3P model, and SHAKE algorithm was used to impose structure constraints on the water molecules. The Lennard-Jones (LJ) parameters of potassium ions were taken from the all atom AMBER03 force field. The force field parameters for SCN- ions were generated with the following procedure using the ANTECHAMBER code in the AMBER11 package: the structure was optimized in Gaussian03 at HF/6-31G* level and the ESP charges of the atoms were generated at B3LYP/cc-pVTZ level(14, 15). The ESP charges were then input into ANTECHAMBER and other force field parameters except the ones for S-C-N angle which were generated based on the GAFF force field data base(16) in AMBER11. The S-C-N angle parameters are not available in the GAFF database and thus we set the equilibrium value ( θ 0 ) as 180 degrees (as the result in the previous optimization at HF/6-31G* level). To generate the force constant, we carried out single point energy calculation at HF/6-31G* level for several values of S-C-N angle θ and fit them to the energy equation E α = Kθ (θ − θ 0 ) 2 . The finally determined angle bending force constant is Kθ = 92.72 kcal/mol/rad2. A cutoff of 9 Å was used for both VdW and short-range electrostatic interactions. The particle mesh Ewald summation technique was used to calculate the long range electrostatic interactions. MD simulation details:

38

In the 10 M solution, 233 KSCN molecules were evenly solvated in a water box with 538 TIP3P waters. Periodic Boundary Condition is used to mimic the macroscopic setting for the system. For the 10M solution, the water/salt ratio is 2.3 (the experimental value is 2.4). For the 4M solution, the water/salt ratio is 10 (the experimental value is 10). For the 1.8M solution, the water/salt ratio is 26 (the experimental value is 25). The number of water molecules is 538 for all the systems. The simulation system was first minimized using a steepest descent algorithm. The minimized system was then equilibrated for 200 ps at a temperature of 300 K and a pressure of 1 atm (an NPT simulation where temperature was set using Langevin Dynamics thermostat). Finally, a 15 ns simulation in canonical ensemble (NVT) with 2 fs time step was carried out and system configurations were stored every 0.2 ps for the last 10 ns for the later analysis. To improve the sampling, we repeated the calculation above for 4 different sets of randomized starting coordinates and velocities. Algorithm of calculating clusters: When a cation and an anion are in the first solvation shell of each other, we define them as “contacted ions”. The cations (anions) shared the same anion (cation) are defined as “neighbor cations (anions)”. If two ions are “contacted” or “neighbor”, they are considered to be “connected” to each other. Additionally, if ion A and B are both connected to C, then A and B are considered to be connected. An ion cluster is a collection of all the ions connected to each other. The first solvation shell is calculated from the first minimum of the radial distribution function (RDF) between K+ and C atom 



of SCN-. The calculated first minimum values are 4.83 Α (10M), 4.79 Α (4M), and 

4.73 Α (1.8M), respectively (fig. S15). The total percentage of ions in clusters (with at

39

least three ions) is calculated to be 99.7% (10M), 79.5% (4M), and 31.4% (1.8M), respectively.

4

10M 4M 1.8M

G(r)

3 2 4.73

1 4.79

0 2

4.83

3 4 5 6 7 8 KC Distance (angstrom)

9

Figure S16. Radius distribution function between K+ and C atom of SCN- of KSCN aqueous solutions at three different concentrations from MD calculations.

40

Numerical Data of Kinetic Analysis Figure 4

Time

0 0.5 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40

Peak 1

Peak 5

Peak3

Peak7

Peak 1 fitting

Peak 3 fitting

0.99999 0.00316 1.00001 0.00224 1 1 0 0 0.92215 0.00173 0.93461 5.59031E-4 0.94243 0.94488 0.00389 0.87544 0.00245 0.89437 0.0038 0.89356 0.89888 0.00737 0.00516 0.86599 0.00231 0.88895 0.00646 0.88469 0.89061 0.00802 0.00561 0.8665 1.17235E-4 0.87087 0.00413 0.87609 0.88262 0.00866 0.85335 0.00196 0.85157 0.00409 0.86776 0.8749 0.00929 0.0065 0.8418 0.00183 0.8579 0.00481 0.85967 0.86743 0.0099 0.00693 0.82973 9.95561E-4 0.86262 0.00617 0.85183 0.86022 0.01051 0.8273 0.00322 0.85454 0.00714 0.84422 0.85323 0.0111 0.00777 0.83112 7.24472E-4 0.84488 0.00431 0.83683 0.84648 0.01168 0.82252 0.00365 0.84583 0.00427 0.82966 0.83994 0.01225 0.00858 0.81747 0.0036 0.85103 0.00724 0.8227 0.8336 0.01281 0.00897 0.81297 0.00607 0.84112 0.00538 0.81594 0.82747 0.01336 0.00935 0.77887 0.00645 0.8082 0.00695 0.78484 0.79949 0.01599 0.01119 0.75261 0.00589 0.7853 0.009 0.75767 0.77535 0.01842 0.0129 0.72893 0.00881 0.76594 0.01173 0.73374 0.75432 0.02069 0.01448 0.71563 0.00992 0.7555 0.01308 0.71249 0.73581 0.02282 0.01598 0.70143 0.01558 0.73544 0.01603 0.69343 0.71933 0.02483 0.01738 0.67543 0.01592 0.71812 0.0158 0.6762 0.70452 0.02673 0.01871 0.66952 0.01637 0.69188 0.01588 0.66048 0.69105 0.02855 0.01998 0.65256 0.02131 0.6871 0.01906 0.64601 0.67869 0.03027 0.02119 0.63932 0.02003 0.67313 0.01782 0.63261 0.66723 0.03193 0.02235 0.62278 0.01937 0.66369 0.01898 0.62008 0.65652 0.03351 0.02346 0.6074 0.02251 0.65114 0.0216 0.6083 0.64643 0.03503 0.02452 0.59115 0.02673 0.63576 0.02349 0.59716 0.63685 0.03649 0.02555 0.58684 0.02659 0.63299 0.02328 0.58655 0.62771 0.0379 0.02653 0.57509 0.02978 0.61747 0.02503 0.5764 0.61894 0.03926 0.02748 0.56681 0.03327 0.61832 0.02829 0.56666 0.61048 0.04056 0.02839 0.55625 0.03204 0.5999 0.02967 0.55727 0.60228 0.04182 0.02928 0.54125 0.03755 0.58942 0.02708 0.53938 0.58657 0.04421 0.03094 0.5236 0.03967 0.57252 0.03157 0.52247 0.5716 0.04642 0.0325 0.50201 0.03956 0.56593 0.03166 0.50637 0.55723 0.04848 0.03394 0.48768 0.04292 0.54412 0.03284 0.49096 0.54336 0.05039 0.03527 0.47633 0.04393 0.52226 0.03399 0.47615 0.52994 0.05216 0.03651 0.45982 0.04786 0.52663 0.03403 0.46188 0.51692 0.05379 0.03765 0.44171 0.05025 0.50195 0.03803 0.44811 0.50427 0.0553 0.03871 0.4291 0.05103 0.48494 0.03941 0.4348 0.49197 0.05668 0.03968 0.41345 0.05418 0.47744 0.03996 0.42193 0.47999 0.05795 0.04056 0.40496 0.05359 0.46127 0.04083 0.40947 0.46834 0.05911 0.04138 0.37933 0.05814 0.43673 0.04028 0.38571 0.44592 0.06112 0.04278 0.34257 0.06262 0.41478 0.04532 0.35278 0.41441 0.06342 0.0444 0.31749 0.06681 0.38325 0.04415 0.32278 0.38524 0.06499 0.04549 0.29805 0.06415 0.3597 0.04646 0.30428 0.36699 0.06568 0.04598 0.26759 0.06783 0.33445 0.04801 0.27859 0.34131 0.06624 0.04637 0.25231 0.0657 0.32176 0.04692 0.26274 0.32524 0.06634 0.04644 0.23296 0.06972 0.29772 0.04841 0.24071 0.30261 0.06614 0.0463 0.21877 0.06857 0.28208 0.04777 0.2271 0.28845 0.06579 0.04605

41

Peak 5 fitting

0.00272

0.00606

0.00735 0.00818

Peak 7 fitting

43 45 48 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250

0.2015 0.06644 0.26391 0.04642 0.2082 0.26849 0.06501 0.0455 0.18739 0.06679 0.2506 0.04764 0.19652 0.256 0.06433 0.04503 0.17706 0.06611 0.23458 0.04507 0.18027 0.23838 0.06312 0.04419 0.16556 0.06295 0.22296 0.04242 0.17023 0.22734 0.06221 0.04354 0.14816 0.06219 0.2 0.04324 0.14763 0.20202 0.05961 0.04173 0.13377 0.05865 0.17746 0.0419 0.12817 0.17964 0.05671 0.0397 0.10883 0.05582 0.15906 0.04055 0.1114 0.15982 0.05361 0.03753 0.10042 0.05174 0.14305 0.03357 0.09693 0.14227 0.05042 0.0353 0.08665 0.04892 0.12102 0.03261 0.08443 0.12672 0.04721 0.03305 0.07502 0.04736 0.10963 0.0303 0.07363 0.11293 0.04404 0.03083 0.064 0.04581 0.09877 0.03083 0.06428 0.10068 0.04094 0.02866 0.05494 0.04345 0.08556 0.02539 0.05619 0.08981 0.03795 0.02656 0.04462 0.03584 0.07879 0.02861 0.04916 0.08015 0.03508 0.02456 0.04124 0.03721 0.06835 0.02523 0.04306 0.07155 0.03236 0.02265 0.02748 0.02741 0.05571 0.01831 0.03315 0.05711 0.02738 0.01917 0.02458 0.02351 0.04378 0.01465 0.02563 0.04564 0.02301 0.01611 0.02236 0.02202 0.03405 0.01568 0.01989 0.03653 0.01925 0.01347 0.01516 0.01762 0.02644 0.00998 0.0155 0.02927 0.01602 0.01122 0.01502 0.01219 0.02206 0.00975 0.01213 0.02349 0.0133 0.00931 0.01088 0.01504 0.01954 0.00775 0.00952 0.01886 0.011 0.0077 0.0081 0.01045 0.01319 0.00405 0.0075 0.01516 0.00908 0.00636 0.00668 0.00972 0.01199 0.00514 0.00592 0.0122 0.00748 0.00523 0.00942 0.01022 0.00877 0.00503 0.00469 0.00982 0.00615 0.0043 0.00529 0.00441 0.00794 0.00223 0.00373 0.00792 0.00505 0.00353 0.00292 0.00537 0.00469 0.00358 0.00297 0.00638 0.00414 0.0029 0.00353 0.00541 0.00464 0.0026 0.00237 0.00515 0.00339 0.00237 -6.02379E-4 0.00174 0.00373 0.00195 0.00189 0.00416 0.00278 0.00194 0.00554 0.00335 0.00129 0.00257 0.00152 0.00336 0.00227 0.00159 0.00378 -0.00238-6.96007E-4 0.00132 0.00122 0.00271 0.00186 0.0013

Figure 5 Time

1:99

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3

0.99999 0.97407 0.98123 0.95951 0.94092 0.96339 0.9372 0.91247 0.91923 0.92998 0.87688 0.89404 0.85834 0.8554 0.83751 0.83327 0.79196 0.80262 0.81736 0.78567 0.78504 0.75882 0.68383

Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3

2:98

Time

0.9527 1.00001 0.95442 0.90438 0.9359 0.93219 0.89919 0.87687 0.89362 0.84496 0.87462 0.86387 0.83714 0.81324 0.80075 0.80341 0.76688 0.77074 0.7382 0.76649 0.79775 0.70106 0.6645

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2.3 2.8 3.3 3.8

10:90

Time

0.97513 0.97144 0.99999 0.95352 0.94504 0.89544 0.88253 0.90976 0.85697 0.88323 0.81404 0.84427 0.82758 0.8154 0.81112 0.82082 0.76281 0.77028 0.75936 0.69751 0.67048 0.63807 0.5898

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3

42

20:80

Time

0.98546 1.00001 0.96219 0.93384 0.93588 0.90028 0.8649 0.85358 0.85151 0.85574 0.82726 0.82152 0.78801 0.78119 0.76536 0.75568 0.72937 0.7339 0.71984 0.705 0.72008 0.66663 0.61014

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.7

50:50

Time

0.99611 1 0.91964 0.88733 0.87482 0.83534 0.84418 0.80584 0.7892 0.74641 0.72882 0.70881 0.6937 0.67757 0.67352 0.66688 0.62533 0.62243 0.6114 0.59514 0.58037 0.57055 0.49038

100:0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.4 2.9 3.4

1.00001 0.94902 0.90021 0.84415 0.81678 0.76929 0.75481 0.71845 0.70777 0.67173 0.62571 0.58438 0.59333 0.5538 0.54681 0.50056 0.48211 0.44717 0.42812 0.41082 0.35764 0.30927 0.24174

3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 9 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50 55 60

0.67627 0.63011 0.60236 0.56631 0.54282 0.49914 0.4821 0.46402 0.43501 0.44222 0.40445 0.32247 0.2981 0.29015 0.27931 0.25816 0.21548 0.19591 0.17205 0.16476 0.12687 0.12858 0.10738 0.07742 0.09582 0.00516 0.04468 0.03283 -0.00328 0.02777 0.0208 0.00101 -0.01734 -0.01531 0.03214 -0.05865 -0.02708

Time

1:99 fitting

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 2 2.5

1 0.98983 0.97976 0.9698 0.95993 0.95017 0.94051 0.93095 0.92148 0.91211 0.90284 0.89366 0.88458 0.87558 0.86668 0.85787 0.84915 0.84052 0.81516 0.77457

3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 9 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50 55 60

Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 2 2.5

0.65992 0.59494 0.59767 0.54515 0.51828 0.51164 0.50559 0.46677 0.43518 0.44152 0.39272 0.34251 0.29112 0.2771 0.26181 0.21956 0.2512 0.21063 0.19209 0.17013 0.1556 0.11541 0.12327 0.07818 0.04966 0.04626 0.03117 0.03152 0.01457 0.04001 0.05628 -0.03468 0.0483 0.0206 -0.0226 0.01028

2:98 fitting

4.3 4.8 5.3 5.8 6.3 6.8 7.3 7.8 8.3 8.8 9.3 9.8 10.8 11.8 12.8 13.8 14.8 15.8 16.8 17.8 18.8 19.8 21.8 24.8 27.8 29.8 32.8 34.8 37.8 39.8 42.8 44.8 47.8 49.8 54.8 59.8

Time

1 0.98955 0.97921 0.96898 0.95885 0.94884 0.93893 0.92912 0.91942 0.90982 0.90031 0.89091 0.88161 0.87241 0.8633 0.85429 0.84538 0.83655 0.81064 0.76924

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2.3

0.53834 0.51259 0.47832 0.46723 0.39502 0.39715 0.3474 0.36566 0.33792 0.33661 0.31408 0.30039 0.21993 0.23342 0.22844 0.18283 0.16814 0.16516 0.12431 0.09163 0.10702 0.10546 0.08424 0.03926 0.02217 0.0212 -0.00426 0.02226 0.02012 0.00978 -0.01935 -0.02316 0.01145 0.03258 0.01253 0.00496

10:90 fitting

3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 38 40 43 45 48 50 55 60

Time

1 0.98732 0.9748 0.96245 0.95026 0.93823 0.92635 0.91463 0.90306 0.89165 0.88038 0.86925 0.85827 0.84744 0.83674 0.82619 0.81577 0.80549 0.79534 0.74653

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2

43

0.55566 0.5158 0.49415 0.46181 0.42557 0.39226 0.40174 0.32408 0.35241 0.31117 0.2786 0.26453 0.20805 0.1895 0.17552 0.15242 0.16876 0.11441 0.11305 0.11326 0.11164 0.10807 0.08814 0.02829 0.0893 0.01728 0.04161 0.02458 -0.00343 -0.01672 0.02129 0.01262 -0.00246 -0.016 -0.02407 0.03856

20:80 fitting

3.2 3.7 4.2 4.7 5.2 5.7 6.2 6.7 7.7 8.7 9.7 10.2 11.2 12.2 13.2 14.2 15.2 16.2 17.2 18.2 19.2 20.2 22.2 25.2 28.2 30.2 33.2 35.2 38.2 40.2 43.2 45.2 48.2 50.2 55.2 60.2

Time

1 0.98454 0.96932 0.95436 0.93963 0.92513 0.91087 0.89684 0.88303 0.86944 0.85608 0.84292 0.82997 0.81724 0.8047 0.79237 0.78023 0.76828 0.75653 0.73358

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2 2.7

0.44383 3.9 0.42421 4.4 0.37365 4.9 0.31 5.4 0.27319 5.9 0.26833 6.4 0.25206 6.9 0.23154 7.4 0.1904 7.9 0.14661 8.4 0.10325 9.4 0.08737 9.9 0.06246 10.9 0.02913 11.9 0.0248 12.9 0.04682 13.9 0.03469 14.9 0.02517 15.9 -0.00299 16.9 0.01663 17.9 0.01796 18.9 0.02224 19.9 0.00683 21.9 -0.02874 24.9 -0.03126 27.9 0.00218 29.9 -0.01594 32.9 -0.01171 34.9 -0.00215 37.9 -0.00305 39.9 -0.02496 42.9 -0.02101 44.9 -0.00429 47.9 -0.0064 49.9 0.00828 54.9 2.69095E-4

50:50 fitting

Time

0.97624 0.95307 0.93047 0.90843 0.88694 0.86597 0.84552 0.82558 0.80612 0.78715 0.76864 0.75059 0.73298 0.7158 0.69905 0.6827 0.66676 0.65121 0.62124 0.52731

0.19451 0.1465 0.14445 0.11026 0.07962 0.09118 0.08544 0.0733 0.06278 0.0668 0.05222 0.0279 0.01687 0.02928 0.02728 0.04272 0.01638 -0.01407 -0.00203 0.01653 0.01321 -0.02588 0.01044 -0.01957 0.0087 0.00988 0.03092 0.01381 -0.01367 -0.00502 -0.00438 -0.00822 0.01836 0.0044 -0.01368 59.9

100:0 fitting 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2.4

1 0.96257 0.92659 0.89199 0.85873 0.82676 0.79601 0.76646 0.73804 0.71071 0.68444 0.65918 0.63489 0.61154 0.58908 0.56749 0.54673 0.52676 0.50756 0.40685

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50 55 60

0.73602 3 0.72997 0.6994 3.5 0.69272 0.6646 4 0.65738 0.63154 4.5 0.62386 0.60014 5 0.59207 0.5703 5.5 0.5619 0.54195 6 0.53329 0.51501 6.5 0.50614 0.48942 7 0.48039 0.46511 7.5 0.45595 0.44201 8 0.43277 0.42006 8.5 0.41078 0.3992 9 0.38991 0.37939 9.5 0.37011 0.36056 10 0.35132 0.32567 11 0.31658 0.29416 12 0.28529 0.26572 13 0.25712 0.24003 14 0.23175 0.21684 15 0.2089 0.19589 16 0.18832 0.17698 17 0.16977 0.1599 18 0.15307 0.14447 19 0.13802 0.13053 20 0.12446 0.10657 22 0.10122 0.07865 25 0.07428 0.05805 28 0.05455 0.04742 30 0.04441 0.03502 33 0.03264 0.02862 35 0.02659 0.02114 38 0.01956 0.01728 40 0.01595 0.01277 43 0.01174 7.81183E-4 0.01044 45 0.00958 6.40319E-4 0.00772 48 0.00706 4.75191E-4 0.00631 50 0.00576 3.8951E-4 0.00382 55 0.00347 2.36945E-4 0.00231 60 0.00209 59.9 1.44138E-4

2.8 3.3 3.8 4.3 4.8 5.3 5.8 6.3 6.8 7.3 7.8 8.3 8.8 9.3 9.8 10.8 11.8 12.8 13.8 14.8 15.8 16.8 17.8 18.8 19.8 21.8 24.8 27.8 29.8 32.8 34.8 37.8 39.8 42.8

0.7008 0.65795 0.61779 0.58016 0.54488 0.51181 0.48081 0.45175 0.42449 0.39892 0.37495 0.35245 0.33135 0.31155 0.29297 0.25917 0.22938 0.20312 0.17995 0.15951 0.14146 0.12552 0.11142 0.09896 0.08794 0.06954 0.04907 0.03477 0.0277 0.01976 0.01581 0.01134 0.00911 0.00657

2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 38 40 43

0.67933 0.62925 0.58301 0.54032 0.50089 0.46446 0.43081 0.3997 0.37095 0.34437 0.31978 0.29704 0.276 0.25653 0.23851 0.22182 0.19204 0.16648 0.1445 0.12559 0.1093 0.09525 0.08311 0.07262 0.06354 0.05567 0.0429 0.0293 0.02023 0.01589 0.01116 0.0063 0.00504 0.00363

3.2 3.7 4.2 4.7 5.2 5.7 6.2 6.7 7.2 7.7 8.2 8.7 9.2 9.7 10.2 11.2 12.2 13.2 14.2 15.2 16.2 17.2 18.2 19.2 20.2 22.2 25.2 28.2 30.2 33.2 35.2 38.2 40.2 43.2

0.4695 0.41837 0.37315 0.33313 0.2977 0.26631 0.23849 0.21381 0.19192 0.17248 0.1552 0.13984 0.12616 0.11399 0.10313 0.08479 0.07013 0.05837 0.04888 0.04118 0.03492 0.02978 0.02554 0.02203 0.0191 0.01455 0.00997 0.00702 0.00561 0.00406 0.00329 0.00241 0.00196 0.00145

2.9 3.4 3.9 4.4 4.9 5.4 5.9 6.4 6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.9 11.9 12.9 13.9 14.9 15.9 16.9 17.9 18.9 19.9 21.9 24.9 27.9 29.9 32.9 34.9 37.9 39.9 42.9

0.33916 0.28342 0.23747 0.19957 0.16827 0.14239 0.12097 0.10321 0.08846 0.07618 0.06594 0.05738 0.0502 0.04417 0.03908 0.0311 0.02528 0.02096 0.01768 0.01513 0.01312 0.01148 0.01013 0.009 0.00803 0.00645 0.00472 0.00348 0.00285 0.00211 0.00173 0.00128 0.00105

44.8

0.00529 45

0.00292 45.2

0.00119 44.9

47.8

0.00384 48

0.00212 48.2

8.7758E-4

47.9

49.8

0.0031

50

0.00172 50.2

7.18527E-4

49.9

54.8

0.00183 55

0.00102 55.2

4.36359E-4

54.9

59.8

0.00108 60

6.08523E-4

60.2

2.65242E-4

S2.A Time

0 0.5 1 1.1 1.2 1.3

KS13C15N (10M)

KSCN (10M)

0.99999 0.92215 0.87544 0.86599 0.8665 0.85335

1.00001 0.93461 0.89437 0.88895 0.87087 0.85157

1 0.94151 0.89192 0.88292 0.87419 0.86574

1 0.94041 0.89086 0.88198 0.8734 0.86512

44

KSCN (10M) fitting

KS13C15N (10M) fitting

1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170

0.8418 0.82973 0.8273 0.83112 0.82252 0.81747 0.81297 0.77887 0.75261 0.72893 0.71563 0.70143 0.67543 0.66952 0.65256 0.63932 0.62278 0.6074 0.59115 0.58684 0.57509 0.56681 0.55625 0.54125 0.5236 0.50201 0.48768 0.47633 0.45982 0.44171 0.4291 0.41345 0.40496 0.37933 0.34257 0.31749 0.29805 0.26759 0.25231 0.23296 0.21877 0.2015 0.18739 0.17706 0.16556 0.14816 0.13377 0.10883 0.10042 0.08665 0.07502 0.064 0.05494 0.04462 0.04124 0.02748 0.02458 0.02236 0.01516 0.01502 0.01088 0.0081

0.8579 0.86262 0.85454 0.84488 0.84583 0.85103 0.84112 0.8082 0.7853 0.76594 0.7555 0.73544 0.71812 0.69188 0.6871 0.67313 0.66369 0.65114 0.63576 0.63299 0.61747 0.61832 0.5999 0.58942 0.57252 0.56593 0.54412 0.52226 0.52663 0.50195 0.48494 0.47744 0.46127 0.43673 0.41478 0.38325 0.3597 0.33445 0.32176 0.29772 0.28208 0.26391 0.2506 0.23458 0.22296 0.2 0.17746 0.15906 0.14305 0.12102 0.10963 0.09877 0.08556 0.07879 0.06835 0.05571 0.04378 0.03405 0.02644 0.02206 0.01954 0.01319

0.85754 0.84959 0.84187 0.83438 0.82711 0.82005 0.81319 0.78166 0.75412 0.72986 0.70829 0.68895 0.67144 0.65546 0.64075 0.62709 0.61433 0.60232 0.59094 0.58011 0.56975 0.5598 0.5502 0.53191 0.51463 0.49818 0.48244 0.46734 0.4528 0.43877 0.42524 0.41216 0.39952 0.37546 0.3422 0.31203 0.29348 0.2678 0.252 0.23011 0.21664 0.19797 0.18647 0.17052 0.16069 0.13865 0.11979 0.10361 0.08974 0.07782 0.06756 0.05873 0.05112 0.04455 0.03887 0.02969 0.02279 0.01757 0.0136 0.01057 0.00824 0.00645

0.85712 0.84939 0.84192 0.83469 0.82771 0.82095 0.8144 0.78464 0.75908 0.73691 0.71748 0.70026 0.68485 0.6709 0.65814 0.64636 0.63538 0.62507 0.61531 0.60602 0.59712 0.58855 0.58027 0.56442 0.54936 0.53492 0.52102 0.50758 0.49457 0.48194 0.46968 0.45776 0.44617 0.42392 0.39273 0.36395 0.34601 0.32083 0.30512 0.28305 0.26927 0.24992 0.23783 0.22083 0.21021 0.18594 0.16458 0.14577 0.1292 0.11457 0.10166 0.09026 0.08018 0.07126 0.06336 0.05016 0.03978 0.03159 0.02512 0.02001 0.01595 0.01273

45

180 190 200 210 220 230 240 250

0.00668 0.01199 0.00507 0.00942 0.00877 0.00399 0.00529 0.00794 0.00315 0.00292 0.00469 0.00249 0.00353 0.00464 0.00198 -6.02379E-4 0.00373 0.00554 0.00129 0.00125 0.00378 -6.96007E-4

0.01016 0.00813 0.0065 0.0052 0.00417 0.00157 0.00334 0.00268 9.9998E-4 0.00215

S2.B Time 0 0.5 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40

Flowing down 1.17235E-4 7.24472E-4 0.0062 0.0038 0.0063 0.00646 0.0064 0.00413 0.00645 0.00409 0.0065 0.00481 0.0067 0.00617 0.0065 0.00714 0.0066 0.00431 0.00645 0.00427 0.007 0.00724 0.0075 0.00538 0.00881 0.00695 0.00992 0.009 0.01558 0.01173 0.01592 0.01308 0.01637 0.01603 0.02131 0.0158 0.02003 0.01588 0.01937 0.01906 0.02251 0.01782 0.02673 0.01898 0.02659 0.0216 0.02978 0.02349 0.03327 0.02328 0.03204 0.02503 0.03755 0.02829 0.0385 0.02967 0.03967 0.02708 0.03956 0.03157 0.04292 0.03166 0.04393 0.03284 0.04786 0.03399 0.05025 0.03403 0.05103 0.03803 0.05418 0.03941 0.05359 0.03996 0.05814 0.04083 0.06262 0.04028 0.06681 0.04532 0.06415 0.04415 0.06783 0.04646 0.0657 0.04801 0.06972 0.04692 0.06857 0.04841 0.06644 0.04777

Pumping up

0.00224 0 0 5.59031E-4 0.00417 0.00292 0.00788 0.00551 0.00857 0.006 0.00925 0.00648 0.00992 0.00694 0.01057 0.0074 0.01121 0.00785 0.01184 0.00829 0.01245 0.00872 0.01306 0.00914 0.01365 0.00955 0.01423 0.00996 0.017 0.0119 0.01956 0.01369 0.02193 0.01535 0.02416 0.01691 0.02626 0.01838 0.02824 0.01977 0.03012 0.02109 0.03192 0.02234 0.03364 0.02355 0.03528 0.0247 0.03686 0.0258 0.03838 0.02686 0.03983 0.02788 0.04124 0.02887 0.04259 0.02981 0.04389 0.03072 0.04636 0.03245 0.04864 0.03405 0.05077 0.03554 0.05274 0.03691 0.05456 0.03819 0.05624 0.03936 0.05778 0.04045 0.0592 0.04144 0.0605 0.04235 0.06169 0.04318 0.06373 0.04461 0.06607 0.04625 0.06764 0.04735 0.06831 0.04782 0.06884 0.04819 0.06891 0.04824 0.06865 0.04806 0.06826 0.04778

46

Flowing down fitting

Pumping up fitting

43 45 48 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250

0.06679 0.06611 0.06295 0.06219 0.05865 0.05582 0.05174 0.04892 0.04736 0.04581 0.04345 0.03584 0.03721 0.02741 0.02351 0.02202 0.01762 0.01219 0.01504 0.01045 0.00972 0.01022 0.00441 0.00441 0.00537 0.00541 0.00174 0.00335 -0.00238

0.04642 0.04764 0.04507 0.04242 0.04324 0.0419 0.04055 0.03357 0.03261 0.0303 0.03083 0.02539 0.02861 0.02523 0.01831 0.01465 0.01568 0.00998 0.00975 0.00775 0.00405 0.00514 0.00503 0.00223 0.00358 0.0026 0.00195 0.00257 0.00132

0.06741 0.06668 0.06539 0.06442 0.06169 0.05865 0.05542 0.0521 0.04876 0.04547 0.04227 0.03917 0.03622 0.03342 0.02828 0.02379 0.01992 0.01661 0.0138 0.01144 0.00946 0.00781 0.00644 0.0053 0.00436 0.00358 0.00294 0.00241 0.00198

0.04718 0.04668 0.04577 0.04509 0.04318 0.04105 0.03879 0.03647 0.03413 0.03183 0.02959 0.02742 0.02535 0.02339 0.0198 0.01666 0.01394 0.01162 0.00966 0.00801 0.00662 0.00547 0.00451 0.00371 0.00305 0.00251 0.00206 0.00169 0.00139

S2.C Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3

KS13C15N (4M)

KSCN (4M)

1.00001 0.99011 0.97047 0.94939 0.93515 0.91021 0.89541 0.88452 0.86167 0.84947 0.83548 0.82215 0.81004 0.79634 0.79005 0.78276 0.7758 0.7649 0.76172 0.74986 0.7414 0.73639 0.73156 0.72326

0.99617 1 0.99253 0.97416 0.96113 0.94601 0.9342 0.92073 0.90856 0.89898 0.88809 0.87986 0.87314 0.86098 0.85386 0.84592 0.83963 0.83116 0.82537 0.81968 0.81518 0.80918 0.80465 0.79426

1 0.98475 0.97008 0.95596 0.94236 0.92926 0.91664 0.90448 0.89275 0.88143 0.8705 0.85996 0.84977 0.83992 0.83041 0.82121 0.8123 0.80369 0.79534 0.78726 0.77943 0.77183 0.76446 0.75732

1 0.9857 0.97196 0.95877 0.9461 0.93392 0.92222 0.91096 0.90012 0.8897 0.87966 0.86998 0.86066 0.85168 0.84301 0.83465 0.82658 0.81878 0.81125 0.80397 0.79693 0.79012 0.78353 0.77715

47

KSCN (4M) fitting

KS13C15N (4M) fitting

2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.4 11.4 12.4 13.4 14.4 15.4 16.4 17.4 18.4 19.4 20.4 23.4 25.4 28.4

0.71925 0.70954 0.70032 0.70125 0.69579 0.68769 0.6858 0.68273 0.67702 0.67032 0.66491 0.66215 0.65738 0.64965 0.64363 0.64235 0.63713 0.6402 0.63118 0.62597 0.62202 0.62518 0.61734 0.6114 0.6109 0.60581 0.60163 0.60186 0.59748 0.58985 0.59079 0.58635 0.5817 0.57722 0.57539 0.57046 0.56625 0.56378 0.56035 0.55969 0.55718 0.54816 0.52892 0.51664 0.49982 0.49411 0.48348 0.46698 0.45676 0.4364 0.41739 0.40339 0.38636 0.36891 0.35534 0.33835 0.32436 0.31044 0.29525 0.26524 0.24391 0.21921

0.79177 0.78365 0.7809 0.77415 0.76996 0.7665 0.76059 0.75593 0.75209 0.74587 0.7425 0.74031 0.73428 0.73117 0.72824 0.72334 0.72136 0.71689 0.70892 0.70617 0.70327 0.70214 0.69766 0.69233 0.68958 0.68671 0.68566 0.68253 0.67628 0.67378 0.66986 0.66752 0.66484 0.66084 0.65784 0.65583 0.65338 0.64983 0.64483 0.63982 0.63782 0.62581 0.61099 0.60077 0.58777 0.5764 0.5661 0.55173 0.54374 0.52555 0.50414 0.487 0.46979 0.45161 0.43707 0.42471 0.40664 0.3965 0.38146 0.35741 0.3333 0.30225

0.75038 0.74364 0.73709 0.73072 0.72453 0.71851 0.71264 0.70693 0.70137 0.69595 0.69066 0.6855 0.68047 0.67555 0.67075 0.66606 0.66147 0.65699 0.6526 0.6483 0.64409 0.63996 0.63592 0.63196 0.62807 0.62425 0.62051 0.61683 0.61322 0.60967 0.60617 0.60274 0.59936 0.59603 0.59276 0.58953 0.58636 0.58322 0.58014 0.57709 0.57409 0.55964 0.54604 0.53315 0.52087 0.50912 0.49783 0.48695 0.47644 0.45638 0.43742 0.41942 0.40227 0.38589 0.37023 0.35524 0.34088 0.32712 0.31392 0.27748 0.2556 0.22599

0.77096 0.76497 0.75915 0.75351 0.74804 0.74272 0.73755 0.73253 0.72764 0.72288 0.71825 0.71374 0.70935 0.70506 0.70088 0.69679 0.69281 0.68891 0.6851 0.68138 0.67774 0.67417 0.67068 0.66725 0.6639 0.6606 0.65737 0.6542 0.65109 0.64803 0.64502 0.64207 0.63916 0.63629 0.63347 0.6307 0.62796 0.62527 0.62261 0.61998 0.6174 0.60493 0.59317 0.58198 0.57129 0.56101 0.55109 0.54149 0.53216 0.51423 0.49712 0.48072 0.46494 0.44975 0.43508 0.42092 0.40724 0.39401 0.38122 0.34533 0.32332 0.29293

48

30.4 35.4 40.4 43.4 45.4 48.4 50.4 55.4 60.4 65.4 70.4 75.4 80.4 85.4 90.4 95.4 100.4 110.4 120.4 130.4 140.4 150.4 160.4 170.4 180.4 190.4 200.4 210.4 220.4 230.4 240.4 250.4

0.19664 0.27916 0.2082 0.27429 0.16339 0.23766 0.16966 0.23275 0.13104 0.20119 0.13831 0.19754 0.11481 0.18191 0.12238 0.17905 0.1021 0.17203 0.1128 0.1677 0.092 0.15533 0.09983 0.15202 0.08261 0.14495 0.09204 0.14239 0.07032 0.12469 0.07513 0.12092 0.05652 0.1055 0.06135 0.10271 0.04435 0.08937 0.05013 0.08726 0.0375 0.07609 0.04098 0.07415 0.02923 0.0641 0.03351 0.06301 0.02414 0.05535 0.02742 0.05356 0.02048 0.04709 0.02245 0.04553 0.01448 0.03894 0.01839 0.03871 0.01336 0.03407 0.01507 0.03291 0.0084 0.02982 0.01236 0.02799 0.0075 0.02071 0.00833 0.02025 0.00494 0.01504 0.00563 0.01466 9.26076E-5 0.01106 0.00381 0.01061 1E-3 0.00825 0.00259 0.00769 0.0012 0.00521 0.00176 0.00557 0.00369 0.00384 0.0012 0.00404 -8.47137E-5 0.0014 8.2429E-4 0.00293 9.268E-4 0.00214 5.6628E-4 0.00212 -6.67856E-4 -9.80186E-4 3.90154E-4 0.00154 -0.00117 0.00202 2.69581E-4 0.00112 -0.00193 5.38995E-4 1.86949E-4 8.11015E-4 -8.39232E-4 7.69612E-4 1.29921E-4 5.88691E-4 -0.00195 2.14259E-4 9.06284E-5 4.27369E-4 0.00283 -8.83906E-5 6.33492E-5 3.10284E-4 1.51583E-4 9.93781E-5 4.44474E-5 2.25358E-4

S2.D Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2

Flowing down

Pumping up

3.20421E-4 6.79497E-5 0 0 0.00177 8.90059E-4 4.4393E-4 3.10751E-4 -2.24788E-4 0.00255 8.76541E-4 6.13579E-4 0.00113 5.82218E-4 0.0013 9.08785E-4 0.00222 0.00237 0.00171 0.0012 0.0016 0.00261 0.00211 0.00148 0.00453 0.00413 0.0025 0.00175 0.00271 0.00254 0.00288 0.00202 0.00433 0.00299 0.00326 0.00228 0.00351 0.00342 0.00362 0.00254 0.00308 0.00375 0.00398 0.00278 0.00508 0.00494 0.00433 0.00303 0.00439 0.00465 0.00467 0.00327 0.00373 0.00337 0.005 0.0035 0.00563 0.00554 0.00533 0.00373 0.00534 0.00421 0.00564 0.00395 0.00463 0.00488 0.00596 0.00417 0.00612 0.00521 0.00626 0.00438 0.00541 0.00402 0.00656 0.00459 0.00613 0.006 0.00686 0.0048 0.00658 0.00694 0.00714 0.005 0.00534 0.00495 0.00743 0.0052 0.0063 0.00706 0.0077 0.00539

49

Flowing down fitting

Pumping up fitting

2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.4 11.4 12.4 13.4 14.4 15.4 16.4 17.4 18.4 19.4 20.4 23.4 25.4

0.00703 0.007 0.00743 0.00753 0.00734 0.00876 0.00762 0.00818 0.00882 0.00904 0.01113 0.00913 0.0096 0.00998 0.01051 0.00996 0.01086 0.01108 0.00991 0.01169 0.01181 0.01185 0.01206 0.01226 0.01234 0.01239 0.01243 0.01258 0.01268 0.01285 0.01351 0.01455 0.0146 0.0147 0.0148 0.0149 0.01501 0.01505 0.01506 0.0151 0.01512 0.01513 0.01474 0.01804 0.01763 0.0179 0.0184 0.02069 0.02 0.01987 0.02241 0.0241 0.02378 0.0247 0.02476 0.02527 0.02574 0.0266 0.02702 0.0272 0.02743 0.02682

0.00526 0.00638 0.00582 0.00711 0.00656 0.00579 0.00753 0.00655 0.00759 0.00842 0.00748 0.00757 0.00941 0.00722 0.00887 0.00899 0.00834 0.00845 0.00871 0.00854 0.00923 0.01006 0.00986 0.00842 0.00807 0.01036 0.0096 0.01028 0.00999 0.00934 0.00942 0.01042 0.0107 0.01075 0.01077 0.01086 0.01091 0.01102 0.01104 0.01106 0.01108 0.00978 0.01304 0.01209 0.01404 0.01306 0.01354 0.0137 0.01386 0.01412 0.01625 0.01589 0.01674 0.01617 0.0166 0.0169 0.01822 0.01635 0.01912 0.01897 0.01893 0.01863

0.00798 0.00824 0.00851 0.00876 0.00902 0.00927 0.00951 0.00975 0.00999 0.01022 0.01045 0.01068 0.0109 0.01112 0.01133 0.01155 0.01176 0.01196 0.01217 0.01237 0.01256 0.01276 0.01295 0.01314 0.01333 0.01352 0.0137 0.01388 0.01406 0.01423 0.01441 0.01458 0.01475 0.01492 0.01509 0.01525 0.01541 0.01557 0.01573 0.01589 0.01604 0.0162 0.01694 0.01764 0.01831 0.01894 0.01954 0.02011 0.02066 0.02117 0.02212 0.02297 0.02373 0.0244 0.02499 0.02551 0.02595 0.02633 0.02665 0.02691 0.02739 0.02748

0.00558 0.00577 0.00595 0.00613 0.00631 0.00649 0.00666 0.00683 0.00699 0.00715 0.00732 0.00747 0.00763 0.00778 0.00793 0.00808 0.00823 0.00837 0.00852 0.00866 0.0088 0.00893 0.00907 0.0092 0.00933 0.00946 0.00959 0.00972 0.00984 0.00996 0.01009 0.01021 0.01033 0.01044 0.01056 0.01067 0.01079 0.0109 0.01101 0.01112 0.01123 0.01134 0.01186 0.01235 0.01282 0.01326 0.01368 0.01408 0.01446 0.01482 0.01548 0.01608 0.01661 0.01708 0.01749 0.01785 0.01817 0.01843 0.01866 0.01884 0.01917 0.01923

50

28.4 30.4 35.4 40.4 43.4 45.4 48.4 50.4 55.4 60.4 65.4 70.4 75.4 80.4 85.4 90.4 95.4 100.4 110.4 120.4 130.4 140.4 150.4 160.4 170.4 180.4 190.4 200.4 210.4 220.4 230.4 240.4 250.4

0.02712 0.01947 0.02734 0.01914 0.02862 0.01842 0.02709 0.01896 0.02656 0.01767 0.02606 0.01824 0.02572 0.01614 0.02461 0.01723 0.02493 0.01614 0.02361 0.01653 0.02391 0.01609 0.02291 0.01604 0.02155 0.01538 0.02183 0.01528 0.02185 0.01432 0.0211 0.01477 0.01998 0.01231 0.01926 0.01348 0.02026 0.01156 0.01744 0.01221 0.01772 0.01016 0.0157 0.01099 0.0148 0.00972 0.01405 0.00984 0.01448 0.00738 0.01252 0.00877 0.01236 0.00811 0.01112 0.00778 0.01039 0.00621 0.00983 0.00688 0.00956 0.00547 0.00867 0.00607 0.00792 0.00502 0.00763 0.00534 0.00739 0.00589 0.00669 0.00468 0.00471 0.00422 0.00512 0.00358 0.00441 0.00309 0.00389 0.00272 0.00306 0.00212 0.00294 0.00206 0.00115 0.00121 0.00221 0.00154 0.00145 6.14085E-4 0.00165 0.00116 0.00113 0.00106 0.00123 8.62862E-4 6.39814E-4 -4.49872E-4 9.17091E-4 6.41963E-4 4.55911E-4 1.01079E-4 6.80548E-4 4.76347E-4 6.39106E-4 -1.38521E-4 5.04013E-4 3.52804E-4 0.00121 0.00124 3.72502E-4 2.6076E-4 4.08294E-4 9.33269E-4 2.74931E-4 1.92454E-4 3.91239E-4 3.3924E-4 2.02579E-4 1.41853E-4 -2.97471E-4 0.00127 1.49105E-4 1.04458E-4 5.92825E-4 -5.12917E-4 1.09652E-4 7.67682E-5 2.45445E-4 8.8445E-4 8.05445E-5 5.64608E-5

S3.A Time

0 0.5 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5

Peak 1

Peak 5

Peak3

Peak7

Peak 1 fitting

Peak 3 fitting

0.99999 0.00316 1.00001 0.00224 1 1 0 0 0.92215 0.00173 0.93461 5.59031E-4 0.94243 0.94488 0.00389 0.87544 0.00245 0.89437 0.0038 0.89356 0.89888 0.00737 0.00516 0.86599 0.00231 0.88895 0.00646 0.88469 0.89061 0.00802 0.00561 0.8665 1.17235E-4 0.87087 0.00413 0.87609 0.88262 0.00866 0.85335 0.00196 0.85157 0.00409 0.86776 0.8749 0.00929 0.0065 0.8418 0.00183 0.8579 0.00481 0.85967 0.86743 0.0099 0.00693 0.82973 9.95561E-4 0.86262 0.00617 0.85183 0.86022 0.01051 0.8273 0.00322 0.85454 0.00714 0.84422 0.85323 0.0111 0.00777 0.83112 7.24472E-4 0.84488 0.00431 0.83683 0.84648 0.01168 0.82252 0.00365 0.84583 0.00427 0.82966 0.83994 0.01225 0.00858 0.81747 0.0036 0.85103 0.00724 0.8227 0.8336 0.01281 0.00897 0.81297 0.00607 0.84112 0.00538 0.81594 0.82747 0.01336 0.00935 0.77887 0.00645 0.8082 0.00695 0.78484 0.79949 0.01599 0.01119 0.75261 0.00589 0.7853 0.009 0.75767 0.77535 0.01842 0.0129 0.72893 0.00881 0.76594 0.01173 0.73374 0.75432 0.02069 0.01448 0.71563 0.00992 0.7555 0.01308 0.71249 0.73581 0.02282 0.01598 0.70143 0.01558 0.73544 0.01603 0.69343 0.71933 0.02483 0.01738 0.67543 0.01592 0.71812 0.0158 0.6762 0.70452 0.02673 0.01871 0.66952 0.01637 0.69188 0.01588 0.66048 0.69105 0.02855 0.01998

51

Peak 5 fitting

0.00272

0.00606

0.00735 0.00818

Peak 7 fitting

6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250

0.65256 0.02131 0.6871 0.01906 0.64601 0.67869 0.03027 0.02119 0.63932 0.02003 0.67313 0.01782 0.63261 0.66723 0.03193 0.02235 0.62278 0.01937 0.66369 0.01898 0.62008 0.65652 0.03351 0.02346 0.6074 0.02251 0.65114 0.0216 0.6083 0.64643 0.03503 0.02452 0.59115 0.02673 0.63576 0.02349 0.59716 0.63685 0.03649 0.02555 0.58684 0.02659 0.63299 0.02328 0.58655 0.62771 0.0379 0.02653 0.57509 0.02978 0.61747 0.02503 0.5764 0.61894 0.03926 0.02748 0.56681 0.03327 0.61832 0.02829 0.56666 0.61048 0.04056 0.02839 0.55625 0.03204 0.5999 0.02967 0.55727 0.60228 0.04182 0.02928 0.54125 0.03755 0.58942 0.02708 0.53938 0.58657 0.04421 0.03094 0.5236 0.03967 0.57252 0.03157 0.52247 0.5716 0.04642 0.0325 0.50201 0.03956 0.56593 0.03166 0.50637 0.55723 0.04848 0.03394 0.48768 0.04292 0.54412 0.03284 0.49096 0.54336 0.05039 0.03527 0.47633 0.04393 0.52226 0.03399 0.47615 0.52994 0.05216 0.03651 0.45982 0.04786 0.52663 0.03403 0.46188 0.51692 0.05379 0.03765 0.44171 0.05025 0.50195 0.03803 0.44811 0.50427 0.0553 0.03871 0.4291 0.05103 0.48494 0.03941 0.4348 0.49197 0.05668 0.03968 0.41345 0.05418 0.47744 0.03996 0.42193 0.47999 0.05795 0.04056 0.40496 0.05359 0.46127 0.04083 0.40947 0.46834 0.05911 0.04138 0.37933 0.05814 0.43673 0.04028 0.38571 0.44592 0.06112 0.04278 0.34257 0.06262 0.41478 0.04532 0.35278 0.41441 0.06342 0.0444 0.31749 0.06681 0.38325 0.04415 0.32278 0.38524 0.06499 0.04549 0.29805 0.06415 0.3597 0.04646 0.30428 0.36699 0.06568 0.04598 0.26759 0.06783 0.33445 0.04801 0.27859 0.34131 0.06624 0.04637 0.25231 0.0657 0.32176 0.04692 0.26274 0.32524 0.06634 0.04644 0.23296 0.06972 0.29772 0.04841 0.24071 0.30261 0.06614 0.0463 0.21877 0.06857 0.28208 0.04777 0.2271 0.28845 0.06579 0.04605 0.2015 0.06644 0.26391 0.04642 0.2082 0.26849 0.06501 0.0455 0.18739 0.06679 0.2506 0.04764 0.19652 0.256 0.06433 0.04503 0.17706 0.06611 0.23458 0.04507 0.18027 0.23838 0.06312 0.04419 0.16556 0.06295 0.22296 0.04242 0.17023 0.22734 0.06221 0.04354 0.14816 0.06219 0.2 0.04324 0.14763 0.20202 0.05961 0.04173 0.13377 0.05865 0.17746 0.0419 0.12817 0.17964 0.05671 0.0397 0.10883 0.05582 0.15906 0.04055 0.1114 0.15982 0.05361 0.03753 0.10042 0.05174 0.14305 0.03357 0.09693 0.14227 0.05042 0.0353 0.08665 0.04892 0.12102 0.03261 0.08443 0.12672 0.04721 0.03305 0.07502 0.04736 0.10963 0.0303 0.07363 0.11293 0.04404 0.03083 0.064 0.04581 0.09877 0.03083 0.06428 0.10068 0.04094 0.02866 0.05494 0.04345 0.08556 0.02539 0.05619 0.08981 0.03795 0.02656 0.04462 0.03584 0.07879 0.02861 0.04916 0.08015 0.03508 0.02456 0.04124 0.03721 0.06835 0.02523 0.04306 0.07155 0.03236 0.02265 0.02748 0.02741 0.05571 0.01831 0.03315 0.05711 0.02738 0.01917 0.02458 0.02351 0.04378 0.01465 0.02563 0.04564 0.02301 0.01611 0.02236 0.02202 0.03405 0.01568 0.01989 0.03653 0.01925 0.01347 0.01516 0.01762 0.02644 0.00998 0.0155 0.02927 0.01602 0.01122 0.01502 0.01219 0.02206 0.00975 0.01213 0.02349 0.0133 0.00931 0.01088 0.01504 0.01954 0.00775 0.00952 0.01886 0.011 0.0077 0.0081 0.01045 0.01319 0.00405 0.0075 0.01516 0.00908 0.00636 0.00668 0.00972 0.01199 0.00514 0.00592 0.0122 0.00748 0.00523 0.00942 0.01022 0.00877 0.00503 0.00469 0.00982 0.00615 0.0043 0.00529 0.00441 0.00794 0.00223 0.00373 0.00792 0.00505 0.00353 0.00292 0.00537 0.00469 0.00358 0.00297 0.00638 0.00414 0.0029 0.00353 0.00541 0.00464 0.0026 0.00237 0.00515 0.00339 0.00237 -6.02379E-4 0.00174 0.00373 0.00195 0.00189 0.00416 0.00278 0.00194 0.00554 0.00335 0.00129 0.00257 0.00152 0.00336 0.00227 0.00159 0.00378 -0.00238-6.96007E-4 0.00132 0.00122 0.00271 0.00186 0.0013

52

S3.B Time

0 0.5 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50 55 60 65

Peak 5

Peak7

0.00316 0.00224 0 0.00173 5.59031E-4 0.00245 0.0038 0.00737 0.00231 0.00646 0.00802 1.17235E-4 0.00413 0.00196 0.00409 0.00929 0.00183 0.00481 0.0099 9.95561E-4 0.00617 0.00322 0.00714 0.0111 7.24472E-4 0.00431 0.00365 0.00427 0.01225 0.0036 0.00724 0.01281 0.00607 0.00538 0.01336 0.00645 0.00695 0.01599 0.00589 0.009 0.01842 0.00881 0.01173 0.02069 0.00992 0.01308 0.02282 0.01558 0.01603 0.02483 0.01592 0.0158 0.02673 0.01637 0.01588 0.02855 0.02131 0.01906 0.03027 0.02003 0.01782 0.03193 0.01937 0.01898 0.03351 0.02251 0.0216 0.03503 0.02673 0.02349 0.03649 0.02659 0.02328 0.0379 0.02978 0.02503 0.03926 0.03327 0.02829 0.04056 0.03204 0.02967 0.04182 0.03755 0.02708 0.04421 0.03967 0.03157 0.04642 0.03956 0.03166 0.04848 0.04292 0.03284 0.05039 0.04393 0.03399 0.05216 0.04786 0.03403 0.05379 0.05025 0.03803 0.0553 0.05103 0.03941 0.05668 0.05418 0.03996 0.05795 0.05359 0.04083 0.05911 0.05814 0.04028 0.06112 0.06262 0.04532 0.06342 0.06681 0.04415 0.06499 0.06415 0.04646 0.06568 0.06783 0.04801 0.06624 0.0657 0.04692 0.06634 0.06972 0.04841 0.06614 0.06857 0.04777 0.06579 0.06644 0.04642 0.06501 0.06679 0.04764 0.06433 0.06611 0.04507 0.06312 0.06295 0.04242 0.06221 0.06219 0.04324 0.05961 0.05865 0.0419 0.05671 0.05582 0.04055 0.05361

Peak 5 fitting 0 0.00389 0.00516 0.00561 0.00866 0.0065 0.00693 0.01051 0.00777 0.01168 0.00858 0.00897 0.00935 0.01119 0.0129 0.01448 0.01598 0.01738 0.01871 0.01998 0.02119 0.02235 0.02346 0.02452 0.02555 0.02653 0.02748 0.02839 0.02928 0.03094 0.0325 0.03394 0.03527 0.03651 0.03765 0.03871 0.03968 0.04056 0.04138 0.04278 0.0444 0.04549 0.04598 0.04637 0.04644 0.0463 0.04605 0.0455 0.04503 0.04419 0.04354 0.04173 0.0397 0.03753

Peak 7 fitting

0.00272

0.00606

0.00735 0.00818

53

70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250

0.05174 0.04892 0.04736 0.04581 0.04345 0.03584 0.03721 0.02741 0.02351 0.02202 0.01762 0.01219 0.01504 0.01045 0.00972 0.01022 0.00441 0.00537 0.00541 0.00174 0.00335 -0.00238

0.03357 0.03261 0.0303 0.03083 0.02539 0.02861 0.02523 0.01831 0.01465 0.01568 0.00998 0.00975 0.00775 0.00405 0.00514 0.00503 0.00223 0.00358 0.0026 0.00195 0.00257 0.00132

0.05042 0.04721 0.04404 0.04094 0.03795 0.03508 0.03236 0.02738 0.02301 0.01925 0.01602 0.0133 0.011 0.00908 0.00748 0.00615 0.00505 0.00414 0.00339 0.00278 0.00227 0.00186

0.0353 0.03305 0.03083 0.02866 0.02656 0.02456 0.02265 0.01917 0.01611 0.01347 0.01122 0.00931 0.0077 0.00636 0.00523 0.0043 0.00353 0.0029 0.00237 0.00194 0.00159 0.0013

S3.C Time

1:99

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

0.99999 0.97407 0.98123 0.95951 0.94092 0.96339 0.9372 0.91247 0.91923 0.92998 0.87688 0.89404 0.85834 0.8554 0.83751 0.83327 0.79196 0.80262 0.81736 0.78567 0.78504 0.75882 0.68383 0.67627 0.63011 0.60236 0.56631 0.54282 0.49914 0.4821 0.46402 0.43501 0.44222

Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

2:98

Time

0.9527 1.00001 0.95442 0.90438 0.9359 0.93219 0.89919 0.87687 0.89362 0.84496 0.87462 0.86387 0.83714 0.81324 0.80075 0.80341 0.76688 0.77074 0.7382 0.76649 0.79775 0.70106 0.6645 0.65992 0.59494 0.59767 0.54515 0.51828 0.51164 0.50559 0.46677 0.43518 0.44152

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2.3 2.8 3.3 3.8 4.3 4.8 5.3 5.8 6.3 6.8 7.3 7.8 8.3 8.8

10:90

Time

0.97513 0.97144 0.99999 0.95352 0.94504 0.89544 0.88253 0.90976 0.85697 0.88323 0.81404 0.84427 0.82758 0.8154 0.81112 0.82082 0.76281 0.77028 0.75936 0.69751 0.67048 0.63807 0.5898 0.53834 0.51259 0.47832 0.46723 0.39502 0.39715 0.3474 0.36566 0.33792 0.33661

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

54

20:80

Time

0.98546 1.00001 0.96219 0.93384 0.93588 0.90028 0.8649 0.85358 0.85151 0.85574 0.82726 0.82152 0.78801 0.78119 0.76536 0.75568 0.72937 0.7339 0.71984 0.705 0.72008 0.66663 0.61014 0.55566 0.5158 0.49415 0.46181 0.42557 0.39226 0.40174 0.32408 0.35241 0.31117

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.7 3.2 3.7 4.2 4.7 5.2 5.7 6.2 6.7 7.7 8.7

50:50

Time

0.99611 1 0.91964 0.88733 0.87482 0.83534 0.84418 0.80584 0.7892 0.74641 0.72882 0.70881 0.6937 0.67757 0.67352 0.66688 0.62533 0.62243 0.6114 0.59514 0.58037 0.57055 0.49038 0.44383 0.42421 0.37365 0.31 0.27319 0.26833 0.25206 0.23154 0.1904 0.14661

100:0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.4 2.9 3.4 3.9 4.4 4.9 5.4 5.9 6.4 6.9 7.4 7.9 8.4

1.00001 0.94902 0.90021 0.84415 0.81678 0.76929 0.75481 0.71845 0.70777 0.67173 0.62571 0.58438 0.59333 0.5538 0.54681 0.50056 0.48211 0.44717 0.42812 0.41082 0.35764 0.30927 0.24174 0.19451 0.1465 0.14445 0.11026 0.07962 0.09118 0.08544 0.0733 0.06278 0.0668

9 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50 55 60

0.40445 0.32247 0.2981 0.29015 0.27931 0.25816 0.21548 0.19591 0.17205 0.16476 0.12687 0.12858 0.10738 0.07742 0.09582 0.00516 0.04468 0.03283 -0.00328 0.02777 0.0208 0.00101 -0.01734 -0.01531 0.03214 -0.05865 -0.02708

Time

1:99 fitting

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5

1 0.98983 0.97976 0.9698 0.95993 0.95017 0.94051 0.93095 0.92148 0.91211 0.90284 0.89366 0.88458 0.87558 0.86668 0.85787 0.84915 0.84052 0.81516 0.77457 0.73602 0.6994 0.6646 0.63154 0.60014 0.5703 0.54195 0.51501 0.48942 0.46511

9 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50 55 60

Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5

0.39272 0.34251 0.29112 0.2771 0.26181 0.21956 0.2512 0.21063 0.19209 0.17013 0.1556 0.11541 0.12327 0.07818 0.04966 0.04626 0.03117 0.03152 0.01457 0.04001 0.05628 -0.03468 0.0483 0.0206 -0.0226 0.01028

2:98 fitting

9.3 9.8 10.8 11.8 12.8 13.8 14.8 15.8 16.8 17.8 18.8 19.8 21.8 24.8 27.8 29.8 32.8 34.8 37.8 39.8 42.8 44.8 47.8 49.8 54.8 59.8

Time

1 0.98955 0.97921 0.96898 0.95885 0.94884 0.93893 0.92912 0.91942 0.90982 0.90031 0.89091 0.88161 0.87241 0.8633 0.85429 0.84538 0.83655 0.81064 0.76924 0.72997 0.69272 0.65738 0.62386 0.59207 0.5619 0.53329 0.50614 0.48039 0.45595

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2.3 2.8 3.3 3.8 4.3 4.8 5.3 5.8 6.3 6.8 7.3

0.31408 0.30039 0.21993 0.23342 0.22844 0.18283 0.16814 0.16516 0.12431 0.09163 0.10702 0.10546 0.08424 0.03926 0.02217 0.0212 -0.00426 0.02226 0.02012 0.00978 -0.01935 -0.02316 0.01145 0.03258 0.01253 0.00496

10:90 fitting

9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 38 40 43 45 48 50 55 60

Time

1 0.98732 0.9748 0.96245 0.95026 0.93823 0.92635 0.91463 0.90306 0.89165 0.88038 0.86925 0.85827 0.84744 0.83674 0.82619 0.81577 0.80549 0.79534 0.74653 0.7008 0.65795 0.61779 0.58016 0.54488 0.51181 0.48081 0.45175 0.42449 0.39892

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

55

0.2786 0.26453 0.20805 0.1895 0.17552 0.15242 0.16876 0.11441 0.11305 0.11326 0.11164 0.10807 0.08814 0.02829 0.0893 0.01728 0.04161 0.02458 -0.00343 -0.01672 0.02129 0.01262 -0.00246 -0.016 -0.02407 0.03856

20:80 fitting

9.7 10.2 11.2 12.2 13.2 14.2 15.2 16.2 17.2 18.2 19.2 20.2 22.2 25.2 28.2 30.2 33.2 35.2 38.2 40.2 43.2 45.2 48.2 50.2 55.2 60.2

Time

1 0.98454 0.96932 0.95436 0.93963 0.92513 0.91087 0.89684 0.88303 0.86944 0.85608 0.84292 0.82997 0.81724 0.8047 0.79237 0.78023 0.76828 0.75653 0.73358 0.67933 0.62925 0.58301 0.54032 0.50089 0.46446 0.43081 0.3997 0.37095 0.34437

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2 2.7 3.2 3.7 4.2 4.7 5.2 5.7 6.2 6.7 7.2 7.7

0.10325 9.4 0.08737 9.9 0.06246 10.9 0.02913 11.9 0.0248 12.9 0.04682 13.9 0.03469 14.9 0.02517 15.9 -0.00299 16.9 0.01663 17.9 0.01796 18.9 0.02224 19.9 0.00683 21.9 -0.02874 24.9 -0.03126 27.9 0.00218 29.9 -0.01594 32.9 -0.01171 34.9 -0.00215 37.9 -0.00305 39.9 -0.02496 42.9 -0.02101 44.9 -0.00429 47.9 -0.0064 49.9 0.00828 54.9 2.69095E-4

50:50 fitting

Time

0.97624 0.95307 0.93047 0.90843 0.88694 0.86597 0.84552 0.82558 0.80612 0.78715 0.76864 0.75059 0.73298 0.7158 0.69905 0.6827 0.66676 0.65121 0.62124 0.52731 0.4695 0.41837 0.37315 0.33313 0.2977 0.26631 0.23849 0.21381 0.19192 0.17248

0.05222 0.0279 0.01687 0.02928 0.02728 0.04272 0.01638 -0.01407 -0.00203 0.01653 0.01321 -0.02588 0.01044 -0.01957 0.0087 0.00988 0.03092 0.01381 -0.01367 -0.00502 -0.00438 -0.00822 0.01836 0.0044 -0.01368 59.9

100:0 fitting

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2.4 2.9 3.4 3.9 4.4 4.9 5.4 5.9 6.4 6.9 7.4

1 0.96257 0.92659 0.89199 0.85873 0.82676 0.79601 0.76646 0.73804 0.71071 0.68444 0.65918 0.63489 0.61154 0.58908 0.56749 0.54673 0.52676 0.50756 0.40685 0.33916 0.28342 0.23747 0.19957 0.16827 0.14239 0.12097 0.10321 0.08846 0.07618

8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50 55 60

0.44201 8 0.43277 0.42006 8.5 0.41078 0.3992 9 0.38991 0.37939 9.5 0.37011 0.36056 10 0.35132 0.32567 11 0.31658 0.29416 12 0.28529 0.26572 13 0.25712 0.24003 14 0.23175 0.21684 15 0.2089 0.19589 16 0.18832 0.17698 17 0.16977 0.1599 18 0.15307 0.14447 19 0.13802 0.13053 20 0.12446 0.10657 22 0.10122 0.07865 25 0.07428 0.05805 28 0.05455 0.04742 30 0.04441 0.03502 33 0.03264 0.02862 35 0.02659 0.02114 38 0.01956 0.01728 40 0.01595 0.01277 43 0.01174 7.81183E-4 0.01044 45 0.00958 6.40319E-4 0.00772 48 0.00706 4.75191E-4 0.00631 50 0.00576 3.8951E-4 0.00382 55 0.00347 2.36945E-4 0.00231 60 0.00209 59.9 1.44138E-4

7.8 8.3 8.8 9.3 9.8 10.8 11.8 12.8 13.8 14.8 15.8 16.8 17.8 18.8 19.8 21.8 24.8 27.8 29.8 32.8 34.8 37.8 39.8 42.8

0.37495 0.35245 0.33135 0.31155 0.29297 0.25917 0.22938 0.20312 0.17995 0.15951 0.14146 0.12552 0.11142 0.09896 0.08794 0.06954 0.04907 0.03477 0.0277 0.01976 0.01581 0.01134 0.00911 0.00657

7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 38 40 43

0.31978 0.29704 0.276 0.25653 0.23851 0.22182 0.19204 0.16648 0.1445 0.12559 0.1093 0.09525 0.08311 0.07262 0.06354 0.05567 0.0429 0.0293 0.02023 0.01589 0.01116 0.0063 0.00504 0.00363

8.2 8.7 9.2 9.7 10.2 11.2 12.2 13.2 14.2 15.2 16.2 17.2 18.2 19.2 20.2 22.2 25.2 28.2 30.2 33.2 35.2 38.2 40.2 43.2

0.1552 0.13984 0.12616 0.11399 0.10313 0.08479 0.07013 0.05837 0.04888 0.04118 0.03492 0.02978 0.02554 0.02203 0.0191 0.01455 0.00997 0.00702 0.00561 0.00406 0.00329 0.00241 0.00196 0.00145

7.9 8.4 8.9 9.4 9.9 10.9 11.9 12.9 13.9 14.9 15.9 16.9 17.9 18.9 19.9 21.9 24.9 27.9 29.9 32.9 34.9 37.9 39.9 42.9

0.06594 0.05738 0.0502 0.04417 0.03908 0.0311 0.02528 0.02096 0.01768 0.01513 0.01312 0.01148 0.01013 0.009 0.00803 0.00645 0.00472 0.00348 0.00285 0.00211 0.00173 0.00128 0.00105

44.8

0.00529 45

0.00292 45.2

0.00119 44.9

47.8

0.00384 48

0.00212 48.2

8.7758E-4

47.9

49.8

0.0031

50

0.00172 50.2

7.18527E-4

49.9

54.8

0.00183 55

0.00102 55.2

4.36359E-4

54.9

59.8

0.00108 60

6.08523E-4

60.2

2.65242E-4

S4.A Time

-1.22E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

KS13C15N (8.8M)

KSCN (8.8M)

1.00001 0.99361 0.97032 0.96399 0.95277 0.93349 0.9309 0.91424 0.89454 0.88618 0.87377 0.86675 0.86283 0.85368 0.84815 0.8341 0.81597 0.81454 0.81692 0.80978

0.9995 1 0.9916 0.97751 0.96218 0.95506 0.94725 0.9377 0.91671 0.91363 0.9085 0.90064 0.89653 0.88601 0.86956 0.86278 0.85645 0.84744 0.84794 0.84048

1 0.98574 0.97205 0.95892 0.9463 0.93418 0.92254 0.91134 0.90057 0.8902 0.88023 0.87062 0.86136 0.85243 0.84382 0.83552 0.8275 0.81976 0.81227 0.80504

1 0.9893 0.97892 0.96886 0.9591 0.94963 0.94044 0.93152 0.92285 0.91443 0.90625 0.8983 0.89057 0.88305 0.87574 0.86862 0.86169 0.85494 0.84836 0.84196

56

KSCN (8.8M) fitting

KS13C15N (8.8M) fitting

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 6.3 6.8 7.3 7.8 8.3 8.8 9.3 9.8 10.8 11.8 12.8 13.8 14.8 15.8 16.8 17.8 18.8 19.8 22.8 24.8 27.8 29.8 34.8

0.79709 0.78732 0.78044 0.77979 0.76963 0.76541 0.77197 0.75803 0.75215 0.74974 0.7442 0.73683 0.74502 0.73371 0.72694 0.71764 0.71397 0.71185 0.70788 0.70937 0.69931 0.69257 0.70261 0.6893 0.6888 0.6811 0.67597 0.6777 0.67446 0.66645 0.66352 0.65426 0.65276 0.6514 0.65691 0.64645 0.64598 0.64285 0.63513 0.62576 0.61037 0.60266 0.58597 0.5782 0.56635 0.54588 0.54065 0.51707 0.49574 0.47643 0.46375 0.44203 0.42733 0.41231 0.397 0.37859 0.36817 0.3326 0.30708 0.277 0.25991 0.21624

0.83439 0.82879 0.82253 0.81662 0.81319 0.8069 0.80186 0.80593 0.79622 0.79168 0.78813 0.78036 0.78044 0.77182 0.76728 0.75732 0.75258 0.75115 0.74854 0.75354 0.74359 0.74314 0.73526 0.73341 0.72898 0.72543 0.72476 0.71694 0.70886 0.70555 0.70891 0.70565 0.69808 0.69405 0.69313 0.693 0.69455 0.6874 0.68149 0.67108 0.65501 0.63681 0.62524 0.61658 0.60415 0.58605 0.5748 0.55653 0.53886 0.51609 0.50007 0.47846 0.46259 0.44669 0.42939 0.41576 0.39905 0.36166 0.33846 0.30821 0.28721 0.24265

0.79804 0.79127 0.78471 0.77836 0.7722 0.76622 0.76042 0.7548 0.74933 0.74401 0.73884 0.73381 0.72892 0.72414 0.71949 0.71496 0.71053 0.70621 0.70199 0.69787 0.69384 0.68989 0.68603 0.68224 0.67854 0.6749 0.67134 0.66784 0.6644 0.66103 0.65772 0.65446 0.65125 0.64809 0.64499 0.64193 0.63891 0.63594 0.63302 0.61894 0.60568 0.59311 0.58111 0.56959 0.55849 0.54775 0.53734 0.51735 0.49834 0.48017 0.46275 0.44603 0.42996 0.4145 0.39962 0.3853 0.37151 0.33311 0.30982 0.27797 0.25864 0.21614

0.83571 0.82962 0.82368 0.81789 0.81223 0.8067 0.80131 0.79603 0.79088 0.78584 0.78091 0.77609 0.77137 0.76675 0.76222 0.75779 0.75344 0.74918 0.745 0.7409 0.73687 0.73292 0.72904 0.72523 0.72148 0.7178 0.71418 0.71062 0.70711 0.70366 0.70026 0.69692 0.69362 0.69038 0.68717 0.68402 0.6809 0.67783 0.6748 0.66021 0.64645 0.63341 0.62098 0.60908 0.59765 0.58663 0.57597 0.55559 0.53629 0.5179 0.50031 0.48344 0.46721 0.45159 0.43654 0.42203 0.40802 0.36885 0.34492 0.312 0.29186 0.24718

57

39.8 42.8 44.8 47.8 49.8 54.8 59.8 64.8 69.8 74.8 79.8 84.8 89.8 94.8 99.8 109.8 119.8 129.8 139.8 149.8 159.8 169.8 179.8 189.8 199.8 209.8 219.8 229.8 239.8 249.8

0.18415 0.20545 0.1808 0.2095 0.1652 0.18867 0.16252 0.18979 0.15409 0.17438 0.1514 0.17771 0.13907 0.15955 0.13617 0.16106 0.12929 0.15084 0.12691 0.15086 0.1118 0.12907 0.10649 0.12817 0.09514 0.11024 0.08944 0.10896 0.08174 0.0933 0.0752 0.0927 0.06933 0.08014 0.06329 0.07892 0.05792 0.06899 0.05332 0.06724 0.0518 0.05836 0.04497 0.05732 0.04216 0.05141 0.03796 0.04889 0.03838 0.0431 0.03207 0.04173 0.02996 0.03729 0.02712 0.03564 0.02583 0.03106 0.02296 0.03045 0.01855 0.02433 0.01649 0.02227 0.01199 0.0202 0.01189 0.01632 0.00944 0.01334 0.0086 0.01198 0.00885 0.01038 0.00624 0.00881 0.00304 0.00838 0.00454 0.00649 0.00313 0.00551 0.00331 0.00479 0.00213 0.00361 0.00242 0.00353 -6.94343E-5 0.00292 0.00177 0.00261 0.0019 4.46018E-4 0.0013 0.00193 0.00105 0.00257 9.59587E-4 0.00143 0.00104 0.00167 7.07591E-4 0.00106 -0.00226 4.92567E-4 5.22638E-4 7.89349E-4 8.67446E-4 4.96339E-5 3.86613E-4 5.86423E-4 -0.00202 0.0026 2.86382E-4 4.35988E-4 -0.00117 -1.55725E-4 2.12406E-4 3.24348E-4

S4.B Time

-1.22E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3

Flowing down

-4.22526E-4 -8.4208E-4 4.90249E-4 3.06712E-4 2.53406E-4 0.00257 0.00205 0.0029 0.00374 0.00284 0.00422 0.00296 0.00527 0.00438 0.00575 0.0044 0.00461 0.00392 0.00586 0.0043 0.00771 0.00603 0.00594 0.00548 0.00635 0.0059 0.00723 0.00713 0.00813 0.00775 0.01015 0.00675 0.0104 0.00854 0.00824 0.00852 0.0082 0.01153 0.01037 0.00889 0.01005 0.01022 0.01007

Pumping up

Flowing down fitting

8.73596E-4 -1.01667E-8 -7.11666E-9 0.00109 8.22839E-4 5.75987E-4 0.00119 0.00163 0.00114 5.18956E-4 0.00241 0.00169 0.00182 0.00317 0.00222 0.00392 0.00274 0.00465 0.00325 0.00536 0.00375 0.00606 0.00424 0.00674 0.00472 0.00741 0.00518 0.00806 0.00564 0.0087 0.00609 0.00933 0.00653 0.00994 0.00696 0.01054 0.00738 0.01113 0.00779 0.01171 0.0082 0.01228 0.0086 0.01284 0.00899 0.01339 0.00937 0.01393 0.00975 0.01446 0.01012 0.01498 0.01049

58

Pumping up fitting

2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 6.3 6.8 7.3 7.8 8.3 8.8 9.3 9.8 10.8 11.8 12.8 13.8 14.8 15.8 16.8 17.8 18.8 19.8 22.8 24.8 27.8 29.8 34.8 39.8 42.8 44.8 47.8

0.00967 0.01127 0.01179 0.0133 0.01369 0.01381 0.01257 0.01323 0.01412 0.01635 0.01594 0.01436 0.01513 0.01659 0.01667 0.01528 0.0163 0.01857 0.01943 0.01904 0.01938 0.01845 0.01923 0.02113 0.01943 0.02215 0.02028 0.02262 0.02272 0.02296 0.02305 0.02351 0.02385 0.02419 0.02463 0.0258 0.02837 0.02876 0.03231 0.03606 0.03357 0.03516 0.03736 0.04005 0.04123 0.0438 0.0446 0.05039 0.05088 0.05068 0.0482 0.04873 0.0509 0.05287 0.05579 0.05648 0.05445 0.05489 0.05178 0.05101 0.04841 0.04905

0.01332 0.01152 0.01038 0.01187 0.01151 0.01341 0.01376 0.01415 0.0144 0.01429 0.01499 0.01453 0.0152 0.01523 0.01527 0.01522 0.01695 0.01712 0.01648 0.01576 0.01688 0.0162 0.0167 0.01667 0.01851 0.01784 0.02127 0.01926 0.01946 0.02041 0.02066 0.02078 0.021 0.0213 0.02037 0.02159 0.02239 0.02507 0.02498 0.026 0.02672 0.02865 0.03007 0.03244 0.0326 0.03449 0.03543 0.03623 0.03543 0.03641 0.03756 0.03815 0.03903 0.0387 0.03998 0.03877 0.03979 0.03707 0.03682 0.03545 0.03446 0.03408

0.0155 0.016 0.0165 0.01699 0.01747 0.01794 0.01841 0.01887 0.01932 0.01977 0.02021 0.02064 0.02107 0.0215 0.02191 0.02233 0.02273 0.02314 0.02353 0.02392 0.02431 0.02469 0.02507 0.02544 0.02581 0.02618 0.02654 0.0269 0.02725 0.0276 0.02794 0.02828 0.02862 0.02895 0.02928 0.03088 0.0324 0.03385 0.03522 0.03653 0.03778 0.03896 0.04009 0.04219 0.04409 0.0458 0.04733 0.0487 0.04992 0.05099 0.05193 0.05274 0.05344 0.05487 0.05536 0.0555 0.05527 0.05378 0.05135 0.04958 0.04832 0.04632

0.01085 0.0112 0.01155 0.01189 0.01223 0.01256 0.01289 0.01321 0.01353 0.01384 0.01415 0.01445 0.01475 0.01505 0.01534 0.01563 0.01591 0.01619 0.01647 0.01675 0.01702 0.01729 0.01755 0.01781 0.01807 0.01833 0.01858 0.01883 0.01907 0.01932 0.01956 0.0198 0.02003 0.02027 0.0205 0.02162 0.02268 0.02369 0.02466 0.02557 0.02644 0.02727 0.02806 0.02953 0.03086 0.03206 0.03313 0.03409 0.03494 0.0357 0.03635 0.03692 0.0374 0.03841 0.03875 0.03885 0.03869 0.03764 0.03594 0.03471 0.03382 0.03243

59

49.8 54.8 59.8 64.8 69.8 74.8 79.8 84.8 89.8 94.8 99.8 109.8 119.8 129.8 139.8 149.8 159.8 169.8 179.8 189.8 199.8 209.8 219.8 229.8 239.8 249.8

0.047 0.02984 0.04495 0.03147 0.04359 0.02918 0.04144 0.02901 0.03884 0.02648 0.03791 0.02654 0.03672 0.02378 0.03446 0.02412 0.03463 0.02346 0.03116 0.02182 0.02935 0.01972 0.02805 0.01964 0.02862 0.01836 0.02515 0.01761 0.02308 0.01636 0.02248 0.01573 0.02388 0.01434 0.02003 0.01402 0.01944 0.01344 0.01779 0.01246 0.01847 0.01306 0.01578 0.01104 0.01513 0.01043 0.01232 0.00863 0.0086 0.00856 0.00956 0.0067 0.00862 0.00732 0.00738 0.00517 0.00784 0.00508 0.00567 0.00397 0.00422 0.00538 0.00434 0.00304 0.00471 0.00405 0.00332 0.00232 0.00335 8.56797E-4 0.00253 0.00177 7.47645E-4 0.00198 0.00192 0.00134 5.3227E-4 1.38413E-4 0.00146 0.00102 0.00281 0.00141 0.0011 7.71822E-4 0.00275 0.00237 8.33978E-4 5.83777E-4 0.00153 5.52012E-4 6.30095E-4 4.41066E-4 0.0024 -3.4671E-4 4.75604E-4 3.32924E-4 2.41125E-4 0.00149 3.58704E-4 2.51085E-4 5.12221E-4 -3.39447E-4 2.70345E-4 1.89242E-4

S4.C Time

100:0

-1.65E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.4 2.9 3.4 3.9 4.4 4.9 5.4 5.9 6.4

0.98574 1.00233 0.93232 0.89324 0.80952 0.80263 0.77197 0.72318 0.70171 0.66055 0.62387 0.60889 0.5804 0.56277 0.54943 0.51179 0.4872 0.48954 0.5053 0.43637 0.41124 0.33252 0.24904 0.21584 0.18936 0.13261 0.12552 0.08984 0.07646

Time

50:50

-1.22E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.4 2.5 3 3.5 4 4.5 5 5.5 5.6

Time

1.00001 0.96114 0.94205 0.9074 0.87455 0.85768 0.83072 0.81939 0.77971 0.76536 0.73595 0.72662 0.71221 0.69374 0.65673 0.64286 0.62964 0.6132 0.60736 0.56552 0.50171 0.50608 0.46385 0.37991 0.33595 0.31753 0.26955 0.21587 0.22471

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6

20:80

Time

0.95708 1.00232 0.96603 0.92875 0.88649 0.87851 0.8896 0.85418 0.83747 0.83512 0.80425 0.7634 0.76502 0.77307 0.75885 0.73843 0.73786 0.67758 0.65191 0.66486 0.63867 0.57338 0.52479 0.48001 0.4378 0.40738 0.34241 0.28749 0.32521

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6

60

2:98 1 0.93436 0.99508 0.94588 0.90822 0.90935 0.91742 0.91805 0.86917 0.83675 0.83105 0.81929 0.83246 0.78038 0.82003 0.83852 0.76915 0.7417 0.71287 0.71057 0.67598 0.64551 0.56604 0.55046 0.52348 0.4939 0.41892 0.42068 0.42121

6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.9 11.9 12.9 13.9 14.9 15.9 16.9 17.9 18.9 19.9 21.9 24.9 27.9 29.9 32.9 34.9 37.9 39.9 42.9 44.9 47.9 49.9

0.05191 5.8 0.05964 6.3 0.05832 6.8 0.06005 7.3 0.04216 7.8 0.03852 8.3 0.0231 8.8 0.01178 9.3 0.03248 9.8 -0.00818 10.8 0.03183 11.8 -0.012 12.8 0.02982 13.8 0.0028 14.8 -1.61673E-4 0.0214 16.8 -0.01985 17.8 0.00591 18.8 0.00197 19.8 -0.00736 22.8 0.01233 24.8 0.00497 27.8 0.00988 29.8 0.01615 34.8 -0.00324 39.8 -0.00324 42.8 8.966E-4 44.8 0.00483 47.8 0.00249 49.8

Time

100:0 fitting

-1.65E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.4 2.9 3.4 3.9 4.4 4.9 5.4 5.9 6.4

1 0.9573 0.91648 0.87747 0.84019 0.80455 0.77049 0.73793 0.7068 0.67705 0.64861 0.62142 0.59542 0.57057 0.54681 0.52409 0.50237 0.4816 0.46174 0.44274 0.35951 0.29285 0.23941 0.1965 0.16197 0.13415 0.11166 0.09346 0.07867

Time

0.2305 7 0.18958 7.5 0.16789 8 0.16788 8.5 0.14585 9 0.11451 9.5 0.10867 10 0.10193 11 0.07867 12 0.06703 13 0.05077 14 0.03907 15 0.03732 16 0.02303 17 15.8 0.0297 0.01001 19 0.00275 20 0.00237 22 0.00377 25 -0.00879 28 -0.00528 30 -0.00295 33 -0.00428 35 -0.01426 38 -0.00292 40 -0.00208 43 0.00842 45 -0.00964 48 -4.78689E-4 50:50 fitting

-1.22E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 5.6

Time

1 0.97145 0.94375 0.91687 0.89078 0.86548 0.84092 0.81709 0.79397 0.77153 0.74975 0.72862 0.70811 0.68821 0.66889 0.65014 0.63195 0.61429 0.59715 0.58051 0.56436 0.49044 0.4267 0.3717 0.32421 0.28317 0.24767 0.21694 0.2113

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

0.26366 7 0.22616 7.5 0.20715 8 0.1812 8.5 0.16149 9 0.1562 9.5 0.11338 10 0.12901 11 0.09961 12 0.0637 13 0.10389 14 0.05797 15 0.04897 16 0.04471 17 18 -0.00743 0.00116 19 -5.3354E-4 0.00325 22 0.01327 25 -0.02475 28 -0.00239 30 0.02205 33 0.0271 35 -0.02442 38 -0.00508 40 0.01071 43 -0.0011 45 0.00957 48 50 -0.00854 20:80 fitting

Time

1 0.98004 0.96049 0.94135 0.9226 0.90423 0.88625 0.86863 0.85138 0.83448 0.81793 0.80172 0.78584 0.77029 0.75506 0.74013 0.72552 0.7112 0.69718 0.66998 0.60671 0.54962 0.4981 0.45158 0.40957 0.37162 0.33731 0.3063 0.27826

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

61

0.33595 0.31329 0.29066 0.30114 0.27036 0.25916 0.24795 0.21883 0.2198 0.16713 0.12967 0.08378 0.08754 0.11175 18 0.05613 0.07623 20 0.06803 0.0465 0.05515 0.04013 0.01159 0.02304 0.00615 0.0199 0.01368 -0.01004 -0.0038 -0.01311 50 -0.00789

2:98 fitting 1 0.98523 0.97068 0.95635 0.94223 0.92832 0.91461 0.90111 0.88782 0.87471 0.86181 0.84909 0.83656 0.82422 0.81206 0.80009 0.78829 0.77666 0.76521 0.74281 0.68966 0.64033 0.59456 0.55207 0.51263 0.47603 0.44206 0.41052 0.38125

6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.9 11.9 12.9 13.9 14.9 15.9 16.9 17.9 18.9 19.9 21.9 24.9 27.9 29.9 32.9 34.9 37.9 39.9 42.9 44.9 47.9 49.9

0.06661 5.8 0.05675 6.3 0.04866 6.8 0.04198 7.3 0.03645 7.8 0.03184 8.3 0.02798 8.8 0.02198 9.3 0.01761 9.8 0.01436 10.8 0.01187 11.8 0.00993 12.8 0.00838 13.8 0.00712 14.8 0.00608 15.8 0.00522 16.8 0.00448 17.8 0.00334 18.8 0.00216 19.8 0.0014 22.8 0.00105 24.8 6.84805E-4 5.14467E-4 3.35044E-4 2.51738E-4 1.63958E-4 1.23195E-4 8.02389E-5 6.02902E-5

0.2005 0.17606 0.15484 0.1364 0.12036 0.10639 0.0942 0.08356 0.07426 0.05897 0.04716 0.038 0.03083 0.02518 0.0207 0.01712 0.01424 0.01191 0.01 0.00606 0.00441 27.8 29.8 34.8 39.8 42.8 44.8 47.8 49.8

7 0.25289 7.5 0.22992 8 0.20913 8.5 0.1903 9 0.17324 9.5 0.15778 10 0.14376 11 0.11949 12 0.09949 13 0.08298 14 0.06933 15 0.05802 16 0.04864 17 0.04084 18 0.03434 19 0.02893 20 0.0244 22 0.01744 25 0.01065 28 0.00658 30 0.0048 0.00278 33 0.00206 35 9.85908E-4 4.78126E-4 3.10567E-4 2.33081E-4 1.51634E-4 1.13878E-4

7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 0.00301 0.00221 38 40 43 45 48 50

0.35407 0.32884 0.30542 0.28367 0.26348 0.24474 0.22733 0.19617 0.16929 0.14612 0.12613 0.10888 0.09401 0.08117 0.07009 0.06054 0.05228 0.03902 0.02517 0.01624 0.01214 33 0.00784 35 0.00587 0.0014 38 0.00104 40 6.64235E-4 4.94125E-4 3.17878E-4 2.3724E-4

0.00379 0.00284 43 45 48 50

0.00184 0.00138 8.91594E-4 6.67784E-4

S5.A Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5

KS13C15N (6.5M)

KSCN (6.5M)

0.99873 1.00001 0.98407 0.97417 0.9643 0.94805 0.93177 0.91698 0.91374 0.89699 0.89668 0.89064 0.87609 0.86904 0.86519 0.85254 0.85169 0.84776 0.84021 0.82941 0.8218 0.81666 0.81445 0.81101 0.80472 0.80224

1.00001 0.98787 0.97282 0.96294 0.94901 0.93579 0.9256 0.9165 0.91067 0.89882 0.89107 0.87742 0.86712 0.85862 0.8546 0.84549 0.84191 0.83724 0.83289 0.82837 0.82178 0.81455 0.81265 0.80873 0.80411 0.79754

1 0.98816 0.97674 0.96571 0.95506 0.94477 0.93482 0.92521 0.91591 0.90692 0.89822 0.88979 0.88163 0.87372 0.86605 0.85861 0.8514 0.8444 0.8376 0.831 0.82458 0.81834 0.81227 0.80636 0.80061 0.79501

1 0.98821 0.97682 0.9658 0.95515 0.94485 0.93488 0.92524 0.9159 0.90686 0.89811 0.88963 0.8814 0.87343 0.8657 0.85819 0.85091 0.84384 0.83697 0.8303 0.82382 0.81751 0.81138 0.80541 0.7996 0.79395

62

KSCN (6.5M) fitting

KS13C15N (6.5M) fitting

2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.7 6.2 6.7 7.2 7.7 8.2 8.7 9.2 10.2 11.2 12.2 13.2 14.2 15.2 16.2 17.2 18.2 19.2 22.2 24.2 27.2 29.2 34.2 39.2 42.2 44.2 47.2 49.2 54.2 59.2 64.2 69.2 74.2 79.2 84.2

0.79999 0.79007 0.78857 0.78029 0.77341 0.76457 0.76695 0.76386 0.75148 0.74827 0.75048 0.74492 0.73299 0.73442 0.72936 0.72957 0.72211 0.71769 0.7096 0.71398 0.70893 0.70369 0.70332 0.69811 0.70002 0.6907 0.69125 0.67603 0.65494 0.64329 0.63022 0.6158 0.60213 0.59067 0.57861 0.5522 0.53476 0.51251 0.49327 0.47738 0.45954 0.44551 0.42425 0.40781 0.39673 0.35459 0.33066 0.29782 0.27457 0.22657 0.1916 0.1732 0.1571 0.14325 0.13606 0.11533 0.09755 0.08458 0.07246 0.0589 0.05312 0.04437

0.78634 0.7864 0.77856 0.77753 0.76643 0.77067 0.76318 0.7547 0.75664 0.74699 0.74096 0.74547 0.73858 0.73507 0.73319 0.73077 0.72176 0.71906 0.71793 0.7127 0.71211 0.70638 0.70119 0.69866 0.69376 0.68827 0.68417 0.66945 0.65946 0.64425 0.62954 0.61926 0.60068 0.58931 0.58107 0.55096 0.53142 0.50904 0.49381 0.48167 0.46247 0.44623 0.43202 0.41294 0.40342 0.36528 0.34083 0.3111 0.29441 0.24798 0.21402 0.19466 0.18286 0.16658 0.15698 0.13656 0.11602 0.09872 0.08458 0.07462 0.06304 0.0538

0.78956 0.78424 0.77905 0.77399 0.76905 0.76422 0.75951 0.7549 0.7504 0.74599 0.74167 0.73745 0.73331 0.72925 0.72528 0.72137 0.71755 0.71379 0.7101 0.70648 0.70291 0.69941 0.69596 0.69257 0.68924 0.68595 0.68271 0.6672 0.65268 0.63897 0.62595 0.61352 0.6016 0.59011 0.579 0.55777 0.53765 0.51847 0.5001 0.48248 0.46553 0.44922 0.43351 0.41836 0.40376 0.36299 0.33815 0.30408 0.28332 0.23745 0.19908 0.17914 0.16697 0.15027 0.14009 0.11757 0.09871 0.08291 0.06966 0.05855 0.04922 0.0414

0.78844 0.78307 0.77784 0.77273 0.76775 0.76289 0.75814 0.75351 0.74898 0.74455 0.74022 0.73599 0.73184 0.72778 0.7238 0.71991 0.71609 0.71235 0.70867 0.70507 0.70153 0.69806 0.69464 0.69129 0.68799 0.68475 0.68156 0.66633 0.65215 0.63886 0.62632 0.6144 0.60302 0.5921 0.58158 0.56156 0.54267 0.52469 0.50749 0.49098 0.47509 0.45977 0.44498 0.43069 0.41689 0.37813 0.35435 0.32149 0.30131 0.25629 0.21806 0.19794 0.18558 0.16849 0.15799 0.13453 0.11459 0.09762 0.0832 0.07092 0.06046 0.05156

63

89.2 94.2 99.2 109.2 119.2 129.2 139.2 149.2 159.2 169.2 179.2 189.2 199.2 209.2 219.2 229.2 239.2 249.2 259.2 269.2 279.2 289.2 299.2

0.03983 0.04613 0.03484 0.04398 0.03125 0.03843 0.02932 0.03753 0.02626 0.03398 0.02469 0.03202 0.02157 0.02596 0.01753 0.02334 0.01558 0.01818 0.01246 0.01702 0.01122 0.01289 0.00887 0.01242 0.00836 0.01093 0.00632 0.00908 0.00907 0.00812 0.00452 0.00663 0.00617 0.00545 0.00323 0.00485 0.00412 0.00286 0.00231 0.00355 0.00379 0.00322 0.00166 0.0026 0.00209 0.0042 0.00119 0.00191 0.00301 0.00219 8.56748E-4 0.0014 0.00423 0.00152 6.17026E-4 0.00103 0.002 6.48443E-4 4.44969E-4 7.52304E-4 0.00254 -1.81632E-4 3.21315E-4 5.52366E-4 5.82006E-4 0.00101 2.32303E-4 4.05754E-4 0.00108 0.00156 1.68153E-4 2.98177E-4 0.00375 0.00154 1.21883E-4 2.19202E-4 2.62824E-4 0.00104 8.84448E-5 1.61212E-4 0.00187 2.09873E-4 6.42465E-5 1.18607E-4 0.00156 3.53553E-5 4.67226E-5 8.72869E-5 3.51054E-4 -7.15441E-4 3.4006E-5 6.42467E-5

S5.B Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1

Flowing down -0.00131 5.1039E-4 4.02662E-4 0.00171 4.94641E-4 0.00156 0.00108 0.00197 0.0014 8.749E-4 0.00152 0.00185 -0.0015 0.00219 0.00228 3.64111E-4 0.00153 0.00305 0.00121 0.00312 0.00151 5.3479E-4 0.00238 9.66755E-4 0.00122 0.00168 0.00432 0.00245 0.00338 0.0047 0.00566 0.00411 0.00508 0.00249 0.00235 0.00545 0.00266 0.00684 0.00581 0.00426 0.00376 0.00616 0.00754 0.00402 0.00651 0.00499 0.00348 0.00685 0.00747 0.00381 0.00718 0.00823 0.00671 0.00751 0.0059 0.00554 0.00784 0.00731 0.0049 0.00816 0.00706 0.00499 0.00847 0.00911 0.00552 0.00878 0.0053 0.00477 0.00908 0.00828 0.00532 0.00938 0.00743 0.00553 0.00967 0.00707 0.00781 0.00996 0.00821 0.0073 0.01024 0.00874 0.00684 0.01052 0.00805 0.00907 0.0108 0.01026 0.00839 0.01107

Pumping up 0 0 4.7804E-4 3.34628E-4 9.44733E-4 6.61313E-4 9.80377E-4 0.00129 0.0016 0.00271 0.00189 0.00219 0.00353 0.00247 0.00393 0.00275 0.00302 0.00329 0.00355 0.00381 0.00407 0.00431 0.00456 0.00479 0.00503 0.00526 0.00549 0.00571 0.00593 0.00614 0.00635 0.00656 0.00677 0.00697 0.00717 0.00737 0.00756 0.00775

64

Flowing down fitting

Pumping up fitting

3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.7 6.2 6.7 7.2 7.7 8.2 8.7 9.2 10.2 11.2 12.2 13.2 14.2 15.2 16.2 17.2 18.2 19.2 22.2 24.2 27.2 29.2 34.2 39.2 42.2 44.2 47.2 49.2 54.2 59.2 64.2 69.2 74.2 79.2 84.2 89.2 94.2 99.2 109.2 119.2 129.2

0.01136 0.0102 0.01148 0.00997 0.00762 0.0076 0.01387 0.01353 0.01104 0.01381 0.01193 0.01412 0.0095 0.01257 0.0128 0.0132 0.0138 0.0142 0.01479 0.0149 0.015 0.0151 0.0159 0.0172 0.0189 0.02 0.02091 0.02276 0.02252 0.02378 0.02623 0.02724 0.02723 0.03002 0.03034 0.02873 0.0294 0.03175 0.0321 0.03289 0.03085 0.03449 0.03322 0.03004 0.03055 0.0291 0.02718 0.02683 0.02825 0.02708 0.02205 0.02497 0.02178 0.01736 0.01864 0.01855 0.01544 0.01304 0.01092 0.01091 0.00793 0.0053

0.0076 0.00757 0.00915 0.00827 0.00774 0.00958 0.00856 0.00627 0.00716 0.00875 0.01161 0.00903 0.01128 0.01021 0.01027 0.00977 0.0113 0.01138 0.01045 0.01058 0.0109 0.0139 0.01369 0.01495 0.01225 0.01304 0.01423 0.01384 0.01809 0.01773 0.01684 0.02077 0.01966 0.01957 0.01923 0.02046 0.02202 0.02118 0.02129 0.02353 0.02356 0.02279 0.02332 0.0231 0.02169 0.02021 0.01876 0.01825 0.01942 0.0186 0.01595 0.01543 0.01409 0.01404 0.01266 0.01138 0.00953 0.00689 0.00844 0.00726 0.00408 0.00379

0.01134 0.0116 0.01187 0.01212 0.01238 0.01263 0.01287 0.01312 0.01336 0.0136 0.01383 0.01407 0.0143 0.01452 0.01475 0.01497 0.01519 0.01541 0.01562 0.01583 0.01604 0.01706 0.01802 0.01894 0.01981 0.02064 0.02143 0.02219 0.02291 0.02426 0.02548 0.02659 0.0276 0.02851 0.02932 0.03005 0.0307 0.03127 0.03176 0.03286 0.0333 0.03359 0.03357 0.03295 0.03171 0.03075 0.03005 0.02892 0.02814 0.0261 0.02401 0.02194 0.01994 0.01803 0.01624 0.01457 0.01302 0.01161 0.01033 0.00811 0.00632 0.0049

0.00794 0.00812 0.00831 0.00849 0.00866 0.00884 0.00901 0.00918 0.00935 0.00952 0.00968 0.00985 0.01001 0.01017 0.01032 0.01048 0.01063 0.01078 0.01093 0.01108 0.01123 0.01194 0.01261 0.01326 0.01387 0.01445 0.015 0.01553 0.01604 0.01698 0.01784 0.01861 0.01932 0.01995 0.02053 0.02104 0.02149 0.02189 0.02223 0.023 0.02331 0.02351 0.0235 0.02307 0.02219 0.02152 0.02103 0.02025 0.0197 0.01827 0.01681 0.01536 0.01396 0.01262 0.01136 0.0102 0.00912 0.00813 0.00723 0.00568 0.00443 0.00343

65

139.2 149.2 159.2 169.2 179.2 189.2 199.2 209.2 219.2 229.2 239.2 249.2 259.2 269.2 279.2 289.2 299.2

0.00523 0.00461 0.00377 0.00264 0.00544 0.00255 0.00289 0.00203 0.00326 0.00233 0.00221 0.00155 0.00172 0.00122 0.00168 0.00118 0.00259 0.00279 0.00128 8.9536E-4 0.00166 0.00302 9.6881E-4 6.78154E-4 0.00255 3.88455E-4 7.32161E-4 5.12509E-4 0.0016 0.00228 5.52239E-4 3.86563E-4 7.87254E-4 -3.04833E-4 4.15814E-4 2.91063E-4 0.00109 -0.0013 3.126E-4 2.18829E-4 -6.831E-5 -1.37719E-4 2.34696E-4 1.6428E-4 -4.63594E-4 5.93392E-4 1.75996E-4 1.23178E-4 0.00267 6.94041E-4 1.31813E-4 9.22631E-5 5.96833E-4 7.69418E-4 9.86241E-5 6.90292E-5 -3.24312E-4 -4.18438E-4 7.37299E-5 5.15954E-5 1.79335E-4 7.106E-5 5.50707E-5 3.85379E-5 -2.32699E-4 -8.4734E-4 4.11139E-5 2.87753E-5

S5.C Time

100:0

Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11

1 0.93935 0.92284 0.92119 0.90928 0.82003 0.76201 0.71944 0.69154 0.65134 0.63181 0.62916 0.56394 0.4954 0.5056 0.49668 0.47241 0.46434 0.43966 0.41035 0.37434 0.32354 0.27122 0.2076 0.15276 0.1505 0.09616 0.12759 0.05915 0.05181 0.05912 0.01831 0.00834 0.0211 0.05157 0.00784 0.01587 -0.00337

-7E-7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 4.8 4.9 5 5.1 5.2 5.7 6.2 6.7 7.2 7.7 8.2 8.7

50:50

Time

0.99999 0.96313 0.91476 0.87057 0.82893 0.79394 0.77499 0.78804 0.76247 0.74293 0.71462 0.70618 0.70404 0.65213 0.62756 0.64925 0.64435 0.63487 0.62146 0.58469 0.55553 0.50213 0.44482 0.40171 0.36401 0.31503 0.28935 0.25347 0.28453 0.27246 0.25175 0.23263 0.20251 0.17409 0.17056 0.13344 0.12509 0.10178

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11

10:90

Time

1 1.00624 0.95157 0.95062 0.91976 0.92368 0.88429 0.89412 0.85478 0.78432 0.78694 0.79959 0.71419 0.75079 0.70134 0.7006 0.74303 0.703 0.67947 0.68099 0.59537 0.53113 0.48601 0.46549 0.36256 0.3494 0.35443 0.31584 0.26101 0.24622 0.21957 0.16904 0.1546 0.14963 0.15316 0.14968 0.12675 0.0929

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11

66

2:98 1 0.94109 0.93463 0.89981 0.86156 0.82443 0.82232 0.81771 0.7754 0.7684 0.78394 0.7216 0.69601 0.73926 0.71285 0.68087 0.66497 0.68371 0.67706 0.67862 0.64871 0.55947 0.43959 0.44244 0.44953 0.35276 0.32062 0.35582 0.28737 0.302 0.22347 0.28801 0.17618 0.16246 0.18844 0.13882 0.16975 0.1786

12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50

0.0094 9.2 0.01682 10.2 7.49796E-4 0.0101 12.2 -0.01307 13.2 0.01899 14.2 -0.00874 15.2 -0.00896 16.2 -0.00947 17.2 -0.00594 18.2 -0.01291 19.2 0.03722 22.2 -0.01594 24.2 0.01457 27.2 -0.01353 29.2 -0.02884 34.2 -0.00684 39.2 -0.00707 42.2 -0.00128 44.2 -0.03747 47.2 -0.00832 49.2

Time

100:0 fitting

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

1 0.95853 0.91886 0.8809 0.84457 0.80981 0.77654 0.74471 0.71424 0.68508 0.65717 0.63046 0.60489 0.58042 0.55699 0.53456 0.51309 0.49253 0.47284 0.45399 0.43594 0.35653 0.29248 0.24075 0.19888 0.16492 0.13733 0.11484 0.09647 0.08141 0.06903 0.05882 0.05036 0.04333 0.03746 0.03253 0.02838

Time

-7E-7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 4.8 4.9 5 5.1 5.2 5.7 6.2 6.7 7.2 7.7 8.2

0.08778 12 0.08529 13 11.2 0.04434 0.03387 15 0.03637 16 0.04928 17 0.02429 18 0.03121 19 0.04453 20 0.02754 22 0.02457 25 0.01835 28 0.01657 30 0.03184 33 0.01281 35 -8.80031E-4 0.00165 40 -0.00166 43 0.00568 45 0.01003 48 -0.01929 50 50:50 fitting

Time

1 0.97048 0.94187 0.91413 0.88725 0.86119 0.83593 0.81145 0.78771 0.7647 0.74239 0.72076 0.69979 0.67946 0.65975 0.64064 0.62211 0.60414 0.58672 0.56982 0.55343 0.47864 0.41443 0.35927 0.31185 0.27103 0.24931 0.24249 0.23587 0.22944 0.2232 0.19461 0.16992 0.14858 0.1301 0.11409 0.1002

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

0.08976 0.07594 14 0.02838 0.05466 0.03256 0.03834 0.01887 0.00856 -0.02676 0.01603 -0.01074 0.009 -0.02378 0.0186 38 0.00859 0.00346 -0.00746 -0.00931 0.01063

10:90 fitting

12 13 0.07391 15 16 17 18 19 20 22 25 28 30 33 35 -0.00102 40 43 45 48 50

Time

1 0.98014 0.96069 0.94163 0.92295 0.90465 0.88672 0.86915 0.85194 0.83508 0.81855 0.80236 0.78649 0.77094 0.75571 0.74078 0.72616 0.71182 0.69778 0.68402 0.67053 0.60705 0.54969 0.49783 0.45096 0.40857 0.37023 0.33555 0.30417 0.27578 0.25008 0.22682 0.20575 0.18668 0.1694 0.15375 0.13956

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

67

0.10984 0.10899 14 0.09896 0.05541 0.07116 0.07597 0.07856 0.03743 0.05604 0.02837 0.03325 0.02394 0.00818 -1.967E-4 -0.031 38 -0.02106 0.01684 -0.01534 0.01385 -0.01678 4.27359E-4

2:98 fitting 1 0.98209 0.9645 0.94722 0.93026 0.9136 0.89725 0.88118 0.86541 0.84992 0.83471 0.81977 0.8051 0.79069 0.77654 0.76265 0.749 0.7356 0.72245 0.70953 0.69684 0.63673 0.58182 0.53167 0.48586 0.44401 0.40578 0.37085 0.33894 0.30979 0.28315 0.25882 0.23658 0.21626 0.19769 0.18072 0.16521

11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50

0.02187 8.7 0.01712 9.2 0.01359 10.2 0.0109 11.2 0.00883 12.2 0.00721 13.2 0.00592 14.2 0.00489 15.2 0.00405 16.2 0.00336 17.2 0.00234 18.2 0.00136 19.2 8.01968E-4 5.63449E-4 3.32165E-4 2.33621E-4 1.37836E-4 9.69694E-5 5.72231E-5 4.02599E-5 2.37592E-5 1.67163E-5

0.08813 0.07763 0.0605 0.04743 0.0374 0.02966 0.02365 0.01895 0.01526 0.01235 0.01003 0.00818 22.2 24.2 27.2 29.2 34.2 39.2 42.2 44.2 47.2 49.2

11 0.11506 12 0.09492 13 0.07836 14 0.06472 15 0.05349 16 0.04424 17 0.03661 18 0.03031 19 0.02511 20 0.02081 22 0.01432 25 0.0082 0.00452 28 0.00308 30 0.00176 33 0.00122 35 4.94308E-4 2.03027E-4 1.19401E-4 8.38755E-5 4.94197E-5 3.47452E-5

11 12 13 14 15 16 17 18 19 20 22 25 0.00471 0.00326 0.00189 0.00131 38 40 43 45 48 50

0.13808 0.11542 0.09649 0.08067 0.06746 0.05641 0.04718 0.03946 0.03301 0.02761 0.01933 0.01133 28 0.00664 30 0.00466 33 0.00273 35 0.00192 7.61848E-4 5.30961E-4 3.09449E-4 2.16129E-4 1.26322E-4 8.83759E-5

38 40 43 45 48 50

0.00113 7.89934E-4 4.64407E-4 3.25983E-4 1.91763E-4 1.34655E-4

S6.A Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2

KS13C15N (4.0M)

KSCN (4.0M)

1.00001 0.99011 0.97047 0.94939 0.93515 0.91021 0.89541 0.88452 0.86167 0.84947 0.83548 0.82215 0.81004 0.79634 0.79005 0.78276 0.7758 0.7649 0.76172 0.74986 0.7414 0.73639 0.73156 0.72326 0.71925 0.70954 0.70032 0.70125 0.69579 0.68769 0.6858 0.68273 0.67702

0.99617 1 0.99253 0.97416 0.96113 0.94601 0.9342 0.92073 0.90856 0.89898 0.88809 0.87986 0.87314 0.86098 0.85386 0.84592 0.83963 0.83116 0.82537 0.81968 0.81518 0.80918 0.80465 0.79426 0.79177 0.78365 0.7809 0.77415 0.76996 0.7665 0.76059 0.75593 0.75209

1 0.97813 0.95767 0.93849 0.92053 0.90368 0.88786 0.873 0.85902 0.84587 0.83347 0.82178 0.81074 0.80031 0.79044 0.78109 0.77222 0.7638 0.7558 0.74818 0.74092 0.73399 0.72737 0.72103 0.71496 0.70914 0.70355 0.69817 0.69299 0.68799 0.68316 0.67849 0.67397

1 0.98732 0.9751 0.96331 0.95195 0.94099 0.93042 0.92021 0.91035 0.90083 0.89163 0.88274 0.87415 0.86583 0.85778 0.84999 0.84245 0.83514 0.82806 0.82119 0.81453 0.80806 0.80179 0.79569 0.78977 0.78401 0.77841 0.77297 0.76766 0.7625 0.75747 0.75257 0.74779

68

KSCN (4.0M) fitting

KS13C15N (4.0M) fitting

3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.4 11.4 12.4 13.4 14.4 15.4 16.4 17.4 18.4 19.4 20.4 23.4 25.4 28.4 30.4 35.4 40.4 43.4 45.4 48.4 50.4 55.4 60.4

0.67032 0.66491 0.66215 0.65738 0.64965 0.64363 0.64235 0.63713 0.6402 0.63118 0.62597 0.62202 0.62518 0.61734 0.6114 0.6109 0.60581 0.60163 0.60186 0.59748 0.58985 0.59079 0.58635 0.5817 0.57722 0.57539 0.57046 0.56625 0.56378 0.56035 0.55969 0.55718 0.54816 0.52892 0.51664 0.49982 0.49411 0.48348 0.46698 0.45676 0.4364 0.41739 0.40339 0.38636 0.36891 0.35534 0.33835 0.32436 0.31044 0.29525 0.26524 0.24391 0.21921 0.19664 0.16339 0.13104 0.11481 0.1021 0.092 0.08261 0.07032 0.05652

0.74587 0.7425 0.74031 0.73428 0.73117 0.72824 0.72334 0.72136 0.71689 0.70892 0.70617 0.70327 0.70214 0.69766 0.69233 0.68958 0.68671 0.68566 0.68253 0.67628 0.67378 0.66986 0.66752 0.66484 0.66084 0.65784 0.65583 0.65338 0.64983 0.64483 0.63982 0.63782 0.62581 0.61099 0.60077 0.58777 0.5764 0.5661 0.55173 0.54374 0.52555 0.50414 0.487 0.46979 0.45161 0.43707 0.42471 0.40664 0.3965 0.38146 0.35741 0.3333 0.30225 0.27916 0.23766 0.20119 0.18191 0.17203 0.15533 0.14495 0.12469 0.1055

0.66959 0.66534 0.66121 0.65719 0.65327 0.64945 0.64573 0.64209 0.63852 0.63504 0.63162 0.62827 0.62498 0.62174 0.61857 0.61544 0.61236 0.60932 0.60633 0.60338 0.60047 0.59759 0.59475 0.59194 0.58916 0.58641 0.58368 0.58099 0.57832 0.57567 0.57305 0.57044 0.55774 0.54548 0.5336 0.52205 0.5108 0.49984 0.48913 0.47867 0.45845 0.43911 0.42061 0.40289 0.38593 0.36968 0.35413 0.33924 0.32498 0.31132 0.27372 0.25123 0.22094 0.20282 0.16381 0.13235 0.11648 0.10698 0.09418 0.08652 0.07 0.05667

0.74313 0.73858 0.73414 0.7298 0.72555 0.72141 0.71735 0.71338 0.7095 0.70569 0.70196 0.6983 0.69472 0.6912 0.68775 0.68436 0.68103 0.67776 0.67454 0.67138 0.66826 0.6652 0.66218 0.65921 0.65629 0.6534 0.65055 0.64775 0.64498 0.64225 0.63955 0.63689 0.62403 0.61185 0.60024 0.58912 0.57842 0.56808 0.55806 0.54833 0.52962 0.51176 0.49465 0.4782 0.46235 0.44707 0.43233 0.41808 0.40432 0.39103 0.35373 0.33089 0.29939 0.28008 0.23713 0.2008 0.18175 0.17007 0.15396 0.14408 0.12207 0.10345

69

65.4 70.4 75.4 80.4 85.4 90.4 95.4 100.4 110.4 120.4 130.4 140.4 150.4 160.4 170.4 180.4 190.4 200.4 210.4 220.4 230.4 240.4 250.4

0.04435 0.08937 0.04589 0.08768 0.0375 0.07609 0.03719 0.07433 0.02923 0.0641 0.03015 0.06302 0.02414 0.05535 0.02446 0.05343 0.02048 0.04709 0.01986 0.04531 0.01448 0.03894 0.01613 0.03843 0.01336 0.03407 0.01311 0.0326 0.0084 0.02982 0.01066 0.02766 0.0075 0.02071 0.00707 0.01991 0.00494 0.01504 0.0047 0.01434 9.26076E-5 0.01106 0.00313 0.01033 1E-3 0.00825 0.0021 0.00745 0.0012 0.00521 0.00141 0.00537 0.00369 0.00384 9.47387E-4 0.00387 -8.47137E-5 0.0014 6.4025E-4 0.00279 9.268E-4 0.00214 4.34332E-4 0.00201 -6.67856E-4 -9.80186E-4 2.95638E-4 0.00145 -0.00117 0.00202 2.01961E-4 0.00105 -0.00193 5.38995E-4 1.38458E-4 7.56723E-4 -8.39232E-4 7.69612E-4 9.52574E-5 5.46252E-4 -0.00195 2.14259E-4 6.58058E-5 3.94372E-4 0.00283 -8.83906E-5 4.55872E-5 2.84752E-4 1.51583E-4 9.93781E-5 3.16891E-5 2.0563E-4

S6.B Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Flowing down

Pumping up

3.20421E-4 6.79497E-5 0 0 0.00177 8.90059E-4 4.77957E-4 3.34571E-4 -2.24788E-4 0.00255 9.39567E-4 6.57696E-4 0.00113 5.82218E-4 0.00139 9.70081E-4 0.00222 0.00237 0.00182 0.00127 0.0016 0.00261 0.00224 0.00157 0.00453 0.00413 0.00264 0.00185 0.00271 0.00254 0.00304 0.00212 0.00433 0.00299 0.00342 0.00239 0.00351 0.00342 0.00379 0.00265 0.00308 0.00375 0.00415 0.00291 0.00508 0.00494 0.0045 0.00315 0.00439 0.00465 0.00485 0.00339 0.00373 0.00337 0.00518 0.00363 0.00563 0.00554 0.00551 0.00386 0.00534 0.00421 0.00583 0.00408 0.00463 0.00488 0.00614 0.0043 0.00612 0.00521 0.00645 0.00451 0.00541 0.00402 0.00674 0.00472 0.00613 0.006 0.00704 0.00493 0.00658 0.00694 0.00732 0.00513 0.00534 0.00495 0.0076 0.00532 0.0063 0.00706 0.00788 0.00552 0.00703 0.00526 0.00815 0.00571 0.007 0.00638 0.00842 0.00589 0.00743 0.00582 0.00868 0.00608 0.00753 0.00711 0.00894 0.00626 0.00734 0.00656 0.00919 0.00643 0.00876 0.00579 0.00944 0.00661 0.00762 0.00753 0.00968 0.00678 0.00818 0.00655 0.00992 0.00695

70

Flowing down fitting

Pumping up fitting

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.4 11.4 12.4 13.4 14.4 15.4 16.4 17.4 18.4 19.4 20.4 23.4 25.4 28.4 30.4 35.4 40.4 43.4 45.4 48.4 50.4

0.00882 0.00904 0.01113 0.00913 0.0096 0.00998 0.01051 0.00996 0.01086 0.01108 0.00991 0.01169 0.01181 0.01185 0.01206 0.01226 0.01234 0.01239 0.01243 0.01258 0.01268 0.01285 0.01351 0.01455 0.0146 0.0147 0.0148 0.0149 0.01501 0.01505 0.01506 0.0151 0.01512 0.01513 0.01474 0.01804 0.01763 0.0179 0.0184 0.02069 0.02 0.01987 0.02241 0.0241 0.02378 0.0247 0.02476 0.02527 0.02574 0.0266 0.02702 0.0272 0.02743 0.02682 0.02712 0.02862 0.02656 0.02572 0.02493 0.02391 0.02155 0.02185

0.00759 0.00842 0.00748 0.00757 0.00941 0.00722 0.00887 0.00899 0.00834 0.00845 0.00871 0.00854 0.00923 0.01006 0.00986 0.00842 0.00807 0.01036 0.0096 0.01028 0.00999 0.00934 0.00942 0.01042 0.0107 0.01075 0.01077 0.01086 0.01091 0.01102 0.01104 0.01106 0.01108 0.00978 0.01304 0.01209 0.01404 0.01306 0.01354 0.0137 0.01386 0.01412 0.01625 0.01589 0.01674 0.01617 0.0166 0.0169 0.01822 0.01635 0.01912 0.01897 0.01893 0.01863 0.01947 0.01842 0.01767 0.01614 0.01614 0.01609 0.01538 0.01432

0.01016 0.01039 0.01062 0.01085 0.01108 0.0113 0.01151 0.01173 0.01194 0.01215 0.01236 0.01256 0.01277 0.01296 0.01316 0.01336 0.01355 0.01374 0.01393 0.01411 0.0143 0.01448 0.01466 0.01484 0.01501 0.01519 0.01536 0.01553 0.0157 0.01587 0.01603 0.0162 0.01636 0.01652 0.01729 0.01803 0.01873 0.0194 0.02003 0.02063 0.0212 0.02173 0.02273 0.02362 0.0244 0.0251 0.02571 0.02624 0.02669 0.02707 0.02738 0.02764 0.02807 0.02813 0.02792 0.02762 0.02645 0.02487 0.02379 0.02305 0.0219 0.02112

0.00711 0.00728 0.00744 0.0076 0.00775 0.00791 0.00806 0.00821 0.00836 0.00851 0.00865 0.00879 0.00894 0.00908 0.00921 0.00935 0.00948 0.00962 0.00975 0.00988 0.01001 0.01014 0.01026 0.01039 0.01051 0.01063 0.01075 0.01087 0.01099 0.01111 0.01122 0.01134 0.01145 0.01156 0.01211 0.01262 0.01311 0.01358 0.01402 0.01444 0.01484 0.01521 0.01591 0.01653 0.01708 0.01757 0.018 0.01837 0.01868 0.01895 0.01917 0.01935 0.01965 0.01969 0.01954 0.01934 0.01852 0.01741 0.01666 0.01613 0.01533 0.01478

71

55.4 60.4 65.4 70.4 75.4 80.4 85.4 90.4 95.4 100.4 110.4 120.4 130.4 140.4 150.4 160.4 170.4 180.4 190.4 200.4 210.4 220.4 230.4 240.4 250.4

0.01998 0.01231 0.01918 0.01343 0.02026 0.01156 0.01729 0.0121 0.01772 0.01016 0.01548 0.01084 0.0148 0.00972 0.01379 0.00965 0.01448 0.00738 0.01223 0.00856 0.01236 0.00811 0.0108 0.00756 0.01039 0.00621 0.00951 0.00666 0.00956 0.00547 0.00835 0.00584 0.00792 0.00502 0.0073 0.00511 0.00739 0.00589 0.00638 0.00446 0.00471 0.00422 0.00483 0.00338 0.00441 0.00309 0.00364 0.00255 0.00306 0.00212 0.00272 0.0019 0.00115 0.00121 0.00203 0.00142 0.00145 6.14085E-4 0.0015 0.00105 0.00113 0.00106 0.00111 7.78637E-4 6.39814E-4 -4.49872E-4 8.20388E-4 5.74272E-4 4.55911E-4 1.01079E-4 6.03649E-4 4.22555E-4 6.39106E-4 -1.38521E-4 4.43279E-4 3.1029E-4 0.00121 0.00124 3.24946E-4 2.27468E-4 4.08294E-4 9.33269E-4 2.37858E-4 1.66507E-4 3.91239E-4 3.3924E-4 1.73887E-4 1.21719E-4 -2.97471E-4 0.00127 1.26978E-4 8.88831E-5 5.92825E-4 -5.12917E-4 9.26289E-5 6.48479E-5 2.45445E-4 8.8445E-4 6.75157E-5 4.72736E-5

S6.C Time

100:0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.4 2.9 3.4 3.9 4.4 4.9 5.4 5.9 6.4 6.9

1 0.95966 0.93176 0.89093 0.83315 0.7899 0.74421 0.69507 0.67848 0.66004 0.61373 0.59049 0.57648 0.53494 0.52536 0.48404 0.48651 0.48801 0.43919 0.47742 0.38139 0.2983 0.2443 0.20249 0.14882 0.12961 0.11013 0.0953 0.08301 0.0636

Time

-8.7E-7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9

50:50

Time

1 0.97284 0.9681 0.94881 0.92687 0.87978 0.86227 0.85273 0.80601 0.78446 0.73733 0.73161 0.71152 0.70188 0.67439 0.64567 0.6269 0.61384 0.59527 0.58978 0.53604 0.50933 0.53894 0.48255 0.49257 0.46772 0.45376 0.44915 0.43366 0.39637

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.4 2.9 3.4 3.9 4.4 4.9 5.4 5.9 6.4 6.9

10:90

Time

0.99999 1.00084 0.98625 0.94006 0.89148 0.88807 0.84434 0.81281 0.7806 0.75242 0.72516 0.73843 0.67615 0.67507 0.62379 0.62422 0.63318 0.61284 0.60236 0.56261 0.52285 0.45725 0.41945 0.35699 0.30648 0.28382 0.26343 0.22664 0.20599 0.15504

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.4 2.9 3.4 3.9 4.4 4.9 5.4 5.9 6.4 6.9

72

2:98

0.99999 0.89015 0.83939 0.901 0.78903 0.73191 0.8317 0.85878 0.70996 0.82175 0.84685 0.70519 0.69779 0.71549 0.69625 0.66475 0.78096 0.61315 0.61081 0.61288 0.49609 0.41263 0.41219 0.2971 0.3314 0.21172 0.26451 0.26579 0.21821 0.18616

7.4 7.9 8.4 8.9 9.4 9.9 10.9 11.9 12.9 13.9 14.9 15.9 16.9 17.9 18.9 19.9 21.9 24.9 27.9 29.9 32.9 34.9 37.9 39.9 42.9 44.9 47.9 49.9

0.06797 0.04721 0.05418 0.04445 0.02364 0.02179 0.00675 0.00873 0.01649 -0.00769 -0.01484 -0.014 -0.00419 0.00542 -0.00799 0.00185 -0.00303 -0.00109 0.00624 -0.01443 -0.00161 0.01861 -0.0116 0.01981 -0.02428 -0.02264 0.01588 -0.00958

3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.7 7.2 7.7 8.2 8.7 9.2 9.7 10.2 11.2 12.2 13.2 14.2 15.2 16.2 17.2 18.2 19.2 20.2 23.2 25.2 28.2 30.2 35.2 40.2 43.2 45.2 48.2 50.2

0.40242 7.4 0.38319 7.9 0.35561 8.4 0.33267 8.9 0.32188 9.4 0.32896 9.9 0.3216 10.9 0.32991 11.9 0.30645 12.9 0.30824 13.9 0.3191 14.9 0.31179 15.9 0.30833 16.9 0.26675 17.9 0.26185 18.9 0.24664 19.9 0.23993 21.9 0.23834 24.9 0.24712 27.9 0.23651 29.9 0.22606 32.9 0.2283 34.9 0.19175 37.9 0.18599 39.9 0.18809 42.9 0.20381 44.9 0.188 47.9 0.16982 49.9 0.17545 0.18257 0.17276 0.19446 0.17179 0.13375 0.12819 0.10863 0.07391 0.06299 0.06012 0.06055 0.05215 0.03199 0.02367 0.04146 0.01879 0.02603 0.00722 0.00743 0.01349 -0.01415 -0.00876 -0.0076 -0.01822 -0.00478 -0.00666 0.00224 -0.01039 0.00351 -0.00821 -1.81284E-4 -0.00367

0.20273 0.14324 0.12304 0.12651 0.10855 0.12082 0.08876 0.04836 0.05128 0.01918 0.0096 0.01413 0.02242 -0.00425 0.03884 0.00191 0.00849 0.05172 -0.01524 0.01106 -0.03658 0.00452 -0.01621 -0.0597 0.01748 -0.00413 0.03434 -0.01113

7.4 7.9 8.4 8.9 9.4 9.9 10.9 11.9 12.9 13.9 14.9 15.9 16.9 17.9 18.9 19.9 21.9 24.9 27.9 29.9 32.9 34.9 37.9 39.9 42.9 44.9 47.9 49.9

73

0.1553 0.18272 0.14057 0.14799 0.09499 0.11713 0.05594 0.01721 0.03621 0.02406 0.00915 0.01587 -0.0091 0.02472 -0.00297 -0.01834 0.01324 0.0026 -0.00728 0.01291 0.01381 0.00221 -0.02199 -0.01539 0.00597 0.00858 -0.01513 -0.02288

Time

100:0 fitting

Time

50:50 fitting

Time

10:90 fitting

Time

2:98 fitting

0 1 -8.7E-7 1 0 1 0 1 0.50404 0.80634 0.50707 0.84512 0.50404 0.87907 0.50404 0.88585 1.00808 0.6515 1.01414 0.71492 1.00808 0.77291 1.00808 0.78476 1.51212 0.52754 1.52121 0.60539 1.51212 0.6797 1.51212 0.69523 2.01616 0.42816 2.02828 0.51317 2.01616 0.59783 2.01616 0.61594 2.5202 0.34837 2.53535 0.43545 2.5202 0.52593 2.5202 0.5457 3.02424 0.28419 3.04242 0.3699 3.02424 0.46275 3.02424 0.4835 3.52828 0.23248 3.54949 0.31456 3.52828 0.40723 3.52828 0.4284 4.03232 0.19072 4.05656 0.2678 4.03232 0.35844 4.03232 0.37959 4.53636 0.15694 4.56364 0.22825 4.53636 0.31554 4.53636 0.33635 5.0404 0.12955 5.07071 0.19476 5.0404 0.27783 5.0404 0.29805 5.54444 0.10729 5.57778 0.16637 5.54444 0.24467 5.54444 0.26412 6.04848 0.08914 6.08485 0.14229 6.04848 0.2155 6.04848 0.23406 6.55253 0.07431 6.59192 0.12183 6.55253 0.18984 6.55253 0.20742 7.05657 0.06216 7.09899 0.10444 7.05657 0.16726 7.05657 0.18382 7.56061 0.05217 7.60606 0.08963 7.56061 0.14739 7.56061 0.16292 8.06465 0.04393 8.11313 0.07701 8.06465 0.1299 8.06465 0.14439 8.56869 0.03712 8.6202 0.06625 8.56869 0.1145 8.56869 0.12797 9.07273 0.03146 9.12727 0.05705 9.07273 0.10094 9.07273 0.11343 9.57677 0.02676 9.63434 0.04919 9.57677 0.08901 9.57677 0.10054 10.08081 0.02282 10.14141 0.04246 10.08081 0.07849 10.08081 0.08911 10.58485 0.01953 10.64848 0.03669 10.58485 0.06923 10.58485 0.07899 11.08889 0.01676 11.15555 0.03174 11.08889 0.06107 11.08889 0.07002 11.59293 0.01442 11.66263 0.02749 11.59293 0.05388 11.59293 0.06207 12.09697 0.01244 12.1697 0.02383 12.09697 0.04754 12.09697 0.05502 12.60101 0.01075 12.67677 0.02068 12.60101 0.04195 12.60101 0.04878 13.10505 0.00932 13.18384 0.01796 13.10505 0.03703 13.10505 0.04324 13.60909 0.00809 13.69091 0.01562 13.60909 0.03269 13.60909 0.03834 14.11313 0.00704 14.19798 0.01359 14.11313 0.02886 14.11313 0.03399 14.61717 0.00614 14.70505 0.01184 14.61717 0.02548 14.61717 0.03013 15.12121 0.00536 15.21212 0.01032 15.12121 0.0225 15.12121 0.02671 15.62525 0.00469 15.71919 0.00901 15.62525 0.01987 15.62525 0.02369 16.12929 0.00411 16.22626 0.00787 16.12929 0.01755 16.12929 0.021 16.63333 0.0036 16.73333 0.00688 16.63333 0.0155 16.63333 0.01862 17.13737 0.00316 17.2404 0.00602 17.13737 0.0137 17.13737 0.01651 17.64141 0.00278 17.74747 0.00527 17.64141 0.0121 17.64141 0.01464 18.14545 0.00245 18.25454 0.00461 18.14545 0.01069 18.14545 0.01298 18.64949 0.00215 18.76162 0.00404 18.64949 0.00945 18.64949 0.01151 19.15354 0.0019 19.26869 0.00355 19.15354 0.00835 19.15354 0.01021 19.65758 0.00168 19.77576 0.00311 19.65758 0.00738 19.65758 0.00905 20.16162 0.00148 20.28283 0.00273 20.16162 0.00653 20.16162 0.00803 20.66566 0.00131 20.7899 0.0024 20.66566 0.00577 20.66566 0.00712 21.1697 0.00115 21.29697 0.00211 21.1697 0.0051 21.1697 0.00631 21.67374 0.00102 21.80404 0.00186 21.67374 0.00451 21.67374 0.0056 22.17778 9.01968E-4 22.31111 0.00164 22.17778 0.00399 22.17778 0.00496 22.68182 7.97988E-4 22.81818 0.00144 22.68182 0.00353 22.68182 0.0044 23.18586 7.06237E-4 23.32525 0.00127 23.18586 0.00312 23.18586 0.0039 23.6899 6.25227E-4 23.83232 0.00112 23.6899 0.00276 23.6899 0.00346 24.19394 5.53661E-4 24.33939 9.85065E-4 24.19394 0.00244 24.19394 0.00307 24.69798 4.90407E-4 24.84646 8.68697E-4 24.69798 0.00216 24.69798 0.00272 25.20202 4.34475E-4 25.35353 7.66342E-4 25.20202 0.00191 25.20202 0.00242 25.70606 3.84997E-4 25.86061 6.76268E-4 25.70606 0.00169 25.70606 0.00214 26.2101 3.41214E-4 26.36768 5.96966E-4 26.2101 0.0015 26.2101 0.0019 26.71414 3.02457E-4 26.87475 5.27117E-4 26.71414 0.00133 26.71414 0.00169 27.21818 2.6814E-4 27.38182 4.65569E-4 27.21818 0.00117 27.21818 0.00149 27.72222 2.37746E-4 27.88889 4.11313E-4 27.72222 0.00104 27.72222 0.00133

74

28.22626 2.10821E-4 28.7303 1.86963E-4 29.23434 1.6582E-4 29.73838 1.47079E-4 30.24242 1.30466E-4 30.74646 1.15736E-4 31.25051 1.02676E-4 31.75455 9.10932E-5 32.25859 8.08209E-5 32.76263 7.17098E-5 33.26667 6.3628E-5 33.77071 5.64588E-5 34.27475 5.00988E-5 34.77879 4.44564E-5 35.28283 3.94503E-5 35.78687 3.50086E-5 36.29091 3.10675E-5 36.79495 2.75706E-5 37.29899 2.44676E-5 37.80303 2.17141E-5 38.30707 1.92706E-5 38.81111 1.71023E-5 39.31515 1.51781E-5 39.81919 1.34705E-5 40.32323 1.19551E-5 40.82727 1.06103E-5 41.33131 9.41676E-6 41.83535 8.35753E-6 42.33939 7.41748E-6 42.84343 6.5832E-6 43.34747 5.84277E-6 43.85152 5.18563E-6 44.35556 4.60242E-6 44.8596 4.0848E-6 45.36364 3.62541E-6 45.86768 3.21769E-6 46.37172 2.85583E-6 46.87576 2.53467E-6 47.3798 2.24962E-6 47.88384 1.99664E-6 48.38788 1.77211E-6 48.89192 1.57282E-6 49.39596 1.39595E-6 49.9 1.23897E-6

28.39596 3.63469E-4 28.90303 3.21264E-4 29.4101 2.8402E-4 29.91717 2.51145E-4 30.42424 2.22118E-4 30.93131 1.9648E-4 31.43838 1.73831E-4 31.94545 1.53817E-4 32.45252 1.36128E-4 32.9596 1.20489E-4 33.46667 1.06661E-4 33.97374 9.44318E-5 34.48081 8.3614E-5 34.98788 7.40434E-5 35.49495 6.55749E-5 36.00202 5.80804E-5 36.50909 5.14469E-5 37.01616 4.55749E-5 37.52323 4.03761E-5 38.0303 3.5773E-5 38.53737 3.16968E-5 39.04444 2.80869E-5 39.55151 2.48895E-5 40.05859 2.20574E-5 40.56566 1.95485E-5 41.07273 1.73259E-5 41.5798 1.53566E-5 42.08687 1.36118E-5 42.59394 1.20657E-5 43.10101 1.06956E-5 43.60808 9.48137E-6 44.11515 8.40529E-6 44.62222 7.45157E-6 45.12929 6.60624E-6 45.63636 5.85697E-6 46.14343 5.19281E-6 46.6505 4.60407E-6 47.15758 4.08217E-6 47.66465 3.6195E-6 48.17172 3.20933E-6 48.67879 2.84569E-6 49.18586 2.52329E-6 49.69293 2.23746E-6 50.2 1.98403E-6

28.22626 9.19208E-4 28.22626 0.00118 28.7303 8.13755E-4 28.7303 0.00104 29.23434 7.20449E-4 29.23434 9.25292E-4 29.73838 6.37883E-4 29.73838 8.20756E-4 30.24242 5.64816E-4 30.24242 7.28039E-4 30.74646 5.0015E-4 30.74646 6.45804E-4 31.25051 4.42914E-4 31.25051 5.72864E-4 31.75455 3.92251E-4 31.75455 5.08168E-4 32.25859 3.47404E-4 32.25859 4.50784E-4 32.76263 3.07702E-4 32.76263 3.99884E-4 33.26667 2.72552E-4 33.26667 3.54735E-4 33.77071 2.4143E-4 33.77071 3.14687E-4 34.27475 2.13873E-4 34.27475 2.79163E-4 34.77879 1.89471E-4 34.77879 2.47652E-4 35.28283 1.67862E-4 35.28283 2.197E-4 35.78687 1.48725E-4 35.78687 1.94905E-4 36.29091 1.31775E-4 36.29091 1.7291E-4 36.79495 1.16763E-4 36.79495 1.53398E-4 37.29899 1.03465E-4 37.29899 1.36089E-4 37.80303 9.16862E-5 37.80303 1.20735E-4 38.30707 8.12516E-5 38.30707 1.07114E-4 38.81111 7.20076E-5 38.81111 9.50301E-5 39.31515 6.38178E-5 39.31515 8.43104E-5 39.81919 5.65618E-5 39.81919 7.48005E-5 40.32323 5.01327E-5 40.32323 6.63638E-5 40.82727 4.4436E-5 40.82727 5.88792E-5 41.33131 3.93881E-5 41.33131 5.22391E-5 41.83535 3.49148E-5 41.83535 4.63482E-5 42.33939 3.09507E-5 42.33939 4.11219E-5 42.84343 2.74376E-5 42.84343 3.64852E-5 43.34747 2.4324E-5 43.34747 3.23715E-5 43.85152 2.15644E-5 43.85152 2.87219E-5 44.35556 1.91185E-5 44.35556 2.54839E-5 44.8596 1.69506E-5 44.8596 2.26111E-5 45.36364 1.50289E-5 45.36364 2.00623E-5 45.86768 1.33255E-5 45.86768 1.78009E-5 46.37172 1.18154E-5 46.37172 1.57945E-5 46.87576 1.04768E-5 46.87576 1.40143E-5 47.3798 9.29009E-6 47.3798 1.24349E-5 47.88384 8.238E-6 47.88384 1.10335E-5 48.38788 7.30525E-6 48.38788 9.79013E-6 48.89192 6.47826E-6 48.89192 8.68691E-6 49.39596 5.74503E-6 49.39596 7.70806E-6 49.9 5.0949E-6 49.9 6.83954E-6

S7.A Time

-8.7E-7 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LiS13C15N (4.0M)

LiSCN (4.0M)

0.99672 1.00001 0.97611 0.94956 0.92749 0.90069 0.87513 0.85229

1.00001 0.98788 0.97148 0.94862 0.93137 0.91212 0.89831 0.88192

1 0.97579 0.95285 0.9311 0.91047 0.8909 0.87231 0.85465

1 0.98109 0.96312 0.94604 0.92979 0.91432 0.89958 0.88554

75

LiSCN (4.0M) fitting

LiS13C15N (4.0M) fitting

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.7 7.2 7.7 8.2 8.7 9.2 9.7

0.83472 0.81566 0.79686 0.78115 0.76965 0.75836 0.74868 0.73863 0.73217 0.71267 0.70246 0.69858 0.69004 0.67639 0.66961 0.65844 0.65464 0.6439 0.63759 0.63644 0.62643 0.62075 0.61115 0.60278 0.60266 0.58824 0.59401 0.58583 0.58495 0.5736 0.57042 0.55813 0.55368 0.55537 0.54767 0.54418 0.54205 0.54724 0.53009 0.52741 0.52209 0.5183 0.51424 0.51498 0.50609 0.50352 0.4982 0.49315 0.49843 0.48808 0.48377 0.48714 0.47987 0.47302 0.46617 0.45761 0.42798 0.41539 0.396 0.38135 0.36734 0.3544

0.87003 0.85385 0.84153 0.83018 0.8181 0.81002 0.79723 0.78742 0.7784 0.77103 0.76721 0.75601 0.74788 0.73975 0.73232 0.72655 0.7178 0.71312 0.70748 0.69805 0.69501 0.69103 0.68055 0.67951 0.67267 0.66566 0.66462 0.65531 0.65194 0.64615 0.64607 0.64015 0.63597 0.62889 0.62467 0.6214 0.61477 0.61619 0.6089 0.60503 0.6006 0.59372 0.5943 0.58848 0.58158 0.58061 0.576 0.57404 0.57089 0.5637 0.55937 0.55785 0.5563 0.5524 0.54827 0.53153 0.51541 0.5006 0.48589 0.474 0.46167 0.44759

0.83786 0.82188 0.80667 0.79217 0.77835 0.76517 0.75258 0.74055 0.72905 0.71804 0.7075 0.69739 0.6877 0.67839 0.66944 0.66084 0.65256 0.64458 0.63689 0.62946 0.62229 0.61536 0.60866 0.60217 0.59587 0.58977 0.58385 0.57809 0.57249 0.56705 0.56175 0.55658 0.55154 0.54663 0.54182 0.53713 0.53254 0.52805 0.52365 0.51934 0.51512 0.51097 0.50691 0.50291 0.49899 0.49513 0.49133 0.4876 0.48392 0.4803 0.47673 0.47322 0.46975 0.46633 0.46296 0.44671 0.43137 0.41682 0.40295 0.38967 0.37694 0.3647

0.87215 0.85936 0.84715 0.83547 0.8243 0.81361 0.80337 0.79355 0.78412 0.77507 0.76637 0.758 0.74995 0.74218 0.7347 0.72747 0.72049 0.71374 0.70721 0.70088 0.69475 0.6888 0.68303 0.67741 0.67196 0.66665 0.66147 0.65643 0.65151 0.64671 0.64201 0.63742 0.63294 0.62854 0.62424 0.62002 0.61588 0.61181 0.60782 0.6039 0.60005 0.59626 0.59253 0.58885 0.58523 0.58166 0.57814 0.57467 0.57125 0.56787 0.56453 0.56123 0.55797 0.55475 0.55156 0.53612 0.52141 0.50731 0.49376 0.48069 0.46805 0.45582

76

10.2 11.2 12.2 13.2 14.2 15.2 16.2 17.2 18.2 19.2 20.2 23.2 25.2 28.2 30.2 35.2 40.2 43.2 45.2 48.2 50.2 55.2 60.2 65.2 70.2 75.2 80.2 85.2 90.2 95.2 100.2 110.2 120.2 130.2 140.2 150.2 160.2 170.2 180.2 190.2 200.2

0.32923 0.43669 0.35292 0.44395 0.32924 0.41503 0.33062 0.42125 0.31164 0.39397 0.30983 0.3998 0.29154 0.37645 0.29042 0.3795 0.27434 0.35503 0.27228 0.36028 0.25681 0.33475 0.25531 0.34206 0.23528 0.31816 0.23943 0.32478 0.22502 0.30482 0.22455 0.30839 0.20838 0.28727 0.21062 0.29285 0.19617 0.27416 0.19757 0.2781 0.18568 0.26027 0.18535 0.26411 0.14871 0.22309 0.15308 0.22625 0.13716 0.20588 0.13479 0.20411 0.11135 0.17664 0.11142 0.17493 0.09471 0.15965 0.09815 0.15784 0.07243 0.12806 0.07153 0.12211 0.05477 0.09986 0.05218 0.0945 0.04445 0.0871 0.04319 0.08104 0.03951 0.07758 0.03808 0.07315 0.03377 0.06748 0.03153 0.06274 0.02585 0.0626 0.02781 0.05663 0.02693 0.05032 0.02032 0.04385 0.01894 0.03769 0.01485 0.03396 0.01243 0.03091 0.01086 0.0263 0.00741 0.02329 0.00795 0.02037 0.00609 0.01959 0.00582 0.01578 0.0041 0.01486 0.00426 0.01223 0.00272 0.01191 0.00313 0.00947 0.00641 0.00827 0.00229 0.00734 0.00677 0.00974 0.00168 0.00569 0.00186 0.00588 0.00124 0.00441 -9.09791E-4 0.00173 6.68273E-4 0.00265 0.00338 0.00154 3.62372E-4 0.00159 8.26094E-4 0.00142 1.97237E-4 9.55531E-4 0.00135 6.93118E-4 1.07746E-4 5.74283E-4 6.69943E-5 -1.92173E-5 5.89876E-5 3.45122E-4 -0.00192 -4.96655E-4 3.24821E-5 2.07512E-4 0.00115 3.99046E-4 1.79208E-5 1.24715E-4 0.00211 -2.09716E-4 9.99349E-6 7.49704E-5 -0.00151 4.81516E-4 5.55269E-6 4.51373E-5 -0.0018 4.94826E-4 3.21608E-6 2.71117E-5

S7.B Time -8.7E-7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

Flowing down

Pumping up

0.00197 4.69538E-5 -6.6923E-9 -4.6846E-9 0.00282 0.0016 7.50925E-4 5.25647E-4 0.00115 7.13746E-4 0.00147 0.00103 0.00136 0.00262 0.00215 0.0015 0.00204 0.00357 0.0028 0.00196 0.00102 0.00334 0.00343 0.0024 0.00106 0.00359 0.00402 0.00281 0.00173 0.0046 0.00459 0.00321 9.74916E-4 0.00467 0.00514 0.0036 0.00101 0.0045 0.00566 0.00396 0.00362 0.00546 0.00616 0.00432 0.0037 0.00681 0.00665 0.00465 0.003 0.00623 0.00711 0.00498 0.00326 0.00724 0.00756 0.00529

77

Flowing down fitting

Pumping up fitting

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.7 7.2 7.7 8.2 8.7 9.2 9.7 10.2 11.2 12.2 13.2 14.2 15.2

0.00391 0.00528 0.00477 0.005 0.00639 0.00542 0.00616 0.00652 0.00746 0.00658 0.00652 0.00682 0.00929 0.00882 0.00964 0.00912 0.00874 0.00913 0.00818 0.00985 0.00971 0.01132 0.01075 0.00979 0.01103 0.01159 0.0106 0.01194 0.01112 0.01195 0.01338 0.01325 0.01329 0.01376 0.01339 0.01335 0.01338 0.01386 0.01395 0.01433 0.01471 0.01515 0.0153 0.0154 0.0158 0.016 0.01625 0.0163 0.0164 0.0164 0.01757 0.01741 0.01793 0.02002 0.02008 0.02043 0.02043 0.02159 0.02168 0.02173 0.02244 0.02115

0.00656 0.0078 0.00785 0.0079 0.00825 0.00796 0.00861 0.0101 0.00937 0.00908 0.00834 0.01003 0.0096 0.01012 0.01013 0.00868 0.00908 0.01098 0.01171 0.01055 0.01088 0.01225 0.01082 0.01209 0.01131 0.0114 0.01324 0.01122 0.01243 0.01156 0.01169 0.01299 0.01197 0.01095 0.01191 0.01229 0.01235 0.01222 0.01334 0.01276 0.01231 0.01317 0.0128 0.01419 0.01321 0.01264 0.01382 0.01346 0.01321 0.01341 0.01341 0.01307 0.01498 0.0137 0.01439 0.01407 0.01524 0.01531 0.01416 0.01514 0.01457 0.01454

0.00799 0.0084 0.0088 0.00918 0.00955 0.00991 0.01025 0.01059 0.01091 0.01122 0.01153 0.01182 0.01211 0.01238 0.01265 0.01291 0.01316 0.01341 0.01364 0.01388 0.0141 0.01432 0.01453 0.01474 0.01494 0.01514 0.01533 0.01552 0.0157 0.01588 0.01605 0.01622 0.01639 0.01655 0.0167 0.01685 0.017 0.01715 0.01729 0.01743 0.01756 0.01769 0.01782 0.01795 0.01807 0.01819 0.0183 0.01842 0.01853 0.01904 0.01948 0.01987 0.02021 0.0205 0.02074 0.02094 0.02111 0.02133 0.02144 0.02144 0.02136 0.02119

0.00559 0.00588 0.00616 0.00643 0.00669 0.00694 0.00718 0.00741 0.00764 0.00786 0.00807 0.00827 0.00847 0.00867 0.00885 0.00904 0.00921 0.00938 0.00955 0.00971 0.00987 0.01002 0.01017 0.01032 0.01046 0.0106 0.01073 0.01086 0.01099 0.01112 0.01124 0.01135 0.01147 0.01158 0.01169 0.0118 0.0119 0.012 0.0121 0.0122 0.01229 0.01239 0.01248 0.01256 0.01265 0.01273 0.01281 0.01289 0.01297 0.01332 0.01364 0.01391 0.01415 0.01435 0.01452 0.01466 0.01477 0.01493 0.01501 0.01501 0.01495 0.01484

78

16.2 17.2 18.2 19.2 20.2 23.2 25.2 28.2 30.2 35.2 40.2 43.2 45.2 48.2 50.2 55.2 60.2 65.2 70.2 75.2 80.2 85.2 90.2 95.2 100.2 110.2 120.2 130.2 140.2 150.2 160.2 170.2 180.2 190.2 200.2

0.02033 0.01473 0.02097 0.01468 0.02054 0.01477 0.02069 0.01448 0.02034 0.01424 0.02037 0.01426 0.01998 0.01322 0.02001 0.01401 0.01961 0.01404 0.01962 0.01373 0.0188 0.01305 0.01831 0.01282 0.01697 0.01252 0.01738 0.01216 0.01669 0.01145 0.01594 0.01116 0.01427 0.01083 0.01498 0.01049 0.01286 0.0098 0.01269 0.00888 0.00999 0.00726 0.0106 0.00742 0.00908 0.00778 0.00947 0.00663 0.0075 0.007 0.00877 0.00614 0.00623 0.00578 0.0078 0.00546 0.00529 0.00467 0.0072 0.00504 0.00389 0.00488 0.00588 0.00411 0.00391 0.00213 0.00477 0.00334 0.00219 0.00304 0.00385 0.0027 0.00171 0.00176 0.0031 0.00217 0.00164 0.00207 0.00248 0.00174 8.99787E-4 7.17123E-4 0.00199 0.00139 3.76282E-4 0.00108 0.00158 0.00111 0.00102 1.23907E-4 0.00126 8.82362E-4 6.91354E-4 3.94976E-4 0.001 7.0059E-4 -4.90169E-5 -6.61067E-5 7.9339E-4 5.55313E-4 -7.49589E-4 2.13642E-5 4.96172E-4 3.47287E-4 -4.81504E-4 1.16637E-4 3.08564E-4 2.16068E-4 -0.00122 -3.60023E-4 1.9105E-4 1.33746E-4 -3.28505E-4 -8.19223E-4 1.17906E-4 8.25009E-5 4.47647E-4 -4.63678E-4 7.25632E-5 5.07053E-5 2.96846E-4 -1.65158E-4 4.44639E-5 3.11481E-5 -5.40495E-5 9.76171E-5 2.72586E-5 1.91751E-5 7.48241E-4 -3.82882E-4 1.66778E-5 1.16503E-5 -5.40495E-5 3.89353E-5 1.01521E-5 7.06881E-6 7.48241E-4 1.3028E-4 6.18467E-6 4.27655E-6

S7.C Time

100:0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

1 0.9967 1.00486 0.91806 0.86598 0.88844 0.82474 0.80884 0.7527 0.73724 0.71968 0.71472 0.67336 0.64944 0.6725 0.65208 0.56756 0.54624 0.54174 0.56828 0.5507

Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

50:50

Time

1 1.00224 0.97574 0.96384 0.94294 0.91538 0.8895 0.88338 0.86844 0.8412 0.82494 0.80754 0.77548 0.76672 0.7671 0.74888 0.75106 0.72504 0.69608 0.67204 0.66684

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

20:80

Time

1 0.97332 0.948 0.95834 0.93082 0.92644 0.8848 0.89138 0.88138 0.85258 0.85726 0.85892 0.83362 0.80632 0.75758 0.79046 0.7387 0.7274 0.78324 0.7243 0.7282

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

79

2:98 0.98866 1.02468 0.9848 0.98514 0.9783 0.97304 0.95338 0.95102 0.93352 0.89212 0.91588 0.86316 0.85814 0.8615 0.85768 0.78702 0.805 0.8064 0.81792 0.78486 0.78786

2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 23 25 28 30 35 40 43 45 48 50

0.49424 2.5 0.37522 3 0.38158 3.5 0.28958 4 0.25046 4.5 0.21396 5 0.23892 5.5 0.17164 5.9 0.1858 6.4 0.1878 6.9 0.15558 7.4 0.12484 7.9 0.12902 8.4 0.08454 8.9 0.13594 9.4 0.12398 9.9 0.0735 10.9 0.09402 11.9 0.06306 12.9 0.04742 13.9 0.03572 14.9 0.04542 15.9 0.05406 16.9 0.02592 17.9 0.01616 18.9 -0.00176 19.9 -0.01666 22.9 -0.00598 24.9 0.00896 27.9 -0.00474 29.9 0.0081 34.9 -2.01802E-5 -0.02628 42.9 -5.22444E-6 -2.32226E-6 0.01198 49.9

Time

100:0 Fitting

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

1 0.96187 0.92546 0.89069 0.85748 0.82576 0.79545 0.7665 0.73884 0.7124 0.68714 0.66299 0.6399 0.61783 0.59673 0.57654 0.55724 0.53877 0.5211 0.50419 0.48801

Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

0.60346 0.5697 0.51738 0.49198 0.45052 0.42784 0.37794 0.34194 0.31812 0.29618 0.28864 0.2579 0.236 0.23452 0.21032 0.17008 0.1503 0.13982 0.11522 0.09692 0.07892 0.0666 0.05914 0.04574 0.02632 0.02464 0.01226 -0.00153 -0.02298 -0.00484 0.0058 39.9 -0.01588 44.9 47.9 0.0064 50:50 Fitting

1 0.97588 0.95247 0.92976 0.90772 0.88633 0.86556 0.84541 0.82584 0.80684 0.7884 0.77049 0.75309 0.7362 0.71979 0.70385 0.68836 0.67331 0.65869 0.64448 0.63067

2.5 3 3.5 4 4.5 5 5.5 5.9 6 6.6 7.6 8.1 8.6 9.1 9.6 10.1 11.1 12.1 13.1 14.1 15.1 16.1 17.1 18.1 19.1 20.1 23.1 25.1 28.1 30.1 35.1 -0.00336 43.1 0.00844 -0.00414 50.1

Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

0.66512 2.5 0.74634 0.62676 3 0.75338 0.59514 3.5 0.66366 0.60432 4 0.65716 0.5246 4.5 0.63944 0.57868 5 0.65888 0.52684 5.5 0.58726 0.4498 5.9 0.61924 0.49608 6.4 0.54456 0.47424 6.9 0.57768 0.38856 7.4 0.48638 0.3645 7.9 0.49076 0.33108 8.4 0.40658 0.29862 8.9 0.39288 0.3099 9.4 0.39722 0.32354 9.9 0.4135 0.2453 10.9 0.30144 0.22358 11.9 0.3296 0.21878 12.9 0.26528 0.15842 13.9 0.23962 0.14942 14.9 0.24812 0.11952 15.9 0.22542 0.03806 16.9 0.13226 0.06346 17.9 0.1239 0.02066 18.9 0.13046 0.04184 19.9 0.08958 -0.00704 22.9 0.0372 0.0021 24.9 0.00412 0.02928 27.9 -9.34966E-4 -0.00554 29.9 0.00388 0.00177 34.9 -7.92724E-4 40.1 8.04048E-4 39.9 -0.00438 0.01238 42.9 -0.02728 45.1 -1.26862E-5 44.9 -0.03338 48.1 0.00292 47.9 0.00101 -3.63464E-6 49.9 -0.0164

20:80 Fitting

Time

1 0.98438 0.96906 0.95403 0.93928 0.92482 0.91062 0.8967 0.88303 0.86962 0.85647 0.84355 0.83088 0.81843 0.80622 0.79423 0.78247 0.77091 0.75957 0.74843 0.73749

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

80

2:98 Fitting

1 0.98952 0.97915 0.96889 0.95875 0.94872 0.9388 0.92899 0.91929 0.90969 0.9002 0.89081 0.88152 0.87233 0.86325 0.85426 0.84537 0.83658 0.82788 0.81928 0.81077

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 23 25 28 30 35

0.47252 0.45769 0.44349 0.42989 0.41686 0.40437 0.39241 0.38095 0.36996 0.35942 0.34931 0.33961 0.33031 0.32138 0.3128 0.30457 0.29666 0.28907 0.28177 0.27475 0.26801 0.26152 0.25528 0.24928 0.24349 0.23793 0.23257 0.2274 0.22242 0.21762 0.213 0.20853 0.20422 0.20006 0.19605 0.19216 0.18841 0.18479 0.17789 0.16249 0.14929 0.13788 0.12793 0.11916 0.11137 0.10439 0.09809 0.08712 0.07783 0.06982 0.06281 0.05662 0.0511 0.04617 0.04174 0.03775 0.03415 0.0253 0.02073 0.01537 0.0126 0.00765

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.4 6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.9 11.9 12.9 13.9 14.9 15.9 16.9 17.9 18.9 19.9 22.9 24.9 27.9 29.9 34.9

0.61724 0.60419 0.5915 0.57916 0.56716 0.5555 0.54415 0.5331 0.52236 0.51191 0.50174 0.49184 0.4822 0.47282 0.46369 0.4548 0.44614 0.4377 0.42949 0.42148 0.41368 0.40608 0.39867 0.39145 0.38441 0.37755 0.37086 0.36433 0.35796 0.35175 0.34569 0.33978 0.33401 0.32838 0.32288 0.31751 0.31226 0.30714 0.30214 0.27879 0.25794 0.23925 0.22244 0.20726 0.1935 0.18099 0.16958 0.14954 0.13254 0.11798 0.10537 0.09437 0.08471 0.07617 0.06858 0.06182 0.05578 0.04112 0.03361 0.02489 0.02038 0.01237

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.6 7.6 8.1 8.6 9.1 9.6 10.1 11.1 12.1 13.1 14.1 15.1 16.1 17.1 18.1 19.1 20.1 23.1 25.1 28.1 30.1 35.1

0.72675 0.7162 0.70584 0.69567 0.68568 0.67586 0.66621 0.65674 0.64743 0.63829 0.6293 0.62047 0.61179 0.60326 0.59488 0.58665 0.57855 0.57059 0.56276 0.55507 0.54751 0.54007 0.53276 0.52557 0.51849 0.51154 0.5047 0.49797 0.49135 0.48485 0.47844 0.47214 0.46594 0.45984 0.45384 0.44794 0.44212 0.4364 0.43077 0.42523 0.39376 0.34735 0.32663 0.30738 0.28946 0.27278 0.25722 0.22911 0.2045 0.18287 0.1638 0.14693 0.13195 0.11863 0.10676 0.09615 0.08666 0.06366 0.05193 0.03834 0.03135 0.019

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.4 6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.9 11.9 12.9 13.9 14.9 15.9 16.9 17.9 18.9 19.9 22.9 24.9 27.9 29.9 34.9

81

0.80235 0.79403 0.78579 0.77764 0.76958 0.76161 0.75372 0.74592 0.73821 0.73057 0.72302 0.71555 0.70816 0.70084 0.69361 0.68645 0.67937 0.67237 0.66544 0.65858 0.6518 0.64509 0.63845 0.63189 0.62539 0.61896 0.6126 0.60631 0.60008 0.59392 0.58783 0.5818 0.57583 0.56993 0.56409 0.55831 0.55259 0.54693 0.54134 0.51422 0.4885 0.4641 0.44095 0.41898 0.39813 0.37835 0.35956 0.3248 0.29346 0.26519 0.23968 0.21665 0.19587 0.1771 0.16015 0.14483 0.13099 0.09696 0.07936 0.05879 0.04814 0.02922

40 43 45 48 50

0.00465 0.00345 0.00283 0.0021 0.00172

39.9 42.9 44.9 47.9 49.9

0.00752 0.00558 0.00457 0.00339 0.00278

40.1 43.1 45.1 48.1 50.1

0.01153 0.00855 0.007 0.00519 0.00425

39.9 42.9 44.9 47.9 49.9

0.01775 0.01316 0.01078 0.008 0.00655

S8.A Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

NaSCN (4.0M)

1.00001 0.98554 0.96293 0.93493 0.91197 0.88698 0.87036 0.84668 0.83463 0.82272 0.80632 0.79349 0.78207 0.76922 0.76018 0.75226 0.7401 0.73405 0.72304 0.71941 0.70916 0.70032 0.69437 0.68754 0.68346 0.67453 0.66693 0.66136 0.65756 0.65226 0.64616 0.64157 0.63594 0.62948 0.62527 0.62024 0.61299 0.61051 0.60868 0.60264 0.59717 0.59273 0.5889 0.58421 0.57925 0.57606 0.57289 0.5708 0.5674

1 0.99893 0.9934 0.98246 0.9727 0.9552 0.93097 0.91463 0.9067 0.8893 0.87933 0.87022 0.85794 0.84519 0.83282 0.82864 0.81752 0.81659 0.81005 0.80031 0.78731 0.78213 0.77858 0.76789 0.76156 0.75996 0.75357 0.74613 0.74069 0.73246 0.73222 0.72839 0.72417 0.71561 0.71338 0.70403 0.70249 0.69278 0.69431 0.68855 0.68416 0.68124 0.67887 0.67182 0.67536 0.67066 0.66292 0.65891 0.65765

1 0.97659 0.9545 0.93365 0.91396 0.89535 0.87777 0.86113 0.84539 0.83048 0.81634 0.80294 0.79022 0.77814 0.76666 0.75574 0.74534 0.73544 0.726 0.71699 0.70839 0.70017 0.6923 0.68477 0.67755 0.67062 0.66397 0.65757 0.65142 0.64549 0.63978 0.63427 0.62895 0.6238 0.61882 0.61399 0.60931 0.60477 0.60036 0.59608 0.5919 0.58784 0.58387 0.58001 0.57623 0.57254 0.56893 0.5654 0.56194

NaS13C15N (4.0M)

1 0.98681 0.97404 0.96167 0.94969 0.93807 0.92681 0.91589 0.90531 0.89504 0.88508 0.87542 0.86604 0.85693 0.84809 0.8395 0.83115 0.82304 0.81516 0.80749 0.80004 0.79279 0.78573 0.77886 0.77217 0.76566 0.75932 0.75314 0.74711 0.74123 0.7355 0.72991 0.72446 0.71913 0.71393 0.70885 0.70388 0.69903 0.69429 0.68965 0.68511 0.68067 0.67633 0.67207 0.6679 0.66381 0.65981 0.65588 0.65203

82

NaSCN (4.0M) fitting

NaS13C15N (4.0M) fitting

4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.8 7.3 7.8 8.3 8.8 9.3 9.8 10.3 11.3 12.3 13.3 14.3 15.3 16.3 17.3 18.3 19.3 20.3 23.3 25.3 28.3 30.3 35.3 40.3 43.3 45.3 48.3 50.3 55.3 60.3 65.3 70.3 75.3 80.3 85.3 90.3 95.3 100.3 110.3 120.3 130.3 140.3 150.3 160.3 170.3 180.3 190.3

0.56094 0.65342 0.55855 0.64826 0.55954 0.64982 0.55522 0.64455 0.5544 0.64659 0.55195 0.64091 0.55181 0.64126 0.54874 0.63734 0.54809 0.63535 0.54559 0.63383 0.54601 0.63986 0.54249 0.63039 0.54261 0.63294 0.53943 0.627 0.53874 0.63275 0.53643 0.62367 0.53804 0.62776 0.53347 0.62039 0.53305 0.62571 0.53055 0.61717 0.5277 0.62814 0.52767 0.614 0.52445 0.62586 0.52483 0.61088 0.52171 0.62314 0.52202 0.60781 0.51626 0.60879 0.51926 0.60478 0.51248 0.61015 0.51652 0.6018 0.49964 0.59194 0.5033 0.58754 0.48658 0.57225 0.49073 0.5742 0.47397 0.55934 0.47869 0.56166 0.45869 0.54794 0.46712 0.5498 0.44682 0.54021 0.45594 0.53852 0.43526 0.52389 0.44511 0.52776 0.42256 0.51554 0.4346 0.51745 0.41502 0.50967 0.42439 0.50753 0.39402 0.48601 0.40476 0.4887 0.37381 0.4649 0.38612 0.471 0.35627 0.44779 0.36837 0.45424 0.33907 0.43205 0.35147 0.43827 0.32309 0.41597 0.33536 0.42301 0.31014 0.40136 0.32 0.40837 0.29332 0.38416 0.30536 0.39431 0.28093 0.3733 0.29139 0.38078 0.27011 0.36008 0.27807 0.36774 0.25609 0.34647 0.26536 0.35518 0.23083 0.31323 0.23066 0.32009 0.20772 0.29383 0.2101 0.29868 0.18288 0.26793 0.18268 0.26925 0.16721 0.24844 0.16643 0.25128 0.13516 0.21152 0.13189 0.21145 0.10696 0.17488 0.10457 0.17797 0.09463 0.15744 0.09099 0.1605 0.08543 0.15031 0.08294 0.14982 0.07674 0.13358 0.07219 0.13512 0.07119 0.12846 0.06582 0.12613 0.05733 0.10881 0.05225 0.1062 0.04507 0.09261 0.0415 0.08944 0.03528 0.07963 0.03298 0.07532 0.02949 0.06562 0.02622 0.06344 0.02281 0.05597 0.02086 0.05344 0.01773 0.04628 0.0166 0.04502 0.01507 0.03885 0.01322 0.03793 0.01045 0.03452 0.01053 0.03196 0.01004 0.02748 0.0084 0.02693 0.00644 0.02397 0.0067 0.0227 0.00117 0.01816 0.00428 0.01612 9.64739E-4 0.01063 0.00274 0.01145 -0.002 0.0086 0.00176 0.00814 -0.00427 0.00517 0.00113 0.00578 -0.00123 0.00518 7.33016E-4 0.00411 -0.00372 0.00489 4.76309E-4 0.00292 -0.00413 0.0012 3.1065E-4 0.00208 -0.00391 0.00104 2.03641E-4 0.00148 -0.00413 9.45587E-4 1.34029E-4 0.00105

83

200.3

-0.0038 -7.25743E-4

8.87474E-5

7.47521E-4

S8.B Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4

Flowing down

Pumping up

-0.00119 3.96875E-4 0 0 -0.00121 -2.5016E-4 4.90589E-4 3.43413E-4 0.00169 0.00173 9.63063E-4 6.74144E-4 -2.06709E-4 0.00164 0.00142 9.929E-4 -0.00146 0.00343 0.00186 0.0013 -5.14906E-4 0.00438 0.00228 0.0016 0.00162 0.00237 0.00269 0.00188 0.00255 0.00221 0.00309 0.00216 0.00125 0.00312 0.00347 0.00243 0.00257 0.00377 0.00384 0.00269 0.00112 0.00488 0.0042 0.00294 0.00216 0.00533 0.00455 0.00318 0.00418 0.00461 0.00489 0.00342 0.00247 0.00567 0.00521 0.00365 0.00523 0.0057 0.00553 0.00387 0.00325 0.00578 0.00584 0.00409 0.00318 0.00538 0.00614 0.0043 0.00544 0.00458 0.00644 0.0045 0.0036 0.00651 0.00672 0.0047 0.00531 0.00663 0.007 0.0049 0.00538 0.00458 0.00727 0.00509 0.00716 0.00636 0.00753 0.00527 0.00704 0.00739 0.00779 0.00545 0.00644 0.00725 0.00804 0.00563 0.00713 0.00617 0.00829 0.0058 0.00737 0.00593 0.00853 0.00597 0.00946 0.00559 0.00877 0.00614 0.00708 0.00652 0.009 0.0063 0.00697 0.00723 0.00922 0.00646 0.00813 0.00831 0.00944 0.00661 0.00881 0.00733 0.00966 0.00676 0.00713 0.00761 0.00987 0.00691 0.00795 0.00674 0.01008 0.00706 0.00651 0.00891 0.01028 0.0072 0.00948 0.00746 0.01048 0.00734 0.00891 0.00666 0.01068 0.00748 0.00923 0.00994 0.01087 0.00761 0.00875 0.00573 0.01106 0.00774 0.00897 0.0091 0.01125 0.00787 0.00983 0.00934 0.01143 0.008 0.01117 0.00935 0.01161 0.00813 0.00952 0.00848 0.01179 0.00825 0.00996 0.00893 0.01196 0.00837 0.00974 0.00725 0.01213 0.00849 0.01179 0.01035 0.0123 0.00861 0.01035 0.00961 0.01247 0.00873 0.01008 0.00918 0.01263 0.00884 0.00919 0.01072 0.01279 0.00895 0.0098 0.00991 0.01295 0.00906 0.01095 0.00955 0.01311 0.00917 0.01426 0.00979 0.01326 0.00928 0.01035 0.00941 0.01341 0.00939 0.01046 0.00889 0.01356 0.00949 0.01036 0.00861 0.01371 0.00959 0.01289 0.00913 0.01385 0.0097

84

Flowing down fitting

Pumping up fitting

5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.8 7.3 7.8 8.3 8.8 9.3 9.8 10.3 11.3 12.3 13.3 14.3 15.3 16.3 17.3 18.3 19.3 20.3 23.3 25.3 28.3 30.3 35.3 40.3 43.3 45.3 48.3 50.3 55.3 60.3 65.3 70.3 75.3 80.3 85.3 90.3 95.3 100.3 110.3 120.3 130.3 140.3 150.3 160.3 170.3 180.3 190.3 200.3

0.01274 0.01024 0.01399 0.0098 0.01299 0.00888 0.01413 0.00989 0.01315 0.00996 0.01427 0.00999 0.01315 0.01101 0.01441 0.01009 0.01346 0.00936 0.01455 0.01018 0.01368 0.01004 0.01468 0.01028 0.0144 0.01128 0.01481 0.01037 0.01503 0.00841 0.01494 0.01046 0.01565 0.01037 0.01507 0.01055 0.01628 0.01067 0.01568 0.01098 0.01722 0.01107 0.01626 0.01138 0.01785 0.01258 0.0168 0.01176 0.01816 0.01204 0.0173 0.01211 0.01843 0.01174 0.01778 0.01245 0.01953 0.01212 0.01822 0.01276 0.01941 0.01215 0.01864 0.01305 0.01931 0.01409 0.01903 0.01332 0.01932 0.01283 0.01973 0.01381 0.0215 0.01353 0.02034 0.01424 0.02272 0.01369 0.02087 0.01461 0.02045 0.01397 0.02132 0.01492 0.02272 0.01585 0.02169 0.01519 0.02128 0.01593 0.022 0.0154 0.023 0.01528 0.02225 0.01558 0.02381 0.01611 0.02244 0.01571 0.02272 0.01556 0.02258 0.01581 0.022 0.01576 0.02268 0.01587 0.0227 0.01532 0.0227 0.01589 0.02185 0.01518 0.02254 0.01578 0.0211 0.01607 0.0221 0.01547 0.02135 0.01554 0.02169 0.01518 0.02008 0.01531 0.02039 0.01427 0.01872 0.01435 0.01885 0.01319 0.01609 0.01337 0.01786 0.0125 0.01601 0.01215 0.01719 0.01203 0.01577 0.01132 0.01618 0.01133 0.01309 0.01121 0.01552 0.01086 0.01278 0.01059 0.01389 0.00972 0.0108 0.00993 0.01234 0.00864 0.00909 0.00794 0.0109 0.00763 0.00892 0.00744 0.00959 0.00671 0.00626 0.00701 0.00839 0.00587 0.00639 0.00628 0.00732 0.00512 0.00577 0.00394 0.00636 0.00445 0.0049 0.00602 0.00552 0.00386 0.00583 0.00289 0.00477 0.00334 0.00231 0.00456 0.00412 0.00288 0.00242 0.00292 0.00305 0.00213 0.0012 9.43396E-4 0.00224 0.00157 -2.41683E-4 0.00174 0.00164 0.00115 4.13763E-4 3.41116E-4 0.0012 8.38285E-4 5.30206E-4 0.0014 8.70159E-4 6.09109E-4 -0.00107 0.00146 6.30497E-4 4.41333E-4 6.89695E-4 -7.43493E-4 4.55735E-4 3.19029E-4 -5.74321E-4 -9.87085E-5 3.28782E-4 2.30132E-4 1.67093E-4 7.16573E-4 2.36759E-4 1.65743E-4 -2.67683E-4 -0.00142 1.70307E-4 1.19199E-4

S8.C

85

Time

100:0

Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50

1.00002 0 1.01348 0.1 1.0016 0.2 0.96418 0.3 0.96727 0.4 0.94312 0.5 0.894 0.6 0.85857 0.7 0.82832 0.8 0.79998 0.9 0.77863 1 0.74978 1.1 0.71427 1.2 0.6602 1.3 0.64823 1.4 0.608 1.5 0.60265 1.6 0.5916 1.7 0.5919 1.8 0.55343 1.9 0.53363 2 0.47962 2.5 0.41707 3 0.37525 3.5 0.27583 4 0.2733 4.5 0.23575 5 0.15788 5.4 0.1893 5.5 0.13778 5.6 0.1524 5.7 0.09822 6.2 0.10533 6.7 0.09622 7.2 0.1035 7.7 0.08823 8.2 0.07395 8.7 0.05473 9.2 0.02063 9.7 0.04865 10.7 0.0344 11.7 0.01918 12.7 0.0146 13.7 0.00642 14.7 0.01623 15.7 0.02343 16.7 2.3892E-4 -0.00868 18.7 -0.00935 19.7 7.31133E-4 0.00288 24.7 9.20437E-4 0.0025 29.7 -0.00902 34.7 -0.02298 39.7 -0.00408 42.7 -0.01775 44.7 -0.01597 47.7 -0.0066 49.7

80:20

Time

0.99998 0.99707 0.94705 0.8734 0.88558 0.85877 0.80275 0.80742 0.79267 0.70962 0.70902 0.72538 0.69203 0.67948 0.67893 0.62293 0.64657 0.57048 0.60465 0.58708 0.5684 0.47595 0.43227 0.38618 0.33345 0.24675 0.2773 0.25717 0.20907 0.19232 0.2236 0.21158 0.1791 0.14158 0.1453 0.13498 0.12503 0.12018 0.09597 0.04753 0.06075 0.02295 0.01705 -0.00373 -0.00912 0.02647 17.7 -0.01632 -0.00106 22.7 0.02088 27.7 -0.01262 -0.00795 -0.01492 -0.021 -0.01127 -0.02502 0.0041

50:50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 6.6 7.1 7.6 8.1 8.6 9.1 9.6 10.1 10.6 11.6 12.6 13.6 14.6 15.6 16.6 17.6 0.01747 19.6 20.6 0.02402 25.6 0.00403 30.6 35.6 40.6 43.6 45.6 48.6 50.6

Time

1.00002 1.00708 1.00733 0.9998 0.99788 0.98125 0.97373 0.93518 0.9406 0.88463 0.85688 0.84033 0.8034 0.7776 0.77952 0.7504 0.71358 0.66432 0.6514 0.64023 0.63512 0.56957 0.53948 0.49692 0.43955 0.3964 0.33882 0.3381 0.2824 0.27055 0.27138 0.237 0.25595 0.2327 0.21152 0.19295 0.17248 0.14262 0.14948 0.16383 0.12447 0.09592 0.07452 0.06035 0.06413 0.04763 18.6 0.05035 0.05032 23.6 -0.0101 28.6 -0.0379 -0.03522 -0.01692 -0.02257 -0.01457 -0.03808 -0.03855

20:80

-1.73E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.3 6.4 6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.4 11.4 12.4 13.4 14.4 15.4 16.4 17.4 0.04048 19.4 20.4 0.0129 25.4 -0.03957 30.4 35.4 40.4 43.4 45.4 48.4 50.4

86

Time

1.00002 0.99987 0.96827 0.94493 0.93978 0.93605 0.95427 0.86473 0.86848 0.85447 0.87317 0.82677 0.82317 0.80138 0.74585 0.78232 0.74437 0.7259 0.77972 0.74285 0.68405 0.65312 0.57923 0.57987 0.48213 0.46008 0.45957 0.40375 0.3296 0.34677 0.33313 0.32877 0.29167 0.28267 0.28467 0.2411 0.18202 0.21402 0.15037 0.12797 0.1263 0.11437 0.06967 0.08215 0.04638 0.0326 18.4 0.03377 0.01508 23.4 0.00565 28.4 0.00312 -0.0175 -0.0081 -0.02405 -0.01733 -0.02437 -0.03323

2:98

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 5.6 5.9 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 0.03993 19 20 0.0132 25 0.00217 30 35 40 43 45 48 50

1 0.9693 0.95362 0.94935 0.91442 0.93592 0.91723 0.87567 0.89065 0.89583 0.78427 0.84525 0.87738 0.82678 0.86325 0.77648 0.8669 0.83763 0.77617 0.71922 0.74307 0.72325 0.70082 0.64945 0.68662 0.58085 0.5194 0.50542 0.46202 0.51282 0.57358 0.48062 0.4118 0.48378 0.39017 0.3611 0.36933 0.31685 0.2738 0.32302 0.25285 0.21072 0.21415 0.21715 0.18422 0.15673 18 0.19343 0.12772 0.09118 23 0.0871 0.06762 28 0.07675 0.0374 0.00562 0.01418 -0.01472 -8.67153E-6 -0.03928 -2.48443E-6

Time

100:0 Fitting

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40

1 0.96506 0.93147 0.89918 0.86814 0.8383 0.80961 0.78202 0.75549 0.72998 0.70545 0.68185 0.65916 0.63733 0.61633 0.59612 0.57669 0.55798 0.53998 0.52266 0.50599 0.43153 0.36987 0.31867 0.27604 0.24044 0.21059 0.18547 0.16425 0.14623 0.13087 0.11771 0.10636 0.09654 0.08798 0.08049 0.07389 0.06284 0.054 0.04678 0.04079 0.03574 0.03144 0.02773 0.02452 0.02171 0.01925 0.01517 0.01065 0.00749 0.00593 0.00417 0.0033 0.00233 0.00184

Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.4 5.5 5.6 5.7 6.2 6.7 7.2 7.7 8.2 8.7 9.2 9.7 10.7 11.7 12.7 13.7 14.7 15.7 16.7 17.7 18.7 19.7 22.7 24.7 27.7 29.7 34.7 39.7

80:20 Fitting

1 0.96968 0.94039 0.91208 0.88473 0.85831 0.83277 0.80809 0.78424 0.76119 0.7389 0.71736 0.69654 0.67641 0.65695 0.63814 0.61994 0.60235 0.58533 0.56887 0.55296 0.48082 0.41962 0.36758 0.32323 0.28534 0.25287 0.23023 0.22498 0.21989 0.21494 0.19227 0.17265 0.1556 0.14073 0.12772 0.11629 0.10621 0.09729 0.08229 0.07025 0.06045 0.05236 0.04561 0.0399 0.03503 0.03084 0.02721 0.02405 0.01674 0.01319 0.00926 0.00732 0.00408 0.00227

Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 6.6 7.1 7.6 8.1 8.6 9.1 9.6 10.1 10.6 11.6 12.6 13.6 14.6 15.6 16.6 17.6 18.6 19.6 20.6 23.6 25.6 28.6 30.6 35.6 40.6

50:50 Fitting

Time

1 0.97665 0.95392 0.93178 0.91022 0.88922 0.86877 0.84886 0.82946 0.81056 0.79215 0.77422 0.75675 0.73973 0.72315 0.70699 0.69124 0.6759 0.66095 0.64638 0.63218 0.56638 0.50842 0.45729 0.41213 0.37217 0.33675 0.3053 0.27733 0.25241 0.24776 0.22601 0.20655 0.18911 0.17344 0.15934 0.14662 0.13513 0.12473 0.10671 0.09178 0.0793 0.0688 0.05991 0.05233 0.04583 0.04024 0.0354 0.0312 0.02153 0.0169 0.0118 0.00931 0.00516 0.00287

20:80 Fitting

-1.73E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.3 6.4 6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.4 11.4 12.4 13.4 14.4 15.4 16.4 17.4 18.4 19.4 20.4 23.4 25.4 28.4 30.4 35.4 40.4

87

Time

1 0.98368 0.96765 0.95191 0.93645 0.92127 0.90636 0.89171 0.87733 0.8632 0.84933 0.8357 0.82231 0.80916 0.79624 0.78355 0.77108 0.75883 0.7468 0.73498 0.72336 0.66825 0.61776 0.57146 0.52898 0.48997 0.45412 0.42116 0.39083 0.3738 0.36831 0.34215 0.31803 0.29578 0.27524 0.25626 0.23871 0.22248 0.20745 0.18062 0.15755 0.13765 0.12045 0.10555 0.09262 0.08138 0.07158 0.06303 0.05555 0.03822 0.02989 0.02076 0.01632 0.00898 0.00497

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 5.6 5.9 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 23 25 28 30 35 40

2:98 Fitting

1 0.98792 0.97598 0.96419 0.95255 0.94105 0.92969 0.91847 0.90739 0.89645 0.88564 0.87496 0.86441 0.85399 0.8437 0.83354 0.8235 0.81359 0.80379 0.79412 0.78456 0.73851 0.6952 0.65447 0.61616 0.58013 0.54623 0.51434 0.50819 0.4902 0.48434 0.45611 0.42955 0.40456 0.38103 0.35889 0.33805 0.31844 0.29997 0.26623 0.23631 0.20979 0.18627 0.1654 0.14689 0.13047 0.1159 0.10296 0.09148 0.06419 0.0507 0.03561 0.02815 0.01565 0.00871

43 45 48 50

0.0013 42.7 0.00103 44.7 7.23766E-4 5.72995E-4 0.0027

0.0016 0.00127 47.7 49.7

43.6 0.00202 45.6 0.0016 8.9302E-4 7.06985E-4

43.4 45.4 48.6 50.6

0.00349 43 0.00276 45 0.00113 48.4 8.92855E-4

0.00613 0.00485 0.00194 48 0.00341 50.4 0.00154 50

S9.A Time

-1.73E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

CsS13C15N (4.0M)

CsSCN (4.0M)

0.99061 0.99999 0.99393 0.99503 0.97751 0.96711 0.94539 0.92892 0.90829 0.89162 0.87939 0.866 0.85863 0.8373 0.83012 0.82525 0.80797 0.80653 0.7975 0.78616 0.78283 0.77469 0.76905 0.76493 0.75428 0.75453 0.74646 0.74086 0.73247 0.72461 0.72134 0.7133 0.71224 0.70882 0.69822 0.70176 0.69361 0.69045 0.68644 0.68725 0.67437 0.67287 0.66603 0.66444 0.6624 0.6626 0.65825 0.6549 0.64727

1 0.992 0.96642 0.94391 0.92139 0.8933 0.87093 0.85626 0.84428 0.83036 0.81756 0.80141 0.79542 0.78194 0.77465 0.76498 0.75949 0.7525 0.74291 0.73513 0.72778 0.71902 0.71611 0.70963 0.70259 0.69853 0.6944 0.69264 0.67796 0.67559 0.67111 0.66387 0.66088 0.65099 0.64901 0.64556 0.6434 0.63611 0.63248 0.62883 0.6251 0.62438 0.61952 0.61975 0.61187 0.61113 0.60249 0.59779 0.59574

1 0.98557 0.97168 0.9583 0.94542 0.933 0.92104 0.9095 0.89837 0.88763 0.87726 0.86725 0.85758 0.84823 0.83919 0.83044 0.82198 0.81378 0.80585 0.79815 0.7907 0.78347 0.77645 0.76963 0.76302 0.75658 0.75033 0.74425 0.73833 0.73257 0.72696 0.72149 0.71616 0.71095 0.70588 0.70092 0.69608 0.69135 0.68672 0.68219 0.67776 0.67343 0.66918 0.66501 0.66093 0.65693 0.653 0.64914 0.64535

1 0.97949 0.96002 0.94152 0.92393 0.90721 0.8913 0.87617 0.86176 0.84804 0.83497 0.82251 0.81062 0.79927 0.78843 0.77808 0.76819 0.75873 0.74967 0.741 0.73269 0.72472 0.71707 0.70973 0.70268 0.6959 0.68938 0.6831 0.67705 0.67121 0.66558 0.66015 0.65489 0.64981 0.6449 0.64014 0.63552 0.63104 0.6267 0.62248 0.61837 0.61438 0.61049 0.6067 0.60301 0.5994 0.59588 0.59244 0.58908

88

CsSCN (4.0M) fitting

CsS13C15N (4.0M) fitting

4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.4 11.4 12.4 13.4 14.4 15.4 16.4 17.4 18.4 19.4 20.4 23.4 25.4 28.4 30.4 35.4 40.4 43.4 45.4 48.4 50.4 55.4 60.4 65.4 70.4 75.4 80.4 85.4 90.4 95.4 100.4 110.4 120.4 130.4 140.4 150.4 160.4 170.4 180.4

0.64367 0.59388 0.63876 0.58704 0.63094 0.58498 0.6297 0.58582 0.62668 0.5789 0.62626 0.57576 0.62244 0.57241 0.61795 0.56918 0.6153 0.56575 0.61155 0.56468 0.60908 0.55802 0.60358 0.55389 0.60131 0.54518 0.59854 0.54086 0.59455 0.53869 0.59019 0.53757 0.57528 0.52666 0.56041 0.51082 0.54802 0.49863 0.53859 0.48983 0.52363 0.47642 0.51481 0.46666 0.50043 0.45602 0.4871 0.44783 0.47077 0.43269 0.44779 0.42079 0.42761 0.40312 0.41093 0.38612 0.39091 0.37277 0.37798 0.35789 0.35898 0.34297 0.344 0.32862 0.32975 0.31567 0.3201 0.30427 0.28177 0.26779 0.25945 0.24708 0.22887 0.22256 0.21446 0.20437 0.17332 0.1691 0.14117 0.13858 0.12585 0.12241 0.11371 0.11477 0.10015 0.10402 0.09411 0.0965 0.07822 0.08154 0.06345 0.0687 0.0517 0.05512 0.04349 0.04398 0.03468 0.03758 0.02755 0.03067 0.02359 0.02483 0.0177 0.02181 0.01773 0.01735 0.01186 0.01581 0.00892 0.00954 0.00486 0.00717 0.0032 0.00424 0.00231 0.00319 0.0021 0.00198 0.002 0.00251 2.66458E-5 3.49317E-4

0.64163 0.58579 0.63797 0.58257 0.63438 0.57942 0.63084 0.57632 0.62736 0.57329 0.62393 0.57031 0.62055 0.56738 0.61723 0.56451 0.61395 0.56168 0.61072 0.5589 0.60754 0.55616 0.60439 0.55347 0.60129 0.55081 0.59823 0.54819 0.59521 0.54561 0.59222 0.54307 0.57781 0.5308 0.56416 0.51921 0.55115 0.50816 0.5387 0.49756 0.52673 0.48735 0.51518 0.47746 0.50401 0.46787 0.49318 0.45855 0.47244 0.44058 0.45275 0.42343 0.43401 0.40702 0.41613 0.39128 0.39902 0.37616 0.38266 0.36165 0.36698 0.3477 0.35196 0.3343 0.33756 0.32142 0.32376 0.30904 0.28567 0.27469 0.26282 0.25395 0.23193 0.22575 0.21338 0.20872 0.17328 0.17157 0.14073 0.14105 0.12422 0.12541 0.11431 0.11597 0.10091 0.10313 0.09287 0.09537 0.07546 0.07843 0.06132 0.06451 0.04984 0.05307 0.04052 0.04367 0.03294 0.03593 0.02679 0.02957 0.02179 0.02434 0.01772 0.02003 0.01442 0.01649 0.01173 0.01358 0.00777 0.00921 0.00515 0.00625 0.00342 0.00424 0.00227 0.00288 0.00151 0.00196 0.001 0.00133 0.00101 6.66238E-4 9.03071E-4 -1.32575E-4 4.43377E-4 6.13949E-4

89

190.4 200.4 210.4 220.4 230.4 240.4 250.4 260.4 270.4 280.4 290.4 300.4

8.86396E-5 0.00106 2.95461E-4 4.17716E-4 -0.00101 1.50992E-4 1.96849E-4 2.84117E-4 -2.17789E-4 -2.73453E-5 1.3142E-4 1.93507E-4 5.62622E-4 6.03644E-4 8.76534E-5 1.31644E-4 3.08E-4 -9.02703E-4 5.8579E-5 8.9727E-5 4.41828E-4 0.00187 3.92135E-5 6.1098E-5 -5.90912E-4 7.61252E-4 2.61383E-5 4.15737E-5 -0.00126 5.39724E-4 1.75621E-5 2.84455E-5 -9.76211E-4 6.39296E-4 1.18258E-5 1.93968E-5 -3.79586E-5 -2.42889E-4 7.92657E-6 1.32358E-5 9.57296E-4 -2.56858E-5 5.30815E-6 9.03338E-6 1.72827E-4 3.17378E-4 3.57504E-6 6.14259E-6

S9.B Time -1.73E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2

Flowing down

Pumping up

Flowing down fitting

2.20678E-4 -2.3E-4 -6.21021E-9 -4.34715E-9 -5.12791E-4 7.5835E-4 3.52483E-4 2.46738E-4 -0.00113 5.16516E-4 6.92448E-4 4.84713E-4 6.03542E-4 -6.34643E-5 0.00102 7.14406E-4 7.96585E-4 8.67241E-4 0.00134 9.36253E-4 4.61469E-4 4.86271E-4 0.00164 0.00115 0.00278 0.00214 0.00194 0.00136 0.00194 0.0045 0.00223 0.00156 0.00149 0.0026 0.0025 0.00175 0.0018 9.28908E-4 0.00277 0.00194 0.0026 9.94552E-4 0.00303 0.00212 0.00351 0.00355 0.00329 0.0023 0.00293 0.0025 0.00353 0.00247 0.00322 0.00314 0.00377 0.00264 0.00351 0.00295 0.004 0.0028 0.004 0.00475 0.00423 0.00296 0.00383 0.00424 0.00445 0.00312 0.00393 0.00421 0.00466 0.00327 0.00401 0.00476 0.00487 0.00341 0.00494 0.00389 0.00508 0.00355 0.00566 0.00518 0.00528 0.00369 0.00527 0.00578 0.00547 0.00383 0.00606 0.00423 0.00566 0.00396 0.00582 0.00497 0.00584 0.00409 0.00596 0.00505 0.00603 0.00422 0.00703 0.00596 0.0062 0.00434 0.00459 0.00421 0.00638 0.00446 0.00597 0.00568 0.00655 0.00458 0.00656 0.00516 0.00671 0.0047 0.00602 0.00675 0.00688 0.00481 0.00584 0.00913 0.00704 0.00492 0.00753 0.00497 0.00719 0.00503 0.00685 0.00704 0.00735 0.00514 0.00725 0.00594 0.0075 0.00525 0.0066 0.00556 0.00765 0.00535 0.00713 0.00583 0.00779 0.00545 0.00709 0.00555 0.00793 0.00555 0.00656 0.00606 0.00807 0.00565 0.00958 0.00676 0.00821 0.00575 0.00794 0.00578 0.00835 0.00584 0.0084 0.00632 0.00848 0.00594 0.00869 0.00744 0.00861 0.00603 0.00815 0.00739 0.00874 0.00612

90

Pumping up fitting

4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.4 11.4 12.4 13.4 14.4 15.4 16.4 17.4 18.4 19.4 20.4 23.4 25.4 28.4 30.4 35.4 40.4 43.4 45.4 48.4 50.4 55.4 60.4 65.4 70.4 75.4 80.4 85.4 90.4 95.4 100.4 110.4 120.4

0.00704 0.00937 0.01089 0.00965 0.00856 0.01014 0.0078 0.00952 0.00913 0.00969 0.00984 0.01038 0.0105 0.0106 0.0108 0.011 0.011 0.0112 0.011 0.0113 0.0112 0.01123 0.01116 0.01187 0.01215 0.01297 0.01347 0.01328 0.0138 0.0143 0.01531 0.01459 0.01555 0.01569 0.01689 0.01743 0.01576 0.01823 0.01744 0.01741 0.01739 0.01662 0.01739 0.01666 0.0163 0.01428 0.01329 0.01417 0.01303 0.01238 0.01138 0.01085 0.00967 0.0076 0.00743 0.00573 0.00591 0.00417 0.00412 0.00317 0.0035 0.00245

0.00926 0.00887 0.00791 0.009 0.00728 0.00912 0.00996 0.00924 0.00646 0.00936 0.00663 0.00948 0.00791 0.0096 0.00641 0.00972 0.00872 0.00983 0.01064 0.00994 0.00869 0.01005 0.00849 0.01016 0.00797 0.01027 0.0073 0.01038 0.00821 0.01048 0.00789 0.01058 0.01046 0.01069 0.00997 0.01079 0.00972 0.01089 0.0088 0.01099 0.00926 0.01108 0.00819 0.01118 0.0094 0.01164 0.01001 0.01208 0.00979 0.01249 0.00922 0.01287 0.01126 0.01324 0.01153 0.01358 0.01117 0.0139 0.01117 0.01421 0.01012 0.01476 0.0101 0.01524 0.011 0.01566 0.01149 0.01602 0.01169 0.01633 0.01034 0.01658 0.01148 0.01679 0.01124 0.01696 0.01157 0.01708 0.01204 0.01717 0.01227 0.01725 0.01085 0.01716 0.01204 0.01686 0.01145 0.01657 0.01014 0.01562 0.00949 0.01446 0.00941 0.01371 0.00859 0.0132 0.00744 0.01244 0.00842 0.01192 0.00816 0.01067 0.00701 0.00948 0.00484 0.00836 0.00428 0.00734 0.00401 0.00641 0.00339 0.00558 0.00223 0.00484 0.00184 0.00418 0.00212 0.0036 0.00222 0.0031 0.00141 0.00227 9.3125E-4

0.00621 0.0063 0.00639 0.00647 0.00656 0.00664 0.00672 0.0068 0.00688 0.00696 0.00704 0.00711 0.00719 0.00726 0.00734 0.00741 0.00748 0.00755 0.00762 0.00769 0.00776 0.00783 0.00815 0.00845 0.00874 0.00901 0.00927 0.00951 0.00973 0.00994 0.01033 0.01067 0.01096 0.01121 0.01143 0.01161 0.01175 0.01187 0.01196 0.01202 0.01207 0.01201 0.0118 0.0116 0.01093 0.01012 0.0096 0.00924 0.0087 0.00835 0.00747 0.00663 0.00586 0.00514 0.00449 0.00391 0.00339 0.00293 0.00252 0.00217 0.00159 0.00165 0.00116

91

130.4 140.4 150.4 160.4 170.4 180.4 190.4 200.4 210.4 220.4 230.4 240.4 250.4 260.4 270.4 280.4 290.4 300.4

4.86459E-4 3.75376E-4 0.0012 8.38018E-4 -2.69312E-4 -5.23368E-4 8.61541E-4 6.03078E-4 2.11112E-4 4.27663E-4 6.17142E-4 4.32003E-4 4.34838E-4 0.00102 4.40298E-4 3.08206E-4 -2.87387E-4 -4.711E-4 3.13036E-4 2.19132E-4 -8.42026E-4 -5.83669E-4 2.21856E-4 1.553E-4 -5.44902E-4 7.26113E-4 1.56833E-4 1.09788E-4 2.02766E-4 -1.15401E-4 1.10573E-4 7.74067E-5 1.11215E-4 -0.00103 7.78274E-5 5.44659E-5 -0.00115 1.31992E-4 5.46301E-5 3.82397E-5 4.35418E-4 2.12927E-4 3.83068E-5 2.68129E-5 -7.73923E-4 2.247E-4 2.68249E-5 1.87753E-5 -0.0012 -5.19215E-4 1.87249E-5 1.31128E-5 -4.05543E-4 6.95981E-4 1.30739E-5 9.15566E-6 -6.85267E-4 -4.09765E-4 9.13881E-6 6.40062E-6 1.19284E-4 -6.81693E-4 6.37076E-6 4.45808E-6 8.54916E-4 -1.9474E-4 4.43691E-6 3.09574E-6 4.05706E-4 0.00115 3.07511E-6 2.1719E-6

S9.C Time

100:0

-1.22E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6

1.00001 0.93366 0.93587 0.89079 0.84481 0.80297 0.78439 0.76643 0.725 0.69917 0.65636 0.63621 0.5893 0.58539 0.55751 0.55754 0.526 0.50866 0.49099 0.4609 0.45209 0.41866 0.42124 0.37847 0.38084 0.362 0.33597 0.34083 0.36103 0.32684 0.32563 0.31426 0.28744 0.31897 0.25131 0.24041 0.21157

Time

50:50

-1.29E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6

Time

1.00001 0.97467 0.92493 0.9119 0.88137 0.86481 0.83023 0.80494 0.77021 0.75031 0.74206 0.72481 0.68493 0.67654 0.64357 0.64829 0.60497 0.61717 0.58509 0.55367 0.55109 0.54521 0.51426 0.51603 0.49109 0.48847 0.4701 0.44723 0.4456 0.42941 0.44257 0.41657 0.39744 0.41309 0.37686 0.36694 0.35536

2:98

-1.22E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6

1.00003 0.97346 0.95004 0.94077 0.93326 0.9005 0.88307 0.84077 0.83059 0.81453 0.7832 0.78387 0.76877 0.76757 0.75227 0.72379 0.7044 0.68473 0.68254 0.6687 0.66503 0.65187 0.6368 0.61439 0.6095 0.6 0.59161 0.57909 0.57003 0.56561 0.52766 0.52067 0.51687 0.51604 0.49801 0.50714 0.48144

92

3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 6.3 6.8 7.3 7.8 8.3 8.8 9.3 9.8 10.8 11.8 12.8 13.8 14.8 15.8 16.8 17.8 18.8 19.8 22.8 24.8 27.8 29.8 34.8 39.8 42.8 44.8 47.8 49.8

0.22844 3.7 0.22524 3.8 0.21476 3.9 0.25836 4 0.21664 4.1 0.23061 4.2 0.16773 4.3 0.19821 4.4 0.16269 4.5 0.18384 4.6 0.17977 4.7 0.14893 4.8 0.12494 4.9 0.1532 5 0.15109 5.1 0.12991 5.2 0.14817 5.3 0.11726 5.4 0.1042 5.5 0.10946 5.6 0.0948 5.9 0.12234 6 0.09086 6.8 0.0971 7.3 0.05509 7.8 0.06123 8.3 0.04314 8.8 0.04034 9.3 0.03017 9.8 0.01859 10.3 0.03037 11.3 0.02417 12.3 -0.00226 13.3 -0.01609 14.3 -0.01603 15.3 -1.76883E-4 -0.01431 17.3 -0.00624 18.3 7.11557E-6 -0.01139 20.3 -0.01804 23.3 8.89263E-4 0.00557 28.3 0.01086 30.3 0.00726 35.3 -0.00119 40.3 -0.00977 43.3 0.01499 45.3 -1.39556E-7 0.00854 50.3

Time

100:0 Fitting

-1.22E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7

1 0.96388 0.9291 0.89561 0.86335 0.83228 0.80236 0.77354

Time

0.35916 3.7 0.48363 0.33496 3.8 0.45894 0.3513 3.9 0.45539 0.3317 4 0.4548 0.32754 4.1 0.44576 0.31011 4.2 0.44266 0.2983 4.3 0.42621 0.28091 4.4 0.40634 0.2746 4.5 0.39091 0.26513 4.6 0.3965 0.2653 4.7 0.39769 0.25576 4.8 0.38486 0.24909 4.9 0.37933 0.26081 5 0.3779 0.24709 5.1 0.37097 0.23569 5.2 0.37646 0.2118 5.3 0.36597 0.22133 5.4 0.34259 0.22217 5.5 0.33806 0.20011 5.6 0.338 0.1809 5.7 0.32689 0.19936 5.8 0.3382 0.16427 6.3 0.26941 0.1485 6.8 0.26173 0.12174 7.3 0.23556 0.11476 7.8 0.21453 0.09027 8.3 0.19897 0.08049 8.8 0.17473 0.07081 9.3 0.17251 0.0668 9.8 0.16211 0.03367 10.8 0.12019 0.02997 11.8 0.10907 0.01543 12.8 0.09134 0.00779 13.8 0.07479 0.01089 14.8 0.05403 16.3 -8.20367E-5 15.8 0.05251 -1.37113E-4 16.8 0.04143 -8.29697E-4 17.8 0.04601 19.3 0.00167 18.8 0.03681 -5.78117E-4 19.8 0.01329 -0.0032 22.8 0.01031 25.3 -0.00976 24.8 0.01504 -0.01446 27.8 7.576E-4 0.00193 29.8 -0.00501 -0.0111 34.8 -0.02907 -0.00304 39.8 -0.01997 0.0149 42.8 -0.01691 0.00491 44.8 -0.02514 48.3 -0.00273 47.8 -0.01527 0.00639 49.8 -0.04293 50:50 Fitting

-1.29E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7

1 0.97181 0.94443 0.91783 0.892 0.86691 0.84254 0.81887

Time

2:98 Fitting

-1.22E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7

1 0.97948 0.95938 0.93969 0.92041 0.90152 0.88302 0.8649

93

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 6.3 6.8 7.3 7.8 8.3 8.8 9.3 9.8 10.8 11.8 12.8

0.74579 0.71905 0.69331 0.66851 0.64462 0.62161 0.59944 0.57809 0.55752 0.53771 0.51862 0.50023 0.48251 0.46544 0.449 0.43315 0.41789 0.40318 0.389 0.37534 0.36218 0.3495 0.33728 0.3255 0.31414 0.3032 0.29266 0.2825 0.2727 0.26326 0.25415 0.24538 0.23692 0.22877 0.22091 0.21333 0.20602 0.19898 0.19218 0.18563 0.17932 0.17322 0.16735 0.16169 0.15622 0.15095 0.14587 0.14097 0.13624 0.13168 0.12728 0.10749 0.09094 0.07707 0.06544 0.05567 0.04745 0.04053 0.03468 0.02556 0.019 0.01424

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.9 6 6.8 7.3 7.8 8.3 8.8 9.3 9.8 10.3 11.3 12.3 13.3

0.79588 0.77355 0.75186 0.73079 0.71032 0.69044 0.67112 0.65236 0.63414 0.61643 0.59923 0.58252 0.56629 0.55052 0.5352 0.52031 0.50585 0.4918 0.47815 0.46489 0.452 0.43948 0.42731 0.41549 0.40401 0.39285 0.382 0.37147 0.36123 0.35128 0.34161 0.33221 0.32308 0.31421 0.30558 0.2972 0.28906 0.28114 0.27345 0.26597 0.25871 0.25164 0.24478 0.2381 0.23162 0.22531 0.21919 0.21323 0.20744 0.19102 0.18585 0.14934 0.13036 0.11386 0.0995 0.08701 0.07613 0.06666 0.0584 0.04491 0.03462 0.02676

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 6.3 6.8 7.3 7.8 8.3 8.8 9.3 9.8 10.8 11.8 12.8

0.84716 0.82978 0.81275 0.79608 0.77975 0.76375 0.74808 0.73274 0.71771 0.70299 0.68857 0.67444 0.66061 0.64706 0.63379 0.62079 0.60806 0.59559 0.58338 0.57142 0.5597 0.54822 0.53698 0.52597 0.51519 0.50463 0.49428 0.48415 0.47422 0.4645 0.45498 0.44565 0.43652 0.42757 0.41881 0.41022 0.40182 0.39358 0.38552 0.37761 0.36988 0.3623 0.35487 0.3476 0.34048 0.3335 0.32667 0.31998 0.31342 0.307 0.30071 0.27115 0.24449 0.22046 0.1988 0.17926 0.16165 0.14577 0.13145 0.1069 0.08694 0.07071

94

13.8 14.8 15.8 16.8 17.8 18.8 19.8 22.8 24.8 27.8 29.8 34.8 39.8 42.8 44.8 47.8 49.8

0.01076 14.3 0.0082 15.3 0.0063 16.3 0.00487 17.3 0.00379 18.3 0.00297 19.3 0.00234 20.3 0.00117 23.3 7.54782E-4 3.9571E-4 2.59352E-4 9.16589E-5 3.27765E-5 1.77293E-5 1.17766E-5 6.37878E-6 4.23947E-6

0.02074 0.01612 0.01256 0.00981 0.00768 0.00603 0.00474 0.00234 25.3 28.3 30.3 35.3 40.3 43.3 45.3 48.3 50.3

13.8 0.05751 14.8 0.04678 15.8 0.03805 16.8 0.03096 17.8 0.02518 18.8 0.02049 19.8 0.01667 22.8 0.00898 0.00148 24.8 7.52149E-4 4.83122E-4 1.63356E-4 5.65494E-5 3.01568E-5 1.98789E-5 1.06688E-5 7.05628E-6

0.00595 27.8 29.8 34.8 39.8 42.8 44.8 47.8 49.8

0.00321 0.00212 7.59256E-4 2.71647E-4 1.46669E-4 9.72652E-5 5.25385E-5 3.4851E-5

S10.A Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7

KS13C15N (1.8M)

KSCN (1.8M)

0.99763 1.00002 0.99023 0.97814 0.95952 0.94484 0.92391 0.90706 0.89446 0.88532 0.87592 0.86869 0.85949 0.85092 0.84349 0.83801 0.82328 0.82292 0.81346 0.80492 0.79692 0.79256 0.7858 0.78365 0.7818 0.78017 0.77708 0.76449 0.75942 0.75094 0.7442 0.74062 0.74289 0.73447 0.72857 0.7231 0.71755 0.71516

1 0.9915 0.98621 0.97082 0.95491 0.94479 0.93388 0.92064 0.90919 0.89854 0.88933 0.8748 0.86794 0.86421 0.85536 0.85309 0.84218 0.83028 0.82325 0.81971 0.81635 0.8186 0.80914 0.80339 0.7981 0.79493 0.78814 0.7816 0.78048 0.77213 0.7719 0.77359 0.76255 0.75559 0.75339 0.74983 0.73785 0.74744

1 0.98494 0.97067 0.95712 0.94426 0.93204 0.9204 0.90933 0.89877 0.88869 0.87906 0.86984 0.86102 0.85257 0.84446 0.83667 0.82917 0.82196 0.815 0.80829 0.80181 0.79554 0.78947 0.78359 0.77789 0.77234 0.76696 0.76171 0.7566 0.75162 0.74676 0.74201 0.73737 0.73283 0.72838 0.72401 0.71974 0.71554

1 0.98916 0.97863 0.96839 0.95843 0.94874 0.93931 0.93014 0.92122 0.91253 0.90406 0.89582 0.88779 0.87997 0.87234 0.8649 0.85765 0.85057 0.84367 0.83693 0.83035 0.82392 0.81764 0.81151 0.80551 0.79965 0.79392 0.78832 0.78283 0.77746 0.7722 0.76706 0.76201 0.75707 0.75223 0.74748 0.74283 0.73826

95

KSCN (1.8M) fitting

KS13C15N (1.8M) fitting

3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.1 5.6 6.4 6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.9 11.9 12.9 13.9 14.9 15.9 16.9 17.9 18.9 19.9 22.9 24.9 27.9 29.9 34.9 39.9 42.9 44.9 47.9 49.9 54.9 59.9 64.9 69.9 74.9 79.9 84.9 89.9 94.9 99.9 109.9 119.9 129.9 139.9 149.9 159.9 169.9 179.9 189.9 199.9

0.70969 0.74248 0.71141 0.73378 0.70786 0.73631 0.70735 0.72938 0.7031 0.73069 0.70336 0.72506 0.69582 0.72663 0.69944 0.72082 0.69572 0.72195 0.69557 0.71666 0.69214 0.71617 0.69175 0.71256 0.68931 0.71279 0.688 0.70854 0.67929 0.70719 0.68429 0.70458 0.68427 0.7048 0.68063 0.70069 0.67342 0.70176 0.67701 0.69687 0.67052 0.69331 0.67344 0.6931 0.66923 0.68916 0.66991 0.6894 0.64535 0.68802 0.66297 0.68216 0.63309 0.67102 0.64623 0.66499 0.62032 0.64802 0.62093 0.63984 0.5983 0.63518 0.60588 0.62534 0.58333 0.61842 0.59131 0.61163 0.56692 0.60812 0.57719 0.5986 0.55644 0.59898 0.56346 0.58616 0.54425 0.5861 0.55011 0.57424 0.52823 0.57111 0.5371 0.56279 0.51678 0.55906 0.52443 0.55175 0.49365 0.53985 0.5 0.53073 0.47336 0.51453 0.47675 0.51094 0.44131 0.50189 0.45459 0.49217 0.42687 0.48499 0.43347 0.47429 0.40231 0.46498 0.41334 0.4572 0.38561 0.44721 0.39415 0.44083 0.37459 0.43324 0.37585 0.4251 0.34905 0.41508 0.3584 0.40998 0.33717 0.39944 0.34176 0.39543 0.32291 0.38877 0.3259 0.38143 0.27723 0.34904 0.2826 0.34238 0.2559 0.32145 0.25698 0.31862 0.22197 0.28989 0.22285 0.28607 0.2039 0.26896 0.20266 0.26624 0.16001 0.22478 0.15983 0.22249 0.12611 0.18618 0.12606 0.18594 0.11266 0.16977 0.10934 0.16696 0.1035 0.1551 0.09944 0.15539 0.08833 0.14035 0.08625 0.13954 0.08256 0.13119 0.07845 0.12988 0.07024 0.11325 0.0619 0.10855 0.05244 0.09301 0.04884 0.09073 0.04099 0.08015 0.03855 0.07584 0.03138 0.06424 0.03042 0.06339 0.02765 0.05541 0.02402 0.05299 0.02178 0.04635 0.01896 0.0443 0.01707 0.03697 0.01497 0.03703 0.01166 0.02894 0.01182 0.03096 0.00752 0.02835 0.00934 0.02588 0.007 0.02076 0.00738 0.02164 0.00743 0.01666 0.00461 0.01512 0.00111 0.0117 0.00288 0.01057 0.00212 0.00548 0.0018 0.00739 0.00133 0.00546 0.00113 0.00517 -8.12127E-5 8.60769E-4 7.07547E-4 0.00361 -4.75198E-5 0.00304 4.44326E-4 0.00253 0.00182 -8.88804E-4 2.79208E-4 0.00177 8.08465E-4 -0.00103 1.75919E-4 0.00123 -7.1744E-4 -0.00235 1.10835E-4 8.63454E-4 -0.00262 -0.00137 7.01606E-5 6.03827E-4

96

209.9 219.9 229.9 239.9 249.9

3.69921E-4 8.65404E-4 4.42967E-5 4.22203E-4 -1.46705E-4 0.00102 2.82059E-5 2.95333E-4 0.00165 -2.55693E-4 1.79009E-5 2.06411E-4 -7.06388E-4 -0.00337 1.13613E-5 1.44491E-4 3.57425E-4 -8.20876E-4 7.36867E-6 1.01048E-4

S10.B Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

Flowing down

Pumping up

Flowing down fitting

-1.13E-4 1.57884E-4 0 0 5.20033E-4 3.87406E-4 2.18814E-4 1.53172E-4 -1.29E-4 0.00161 4.31899E-4 3.0234E-4 0.00127 8.08382E-4 6.39536E-4 4.47687E-4 -5.48279E-4 0.0019 8.41978E-4 5.89394E-4 0.00123 0.0014 0.00104 7.27634E-4 3.80467E-4 0.00149 0.00123 8.62563E-4 0.00127 0.00259 0.00142 9.94333E-4 -1.64792E-4 0.00246 0.0016 0.00112 -3.76821E-4 0.00266 0.00178 0.00125 -8.60494E-4 0.00442 0.00196 0.00137 0.00245 0.00368 0.00213 0.00149 4.64708E-4 0.00346 0.0023 0.00161 0.00158 0.00361 0.00247 0.00173 0.00408 0.00435 0.00263 0.00184 0.00259 0.00371 0.00279 0.00195 0.00434 0.0032 0.00294 0.00206 0.00102 0.00443 0.00309 0.00217 6.20315E-4 0.00426 0.00324 0.00227 8.2264E-4 0.00466 0.00339 0.00237 5.36347E-4 0.00413 0.00353 0.00247 0.00153 0.00476 0.00368 0.00257 0.0035 0.00542 0.00382 0.00267 0.0011 0.00567 0.00395 0.00277 0.00253 0.0053 0.00409 0.00286 0.00159 0.00538 0.00422 0.00295 0.00314 0.00495 0.00435 0.00304 0.00401 0.00592 0.00448 0.00313 0.00248 0.00522 0.0046 0.00322 0.00178 0.00526 0.00473 0.00331 0.00418 0.00603 0.00485 0.00339 0.00445 0.00461 0.00497 0.00348 0.00542 0.00358 0.00509 0.00356 0.00471 0.00531 0.0052 0.00364 0.0071 0.00605 0.00532 0.00372 0.00425 0.00478 0.00543 0.0038 0.0045 0.00665 0.00554 0.00388 0.00346 0.00553 0.00565 0.00396 0.00406 0.00619 0.00576 0.00403 0.00555 0.00539 0.00587 0.00411 0.0061 0.00569 0.00598 0.00418 0.00334 0.00657 0.00608 0.00426 0.0044 0.00691 0.00618 0.00433 0.00615 0.00647 0.00628 0.0044 0.00581 0.00685 0.00638 0.00447 0.00287 0.00619 0.00648 0.00454 0.0066 0.00643 0.00658 0.00461 0.00688 0.00542 0.00668 0.00467 0.00702 0.00569 0.00677 0.00474 0.00612 0.0063 0.00686 0.00481

97

Pumping up fitting

5.1 5.6 6.4 6.9 7.4 7.9 8.4 8.9 9.4 9.9 10.9 11.9 12.9 13.9 14.9 15.9 16.9 17.9 18.9 19.9 22.9 24.9 27.9 29.9 34.9 39.9 42.9 44.9 47.9 49.9 54.9 59.9 64.9 69.9 74.9 79.9 84.9 89.9 94.9 99.9 109.9 119.9 129.9 139.9 149.9 159.9 169.9 179.9 189.9 199.9 209.9 219.9 229.9 239.9 249.9

0.00776 0.0075 0.00705 0.00493 0.00507 0.00787 0.00749 0.00524 0.00793 0.00701 0.00814 0.0057 0.00756 0.0077 0.00851 0.00596 0.00823 0.00816 0.00886 0.0062 0.0074 0.00893 0.0092 0.00644 0.00908 0.00788 0.00951 0.00666 0.01111 0.00868 0.0098 0.00686 0.01076 0.00802 0.01008 0.00705 0.01037 0.00849 0.01034 0.00724 0.01136 0.00837 0.01081 0.00757 0.01019 0.00834 0.01122 0.00785 0.01178 0.00845 0.01158 0.00811 0.01208 0.00924 0.01189 0.00832 0.01139 0.00866 0.01215 0.00851 0.01289 0.00954 0.01238 0.00866 0.01295 0.00799 0.01256 0.00879 0.01181 0.0087 0.01271 0.0089 0.01182 0.00875 0.01282 0.00898 0.01182 0.00932 0.01291 0.00904 0.01173 0.00942 0.013 0.0091 0.01314 0.00869 0.01295 0.00907 0.01281 0.00872 0.01274 0.00892 0.01343 0.00845 0.01253 0.00877 0.01219 0.00839 0.01181 0.00827 0.0115 0.00629 0.01093 0.00765 0.01047 0.00719 0.01036 0.00725 0.01042 0.00677 0.00997 0.00698 0.00913 0.00585 0.00938 0.00657 0.00927 0.00675 0.00899 0.00629 0.00846 0.00583 0.00803 0.00562 0.00639 0.00421 0.00712 0.00498 0.00556 0.00413 0.00627 0.00439 0.00507 0.00344 0.0055 0.00385 0.00512 0.0036 0.0048 0.00336 0.00481 0.00191 0.00417 0.00292 0.00388 0.00207 0.00361 0.00252 0.00307 0.0023 0.00311 0.00218 0.00247 0.00258 0.00268 0.00188 0.00209 0.00163 0.0023 0.00161 0.00169 0.00135 0.00169 0.00118 -7.57099E-6 9.40166E-4 0.00123 8.58705E-4 7.28106E-4 0.00119 8.87582E-4 6.21285E-4 8.56983E-4 0.00105 6.39154E-4 4.47403E-4 -4.94226E-5 8.94217E-4 4.58443E-4 3.20912E-4 2.13404E-4 9.77246E-4 3.27743E-4 2.29419E-4 0.00123 2.02979E-4 2.33626E-4 1.63542E-4 4.70494E-4 -3.12061E-4 1.66153E-4 1.16308E-4 -5.791E-4 2.33428E-4 1.17906E-4 8.25387E-5 2.44488E-4 5.07285E-4 8.35428E-5 5.8473E-5 5.75289E-4 -3.82052E-4 5.9066E-5 4.13548E-5 8.80234E-4 5.54893E-4 4.17456E-5 2.92215E-5 1.54658E-4 8.51775E-4 2.94428E-5 2.0611E-5 3.52846E-4 -2.86148E-4 2.07314E-5 1.45299E-5 7.0935E-4 7.9703E-5 1.46329E-5 1.02435E-5

S10.C Time

100:0

Time

50:50

98

Time

2:98

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50 Time

1 0.95006 0.88114 0.89409 0.7502 0.75326 0.74391 0.68986 0.69291 0.6106 0.6234 0.59446 0.53409 0.50851 0.50443 0.49211 0.46463 0.42703 0.39197 0.41294 0.412 0.31557 0.27451 0.13554 0.20446 0.13854 0.08754 0.07531 0.0566 0.05397 0.08897 0.05397 0.01523 0.01083 0.05303 0.05374 0.04617 0.05694 0.01746 -0.01234 0.00394 -0.00411 0.03434 0.00937 -0.00491 0.0234 -0.01117 -0.03374 -0.00577 0.03737 0.01506 -0.00247 0.02003 -0.00363 -0.00631 0.00303 0.02531 0.02374 0.04211

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 4.8 4.9 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 23 25 28 30 35 40 43 45 48 50 100:0 Fitting

1 0 1.02589 0.1 1.06234 0.2 0.99163 0.3 0.93449 0.4 0.90197 0.5 0.91911 0.6 0.87109 0.7 0.79834 0.8 0.81537 0.9 0.75674 1 0.76689 1.1 0.75257 1.2 0.68829 1.3 0.66471 1.4 0.6902 1.5 0.64894 1.6 0.63534 1.7 0.62749 1.8 0.58546 1.9 0.62446 2 0.51746 2.5 0.49646 3 0.40257 3.5 0.34306 4 0.32249 4.5 0.304 5 0.30317 5.5 0.31086 6 0.25611 6.5 0.26163 7 0.22514 7.5 0.16311 8 0.13794 8.5 0.15929 9 0.13209 9.5 0.0806 10 0.10966 11 0.0984 12 0.08229 13 0.09186 14 0.02214 15 2.51827E-4 0.01851 17 0.01946 18 -0.00583 19 0.00171 20 -0.00631 22 0.01477 25 -0.00277 28 -0.00248 30 0.01377 33 0.01551 35 0.00414 38 0.00669 40 0.00631 43 0.02306 45 9.05863E-4 -0.00213 50 Time

0.99997 0.93606 0.81626 0.86663 0.8654 0.83309 0.7654 0.74406 0.80051 0.77111 0.71411 0.77086 0.78714 0.71249 0.74394 0.73483 0.61966 0.71866 0.68354 0.71031 0.66263 0.67023 0.63377 0.472 0.4752 0.38711 0.34743 0.30797 0.2628 0.23843 0.26663 0.24329 0.13709 0.14697 0.16286 0.13966 0.13154 0.06371 0.11171 0.08486 0.06806 0.07269 16 0.07411 0.1074 0.07811 0.05106 0.06283 0.00989 0.03571 0.02831 -0.01954 -0.03009 0.01611 0.00757 -0.03074 -0.0316 -0.0218 48 5.01969E-5 -0.02429 50:50 Fitting

99

Time

2:98 Fitting

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 22 25 28 30 33 35 38 40 43 45 48 50

1 0 0.96246 0.1 0.92642 0.2 0.89181 0.3 0.85858 0.4 0.82665 0.5 0.796 0.6 0.76655 0.7 0.73826 0.8 0.71108 0.9 0.68498 1 0.65989 1.1 0.63579 1.2 0.61263 1.3 0.59038 1.4 0.56899 1.5 0.54843 1.6 0.52867 1.7 0.50968 1.8 0.49142 1.9 0.47386 2 0.3957 2.5 0.33133 3 0.27822 3.5 0.2343 4 0.19788 4.5 0.16762 4.8 0.1424 4.9 0.12133 5 0.10368 5.5 0.08885 6 0.07635 6.5 0.06579 7 0.05684 7.5 0.04923 8 0.04274 8.5 0.03719 9 0.02835 9.5 0.02177 10 0.01684 11 0.0131 12 0.01024 13 0.00804 14 0.00634 15 0.00501 16 0.00397 17 0.00315 18 0.00199 19 0.00101 20 5.16221E-4 3.30224E-4 1.69196E-4 1.084E-4 30 5.56157E-5 3.56502E-5 1.82991E-5 1.1732E-5 6.02292E-6 3.86166E-6

1 0 1 0.97021 0.1 0.97771 0.94136 0.2 0.95592 0.9134 0.3 0.93461 0.88631 0.4 0.91378 0.86006 0.5 0.89342 0.83464 0.6 0.87351 0.80999 0.7 0.85405 0.78612 0.8 0.83502 0.76298 0.9 0.81642 0.74055 1 0.79824 0.71882 1.1 0.78046 0.69776 1.2 0.76307 0.67735 1.3 0.74608 0.65756 1.4 0.72947 0.63838 1.5 0.71322 0.61979 1.6 0.69734 0.60177 1.7 0.68182 0.5843 1.8 0.66664 0.56736 1.9 0.6518 0.55094 2 0.63729 0.47603 2.5 0.56947 0.41179 3 0.50888 0.35663 3.5 0.45476 0.30921 4 0.4064 0.26841 4.5 0.36321 0.2467 5 0.32461 0.23988 5.5 0.29013 0.23326 6 0.25932 0.20294 6.5 0.23178 0.17677 7 0.20718 0.15413 7.5 0.1852 0.13455 8 0.16555 0.11757 8.5 0.14799 0.10285 9 0.1323 0.09006 9.5 0.11827 0.07894 10 0.10574 0.06926 11 0.08452 0.06082 12 0.06756 0.04704 13 0.05402 0.0365 14 0.04319 0.02841 15 0.03453 0.02218 16 0.02762 0.01737 17 0.02209 0.01363 18 0.01766 0.01072 19 0.01413 0.00845 20 0.0113 0.00667 22 0.00723 0.00527 25 0.0037 23 0.00263 28 25 0.00166 30 28 8.40711E-4 5.3512E-4 35 35 1.7412E-4 40 5.69798E-5 43 2.91946E-5 45 1.87009E-5 48 9.59142E-6 50 6.14682E-6

0.0019 0.00122 33 6.22941E-4 3.99058E-4 38 2.04644E-4 40 1.31126E-4 43 6.72636E-5 45 4.31065E-5 48 2.21173E-5 50 1.41759E-5

100

S11.A Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12

KS13C15N (1.0M)

KSCN (1.0M)

0.99027 0.99999 0.99783 0.99049 0.95141 0.93526 0.92957 0.89894 0.88014 0.86089 0.84951 0.8385 0.82282 0.81626 0.80261 0.79766 0.78082 0.77914 0.76287 0.76593 0.74886 0.73563 0.73188 0.72714 0.7221 0.7207 0.71638 0.7035 0.69617 0.69747 0.68552 0.69312 0.6992 0.68483 0.67881 0.67806 0.67345 0.65879 0.66079 0.65051 0.6532 0.61036 0.60454 0.58538 0.56637 0.56134 0.53736 0.52174 0.50222 0.49121 0.47235 0.47073 0.45738 0.43643 0.40713

1 0.99017 0.98207 0.9618 0.94055 0.92325 0.91304 0.89959 0.88597 0.88337 0.86606 0.85856 0.84768 0.8435 0.8353 0.82428 0.81677 0.81227 0.807 0.80425 0.79249 0.78531 0.78724 0.77735 0.77667 0.76835 0.76277 0.76273 0.75473 0.74906 0.74326 0.73975 0.7305 0.72475 0.7218 0.71975 0.71721 0.70849 0.70206 0.70019 0.7003 0.68044 0.66101 0.63905 0.62806 0.6146 0.6027 0.58672 0.57361 0.56154 0.54919 0.53851 0.53 0.52186 0.5026

1 0.98201 0.96485 0.94848 0.93286 0.91794 0.9037 0.89008 0.87705 0.86459 0.85265 0.84121 0.83024 0.81972 0.80962 0.79992 0.79059 0.78163 0.77299 0.76467 0.75666 0.74892 0.74146 0.73425 0.72728 0.72054 0.71401 0.70768 0.70155 0.6956 0.68983 0.68422 0.67876 0.67345 0.66828 0.66324 0.65833 0.65354 0.64886 0.64429 0.63982 0.61884 0.59976 0.58219 0.56582 0.55042 0.53582 0.5219 0.50855 0.4957 0.4833 0.4713 0.45966 0.43737 0.41627

1 0.98435 0.96949 0.95537 0.94194 0.92916 0.91699 0.9054 0.89435 0.88382 0.87376 0.86415 0.85496 0.84617 0.83776 0.8297 0.82198 0.81456 0.80744 0.8006 0.79402 0.78768 0.78157 0.77568 0.77 0.76451 0.7592 0.75406 0.74909 0.74426 0.73958 0.73504 0.73062 0.72633 0.72215 0.71807 0.7141 0.71022 0.70643 0.70273 0.69911 0.68208 0.66651 0.65208 0.63852 0.62567 0.61338 0.60155 0.59012 0.57903 0.56823 0.5577 0.54741 0.52749 0.50837

101

KSCN (1.0M) fitting

KS13C15N (1.0M) fitting

13 14 15 16 17 18 19 20 23 25 28 30 35 40 43 45 48 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250

0.39213 0.4855 0.37553 0.4681 0.35936 0.44997 0.33738 0.4328 0.32392 0.41702 0.30641 0.4011 0.29449 0.386 0.27298 0.37356 0.23876 0.33418 0.21834 0.30966 0.18602 0.27925 0.16979 0.26215 0.13221 0.21654 0.10371 0.18224 0.09059 0.16415 0.07964 0.15246 0.07152 0.13646 0.06352 0.1276 0.05374 0.11186 0.04191 0.09073 0.03467 0.07688 0.02487 0.06445 0.01818 0.05364 0.01459 0.04585 0.01201 0.03859 0.00999 0.03263 0.00735 0.02688 0.00517 0.0222 0.00355 0.01633 0.00376 0.01174 0.00214 0.0082 2.82076E-4 3.93942E-4 -3.2635E-6 5.57667E-5 4.59095E-4 5.28503E-4 -3.51326E-4 -4.07957E-4 -2.29471E-4 -2.0012E-4 6.62507E-4 -2.04122E-4

0.39625 0.48999 0.37723 0.47229 0.35914 0.45524 0.34193 0.43882 0.32555 0.42299 0.30996 0.40773 0.29512 0.39303 0.28099 0.37886 0.24254 0.33934 0.21988 0.31531 0.18979 0.28242 0.17206 0.26243 0.13465 0.21842 0.10538 0.1818 0.09097 0.16284 0.08248 0.15132 0.0712 0.13554 0.06456 0.12595 0.05053 0.10483 0.03956 0.08726 0.03096 0.07263 0.02424 0.06046 0.01898 0.05033 0.01486 0.04189 0.01164 0.03487 0.00911 0.02903 0.00714 0.02417 0.00559 0.02012 0.00343 0.01394 0.00211 0.00966 0.00129 0.0067 0.00501 7.95392E-4 0.00464 0.00411 4.89212E-4 0.00322 0.00243 3.00999E-4 0.00223 0.0026 1.85514E-4 0.00154 0.00109 1.14273E-4 0.00107 6.70033E-4 7.06092E-5 7.42078E-4 0.00108 4.35326E-5 5.14225E-4 1.5807E-4 2.70345E-5 3.56529E-4 2.34261E-4 1.66546E-5 2.46996E-4 1.22817E-4 1.03659E-5 1.71303E-4 -2.50353E-4 6.48759E-6 1.18669E-4 -2.02352E-4 3.95996E-6 8.22421E-5

S11.B Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Flowing down 4.80041E-4 -6.99436E-4 2.37165E-4 3.38726E-4 3.23359E-4 7.52293E-4 5.68838E-4 -6.08961E-5 8.33584E-4 5.00952E-4 -5.77613E-4 0.00122 0.00124 0.00154 0.00234

Pumping up

-8.32068E-4 0 0 5.09048E-4 1.50342E-4 4.49636E-4 2.95613E-4 1.99578E-4 4.36098E-4 2.99164E-4 5.72059E-4 -3.26594E-4 7.03745E-4 3.77775E-4 8.31385E-4 4.45195E-4 9.55202E-4 0.00122 0.00108 7.52818E-4 0.0019 0.00119 8.3455E-4 0.00217 0.00131 9.14019E-4 0.00142 9.91349E-4 0.00152 0.00107

102

Flowing down fitting

1.05241E-4 2.06944E-4 3.05301E-4 4.00489E-4 4.92677E-4 5.82026E-4 6.68691E-4

Pumping up fitting

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 23 25 28 30 35 40 43 45 48 50 55 60

0.00195 0.00188 0.00316 0.00159 0.00169 0.00127 0.00221 0.00296 0.00194 0.00203 0.00207 0.00188 0.00156 0.00324 0.00241 0.00257 0.00284 0.00289 0.00239 0.00368 0.0021 0.00363 0.00312 0.00403 0.00277 0.00448 0.00323 0.00417 0.00512 0.00398 0.00599 0.00464 0.0059 0.00544 0.00589 0.00585 0.0067 0.00544 0.00589 0.00688 0.00714 0.0077 0.00716 0.00791 0.00795 0.00804 0.00748 0.00807 0.00748 0.008 0.00768 0.00759 0.00722 0.00722 0.0067 0.0059 0.00573 0.00498 0.00553 0.00524 0.00494 0.00401

0.00274 0.00305 0.00218 0.00199 0.00295 0.00199 0.00184 0.00223 0.00389 0.00288 0.00294 0.00338 0.00276 0.00239 0.00197 0.00211 0.0018 0.00232 0.00285 0.00252 0.0029 0.00278 0.00313 0.00338 0.00436 0.00251 0.00395 0.00197 0.00335 0.00309 0.00378 0.00361 0.00343 0.00446 0.00371 0.0043 0.00515 0.00498 0.0045 0.005 0.00525 0.00543 0.00511 0.0052 0.00496 0.0053 0.00524 0.0055 0.0049 0.00494 0.00549 0.00489 0.00515 0.00499 0.00452 0.0045 0.00393 0.00349 0.00415 0.00325 0.003 0.00248

0.00163 0.00173 0.00183 0.00193 0.00202 0.00212 0.00221 0.0023 0.00238 0.00247 0.00255 0.00263 0.00271 0.00279 0.00287 0.00295 0.00302 0.00309 0.00317 0.00324 0.00331 0.00338 0.00344 0.00351 0.00358 0.00364 0.0037 0.00377 0.00407 0.00435 0.00461 0.00486 0.0051 0.00532 0.00552 0.00572 0.0059 0.00608 0.00624 0.00639 0.00667 0.00691 0.00712 0.0073 0.00745 0.00758 0.00768 0.00776 0.00782 0.00786 0.00789 0.00784 0.00769 0.00754 0.00707 0.0065 0.00614 0.0059 0.00553 0.00529 0.0047 0.00414

0.00114 0.00121 0.00128 0.00135 0.00142 0.00148 0.00154 0.00161 0.00167 0.00173 0.00179 0.00184 0.0019 0.00195 0.00201 0.00206 0.00211 0.00217 0.00222 0.00227 0.00232 0.00236 0.00241 0.00246 0.0025 0.00255 0.00259 0.00264 0.00285 0.00305 0.00323 0.0034 0.00357 0.00372 0.00387 0.004 0.00413 0.00425 0.00437 0.00447 0.00467 0.00484 0.00498 0.00511 0.00522 0.00531 0.00538 0.00543 0.00548 0.0055 0.00552 0.00549 0.00538 0.00528 0.00495 0.00455 0.0043 0.00413 0.00387 0.0037 0.00329 0.0029

103

65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250

0.00381 0.00221 0.00363 0.00254 0.00273 0.00305 0.00316 0.00221 0.00223 0.00125 0.00275 0.00192 0.00183 0.00223 0.00237 0.00166 0.00127 0.00205 0.00204 0.00143 0.00115 0.00153 0.00175 0.00123 0.0013 0.00199 0.0015 0.00105 0.00141 9.99525E-4 0.00128 8.97764E-4 0.00107 6.13151E-4 9.30029E-4 6.50998E-4 8.10535E-4 7.42626E-4 6.6976E-4 4.68825E-4 3.83717E-4 2.94303E-4 4.79627E-4 3.35733E-4 -1.41823E-4 -3.29591E-4 3.41871E-4 2.39307E-4 -1.31815E-4 -2.86301E-5 2.42738E-4 1.69913E-4 6.25934E-4 7.58403E-4 1.71788E-4 1.20246E-4 5.17412E-4 -4.09829E-6 1.21244E-4 8.48714E-5 -3.65208E-7 -2.25435E-4 8.53616E-5 5.97606E-5 5.12629E-4 8.65237E-4 5.99887E-5 4.19979E-5 4.22378E-4 4.96664E-4 4.20724E-5 2.94524E-5 3.19677E-4 -3.63577E-4 2.94795E-5 2.06308E-5 -6.09744E-4 2.74745E-4 2.06089E-5 1.44311E-5 -1.08255E-4 8.30175E-4 1.44106E-5 1.0093E-5 3.81195E-4 -1.24638E-4 1.00626E-5 7.0388E-6 -9.52953E-5 -8.30005E-5 6.99815E-6 4.90849E-6

S11.C Time -1.65E-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.4 2.9 3.4 3.9 4.4 4.9 5.4 5.9 6.4 6.9 7.4 7.9 8.4

100:0 1 0.92774 0.84344 0.84952 0.85874 0.727 0.74496 0.73656 0.65719 0.68326 0.65807 0.54415 0.56811 0.621 0.6537 0.51593 0.47548 0.46863 0.54996 0.37441 0.40011 0.45107 0.34774 0.31756 0.2677 0.2147 0.13504 0.13119 0.15989 0.14778 0.08107 0.13004 0.08807

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2

Time 1 0.97937 0.94974 0.91593 0.86452 0.91581 0.83737 0.80993 0.77256 0.72896 0.73819 0.75804 0.72048 0.64056 0.67148 0.71574 0.66293 0.58419 0.68081 0.56167 0.5987 0.61885 0.54659 0.56452 0.52856 0.55474 0.46981 0.45752 0.46259 0.42067 0.42074 0.41904 0.48052

50:50 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.4 2.9 3.4 3.9 4.4 4.9 5.4 5.9 6.4 6.9 7.4 7.9 8.4

Time 0.99996 1.03893 0.85615 0.70767 0.72085 0.75411 0.78193 0.75174 0.66515 0.65881 0.53985 0.52156 0.72944 0.61589 0.65485 0.56178 0.5693 0.70956 0.51222 0.45456 0.39267 0.4663 0.39274 0.3297 0.27511 0.3643 0.36104 0.21259 0.18963 0.21107 0.15544 0.18096 0.20693

104

10:90

8.9 9.4 9.9 10.9 11.9 12.9 13.9 14.9 15.9 16.9 17.9 18.9 19.9 21.9 24.9 27.9 29.9 32.9 34.9 37.9 39.9 42.9 44.9 47.9 49.9

Time

-1.65E-6 0.50404 1.00808 1.51212 2.01616 2.5202 3.02424 3.52828

0.05978 0.03485 0.10744 0.01819 -0.05863 0.01048 -0.01722 0.0057 0.008 -0.02163 -0.0147 -0.033 -0.03104 -0.00519 -0.04359 -0.01589 0.01567 0.02781 -0.01756 0.00674 -0.07844 0.00793 -0.00108 0.03307 -0.00118

3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.8 6.3 6.8 7.3 7.8 8.3 8.8 9.3 10.3 11.3 12.3 13.3 14.3 15.3 16.3 17.3 18.3 19.3 22.3 24.3 27.3 29.3 34.3 39.3 42.3 44.3 47.3 49.3

100:0 Fitting

1 0.8365 0.70115 0.58895 0.49575 0.41822 0.35359 0.29961

0.40474 0.41526 0.38189 0.43404 0.34748 0.45378 0.43107 0.40804 0.38041 0.44078 0.33519 0.33893 0.31556 0.28522 0.255 0.26744 0.22622 0.33644 0.30037 0.31889 0.25604 0.27285 0.24004 0.18781 0.14204 0.17267 0.15763 0.11756 0.1047 0.13656 0.04119 0.04244 0.03463 0.06393 0.08522 0.02193 0.00822 0.03778 0.0263 0.02611 0.01963 0.03319 -0.01881 0.03993 0.02719 0.02296 0.02519 -0.0103 0.05822 Time

0 0.49798 0.99596 1.49394 1.99192 2.4899 2.98788 3.48586

1 0.86436 0.74783 0.64764 0.56142 0.48713 0.42308 0.36779

8.9 9.4 9.9 10.9 11.9 12.9 13.9 14.9 15.9 16.9 17.9 18.9 19.9 21.9 24.9 27.9 29.9 32.9 34.9 37.9 39.9 42.9 44.9 47.9 49.9

50:50 Fitting

0 0.50404 1.00808 1.51212 2.01616 2.5202 3.02424 3.52828

0.15963 0.15374 0.0687 0.10159 0.02552 -0.00589 0.06093 0.04267 0.04037 -0.02356 6.50444E-4 -0.07219 0.01096 0.01311 0.03933 -0.036 0.06626 0.04385 0.07111 0.07922 -3.02693E-5 0.02222 0.02559 -0.1033 0.03137

Time

1 0.8845 0.78249 0.69237 0.61275 0.54238 0.48018 0.42518

105

10:90 Fitting

4.03232 0.25444 3.98384 0.32002 4.03232 0.37654 4.53636 0.21656 4.48182 0.27871 4.53636 0.33352 5.0404 0.18473 4.9798 0.24295 5.0404 0.29546 5.54444 0.15793 5.47778 0.21197 5.54444 0.26178 6.04848 0.13531 5.97576 0.1851 6.04848 0.23198 6.55252 0.11617 6.47374 0.16177 6.55253 0.2056 7.05656 0.09995 6.97172 0.14149 7.05657 0.18224 7.5606 0.08617 7.4697 0.12386 7.56061 0.16156 8.06465 0.07443 7.96768 0.10851 8.06465 0.14325 8.56869 0.06442 8.46566 0.09514 8.56869 0.12702 9.07273 0.05585 8.96364 0.08347 9.07273 0.11265 9.57677 0.04851 9.46162 0.07329 9.57677 0.09992 10.08081 0.0422 9.9596 0.06439 10.08081 0.08864 10.58485 0.03677 10.45758 0.05662 10.58485 0.07863 11.08889 0.03209 10.95556 0.04981 11.08889 0.06977 11.59293 0.02805 11.45354 0.04385 11.59293 0.06191 12.09697 0.02454 11.95152 0.03863 12.09697 0.05494 12.60101 0.02151 12.44949 0.03405 12.60101 0.04876 13.10505 0.01887 12.94747 0.03002 13.10505 0.04328 13.60909 0.01657 13.44545 0.02649 13.60909 0.03842 14.11313 0.01457 13.94343 0.02339 14.11313 0.03411 14.61717 0.01282 14.44141 0.02066 14.61717 0.03029 15.12121 0.01129 14.93939 0.01825 15.12121 0.02689 15.62525 0.00996 15.43737 0.01614 15.62525 0.02388 16.12929 0.00878 15.93535 0.01427 16.12929 0.02121 16.63333 0.00775 16.43333 0.01263 16.63333 0.01883 17.13737 0.00685 16.93131 0.01118 17.13737 0.01673 17.64141 0.00606 17.42929 0.0099 17.64141 0.01486 18.14545 0.00536 17.92727 0.00877 18.14545 0.0132 18.64949 0.00474 18.42525 0.00777 18.64949 0.01173 19.15353 0.0042 18.92323 0.00689 19.15354 0.01042 19.65757 0.00372 19.42121 0.0061 19.65758 0.00926 20.16162 0.0033 19.91919 0.00541 20.16162 0.00823 20.66566 0.00292 20.41717 0.0048 20.66566 0.00731 21.1697 0.00259 20.91515 0.00426 21.1697 0.0065 21.67374 0.0023 21.41313 0.00378 21.67374 0.00577 22.17778 0.00204 21.91111 0.00336 22.17778 0.00513 22.68182 0.00181 22.40909 0.00298 22.68182 0.00456 23.18586 0.00161 22.90707 0.00265 23.18586 0.00405 23.6899 0.00143 23.40505 0.00235 23.6899 0.0036 24.19394 0.00127 23.90303 0.00209 24.19394 0.0032 24.69798 0.00113 24.40101 0.00186 24.69798 0.00285 25.20202 0.001 24.89899 0.00165 25.20202 0.00253 25.70606 8.88674E-4 25.39697 0.00147 25.70606 0.00225 26.2101 7.89788E-4 25.89495 0.00131 26.2101 0.002 26.71414 7.01995E-4 26.39293 0.00116 26.71414 0.00178 27.21818 6.24034E-4 26.89091 0.00103 27.21818 0.00158 27.72222 5.54789E-4 27.38889 9.18001E-4 27.72222 0.00141 28.22626 4.93276E-4 27.88687 8.16609E-4 28.22626 0.00125 28.7303 4.38622E-4 28.38485 7.26496E-4 28.7303 0.00111 29.23434 3.90055E-4 28.88283 6.46396E-4 29.23434 9.88675E-4 29.73838 3.4689E-4 29.38081 5.75184E-4 29.73838 8.79208E-4 30.24242 3.08523E-4 29.87879 5.11865E-4 30.24242 7.81885E-4 30.74646 2.74417E-4 30.37677 4.55557E-4 30.74646 6.95355E-4 31.2505 2.44094E-4 30.87475 4.05477E-4 31.25051 6.18418E-4 31.75454 2.17133E-4 31.37273 3.60931E-4 31.75455 5.50008E-4 32.25859 1.93158E-4 31.87071 3.21302E-4 32.25859 4.89178E-4 32.76263 1.71838E-4 32.36869 2.86044E-4 32.76263 4.35087E-4 33.26667 1.52877E-4 32.86667 2.54672E-4 33.26667 3.86985E-4 33.77071 1.36013E-4 33.36465 2.26755E-4 33.77071 3.4421E-4 34.27475 1.21013E-4 33.86263 2.01909E-4 34.27475 3.06169E-4 34.77879 1.0767E-4 34.36061 1.79796E-4 34.77879 2.72339E-4

106

35.28283 9.58012E-5 34.85859 1.60113E-4 35.28283 2.42251E-4 35.78687 8.52427E-5 35.35657 1.42592E-4 35.78687 2.15492E-4 36.29091 7.58494E-5 35.85455 1.26993E-4 36.29091 1.91692E-4 36.79495 6.74926E-5 36.35253 1.13106E-4 36.79495 1.70524E-4 37.29899 6.00575E-5 36.85051 1.00742E-4 37.29899 1.51696E-4 37.80303 5.34424E-5 37.34848 8.97325E-5 37.80303 1.34949E-4 38.30707 4.75567E-5 37.84646 7.99291E-5 38.30707 1.20053E-4 38.81111 4.23197E-5 38.34444 7.11991E-5 38.81111 1.06803E-4 39.31515 3.76599E-5 38.84242 6.34247E-5 39.31515 9.5017E-5 39.81919 3.35135E-5 39.3404 5.65008E-5 39.81919 8.45327E-5 40.32323 2.9824E-5 39.83838 5.03342E-5 40.32323 7.52063E-5 40.82727 2.65409E-5 40.33636 4.48418E-5 40.82727 6.69098E-5 41.33131 2.36194E-5 40.83434 3.99497E-5 41.33131 5.95293E-5 41.83535 2.10196E-5 41.33232 3.55922E-5 41.83535 5.29635E-5 42.33939 1.87062E-5 41.8303 3.17106E-5 42.33939 4.71226E-5 42.84343 1.66474E-5 42.32828 2.8253E-5 42.84343 4.19262E-5 43.34747 1.48154E-5 42.82626 2.51728E-5 43.34747 3.73033E-5 43.85151 1.3185E-5 43.32424 2.24289E-5 43.85152 3.31905E-5 44.35556 1.17341E-5 43.82222 1.99844E-5 44.35556 2.95315E-5 44.8596 1.04429E-5 44.3202 1.78066E-5 44.8596 2.62761E-5 45.36364 9.29381E-6 44.81818 1.58663E-5 45.36364 2.33798E-5 45.86768 8.2712E-6 45.31616 1.41377E-5 45.86768 2.08029E-5 46.37172 7.36113E-6 45.81414 1.25976E-5 46.37172 1.85102E-5 46.87576 6.55121E-6 46.31212 1.12254E-5 46.87576 1.64704E-5 47.3798 5.83042E-6 46.8101 1.00028E-5 47.3798 1.46554E-5 47.88384 5.18895E-6 47.30808 8.91342E-6 47.88384 1.30406E-5 48.38788 4.61807E-6 47.80606 7.94278E-6 48.38788 1.16038E-5 48.89192 4.11E-6 48.30404 7.07791E-6 48.89192 1.03254E-5 49.39596 3.65783E-6 48.80202 6.30727E-6 49.39596 9.18784E-6 49.9 3.25542E-6 49.3 5.62059E-6 49.9 8.1757E-6

107

References 1.

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3. 4. 5.

6. 7.

8. 9.

10. 11. 12.

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