Tunable Percolation in Semiconducting Binary Polymer Nanoparticle ...
SUPPORTING INFORMATION
Tunable Percolation in Semiconducting Binary Polymer Nanoparticle Glasses Lawrence A. Renna,† Monojit Bag,†,§ Timothy S. Gehan,† Xu Han,‡ Paul M. Lahti,† Dimitrios Maroudas,‡ D. Venkataraman*,† †
Department of Chemistry, University of Massachusetts Amherst, Amherst, Massachusetts 01003-9303, U.S.A.
‡
Department of Chemical Engineering, University of Massachusetts Amherst, Amherst, Massachusetts 01003-9303, U.S.A. §
Present Address: Department of Physics, Indian Institute of Technology Roorkee, Rookee 247667, Uttarakhand, India *(DV) E-mail [email protected]
ph. (413) 545-2028
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Figure S1. (a) NTA results showing the concentration (# nanoparticles /mL) vs. diameter (nm) of separate dispersions of post-polymerization miniemulsion prepared P3HT and PS nanoparticles. (b) Tapping mode AFM of P3HT and PS nanoparticles. (c) Average SAXS profile of drop-cast binary P3HT/PS polymer nanoparticle glass (η ~ 60%). The SAXS intensity pattern is shown in the inset.
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Figure S2. Height and current maps respectively for (a),(b), η = 20% (c),(d), η = 40% (e),(f), η = 60% (g),(h), η = 70% (i),(j), and η = 80%. S3
Figure S4. (a) Pair correlation function for simulated disordered nanoparticle network assemblies. The green dashed line marks d + δ. (b) fraction of particles on the surface of a simulated assembly that have at least one percolation pathway to the planar electrode for h = 2.5, 3.0 and 6.0 with respect to η (c), common distribution for coordination angle S4
between any three connected particles in a simulated nanoparticle network, the most common coordination angle is 60°, result is reproduced for all h and η. Distributions for number of contacts for (d) h = 2.5 , (e) h = 3.0, (f) h = 6.0 for η = 10% - 90%. Simulated average effective surface current distributions for (g) h = 6.0, (h) h = 2.5, (i) h = 3.0 for η = 10% - 90%.
Table S1. Fraction of Particles on the Surface of Simulated Assembly That Have at Least One Percolation Pathway to the Bottom Planar Electrode for h = 2.5, 3.0 and 6.0 with respect to η
η 10% 20% 30% 40% 50% 60% 70% 80% 90%
h = 2.5 0.027 ± 0.053 0.206 ± 0.046 0.402 ± 0.051 0.666 ± 0.048 0.846 ± 0.013 0.941 ± 0.003 0.982 ± 0.003 0.995 ± 0.0 0.999 ± 0.0
h = 3.0 0.004 ± 0.050 0.121 ± 0.062 0.281 ± 0.035 0.607 ± 0.042 0.822 ± 0.011 0.980 ± 0.005 0.980 ± 0.005 0.993 ± 0.002 0.998 ± 0.001
h = 6.0 0.0 ± 0.048 0.0 ±0.026 0.037 ± 0.041 0.380 ± 0.018 0.738 ± 0.029 0.971 ± 0.019 0.972 ± 0.001 0.989 ± 0.003 0.999 ± 0.0
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Table S2. Mode Number of Connections of Simulated Disordered Nanoparticle Networks for Nanoparticles for h = 2.5, 3.0 and 6.0 for η from 10% to 90%.
η 10% 20% 30% 40% 50% 60% 70% 80% 90%
h = 2.5 0.0 0.909 ± 0.07 1.606 ± 0.10 2.256 ± 0.08 2.921 ± 0.01 3.513 ± 0.14 3.974 ± 0.05 4.510 ± 0.14 5.102 ± 0.04
h = 3.0 0.0 0.984 ± 0.16 1.833 ± 0.04 2.489 ± 0.04 3.293 ± 0.01 3.846 ± 0.09 4.333 ± 0.08 4.727 ± 0.05 5.170 ± 0.01
h = 6.0 0.0 1.073 ± 0.11 1.910 ± 0341 2.651 ± 0.04 3.411 ± 0.03 4.168 ± 0.05 4.891 ± 0.06 5.615 ± 0.07 6.426 ± 0.06
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Figure S5. TOF transients and results from numerical simulations of TOF data. TOF transients measured at 2V, 3V, 5V, 7V, and 10V for nanoparticle films with (a) η = 40%, (b) η = 60%, and (c) η = 80%. Numerical simulations (red dashed lines) of TOF transients (black markers) from deterministic hole transport model at 2V and 3V for (d) η = 40%, (e) η = 60%, and (f) η = 80%. (g) Table of hole transport coefficients, kinetic
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parameters, and material properties derived from fitting modeling predictions. Where Cdt = C0 exp(-Etn/kBT) and Etn is the trap energy depth.
Figure S6. A visual representation of the tunability of percolation in binary polymer nanoparticle glasses. Top: Simulated assemblies of binary nanoparticle glasses at η = 20%, 60%, and 80%. Bottom: The insulating nanoparticles, colored grey on top, are removed to reveal the percolation network of conducting nanoparticles colored blue on top and bottom. This demonstrates how the structure of a polymer percolation network can be tuned by simply varying η.
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Tunable Percolation in Semiconducting Binary Polymer Nanoparticle Glasses Lawrence A. Renna,† Monojit Bag,†,§ Timothy S. Gehan,† Xu Han,‡ Paul M. Lahti,† Dimitrios Maroudas,‡ D. Venkataraman*,† †
Department of Chemistry, University of Massachusetts Amherst, Amherst, Massachusetts 01003-9303, U.S.A.
‡
Department of Chemical Engineering, University of Massachusetts Amherst, Amherst, Massachusetts 01003-9303, U.S.A. §
Present Address: Department of Physics, Indian Institute of Technology Roorkee, Rookee 247667, Uttarakhand, India *(DV) E-mail [email protected]
ph. (413) 545-2028
S1
Figure S1. (a) NTA results showing the concentration (# nanoparticles /mL) vs. diameter (nm) of separate dispersions of post-polymerization miniemulsion prepared P3HT and PS nanoparticles. (b) Tapping mode AFM of P3HT and PS nanoparticles. (c) Average SAXS profile of drop-cast binary P3HT/PS polymer nanoparticle glass (η ~ 60%). The SAXS intensity pattern is shown in the inset.
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Figure S2. Height and current maps respectively for (a),(b), η = 20% (c),(d), η = 40% (e),(f), η = 60% (g),(h), η = 70% (i),(j), and η = 80%. S3
Figure S4. (a) Pair correlation function for simulated disordered nanoparticle network assemblies. The green dashed line marks d + δ. (b) fraction of particles on the surface of a simulated assembly that have at least one percolation pathway to the planar electrode for h = 2.5, 3.0 and 6.0 with respect to η (c), common distribution for coordination angle S4
between any three connected particles in a simulated nanoparticle network, the most common coordination angle is 60°, result is reproduced for all h and η. Distributions for number of contacts for (d) h = 2.5 , (e) h = 3.0, (f) h = 6.0 for η = 10% - 90%. Simulated average effective surface current distributions for (g) h = 6.0, (h) h = 2.5, (i) h = 3.0 for η = 10% - 90%.
Table S1. Fraction of Particles on the Surface of Simulated Assembly That Have at Least One Percolation Pathway to the Bottom Planar Electrode for h = 2.5, 3.0 and 6.0 with respect to η
η 10% 20% 30% 40% 50% 60% 70% 80% 90%
h = 2.5 0.027 ± 0.053 0.206 ± 0.046 0.402 ± 0.051 0.666 ± 0.048 0.846 ± 0.013 0.941 ± 0.003 0.982 ± 0.003 0.995 ± 0.0 0.999 ± 0.0
h = 3.0 0.004 ± 0.050 0.121 ± 0.062 0.281 ± 0.035 0.607 ± 0.042 0.822 ± 0.011 0.980 ± 0.005 0.980 ± 0.005 0.993 ± 0.002 0.998 ± 0.001
h = 6.0 0.0 ± 0.048 0.0 ±0.026 0.037 ± 0.041 0.380 ± 0.018 0.738 ± 0.029 0.971 ± 0.019 0.972 ± 0.001 0.989 ± 0.003 0.999 ± 0.0
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Table S2. Mode Number of Connections of Simulated Disordered Nanoparticle Networks for Nanoparticles for h = 2.5, 3.0 and 6.0 for η from 10% to 90%.
η 10% 20% 30% 40% 50% 60% 70% 80% 90%
h = 2.5 0.0 0.909 ± 0.07 1.606 ± 0.10 2.256 ± 0.08 2.921 ± 0.01 3.513 ± 0.14 3.974 ± 0.05 4.510 ± 0.14 5.102 ± 0.04
h = 3.0 0.0 0.984 ± 0.16 1.833 ± 0.04 2.489 ± 0.04 3.293 ± 0.01 3.846 ± 0.09 4.333 ± 0.08 4.727 ± 0.05 5.170 ± 0.01
h = 6.0 0.0 1.073 ± 0.11 1.910 ± 0341 2.651 ± 0.04 3.411 ± 0.03 4.168 ± 0.05 4.891 ± 0.06 5.615 ± 0.07 6.426 ± 0.06
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Figure S5. TOF transients and results from numerical simulations of TOF data. TOF transients measured at 2V, 3V, 5V, 7V, and 10V for nanoparticle films with (a) η = 40%, (b) η = 60%, and (c) η = 80%. Numerical simulations (red dashed lines) of TOF transients (black markers) from deterministic hole transport model at 2V and 3V for (d) η = 40%, (e) η = 60%, and (f) η = 80%. (g) Table of hole transport coefficients, kinetic
S7
parameters, and material properties derived from fitting modeling predictions. Where Cdt = C0 exp(-Etn/kBT) and Etn is the trap energy depth.
Figure S6. A visual representation of the tunability of percolation in binary polymer nanoparticle glasses. Top: Simulated assemblies of binary nanoparticle glasses at η = 20%, 60%, and 80%. Bottom: The insulating nanoparticles, colored grey on top, are removed to reveal the percolation network of conducting nanoparticles colored blue on top and bottom. This demonstrates how the structure of a polymer percolation network can be tuned by simply varying η.
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