A Combined Kinetic and Thermodynamic ... - Wiley Online Library
DOI: 10.1002/chem.201300181
A Combined Kinetic and Thermodynamic Approach for the Interpretation of Continuous-Flow Heterogeneous Catalytic Processes Olga Bortolini,[a] Alberto Cavazzini,*[b] Pier Paolo Giovannini,[a] Roberto Greco,[b] Nicola Marchetti,[b] Alessandro Massi,*[a] and Luisa Pasti[b] Dedicated to Professor Alessandro Dondoni on the occasion of his retirement
Abstract: The heterogeneous prolinecatalyzed aldol reaction was investigated under continuous-flow conditions by means of a packed-bed microreactor. Reaction-progress kinetic analysis (RPKA) was used in combination with nonlinear chromatography for the interpretation, under synthetically relevant conditions, of important mechanistic aspects of the heterogeneous catalytic process at a molecular level. The
information gathered by RPKA and nonlinear chromatography proved to be highly complementary and allowed for the assessment of optimal operating variables. In particular, the determinaKeywords: aldol reaction · flow chemistry · heterogeneous catalysis · nonlinear chromatography · organocatalysis
Introduction Currently, continuous-flow microreactors are emerging as new synthetic platforms for the sustainable, safe, and intensified production of fine chemicals and pharmaceuticals.[1] In particular, heterogeneous catalysis under a flow regime provides a useful addition to microreactor technology and allows for simple product/catalyst separation, high resistance of supports to mechanical degradation, and long-term usage of (often costly) catalytic packing materials.[2] Very recently, organocatalytic packed-bed microreactors[3] have been demonstrated to show additional and unusual benefits, such as the absence of metal leaching and high levels of stereoselectivity in continuous-flow syntheses of valuable chiral molecules.[4] In those studies,[3, 4] operative flow conditions (feed composition and temperature) typically result from the direct translation of batch-mode conditions with only minor empirical adjustments. Furthermore, shorter (minutes versus [a] O. Bortolini, P. P. Giovannini, Dr. A. Massi Dipartimento di Scienze Chimiche e Farmaceutiche Laboratorio di Chimica Organica Universit di Ferrara, Via L. Borsari 46 44121 Ferrara (Italy) Fax: (+ 39) 0532-455183 E-mail: [email protected] [b] Dr. A. Cavazzini, R. Greco, N. Marchetti, L. Pasti Dipartimento di Scienze Chimiche e Farmaceutiche Laboratorio di Chimica Analitica Universit di Ferrara 44100 Ferrara (Italy) E-mail: [email protected] Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/chem.201300181.
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tion of the rate-determining step was pivotal for optimizing the feed composition. On the other hand, the competitive product inhibition was responsible for the unexpected decrease in the reaction yield following an apparently obvious variation in the feed composition. The study was facilitated by a suitable 2D instrumental arrangement for simultaneous flow reaction and online flow-injection analysis.
hours) residence/reaction times are normally detected in the flow regime to reach the same level of batch conversion. A rationalization for these observations, however, is generally not supported by a true understanding of the heterogeneous catalytic process. Indeed, although the microreactor inlet and outlet can be transparently examined during the course of the reaction, the catalytic bed is an opaque medium, which severely complicates the interpretation of the heterogeneous process. Therefore, despite some spectroscopic methods having been developed for in situ analysis of the active catalysts,[5] noninvasive and cost-effective measurements for investigating mechanism, kinetics, and thermodynamics of the process under the real working conditions are still a challenge. Herein, we propose a practical method to approach the above issues. This relies on the combination of reaction progress kinetic analysis (RPKA), a powerful methodology developed by Blackmond for the study of kinetic and mechanistic properties under synthetically relevant conditions,[6] and nonlinear chromatography tools (principally, frontal analysis measurements[7]) for the thermodynamic interpretation of the catalytic process in the flow regime. The data described herein finally show that merging kinetic and thermodynamic information with a deep understanding of mechanistic constraints might result in the effective design of productivity-enhancing improvements.
Results and Discussion The previously investigated[4a,d] heterogeneous proline-catalyzed continuous-flow aldol reaction of cyclohexanone (1)
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Scheme 1. Continuous-flow model aldol reaction.
with p-nitrobenzaldehyde (2) was considered as the benchmark for this proof-of-concept study. The generally accepted mechanism for the reaction in Scheme 1 involves the nucleophilic attack of silica-supported proline (3) on carbonyl compound 1 to form enamine 5, followed by its attack on electrophile 2 to yield product 4 with release of catalyst 3. The proposal of Scheme 1 simplifies the whole mechanistic picture as it omits the intrinsic effect of water within the catalytic cycle.[8] Accordingly, the possible kinetic role of added water, for which a negative order dependence was ascertained by Blackmond and coworkers in a similar process under homogeneous catalysis,[9] is not considered in the present study. Hence, the overall sequence of Scheme 1 appears reminiscent of the Michaelis–Menten enzymatic reaction for which the applicable rate expression might be written in power-law form as in Equation (1), in which the constant proline 3 concentration (i.e., the loaded amount of catalyst) has been grouped into the constant k*.
of the process and its long timescale. A suitable instrumental setup facilitated the experimental work because it allowed online monitoring by HPLC analysis with a high density of data collection. For the sake of validation, correlation between the measured reactant/product concentrations and reaction progress was also confirmed by discontinuous sampling and NMR spectroscopic analysis of the eluate. Figure 1 describes the whole 2D equipment for simultaneous flow-reaction and flow-injection analysis. Concisely (for a more detailed description, see the Supporting Information), in direction-1, the microreactor R (stainless-steel packed column, 100 2.1 mm) is connected to pump-1 through a mixer chamber. Channels A and B are used to deliver the solutions of 1 and 2 in toluene, respectively. The effluent from the microreactor is redirected to a 6-port 2-position switching valve. In direction-2, the binary pump-2 delivers a hexane/iPrOH solution into a hydrophilic interaction liquid chromatography (HILIC) column by passing through the switching valve. This is controlled by software and allows for the switching from the “load” position (Figure 1, lower left), in which the sampling loop (2–5) is filled with the effluent from the microreactor, to the “inject” position (Figure 1, lower right), for flushing the content of the loop into the HILIC column for fraction conversion determination. The main features of the packed-bed microreactor R (hold-up volume V0, total porosity, and loading of silica 3) were determined by pycnometry and elemental analysis (see the Supporting Information). They are summarized in Table 1. According to RPKA, the concentration dependencies and the stability of the catalytic system can be probed using the
Rate ¼ k½1x ½2y ½3 ¼ k* ½1x ½2y ð1Þ The determination of the reaction order and interpretation of the reaction mechanism by RPKA are, however, complicated by the heterogeneous nature
Figure 1. Scheme of the 2D instrumental setup for flow-reaction and flow-injection analysis. Top: Block diagram (R: microreactor; 6p2p valve: 6-port, 2-position switching valve). Bottom: Magnification on the 6-port 2position valve to show the “load” (left) and the “inject” (right) position.
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Table 1. Main features of microreactor R. Loading of 3 [mmol g1][a]
Amount of 3 [mg][b]
V0 VG Vbed t Total [mL][b] [mL][b,c] [mL][b,d] ACHTUNGRE[min][e] porosity[f]
0.81
190
230
346
110
46
0.67
[a] Determined by elemental analysis. [b] See the Supporting Information. [c] Geometric volume. [d] Vbed = VGV0. [e] Residence time calculated at 5 mL min1. [f] Total porosity etot = V0/VG.
“different excess” and “same excess” protocols, respectively.[6] In the context of RPKA, the term “excess” [e] defines the difference in initial concentrations of two reactants (i.e., [e] = [1]0[2]0).[6] In the case of heterogeneous reactions, the excess must refer to the system taken as a whole.[10] However, as long as mass transfer and adsorption–desorption processes are so rapid that a constant equilibrium state can be assumed between the bulk and the solid phase,[11] RPKA can be properly employed.[10] Table 2 reports the initial con-
Figure 2. Kinetic profile for the model aldol reaction carried out under conditions shown in Table 2 (entry 1). Diamonds: 2 (left y axis); circles: percentage fraction conversion (right y axis) estimated by HPLC (*) and NMR spectroscopy (*).
Table 2. Experimental conditions for reaction-progress kinetic analysis of continuous-flow proline 3-catalyzed aldol reaction of cyclohexanone 1 with aldehyde 2 at 25 8C in toluene.[a] Entry 1 2 3 4
[1]0 [m]
[2]0 [m]
Excess [m]
2.40 2.35 1.80 1.20
0.10 0.05 0.10 0.10
2.30 2.30 1.70 1.10
[a] See the Supporting Information for experimental procedures.
centrations of substrates 1 and 2 and the excess value for each of the four kinetic runs in this study. Reaction results for the illustrative first experiment are plotted in Figure 2 as conversion of 2 relative to residence time. Indeed, to the best of our knowledge, this study represents the first example of application of RPKA under heterogeneous flow conditions.[12] Thus, the curve of Figure 2 was obtained by measuring the steady-state conversion of different experiments performed with the same reactor and feed composition but at different flow rates.[13] The more informative rate versus [2] plot (Figure 3) was then generated by differentiation of the concentration profile of Figure 2; the same plot was also produced for run 2, which was performed at the half-life of run 1. The overlay in Figure 3 of these “same excess” experiments confirmed that the total concentration of active catalyst 3 remained constant during the continuous-flow process, and that the rate is not significantly influenced by product inhibition (at least under conditions of runs 1 and 2).[14] Reaction orders of reactants 1 and 2 were next determined by the “different excess” protocol. Accordingly, kinetic profiles were obtained for runs 3 and 4 and plotted as in Figure 4 (“normalized” rate versus concentration). While the overlay between the two curves showed first-order kinetics in the “normalized” substrate [1] (x = 1), the found
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Figure 3. Rate versus [2] for “same excess” experiments as given in Table 1 (*: entry 1; *: entry 2).
Figure 4. Rate/[1] versus 2 for “different excess” experiments as given in Table 2 (*: entry 3; *: entry 4).
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linear correlation reflected first-order kinetics in [2] (y = 1).[6] The catalytic network of Scheme 1 is suitably described by the full steady-state rate Equation (2), which is written in terms of the elementary-step rate constants. Rate ¼ k1 k2 ½1½2½3tot =ðk1 þ k1 ½1 þ k2 ½2Þ
½3tot ¼ ½3 þ ½5 ð2Þ
It becomes evident from the presence of the denominator term in Equation (2) that simple first-order dependence in the concentration of reactants cannot be assumed as a general result, and that the intrinsic kinetic role of both substrates can be quite complicated. Hence, following the approach described by Blackmond and co-workers in their batch study on a homogeneous proline-catalyzed aldol reaction,[9] a possible correlation between the theoretical steadystate and experimentally found power-law rate equations was considered in the two limiting cases in which: 1) the reaction that consumes enamine 5 is the slow step [in this case, Eq. (2) is reduced to Eq. (3)]; 2) the rate-determining step is the formation of enamine 5, and the unactivated catalyst 3 represents the “resting state” of the catalyst [Eq. (4)]. Rate ¼ k2 ½5½2
ð3Þ
Rate ¼ k1 ½1½3
ð4Þ
We shall see that the observed first-order dependence of rate on [1] and [2] is consistent only with Equation (3). Indeed, since for each molecule of cyclohexanone adsorbed on the immobilized proline (1ads), one molecule of enamine 5 is formed, Equation (3) can be recast in the form of Equation (5), provided that mass-transfer effects are negligible.[11] Rate ¼ k2 ½1ads ½2
ð5Þ
The importance of this formulation is that it establishes a connection between the measurable quantity [1ads] and the reaction rate. In fact, [1ads] can be measured through the (competitive) adsorption isotherm, which relates the adsorbed amount to the bulk fluid phase concentrations of substrates 1, 2, and even product 4, which is produced in the microreactor during the process.[7] Equation (5) thus gives an appropriate mathematical form to use in testing a proposed reaction rate expression. The basis for most analyses of this type is the Langmuir competitive isotherm [Eq. (6), in which qs = monolayer saturation capacity [m], a, b, c = adsorption equilibrium constants[15] for substrates 1, 2, and 4, respectively [m1]]. This model assumes that both 2 and product 4 might compete with 1 for the adsorption on the (homogeneous) silica surface.[16] The product terms, b[2] and c[4], quantify the competitive adsorption by 2 and 4.[17] ½1ads ¼ qs a½1=ð1 þ a½1 þ b½2 þ c½4Þ
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ð6Þ
If one assumes that, in the denominator of Equation (6), a[1] outweighs the other two product terms (which means the absence of competitive adsorption) and, simultaneously, that a[1] ! 1 (that is, [1] belongs to the linear range of the adsorption isotherm), [1ads] would be linearly proportional to the bulk concentration of cyclohexanone 1 ([1ads] = qsa[1]), and the rate Equation (5) would reduce to Equation (7) [k’2 = k2qsa], which is consistent with our experimental finding (first-order dependence in either reactants). Rate ¼ k0 2 ½1½2
ð7Þ
Thus, the validity of the assumptions that lead to simplified rate Equation (7) has been examined for the experimental conditions of Table 2 by a chromatographic study. Essentially, our scope is to test that competitive adsorption can be neglected and that the isotherm is linear. To this end, both linear measurements (namely, the retention factors of 1, 2, and 4 on the silica-supported proline 3 using toluene as eluent) and nonlinear measurements (i.e., the adsorption isotherm of cyclohexanone 1 from toluene on silica-supported proline 3)[18] were performed (details in the Supporting Information). Since, under the assumption of the same saturation factor, the ratio of the retention factors of two substrates corresponds to the ratio of their adsorption equilibrium constants,[19] the chromatographic study allows us to establish that the adsorption constant of 2 [b in Eq. (6)] is roughly twice that of 1 [a in Eq. (6)], and that c (the adsorption constant of product 4) is about four times larger than a. Accordingly, the denominator of Equation (6) can be rewritten as Equation (8), which has the advantage of permitting an easier comparison of the relative magnitude of the terms in brackets. 1 þ að½1 þ 2½2 þ 4½4Þ
ð8Þ
Since the concentration ratio of feed components [1]0/[2]0 was 18:1 and 12:1, respectively, for entries 3 and 4 of Table 2, the assumption that p-nitrobenzaldehyde 2 does not compete for the adsorption with cyclohexanone 1 (i.e., 2[2] ! [1]) appears to be entirely reasonable. As for the competitive adsorption by product 4, the situation is complicated by the fact that 4 is generated inside the reactor. RPKA, however, comes to our aid, as the “same excess” experiments excluded product inhibition (Figure 3). Inasmuch as the competitive adsorption by the product would reasonably be a source of catalyst deactivation, the conclusion that product 4 does not compete for the adsorption under the conditions of Table 2 would seem to be sound. Translated into a mathematical form, this means 4[4] ! [1]. A deeper examination of this last inequality is central to our subsequent rationalization, and it requires knowledge of fraction conversions. Under the conditions of Table 2, entry 3, a 52 % conversion is achieved with a residence time of 45 min.[20] Accordingly, [4] at the microreactor outlet is about 0.05 m, and the term 4[4], which we might refer to as the competition factor of product 4, results in roughly 10 %
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Table 3. Relationship between concentration of cyclohexanone 1 in the feed ([1]0) and amount of adsorbed cyclohexanone (1ads), relative surface coverage (q), and percentage fraction conversion (f). Process conditions: residence time, 45 min; constant ratio of feed concentrations, [1]0/[2]0 = 24:1. Entry 1 2 3 4 5 6 7 8 9
[1]0 [m] 0.2 0.6 1.2 1.8 2.4 3.6 4.0 4.4 5.0
1ads [mmol][a]
q[b]
f [%]
12 40 77 106 119 142 143 144 146
0.08 0.26 0.50 0.68 0.77 0.92 0.93 0.94 0.95
8 20 40 56 64 85 83 84 82
[a] Per reactor. Calculated by frontal analysis. [b] Calculated as the ratio between 1ads and the total amount of silica-supported proline 3 in the reactor (154 mmol). See the Supporting Information for details.
3.6), which indicates that saturation capacity has been reached (fractional surface coverage is given in column 4 of Table 3). Thus for [1]0 > 1.8, the simple kinetic model given by Equation (7) is not expected to hold any longer. Consequently, a series of ad hoc experiments were conducted to investigate the process outcome under these regimes (entries 5–9 in Table 3) and eventually find a correlation between the estimated surface coverage (Table 3, column 4) and fraction conversion (Table 3, column 5). In the concentration interval 1.8 < [1]0 < 3.6, the steadystate rate Equation (2) assumes the form given by Equation (9), since the competitive adsorption by both p-nitrobenzaldehyde 2 and product 4 can be neglected under the conditions of runs 4 and 5 of Table 3. The statement on [2] is justified by the strongly unfavorable 24:1 feed ratio [1]0/[2]0, whereas that on [4] comes from the consideration that the product term 4[4] is smaller than 10 % of [1]0, as it was in the case in which RPKA excluded product inhibition. Rate ¼ k0 2 ½1½2=ð1 þ a½1Þ
ð9Þ
Since the first-order dependence of [1] in the numerator is tempered by the concentration term in the denominator, the fraction conversion is expected to increase more slowly as [1]0 increases than in the linear range of the isotherm. This is demonstrated by the change in the slope of the plot of fraction conversion relative to [1]0 (dotted line in Figure 5), which drops from about 30 when [1]0 < 1.8 (Table 3, entries 1–4) to less than 15 if 1.8 < [1]0 < 3.6 (Table 3, entries 4–6). Finally, at the isotherm plateau (i.e., for [1]0 > 3.6), the fraction conversion is found to be practically constant (Table 3, entries 7–9). Figure 5. Adsorption isotherm of cyclohexanone from toluene on silicasupported proline 3 (*, left y axis) and percentage fraction conversion (*, right y axis) versus cyclohexanone concentration [1]0. Adsorbed concentration of cyclohexanone 1 ([1ads]) in micromole per microliter of packing (Vbed). Process conditions as in Table 3.
of the cyclohexanone concentration in the feed ([4]/[1]0 = 0.2:1.8). Thus, this simple reasoning will be employed as an indication for estimating the presence of competitive adsorption by the product (see below). The adsorption isotherm of cyclohexanone 1 (columns 2 and 3 in Table 3 and Figure 5) allowed us to evaluate the meaning of the last approximation introduced to obtain Equation (7) with regard to the linearity of the adsorption isotherm (or, a[1] ! 1). As the isotherm exhibits a substantially linear behavior until [1]0 = 1.8 m, the condition holds in the concentration ranges of entries 3 and 4 of Table 2. Hence, it is possible to conclude that under these conditions, the full steady-state rate Equation (2) simplifies to Equation (7), and that enamine addition to aldehyde is the ratedetermining step, which is in agreement with the homogeneous case.[9] By increasing the concentration of 1 in the feed above 1.8 m, however, the adsorption isotherm exhibits at first a curvature (for 1.8 < [1]0 < 3.6), and then it flattens out ([1]0 >
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Under these conditions, all the available silica-supported proline 3 is transformed to enamine 5 (Table 3, column 4), and any further increase in concentration (keeping the ratio [1]0/[2]0 and residence time constant) does not affect the conversion efficiency (Table 3, column 5). These considerations show that 3.6 m is the optimal cyclohexanone feed concentration for the reactor R employed in this work. The study was concluded with the evaluation of the optimal concentration of aldehyde 2 in the feed by performing different experiments in which [1]0 was kept constant at the 3.6 m value. After some experimentation, it turned out that [2]0 = 0.1 m furnished an almost quantitative conversion (f = 98 %). A full explanation of this result is not a trivial task, as it requires the modeling of the spatial and temporal distribution of the concentration profiles of all compounds (1, 2, and 4) between the bulk and the adsorbed phase inside the microreactor. This study is currently underway in our laboratories and will be the subject of a forthcoming publication.
Conclusion In this proof-of-concept study, we have proposed an innovative approach for the characterization of heterogeneous catalytic reactions in flow mode. In particular, we have focused
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on the proline-catalyzed aldol reaction, which has been extensively investigated under homogeneous batch conditions. Essentially, we have coupled the kinetic information that comes from the application of reaction-progress kinetic analysis (RPKA) with the thermodynamic information that results from nonlinear chromatographic measurements. Significantly, the two methodologies turned out to be strongly complementary and allowed for a clear understanding of important features of the heterogeneous continuous-flow process, such as the dependence of the reaction order on feed composition and saturation capacity of the catalytic bed.
[2] [3]
[4]
Experimental Section Microreactor packing: Microreactor R was fabricated by using a 100 2.1 mm stainless-steel column, which was filled with silica 3 by slurrypacking. Slurry-packing was performed under constant pressure (300 bar, 30 min, toluene as solvent) by using an air-driven liquid pump. The slurry was prepared by suspending an excess in weight of functionalized silica in toluene. Kinetic analysis: For the determination of reaction profiles at constant flow rate (reaction isotherm curve; Figure S2 in the Supporting Information), microreactor R was fed with a solution of 1 (2.40 m) and 2 (0.10 m) in toluene and operated at 25 8C for about 4 h at 2 mL min1. Fraction conversion was determined by online HPLC analysis (see Figure 1) and by 1H NMR spectroscopic analysis (a sample of the eluate was taken every 40 min). The collected solution at the steady-state regime was finally concentrated and eluted from a column of silica gel with 5:1 toluene/ AcOEt to give the corresponding mixture of anti/syn adducts 4. This kinetic study was repeated with the same feed composition but at different flow rates to determine the kinetic profile depicted in Figure 2. To complete the RPKA of the model reaction, the above approach was then applied to all the experiments of Table 2. Chromatographic measurements: The binary pump-2 delivered a hexanes/iPrOH 99.7:0.3 (v/v) solution into a 150 4.6 mm 5 mm-particle-diameter HILIC column by passing through the switching valve (see Figure 1). The flow rate along direction-2 was 1 mL min1. Under these conditions, the retention times of 2, syn-, and anti-aldol product were 2.3, 6.4, and 11.2 min, respectively. The detector was calibrated at 290 nm for both 2 and 4 (different calibration curves were employed depending on the concentration of cyclohexanone 1 in the feed). In separate experiments, microreactor R was used as a chromatographic column for determining the retention factors of 1, 2, and 4. The mobile phase was pure toluene. The adsorption isotherm of 1 on silica 3 was measured from toluene by frontal analysis (see the Supporting Information for details).
[5] [6]
[7]
[8]
[9] [10]
Acknowledgements We gratefully acknowledge the Italian Ministry of University and Scientific Research (Progetto PRIN grant nos. 2009ZSC5K2 004 and 20098SJX4F 004) for financial support. Thanks are also given to Mr. Paolo Formaglio for NMR spectroscopic experiments and to Mrs. Ercolina Bianchini for elemental analyses.
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[12] [13]
[14]
[15]
[16]
than one were obtained in confirmation that mass-transfer effects can be neglected. For reaction-progress kinetic analysis of the continuous-flow aldol reaction in a liquid–liquid microfluidic device, see reference [1c]. Achievement of the steady-state regime was assumed when constant reactants/product outlet concentrations accompanied by complete inlet mass recovery in the eluate were detected (see the reaction isotherm curve in the Supporting Information). Progressive loss of catalytic activity of the packing material 3 was observed at 25 8C after approximately 24 h on stream. For the utilization of the more stable 5-pyrrolidin-2-yl)tetrazole-functionalized silica in the same aldol process, see reference [4a]. Adsorption constants can be determined by chromatographic experiments. The chromatographic retention factor, kchrom, traditionally defined as the ratio between the correct retention time and the hold-up time, in fact, also corresponds to the product between the so-called Henry constant of adsorption (H) and the phase ratio, F (i.e., the ratio between the stationary and the mobile phase): kchrom = HF. In turn, H is the product between the saturation constant (achievable by the adsorption isotherm) and the equilibrium adsorption constant a (i.e., H = qsa). The assumption that only one type of adsorption site (namely, the catalytic sites) is present on the surface was verified by considering the retention behavior of cyclohexanone 1 on an alkylated silica gel (by TEC of mercaptopropyl thiol silica and 1-heptene) through a
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[17]
[18]
[19]
[20]
series of dedicated HPLC experiments using toluene as the eluent. See the Supporting Information for details. Incidentally, we want to remark here that, also in steady-state conditions, [1] and [2] in Equation (6) do not correspond to the feed concentrations [1]0 and [2]0 since the system is reactive. This is a necessary simplification. Equation (6) is in fact a competitive adsorption isotherm. Accordingly, the amount of adsorbed cyclohexanone should not be a function of only its bulk concentration (as we are assuming here) but also of the concentration of 2 and 4. Nevertheless, as the system is reactive, the competitive isotherm of 1 cannot be experimentally measured. In light of the excess amount of 1 with respect to 2 and 4, however, this appears a physically sound approximation at this stage of the study. By assuming the same saturation capacity for 1, 2, and 4 (which is reasonable in light of their similar molecular dimensions), the ratio of retention factors correspond to the ratio of the adsorption equilibrium constants, the phase ratio F being the same in all the cases (see also ref. [15]). The retention factors for 1, 2, and 4, using toluene as eluent, were 0.52, 1.10, and 2.10, respectively (see the Supporting Information). Since the reaction studied in this work is quite slow, a residence time of 45 min was taken for these experiments as a reasonable compromise between fraction conversion and analysis time.
2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Received: January 17, 2013 Published online: April 15, 2013
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A Combined Kinetic and Thermodynamic Approach for the Interpretation of Continuous-Flow Heterogeneous Catalytic Processes Olga Bortolini,[a] Alberto Cavazzini,*[b] Pier Paolo Giovannini,[a] Roberto Greco,[b] Nicola Marchetti,[b] Alessandro Massi,*[a] and Luisa Pasti[b] Dedicated to Professor Alessandro Dondoni on the occasion of his retirement
Abstract: The heterogeneous prolinecatalyzed aldol reaction was investigated under continuous-flow conditions by means of a packed-bed microreactor. Reaction-progress kinetic analysis (RPKA) was used in combination with nonlinear chromatography for the interpretation, under synthetically relevant conditions, of important mechanistic aspects of the heterogeneous catalytic process at a molecular level. The
information gathered by RPKA and nonlinear chromatography proved to be highly complementary and allowed for the assessment of optimal operating variables. In particular, the determinaKeywords: aldol reaction · flow chemistry · heterogeneous catalysis · nonlinear chromatography · organocatalysis
Introduction Currently, continuous-flow microreactors are emerging as new synthetic platforms for the sustainable, safe, and intensified production of fine chemicals and pharmaceuticals.[1] In particular, heterogeneous catalysis under a flow regime provides a useful addition to microreactor technology and allows for simple product/catalyst separation, high resistance of supports to mechanical degradation, and long-term usage of (often costly) catalytic packing materials.[2] Very recently, organocatalytic packed-bed microreactors[3] have been demonstrated to show additional and unusual benefits, such as the absence of metal leaching and high levels of stereoselectivity in continuous-flow syntheses of valuable chiral molecules.[4] In those studies,[3, 4] operative flow conditions (feed composition and temperature) typically result from the direct translation of batch-mode conditions with only minor empirical adjustments. Furthermore, shorter (minutes versus [a] O. Bortolini, P. P. Giovannini, Dr. A. Massi Dipartimento di Scienze Chimiche e Farmaceutiche Laboratorio di Chimica Organica Universit di Ferrara, Via L. Borsari 46 44121 Ferrara (Italy) Fax: (+ 39) 0532-455183 E-mail: [email protected] [b] Dr. A. Cavazzini, R. Greco, N. Marchetti, L. Pasti Dipartimento di Scienze Chimiche e Farmaceutiche Laboratorio di Chimica Analitica Universit di Ferrara 44100 Ferrara (Italy) E-mail: [email protected] Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/chem.201300181.
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tion of the rate-determining step was pivotal for optimizing the feed composition. On the other hand, the competitive product inhibition was responsible for the unexpected decrease in the reaction yield following an apparently obvious variation in the feed composition. The study was facilitated by a suitable 2D instrumental arrangement for simultaneous flow reaction and online flow-injection analysis.
hours) residence/reaction times are normally detected in the flow regime to reach the same level of batch conversion. A rationalization for these observations, however, is generally not supported by a true understanding of the heterogeneous catalytic process. Indeed, although the microreactor inlet and outlet can be transparently examined during the course of the reaction, the catalytic bed is an opaque medium, which severely complicates the interpretation of the heterogeneous process. Therefore, despite some spectroscopic methods having been developed for in situ analysis of the active catalysts,[5] noninvasive and cost-effective measurements for investigating mechanism, kinetics, and thermodynamics of the process under the real working conditions are still a challenge. Herein, we propose a practical method to approach the above issues. This relies on the combination of reaction progress kinetic analysis (RPKA), a powerful methodology developed by Blackmond for the study of kinetic and mechanistic properties under synthetically relevant conditions,[6] and nonlinear chromatography tools (principally, frontal analysis measurements[7]) for the thermodynamic interpretation of the catalytic process in the flow regime. The data described herein finally show that merging kinetic and thermodynamic information with a deep understanding of mechanistic constraints might result in the effective design of productivity-enhancing improvements.
Results and Discussion The previously investigated[4a,d] heterogeneous proline-catalyzed continuous-flow aldol reaction of cyclohexanone (1)
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Scheme 1. Continuous-flow model aldol reaction.
with p-nitrobenzaldehyde (2) was considered as the benchmark for this proof-of-concept study. The generally accepted mechanism for the reaction in Scheme 1 involves the nucleophilic attack of silica-supported proline (3) on carbonyl compound 1 to form enamine 5, followed by its attack on electrophile 2 to yield product 4 with release of catalyst 3. The proposal of Scheme 1 simplifies the whole mechanistic picture as it omits the intrinsic effect of water within the catalytic cycle.[8] Accordingly, the possible kinetic role of added water, for which a negative order dependence was ascertained by Blackmond and coworkers in a similar process under homogeneous catalysis,[9] is not considered in the present study. Hence, the overall sequence of Scheme 1 appears reminiscent of the Michaelis–Menten enzymatic reaction for which the applicable rate expression might be written in power-law form as in Equation (1), in which the constant proline 3 concentration (i.e., the loaded amount of catalyst) has been grouped into the constant k*.
of the process and its long timescale. A suitable instrumental setup facilitated the experimental work because it allowed online monitoring by HPLC analysis with a high density of data collection. For the sake of validation, correlation between the measured reactant/product concentrations and reaction progress was also confirmed by discontinuous sampling and NMR spectroscopic analysis of the eluate. Figure 1 describes the whole 2D equipment for simultaneous flow-reaction and flow-injection analysis. Concisely (for a more detailed description, see the Supporting Information), in direction-1, the microreactor R (stainless-steel packed column, 100 2.1 mm) is connected to pump-1 through a mixer chamber. Channels A and B are used to deliver the solutions of 1 and 2 in toluene, respectively. The effluent from the microreactor is redirected to a 6-port 2-position switching valve. In direction-2, the binary pump-2 delivers a hexane/iPrOH solution into a hydrophilic interaction liquid chromatography (HILIC) column by passing through the switching valve. This is controlled by software and allows for the switching from the “load” position (Figure 1, lower left), in which the sampling loop (2–5) is filled with the effluent from the microreactor, to the “inject” position (Figure 1, lower right), for flushing the content of the loop into the HILIC column for fraction conversion determination. The main features of the packed-bed microreactor R (hold-up volume V0, total porosity, and loading of silica 3) were determined by pycnometry and elemental analysis (see the Supporting Information). They are summarized in Table 1. According to RPKA, the concentration dependencies and the stability of the catalytic system can be probed using the
Rate ¼ k½1x ½2y ½3 ¼ k* ½1x ½2y ð1Þ The determination of the reaction order and interpretation of the reaction mechanism by RPKA are, however, complicated by the heterogeneous nature
Figure 1. Scheme of the 2D instrumental setup for flow-reaction and flow-injection analysis. Top: Block diagram (R: microreactor; 6p2p valve: 6-port, 2-position switching valve). Bottom: Magnification on the 6-port 2position valve to show the “load” (left) and the “inject” (right) position.
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Table 1. Main features of microreactor R. Loading of 3 [mmol g1][a]
Amount of 3 [mg][b]
V0 VG Vbed t Total [mL][b] [mL][b,c] [mL][b,d] ACHTUNGRE[min][e] porosity[f]
0.81
190
230
346
110
46
0.67
[a] Determined by elemental analysis. [b] See the Supporting Information. [c] Geometric volume. [d] Vbed = VGV0. [e] Residence time calculated at 5 mL min1. [f] Total porosity etot = V0/VG.
“different excess” and “same excess” protocols, respectively.[6] In the context of RPKA, the term “excess” [e] defines the difference in initial concentrations of two reactants (i.e., [e] = [1]0[2]0).[6] In the case of heterogeneous reactions, the excess must refer to the system taken as a whole.[10] However, as long as mass transfer and adsorption–desorption processes are so rapid that a constant equilibrium state can be assumed between the bulk and the solid phase,[11] RPKA can be properly employed.[10] Table 2 reports the initial con-
Figure 2. Kinetic profile for the model aldol reaction carried out under conditions shown in Table 2 (entry 1). Diamonds: 2 (left y axis); circles: percentage fraction conversion (right y axis) estimated by HPLC (*) and NMR spectroscopy (*).
Table 2. Experimental conditions for reaction-progress kinetic analysis of continuous-flow proline 3-catalyzed aldol reaction of cyclohexanone 1 with aldehyde 2 at 25 8C in toluene.[a] Entry 1 2 3 4
[1]0 [m]
[2]0 [m]
Excess [m]
2.40 2.35 1.80 1.20
0.10 0.05 0.10 0.10
2.30 2.30 1.70 1.10
[a] See the Supporting Information for experimental procedures.
centrations of substrates 1 and 2 and the excess value for each of the four kinetic runs in this study. Reaction results for the illustrative first experiment are plotted in Figure 2 as conversion of 2 relative to residence time. Indeed, to the best of our knowledge, this study represents the first example of application of RPKA under heterogeneous flow conditions.[12] Thus, the curve of Figure 2 was obtained by measuring the steady-state conversion of different experiments performed with the same reactor and feed composition but at different flow rates.[13] The more informative rate versus [2] plot (Figure 3) was then generated by differentiation of the concentration profile of Figure 2; the same plot was also produced for run 2, which was performed at the half-life of run 1. The overlay in Figure 3 of these “same excess” experiments confirmed that the total concentration of active catalyst 3 remained constant during the continuous-flow process, and that the rate is not significantly influenced by product inhibition (at least under conditions of runs 1 and 2).[14] Reaction orders of reactants 1 and 2 were next determined by the “different excess” protocol. Accordingly, kinetic profiles were obtained for runs 3 and 4 and plotted as in Figure 4 (“normalized” rate versus concentration). While the overlay between the two curves showed first-order kinetics in the “normalized” substrate [1] (x = 1), the found
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Figure 3. Rate versus [2] for “same excess” experiments as given in Table 1 (*: entry 1; *: entry 2).
Figure 4. Rate/[1] versus 2 for “different excess” experiments as given in Table 2 (*: entry 3; *: entry 4).
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linear correlation reflected first-order kinetics in [2] (y = 1).[6] The catalytic network of Scheme 1 is suitably described by the full steady-state rate Equation (2), which is written in terms of the elementary-step rate constants. Rate ¼ k1 k2 ½1½2½3tot =ðk1 þ k1 ½1 þ k2 ½2Þ
½3tot ¼ ½3 þ ½5 ð2Þ
It becomes evident from the presence of the denominator term in Equation (2) that simple first-order dependence in the concentration of reactants cannot be assumed as a general result, and that the intrinsic kinetic role of both substrates can be quite complicated. Hence, following the approach described by Blackmond and co-workers in their batch study on a homogeneous proline-catalyzed aldol reaction,[9] a possible correlation between the theoretical steadystate and experimentally found power-law rate equations was considered in the two limiting cases in which: 1) the reaction that consumes enamine 5 is the slow step [in this case, Eq. (2) is reduced to Eq. (3)]; 2) the rate-determining step is the formation of enamine 5, and the unactivated catalyst 3 represents the “resting state” of the catalyst [Eq. (4)]. Rate ¼ k2 ½5½2
ð3Þ
Rate ¼ k1 ½1½3
ð4Þ
We shall see that the observed first-order dependence of rate on [1] and [2] is consistent only with Equation (3). Indeed, since for each molecule of cyclohexanone adsorbed on the immobilized proline (1ads), one molecule of enamine 5 is formed, Equation (3) can be recast in the form of Equation (5), provided that mass-transfer effects are negligible.[11] Rate ¼ k2 ½1ads ½2
ð5Þ
The importance of this formulation is that it establishes a connection between the measurable quantity [1ads] and the reaction rate. In fact, [1ads] can be measured through the (competitive) adsorption isotherm, which relates the adsorbed amount to the bulk fluid phase concentrations of substrates 1, 2, and even product 4, which is produced in the microreactor during the process.[7] Equation (5) thus gives an appropriate mathematical form to use in testing a proposed reaction rate expression. The basis for most analyses of this type is the Langmuir competitive isotherm [Eq. (6), in which qs = monolayer saturation capacity [m], a, b, c = adsorption equilibrium constants[15] for substrates 1, 2, and 4, respectively [m1]]. This model assumes that both 2 and product 4 might compete with 1 for the adsorption on the (homogeneous) silica surface.[16] The product terms, b[2] and c[4], quantify the competitive adsorption by 2 and 4.[17] ½1ads ¼ qs a½1=ð1 þ a½1 þ b½2 þ c½4Þ
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ð6Þ
If one assumes that, in the denominator of Equation (6), a[1] outweighs the other two product terms (which means the absence of competitive adsorption) and, simultaneously, that a[1] ! 1 (that is, [1] belongs to the linear range of the adsorption isotherm), [1ads] would be linearly proportional to the bulk concentration of cyclohexanone 1 ([1ads] = qsa[1]), and the rate Equation (5) would reduce to Equation (7) [k’2 = k2qsa], which is consistent with our experimental finding (first-order dependence in either reactants). Rate ¼ k0 2 ½1½2
ð7Þ
Thus, the validity of the assumptions that lead to simplified rate Equation (7) has been examined for the experimental conditions of Table 2 by a chromatographic study. Essentially, our scope is to test that competitive adsorption can be neglected and that the isotherm is linear. To this end, both linear measurements (namely, the retention factors of 1, 2, and 4 on the silica-supported proline 3 using toluene as eluent) and nonlinear measurements (i.e., the adsorption isotherm of cyclohexanone 1 from toluene on silica-supported proline 3)[18] were performed (details in the Supporting Information). Since, under the assumption of the same saturation factor, the ratio of the retention factors of two substrates corresponds to the ratio of their adsorption equilibrium constants,[19] the chromatographic study allows us to establish that the adsorption constant of 2 [b in Eq. (6)] is roughly twice that of 1 [a in Eq. (6)], and that c (the adsorption constant of product 4) is about four times larger than a. Accordingly, the denominator of Equation (6) can be rewritten as Equation (8), which has the advantage of permitting an easier comparison of the relative magnitude of the terms in brackets. 1 þ að½1 þ 2½2 þ 4½4Þ
ð8Þ
Since the concentration ratio of feed components [1]0/[2]0 was 18:1 and 12:1, respectively, for entries 3 and 4 of Table 2, the assumption that p-nitrobenzaldehyde 2 does not compete for the adsorption with cyclohexanone 1 (i.e., 2[2] ! [1]) appears to be entirely reasonable. As for the competitive adsorption by product 4, the situation is complicated by the fact that 4 is generated inside the reactor. RPKA, however, comes to our aid, as the “same excess” experiments excluded product inhibition (Figure 3). Inasmuch as the competitive adsorption by the product would reasonably be a source of catalyst deactivation, the conclusion that product 4 does not compete for the adsorption under the conditions of Table 2 would seem to be sound. Translated into a mathematical form, this means 4[4] ! [1]. A deeper examination of this last inequality is central to our subsequent rationalization, and it requires knowledge of fraction conversions. Under the conditions of Table 2, entry 3, a 52 % conversion is achieved with a residence time of 45 min.[20] Accordingly, [4] at the microreactor outlet is about 0.05 m, and the term 4[4], which we might refer to as the competition factor of product 4, results in roughly 10 %
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Table 3. Relationship between concentration of cyclohexanone 1 in the feed ([1]0) and amount of adsorbed cyclohexanone (1ads), relative surface coverage (q), and percentage fraction conversion (f). Process conditions: residence time, 45 min; constant ratio of feed concentrations, [1]0/[2]0 = 24:1. Entry 1 2 3 4 5 6 7 8 9
[1]0 [m] 0.2 0.6 1.2 1.8 2.4 3.6 4.0 4.4 5.0
1ads [mmol][a]
q[b]
f [%]
12 40 77 106 119 142 143 144 146
0.08 0.26 0.50 0.68 0.77 0.92 0.93 0.94 0.95
8 20 40 56 64 85 83 84 82
[a] Per reactor. Calculated by frontal analysis. [b] Calculated as the ratio between 1ads and the total amount of silica-supported proline 3 in the reactor (154 mmol). See the Supporting Information for details.
3.6), which indicates that saturation capacity has been reached (fractional surface coverage is given in column 4 of Table 3). Thus for [1]0 > 1.8, the simple kinetic model given by Equation (7) is not expected to hold any longer. Consequently, a series of ad hoc experiments were conducted to investigate the process outcome under these regimes (entries 5–9 in Table 3) and eventually find a correlation between the estimated surface coverage (Table 3, column 4) and fraction conversion (Table 3, column 5). In the concentration interval 1.8 < [1]0 < 3.6, the steadystate rate Equation (2) assumes the form given by Equation (9), since the competitive adsorption by both p-nitrobenzaldehyde 2 and product 4 can be neglected under the conditions of runs 4 and 5 of Table 3. The statement on [2] is justified by the strongly unfavorable 24:1 feed ratio [1]0/[2]0, whereas that on [4] comes from the consideration that the product term 4[4] is smaller than 10 % of [1]0, as it was in the case in which RPKA excluded product inhibition. Rate ¼ k0 2 ½1½2=ð1 þ a½1Þ
ð9Þ
Since the first-order dependence of [1] in the numerator is tempered by the concentration term in the denominator, the fraction conversion is expected to increase more slowly as [1]0 increases than in the linear range of the isotherm. This is demonstrated by the change in the slope of the plot of fraction conversion relative to [1]0 (dotted line in Figure 5), which drops from about 30 when [1]0 < 1.8 (Table 3, entries 1–4) to less than 15 if 1.8 < [1]0 < 3.6 (Table 3, entries 4–6). Finally, at the isotherm plateau (i.e., for [1]0 > 3.6), the fraction conversion is found to be practically constant (Table 3, entries 7–9). Figure 5. Adsorption isotherm of cyclohexanone from toluene on silicasupported proline 3 (*, left y axis) and percentage fraction conversion (*, right y axis) versus cyclohexanone concentration [1]0. Adsorbed concentration of cyclohexanone 1 ([1ads]) in micromole per microliter of packing (Vbed). Process conditions as in Table 3.
of the cyclohexanone concentration in the feed ([4]/[1]0 = 0.2:1.8). Thus, this simple reasoning will be employed as an indication for estimating the presence of competitive adsorption by the product (see below). The adsorption isotherm of cyclohexanone 1 (columns 2 and 3 in Table 3 and Figure 5) allowed us to evaluate the meaning of the last approximation introduced to obtain Equation (7) with regard to the linearity of the adsorption isotherm (or, a[1] ! 1). As the isotherm exhibits a substantially linear behavior until [1]0 = 1.8 m, the condition holds in the concentration ranges of entries 3 and 4 of Table 2. Hence, it is possible to conclude that under these conditions, the full steady-state rate Equation (2) simplifies to Equation (7), and that enamine addition to aldehyde is the ratedetermining step, which is in agreement with the homogeneous case.[9] By increasing the concentration of 1 in the feed above 1.8 m, however, the adsorption isotherm exhibits at first a curvature (for 1.8 < [1]0 < 3.6), and then it flattens out ([1]0 >
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Under these conditions, all the available silica-supported proline 3 is transformed to enamine 5 (Table 3, column 4), and any further increase in concentration (keeping the ratio [1]0/[2]0 and residence time constant) does not affect the conversion efficiency (Table 3, column 5). These considerations show that 3.6 m is the optimal cyclohexanone feed concentration for the reactor R employed in this work. The study was concluded with the evaluation of the optimal concentration of aldehyde 2 in the feed by performing different experiments in which [1]0 was kept constant at the 3.6 m value. After some experimentation, it turned out that [2]0 = 0.1 m furnished an almost quantitative conversion (f = 98 %). A full explanation of this result is not a trivial task, as it requires the modeling of the spatial and temporal distribution of the concentration profiles of all compounds (1, 2, and 4) between the bulk and the adsorbed phase inside the microreactor. This study is currently underway in our laboratories and will be the subject of a forthcoming publication.
Conclusion In this proof-of-concept study, we have proposed an innovative approach for the characterization of heterogeneous catalytic reactions in flow mode. In particular, we have focused
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on the proline-catalyzed aldol reaction, which has been extensively investigated under homogeneous batch conditions. Essentially, we have coupled the kinetic information that comes from the application of reaction-progress kinetic analysis (RPKA) with the thermodynamic information that results from nonlinear chromatographic measurements. Significantly, the two methodologies turned out to be strongly complementary and allowed for a clear understanding of important features of the heterogeneous continuous-flow process, such as the dependence of the reaction order on feed composition and saturation capacity of the catalytic bed.
[2] [3]
[4]
Experimental Section Microreactor packing: Microreactor R was fabricated by using a 100 2.1 mm stainless-steel column, which was filled with silica 3 by slurrypacking. Slurry-packing was performed under constant pressure (300 bar, 30 min, toluene as solvent) by using an air-driven liquid pump. The slurry was prepared by suspending an excess in weight of functionalized silica in toluene. Kinetic analysis: For the determination of reaction profiles at constant flow rate (reaction isotherm curve; Figure S2 in the Supporting Information), microreactor R was fed with a solution of 1 (2.40 m) and 2 (0.10 m) in toluene and operated at 25 8C for about 4 h at 2 mL min1. Fraction conversion was determined by online HPLC analysis (see Figure 1) and by 1H NMR spectroscopic analysis (a sample of the eluate was taken every 40 min). The collected solution at the steady-state regime was finally concentrated and eluted from a column of silica gel with 5:1 toluene/ AcOEt to give the corresponding mixture of anti/syn adducts 4. This kinetic study was repeated with the same feed composition but at different flow rates to determine the kinetic profile depicted in Figure 2. To complete the RPKA of the model reaction, the above approach was then applied to all the experiments of Table 2. Chromatographic measurements: The binary pump-2 delivered a hexanes/iPrOH 99.7:0.3 (v/v) solution into a 150 4.6 mm 5 mm-particle-diameter HILIC column by passing through the switching valve (see Figure 1). The flow rate along direction-2 was 1 mL min1. Under these conditions, the retention times of 2, syn-, and anti-aldol product were 2.3, 6.4, and 11.2 min, respectively. The detector was calibrated at 290 nm for both 2 and 4 (different calibration curves were employed depending on the concentration of cyclohexanone 1 in the feed). In separate experiments, microreactor R was used as a chromatographic column for determining the retention factors of 1, 2, and 4. The mobile phase was pure toluene. The adsorption isotherm of 1 on silica 3 was measured from toluene by frontal analysis (see the Supporting Information for details).
[5] [6]
[7]
[8]
[9] [10]
Acknowledgements We gratefully acknowledge the Italian Ministry of University and Scientific Research (Progetto PRIN grant nos. 2009ZSC5K2 004 and 20098SJX4F 004) for financial support. Thanks are also given to Mr. Paolo Formaglio for NMR spectroscopic experiments and to Mrs. Ercolina Bianchini for elemental analyses.
[1] a) J. Wegner, S. Ceylan, A. Kirschning, Adv. Synth. Catal. 2012, 354, 17 – 57; b) I. R. Baxendale, J. J. Hayward, S. Lanners, S. V. Ley, C. D. Smith, Microreactors in Organic Synthesis and Catalysis (Ed.: T. Wirth), Wiley, New York, 2008; c) F. E. Valera, M. Quaranta, A. Moran, J. Blacker, A. Armstrong, J. T. Cabral, D. G. Blackmond,
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[11]
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than one were obtained in confirmation that mass-transfer effects can be neglected. For reaction-progress kinetic analysis of the continuous-flow aldol reaction in a liquid–liquid microfluidic device, see reference [1c]. Achievement of the steady-state regime was assumed when constant reactants/product outlet concentrations accompanied by complete inlet mass recovery in the eluate were detected (see the reaction isotherm curve in the Supporting Information). Progressive loss of catalytic activity of the packing material 3 was observed at 25 8C after approximately 24 h on stream. For the utilization of the more stable 5-pyrrolidin-2-yl)tetrazole-functionalized silica in the same aldol process, see reference [4a]. Adsorption constants can be determined by chromatographic experiments. The chromatographic retention factor, kchrom, traditionally defined as the ratio between the correct retention time and the hold-up time, in fact, also corresponds to the product between the so-called Henry constant of adsorption (H) and the phase ratio, F (i.e., the ratio between the stationary and the mobile phase): kchrom = HF. In turn, H is the product between the saturation constant (achievable by the adsorption isotherm) and the equilibrium adsorption constant a (i.e., H = qsa). The assumption that only one type of adsorption site (namely, the catalytic sites) is present on the surface was verified by considering the retention behavior of cyclohexanone 1 on an alkylated silica gel (by TEC of mercaptopropyl thiol silica and 1-heptene) through a
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series of dedicated HPLC experiments using toluene as the eluent. See the Supporting Information for details. Incidentally, we want to remark here that, also in steady-state conditions, [1] and [2] in Equation (6) do not correspond to the feed concentrations [1]0 and [2]0 since the system is reactive. This is a necessary simplification. Equation (6) is in fact a competitive adsorption isotherm. Accordingly, the amount of adsorbed cyclohexanone should not be a function of only its bulk concentration (as we are assuming here) but also of the concentration of 2 and 4. Nevertheless, as the system is reactive, the competitive isotherm of 1 cannot be experimentally measured. In light of the excess amount of 1 with respect to 2 and 4, however, this appears a physically sound approximation at this stage of the study. By assuming the same saturation capacity for 1, 2, and 4 (which is reasonable in light of their similar molecular dimensions), the ratio of retention factors correspond to the ratio of the adsorption equilibrium constants, the phase ratio F being the same in all the cases (see also ref. [15]). The retention factors for 1, 2, and 4, using toluene as eluent, were 0.52, 1.10, and 2.10, respectively (see the Supporting Information). Since the reaction studied in this work is quite slow, a residence time of 45 min was taken for these experiments as a reasonable compromise between fraction conversion and analysis time.
2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Received: January 17, 2013 Published online: April 15, 2013
Chem. Eur. J. 2013, 19, 7802 – 7808
