Catalytic Hydrogenation of 2-((1-Benzyl-1,2,3,6-tetrahydropyridin-4

Article pubs.acs.org/IECR

Catalytic Hydrogenation of 2‑((1-Benzyl-1,2,3,6-tetrahydropyridin-4yl)methylene)-5,6-dimethoxy-2,3-dihydroinden-1-one Hydrochloride: Fractal-like and Weibull Model Kinetics Ž . Jelčić,*,† Z. Mastelić Samardžić,† and S. Zrnčević‡ †

PLIVA Croatia Ltd., R&D, Chemistry, Prilaz Baruna Filipovića 25, 10000 Zagreb, Croatia Faculty of Chemical Engineering and Technology, University of Zagreb, 10000 Zagreb, Croatia

‡

S Supporting Information *

ABSTRACT: The hydrogenation of 2-((1-benzyl-1,2,3,6tetrahydropyridin-4-yl)methylene)-5,6-dimethoxy-2,3-dihydroinden-1-one hydrochloride (1) over a 5% Pt/C industrial catalyst is strongly influenced by solvents (methanol, ethanol, acetone, water) and reaction conditions such as temperature, catalyst loading, hydrogen partial pressure, and compound 1 concentration. The solvent has a strong influence on hydrogenation of compound 1 on a Pt/C catalyst. Different physical and electronic properties (given as molecular descriptors) of nonreactive solvents were related to the fractal-like and Weibull model kinetics parameters. The best relation was established between the fractal kinetic index, h, and the solvent H-bond acceptor ability (represented by the Abraham descriptor B, the solute hydrogen-bond basicity). The apparent activation energy of hydrogenation step was determined to be 20 kJ mol−1. The fractal-like and Weibull model kinetic terms indicate that the formation of 2-((1-benzylpiperidin-4-yl)methyl)-5,6-dimethoxy-2,3-dihydroinden-1-one hydrochloride, compound 2, can be correlated with the complex distribution of the reactive species.

1. INTRODUCTION Catalytic hydrogenation of double and triple carbon−carbon bonds is certainly one of the most applied methods for the synthesis of fine chemicals. The hydrogenation of 2-((1-benzyl1,2,3,6-tetrahydropyridin-4-yl)methylene)-5,6-dimethoxy-2,3dihydroinden-1-one hydrochloride (1) that results in the 2-((1benzylpiperidin-4-yl)methyl)-5,6-dimethoxy-2,3-dihydroinden1-one hydrochloride (2) is one such industrially important reaction. There are many processes described mainly in patents described in refs 1−3 for producing 2. Complete chemoselectivity is unlikely because the starting compound 1 has more than a single functionality susceptible to hydrogenation. Recently, the authors presented a detailed study of the search for a Pt/C catalyst that would meet requirements for high reaction selectivity, high activity, good stability, and prospect of the catalyst’s reuse.4 An experimentally based simple reaction scheme given in Figure 1 was derived for the hydrogenation of 1 to 2, with high selectivity of compound 2 formation.5,6 The liquid-phase hydrogenation of 1 over heterogeneous 5% Pt/C catalyst is conducted in a rotary agitated batch reactor. Liquid− solid, gas−liquid, and intraparticle diffusion resistances are expected for solid−liquid−gas flows in the impeller agitated vessel. The contribution of mass transfer between gas and liquid through their interface should be appropriately incorporated in the kinetic model or deemed irrelevant under the reaction conditions studied. Multiphase hydrogenation of 1 © XXXX American Chemical Society

to 2 is modeled in detail, considering the industrial significance of this process, by fractal-like and Weibull kinetic models. The objectives of this study are to evaluate the Pt/C catalyzed hydrogenation kinetics of compound 1, to determine factors that affect the rate of the reaction, and to establish relationships between factors and the hydrogenation reaction rate. The central goal is to prove whether fractal-like and Weibull model kinetic parameters are mostly equivalent.

2. EXPERIMENTAL SECTION The kinetic experiments and the details of the reactor setup were the same as those described in our earlier papers.4,5 Samples of the reaction mixture were taken periodically from the reactor, diluted with methanol, and analyzed using highpressure liquid chromatography. In the reaction mixture, the concentrations of reactant 1 and product 2 were monitored. The ranges of operating conditions are given in Table 1. 2.1. Materials. Structure of compound 1, produced according to WO/2007/015052 A1, was confirmed by mass spectrum m/e 376 (M+, H+) and by H1 NMR (CF3 COOD, 600 MHz) analysis: δ 3.30 (m, 1H), 3.55 (m, 1H), 3.70 (m, Received: December 22, 2015 Revised: March 11, 2016 Accepted: March 23, 2016

A

DOI: 10.1021/acs.iecr.5b04864 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 1. Reaction scheme of catalytic hydrogenation of compound 1 to compound 2.

proton affinity, PA, in the gas phase can be also used to estimate the solvent effect (Table S2). The term pKBH+ in water corresponds to the logarithmic strength of a neutral base B as described in terms of the Ka of its conjugate acid BH+. A strong Brønsted base has a large positive value and a weak Brønsted base has a small or negative pKBH+ value. The heat of transfer of the base from infinite dilution in the inert solvent CCl4 to infinite dilution in the (frequently) completely protonating solvent HSO3F relates to the heat of protonation (ionization), ΔHi. Enthalpies of protonation are well related to the matching aqueous pKBH+ values. Standard Gibbs energy change, ΔG0, and standard enthalpy change, ΔH0, of the formal deprotonation reaction BH+ → B + H− define the gas-phase basicity, GB, and the proton affinity, PA, of a base B, respectively. 2.2.1.3. Gutman’s Donor Number (DN) (or SbCl5 Affinity Scale).25 Gutman’s donor number (DN) is an empirical solvent cation’s solvation parameter that quantifies the solventresponsive physical property of a model solute (Table S3). 2.2.1.4. Hydrophilicity or Hydrophilic Index, Hy. The hydrophilicity or hydrophilic index,9 Hy, is a simple descriptor expressed largely in terms of the number of hydrophilic groups.10 It is defined by

Table 1. Range of Reaction Parameters Pt/C catalyst loading (g dm−3) stirring speed (r/min) H2 partial pressure (MPa) compound 1 concentration (mol dm−3) temperature (K) solvents

0.57−2.86 100−500 0.2−3.0 73−243 298−318 methanol, ethanol, acetone, and water

1H), 4.20−4.36 (m, 2H), 4.30 (s, 2H), 4.33 (s, 3H), 4.39 (s, 3H), 4.49 (m, 1H), 4.81 (m, 1H), 6.69 (s, 1H), 7.46 (s, 1H), 7.76 (s, 1H), 7.78−7.87 (m, 5H), 7.90 (s, 1H). 2.2. Catalyst Characterization. Commercial 5% Pt/C catalyst (BASF, Italy) was used in hydrogenation experiments as received. The Brunauer−Emmett−Teller (BET) specific surface area of the Pt/C catalyst samples was calculated using the multipoint BET method on five points of the nitrogen adsorption isotherms at 77 K near monolayer coverage. The crystalline patterns of 5% Pt/C catalyst were recorded over a 15° < 2θ < 70° range (Philips PW 1830 diffractometer using Ni-filtered Cu Kα radiation operating at 40 kV and 30 mA, step size of 0.02°). The Pt/C catalyst consists of carbon precursor and platinum structures with sizes of about 10−80 nm. 2.2.1. Solvent Descriptors. The systematic and quantitative investigation of the way in which different chemical components, such as the type of solvent, affect a given reaction involves significant changes in the properties on the molecular level. The inclusion of the supplementary solvent descriptors that describe the solubility capacity of the solvent and interaction with the Pt/C catalyst and substrate are beneficial to understanding solvent effects. 2.2.1.1. Abraham Descriptors. The Abraham general solvation model7 could be useful for improving the accuracy of predicting potential efficient solvents for the catalytic hydrogenation. The method relies on linear free-energy relationships, one for transfer processes occurring within condensed phases8 and another for processes involving gasto-condensed phase transfer. The dependent variable, P, includes various Pt/C catalytic hydrogenation reaction parameters: P = c + e·E + s·S + a·A + b·B + l·L

Hy =

(1 + NHy )·log 2(1 + NHy ) + Nc·

( A1 log 2 A1 ) +

NHy A2

log 2(1 + A) (2)

where NHy is the number of hydrophilic groups (−OH, −SH, −NH), Nc the number of carbon atoms, and A the number of atoms (excluding hydrogen). 2.2.2. Fractal-like Kinetics. Kopelman11 has proposed a fractal-like depiction of nonhomogeneous reaction kinetics. This approach suggests the following equation to convey obstruction to diffusion in nonideal reaction conditions on the rates: k(t ) = k 0t −h

(3)

where k0 is the initial reaction rate at time 1 and h is an arbitrary constant or fractal kinetic index. The fractal exponent should range from 0 to 1 according to fractal kinetic theory.11 This time-dependent equation is appropriate for relating all diffusion-controlled reactions, i.e., all those of second or higher order. First-order reactions preserve their time-free form because they have no restrictions on diffusion and mixing. The equation can be linearized as log k = −h·log t + log k0. The term h has been explained as related to the system dimensionality. In homogeneous space settings in accord with classical kinetics, h = 0; thus, k is a constant. If a nonhomogeneous system is made uniform by vigorous stirring, h will again tend to 0. However, h > 0 and consequently a timedependent k is given for diffusion-limited reactions that occur in fractal spaces. An initially well-mixed solution will convert to a diffusion-limited mode as a reaction progresses because of the failure of reactants to rediffuse throughout the solution. A hydrogenation reaction over the catalyst surface (a surface

(1)

where Abraham descriptors include dispersion interactions (E), dipolar/polarizability interactions (S), hydrogen bond acid (A) and hydrogen bond base (B) interactions, and solute size (V) and L is the logarithm of the solute gas-phase dimensionless Ostwald partition coefficient for hexadecane at 298 K. The molecular descriptors, E, S, A, B, V, and L as independent variables, are related to the hydrogenation kinetic model parameters (Table S1). The regression models contain the measured fitted reaction model terms, single-molecular solute descriptor, and calculated equation coefficients. 2.2.1.2. Brønsted Basicity and Affinity. Thermodynamic parameters for protonation of organic bases: pKBH+ and ΔHi (kJ·mol−1) in fluorosulfuric acid and gas-phase basicity, GB, and B


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dimension derived from the (220) plane XRD peak nanocrystals broadening, by applying the Scherrer’s equation, was 7.6 nm. 2.5. Kinetics Studies. The hydrogenation experiments using 5% Pt/C catalyst were performed to understand the overall kinetics of this reaction. For this purpose, experimental data showing the progression of hydrogenation of compound 1 (presented in ref 4 and in Supporting Information) were obtained by varying the operating conditions to observe the rate of hydrogenation as well as the integral concentration− time profiles. The reaction route, as presented in Figure 1, includes the formation of compound 2. The values for the impurities were below prescribed values in all experiments.4

reaction) is dimensionally constrained, and this reaction can exhibit fractal kinetics. 2.2.3. Weibull Model Function of the Reaction. A common model for nonlinear kinetics is the stretched exponential (Weibull) model, of which the first-order is a special case (β = 1). Formation of compound 2 can be expressed by the Weibull model function, with two parameters: ⎡ ⎛ ⎞β⎤ t α = exp⎢ −⎜ ⎟ ⎥ ⎢⎣ ⎝ η ⎠ ⎥⎦

(4)

where t is the reaction time, η the Weibull scale/rate parameter with time dimension, and β the dimensionless Weibull shape parameter. The inherent assumption was that the compound 2 formation rate is related to the probability value of reaction times given by a cumulative Weibull probability distribution function.12 The formation of compound 2 was analyzed with the Weibull reaction model using the least-squares method. A linearized form of eq 4 defines the values of the Weibull function’s parameters, η and β: ln[− ln(α)] = −β ·ln(η) + β ·ln t

3. RESULTS AND DISCUSSION 3.1. Mass Transfer. Ideally, the hydrogenation reaction is operated under mass transfer free conditions, at low temperatures, with powerful mixing, and at low small loadings of smallsized particle Pt/C catalyst. A minimal stirrer speed of 100 r/ min is required to eliminate any external mass transfer limitations. The exclusion of the gas−liquid mass transfer finished up with setting the effective stirring speed at more than 400 r/min and at Pt/C catalyst concentration of less than 0.57 g dm−3. 3.1.1. Effect of Catalyst Loading. The hydrogenation reaction rate should not be significantly affected by mass transfer limitation.15 The importance of gas−liquid, liquid− solid, and mass transfer resistance on the fractal-like model initial rates of reaction k0 were analyzed (Table S3). The inverse of the initial reaction rate k0 is linearly related to the inverse of catalyst mass density, which varied from 0.57 to 2.86 g dm−3 (Figure 2). The intercept represents a resistance to gas

(5)

The slope and intercept with the y-axis of linear dependences of ln[−ln(α)] vs ln(t) produce the η and β values, respectively. The order of reaction is quantified by the Weibull shape parameter, β. The Weibull function is reduced to an exponential function for the first-order reactions, and then β = 1. At the same time, β is a measure of the extent by which the reaction rate is accelerated. The reaction time scale (position) is revealed by the Weibull scale or rate parameter, η. The effect of reaction kinetics broadening and delaying in time is observed with the increase in the value of Weibull scale and rate parameter η (while Weibull shape parameter β is constant). 2.3. Regression Models. This paper compares the ability of different mathematical models to depict compound 1 hydrogenation and compound 2 formation curves for various conditions. Fractal-like kinetic and Weibull mathematical models are developed in the present paper. The most illustrative equations (with the corresponding correlation coefficients and significance) are presented for the dependence between the parameters of the catalytic hydrogenation process (conversion, selectivity, yield, and pressure) and mathematical models. The mathematical models adequately describe the experimental points, with similar kinetic curves shapes and high coefficients of determination. Curve fitting and statistical analysis was done using the program Statgraphics XV Centurion (Statpoint Technologies, Inc., United States). Among the statistics reported, the following were used to evaluate a fit: coefficient of determination (R2), 95% confidence limits, and p-values of the parameters. R2 was used as an overall measure of fit rather than as a basis for choosing between closefitting alternative models. 2.4. Pt/C Catalyst Characterization. Platinum arranges with sizes of about 10−80 nm on Pt/C catalyst carbon precursor. The surface area, total pore volume, and mean diameter of pores of the supported Pt catalyst were 761 m2 g−1, 0.39 cm3 g−1, and 2.04 nm, respectively. The catalyst exhibits a typical face-centered cubic (fcc) packing, with the diffraction peaks at ∼39° (111), 46° (200), and 67° (220) assigned to the corresponding planes in parentheses. The strongest sharp graphitic reflection is a symmetrical peak at 2θ = 26.3° assigned as the [002] plane of graphite.13,14 The mean crystallite

Figure 2. Effect of the catalyst mass density on the (●) fractal index h and (■) the initial reaction rate k0 (mol m−3 min−1) of fractal-like formation of compound 2 (VMeOH = 0.175 dm3, T = 318 K, c(1) = 0.14 mol dm−3, pH2= 0.2 MPa, N = 400 min−1).

adsorption across the gas−liquid interface (gas−liquid mass transfer coefficient is ≈1.7 min−1). The slope corresponds to the sum of the term that represents resistance associated with transport of hydrogen through bulk liquid and the term that represents a resistance associated with the surface reaction. Reaction rate is clearly a linear function of the overall amount of active catalyst used, strongly indicating that the process is kinetically limited as presumed. Also, increasing the amount of Pt/C catalyst increased the compound 1 hydrogenation rate. Weibull shape β parameter, similarly to the fractal index h, does not depend on the catalyst amount. Weibull scale η parameter C


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Industrial & Engineering Chemistry Research inversely depends on the catalyst amount (Table S4, Figure S9). Conversion rate is weakly a linear function of the overall amount of active Pt/C catalyst used, indicating that the process is kinetically limited as expected. 3.1.2. Effect of Mixing Rate. The agitation rate is the most used reaction parameter that evaluates the impact of gas−liquid mass transfer. The observed reaction rate changes only when gas−liquid mass transfer is at least partially rate-controlling. The effect of agitation on conversion was significant. It should be noted that the drop in conversion in the low agitation range (400 r/ min). Fractal kinetic index h is apparently linearly decreasing with the increase in the mixing rate (Figure 3, Table S1).

Figure 4. Effect of the mixing rate on the Weibull scale η (min−1) and shape β parameters for formation of compound 2 (VMeOH= 0.175 dm3, T = 318 K, pH2= 0.2 MPa, mcat = 1.71 g dm−3, c(1)= 0.14 mol dm−3).

3.2. Solvent. The rate of hydrogenation16 of compouund 1 in four solvents (water, ethanol, methanol, and acetone4) was investigated at 313 K and pH2 = 0.2 MPa; it is interesting that these solvents exemplify distinct solvent clusters.17 The major effect of the solvent on the rates of catalytic hydrogenations is attributable18 to hydrogen solubility, thermodynamic interaction of solvent with reactants and products, competitive adsorption of solvent, etc. Recent experimental data regarding effect of solvent polarity suggest that polar solvents enhance the hydrogenation of CO bonds and raise the selectivity toward the unsaturated alcohol, whereas nonpolar solvents favor hydrogenation of the nonpolar CC bond.19−21 Pure water22 and water/organic solvent mixtures23 enable selective hydrogenation of the hydrophilic CO bond. The variation in the hydrogenation rates may be justified by the variation in the hydrogen solubility.24 The reaction rates were linearly regressed by a molecular descriptor, the simple hydrophilic index (Hy), and terms from the Abraham solubility model (Tables S11 and S12). The hydrogenation results obtained suggest that the product is controlled through direct competition of compound 1 and solvent for catalyst sites. The hydrogenation varied widely with the solvent. The hydrophilic capacity of the solvent may support the hydrogenation of compound 1. The solvent is thought to control by competition the extent to which the amine function of the compound 1 was adsorbed on the catalyst. For the hydrophilic solvents, methanol, ethanol, and water, the rate parallels the progressive masking of the hydroxyl function, which renders the heavier alcohol less prone to adsorb competitively on the catalyst. Table S13 presents change for the values of the following parameters of fractal-like formation of compound 2: fractal index, h; initial rate, k0; squared linear correlation coefficients, R2 (adjusted for degrees of freedom); and significance (p-value) with solvent. The fitting of the experimental results with the fractal-like model is acceptable, quantified with R2adj. Compound 2 formation is extremely prolonged because of poor solubility, despite the fact that water has the highest value of the dielectric constant and high polarity. Compared with the methanol, the activity and selectivity of the catalyst in acetone is much lower. Acetone as aprotic solvent is characterized by the creation of an electron donor−acceptor complex so that the acetone may be adsorbed on the metal surface. This interaction between the catalyst and solvent has a definite impact on the reaction.

Figure 3. Effect of the mixing rate on fractal kinetic index h (●) and the initial reaction rate k0 term (■) of fractal-like formation of compound 2 (c(1) = 0.14 mol dm−3, T = 318 K, pH2 = 0.2 MPa, mcat = 1.71 g dm−3, VMeOH = 0.175 dm3).

Apparent linear dependence is given as h = −0.0005(mixing rate (r/min)) + 1.161 (R2 = 0.685); because the p-value is 400 r/min). Weibull scale η and shape β parameters for formation of compound 2 are apparently weakly decreasing with the increase in the mixing rate (Table S2, Figure 4) (R2 (adj.) = 0.7208; p = 0.009). D


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Industrial & Engineering Chemistry Research Dielectric constant, εr, can appropriately describe the solvent effect on the fractal model terms fractal index, h, and initial reaction rate, k0. The other descriptors have been also used to derive the solvent effect on the hydrogenation reaction (Tables S14−S16). The fractal kinetic index h is very well correlated with the solvent hydrophilic index, Hy, with some other Abraham descriptors: the excess molar refraction (E), the solute hydrogen-bond acidity (A) (Figure S15), the McGowan volume of the solute (V), and the logarithm of the solute gasphase dimensionless Ostwald partition coefficient into hexadecane at 298 K (L), Hildebrand solubility (HS) and Brønsted terms gas-phase basicity (GB), and proton affinity (PA) (Figures S16 and S17). However, because the p-value is ≥0.05, there is not a statistically significant relationship between fractal kinetic index h and Abraham descriptors (A, L, E, S, and V) (Table S11). Still, the correlation coefficients indicate a moderately strong relationship between the fractal kinetic index h and Abraham descriptors (Table 2).

Figure 5. Effect of hydrophilic index Hy on fractal kinetic index h (●) and the initial reaction rate k0 term (■) of fractal-like formation of compound 2 (c(1) = 0.14 mol dm−3, T = 318 K, pH2 = 0.2 MPa, mcat = 1.71 g dm−3, N = 400 min−1).

Table 2. Solvent Descriptors Effect on the Fractal Kinetic Index h Term in the Fractal Reaction Kinetic Equation [Degrees of Freedom df (Model = 1, Residuals = 2)]a equation equation equation equation equation equation equation equation equation

6 7 8 9 10 11 12 13

h h h h h h h h

= = = = = = = =

0.7292 + 0.2804·Hy 1.5550 − 2.9547·E 1.9157 − 1.7513·S 0.4948 + 1.30341·A 3.9683 − 6.5533·B 1.87663 − 2.28657·V 1.7171 − 0.6178·L 0.4160 + 0.0064·DN

R2 (adj.)

p-value

0.7988 0.5268 0.0910 0.8247 0.9049 0.5973 0.6891 0.2676

0.069 0.173 0.478 0.060 0.032 0.145 0.110 0.6064

a Solvent descriptors: hydrophilic index, Hy; Abraham descriptor A, the solute hydrogen-bond acidity; Abraham descriptor B, the solute hydrogen-bond basicity; Abraham descriptor L, the logarithm of the solute gas-phase dimensionless Ostwald partition coefficient into hexadecane at 298 K; the excess molar refraction, E; the McGowan volume of the solute, V (c(1) = 0.14 mol dm−3, T = 318 K, pH2 = 0.2 MPa, mcat = 1.71 g dm−3, N = 400 min−1).

Figure 6. Effect of Abraham descriptor A on the fractal index h (●) and the initial reaction rate k0 term (■) of fractal-like formation of compound 2 (c(1) = 0.14 mol dm−3, T = 318 K, pH2 = 0.2 MPa, mcat = 1.71 g dm−3, N = 400 min−1).

The correlation coefficient between fractal kinetic index h and the Abraham descriptor B, the solute hydrogen-bond basicity, indicates a relatively strong relationship between the variables, at the 95.0% or higher confidence level. Fractal kinetic model formation initial reaction rate k0 has an apparently good dependence on the hydrophilic index, Hy, Abraham descriptor for the solute hydrogen-bond acidity (A), and Abraham descriptor for the solute hydrogen-bond basicity (B); however, because the p-value is greater than or equal to 0.05, there is not a statistically significant relationship between initial fractal reaction rate k0 and Hy or Abraham descriptors (A, B, L, E, S, and V) at the 95.0% or higher confidence level. Figure 5 presents the effect of hydrophilic index Hy on fractal kinetic index h and the initial reaction rate k0 term. Figure 6 presents effect of Abraham descriptor A (the solute hydrogen-bond acidity) on fractal kinetic exponent h and the initial reaction rate k0. The effect of diverse solvent descriptors on fractal initial reaction rate k0 in the fractal-like reaction equation is presented in Tables S11−S19. Because the p-value is ≥0.05, there is not a statistically significant relationship between initial reaction rate k0 and the descriptors, at the 95%

confidence level. The R2 statistic indicates a moderately strong relationship between the descriptors and initial rate k0. The goodness of fitting of the reaction curves with the fractal-like model signifies a complicated structure for the kinetic model of the compound 2 formation process. This complex kinetics can be assumed to be linked to the fractal-like model premise of obstruction to diffusion in nonideal reaction environments. Fractal kinetic model formation reaction index dependence on Gutman’s donor number (DN) (or SbCl5 affinity scale)25 is nonlinear because of decreased h value for the ethanol. It can be hypothesized that ethanol, with a higher donor number DN than water and methanol, is more difficult to displace from the platinum primary coordination sphere. On the other hand, in acetone, a solvent with a very low donor number, the complexes form quite readily. Gutman donor number (DN) is not successful in describing the fractal kinetic index h and initial reaction rate k0 in the fractal reaction kinetic equation (Table S14). The Brønsted solvent descriptors dependences of fractal kinetic exponent (h), initial reaction rate (k0), the gasphase basicity (GB), and proton affinity (PA) values are presented in Figures S15 and S16. E


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Industrial & Engineering Chemistry Research The solubility and chemisorption of H2 alter the liquid-phase hydrogenation reaction on the catalyst suspended in the solvent. The solubility and chemisorption of H2 in a nonpolar solvent are greater than in polar solvents.16 The acidic/basic character of the solvent (by the Abraham descriptor A, the solute hydrogen-bond acidity, or Abraham descriptor for the solute hydrogen-bond basicity, B) and hydrophilic descriptor (Hy) were the principal solvent descriptors for the hydrogenation fractal-like kinetic parameters. The other descriptors can be neglected as insignificant terms from the regression models. This result could help in the solvent selection for the industrial process of compound 1 hydrogenation. The solid−liquid catalytic reaction rates are highly affected by the solvents’ polarities and dielectric constants. Different reaction rates have been observed with the various solvents. The solvent can influence a catalytic reaction both by direct interaction with the Pt/C catalyst and by influencing the solvation of the substrates and products in the reaction medium. The order of reactivity of compound 1 catalytic hydrogenation rate increased with the dielectric constant (εr) and with the Reichardt-Dimroth empirical polarity parameter (measure of the ionizing power of a solvent) of the solvents: methanol > ethanol > water > acetone. Acetone, a solvent with a low dielectric constant, and water, a high dielectric constant solvent, are disadvantageous for the hydrogenation reaction. The solvent molecules may be entering in the channels and adsorbing on the active sites of Pt/C catalysts, excluding diffusion of the reactant to the active reaction sites. Table S17 gives the values of the Weibull scale and shape parameters η and β. The quality of fitting the experimental results with the Weibull distribution function, quantified with R2, and the statistical significance are satisfactory (Tables S18−S21). The use of different solvents did significantly affect the formation kinetics of compound 2. In polar protic solvents, such as ethanol and methanol and especially water, the η and β parameters increase, in general, with the relative permittivity, εr. This increase in Weibull η and β terms was attributed to the protic nature of solvents. The lowest values for the shape term β and scale term η are observed for the polar aprotic solvent, acetone. This signifies a complicated structure for the kinetic model of the compound 2 formation process. This complex kinetics can be related to the Weibull probability model supposition of the distribution of reaction species. 3.3. Concentration. The classical reaction kinetics theory explains reaction in homogeneous media with dilute, perfectly mixed reactants when the reactant concentration is changed. These conditions are entirely distinctive from the substantially configured systems, so the classic kinetics theory may not apply to this setting in the concentration range of compound 1 up to 200 mol·m−3 (Figure 7, Table S5). However, in terms of reactant 1 concentration, the fractal reactions are similar because the reaction occurs at the solid−liquid interface (h ≈ 1) (Figure 7). Fractal kinetic index, h, and fractal initial reaction rate, k0, are apparently optimal for compound 1 concentration around 140 mol·m−3. However, this may be just apparent because of the outlier value for the very low concentration of compound 1. The increase in the concentration increases the fractal kinetic index, h, and decreases the initial reaction rate, k0. Weibull scale η and shape β parameters for formation of compound 2 are apparently optimal for the compound 1 concentration of around 100−200 (mol·m−3) (Table S6, Figure S10).

Figure 7. Effect of compound 1 concentration on fractal kinetic index h (●) and the initial reaction rate k0 term (■) of fractal-like formation of compound 2 (VMeOH = 0.175 dm3, T = 318 K, pH2 = 0.2 MPa, mcat = 1.71 g dm−3, N = 400 min−1).

3.4. Pressure. Changing hydrogen partial pressures can change the relative rates of hydrogenation reactions and can result in Pt/C catalyst deactivation and low conversions.26 The relative role that gas−liquid mass transfer and transport mechanisms play in this is important. Hydrogen pressure has a strong influence on the fractal kinetic index h of compound 2 formation (as measure of hydrogenation activity) at low pressures (Figure 8, Table S7). The initial reaction rate k0

Figure 8. Effect of pressure on fractal kinetic index h (■) and initial reaction rate k0 (●) of formation of compound 2 (VMeOH = 0.175 dm3, T = 318 K, c(1) = 0.14 mol dm−3, mcat = 1.71 g dm−3, N = 400 min−1).

appears to be effectively independent of hydrogen pressure above about 1 MPa. The initial reaction rate k0 does not change with a further increase in hydrogen pressure while the catalyst surface is largely saturated with hydrogen. Apparent (weak) linear dependence for the fractal kinetic index h is given as h = −0.0039(pressure (MPa)) + 0.8329 (R2 = 0.002). However, the fractal kinetic index h appears to be a constant: 0.83 (±0.07). Catalyst Pt/C was deactivated to a greater extent at reduced hydrogen pressures, below 1 MPa (Figure 8). Apparent linear dependence for initial reaction rate for the formation of compound 2 is given as k 0 (mol m−3 min−1) = 2.245 + 0.445(pressure (MPa)) (R2 = 0.167). Alternatively, a better dependence has been observed as logarithmic function of pressure (Figure S11). Decrease in F


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Industrial & Engineering Chemistry Research hydrogen partial pressure has caused a decrease in the amount of adsorbed hydrogen on the catalyst surface, most probably because of lower mass transfer rates or because of decrease in the dissolved hydrogen concentration in the reactant. Dissolved hydrogen concentration (i.e., hydrogen partial pressure, up to 3 MPa) does not change the apparently fractal-like kinetics and the fractal kinetic index h of hydrogenation of compound 1. However, the catalyst deactivated to a greater extent at reduced hydrogen pressures (up to 1 MPa), which induces lower fractal kinetic model formation initial reaction rate, k0. The increasing hydrogen pressure is undoubtedly favorable in terms of the rate of hydrogenation, reducing the reaction time, and efficient use of catalyst. Hydrogenation activity derived as Weibull scale/rate η and shape β parameters of compound 2 formation (Table S8, Figure 9) are apparently decreasing with the hydrogen pressure

Figure 10. Apparent isoconversional activation energy for fractal-like formation of compound 2 by the isoconversional method for a set of isothermal curves from 298 K up to 318 K (VMeOH = 0.175 dm3, pH2 = 0.2 MPa, c(1) = 0.14 mol dm−3, mcat = 1.71 g dm−3, N = 400 min−1).

the catalyst surface. The initial reaction rate k0 is increased with the increase in temperature with the apparent activation energy Ea= 11.5 (±0.2) kJ mol−1. The apparently low value of apparent activation energy Ea indicates that the hydrogenation reaction is controlled by liquid-phase reaction. However, the fractal index h of fractal-like formation of compound 2 is not thermally activated, Ea = 2.8 (±0.3) kJ mol−1, signifying that the fractallike reaction is not changing with the thermal activation. A catalyst provides a fractal-like alternative route for the formation reaction of compound 2, with very low activation energy. The value of the apparent activation energies of the fractal-like reaction kinetics terms is in agreement with those generally reported for the double bond hydrogenation reaction carried out in the kinetic regime.29,30 Elevating temperatures and pressures is favorable for increasing the rate of hydrogenation and hence shortening the reaction time. Weibull model scale η parameter of compound 2 formation reaction (Table S10, Figure S14) is not thermally activated, Ea= 10.3 (±7.1) kJ mol−1. Also, the Weibull model shape β parameter of compound 2 formation is not thermally activated, Ea = 6.0 (±1.1) kJ mol−1, indicating that the reaction temporal shape is not changing with the thermal activation. The Pt/C catalyst provides an alternative route for the formation reaction of compound 2, with very low activation energy. The Weibull shape β parameter of compound 2 formation is almost constant with the value 0.209 ± 0.013, as is the Weibull model scale η parameter (0.099 ± 0.015). 3.6. Catalyst Recycling. In a typical catalyst recycle experiment, the Pt/C catalyst is separated from the reaction mixture by filtration after completion of reaction and reused in the next reaction without any treatment. After the first cycle, the activity is slightly lowered, but then in the next 6 recycles, the Pt/C catalyst maintain high activity and selectivity with the conversion of compound 1 over 95% and the yield of compound 2 over 92% after reaction for 2−6 h. In the last two cycles, the catalytic activity of hydrogenation reaction decreased gradually. The Pt/C catalyst can be recycled several times, leading to a cost-efficient practice.31 Fractal kinetic index h is apparently decreasing after the first cycle; however, in the next recycling steps, h is almost constant, 0.746 ± 0.076 (Figure 11, Table S22). Fractal initial reaction rate k0 is apparently constant in the subsequent recycling steps: 3.089 ± 0.770 mol m−3 min−1. The results of the Pt/C catalyst recovery show

Figure 9. Effect of hydrogen pressure on the Weibull scale η (●) and shape β (■) parameters of compound 2 formation.

increase and are positively related. Alternatively, a better dependence has been observed as reciprocal function of pressure (Figure S12). However, Weibull shape β parameter of compound 2 formation appears almost constant: 0.177 (±0.016) over this pressure range. Weibull scale/rate η parameter of compound 2 formation seems to increase below pH2 < 1 MPa, indicating shifting of the compound 2 formation to longer times. Catalyst Pt/C was inactive to a greater extent at reduced hydrogen pressures (below 1 MPa). 3.5. Temperature. The apparent activation energy, Ea, can be evaluated by the model-free isoconversional method at progressive conversion values (α).27,28 Activation energy for each conversion point (Ea, α) are calculated from reaction curves at several different temperatures in the 298−318 K range at the same value of conversion, α (Figure 10). The apparent isoconversional activation energy for hydrogenation of compound 1 is almost constant, around 32.4 ± 4.5 kJ mol−1, and that for the formation of compound 2 is also almost constant and with similar value, around 31.9 ± 1.9 kJ mol−1, over the whole conversion range. In another approach, the activation energies were calculated from the temperature dependence of the initial reaction rate k0 and fractal kinetic index h of fractal-like formation of compound 2 rate parameters. The initial reaction rate k0 apparently increased upon increasing temperature (Table S9, Figure S13). This increase in conversion indicates that, at a higher temperature, the reactant molecules effortlessly move over G


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Figure 11. Catalyst recycling steps effect on the fractal-like model terms: fractal index h (●, full line) and initial reaction rate k0 (■, dashed line) of compound 2 formation (c(1) = 0.14 mol dm−3, pH2 = 0.2 MPa, T = 318 K, mcat = 1.71 g dm−3, mixing rate = 400 r/min).

Figure 12. Linear relation of fractal index h and the Weibull shape β parameters of compound 2 formation.

that the catalysts can be reused several times for the hydrogenation of compound 1. Weibull shape β parameter for formation of compound 2 is apparently dropping after the first step; afterward, it is almost constant: β = 0.173 ± 0.017 (Table S23). However, the Weibull scale η parameter is, also, apparently dropping after the first step; afterward, it is slightly decreasing with the recycling steps η = 0.173 ± 0.017 (Figure S21). We already proved that the fractal-like kinetics model gives a good estimate of the probable effect of a fractal Pt/C catalyst on hydrogenation. We guess that at the initial conditions, elimination of the carbon support and product can influence reaction through the values of the time-changing reaction rates. The fractal index h-value is diminished after the first recycling step, h ≃ 0.8. The subsequent rate parameters of compound 2 formation may be larger than the rate parameters of the first recycling step. 3.7. Scale-up of Reactor. Scale-up follows the progression32 from the laboratory (75− 600 mL), pilot scale (4 L), up to the commercial plant reactor volume (600 L) (Table S24, Figure S22). Fractal kinetic index h does not depend on the reactor volume and is apparently almost constant (0.915 ± 0.051). The initial reaction rate k0 decreases very slightly and is apparently constant (1.116 ± 0.237 mol m−3 min−1). Weibull shape β parameter for formation of compound 2 is apparently slightly decreasing, with average value β = 0.235 ± 0.079 (Table S25, Figure S23). The Weibull scale η parameter decreases very slightly from the laboratory to pilot scale, with an average value of 0.239 ± 0.0.15 min. The fractal and Weibull kinetic models show that the reactor volume does not impact the reaction kinetics.

within a certain limited time interval, yield similar concentration−time profiles that are nearly indistinguishable. The fractal index h can be related to the dimensionality of the reaction media; for example, zero-valued index h corresponds to the three-dimensional Euclidian space (nonfractal), h ≈ 0.3 to reaction on a percolation cluster, h ≈ 0.5 to a reaction in a one-dimensional channel, and h ≈ 1 to a reaction on a lowdimensional, fractal object. Most of β values are in the 0.15−0.3 range, indicating diffusion in a fractal or disordered substrate. The β values in the range above 0.25 and h > 1 indicate that there is an additional reaction mechanism, which is in agreement with the electrostatic interactions between compound 1 and the Pt/C catalyst and solvent.

5. CONCLUSIONS The apparent rate of compound 1 hydrogenation at various conditions, using a 5% Pt/C catalyst, were estimated by the fractal kinetic and Weibull model approach. Irregular distribution of reactive sites on the catalyst surface and inconsistent diffusion of reactive substances modifies the classical kinetic rate laws. Very good agreement between experimentally recorded concentrations and those modeled by the fractal-like kinetic model and Weibull model was achieved. The hydrogenation process on the Pt/C catalyst is clearly a heterogeneous process, with a rate-limiting diffusion process that occurs in a convoluted Pt/C matrix with fractal motif as verified elsewhere. The hydrogenation reaction of compound 1 may be diffusion-limited because the large molecules of compound 1 have to diffuse to the Pt/C fractal surface and react with hydrogen. In this case, the rate law will strongly depend on the dimensionality and topology of the medium in which the reaction occurs. We propose that the Pt/C catalyst low-dimensional fractal environment contributes to fractal-like hydrogenation kinetics. The reaction rates are described in the fractal kinetics theory as time-variant and related to the nonEuclidian fractal dimension of heterogeneous catalyst surface. In this work, the fractal kinetic parameters fractal index h and initial reaction rate k0 were calculated for the catalytic hydrogenation of compound 1 on the fractal Pt/C catalyst. However, stricter inspection of the fractal-like kinetic model fit, for experimental treatments, necessitates a more complex kinetic model. Consequently, the data were re-evaluated utilizing the Weibull model. The reaction rate described by

4. RELATIONS OF FRACTAL-LIKE MODEL TERMS AND WEIBULL MODEL PARAMETERS Fractal index h and the initial rate k0 of compound 2 formation are exponentially inter-related (Figure S24), and Weibull scale/ rate η and shape β parameters are related by a power function (Figure S25). The fractal index h and the Weibull shape β parameters of compound 2 formation are linearly related (β = 0.382h − 0.1184; R2 = 0.8945; Figure 12). The fractal initial reaction rate k0 and Weibull scale/rate η parameters are also exponentially related (Figure S26). The fractal and Weibull kinetic models are equivalent, and their parameters are inter-related. These two models generally, H


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the Weibull parameter β and Weibull shape parameter η produced a consistently good fit that sufficiently predicts the kinetic parameters at different processing conditions. The fractal-like kinetic and the Weibull distribution model do not lessen the influence of the various reaction attributes. These models plainly tie the geometric constrains on a special, catalytic hydrogenation kinetic. It may be affirmed that fractallike kinetic works are superimposed as a background on “classical” chemical kinetics as a supplementary factor, thus providing hydrogenation kinetics. Our results show that the Weibull function is more appropriate for the entire duration of the hydrogenation reaction and additionally provide a more generalized picture. The fractal and Weibull model highlight the links between the fractal structure of the Pt/C catalyst and the hydrogenation reaction leading to compound 2 formation. The apparent relation of parameters from both models support the hypothesis that fractal-like kinetics model and the Weibull distribution model may play a role in hydrogenation of compound 1 and formation of compound 2. In fact, the fractal and Weibull model kinetics can be useful hypothetical tools for analysis of reaction kinetics practices. We would contend that experimental figures should always be checked against fractallike and Weibull kinetic models. The simplest efficient test is to measure the equilibrium concentrations of reactants and products (including various experimental conditions), and then fitting reaction evolution curves should be performed to determine whether the expressions for fractal-like or Weibull model rate parameters can statistically reliably describe the concentration profiles in time.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b04864. Additional discussion of fitting by kinetics models, mass transfer effect, compound 1 concentration, pressure effect on the fractal and Weibull model terms, temperature, solvent effect, catalyst recycling, scale up, and relations of fractal-like model terms and Weibull model parameters (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Catalytic Hydrogenation of 2-((1-Benzyl-1,2,3,6-tetrahydropyridin-4

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