Effect of Polymer Size on Heterogeneous Catalytic Polystyrene

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Ind. Eng. Chem. Res. 2010, 49, 11280–11286

Effect of Polymer Size on Heterogeneous Catalytic Polystyrene Hydrogenation Laura Beth Dong,*,†,‡ Salomon Turgman-Cohen,† George W. Roberts,† and Douglas J. Kiserow†,§ Department of Chemical and Biomolecular Engineering, North Carolina State UniVersity, Campus Box 7905, Raleigh, North Carolina 27695-7905, United States, and United States Army Research Office, P.O. Box 12211, Research Triangle Park, North Carolina 27709-2211, United States

The effect of polymer coil size on the rate of polystyrene (PS) hydrogenation was studied in a slurry reactor with mixtures of decahydronaphthalene (DHN) and carbon dioxide (CO2) as the solvent for the polymer. The PS coil size was changed by varying the polymer molecular weight from 9300 g/mol to 357 000 g/mol and by varying the CO2 concentration. Using a 5% Pd/5% Ru/SiO2 catalyst, the rate of aromatic ring hydrogenation at 150 °C was found to be strongly dependent on the size of a polymer coil relative to the average pore diameter of the catalyst. Significant pore diffusion limitations, as indicated by values of the Weisz modulus, were observed with increasing polymer molecular weight. Increasing the concentration of CO2 resulted in increased reaction rates, with an improvement of nearly 2 orders of magnitude at the highest PS molecular weight. 1. Introduction Catalytic polymer hydrogenation can be used to create products that, when compared to their unsaturated counterparts, exhibit improved physical properties.1-3 The use of homogeneous and heterogeneous catalysts to hydrogenate polymers has been reviewed by McManus et al.2 and McGrath et al.4 Much of the polymer hydrogenation literature focuses on the hydrogenation of olefinic polymer bonds using homogeneous catalysts; these reactions typically have milder operating conditions and good product selectivity. However, the removal of homogeneous catalysts from the final polymer product is often incomplete, which can result in accelerated polymer degradation. The use of heterogeneous catalysts in polymer hydrogenation offers the advantage of facile separation of catalyst and polymer solution, but the transport processes associated with heterogeneously catalyzed reactions must be considered when choosing between homogeneous and heterogeneous catalysts. The influence of mass transfer in heterogeneous catalytic reactions has been discussed in much detail,5,6 generally for situations where the diameter of the reactant molecules is small compared to the diameter of the catalyst pores. However, when the sizes of reactant molecules and catalyst pores are comparable, analysis of internal mass transport (pore diffusion) can be more challenging. For example, catalyst pore size was found to affect the rates of hydrotreatment of petroleum molecules, which can be comparable to the size of the pores in typical hydrotreating catalysts.7,8 Similarly, Chang and Huang9 and Shirai et al.10 demonstrated that copolymer hydrogenation rates and selectivity depended on catalyst pore size. Chang and Huang found that the catalyst pore size and metal dispersion affected the extent to which the olefinic portion of the block copolymer polystyrene-b-polybutadiene-b-polystyrene was hydrogenated.9 To study the effect of pore size on polymer hydrogenation, Chang and Huang prepared three 0.5% Pd/Al2O3 catalysts with average pore diameters of 17.1, 38.9, and 64.6 nm; the corresponding Pd dispersions, as measured by carbon monoxide (CO) chemisorption, were 58%, 36%, and 28%. These * To whom correspondence should be addressed. E-mail: [email protected]. † North Carolina State University. ‡ Present address: Albemarle Corp., Baton Rouge, LA. § United States Army Research Office.

authors measured the conversions of vinyl-1,2 olefinic groups, trans-1,4 olefinic groups, and aromatic rings. For all three catalysts, the one with the smallest pore size had the lowest conversions, despite having the highest dispersion, for all three reactions. For aromatic ring hydrogenation, conversions decreased with increasing pore size. However, for the olefinic groups, the conversions with the catalyst with the 38.9 nm pores and 36% Pd dispersion were somewhat higher than those with the 64.6 nm pores and 28% dispersion. The authors hypothesized that a trade-off between pore size and metal dispersion mitigated the effect of increasing pore diameter on the hydrogenation rate of olefinic microstructures. Shirai and co-workers studied the hydrogenation kinetics of acrylonitrile-butadiene rubber (NBR) on a series of palladium catalysts on smectite supports with a range of average pore sizes from 27 to 132 Å10. In carbon tetrachloride (CCl4), the conversion of vinyl groups was essentially nil for pore sizes between 27 and 63 Å, at 1 atm H2 pressure and a constant reaction time. At 50 atm H2, the conversion in this range of pore sizes was about 40%, with no significant variation with pore size. However, at all conditions shown, the conversion increased rapidly in the 40-80 Å range of pore sizes and then leveled out above about 80 Å. A few experiments were also run in acetone, which is a better solvent for NBR than CCl4. After 15 h of hydrogenation at 323 K and 50 atm H2, the conversions in acetone were substantially lower than in CCl4, although in acetone the shape of the conversion/pore size curve was essentially linear. These differences in the observed behaviors of NBR hydrogenation in CCl4 and acetone were attributed to the relaxation of NBR in the good solvent, i.e., the polymer coil size was larger in acetone than in CCl4. The results of dynamic light scattering experiments by Shirai et al. indicated that the NBR had a slight size distribution (ranging from 35 to 77 Å) and an average coil size of 42 Å. Therefore, the rapid increase in NBR hydrogenation rate that occurred between 42 and 63 Å is reasonable, since most of the polymer coils could not diffuse inside the catalyst with pore diameters smaller than the coil size. Another possibility for explaining the differences in NBR hydrogenation in CCl4 and acetone is that the solvent quality may affect polymer adsorption to catalytic sites and, thus, affect reaction rates.

10.1021/ie1011905  2010 American Chemical Society Published on Web 10/18/2010

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The role of solute diffusivity on internal mass transport in an irreversible, heterogeneously catalyzed reaction can be analyzed through the Weisz modulus (Φ): Φ)

(n + 1)2lc2(-RA,v) 2DA,effCA,s

(1)

As shown in eq 1, Φ is a function of the order of the reaction with respect to species A (n), the characteristic length of the catalyst particle (lc), the measured reaction rate of species A per geometric catalyst volume (-RA,v), the effective diffusion coefficient of species A (DA,eff) and the surface concentration of species A (CA,s). The characteristic length is a function of the particle geometry; for a sphere, lc ) R/3, where R is the radius of the catalyst particle. The Weisz modulus can then be used to estimate an effectiveness factor (η); plots of η versus Φ can be found in many references, e.g., ref 11. In order to calculate a value of Φ, a value of DA,eff must be estimated for the system comprising the polymer being hydrogenated and the hydrogenation catalyst. Satterfield et al.12 suggested that, at steady state, the DA,eff of species A diffusing through a porous membrane could be described by DA,eff ) D0

θKpKr τ

(2)

where D0 is the infinite dilution diffusion coefficient of species A in the bulk fluid, θ is the catalyst porosity, τ is the catalyst tortuosity, Kp is the equilibrium partition coefficient, and Kr is the reduction of diffusivity that occurs when the solute and pore size are similar in size. The equilibrium partition coefficient, as described by Ferry,13 is Kp ) (1 - λ)2

(3)

where λ is ratio of the solute diameter to the pore diameter. The product of the D0, Kp, and Kr in eq 2 describes the steric and frictional resistances of a hard sphere in a pore and is the diffusion coefficient, D, of the solute in the pores of the catalyst. This reduces eq 2 to Deff )

Dθ τ

(4)

which is commonly used to calculate effective diffusion coefficients for heterogeneously catalyzed, small-molecule reactions. For λ < 0.5, a value of D can be predicted using the Renkin equation (eq 5):14 D ) D0(1 - λ)2[1 - 2.1044λ + 2.0888λ3 - 0.948λ5]

(5) For λ > 0.5, D can be estimated using Kr values from Paine and Scherr15 and eq 3 for Kp. Colton et al. measured the Deff values of monodisperse polystyrenes (PS) in porous borosilicate glass cubes with different average pore diameters.16 The pore size distributions of the cubes were narrow, generally with greater than 90% of the pore volume being within 10% of the average pore diameter. The Deff values were used to compute Deff/D0 for PS in 1,2dichloroethane and chloroform, and it was found that the ratio was higher in 1,2-dichloroethane than in chloroform. This finding supports the hypothesis that solvent quality plays a role in polymer diffusion in pores. While the radii of gyration of PS in the bulk solvents were comparable at each molecular weight, 1,2-dichloroethane is a poorer solvent for PS than

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chloroform (based on the scaling relationships used by Colton et al.). The attraction between the polymer units in the poorer solvent (1,2-dichloroethane) is stronger than the attraction between the solvent and polymer molecules. With the opposite observed in the good solvent (chloroform), the polymer molecules may be less likely to reconfigure themselves in 1,2dichloroethane than in chloroform; therefore, they have less difficulty moving through the porous structure (i.e., have a higher diffusion coefficient) in a poor solvent. Kathawalla and co-workers studied the effect of coil relaxation on PS diffusion coefficients through a membrane immersed in tetrahydrofuran (THF), a good solvent for PS.17 They compared their data to predictions from the Renkin equation and found that, for small λ, the Renkin equation overpredicted Deff/D0. For larger λ, the converse was true. These authors attributed the underprediction of Deff/Do to overestimation of the reduction in polymer mobility, i.e., too large of a reduction calculated for the Kr term in eq 2. The error may be due to the fact that the Renkin equation was developed for the diffusion of hard spheres in porous media; it does not take into the account the ability of a polymer to reconform itself to fit inside pores. This research explores the effect of λ and polymer diffusion coefficient on PS hydrogenation kinetics in a batch, slurry reactor. Solvent quality was varied by dissolving various concentrations of carbon dioxide (CO2) into the main solvent for the polymer (decahydronaphthalene, DHN) and by using monodisperse PS ranging from 9300 to 357 000 g/mol in number-average molecular weight (which corresponds to average coil diameters ranging from 5 to 34 nm). Previous research demonstrated that the expansion of PS-DHN solutions with CO2 reduces polymer solution viscosity,18 increases PS diffusivity,19 and leads to higher PS hydrogenation rates in CO2-DHN than in neat DHN when a bimetallic catalyst system is used.20,21 2. Experimental Section 2.1. Materials. The 5% Pd/5% Ru/SiO2 catalyst used in this research was donated by BASF Catalysts, LLC. The BET surface area was 94 m2/g. An average pore diameter of 30 nm was calculated from mercury intrusion volume and BET surface area measurements. The pore-size distribution was narrow with nearly 90% of the pore volume within 20% of the average pore diameter. The catalyst porosity was 0.48 and the particle density was 1.39 g/mL, both determined by mercury porosimetry. An average particle size of 102 µm was measured by electron microscopy. Polystyrene standards were purchased from Pressure Chemical (Pittsburgh, PA) and Polymer Source, Inc. (Montreal, Canada) and used as received. Molecular weights of the PS standards were measured by gel permeation chromatography (GPC) with tetrahydrofuran (THF) as the mobile phase. An Optilab rEX refractometer (Wyatt Technology, Santa Barbara, CA) was used in conjunction with a minDAWN Tristar light scattering detector (Model WTR-02, Wyatt Technology, Santa Barbara, CA). ASTRA software (Version 5.3.2.20, Wyatt Technology, Santa Barbara, CA) was used to correlate the polymer concentrations and intensities of scattered light to obtain the number-average and weight-average molecular weights (Mn and Mw, respectively). The resulting molecular weights of the PS standards are provided in Table 1. The PS samples are labeled according to the Mn (in kilodaltons, 1 kDa ) 1000 g/mol) provided by the suppliers. The measured molecular weights are shown in the last two columns. In some cases, the supplied Mn did not match the Mn measured by GPC.

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Table 1. Characteristics of Polystyrene Standardsa sample

Mw (g/mol)

Mn (g/mol)

PS-9.3 PS-24 PS-46 PS-100 PS-131 PS-160 PS-392

9 580 22 400 43 100 102 000 146 000 158 000 365 400

9 290 22 300 42 600 100 000 143 000 154 000 356 800

Gel permeation chromatography (mobile phase ) THF, light scattering and refractive index detectors). a

Table 2. Liquid Phase Compositions in PS Hydrogenation Reactor at 150 °Ca gas feed

xH2

xCO2

xDHN

800 psig of H2 800 psig of H2 + 1200 psig of CO2 800 psig of H2 + 2200 psig of CO2

0.04 0.02 0.03

0.37 0.54

0.96 0.61 0.43

a

H2-trans-DHN or H2-trans-DHN-CO2.

Table 3. Effect of CO2 on Properties of PS-160 in DHN (T ) 150 °C)a CO2 (mol %)

pressure (psig)

kD (cm3/g)

D0 × 106 (cm2/s)

RH(nm)

0 37 54

0 2000 3000

16 3.5 12

0.609 1.10 2.12

11.1 8.9 6.8

a

PS (Mn ) 154 000 g/mol, Mw ) 158 000 g/mol).

the reaction procedure and the subsequent analysis can be found in Dong et al.21 3. Results and Discussion

Figure 1. Cumulative molecular weight distribution of commercial polystyrene (mobile phase ) THF, refractive index detector).

Commercial PS (Sigma-Aldrich, St. Louis, MO) was used as received. Information provided by the supplier gave an approximate average Mw of 350 000 g/mol and an approximate average Mn of 170 000 g/mol. The average of four independent GPC measurements resulted in Mw ) 230 000 g/mol and Mn ) 130 000 g/mol for the commercial PS. The mass fraction distribution of a GPC measurement of the commercial PS is shown in Figure 1. Anhydrous DHN, a 24/76 mixture of cis and trans isomers, was purchased from Sigma-Aldrich (St. Louis, MO) and used as received. Carbon dioxide (g99.99%) and hydrogen (g99.999%) were purchased from Airgas National Welders (Charlotte, NC). 2.2. High-Pressure Dynamic Light Scattering. High-pressure dynamic light scattering (DLS) was used to determine PS diffusion coefficients at 150 °C. Details of the experimental technique may be found in Dong et al.19 The diffusion coefficients of PS-160 were measured at a scattering angle of 90° for polymer solutions containing 1, 2, and 3 wt % PS (concentration before the addition of CO2). As discussed in detail later, at reaction pressures of 2000 and 3000 psig, the mole fractions of CO2 in the liquid phase at these pressures are approximately 0.37 and 0.54. Volumes of CO2 were added to the DLS cell to achieve these CO2 mole fractions. The pressure was then increased to the total pressure of the CO2-containing reaction system, 2000 or 3000 psig, before DLS measurements were made. 2.3. Hydrogenation Experiments. Polystyrene was hydrogenated using a slurry reactor at 150 °C and an agitation rate of 2500 rpm. Hydrogen pressure was maintained at 800 psig. For the CO2-containing reactions, the CO2 pressure was either 1200 or 2200 psig. The concentration of aromatic rings was monitored at 261.5 nm using UV-vis spectroscopy and used to calculate the fractional conversion of aromatic rings (xA), also referred to as the degree of hydrogenation. Further details of

3.1. Polystyrene Diffusion Coefficients. The H2-CO2DHN liquid phase compositions were estimated using the Peng-Robinson equation of state (PR-EOS). Since the DHN used in this research is 76 mol % trans isomer, the calculations were based on trans-DHN. Binary interaction parameters of -0.162, 0, and 0.125 were used for H2-CO2, H2-trans-DHN, and CO2-trans-DHN.22 As shown in Table 2, CO2 solubility in trans-DHN increased when CO2 pressure was increased from 1200 to 2200 psig. The bulk diffusion coefficients of PS (Dbulk), which were measured at the reaction conditions (T ) 150 °C, total pressure ) 2000 or 3000 psig, and CO2 concentration ) 37 or 54 mol % CO2), were found to be linearly dependent on polymer concentration (cPS). The y-intercepts of Dbulk versus cPS curves yielded PS infinite dilution diffusion coefficients (D0), while the dynamic second virial coefficients (kD), estimators of solvent quality, were obtained from the slopes of the best-fit lines. The Stokes-Einstein equation (eq 6) was used to determine hydrodynamic radii (RH) of the polymer coils from the values of D0. RH )

k BT 6πηD0

(6)

In eq 6, kB is Boltzmann’s constant, T is the absolute temperature, and η is the solvent viscosity. Carbon dioxide-DHN viscosities were obtained from Cain.19,23 As shown in Table 3, D0 increased by a factor of 3.5 as the CO2 concentration increased from 0 to 54 mol %. The mixture of CO2 and DHN is a poorer solvent for PS than neat DHN, as indicated by the decreased kD when CO2 was present. Also note that RH decreased 40% as CO2 concentration increased. When no CO2 is present, one coil can fit inside a catalyst pore. At the higher CO2 concentration, two coils can enter the pore at the same time. The decrease in RH suggests that more polymer coils can fit inside catalyst pores as CO2 concentration increases and that the diffusion coefficient of PS in the catalyst pores, D, should increase because the value of λ decreases with increasing CO2 concentration. The decreased values of kD, i.e. decreased solvent quality, for CO2-DHN mixtures suggest that polymer adsorption to catalytic sites might be enhanced. The decrease in solvent quality results in the polymer-solvent interactions becoming less favorable; as a result, polymer-polymer or polymer-catalyst interactions become more favorable.

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Table 4. Ratios of PS Diameter to Average Pore Diameter (λ) in Neat DHN (T ) 150 °C) samplea

λ

PS-9.3 PS-24 PS-46 PS-100 PS-131 PS-160 PS-392

0.19 0.29 0.40 0.51 0.72 0.75 1.14

a The numbers following “PS” are the manufacturer-provided number-average molecular weights (in kDa).

The effect of solvent quality on polymer adsorption was demonstrated by Kawaguchi et al.24,25 They found that more PS adsorbed onto a chrome substrate when the θ-solvent cyclohexane was used, instead of the good solvents CCl4 or toluene.24 In subsequent studies, they found that the equilibrium concentration of 355 kDa of PS on a SiO2 particle with an average pore diameter of 30 nm was 0.3 × 10-4 g/m2 when CCl4 was the solvent.25 When cyclohexane, a poorer solvent, was used, the equilibrium concentration was approximately 1 × 10-4 g/m2 for the same PS-SiO2 combination. These results indicated that less polymer adsorbs onto porous SiO2 from a good solvent than from a poor solvent. Similarly, in this research, the use of CO2-DHN, which is a poorer solvent for PS than neat DHN, may promote polymer adsorption to active catalytic sites and result in increased polymer hydrogenation. The infinite dilution diffusion coefficient (D0) of each PS used in this research was scaled from the measured value for PS160 using the relationship D2 ∝ D1(MW1/MW2)0.5. The scaling relationship [D ∝ (MW)-0.5] is based on the bead-spring theory of a polymer diffusing in a dilute solution. After calculating RH values from the scaled D0 values, the hydrodynamic radii for the polymer dissolved in neat DHN and the average pore diameter were used to determine λ values at each polymer molecular weight. The λ values, which are provided in Table 4, ranged from 0.19 to 1.14. 3.2. Effect of Molecular Weight on PS Hydrogenation. To illustrate the effect of molecular weight on PS hydrogenation, a series of monodisperse PS’s (ranging from Mn ) 9300 g/mol to Mn ) 357 000 g/mol) were hydrogenated using 5% Pd/5% Ru/SiO2 for 2 h at 150 °C. The resulting degrees of hydrogenation, which are shown in Figure 2, show that hydrogenation of the polymer becomes progressively slower as its molecular weight increases. For molecular weights below approximately 22 000 g/mol (λ ca. 0.3), the conversion of the aromatic rings is essentially complete at the specified conditions. However, for the polymer with Mn ) 357 000 g/mol (λ ) 1.14), the conversion of aromatic rings was only about 10% at the same conditions. The degree of hydrogenation starts to decrease below 1 rather precipitously when λ exceeds about 0.35. In the region of λ ) 0.8, the decrease in the degree of hydrogenation appears to abate. The importance of the ratio of polymer size to support pore diameter corresponds to the findings of Kawaguchi et al. for PS adsorption on porous silicas. They hypothesized that at λ > 0.4 the polymer molecule had to deform to fit inside the SiO2 pores; the need for deformation resulted in lower equilibrium polymer concentration.25,26 A critical λ was also observed by Shirai and co-workers, who saw a dramatic increase in NBR hydrogenation when λ was less than 0.6.10 The potential effect of diffusion limitations on polymer hydrogenation was noted by Ness and co-workers when they hydrogenated PS using an ultrawide pore Pt/SiO2 catalyst with an average pore diameter of 380 nm.27,28 They saw a drastic

Figure 2. Effect of polymer molecular weight on polystyrene hydrogenation (T ) 150 °C, t ) 2 h, 3 wt % PS-DHN, 800 psig H2, 1 g of catalyst/g of PS, 2500 rpm).

Figure 3. Effective polystyrene diffusion coefficients in DHN (T ) 150 °C); Deff ) Dθ/τ, τ ) 6, θ ) 0.48.

decrease in the initial rate of hydrogenation when the PS molecular weight reached 200 000 g/mol and attributed the behavior to pore diffusion resistances and differences in the adsorption of the polymer molecules to the catalyst surface. The results shown in Figure 2 are consistent with these results, since the diffusivity of the polymer molecule decreases as its molecular weight increases. Figure 3 shows the impact of varying λ on effective PS diffusivity; the values of λ were changed by altering polymer molecular weight for a constant catalyst pore size. Infinite dilution diffusion coefficients for the various PS’s were obtained by scaling as described in section 3.1. A tortuosity (τ) of 6 for the catalyst particle was assumed, and effective PS diffusion coefficients were calculated using eq 4. As illustrated in Figure 3, PS diffusion coefficients begin to significantly increase when the value of λ falls below about 0.7. This behavior is not unlike that of xA shown in Figure 2. The increase in polymer diffusivity below approximately λ ) 0.7 appears to positively influence the PS hydrogenation process. The effective diffusivity of PS392 was not calculated because the procedures used to calculate Deff values for the polymers with Mn < 275 000 g/mol (λ < 1) are not valid when λ > 1. 3.3. Effect of CO2 on Monodisperse PS Hydrogenation. The effect of 1200 psig of CO2, which corresponds to roughly 37 mol % CO2 in the liquid phase, on 5% Pd/5% Ru/SiO2catalyzed PS hydrogenation in DHN was determined at several different polymer molecular weights. A second CO2 concentra-

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Table 5. Observed Rate Constantsa for Aromatic Ring Hydrogenationb polymer PS-24 PS-46 PS-100 PS-131 PS-160 PS-392

0 psig of CO2

1200 psig of CO2

2200 psig of CO2

-5

2.15 × 10 6.74 × 10-6 1.63 × 10-6 9.29 × 10-7 7.14 × 10-7 6.24 × 10-8

1.21 × 10-5 5.93 × 10-6 2.70 × 10-6 2.15 × 10-6

8.31 × 10-6 4.34 × 10-6

a Units for the observed rate constant are L/g cat./s. b T ) 150 °C, 3 wt % of PS-DHN, 800 psig of H2, 1 g of catalyst/g of PS, 2500 rpm.

160 decreasing from 0.75 in neat DHN to 0.60 in the presence of 1200 psig of CO2 to 0.46 for the 2200 psig of CO2-containing system. As a result, the observed rate constants for PS-160 with 1200 and 2200 psig of CO2 are comparable to those observed for lower molecular weight PS’s with similar λ values. These results illustrate how pore diffusion and size restrictions strongly influence the kinetics of PS hydrogenation. This research also demonstrates how the utility of an antisolvent such as CO2 in heterogeneous polymer hydrogenation can create an environment that allows more polymer molecules to access the active sites in the catalyst interior; thus, increased reaction rates are observed. 3.4. Analysis of Mass Transport. In order to support the interpretation of the data in sections 3.1-3.3, values of the Weisz modulus (Φ) and the effectiveness factor (η) were calculated for each experiment with the polymers whose molecular weights were 160 kDa or less. Obviously, low values of η and high values of Φ would be consistent with a strong influence of pore diffusion, as suggested in sections 3.1-3.3. The rate of reaction of aromatic rings is expressed as -RA ) ηWk′CA,s

Figure 4. Dependence of observed rate constants for PS hydrogenation on λ ) RH/rpore (T ) 150 °C, 3 wt % of PS-DHN, 800 psig of H2, 1 g of catalyst/g of PS, 2500 rpm).

tion (54 mol percent CO2 in the liquid phase) was used in the hydrogenations of PS-160 and PS-392. At low to moderate degrees of hydrogenation, the rates of disappearance of aromatic rings were first-order in aromatic ring concentration, first-order in catalyst concentration (Ccat), and zero-order in hydrogen concentration. Observed rate constants (kobs) were obtained from the slopes of the best-fit lines to -ln(1 - xA) versus Ccatt. As shown in Table 5, the addition of CO2 increases the rate of hydrogenation, as described by kobs, for each of the polymers studied. Furthermore, the presence of 2200 psig of CO2 results in an order of magnitude increase in the observed rate constant for the hydrogenation of PS-160 relative to the rate constant for neat DHN. The positive effect of CO2 on kobs spans nearly 2 orders of magnitude for the hydrogenation of PS-392. The 2-fold difference in the kobs values for PS-392 with 1200 and 2200 psig of CO2 is smaller than the difference between the analogous kobs values for PS-160. The polymer diffusion coefficients measured using DLS (section 3.1) and the parameters calculated from them (polymer hydrodynamic radii, dynamic second virial coefficients) can be used to explain the behavior of kobs. The order of magnitude increase in kobs for PS-160 with the addition of 2200 psig of CO2 cannot be solely explained by the 3.5-fold increase in polymer diffusion coefficient. The decrease in polymer coil size that is accompanied by decreasing solvent quality associated with increasing CO2 concentration should facilitate faster polymer diffusion into the catalyst interior. Moreover, with the decrease of λ associated with the smaller polymer coils, more PS molecules should be able to enter the pores, thereby increasing the apparent value of kobs and producing higher rates of hydrogenation. The rate constants in Table 5 for the reactions in neat DHN and for all reactions with PS-160 are plotted as a function of the ratio of polymer size to pore size (λ) in Figure 4. The addition of CO2 to the reaction system results in the λ of PS-

(7)

where η is the effectiveness factor, W is the mass of catalyst, k′ is the intrinsic rate constant based on catalyst weight, and CA,s is the aromatic ring concentration at the surface of the catalyst. The rate of mass transport of aromatic rings from the bulk liquid to the surface of the catalyst particle is -RA ) kLSALS(CA,b - CA,s)

(8)

where kLS is the liquid-solid mass transfer coefficient, ALS is the liquid-solid interfacial area, and CA,b is the aromatic ring concentration in the bulk liquid. The ratio ηWk′/kLSALS is the maximum possible kinetic rate (including pore diffusion) divided by the maximum possible rate of external mass transport. If this ratio is sufficiently low (say