Ind. Eng. Chem. Res. 1991,30,822-828
a22
Solvent Effects on Reactions in Supercritical Fluids Benjamin C. Wu, Michael T. Klein,* and Stanley I. Sandler Center for Catalytic Science and Technology, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
Supercritical fluid (SCF) solvents represent a unique and powerful reaction medium because of the strong pressure dependence of their densities and solvent properties (v, 9 , 6, e, and D ) . This offers the capability of controlling the solvent properties and reaction rates and selectivities through pressure manipulations. Transition-state theory was used herein to interpret the effect of pressure on the overall reaction rate as an apparent activation volume that can be further decomposed into various contributions: AV,, = -RT(d In r / d P ) = AVtnt AV;, AVtlec accounting for mechanical pressure effects, solvent compressibility, diffusional limitations, electrostatic interactions, and phase behavior effects, respectively. The present investigation emphasized the latter three and evaluated their contributions as AViiff = 1090 cm3/mol for benzyl phenyl ether pyrolysis; = -3700, -2600, and -220 cm3/mol for hydrolysis of dibenzyl ether, phenethyl phenyl ether, and guaiacol, respectively; and A 5 = 1600 cm3/mol for dibenzyl ether pyrolysis in toluene.
+
+
+
+ AF,
AClec
Introduction The considerable interest in supercritical fluid (SCF) solvents is largely because of their promise in separation/extraction processes (Paulaitis et al., 1983a,b; Kim et al., 1985; Eisenbach et al., 1983; Schneider, 1983; Maddocks and Gibson, 1977; Maddocks et al., 1979; Amestica and Wolf, 1984; Barton, 1983; Towne et al., 1985; McHugh, 1981; Kershaw and Overbeck, 1984; Bartle et al., 1979a-c; Stewart and Dyer, 1973). Often viewed as “dense gases”, these fluids exhibit physicochemical properties, such as density ( p ) , viscosity ( T ) , dielectric constant (E), and solubility parameter (a), intermediate between those of liquids and gases. Moreover, these properties can be easily controlled and manipulated by pressure. Herein we examine the unique pressure dependence of SCF solvent effects with an eye toward the elucidation of the mechanisms of reactions in SCF solvents. The critical point is defined as the point at which two fluid phases, liquid and vapor, become indistinguishable. A SCF solvent, by convention, is above its critical temperature (T,) and pressure ( P J . The density of a supercritical fluid near T,and P, can be of the order 0.2 g/cm3, closer to that of a liquid than that of a gas. In this region of temperature and pressure, SCF solvents are highly compressible, and their densities can be easily controlled between liquidlike and gaslike extremes by changing pressure. This helps to explain their appeal in separation processes, where solute solubility scales roughly with solvent density. The industrial involvement of SCF solvents in a coffee decaffeination process (Rozelius et al., 1974) utilizes this pressure-adjustable solvation power. Other possible applications for SCF solvents include enhanced oil recovery with supercritical C02 (Doscher and El-Arabi, 1982), wet-air oxidation of organics in supercritical water (Helling and Tester, 1987, 1988; Yang and Eckert, 1988), coal liquefaction in supercritical toluene (Amestica and Wolf, 1984; Maddocks and Gibson, 1977; Maddocks et al., 1979; Bartle et al., 1979a,c; Kershaw and Overbeek, 1984), catalytic disproportionation of near-critical toluene (Collins et al., 1988), bitumen extraction from oil shale (Eisenbach and Niemann, 1981; Eisenbach et al., 1981), activated carbon regeneration (DeFillipi et al., 1980), and supercritical chromatography (Yonker et al., 1987). These applications have in common their exploitation of the pressure-adjustable density of SCF solvents.
* Author
to whom correspondence should be addressed.
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Table I. Solvent Effects on Reactions in the Liquid Phase solvent property analysis c, dielectric constant Kirkwood 6, solubility parameter Herbrandson-Neufeld p, ionic strength deb ye-Huckel D / T , diffusivity/viscosity cage effects
The influence of the unique pressure-dependent properties of an SCF solvent should not be limited to the extraction process. For example, chemical reactions are well-known to be influenced by solvent effects. Those observed in the more traditional liquid phase offer hints on how SCF solvents can influence reactions. These effects have long been known and theories have been developed to correlate observed kinetics with solvent properties. Listed in Table I are some of the classic kinetics analyses. Solvent polarity, as measured by scales such as the dielectric constant (e), ionic strength (p),and solubility parameter @),influences a number of reaction classes. These include the Diels-Alder isomerization of isoprene (Eckert, 1967), Diels-Alder addition of isoprene to maleic anhydride (Wong and Eckert, 1969; Greiger and Eckert, 1970; Eckert et al., 1974),Diels-Alder dimerization of cyclopentadiene (Wong and Eckert, 1969), Menschutkin reaction of a-picoline with w-bromoacetophenone (Eckert, 1967),the ionic reaction of bromoacetate-thiosulfate (Eckert et al., 1974), and reaction of pyridine with methyl iodide (Moore and Pearson, 1981). These and other polar reactions have been interpreted along the lines of the Herbrandson-Neufeld formalism (1966),the classic Kirkwood analysis (19341, and classic electrostatic theory (Moore and Pearson, 1981). Free-radical reactions are susceptible to viscosity-related solvent effects (Pryor and Smith, 1970; Ishihara et al., 1974; Aleksandrov and Gol’danskii, 1984). An increase in viscosity is manifested as a decrease in the diffusivities of the reactants. The effect of this on kinetics is typically interpreted in terms of the cage-effect theory. Evidence for molecular cages is found through recombination of the geminate radicals (Moore and Pearson, 1981) and decreased decomposition rate constants. Pryor and Smith (1970) studied the decomposition rate constants for a number of free-radical initiators in a series of paraffins and were able to correlate them to the solvent viscosities. It would seem reasonable that these and other solvent effects would be operable for reactions in SCF solvents as well. The object of this paper is to set forth a useful formalism for thinking about reactions in SCF solvents. The development of this formalism was motivated by the extreme pressure dependence of the properties of SCF 0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 823 solvents. Pressure is a natural experimental or processing lever for analyzing or exploiting, respectively, SCF solvents. However, because of the high compressibilityof SCFs near T,and P,,many SCF solvent effects will also vary and influence reaction rates dramatically. It would be useful, at least in thought, to separate the change in rate due to changes in pressure from the change in rate due to changes in the dielectric constant. Along these lines, the specific goal of the paper can be concisely summarized as the advancement of the formalism of the pressure derivative of the reaction rate (d In r/dP). The unique challenge is that all SCF solvent properties change with changes in the pressure, and each can affect chemical reactions differently. These complications can generally be neglected in traditional liquid-phase analyses, where the various effects of solvents on reactions can be addressed independently. The total pressure derivative of eq 1essentially lists the effect of the simultaneous variation of the solvent properties of a SCF solvent on reaction rates. In eq 1,N is
the number of solvent or reaction medium properties or attributes, xi, that both change with pressure and affect the reaction rate. The objective of the discussion to follow is to reduce each of the terms contributing to d In r / d P to a "product" of a classical model of solvent effects (as in Table I) and a model of the dependence of the solvent property on pressure. We wish to stress that, in general, many solvent properties change simultaneously with changes in the pressure of a single SCF solvent. Also, it is not our objective to provide a single continuous function r(xi)for use in eq 1. We will, however, show cases where only a few of the terms of eq 1are important by considering examples of different reactions in different SCF solvents. That is, we sought experimental systems where we could highlight various terms of eq 1. Transition-state theory provides a convenient formalism with which to evaluate direct pressure effects. For the bimolecular reaction A B C (where r = kcCACB),this is given as the partial derivative:
+
-
The isothermal compressibility term vanishes for unimolecular reaction!. The activation volume is defined as AV,* = V, - V , - VB, where Vi is the partial molar volume and M indicates the transition-state species. AVc: provides valuable mechanistic information about the transition state that complements that gained from the activation enthalpy, AH,', and entropy, AS,*. Typically the magnitude of the intrinsic activation volume is f25 cm3/mol (leNoble, 1978). In a condensed phase, AVc*is essentially the total pressure derivative since liquid solvent properties are essentially pressure independent. The challenge to modeling pressure effects on reaction rates in SCF solvents is that the solvent properties are extremely pressure sensitive. The challenge in the interpretation of AV,' is to account for these changes in solvent properties with changes in pressure. Unusually large activation volumes (IAV*I> lo3cm3/mol) have been reported for reactions in SCF solvents (Alexander, 1985; Simmons and Mason, 1972a,b;Flarsheim et al., 1989; Johnston and Haynes, 1987) which account not only for the direct effect of pressure, as in eq 2, but also for the variation of solvent
properties with P. This motivates ow interest in advancing the formalism of eq 1to express the pressure dependence of reactions in SCF solvents as a total derivative, which, unlike the case in liquid solvents, does not closely approximate the partial derivative. The pressure derivative of eq 1 defines an apparent activation volume as
. R { S )
--
+ RT( d7) In [A] + R { y )
(3)
where the pressure derivatives of [A] and [ B ]are at constant total concentrations and represent phase change only (see below). The rate constant k , = kc(P,T,Ni,D,E)and reactant concentrations [A] = A(P,T,Ni) and [ B ] = B(P,T,Ni) are dependent on the pressure and solvent transport (D) and electrostatic (E)properties. The analysis can be simplified be examining only reactions of isothermal systems in a dilute solution of solutes in a given SCF solvent so that the temperature and mole number (Ni) dependence of k,, A, and B can be ignored. In this instance eq 3 can be rewritten as
*RT
-- VwP =
(s) =(T) (,)(5) d In k ,
+
d In k ,
+
This defines the present formalism for the components of the apparent activation volume as The remainder of this paper is devoted to the evaluation of each of the terms in eq 5.
Effect of Phase Behavior The importance of the phase behavior of systems involving supercritical fluids can be viewed from two perspectives. First, kinetic analysis of reactions in supercritical fluids clearly requires calculation of the number and composition of equilibrium phases. Second, industrial-scale reactions will involve whatever number and compositions of equilibrium phases the overall process economics dictate. Design, scale-up, and production, therefore, require thermodynamic as well as kinetic analysis. This section focuses on the influence of phase equilibria on the kinetics of reactions in SCF solvents. The pyrolysis of dibenzyl ether (DBE) in SC toluene is chosen as an example that allows assessment of AQ. DBE (PhCH20CH2Ph)is an excellent probe reactant because its global chemistry and elementary steps of reaction to benzaldehyde and toluene have been well studied (Brucker and Kolling, 1965; Cronauer et al., 1979; Schlosberg et al., 1981a,b;Gilbert and Gajewski, 1982; Simmons and Klein, 1985;Townsend and Klein, 1985; O'Malley et al., 1985) and the reaction rate can be expressed as r = k[DBE]3/2 (Wu, 1990). Toluene was selected as the SCF solvent because the phase behavior of the DBE/toluene system can be predicted adequately by using the Peng-Robinson equation of state and because toluene shares structural features with dibenzyl ether (DBE) and its pyrolysis products. It was anticiptated that electrostatic effects would be minor so that the analysis could focus on AV". The calculated phase behavior for D6E/biphenyl/toluene system at experimental conditions (Wu et al., 1989)
824 Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991
Toluene Loading (g/cm 0.05
0
0.10 0.20 1
I
i) 1
I
M at 45 atm) and volume fractions ( 4 =~0.1~at 5 atm and 0.6 at 45 atm) calculated from the Peng-Robinson equation of state. That is, the apparent rate constant i~ the product $UqkUqof his and the rate constant kbq (0.002 98 M-1/2s-l). The resulting value of A T = 1600 cm3/mol is 2 orders of magnitude greater than intrinsic activation volumes (leNoble, 1978).
Influence of Diffusion on Reaction Rates in SCF Solvents The focus in this section is on elucidation of the contribution of transport limitations to the overall pressure derivative d In r / d P . This defines Aa, as 0
~ " 0.0
"
"
0.2
"
"
"
"
0.4
(7)
~
0.8
0.6
1.0
Mole Fraction Toluene Figure 1. Phase behavior of DBE/biphenyl/toluene system at 375 OC.
0.4
1
AB Experimental Data
-
Model Prediction
0.0 0.00
It is informative to a compare liquid- and gas-phase theories of reaction kinetics as extremes to that which a model for SCF solvents must approach in the limit of high and low pressure, respectively. The classic model for reactions in liquid solution involves the cage-effect theory (Rabinowitch, 1937; Moore and Pearson, 1981; Rohr and Klein, 1990). In its simplest form, it is a recognition of the serial events of diffusion and chemical transformation in an overall chemical reaction. This is illustrated in eq 8 for unimolecular bond fission.
0.10
Toluene Loading (g/cm
0.20
3
e x
[A + B]*
-+ A1
A
B
(8)
In this reaction, the initially formed radicals are trapped in the solvent cage as an encountered pair, [A + B]*. The overall reaction is realized only when the members of the encountered pair diffuse apart (A2) to break off an encounter. The competition between the recombination (hl) and disencounter (A,) rates controls the overall rate of this elementary reaction as
Figure 2. Effect of toluene loading on DBE conversion at 375 ' C : experimental data and model prediction.
is shown in Figure 1as a P-x diagram. The solid points represent experimental loadings, i.e., the amount of toluene charged to the reactor. The biphenyl was in a small constant concentration, and Figure 1 should be viewed essentially as a P-x diagram for a binary system. For neat pyrolysis approximately 80% of the DBE was present in the liquid phase at a pressure of approximately 5 atm. The addition of toluene had two immediate effects. First, the DBE concentration in the liquid phase was diluted because toluene entered the liquid phase. Second, the number of moles of DBE in the liquid phase decreased as some of the DBE dissolved into the toluene-rich vapor phase. Figure 2 summarizes the experimental results. The conversion of DBE dropped from 90% at neat conditions to 50% at a toluene loading of 0.21 g/cm3 where P r 45 atm. The global reaction rate law ~ D B E= 41iqkliq[DBE11i~'2+ 4vapkvap[DBEIvapB/' (6) where 4i is the volume fraction of the i phase, was fit to the data to obtain optimized values for the rate constants of kli, = 0.002 98 M-lj2 s-l and Itvap = 0.008 95 M-1/2 s-l. Virtually all the reaction occurs in the liquid phase because of the 2 orders of magnitude difference in concentration: [DBE], = 3.5 M and [DBE], = 0.02 M. The suppression of the overall reaction rate is therefore caused by the dilution of [DBEIU and diminution of DBE from the faster reacting liquid piase. The contribution to AVap of AV; was calculated on the basis of the concentration ([DBE],,, = 3.5 M at 5 atm, 0.5
+
where v0 = 1/(1 Da)and Da = ( ~ p - , e - ~ - i / ~ T ) / ( 3 0 / d ~ * ) . The influence of diffusion is therefore quantitively summarized in the Damkohler number, Da. Because of the changes in typical small-moleculediffusivities from lo-' cmz/s in the gas phase to cm2/s in the liquid phase, it is reasonable to expect Da,and therefore the influence of diffusion, to vary through the supercritical region from gaslike to liquidlike. For Da
