D. Thermodynamic Pressure Effects on Reaction Rates

state species that has the required energy and conformation corresponding to

the internal energy barrier for chemical reaction. This transition state complex

then proceeds directly to products, and the rate of the chemical reaction is governed by the rate constant for this decomposition from the activated state. This

is illustrated for a bimolecular reaction between reactants A and B forming the

transition state M‡ by

A+B



M‡ → products



The pressure dependence of the reaction rate constant is given by the following

relation in terms of partial molar volumes and isothermal compressibility (90):

∂ ln kbm

∂P



=−



ν‡

− kT

RT



where kbm = bimolecular rate constant (mol/L-min), ν‡ = νM‡ − νA − νB =

activation volume (the difference between the partial molar volumes of the transition state species and that of the reactants), νi = partial molar volume of

component i at reaction conditions, kT = mixture isothermal compressibility,

and R = universal gas constant. Note that the isothermal compressibility term

in the above equation accounts for changes in the reactant concentrations with

pressure. This term is not included if the rate constant is expressed in pressureindependent units, such as mole fraction or molality (84,91). A more general

expression for the pressure effect on the rate constant that accounts for the

number of reactant species is given by

∂ ln k

∂P



=−



ν‡

+ (1 − n)kT

RT



where n is defined as the sum of the stoichiometric coefficients of the reactants

(78,91).

Note from these expressions that a chemical reaction is accelerated by

pressure if its activation volume is negative. This is generally the case for most

addition reactions, and as an example, this effect has been exploited advantageously to accelerate cycloaddition reactions by pressure (92). In addition,

dissociation reactions can be favored by pressure if charged species are formed

through electrostriction effects. This causes an ordering of charged (ions) and

uncharged (e.g., solvent) species, which results in a significant decrease in molar volume (93). The partial molar volumes and isothermal compressibility of

the reaction mixture can be estimated from an equation of state. Brennecke

and coworkers (90,94) present the appropriate thermodynamic correlations to

estimate these values, and they have applied these calculations using the Peng–

Robinson equation of state (95).



Copyright 2002 by Marcel Dekker. All Rights Reserved.



E. Activation Volumes

As noted previously, the activation volume can be defined as the difference

between the partial molar volumes of the activated intermediate, or transition

state, species and that of the reactants. Activation volumes for liquid-phase

reactions are typically on the order of ±50 cm3 /mol (31,83,96), whereas apparent activation volumes of greater than ±1000 cm3 /mol have been reported for

SCF reactions (96). For example, Johnston and Haynes (78) report an activation volume of −6000 cm3 /mol for the unimolecular thermal decomposition of

α-chlorobenzylmethylether in 1,1-difluoroethane near the critical point. Eyring

and coworkers (97,98) have observed activation volumes of as high as +7000

cm3 /mol at just above the critical point for the ring closure reaction of a metal

carbonyl in both supercritical CO2 and ethane. Such large positive-to-negative

variations have been explained by considering the activation volume to be the

sum of two contributing terms (26,78,97): (a) a repulsive or intrinsic component

resulting from the change in occupied volume between the reactants and the

transition state, and (b) an attractive contribution due to solute–solvent intermolecular forces. The repulsive part can be significant depending on changes in

molecular volume (i.e., bond lengths) resulting from the breakage or formation

of bonds. The attractive contribution is significant, for example, when there are

large changes in polarity between the reactants and the transition state. Johnston

and Haynes (78) attributed their large negative activation volume to this latter

attractive contribution, which resulted from a more ordered solvent structure

about a proposed highly polar transition state than about the reactant due to interactions of the strong dipole with the dielectric solvent (i.e., electrostriction).

Conversely, Eyring and coworkers (97,98) attributed their large and positive activation volumes to a large repulsive (or intrinsic) contribution resulting from

the dissociation of CO during the ring closure reaction.

The extreme divergences in activation volumes observed in SCF media

are restricted to the region in the immediate vicinity of the critical point and

approach liquid-like values at conditions removed from this critical transition

(31,96). For example, the value of −6000 cm3 /mol reported by Johnston and

Haynes (78) occurred at reduced conditions of about Tr = 1.04 and Pr ≈ 1.0.

They report a corresponding value of −71.6 cm3 /mol at Tr = 1.09 and Pr ≈ 6.1.

This large variation in activation volume is attributed to the pronounced pressure

dependence of the compressibility of the SCF media. This same correspondence

with compressibility has also been reported for partial molar volume data for

several solutes in supercritical CO2 and ethylene (99). Johnston and Haynes (78)

provide an excellent summary of the thermodynamic arguments for these significant variations in activation volume and partial molar volume with pressure.

To simplify and summarize these arguments, the dramatic variations in these

parameters result from the sharp divergence of the isothermal compressibility



Copyright 2002 by Marcel Dekker. All Rights Reserved.



toward infinity at the solvent critical point. The practical application of these observations is that the thermodynamic pressure effect on chemical reaction rates

can be substantially higher in SCF media than in liquids and is most significant

in the vicinity of the mixture critical point.

F. Clustering in SCF Media

There is a large and growing body of published experimental, theoretical, and

simulation reports (56,81,90,100–124) that suggest that the time-averaged solvent density and composition in the immediate vicinity of a solute molecule

may be significantly different from the bulk solution values for dilute SCF solutions. This phenomenon has generally been termed “solvent-solute clustering”

(101,125). This clustering effect has also been reported for cosolvents or solutes

about another solute molecule within an SCF phase (56,81,86,90,94,100,102,

106,109,126–130). These local density augmentations are reported to have typical values on the order of two to four times the bulk value (113,119,123), and

as demonstrated in examples of cosolvent clustering around a solute molecule,

they can result in local composition enhancements as high as seven times the

bulk value (100,131). These local density and composition enhancements are

generally believed to result primarily from specific short-range solvation effects

associated with this molecular disparity and not long-range solvent critical phenomena that underlie the large compressibilities characteristic of these systems

(26,90,101,107,108,122). In addition, this clustering phenomenon is believed to

be a very dynamic process with rapid exchange of the clustering molecules with

the bulk fluid occurring on the picosecond time scale (94,132). Spectroscopic

experiments and molecular dynamics simulations have shown that these geometrically defined clusters may persist on the order of 100 ps (108). This topic of

solvent-solute and solute-solute clustering has recently been reviewed in more

detail by Brennecke and Chateauneuf (122) and Tucker (123).

This clustering phenomenon is important for consideration of organic

chemical transformations in SCF media because cluster formation may influence the chemical reactivity (56,81,90,94,109–112,115,118,120–122,128–130,

133–136). For example, an enhanced local solvent density in the cluster around

a solute molecule can significantly change the local values of density-dependent

properties such as the dielectric constant (31,78,79), diffusivity (137), and viscosity (118,136). Such changes in the local solvent environment can consequently

affect the reaction pathway through, for example, influencing the stability of

a polar transition state species (122). The molecular solvent cluster can also

enhance solvent cage effects around reactants or corresponding activated complexes, thus inhibiting the mass transfer of reactive species (81,86,103,118,133).

However, for solvent cage effects to influence the chemical reactivity, the time

scale of the reaction must be within that for which the cluster maintains its



Copyright 2002 by Marcel Dekker. All Rights Reserved.



structural integrity (86,94,104,122). Finally, the local composition enhancements

associated with the clustering phenomenon can result in an increased local concentration of reactive species which, in turn, can influence reaction rates through

simple concentration effects (90).

In summary, the considerable “clustering” literature for SCF-mediated reactions suggests that the bulk physical properties of the SCF solvent media are

the primary factors affecting chemical reactivity and selectivity (122). However,

local molecular phenomenon can also influence these parameters in certain applications, so that the specific reaction mechanism must be considered to determine

the relative influence of these factors.



III. APPLICATIONS

A. Carbon Dioxide as a C1 Building Block

Utilization of scCO2 as both a reaction solvent and a C1 building block affords particular opportunities in CO2 -mediated reactions. Carbon dioxide is an

abundant natural carbon source (138) that is relatively benign with regard to

both environmental and health effects. As a result, CO2 has found widespread

use in a variety of industrial applications, including as a protective gas for

sensitive foods, a source of beverage “carbonation,” a fire-extinguishing agent,

and an extraction solvent (139). Largely as a result of this abundance and benign nature, considerable efforts have been made in recent years to utilize CO2

as a feedstock for the synthesis of valuable chemicals and fuels (139–149).

Various intermediates and products that have been suggested include formic

acid, alkyl formates, formamides, amines, methane and other hydrocarbons,

methanol and higher alcohols, isocyanates, organic carbonates, carbamates, and

even polycarbonate-based polymers. A number of these products are manufactured industrially using carbon monoxide and phosgene as reactants; hence the

toxicological and physiological effects, corrosion, and environmental risks associated with these feedstocks make CO2 a very attractive alternative for consideration (143,149,150). In fact, there are at least four important commercial-scale

processes in which CO2 is used for organic syntheses, including the manufacture of urea, cyclic carbonates, salicylic acid (the Kolbe–Schmitt process), and

methanol (140).

Due to the relative inertness, readily attainable critical properties, and

minimal environmental impact of CO2 that was described previously, the vast

majority of research and development in conducting chemical transformations

in SCF media has utilized scCO2 as the reaction medium (31,33,35). Thus,

activation of CO2 for use as a reactant for organic synthesis combined with the

simultaneous use of scCO2 as the reaction medium is an obvious synergy. A

number of such studies have been reported in recent years.



Copyright 2002 by Marcel Dekker. All Rights Reserved.