Handbook of Solvents - George Wypych - ChemTech - Ventech!

21.1 Supercritical solvents 1437
*
⎛∂lnk
⎞ V ∂lnκ ⎜ ⎟ =− + κT
⎝ ∂P⎠
RT ∂P
⎛ Δ
⎞
⎜ ⎟ + − − −
⎝ ⎠
T T
( 1 a b �)
If the volume of activation is positive, the reaction is hindered by pressure. However, for
high negative values of the volume of activation, the pressure enhances the rate of the reaction.
Therefore, supercritical fluids that exhibit very high negative activation volumes for
certain reactions will improve the rate of the reaction.
The volume of reaction, rather than activation, is crucial in determining the effect
of pressure on the equilibrium constant.
⎛∂lnK
⎜
⎝ ∂P
x
⎞ Vf
⎟ =−
⎠ RT
Δ
T, x
where:
ΔVf reaction volume (difference between partial molar volumes of products and reactants)
If the equilibrium constant is expressed in terms of pressure dependent units (such as concentration),
the relevant equation is:
⎛∂lnK
⎞ ΔVr
⎜ ⎟ =− + κ ∑v
⎝ ∂P
⎠ RT
T, x
T i
where:
vi stoichiometric coefficient
As the above equation implies, supercritical fluids that exhibit very high negative activation
volumes for certain reactions will improve the equilibrium conversion of the reaction.
21.1.2.5 Sorption behavior of supercritical solvents
Both adsorption from a supercritical fluid to an adsorbent and desorption from an adsorbent
find applications in supercritical fluid processing. 54,55 The extrapolation of classical sorption
theory to supercritical conditions has merits. The supercritical conditions are believed
to necessitate monolayer coverage and density dependent isotherms. Considerable success
has been observed by the authors in working with an equation of state based upon the Toth
isoterm. 56 It is also important to note that the retrograde behavior observed for vapor-liquid
phase equilibrium is experimentally observed and predicted for sorptive systems.
21.1.2.6 Swelling with supercritical solvents
As the pressure of the gas is increased, the solubility of the supercritical gas in the solid
polymer increases resulting in swelling, a phenomena that could be advantageous in certain
applications while its deleterious impact should be minimized, if not totally eliminated, in
other instances.
The sorption of supercritical solvent and the resulting swelling could be very high, for
example around 30% and 20% respectively for carbon dioxide in polymethylmethacrylate
(PMMA). In such instances, the experimental information could be summarized using polymer
equation of states such as Sanchez-Lacombe where a single mixture fitting parameter is
used. 6