Handbook of Solvents - George Wypych - ChemTech - Ventech!

13.1 Solvent effects on chemical reactivity 765
thermodynamic 123,124 and depolarized Rayleigh scattering data, 125,126 and vibrational spectra.
127
For nonprotic fluids, as Table 13.1.6 further shows, the vaporization entropy is
strongly dominated by the entropy of HS depacking. This is an at least qualitative representation
of the longstanding claim that repulsions play the major role in the structure of dense
fluids. 37 This circumstance is ultimately responsible for the striking success of the description
of neutral reactions in the framework of a purely HS liquid, as discussed in Section
13.1.6.
Also included in the Table are values of gK as determined in the framework of a generic
mean spherical approximation. 128 Since these values differ from those from other
sources, 129,121 because of differences in theory, we refrain from including the latter. It is seen
that the gK parameter is unsuited to scale order, since positional order is not accounted for.
On the other hand, values of gK exceed unity for the highly dipolar liquids and thus both Sex and gK attest to some degree of order present in them.
Solvent reorganization energy in ET
Electron transfer (ET) reactions in condensed matter continue to be of considerable interest
to a wide range of scientists. The reasons are twofold. Firstly, ET plays a fundamental role
in a broad class of biological and chemical processes. Secondly, ET is rather simple and
very suitable to be used as a model for studying solvent effects and to relate the kinetics of
ET reactions to thermodynamics. Two circumstances make ET reactions particularly appealing
to theoreticians:
• Outer-sphere reactions and ET within rigid complexes of well-defined geometry
proceed without changes in the chemical structure, since bonds are neither formed
nor broken.
• The long-ranged character of interactions of the transferred electron with the
solvent’s permanent dipoles.
As a consequence of the second condition, a qualitative (and even quantitative) description
can be achieved upon disregarding (or reducing through averaging) the local liquid
structure changes arising on the length of molecular diameter dimensions relative to the
charge-dipole interaction length. Because of this, it becomes feasible to use for outer-sphere
reactions in strongly polar solvents the formalism first developed in the theory of polarons
in dielectric crystals. 130 In the treatment, the polar liquid is considered as a dielectric continuum
characterized by the high-frequency ε ∞ and static εs dielectric constants, in which the
reactants occupy spherical cavities of radii Ra and Rd, respectively. Electron transitions in
this model are supposed to be activated by inertial polarization of the medium attributed to
the reorientation of permanent dipoles. Along these lines Marcus 131 obtained his
well-known expression for the free energy ΔF of ET activation
ΔF
=
( ΔF
+ E )
o r
4E
r
2
[13.1.24]
where ΔF o is the equilibrium free energy gap between products and reactants and E r is the reorganization
energy equal to the work applied to reorganize inertial degrees of freedom
changing in going from the initial to the final charge distribution and can be dissected into
inner-sphere and solvent contributions: