Handbook of Solvents - George Wypych - ChemTech - Ventech!

648 Mati Karelson
where A i are the solvent-accessible surface areas of different atoms in the solute molecule
and C is an empirically adjustable parameter. The quality of the description of experimental
data has been, however, not significantly improved by the introduction of individual atomic
surface tension characteristics.
Another theoretical approach for the calculation of the free energy of cavity formation
proceeds from the theory of microscopic curved surfaces. According to this theory, 6
ΔG k V ⎛
cav = ⎜ s ⎜
⎝V
g S
M
⎞
⎟
σ S
[11.1.8]
⎠
g
where S is the area of the cavity and k s(V
S /V M) is a correction factor, characteristic of a
given solvent and depending on the ratio of molecular volumes of the solvent and solute.
This factor has been approximated by the following formula
k V ⎛
⎜ s ⎜
⎝V
g S
M
23 /
⎞ V ⎞ S ⎟
= 1+⎛ ⎜
⎟
⎠ ⎝V
⎟
1 1
M ⎠
g [ ks()
−]
[11.1.9]
g
where k s(1)is
estimated from the solubility of a given solute in a given solvent. The main
deficiency of this approach is connected with the introduction of additional empirical information,
often not readily available.
The free energy of cavity formation has been also estimated from the data on isothermal
compressibility, βT, as follows 7
ΔG
cav
Vcav
= + C
β
T
[11.1.10]
where V cav is the volume of the cavity and C is a constant term. However, the microscopic
isothermal compressibility of water, calculated from the slope of Eq. [11.1.10], was found
to be about an order higher than the respective experimental value for water (β T(calc) = 23.5
vs.β T(exp) = 3.14). Therefore, the use of the macroscopic surface tension or compressibility
of the solvent for the respective microscopic model quantities is questionable.
An entropic approach to the calculation of the free energy of cavity formation proceeds
from the scaled particle theory (SPT). 8,9 The free energy of the formation of a spherical
cavity in a solvent, ΔG cav, can be calculated proceeding within the framework of SPT as
follows
where
2
2
⎧⎪
⎛ 3y
⎞ a ⎡
M 3y
9 ⎛ y ⎞ ⎤ ⎛a
⎞ ⎫
M ⎪
ΔGcav = RT⎨1−ln( 1−
y)
+ ⎜ ⎟ + ⎢ + ⎜ ⎟ ⎥ ⎜
⎝1−y⎠
aS⎣⎢1−y
2 ⎝1−y
⎜
⎟ ⎬
⎩⎪
⎠ ⎦⎥
⎝ aS
⎠ ⎭⎪
y = 4πρ
3
2
as [11.1.11]
[11.1.12]