Chemistry Reference
In-Depth Information
∂
ln
K
∑
∂
∂
βµ
ρ
i
=
(
NN
−
n
)
(1.98)
A
i
M
i
∂
ρ
j
j
β
,,{}
pm
′
β,,{}
pm
′
i
Both expressions are valid for systems containing any number of components
at any composition. The chemical potential derivatives are provided by the expres-
sions for an
n
c
component system. For low solute concentrations, the former equa-
tion also provides an expression for the standard volume change for the process. A
particularly common situation involves the effect of a single cosolvent on the con-
formational equilibrium (n = 1,
D
→
N
) of an infinitely dilute solute. In this case,
Equation 1.98 then reduces to
∞
∞
∞
∂
ln
K
1
ΓΓ
−
+−
D
3
N
3
=
(1.99)
∂
ρ
ρ
1
NN
3
3
33
13
β
,
p
after application of the GD expression to eliminate one of the chemical potential
derivatives, and using the definitions provided in Equation 1.87 for the Γs. This is the
FST expression for the
m
-value of protein denaturation studies, which indicates that
the above derivatives often appear to be constant over a range of cosolvent concentra-
tion (Greene and Pace 1974).
1.3.9 T
echnical
i
ssues
s
urrounding
The
a
PPlicaTion
oF
F
lucTuaTion
s
oluTion
T
heory
The expressions provided by FST are exact within the normal assumptions of statis-
tical thermodynamics. This is a major advantage of the theory. There are, however,
various technical issues that arise when applying the theory. These basically fall
into two categories. The first is related to the analysis of the experimental thermo-
dynamic data, and the second related to obtaining the KBIs from simulation data.
The KB inversion process involves the extraction of KBIs from the available
experimental data. The experimental data required for this process—derivatives of
the chemical potentials, partial molar volumes, and the isothermal compressibil-
ity—are all generally obtained as derivatives of various properties of the solution.
Obtaining reliable derivatives can be challenging and will depend on the quality of
the source data and the fitting function. Unfortunately, the experimental data often
appear without a reliable statistical analysis of the errors involved, and hence the
quality of the data is difficult to determine. Matteoli and Lepori have performed a
fairly rigorous analysis of a series of binary mixtures and concluded that, for sys-
tems under ambient conditions, the quality of the resulting KBIs is primarily deter-
mined by the chemical potential data, followed by the partial molar volume data,
whereas errors in the compressibility data have essentially no effect on the KBI
values (Matteoli and Lepori 1984). Excess chemical potentials are typically obtained
from partial pressure data, either isothermal or bubble point determinations, and
from osmotic pressure or even electrochemical measurements. The particle number
