Chemistry Reference
In-Depth Information
ionic groups, as well as an estimate of the ratio of electrolyte groups to backbone
monomers. The accessible information on the counterions is often limited to the
chemical nature and a more or less rough estimate for the ratio of different counter-
ions, e.g., the ratio of hydrogen counterions to sodium counterions of an anionic
polyelectrolyte. Very often, the degree of polymerization is given only as an
estimate of either the number-averaged or the mass-averaged molecular mass, but
detailed information on the polydispersity is missing. Thus, the characterization of
the polyelectrolyte is often far from satisfactory (at least from the viewpoint of
thermodynamics) and, consequently, reported thermodynamic data are often of very
limited use, e.g., for testing and developing of models for describing and predicting
the thermodynamic properties of such solutions.
3 Experimental Data for the Vapor-Liquid Equilibrium
of Aqueous Polyelectrolyte Solutions
Because polyelectrolytes are nonvolatile, the most important thermodynamic prop-
erty for vapor + liquid phase equilibrium considerations is the vapor pressure of
water
p
w
above the aqueous solution. Instead of the vapor pressure, some directly
related other properties are used, e.g., the activity of water
a
w
, the osmotic pressure
p
, and the osmotic coefficient
F
. These properties are defined and discussed in
Sect. 4. Membrane osmometry, vapor pressure osmometry, and isopiestic experi-
ments are common methods for measuring the osmotic pressure and/or the osmotic
coefficient. A few authors also reported experimental results for the activity coeffi-
cient
g
CI
of the counterions (usually determined using ion-selective electrodes) and
for the freezing-point depression of water
D
T
FP
. The activity coefficient is the ratio
of activity to concentration:
a
ðkÞ
CI
g
ðkÞ
CI
¼
k
;
(4)
where
k
in the denominator is used to express a certain concentration scale (e.g.,
mole fraction
x
, molarity
c
or molality
m
). Superscript (
k
) indicates that the activity
coefficient and the activity are defined using a certain reference state, which
depends on the selection of the scale used to express the composition of the
solution. Some authors report experimental data for the freezing point depression
of an aqueous solution:
T
SLE
T
SLE
purewater
D
T
¼
;
(5)
F
ðkÞ
T
and convert that data to an osmotic coefficient
by:
D
T
F
ðkÞ
T
¼
;
(6)
T
ðkÞ
id
:
liq
:
mix
:
D
