Chemistry Reference
In-Depth Information
0
;ðm
p
is either determined from experimental results for the osmotic coefficient
or estimated using the results of Manning's theory (in that case the length of a
repeating unit has to be known). For a polyion that consists only of a single
repeating unit, the number of repeating units
n
is calculated from the number-
averaged molecular mass of the polyion and the molecular mass of the repeating
unit. It is assumed that binary interaction parameters between species carrying
electrical charges of the same sign can be neglected (i.e., they are set to zero).
Therefore, there are only two, nonzero binary parameters for interactions between a
repeating (subscript
p
) unit and the counterion
l
ð
0
Þ
p
CI
F
and
l
ð
1
Þ
p
CI
. These interaction
parameters are fitted to some experimental properties such as the osmotic coeffi-
cient. Figure
12
shows a typical example for a correlation. The model can be
straightforwardly extended to aqueous solutions of a single polyion and a single
low molecular weight strong electrolyte (cf. Fig.
13
) but also to aqueous solutions
of a polyion and a neutral polymer. Such mixtures often form aqueous two-phase
systems. Figure
14
gives a typical example.
5.6 VERS-PE Model
Lammertz et al. [
116
] extended the
V
irial-Equation with
Re
lative
S
urface Fractions
(VERS) model of Großmann et al. [
112 114
] for the excess Gibbs energy of
aqueous solutions of neutral polymers and low molecular weight electrolytes to
the treatment of aqueous solutions that also contain polyions. That extension is
Fig. 12 Osmotic coefficient of aqueous solutions of NaPA at 298.15 K. Experimental data [
41
]:
closed squares
NaPA 5;
open squares
NaPA 15.
Lines
show the modeling
