Chemistry Reference
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polyelectrolyte in water). For example, they treat an aqueous solution of a single
polyelectrolyte as a three-component mixture consisting of the solvent, the coun-
terion, and the polyion backbone that is approximated by its charged repeating
units. As the electrolyte-NRTL model is a “local composition” model, such a
solution is described by cells. There are as many types of cells as there are different
species in the mixture. Each cell type consists of a single species surrounded by its
nearest neighbors. There are three different cells in an aqueous solution of a single
polyion, i.e., with a water molecule, a counterion, or a repeating unit, in the center
The cell with water as the central species might be surrounded by other water
molecules, counterions, and repeating units of the polyion. The nearest neighbor-
hood of a cell with a central counterion also contains water and repeating units of
the polyion, but it is assumed that there are no further counterions. The nearest
neighborhood of a cell with a central repeating unit consists of two further repeating
units (its neighbors in the polyion), counterions, and water molecules. In contrast to
Chen and Evans, Danner and coworkers [
101
,
102
] do not assume that the criterion
of electroneutrality is fulfilled in each cell. Because the electrolyte-NRTL model is
commonly given for a symmetrical convention, whereas polyelectrolyte systems
are normalized according to the unsymmetrical convention, Danner et al. use the
following expression for
G
E;
SR
of a multicomponent solution:
X
G
E;
SR
n
T
RT
¼
G
E;
SR
;
sym
n
T
RT
SR
;ð
x
Þ;1
x
j
ln
g
;
(95)
j
all solutes j
where
G
E;
SR
;
sym
is the excess Gibbs energy in the symmetrical convention,
n
T
is
the total mole number of the solution:
X
n
T
¼
n
j
j
¼
w
;
a
;
c
(96)
all components
j
Þ;
j
is the contribution of the short-range interactions to the activity
coefficient of solute
j
(i.e., either a cation
c
or anion
a
, in the symmetrical
convention, on the mole fraction scale at infinite dilution in water).
SR
;ð
x
and
g
SR
;ð
x
Þ;1
SR
;ð
x
Þ
g
¼
n
k
!
0
g
lim
;
(97)
j
j
where subscript
k
stands for all solutes and:
G
E;
SR
;
sym
@
@
SR
;ð
x
Þ
j
RT
ln
g
¼
j;p;T
:
(98)
n
j
n
k6
The mole fraction of species in a shell of nearest neighbors around a central
species is expressed using a Boltzmann term as a weighting factor. Danner et al.
give the following expression for the contributions of short-range forces to the
