Chemistry Reference
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NaPS (sulfonated Polystyrene)
Fig. 13 Mapping scheme of a PSS polymer onto a generic charged bead-spring model with an
implicit solvent representation and counterions. Figure adapted from [
116
]
found by simulations and experiments, and intensively studied during the last 10
years [
120
,
125
-
129
]. Another interesting polyelectrolyte is, of course, DNA,
which is a negatively charged PE. Since the persistence length of DNA is around
50 nm, on short length scales DNA can be considered as a charged rod. This rod
can, to a certain extent, be modeled as an infinite charged cylinder within a cell
model [
130
]. Furthermore, synthetic model systems have been synthesized that
are strongly charged like DNA and rodlike, and can therefore serve as simple
systems, where effects like counterion condensation or mean-field approaches can
be studied. We will illustrate here as an example a comparison between osmotic
coefficient data of short and stiff polyelectrolyte rods [
131
] and several simulation
studies [
132
-
134
]. The target quantity here is the reduced thermodynamic activity
of the counterions that can be expressed in terms of the osmotic coefficient:
f ¼
P
P
id
;
(7)
where
c
c
k
B
T
is the ideal gas pressure at given counterion concentration
c
c
and temperature
T
, and
k
B
is the Boltzmann constant. Experimental studies of
strongly charged polyelectrolytes show that
P
id
¼
is a weak function of polymer
concentration, and typically measured values are of the order of 0.2-0.3 for
univalent counterions in the dilute regime; see references in [
118
]. In our first
paper [
132
] we used the Poisson-Boltzmann (PB) solution of the infinite-rod cell
model for strongly charged polyelectrolyte solutions that neglects electrostatic
correlations and the finite sizes of the rods and compared it to explicit ion simula-
tions. The correlation effects were found to decrease the osmotic pressure by
approximately 7% [
132
] at low concentrations, but overall the main part of the
decrease of the osmotic coefficient was captured by the model. However, in a later
f
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