Modeling of Polyelectrolyte Gels in Equilibrium with
Salt Solutions
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Abstract
We use hybrid molecular dynamics/Monte
Carlo simulations and coarse-grained
polymer models to study the swelling of polyelectrolyte gels in salt
solutions. Besides existing industrial applications, such gels have
been recently proposed as a promising agent for water desalination.
We employ the semi-grand canonical ensemble to investigate partitioning
of the salt between the bulk solution and the gel and the salt-induced
deswelling of the gels under free swelling equilibrium and under compression.
We compare our findings to the analytic model of Katchalsky and Michaeli
which explicitly accounts for electrostatic effects. The partitioning
of small ions predicted by the model well captures the deviations
from the simple Donnan approximation observed in the simulation data.
In contrast, the original model highly overestimates the gel swelling,
predicting even chain stretching beyond contour length. With a modified
model, where we replace the Gaussian elasticity with the Langevin
function for finite extensibility, we obtain nearly quantitative agreement
between theory and simulations both for the swelling ratio and for
the partitioning of salt, across the whole range of studied gel parameters
and salt concentrations. The modified model thus provides a very good
description of swelling of polyelectrolyte gels in salt solutions
and can be used for theoretical predictions of water desalination
using hydrogels. These predictions are much less computationally demanding
than the simulations which we used to validate the model