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In this study the constitutive equations of motion of the
displacement variable of the swelling kinetics of spherical
polyelectrolyte (PE) gels are numerically solved in salt free
conditions using two already developed theoretical methods, named as
Bulk Modulus Method (BMM) (analytical method) and Stress Relaxation
Method (SRM) (phenomenological method). From the solution we obtain
the time evolution profiles of the dynamical variables such as polymer
density, osmotic stress, which are also changing spatially during
swelling phenomena at each point inside the PE gel network. This
results lead us to estimate a response function of the PE gel, the
bulk modulus (K) from the matching of the gel-solvent interfaces
obtained from these two above-mentioned methods. We also calculate the
variations of the bulk modulus for the fixed and variable charge cases
of the PE gels, which show, a monotonic decrease with fixed charge,
and a non-monotonic behaviour with the dielectric mismatch parameter
for the variable charge case. In addition to the charge dependency, we
also obtain the effects of parameters such as hydrophobicity, gel
cross-link density on the swelling kinetics of PE gels. With the
parameter space study we also capture the dependencies of K and the
swelling relaxation time on the solvent quality, cross-link density
etc.. All these behaviours are also in a line with the experimental
results. |