Hybrid Monte Carlo self-consistent field approach to model a thin layer of a polyelectrolyte gel near an adsorbing surface.

The use of thin layers of a surface bound (polyelectrolyte) hydrogels for measuring the concentration of metal ions from electrolyte solutions is our motivation for modeling such hydrogels. The gels are composed of polymeric species with conformational degrees of freedom on the nanometer scale. The polymer conformations are affected by the presence of cross-links in the gel on a five to ten times larger length scale, and the repulsive interactions generated by the charges along the chains. Here we present a hybrid computational Monte Carlo Self-consistent field (MC-SCF) approach to model such hydrogels. The SCF formalism is used to evaluate the conformational properties of the chains, implementing a freely jointed chain model, in between featureless cross-links. The Monte Carlo simulation method is used to sample the (restricted) translational degrees of freedom of the cross-links in the gel. We consider the case that the polymers in the gel have an affinity for surface positioned at the edge of the simulation volume. The polymer density decays as a power-law from the surface to the gel-density with an exponent close to -4/3. The gel features relatively large density fluctuations which is natural for a gel with a low density (φ ≈ 0.035), a low degree of cross-linking (average of three chainparts per cross-link), and relatively large chains (N = 50) in between the cross-links. Some parts of the gel can break loose from the gel and sample the adjoining volume. Representative snapshots exemplify large density fluctuations, which explain the large pore size distribution observed in experimental counterparts.