Comparison of a hydrogel model to the Poisson–Boltzmann cell model

Abstract

We have investigated a single charged microgel in aqueous solution with a combined simulational model and Poisson-Boltzmann theory. In the simulations we use a coarse-grained charged bead-spring model in a dielectric continuum, with explicit counterions and full electrostatic interactions under periodic and nonperiodic boundary conditions. The Poisson-Boltzmann hydrogel model is that of a single charged colloid confined to a spherical cell where the counterions are allowed to enter the uniformly charged sphere. In order to investigate the origin of the differences these two models may give, we performed a variety of simulations of different hydrogel models which were designed to test for the influence of charge correlations, excluded volume interactions, arrangement of charges along the polymer chains, and thermal fluctuations in the chains of the gel. These intermediate models systematically allow us to connect the Poisson-Boltzmann cell model to the bead-spring model hydrogel model in a stepwise manner thereby testing various approximations. Overall, the simulational results of all these hydrogel models are in good agreement, especially for the number of confined counterions within the gel. Our results support the applicability of the Poisson-Boltzmann cell model to study ionic properties of hydrogels under dilute conditions.

Influence of network topology on the swelling of polyelectrolyte nanogels

“…2(b)). These results corroborate the equilibrium behaviour observed in previous simulations 11,17 . However, in contrast to the previous theoretical studies 15,16 that predicted a scaling Z eff ∼ f 0.5 , our results suggest a more linear behavior, which might be related to the relatively small size of the polyelectrolyte networks considered in our simulations.…”

“…The dissociated counterions can diffuse around the polyelectrolyte network, so that the nanogel particles acquire an effective net charge [15][16][17]42,43 , which is smaller than the bare charge Z of the polyelectrolyte backbone. The effective charge is given by, Z eff = Z − (N + − N − ), where N + and N − are the number of positive and negative ions inside the nanogel volume, respectively.…”

“…In principle, such relationship can be verified by computer simulations considering explicit network structures, but to our knowledge current studies have so far only exploited polyelectrolyte networks with diamond-like structures (i.e. with tetrafunctional crosslinks) 11,[17][18][19][20] .…”

Impact of volume transition on the net charge of poly-N-isopropyl acrylamide microgels

“…To account for the loss of charge related to the volume phase transition of our microgels we consider a model [10,13] inspired by the Poisson-Boltzmann cell model (PB cell model), previously used by Alexander et al for the description of charged impermeable colloids [40]. The basic assumptions of our model are (i) the counterion distribution is mainly governed by electrostatic interactions and thermal motion; (ii) the microgel is a permeable sphere whose charged groups are uniformly distributed and, therefore, its charge density is for a negatively charged microgel given by −3Ze/4πR 3 ; (iii) the counterions can move through the microgel without undergoing significant excluded volume effects.…”

“…Theoretically only a few attempts have been made to describe the net and/or effective charge of microgels by considering the penetration of ions into the gel network to properly account for the electrical double layer of microgels [8][9][10][11][12][13][14][15][16]. Among these attempts, Denton derived an expression for the interaction energy between charged microgels * cehp@azc.uam.mx † veronique.trappe@unifr.ch in the linear screening regime, whose functional form for nonoverlapping particles is similar to the classical Yukawa electrostatic interaction potential of plain colloids [8].…”