Abstract
The fundamental attributes of charged hydrogels containing predominantly water and controllable amounts of low molar mass electrolytes are of tremendous significance in biological context and applications in healthcare. However, a rigorous theoretical formulation of gel behavior continues to be a challenge due to the presence of multiple length and time scales in the system which operate simultaneously. Furthermore, chain connectivity, the electrostatic interaction, and the hydrodynamic interaction all lead to long-range interactions. In spite of these complications, considerable progress has been achieved over the past several decades in generating theories of variable complexity. The present review presents an analytically tractable theory by accounting for correlations emerging from topological, electrostatic, and hydrodynamic interactions. Closed-form formulas are derived for charged hydrogels to describe their swelling equilibrium, elastic moduli, and the relationship between microscopic properties such as gel diffusion and macroscopic properties such as elasticity. In addition, electrostatic coupling between charged moieties and their ion clouds, which significantly modifies the elastic diffusion coefficient of gels, and various scaling laws are presented. The theoretical formulas summarized here are useful to adequately capture the essentials of the physics of charged gels and to design new hydrogels with specified elastic and dynamical properties.
Highlights
Many important hydrogels occurring in various biological contexts are constituted by charged macromolecules
In the derivation of swelling equilibrium discussed in the subsection, we mainly focus on the mean-field theory without considering fluctuations
A mean-field theory has been developed for polyelectrolyte gels by accounting for the free energy of mixing, elasticity, electrostatic interactions among segments and the Donnan equilibrium
Summary
Many important hydrogels occurring in various biological contexts are constituted by charged macromolecules. The aforementioned theoretical approaches have been extensively discussed in attempts to explain various experimental data on many charged gels [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42] In this brief review, we summarize the recent generalized mean-field theory to treat polyelectrolyte gels by accounting for most of the aforementioned issues.
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