Chemically induced swelling of hydrogels

Abstract

We present a theory for the chemically-induced volume transitions of hydrogels. Consistent with experimental observations, we account for a sharp interface separating swelled and collapsed phases of the underlying polymer network. The polymer chains are treated as a solute with an associated diffusion potential and their concentration is assumed to be discontinuous across the interface. In addition to the standard bulk and interfacial equations imposing force balance and solute balance, the theory involves an ancillary interfacial equation imposing configurational force balance. Motivated by experimental observations, we specialize the theory to the situation where the time scale associated with the interface motion is slow compared to those associated with diffusion in the bulk phases. We present a hybrid eXtended-Finite-Element/Level-Set Method (XFE/LSM) for obtaining approximate solutions to the equations arising under this specialization. As an application, we consider the swelling of a spherical specimen whose boundary is traction-free and is in contact with a reservoir of uniform chemical potential. Our numerical results exhibit good qualitative comparison with experimental observations and predict characteristic swelling times that are proportional to the square of the specimen radius. Our results also suggest several possible synthetic pathways that might be pursued as a means to engineer hydrogels with optimal response times.

A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints

“…Complex material behaviors of hydrogels with large, reversible deformation and various instability patterns have been observed in experiments [8][9][10][11][12][13][14][15][16][17], which have motivated a large body of theoretical and numerical studies [18][19][20][21][22][23][24][25][26][27][28][29][30]. Recently, following the classical works by Gibbs [31] and Biot [32,33], Hong et al [27] formulated a nonlinear field theory coupling diffusion of solvent molecules and large deformation of polymeric gels.…”

An extended finite element library

“…Multiscale work has been performed with micro-macro crack models based on the LATIN methods (LArge Time INcrement method) in [36]. The XFEM has also been used to model computational phenomena in areas such as fluids mechanics, phase transformations [37], material science and biofilm growth [38,39], Chemically-induced swelling of hydrogels [40], among others. Fluid-structure interaction problems are also freeboundary problems, where the "free" boundary usually is the structure.…”

A numerical strategy for investigating the kinetic response of stimulus-responsive hydrogels

“…The next Section details important theoretical developments for our sharp interface model of SRH kinetics. Section 3 provides a complete development of the theory, which extends that used by Dolbow et al (2004) to account for dissipative interfacial kinetics. The representation of the interface with level sets and the variational formulation are described in Sections 4 and 5, respectively.…”