Inhomogeneous Equilibrium Swelling of Core-Shell-Coating Gels

Abstract

A gel refers to a soft material constituting of a polymeric network and mobile water molecules. In many applications, the gel is often integrated with hard materials, resulting in a hybrid structure of soft and hard materials. Mechanical constraint in the hybrid structure leads the gel to exhibit an inhomogeneous swelling behavior. In addition, the cross-link density inside the gel is usually inhomogeneous, which can also markedly affect the swelling behavior of the gel and should be taken into consideration. In this paper, we study the effects of the hard material and the inhomogeneous cross-link density on the swelling behavior of the gel by proposing a simple core-shell-coating structure, where a shell of a gel is bonded to a rigid core and is coated by a layer of a densely cross-linked gel. We model the structure by two nonlinear differential equations, and show that the presence of the densely cross-linked coating layer has a substantial influence on the fields of stress and solvent concentration in the structure.