Abstract：For some polymers at temperatures near or below their glass transition temperature, one particular instance of non-Fickian solvent diffusion is usually observed, which is called Case II diffusion. In order to describe the coupling effect of Case II diffusion and swelling deformation in polymers, a set of theoretical models are established based on the continuum mechanics framework. Here, the governing equations for solvent penetration into polymer are derived and then specialized in reference configuration, including the mechanical-chemical equilibrium state equation, the concentration-dependent diffusion equation, and the molecular number conservation equation. Besides, the visco-hyperelastic constitutive equation taking into account the time-dependent deformation characteristics of material is integrated, which can reflect the competition mechanism between relaxation rate of polymeric network and migration of solvent in case II diffusion. This modeling approach is used to analyze the transient free swelling process for two material systems, so as to investigate the behavior of unidirectional Case II diffusion in columnar and tabular polymer specimens without constraint. According to those appropriate boundary conditions and initial conditions, the concentration, stress and deformation field variables during the unidirectional diffusion are directly obtained. The distribution and evolution of these calculation results are compared with the experimental observations, which moderately verifies the effectiveness and adaptability of the proposed coupling analysis method concerning with polymer swelling. The theory developed in this article may provide important guidance for practical applications (such as membranes designing or drug-delivery systems), in which Case II diffusion can commonly occur. It is also helpful to enhance understanding on combination of different polymer-solvent diffusion, from Fickian to non-Fickian circumstances.
2024, Vol. 45 
