Simple model for the kinetics of stimuli-responsive gels with porous structures

Stimuli-responsive gels are the gels that vary the volume depending on environmental conditions. It has been reported that the stimuli-responsive gel with an inhomogeneous structure exhibits faster volume change than the gel without it. It is understood as a difference in the transfer dynamics of the solvent, though, there are few models for discussing the effect of inhomogeneity explicitly. In this paper, we propose a simple model for the kinetics of volume change by introducing inhomogeneity as the probability distribution for a random variable that characterizes the structure. Under this framework, we demonstrate that inhomogeneity actually increases the rate of volume change. Furthermore, through analysis of a simplified example, we show that some features that are often seen in experiments can be reproduced by the model. This model provides a simple equation for the time series of volume change that can be used to characterize the experimental data based on a simple physical picture of the phenomenon.