Water uptake of polymer/clay nanocomposites: Model development

Abstract

Abstract: Numerous models have been proposed for modeling water diffusion behavior in polymers and polymer composites. The most common approach is to apply Fick’s law to simple single-free-phase diffusion, due to its simplicity and mathematical tractability [1]. However, it has been demonstrated that diffusion of water in some glassy polymers is anomalous (non-Fickian). Two main approaches are proposed to model the anomalous diffusion. One is the Langmuir-type model for diffusion (LMD), assuming that absorbed water molecules consist of mobile and bound phases [2,3]; the other is the diffusion with time-varying diffusivity model (DTVD), where a constant coefficient of diffusion is replaced by a decreasing function of time (by analogy with a relaxation modulus for a viscoelastic solid) [4,5]. Several models have been proposed to predict the behavior of composites based on the analogy between thermal conductivity and diffusivity [6,7]. The most extensively cited model in polymer/clay nanocomposites is the Nielsen model, which predicts that relative permeability is only a function of the aspect ratio at a given loading of clay, for all percents [8].