Effect of film thickness on the changes in gas permeability of a glassy polyarylate due to physical aging Part II. Mathematical model

Part I of this series documented a substantial loss in gas permeability over time for thin films of a glassy polyarylate made from bisphenol-A-benzophenone dicarboxylic acid. The rate of permeability loss, and, thus, aging was found to be dependent on film thickness in a way that suggested that physical aging occurs by two mechanisms. In this paper, a mathematical model was developed to quantitatively describe the physical aging process in terms of the free volume (permeability) loss observed using reasonable physical parameters. The model describes two simultaneous mechanisms of free volume loss: free volume diffusion to the film surface (thickness dependent) and lattice contraction (thickness independent). A step-wise model development is described with comparison to the data and optimization of the model parameters at each step. The final dual-mechanism model describes the experimental data presented in Part I remarkably well. (C) 1999 Elsevier Science Ltd. All rights reserved.