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 ove r time for thin films of a glassy polyarylate made from bisphenol-A-benzoph enone dicarboxylic acid. The rate of permeability loss, and, thus, aging wa s found to be dependent on film thickness in a way that suggested that phys ical aging occurs by two mechanisms. In this paper, a mathematical model wa s developed to quantitatively describe the physical aging process in terms of the free volume (permeability) loss observed using reasonable physical p arameters. The model describes two simultaneous mechanisms of free volume l oss: free volume diffusion to the film surface (thickness dependent) and la ttice contraction (thickness independent). A step-wise model development is described with comparison to the data and optimization of the model parame ters at each step. The final dual-mechanism model describes the experimenta l data presented in Part I remarkably well. (C) 1999 Elsevier Science Ltd. All rights reserved.