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Sharp Fronts Due to Diffusion and Viscoelastic Relaxation in Polymers

Cohen, Donald S. and White, Andrew B., Jr. (1991) Sharp Fronts Due to Diffusion and Viscoelastic Relaxation in Polymers. SIAM Journal on Applied Mathematics, 51 (2). pp. 472-483. ISSN 0036-1399. doi:10.1137/0151023.

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A model for sharp fronts in glassy polymers is derived and analyzed. The major effect of a diffusing penetrant on the polymer entanglement network is taken to be the inducement of a differential viscoelastic stress. This couples diffusive and mechanical processes through a viscoelastic response where the strain depends upon the amount of penetrant present. Analytically, the major effect is to produce explicit delay terms via a relaxation parameter. This accounts for the fundamental difference between a polymer in its rubbery state and the polymer in its glassy state, namely the finite relaxation time in the glassy state due to slow response to changing conditions. Both numerical and analytical perturbation studies of a boundary value problem for a dry glass polymer exposed to a penetrant solvent are completed. Concentration profiles in good agreement with observations are obtained.

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Additional Information:©1991 Society for Industrial and Applied Mathematics. Received by the editors August 8, 1989; accepted for publication (in revised form) April 9, 1990. [D.S.C.'s] work was performed under United States Army Research Office (Durham) contract DAAG29-85-K0092, National Science Foundation grant DMS84-00885, Air Force Office of Scientific Research grant AFOSR-87-0270, and Department of Energy grant W-7405-ENG-36 at the Center for Nonlinear Studies at Los Alamos. [A.B.W.'s] work was performed under United States Department of Energy contract W-7405-ENG-36.
Funding AgencyGrant Number
Army Research OfficeDAAG29-85-K0092
National Science FoundationDMS84-00885
Air Force Office of Scientific ResearchAFOSR-87-0270
Department of EnergyW-7405-ENG-36
Subject Keywords:non-Fickian diffusion; polymers; singular perturbation
Issue or Number:2
Record Number:CaltechAUTHORS:COHsiamjam91
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12832
Deposited On:09 Jan 2009 06:24
Last Modified:08 Nov 2021 22:33

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