An Improved Phenomenological Model for Polymer Desorption

Authors: Joanna Sooknanan, Donna Comissiong

Abstract:

We propose a phenomenological model for the process of polymer desorption. In so doing, we omit the usual theoretical approach of incorporating a fictitious viscoelastic stress term into the flux equation. As a result, we obtain a model that captures the essence of the phenomenon of trapping skinning, while preserving the integrity of the experimentally verified Fickian law for diffusion. An appropriate asymptotic analysis is carried out, and a parameter is introduced to represent the speed of the desorption front. Numerical simulations are performed to illustrate the desorption dynamics of the model. Recommendations are made for future modifications of the model, and provisions are made for the inclusion of experimentally determined frontal speeds.

Keywords: Phenomenological Model, Polymer, Desorption, Trapping Skinning

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1085930

References:

[1] M. A. Samus and G. Rossi. Methanol absorption in ethylene-vinyl achohol copolymers: Relation between solvent diffusion and changes in glass transition temperature in glassy polymeric materials. Macromolecules, 29(6):2275-2288, 1996.
[2] G. Astarita and S. Joshi. Simple dimension effect in the sorption of solvents in polymer - a mathematical model. J. Membr. Sci., 4:165- 182, 1978.
[3] G. Astarita and G. C. Sarti. A class of mathematical models for the sorption of swelling solvent in glassy polymers. Polym. Eng. Sci., 18:388-397, 1978.
[4] A. Friedman and G. Rossi. Phenomenological continuum equations to describe case ii diffusion in polymeric materials. Macromolecules, 30:153-154, 1997.
[5] A. Peterlin. Diffusion in a network with discontinuous swelling. J. Poly. Sci. B: Polym. Lett., 3:1083-1092, 1965.
[6] T. Qian and P. L. Taylor. From the thomas windle model to a phenomenological description of case ii diffusion in polymers. Polymer, 52(19):7159-7163, 2000.
[7] G. Rossi, P. A. Pincus, and P. G. De Gennes. A phenomenological description of case ii diffusion in polymeric materials. Europhys. Lett., 32:391-396, 1995.
[8] N. L. Thomas and A. H. Windle. Transport of methanol in poly(methylmethocrylate). Polymer, 19:255-265, 1978.
[9] N. L. Thomas and A. H. Windle. A deformation model for case ii diffusion. Polymer, 21:613-619, 1980.
[10] N. L. Thomas and A. H. Windle. Diffusion mechanics of the system pmma-methanol. Polymer, 22:627-639, 1981.
[11] N. L. Thomas and A. H. Windle. A theory of case ii diffusion. Polymer, 23:529-542, 1982.
[12] R. W. Cox and D. S. Cohen. A mathematical model for stress driven diffusion in polymers. J. Poly. Sci. B: Poly. Phys., 27(3):589-602, 1989.
[13] D. A. Edwards. A spatially nonlocal model for polymer-penetrant diffusion. J. Appl. Math. Phys., 52:254-288, 2001.
[14] D. A. Edwards. A mathematical mode for trapping skinning in polymers. Stud. Appl. Math., 99:49-80, 1997.
[15] D. A. Edwards and R. A. Cairncross. Desorption overshoot in polymerpenetrant systems: Asymptotic and computational results. SIAM J. Appl. Math., 63:98-115, 2002.
[16] M. Sanapoulou, D. F. Stamatialis, and J. H. Petropoulos. Investigation of case ii behavior. 1. theoretical studies based on the relaxation dependent solubility model. Macromolecules, 35(3):1012-1020, 2002.
[17] D. M. G. Comissiong, J. A. Ferreira, and P. de Oliveira. A phenomenological model for desorption in polymers. University of Coimbra,CMUC Technical Report 06-35, 2006.
[18] M. Sanopoulou and J. H. Petropoulos. Systematic analysis and model interpretation of micromolecular non-fickian sorption kinetics in polymer films. Macromolecules, 34:1400-1410, 2001.
[19] C.Y. Hui, R. C. Wu, R. C. Lasky, and E. J. Kramer. Case ii diffusion in polymers. ii. steady state front motion. J. Appl. Phys., 61:5137-5149, 1987.
[20] D. A. Edwards. Skinning during desorption of polymers: An asymptotic analysis. SIAM J. Appl. Math., 59:1134-1155, 1999.
[21] J. Crank. The Mathematics of Diffusion. Oxford University Press, Oxford, U.K., 1973.
[22] J. Crank. A theoretical investigation of the influence of molecular relaxation and internal stress. J. Poly. Sci., 11:151-168, 1953.
[23] E. Bagley and F. A. Long. 2-stage sorption and desorption of organic vapours in cellulose acetate. J. Am. Chem. Soc., 77:2172-2178, 1955.
[24] D. A. Edwards. An asymptotic analysis of polymer desorption and skinning. Macromolecular Theory and Simulations, 8:10-14, 1999.
[25] G. Powers and J. Collier. Experimental modeling of solvent-casting thin polymer films. J. Poly. Eng. Sci., 30:118-123, 1990.