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Review Articles

Models of Solvent Penetration in Glassy Polymers With an Emphasis on Case II Diffusion. A Comparative Review

[+] Author and Article Information
S. Bargmann

 Institute of Mechanics, Technische Universität Dortmund, Leonhard-Euler-Str. 5, 44227 Dortmund, Germanyswantje.bargmann@tu-dortmund.de

A. T. McBride1

Lehrstuhl für Technische Mechanik,  Universität Erlangen-Nürnberg, Egerland-Str. 5, 91058 Erlangen, Germanyandrew.mcbride@ltm.uni-erlangen.de

P. Steinmann

Lehrstuhl für Technische Mechanik,  Universität Erlangen-Nürnberg, Egerland-Str. 5, 91058 Erlangen, Germanypaul.steinmann@ltm.uni-erlangen.de

The model of Kalospiros et al.  [17] purports to capture all anomalous experimental observations concerning mass transfer in solids.

We adopt here the sign convention widely used in the fluid mechanics literature wherein a compressive stress is defined as positive. Aifantis [27] adopts a sign convention standard in solid mechanics wherein a tensile stress is defined as positive.

For a comprehensive review of polymeric fluids the reader is referred to Bird et al.  [74-75].

While not widely adopted, the Hamiltonian setting can be used to describe the deformation of solids [81].

The definition of the Helmholtz energy adopted by Govindjee and Simo [6], i.e., Ψ=U-TS, excludes contributions from the kinetic energy.

A promising alternative methodology to link the meso- and macro-scales is numerical homogenization. For example, Zohdi et al.  [83] use homogenization to determine the diffusivity coefficient in heterogenous material.

1

Corresponding author.

Appl. Mech. Rev 64(1), 010803 (Oct 03, 2011) (13 pages) doi:10.1115/1.4003955 History: Published October 03, 2011; Online October 03, 2011

The objective of this review is to provide an overview and a classification of the key literature on models of non-Fickian case II type diffusion. Several extensive review articles concerning non-Fickian diffusion exist in the literature; our objective is not to reproduce these worthy contributions. Rather, we focus on a limited number of, seemingly disparate, notable models and attempt to unify them using the language of thermodynamics and continuum mechanics. This attempted unification of selected models arising from various modeling communities serves to elucidate the key strengths and potential weaknesses of the models.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

Grahic Jump Location
Figure 1

Motion from the reference configuration Ω to the current configuration S

Grahic Jump Location
Figure 2

One-dimensional representation of (a) a standard solid and (b) a Maxwell solid. When modeling case II diffusion in polymers, the viscosity η may depend on the solvent concentration c, see e.g., Govindjee and Simo [6].

Grahic Jump Location
Figure 3

Schematic representation of (a) a single polymer molecule, and (b) its idealization as a series of masses connected via nonlinear springs

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