Solvent-induced stresses in glassy polymer: Elastic model
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Solvent-induced stresses in glassy polymer: Elastic model Wei-Lung Wang, J.R. Chen, and Sanboh Lee Department of Materials Science, National Tsing Hua University, Hsinchu, Taiwan (Received 17 November 1998; accepted 23 July 1999)
The solvent-induced stresses in glassy polymers were investigated. The mass transport accounts for case I, case II, and anomalous transport. Case I transport is attributed to the concentration gradient, whereas case II transport is attributed to stress relaxation. Anomalous transport is the mixture of case I and case II. Both one-side and two-side mass transports with the boundary condition of constant surface concentration are considered. The stresses and longitudinal displacement arising from the mass transport are formulated based on the linear elasticity theory. The maximum stress is always located at the surface at the initial time. The stresses are a function of the partial molal volume, Young’s modulus, and Poisson’s ratio. From the longitudinal displacement data, the partial molal volume was determined.
I. INTRODUCTION
Solvent transport in glassy polymers is often observed as case I, case II, and anomalous transport. Case I and case II transport are the two limiting types of transport process and anomalous transport lies between them. The deviations from case I transport are attributed to the finite rate of polymer structure rearrangement to accommodate the penetrant molecules. Alfrey et al.1 categorized it as case I when the penetrant mobility is much less than the stress relaxation rate of polymeric structure; case II occurs when the penetrant mobility is much greater than the stress relaxation rate; and anomalous transport occurs when both mobility and stress relaxation rate are comparable. Case I transport was extensively studied by Chen and Edin2 and the authors cited by Crank.3 The mechanism of case II transport has attracted much attention by many researchers.4–11 Kwei and coworkers12–16 first proposed an equation for the anomalous transport. Kwei’s equation is valid only for a semiinfinite medium but is incorrect for a finite medium. Harmon et al.17,18 modified Kwei’s equation and applied it to specimens of finite size. Lee and coworkers19–23 also applied this model to various glassy polymers. Diffusion-induced stresses in semiconductor materials were first proposed by Prussin.24 Li25 analyzed the diffusion-induced stresses in a single-phase elastic medium of various geometry. Lee and coworkers26–28 studied composite materials of different geometry. Larche and Cahn29,30 investigated the stresses arising from composition inhomogeneities and sample geometry. The above studies focused on atomic diffusion. The large molecular transport related to such stresses was addressed by Kim and Neogi31 but not in great detail. J. Mater. Res., Vol. 14, No. 10, Oct 1999
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Two solvent transports in glassy polymers are usually undertaken. One is to immerse the polymeric material in a solven
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