A Brief Review of Classical Diffusion

It was also noted that at sufficiently high temperatures diffusion and hydrolysis may occur simultaneously (Abeysinghe et al. 1982) and that hydrolysis lowers Tg (Zhou and Lucas 1999). A theoretical model that employs probabilistic considerations for chain scissions by chemically reacted water, and thereby weight loss, had successfully predicted such combined weight gain/weight loss data (Xiao and Shanahan 1997). Those data correspond to curve D in Fig. 4.2. 

In addition, it was shown by thermal-energetic arguments that Moo may increase, decrease, or be independent of temperature T (Li et al., private communication Medras et al., private communication). 

The availability of bonding sites and free volume depends strongly on departures from stoichiometry of various polymeric components, like those in epoxy. Such departures may occur within the interphase regions surroxmding the fibers bringing about the accumulation of water therein (Gupta et al. 1985 Grave et al. 1998). 

Diffusion is a process by which matter is transported from one part of a system to another as a result of random molecular motions (Ghez 1988). A discretized model for isotropic one-dimensional diffusion can be viewed as a random walk model along, say, the x axis. Accordingly, let A,- denote the number of particles located at sites x, = ia, i = 0, 1, 2. and assume that each particle can jump to adjacent sites with an equal frequency co that does not depend on i. Thus, particles jump from site i to site i + 1 per tmit time, while j oNi+i particles jump from + 1 to i and similarly between sites i — 1 and i. Omitting the details which are derived in the monograph (Ghez 1988), one obtains the following expressions. 

Upon assuming, a priori, a continuous mass distribution m x,t) = aN one obtains the counterparts to expressions (3.1)-(3.3), namely 

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