Non-Gaussian Chain Statistics and Network Theory
Leslie R. G. Treloar · 2005
Abstract UP to this point the development of the statistical theory of the network has been based upon the approximate or ‘Gaussian’ distribution function (3.3) for the single chain, whose derivation assumes that the end-to-end distance r is very much Jess than the fuJiy extended Length of the chain R. The results derived on this basis are therefore limited to strains which are not too large, that is to say, to strains which do not begin to approach the limiting deformability of the network. In comparing the experimental stress-strain curves with the formulae derived from the Gaussian theory attention has already been drawn to the marked upturn in the stress in the region of very Jarge strains, which is particularly evident in the case of simple extension (Fig. 5.4, p. 87). In this region, where an appreciable proportion of the chains become highly extended, the Gaussian statistical treatment is no longer valid, and a more accurate ‘non–Gaussian’ form of theory becomes essential.