The Visco-elastic Properties of Network Structure I. General Formalism

概要

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Many kinds of amorphous high polyrner substances show the non-ideal rheological behaviours even in the "static" observations. In this paper, the general stress-strain-time relation and energy of dissipation of these systems are treated by adopting the modified rubber-like network model in which the junctions connecting the polymer chains break up and reform continually. The probability of the breakage of the junction, namely the breakage of the chain, per unit time is not a constant but a functions of both the number of segments which construct the chain and the end-to-end distance of the chain. It is assumed that the velocities of deformation of the system and of the change of the situation of network structure are extremely slower than those of the micro-Brownian movements of polymer segments. Therefore the statistical mechanical considerations of equilibrium states may be used to derive the stressstrain-time(S-S-T)relation at each "instance" of macroscopic observations. From our general expression of S-S-T relation it is pointed out that, in the case of small deformation, the S-S-T relation is essentially similar to that of the phenomenological generalized Maxwell model and the reciprocal of the probability of chain-breakage corresponds to the relaxation time of each Maxwell element.
社団法人日本物理学会の論文
1956-04-05