Diffusion Controlled Mechanical Properties of Uncoated Cellophanes

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• Analyzing mechanical elongation of polymer films having water-sensitive functional group such as hydroxyl group under the diffusion controlled condition, we intended to study the mechanism of diffusion of water into polymer films at various temperatures and under various relative humidities. While one of us has already reported a work on polyvinyl alcohol and in its formalized films, this is to be presented our measurement in the creeps and the adsorption for uncoated cellophanes.Although a report on the theoretical treatments of the results has been made, the following brief account is given.It is assumed that crystalline region and amorphous region in polymer films are evidently distinguishable, and that a elastomer characteristically corresponds to the network and to the network-chain in vulcanized rubber. When stress is applied, the hydrogen bonds, water-sensitive and resistive to elongation, are partially broken and the resultant strains, in the form of elongation, appear.The displacement length of the chains are calculated here on the assumption that, although each network-chain interacts with hydrogen bonds, the total number of configurations of network-chains is to be approximately computed according to the Gaussian distribution law. Furthermore, considering the orientation of crystalline parts in the samples, the elongation of polymer films at equilibrium adsorption of water, γ∞, is expressed by the following equation, γ∞=fκa0/6ν5/3kT·Nn/N+n, where N is the number of OH-radicals per unit volume of the sample, n the total number of the water molecules, ν the number of network-chains per unit volume of sample, f the stress, k Boltzmann constant, T absolute temperature, and a0 and κ constants related to potentials among the network-chains. Since the process involves the diffusion of water into the samples, n is a function of time, whereas, as non-Fickian type of diffusion into such uncoated cellophanes is to be expected here, n, as a function of time, is expressed by the following equation, n=ns(1-e-αt)2, where ns is the number of water molecules in the samples at equilibrium, and α a parameter for the rate of diffusion process of water molecule into the samples.Furthermore, it is assumed that the elongations, when the constant amounts of water is absorbed, are given by the simple Voigt model of network-chains, and that the elongations attending the adsorption process are given by the accumulation of each small successive elongations, Δγ, Thus, following the simple Voigt model, a differential equation for elongation, γ∞, is obtained, γ+kγ=kγ∞, where γ is any elongation of sample, and k a parameter for the rate of deformation (of course, a function of time). Conveniently we regard as the average quantity depending exclusively upon the final amounts of adsorption. Now, α and k, having, in above equations, an analogous meaning for the both processes, are assumed equal in later computations. Finally, we obtained an equation concerning the length at any time, γ=γ∞/s+1{(s+1)(1-e-kt)-2kte-kt-se-kt(1-e-kt)2+(1-s)e-kt(1-e-kt)}, where s-represents ns/N.The equation thus obtained shows a creep-curve having a point of inflection, ti, at which the following equation is derived

• 社団法人 日本材料学会の論文

社団法人 日本材料学会 | 論文

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