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• W2322299506 abstract "A molecular theoretical investigation of the viscoelastic properties of amorphous polymeric substances in the range of long relaxation time has been made using the temporarily cross-linked network-structure-model. The origin of the energy dissipation is ascribed to the slipping of chains and the change of number of chains induced by deformation.When the network structure is deformed each chain will slip since the network structure does not return to its initial state when the deformation is taken off. As the chains slip the deformations of chains do not coinside with that of the network structure. Then we introduce the two kinds of deformation tensor, one is the observable deformation tensor of the netwok structure and the other is the inner deformation tensor of each chain. Assuming that the deformation of all chains can be characterized by a single average inner deformation tensor, we obtain Eq. (7) which expresses the relation between the observable and the inner deformation tensors.We can also obtain Eq. (31) expressing the change of the number of chains which depends upon the time and the deformation. Eq. (31) has the same form to that of the chemical reaction as expected by the theory of rate process.The strain free energy of each chain is assumed to depend only on the end-to-end distance of each chain and the free energy of whole system is assumed to be given by the sum of the said strain free energy of each chain and the free energy depending on the density of segments which corresponds to the inner pressure of the system.Accordingly the stress is obtained by Eq. (17) as the function of the inner deformation tensor. Using the relation between the observable and the inner deformation tensors, Eq. (7), we obtain the stress- time-deformation relation Eq. (20), which is the natural generalization of equation of Maxwell model. In small deformation the tensors are automatically symmetrized and we obtain Eq. (33) which is just the same formula with that of Maxwell model. As we assume the average inner deformation tensor, namely the average slipping of each chain we have only a single relaxation time which is the average relaxation time in the range of box type relaxation time spectrum. In this formalism, as the average inner deformation is assumed we can not explain that the system must have the box type relaxation time spectrum in the range of the long relaxation time.The energy dissipation expressed by Eq. (37) has two terms, one is due to the slipping of chains and the other for the change of the number of chains.Some applications of the theory are made in last section. We define the stationary state by the state of constant inner deformation tensor. In stationary state the number of chains are kept constant and the origin of the energy dissipation is ascribed to the slipping of chains only. First, we treat the stationary simple elongation, the stress and the energy of dissipation are expressed by Eq. (42) and Eq. (43) respectively and the tensile viscosity coefficient η* is expressed by Eq. (45) in case of no volume change. Secondly, we treat the stationary simple shear, in this case the normal stress effect appears as is shown by Eq. (47) and we have Eq. (49) as the relation between the tensile and the shear viscosity coefficients, which is known as Trouton's law. Lastly we treat the instantaneous simple elongation, as is shown by Eq. (50) and Eq. (51) the stress shows nearly exponential decay since the number of chains changes slowly with time. The inner deformation decreases monotonously and tends to return to its initial state, on the other hand the number of chains decreases at first and passes a minimum value then increases again and tends to approach to the equilibrium value." @default.
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• W2322299506 date "1960-01-01" @default.
• W2322299506 modified "2023-10-03" @default.
• W2322299506 title "Viscoelastic Property of Network-Structure" @default.
• W2322299506 doi "https://doi.org/10.2472/jsms1952.9.250" @default.
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