Abstract
A molecular theory relating to entanglement is presented herein. The concept of our model is similar to that of Chompff, et al. Since only long relaxation times are important, a light elastic string model is used instead of the Rouse chain. The molecular string is immersed in a viscous medium, and also, due to entanglements, δ function-like frictional forces are exerted on p points randomly distributed along the string. An exact characteristic equation for relaxation times is obtained. Relaxation spectra in cases where p=2, 4, 6 and 8, are computed numerically. It is shown that the spectrum consists of three parts: a short time region of the wedge type having a slope, −1/2, a middle time region of the flat type, and a long time region having a hump. Also, the maximum relaxation time is proportional to M3 if the parameter of the enhanced friction at an entangled point is independent of M, where M is the molecular weight of polymer.
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Chikahisa, Y., Morooka, T. A Theory of Entangled Polymers. Polym J 11, 145–151 (1979). https://doi.org/10.1295/polymj.11.145
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DOI: https://doi.org/10.1295/polymj.11.145
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