Abstract
Monte Carlo Studies are made to examine the validity of the de Gennes’ theory of the stochastic motion of a polymer chain in the presence of fixed obstacles. The two-dimensional cases are treated. The topological requirement that the chain cannot intersect any of the obstacles is imposed on the stochastic motion. Observations are made on the diffusion coefficient of the center of mass, the relaxation time of the end-to-end vector and the mean-square displacement of a monomer, by varying the chain length and the concentration of the obstacles. The results are compared with those of de Gennes’ theory and Rouse’s. It is found that de Gennes’ theory provides a reasonable explanation for the slow relaxation phenomena under topological restrictions. Some minor revisions are made to obtain better agreement. It is found that, for the fast relaxation phenomena, the agreement is not good even if the concentration of the obstacles is sufficiently large. The condition for the applicability of the de Gennes’ theory is also discussed. The transition from the Rouse-type motion to the de Gennes-type motion is observed and found to be rather diffuse.
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Doi, M. Monte Carlo Studies of the Brownian Motion of a Polymer Chain under Topological Constraints. Polym J 5, 288–300 (1974). https://doi.org/10.1295/polymj.5.288
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DOI: https://doi.org/10.1295/polymj.5.288