Abstract
The excluded-volume effects on polymers were studied by a method developed for a random walk problem by Tsuda et al. on the basis of Feynman’s path integral concept. The method was applied to ring chains interacting through a soft-core potential, i.e., V(r)=γ for r<d and V(r)=0 for r≥d. The exponent ν which characterizes the dependence of the chain dimensions on N (number of segments) was found to be about 0.58 for repulsive interaction. However, no definite value of ν was obtained for attractive interaction because of large statistical scatters. An investigation was also made for chain dimensions as a function of N1/2, γ, and N1/2γ.
Similar content being viewed by others
Article PDF
References
T. Tsuda, K. Ichida, and T. Kiyono, Numerische Mathematik, 10, 110 (1967).
T. Tsuda, “Monte Carlo Method and Simulation,” (in Japanese), Baifukan, Tokyo, 1977, p 162.
Precise estimation of the path integral by Monte Carlo simulation is found.
G. Sher, M. Smith, and M. Baranger, Anal. Phys., 130, 290 (1980).
C. Domb, Adv. Chem. Phys., 15, 229 (1969).
D. S. McKenzie, Phys. Rep., 27C, 35 (1978).
F. T. Wall, S. Windwer, and P. J. Gans, “Monte Carlo Method applied to Configuration of Flexible Polymer Molecules,” in Method of Computational Physics, Vol. 1, Academic Press, New York, N. Y., 1963.
P. G. de Gennes, Phys. Lett., 38A, 339 (1972).
A. Baumgärtner and K. Binder, J. Chem. Phys., 71, 2541 (1979).
A. Baumgärtner, J. Chem. Phys., 72, 871 (1980).
A. Baumgärtner, J. Chem. Phys., 73, 2489 (1980).
D. Ceperley, M. H. Kalos, and J. L. Lebowithz, Macromolecules, 14, 1472 (1981).
I. Webman, J. L. Lebowitz, and M. H. Kalos, Macromolecules, 14, 1495 (1981).
I. Webman, J. L. Lebowitz, and M. H. Kalos, Phys. Rev., B21, 5540 (1980).
I. Webman, J. L. Lebowitz, and M. H. Kalos, Phys. Rev., A23, 316 (1981).
Dynamic Monte Carlo method has been applied to multiple chain systems. See, A. Baumgärtner and K. Binder, J. Chem. Phys., 75, 2994 (1981).
P. G. de Gennes, “Scaling Concepts in Polymer Physics,” Cornell University Press, Ithaca, N. Y., 1979.
See, for example, ref 4.
P. G. de Gennes, Macromolecules, 13, 1069 (1980).
P. Dejardin and R. Varoqui, J. Chem. Phys., 75, 4115 (1981).
A. T. Clark and M. Lal, “The Effect of Polymers on Dispersion Properties,” Th. F. Tadros, Ed., Academic Press, New York, 1982, p 169, and references cited therein.
S. Chandrasekhar, Rev. Mod. Phys., 15, 1 (1943).
R. P. Feynman and A. R. Hibbs, “Quantum Mechanics and Path Integrals,” McGraw-Hill, New York, N. Y., 1965.
R. P. Feynman, “Statistical Mechanics,” Benjamin, Massachusetts, 1972.
K. F. Freed, Adv. Chem. Phys., 22, 1 (1972).
P. Levy, “Processus Stochastiques et Mouvement Brownien,” Gauthier-Villars, 1965.
R. E. A. C. Paley and N. Wiener, “Fourier Transforms in the Complex Domain,” American Mathematical Society Colloquim Pub. XIX, 1934.
T. Hida, “Brownian Motion,” in Japanese, Iwanami, Tokyo, 1975.
A. Baumgärtner and K. Binder, J. Chem. Phys., 71, 2541 (1979).
F. L. McCrackin, J. Mazur, and C. M. Guttman, Macromolecules, 6, 859 (1973).
N. C. Smith and R. J. Fleming, J. Phys. A, 8, 938 (1975).
W. Bruns, J. Phys. A, 10, 1963 (1977).
S. F. Edwards, Proc. Phys. Soc., 85, 613 (1965).
J. des Cloizeaux, J. Phys. (Paris), 42, 635 (1981).
T. Minato, K. Ideura, and A. Hatano, Polym. J., 14, 579 (1982).
See, for example, ref 7, 19, and 20.
C. Domb, Polymer, 15, 259 (1974).
S. F. Edwards, in “Critical Phenomena,” Natural Bureau of Standards Miscell. Pub., Washington, D. C., 1966.
H. Yamakawa, “Modern Theory of Polymer Solutions,” Harper and Row, New York, N. Y., 1971.
C. Domb, A. J. Barrett and M. Lax, J. Phys. A, 6, L82 (1973).
See, for example, ref 6, 7, 8, and 18.
T. Minato and A. Hatano, in preparation.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Minato, T., Hatano, A. Monte Carlo Simulation of Interacting Polymer Systems. I. Behavior of Ring Chain Interacting via Soft-Core Potential. Polym J 14, 931–939 (1982). https://doi.org/10.1295/polymj.14.931
Issue Date:
DOI: https://doi.org/10.1295/polymj.14.931