Abstract
As a continuation of a previous paper, an analysis is made of the diffusion-controlled ring closure reaction of a harmonic spring model of polymers for the case of finite k (k being an intrinsic second-order reaction rate constant). The upper bound and the lower bound for an apparent first-order reaction rate constant k1 are calculated by the variational principle of Rayleigh—Ritz and that of Doi respectively. These bounds are found to have very close values, and with the use of them, the error produced by the closure approximation is estimated for all values of k.
Similar content being viewed by others
Article PDF
References
S. Sunagawa and M. Doi, Polym. J., 7, 604 (1975).
G. Wilemski and M. Fixman, J. Chem. Phys., 58, 4009 (1973).
G. Wilemski and M. Fixman, J. Chem. Phys., 60, 866 (1974).
G. Wilemski and M. Fixman, J. Chem. Phys., 60, 878 (1974).
M. Doi, Chem. Phys., 11, 107 (1975).
M. Doi, Chem. Phys., 11, 115 (1975).
P. M. Morse and H. Feshbach, “Methods of Theoretical Physic”, MacGraw-Hill, New York, N.Y., 1953, Chapter 9.
M. Doi, Chem. Phys., 9, 455 (1975).
H. C. Burger, Proc. Roy. Acad. Amst., 20, 642 (1918).
F. C. Collins and G. E. Kimball, J. Colloid Sci., 4, 425 (1949).
G. Wilemski, private communication.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sunagawa, S., Doi, M. Theory of Diffusion-Controlled Intrachain Reactions of Polymers. II.. Polym J 8, 239–246 (1976). https://doi.org/10.1295/polymj.8.239
Issue Date:
DOI: https://doi.org/10.1295/polymj.8.239