RENORMALIZATION-GROUP SCALING THEORY FOR FLEXIBLE AND WORMLIKE POLYMER-CHAINS

Using an argument based on renormalization-group scaling, we study the structure of the functions corresponding to the mean square end-to-end separation, and radius of gyration, and the second virial coefficient for a flexible polymer chain including the finite effect of excluded volume. With the aid of recent accurate calculations of asymptotic properties [M. Muthukumar and B. G. Nickel, J. Chem. Phys. 86, 460 (1987)], we establish the form of the functions for these physical quantities at an arbitrary scaled excluded-volume parameter. We also propose approximations for the above-mentioned quantities for a wormlike polymer chain, which successfully interpolate the limiting flexible and hard-rod behavior.