Configurational properties of dilute polymer solutions, dimensionality and perturbation theory

Abstract

By using second-order perturbation theory in the small parameter epsilon =4-d to 0, the author determines a specific value of the excluded volume parameter u equivalent to the fixed point value given by renormalisation group theory. For this value of the excluded volume parameter each expansion series in epsilon can be summed to an exponential function. The author thus studies the total number of configurations, C, the number of configurations returning to the origin, U, and the mean square end-to-end distance, (R2), of the polymer coil. An interdimensional relationship developed by Kosmas and Freed (1978) is used to extrapolate the authors results to lower dimensions. Finally, the author compares his results with those of previous theories and lattice enumerations, discussing possible differences between the Gaussian excluded volume model used by him and the self-avoiding walk model, close to dimensionality d=1.