Intrinsic Viscosity of Polymer Chains with Small Excluded Volume

Abstract

The intrinsic viscosity of polymer chains with small excluded volume is calculated on the basis of the Fixman—Pyun theory for unperturbed chains. The eigenfunctions of the unperturbed free‐draining time evolution operator are chosen as the basis set, and the formulation is made so as to take into account the coupling of the normal coordinates for excluded‐volume interactions but not for hydrodynamic interactions. An additional approximation introduced is the preaveraging of the Oseen hydrodynamic interaction tensor. Therefore, the present theory gives the same result as the Zimm theory in Hearst's version for vanishing excluded volume. Evaluation is carried out only in the nondraining limit, and the cubed viscosity—expansion factor is obtained as α η 3 = 1+1.06z –··· , where z is the well‐known excluded‐volume parameter. This is consistent with the recent experimental results. Furthermore, it is emphasized that the present value for the coefficient of z is smaller than the corresponding value of 1.80 predicted by the boson‐operator theory of Fixman and also the value of 1.55 obtained by Kurata and Yamakawa. It is noted that if the coupling of the normal coordinates is completely ignored, the corresponding value is 0.810.