Polymer conformational statistics. III. Modified Gaussian models of stiff chains

Abstract

Several attempts have been made to account for polymer chain stiffness or excluded volume effects in non‐Newtonian viscosity theory with the use of a modified Gaussian probability for intrachain distances. This method is here tested for the freely rotating chain by an application to the equilibrium expectation of the end‐to‐end vector R in the presence of an external potential $-\mathbf{R}·\mathbf{f}$ . The Gaussian parameters are varied as f increases to keep Gaussian estimates of the bond length and bond angle constant. Numerical tests are made for the limits of a freely jointed chain and the worm chain, and the modified Gaussian approach is found to work very well.