Calculation of the persistence length of a flexible polymer chain with short range self-repulsion

TL;DR

This paper calculates the persistence length of a self-repelling polymer chain using renormalization group methods, revealing its scaling behavior and confirming results with simulations, especially in three dimensions.

Contribution

It provides a novel analytical calculation of the persistence length for self-repelling polymers, including the scaling function and behavior in different dimensions.

Findings

Persistence length scales as (j(n-j)/n)^{2nu-1} in 3D.

Simulation results agree with analytical predictions.

Logarithmic anomalies are suggested in 2D cases.

Abstract

For a self-repelling polymer chain consisting of n segments we calculate the persistence length L(j,n), defined as the projection of the end-to-end vector on the direction of the j`th segment. This quantity shows some pronounced variation along the chain. Using the renormalization group and epsilon-expansion we establish the scaling form and calculate the scaling function to order epsilon^2. Asymptotically the simple result L(j,n) ~ const(j(n-j)/n)^(2nu-1) emerges for dimension d=3. Also outside the excluded volume limit L(j,n) is found to behave very similar to the swelling factor of a chain of length j(n-j)/n. We carry through simulations which are found to be in good accord with our analytical results. For d=2 both our and previous simulations as well as theoretical arguments suggest the existence of logarithmic anomalies.