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

摘要

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 ε-expansion we establish the scaling form and calculate the scaling function to order ε~2. Asymptotically, the simple result L(j,n) ≈ const (j(n-j))~(2v-1) emerges for dimension d = 3. Also away from 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) . 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.