Abstract.
For a self-repelling polymer chain consisting of n segments we calculate the persistence length \(L\left(j,n\right)\), 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 \(L\left(j,n\right) \approx \mbox{const} \left(j\left(n-j\right)/n\right)^{2\nu-1}\) emerges for dimension d = 3. Also away from the excluded-volume limit \(L\left(j,n\right)\) is found to behave very similar to the swelling factor of a chain of length \(j \left(n-j\right)/n\). 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.
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Received: 17 November 2003, Published online: 30 March 2004
PACS:
61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 05.10.Cc Renormalization group methods
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Schäfer, L., Elsner, K. Calculation of the persistence length of a flexible polymer chain with short-range self-repulsion. Eur. Phys. J. E 13, 225–237 (2004). https://doi.org/10.1140/epje/i2003-10071-1
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DOI: https://doi.org/10.1140/epje/i2003-10071-1