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Soft Matter and Biological Physics


Eur. Phys. J. E 4, 475-487

Weak violation of universality for polyelectrolyte chains: Variational theory and simulations

G. Migliorini1, V.G. Rostiashvili1 and T.A. Vilgis1, 2

1  Max Planck Institute for Polymer Research, 10 Ackermannweg, 55128 Mainz, Germany
2  Laboratoire Européen Associé, Institute Charles Sadron, 6 rue Boussingault, 67083 Strasbourg Cedex, France

vilgis@mpip-mainz.mpg.de

(Received 8 August 2000 and Received in final form 19 December 2000)

Abstract
A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in d dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present, in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain length N. We find $R \simeq N^{\nu}(\log
N)^{\gamma}$, where $\nu = \frac{3}{\lambda+2}$ and $\lambda$ is the exponent which characterizes the long-range interaction $U \propto 1/r^{\lambda}$. The exponent $\gamma$ is shown to be non-universal, depending on the strength of the Coulomb interaction. We check our findings by a direct numerical minimization of the variational energy for chains of increasing size 24< N< 215. The electrostatic blob picture, expected for small enough values of the interaction strength, is quantitatively described by the variational approach. We perform a Monte Carlo simulation for chains of length 24< N< 210. The non-universal behavior of the exponent $\gamma$ previously derived within the variational method is also confirmed by the simulation results. Non-universal behavior is found for a polyelectrolyte chain in d=3 dimension. Particular attention is devoted to the homopolymer chain problem, when short-range contact interactions are present.

PACS
02.50.-r - Probability theory, stochastic processes, and statistics.
36.20.Ey - Conformation (statistics and dynamics).
61.25.Hq - Macromolecular and polymer solutions; polymer melts; swelling.


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001