Weak violation of universality for Polyelectrolyte Chains: Variational Theory and Simulations

Details Weak violation of universality for Polyelectrolyte Chains: Variational Theory and Simulations Weak violation of universality for Polyelectrolyte Chains: Variational Theory and Simulations

2001-02-07

arxiv.org/abs/cond-mat/0102121v1

Eur. Phys. J. E 4, 475-487 (2001)

Physics

Condensed Matter

Soft Condensed Matter

to appear in European Phys. Journal E (soft matter)

Scientific paper

10.1007/s101890170103

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 characterize 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 $2^4

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