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

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 ≃ N ν (log N ) γ where ν = 3 λ +2 and λ is the exponent which characterize the long-range interaction U ∝ 1 /r λ . The exponent γ 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 < N < 2 15 . 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 2 4 < N < 2 10 . The non universal behavior of the exponent γ 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.