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

A variational approach is considered to calculate the free energy and the c onformational properties of a polyelectrolyte chain in d dimensions. We con sider in detail the case of pure Coulombic interactions between the monomer s, when screening is not present, in order to compute the end-to-end distan ce and the asymptotic properties of the chain as a function of the polymer chain length N. We find R similar or equal to N-nu (log N)(gamma), where nu = 3/lambda +2 and lambda is the exponent which characterizes the long-rang e interaction U proportional to 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 e nergy for chains of increasing size 2(4) < N < 2(15). The electrostatic blo b picture, expected for small enough values of the interaction strength, is quantitatively described by the variational approach. We perform a Monte C arlo simulation for chains of length 2(4) < N < 2(10). The non-universal be havior of the exponent gamma previously derived within the variational meth od is also confirmed by the simulation results. Non-universal behavior is f ound for a polyelectrolyte chain in d = 3 dimension. Particular attention i s devoted to the homopolymer chain problem; when short-range contact intera ctions are present.