Monte Carlo simulations of polyelectrolytes: Isolated fully ionized chains with screened Coulomb interactions

We present Monte Carlo simulation results for an isolated polyelectrolyte chain where the charged groups interact via a screened Coulomb interaction of Debye-Hückel form. The chain consists of hard spheres on a backbone with fixed bond angles and either free rotation or a torsional potential that produces hindered rotation. Parameters have been chosen to roughly mimic polyacrylic acid (PAA). We give results for the mean square end-to-end distance 〈r²〉, mean square radius of gyration 〈s ²〉, and finite-chain persistence length for chains of up to 320 beads and salt concentrations ranging from 0.1 to 0.0001 mol dm^-3. Both 〈r²〉 and 〈s²〉 show power law behavior for chains larger than 80 beads at 0.1 mol dm^-3 - the scaling exponents are intermediate between rigid rod and self-avoiding walk values. No scaling behavior can be observed at lower concentrations because of the limitations on the chain lengths that can be simulated. At 0.1 and possibly at 0.01 mol dm^-3 the infinite-chain persistence length can be obtained by extrapolation of the distribution of angles of the chain bonds relative to the central bond. These values are in rough agreement with the worm-like chain calculations of Skolnick, Fixman, and Odijk. Our calculations would be expected to give larger values for the persistence length than theories which include ionic degrees of freedom, such as the Poisson-Boltzmann calculations of Le Bret and Fixman. At 0.1 mol dm^-3, however, their results are larger than ours, a result we find puzzling.