Scaling behavior of polyelectrolytes and polyampholytes: Simulation by an ensemble growth method

We use a nondynamical Monte Carlo method to simulate chains with charged monomers interacting via Coulomb potentials and short-range excluded volume potentials. An ensemble of chains of length N is created by adding monomers to the end of chains in an existing ensemble of length N−1. This is done in such a way that the ensemble remains at equilibrium at each stage of the process. For a weakly charged polyelectrolyte in a θ solvent the chain remains Gaussian for short lengths (R2∼N) but becomes linear (R2∼N2) for N greater than a ‘‘blob’’ size N0. The crossover point N0 decreases with increasing charge density. The results support the predictions of scaling theories and show that the ‘‘electrostatic blob’’ idea can be taken quite literally. For a polyelectrolyte in a poor solvent the Coulomb repulsions are in competition with attractive short-range interactions. The chain configuration is found to be collapsed (R2∼N2/3) for NNτ, where the blob size Nτ is a function of a charge density and the excluded volume. If the Coulomb interactions are screened then there is a configurational change of the polymer when the screening length κ−1 is reduced to the electrostatic blob radius. This is shown to happen very gradually over a range of κ−1 for the θ solvent case, but abruptly for the poor solvent case, again in agreement with theory. We also consider a neutral polyampholyte chain containing an equal number of positive and negative charges. The effect of the Coulomb interactions is shown to be attractive, but we are unable to see the long-chain scaling behavior for the chains of length 220 generated here. We discuss the statistical errors and correlations in the ensemble growth method. The efficiency of the method compares favorably with dynamical Monte Carlo methods (e.g., reptation algorithm) since it permits the whole range of lengths 1−N to be studied in a single run.