Conformational free energy of lattice polyelectrolytes with fixed endpoints .1. Single-chain simulation and theory

Using Monte Carlo methods, the conformational free energy of an isolated lattice polyelectrolyte with fixed endpoints was calculated directly as a function of the chain length, the number of charges on the chain, the end-to-end distance of the chain, and the value of the Debye screening length. Lattice polyelectrolytes are self-avoiding random walks on a cubic lattice, bearing equidistantly-fixed, discrete charges. For the electrostatic interaction, a Debye-Huckel potential is used. To comprehend the simulation data, a descriptive analytical expression is proposed, which gives, in particular for charge densities around Manning's condensation threshold, a good estimate for the conformational free energy of a polyelectrolyte chain as a function of the relevant parameters. Furthermore, the simulation data are compared to the predictions of the theory of Katchalsky for a Gaussian chain with fixed endpoints and with screened electrostatic interactions between the charged segments. The derivation of this expression and the approximations involved are reinspected, and a better expression for the description of this model is proposed. For charge densities below Manning's condensation threshold, the results of this expression are in good agreement with the simulation data.