CONFORMATIONAL FREE-ENERGY OF LATTICE POLYELECTROLYTES WITH FIXED END-POINTS .1. SINGLE-CHAIN SIMULATION AND THEORY

Using Monte Carlo methods, the conformational free energy of an isolat ed lattice polyelectrolyte with fixed endpoints was calculated directl y as a function of the chain length, the number of charges on the chai n, the end-to-end distance of the chain, and the value of the Debye sc reening length. Lattice polyelectrolytes are self-avoiding random walk s on a cubic lattice, bearing equidistantly-fixed, discrete charges. F or the electrostatic interaction, a Debye-Huckel potential is used. To comprehend the simulation data, a descriptive analytical expression i s proposed, which gives, in particular for charge densities around Man ning's condensation threshold, a good estimate for the conformational free energy of a polyelectrolyte chain as a function of the relevant p arameters. Furthermore, the simulation data are compared to the predic tions of the theory of Katchalsky for a Gaussian chain with fixed endp oints and with screened electrostatic interactions between the charged segments. The derivation of this expression and the approximations in volved are reinspected, and a better expression for the description of this model is proposed. For charge densities below Manning's condensa tion threshold, the results of this expression are in good agreement w ith the simulation data.