Titrating Polyelectrolytes - Variational Calculations and Monte Carlo Simulations
B. Jönsson, M. Ullner, C. Peterson, O. Sommelius, B. Söderberg
Abstract
Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. The Coulomb interactions are emulated by harmonic repulsive forces, the force constants being used as variational parameters to minimize the free energy. For the titrating charges, a mean field approach is used.
The accuracy is tested against Monte Carlo data for up to 1000 monomers. For an unscreened chain, excellent agreement is obtained for the end-to-end distance and the apparent dissociation constant. With screening, the thermodynamical properties are invariably well described, although the structural agreement deteriorates.
A very simple rigid-rod approximation is also considered, giving surprisingly good results for certain properties.