Monte Carlo simulations of a single polyelectrolyte in solution: Activity coefficients of the simple ions and application to viscosity measurements

Monte Carlo simulations of linear polyelectrolytes together with explicit ions have been performed in a spherical cell model to study conformational changes and activity coefficients in relation to the isoionic dilution method used in viscosity measurements. The results show that it is possible to define an effective ionic strength that will keep the average chain conformation constant on isoionic dilution and that this ionic strength can be predicted from the activity of the counterions, as has been suggested experimentally. Activity coefficients have been calculated from the simulations and compared with theoretical estimates based on various applications of the Debye-Hückel approximation, including Manning theory and an expression for a rigid rod with discrete charges. Manning theory generally gives poor agreement with the simulations, while the rigid-rod expression, which includes an ion-ion term, is able to predict the mean activity coefficient at not too high charge densities. Assuming that the co-ions are completely inert, the rigid-rod expression also leads to a reasonable approximation for the counterion activity. The simulation results have been used as input for two theoretical expressions for the reduced viscosity. The first, which is only based on the average chain conformation, does not reproduce the qualitative features of experimental curves. Our chains, with only 80 monomers do not display large conformational changes upon dilution with salt solutions of varying ionic strength. In contrast, the second viscosity expression, which takes intermolecular electrostatic interactions into account, gives a correct qualitative behavior.