Counterion condensation theory for finite polyelectrolyte and salt concentrations

Abstract

In the present work we analyze the physical fundamentals of Manning’s counterion condensation using his charged line model in a simple salt solution. We extend the theory for the cases of finite saline concentration and polymeric concentration tending to zero and the case of both finite concentrations. To find the equilibrium between the phases of free and condensed counterions, besides minimizing the free energy, we deduce auxiliary equation to determine the two characteristic parameters of the theory, the fraction fo condensed counterions and the volume of condensation. We compare the obtained results in the present work for only one infinite charged line with the ones of counterion condensation theory by Schurr and Fujimoto. We find that the linear density of critical charge depends on the concentration of added salt and takes values higher than one, instead of unitary value predicted by Manning. We obtain the equations by the activity and osmotic coefficients in function of the critical charge density. We compare them with the corresponding equations by Manning for these parameters. We extend the counterion condensation theory to solutions of linear polyelectrolytes for finite saline and polymeric concentrations using a cell model. We modify the electrostatic contribution to the Gibbs energy adding, to the traditional one calculated by Manning, the energy excess due to the macroion being in a cylindrical cell. We apply the theory to obtain the osmotic coefficient and we compare our results with experimental data of DNA osmotic coefficient and with theoretical adjustment using the Poisson-Boltzmann equation.

Special issue on soft matter research in Latin America

“…The presence of charges is known to introduce substantial complications in the behavior of physico-chemical systems, and their role is essential in biological soft matter. In their contribution, Bertolotto and Umazano [20] review and extend Manning's counterion condensation theory for the cases of finite saline and polymeric concentrations. The theory they present allows for a satisfactory comparison with experimental data for DNA osmotic coefficients.…”