**Coulomb Correlation Between Counterions in the Double Layer
Around Cylindrical Polyions**

**Jesus Piñero ^{a}, Lutful B. Bhuiyan^{a}, Jurij Reščič^{b}
and Vojko Vlachy^{b}***

^{a}Laboratory of Theoretical Physics Department of Physics,
University of Puerto Rico San Juan, Puerto Rico 00931-3343

^{b}Faculty of Chemistry and Chemical Technology, University of
Ljubljana, 1000 Ljubljana, Slovenia

Absrtract

Monte Carlo simulation and theoretical
results on some aspects of structure and thermodynamics of polyelectrolyte
solutions at room temperature are presented. The solution is mimicked by an
infinitely long cylindrical polyion surrounded by point counterions. Both
standard histogram method and Widom’s particle insertion method are utilized in
the simulations based on the cylindrical cell model. The osmotic coefficient is
determined via different equations (approaches) to determine the internal
consistency of the equations as also the numerical accuracy of the calculations.
Contributions to the osmotic coefficient arising out of polyion-counterion and
counterion-counterion interactions are explicitly evaluated. The study clearly
demonstrates (i) that the good agreement between the Poisson-Boltzmann
predictions and the simulations is partly due to some serendipitous cancellation
of errors, and (ii) that it is the neglect of the inter-ionic correlations in
the mean field approach that leads to a partial compensation of the shortcomings
of the Poisson-Boltzmann osmotic equation. Simulations results are also reported
for the ion-ion correlations in the inhomogeneous diffuse double layer
surrounding the polyion.

**Key words:** polyelectrolyte solution,
Monte Carlo, Poisson-Boltzmann, osmotic coefficient, heat of dilution