Abstract
We study the counterion distribution around a spherical macroion and its osmotic pressure in the framework of the recently developed Debye-Hückel-hole-cavity (DHHC) theory. This is a local density functional approach which incorporates correlations into Poisson-Boltzmann theory by adding a free energy correction based on the one-component plasma. We compare the predictions for ion distribution and osmotic pressure obtained by the full theory and by its zero temperature limit with Monte Carlo simulations. They agree excellently for weakly developed correlations and give the correct trend for stronger ones. In all investigated cases the DHHC theory and its computationally simpler zero temperature limit yield better results than the Poisson-Boltzmann theory.
Highlights
The screening of charged macromolecules in an electrolyte solution is a long standing problem which has prompted many attempts aiming at a theoretical explanation
In the inhomogeneous case integral equation theories [6, 7, 8, 9] and recently field theories [10] have become very popular in calculating correlation corrections to mean field double layers
Since in some of these methods, the free energy is not defined in a unique way, it becomes impossible to determine the specific role played by each source of correlations in the system
Summary
The screening of charged macromolecules in an electrolyte solution is a long standing problem which has prompted many attempts aiming at a theoretical explanation. If one uses the OCP free energy density as a correlation correction to the mean field functional describing the double layer at a charged surface, one has all the charge opposite to the counterions located on that surface, rather than homogeneously distributed as a stabilizing background. We only ever need a stabilizing cutoff close to the charged surface, where the ion density is largest This suggests the following simplification: Instead of using a cutoff function a(nPB(r)) depending on the local PB density, we pick a constant a from a worstcase scenario, namely, the value which it has at contact. Formula (14) nicely demonstrates that in this limit the cavity size, measured in the appropriate length scale l (see the scaling discussion in the Appendix), is another measure of the coupling strength
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