Correlation effects, image charge effects and finite size in the macro-ion-electrolyte system: a field-theoretic approach

Beyond Poisson-Boltzmann: fluctuations and fluid structure in a self-consistent theory

Poisson-Boltzmann (PB) theory is the classic approach to soft matter electrostatics and has been applied to numerous physical chemistry and biophysics problems. Its essential limitations are in its neglect of correlation effects and fluid structure. Recently, several theoretical insights have allowed the formulation of approaches that go beyond PB theory in a systematic way. In this topical review, we provide an update on the developments achieved in the self-consistent formulations of correlation-corrected Poisson-Boltzmann theory. We introduce a corresponding system of coupled non-linear equations for both continuum electrostatics with a uniform dielectric constant, and a structured solvent-a dipolar Coulomb fluid-including non-local effects. While the approach is only approximate and also limited to corrections in the so-called weak fluctuation regime, it allows us to include physically relevant effects, as we show for a range of applications of these equations.

Opposite counter-ion effects on condensed bundles of highly charged supramolecular nanotubes in water

Although ion specificity in aqueous solutions is well known, its manifestation in unconventional strong electrostatic interactions remains implicit. Herein, the ionic effects in dense packing of highly charged polyelectrolytes are investigated in supramolecular nanotube prototypes. Distinctive behaviors of the orthorhombic arrays composed of supramolecular nanotubes in various aqueous solutions were observed by Small Angle X-ray Scattering (SAXS), depending on the counter-ions' size and affiliation to the surface -COO(-) groups. Bigger tetra-alkyl ammonium (TAA(+)) cations weakly bonding to -COO(-) will compress the orthorhombic arrays, while expansion is induced by smaller alkaline metal (M(+)) ions with strong affiliation to -COO(-). Careful analysis of the changes in the SAXS peaks with different counter/co-ion combinations indicates dissimilar mechanisms underlying the two explicit types of ionic effects. The pH measurements are in line with the ion specificity by SAXS and reveal the strong electrostatic character of the system. It is proposed that the small distances between the charged surfaces, in addition to the selective adsorption of counter-ions by the surface charge, bring out the observed distinctive ionic effects. Our results manifest the diverse mechanisms and critical roles of counter-ion effects in strong electrostatic interactions.

Correlation forces between helical macro-ions in the weak coupling limit

When correlation effects are relatively weak, electrostatic interaction forces between cylindrical macro-ions may be divided into two contributions (Lee 2010 J. Phys.: Condens. Matter 22 414101). Firstly, there is a mean field contribution, described by the theory of Kornyshev and Leikin (1997 J. Chem. Phys. 107 3656) at large separations. Secondly, we have correlation forces, which we analyze by performing an expansion in the number density of condensed ions. We see three distinct contributions, for which analytical expressions are given for both general and helical contributions. Firstly, there is a term (of leading order in the expansion) that is a change in the solvation energies of uncondensed counter-ions due to two macro-molecular interfaces. Secondly, we have a contribution that comes from fluctuations in the condensed ion charge density being repelled by their 'images' in the other molecule. Both of these contributions are repulsive. Lastly, there exists an attractive Oosawa contribution that arises from fluctuations in the condensed ions about one molecule correlating with those about the other molecule. The first two forces do not depend on the orientation of the molecules about their long axes. However, the Oosawa force may do so, depending on the pattern of bound and fixed charges. For a DNA like charge distribution, we see that the strength of this dependence is governed by the relative proportion of bound ions, between two positions that represent the DNA groove centers. We see that, at a Debye screening length equivalent to physiological salt concentrations, the correlation forces can be neglected for univalent ions. For divalent ions, they contribute a small, albeit significant, correction. Our calculations suggest that increasing the salt concentration reduces the size of these forces.

Charge renormalization of helical macromolecules

Some time ago a theory of electrostatic interaction between helical macromolecules was proposed (Kornyshev and Leikin 1997 J. Chem. Phys. 107 3656): the Kornyshev-Leikin (KL) theory. We place this theory on a more rigorous statistical mechanical grounding, starting from the free energy that can be derived from a grand partition function. We see that the long range behaviour of the force is indeed given by the KL theory, no matter whether the distributions of 'condensed' ionic charge are at the surface of the macromolecule or extend away from it. Thus, for the limiting behaviour, we need only self-consistently calculate the distribution of the condensed fraction of ions for a single macro-ion. This distribution can be related back to interaction parameters: KL parameters. Furthermore, we are able to see within the formalism where corrections due to the hard core radius of the ion enter. For the adjustment of the 'condensed' ions, we show an expression for the leading order contribution, as well as relevant decay lengths. As a demonstration of the theoretical 'machinery', as well as a study of qualitative effects, we calculate the KL parameters in one instance. We use a DNA-like surface charge distribution, where a fraction of the ions are assumed to be bound in the grooves at the surface of a DNA molecule, whereas the rest of the charge distribution is calculated self-consistently. Also, the electrostatic contribution to the counter-ion binding potentials that ions experience within the grooves can be calculated.

Monte Carlo determination of mixed electrolytes next to a planar dielectric interface with different surface charge distributions

Employing canonical ensemble Monte Carlo simulations, we report a calculation of the distribution of small ions next to a planar negatively charged surface in the presence of mixed electrolytes of monovalent and trivalent salt ions within the framework of the primitive model under more realistic hydrated ion size conditions. The effects of surface charge discreteness and dielectric breakdown on charge inversion are discussed based on increasing concentration of both monovalent and trivalent salt. Moreover, a comparison of the simulation results for different discretization models is made along with the case of uniformly distributed charge in terms of the ionic density profiles as well as the integrated charge distribution function. For finite size charged groups located inside the lower dielectric region, a complete equivalence with the case of uniform distribution is observed if the quantities of interest are exclusively analyzed as a function of the distance to the charged interface. With protruding head groups into the aqueous solution, the excluded volume dominates over the correlation effect, therefore the ions are less accumulated in the vicinity of the charged surface, inducing that the onset position of charge inversion experiences an evident shift toward the aqueous environment. Overall, the effect of repulsive image forces on the diffuse double layer structure can be significant at low surface charge density irrespectively of surface charge distributions.