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Charge inversion is the phenomenon in which an electric double layer contains more counterions than needed to compensate the surface charge. For colloidal particles this has the consequence that the apparent surface charge, as inferred from electrophoresis or interaction studies, has a sign opposite to that of the actual surface charge, obtainable by titration. This phenomenon has been known for over a century. According to the traditional interpretation, the inversion is caused by (chemical) specific adsorption of ions. However, beginning in the early 1980s it has been predicted by a large number of workers that charge inversion should occur as a consequence of many-body ion−ion correlations. For surfaces of sufficiently high surface charge density in the presence of divalent or multivalent counterions, charge inversion is expected to be ubiquitous even in the absence of specific adsorption. Testing this prediction has proved difficult because chemical specific adsorption is a very common phenomenon and can outweigh the effects of ion correlations. So far, no experimental systems have been thoroughly investigated where strong specific adsorption could be unambiguouslyruled out under conditions where charge inversion due to ion−ion correlations is predicted. Here, we solve this problem by studying the mercury/aqueous MgSO4interface. This system has the advantage that highly accurate double layer data are available for a variety of conditions, including some where chemical specific adsorption is known to be absent (or at least very weak). From precise data for this system [Harrison, J. A.; Randles, J. E. B.; Schiffrin, D. J. J. Electroanal. Chem.1970, 25, 197] one can establish the ionic components of charge and surface charge density. To extract quantitative theoretical predictions about the consequences of ion−ion correlations, we use the highly accurate anisotropic hypernetted chain (AHNC) method, where ion−ion correlations in the double layer are taken into account in a fully self-consistent fashion. It is found that for moderate to large negative surface charge densities and not too high concentration, the variation in the ionic components of charge with the surface charge density can to a large extent be quantitatively explained by enrichment of ions close to the surface due to ion−ion correlations. That chemical specific adsorption of Mg2+is negligible is supported by considering the properties of the double layer close to the electrocapillary maximum. In view of the large body of evidence indicating that the counterions tend to specifically adsorb on the mercury surface for positivepolarization but not for negative, the agreement between theory and experiment for negative surface charge constitutes strong evidence for ion−ion correlations as the origin of charge inversion.

Double-layer interactions and ion density profiles are calculated in the anisotropic reference hypernetted chain (RHNC) approximation, which uses the RHNC approximation for the anisotropic ion-ion correlation functions in the double layer. The ion-ion bridge functions are taken from a hard sphere reference system with the same density profiles as the full system. Excellent agreement with simulation results is obtained even at high concentrations and surface charges. If the bridge functions are neglected (i.e. the anisotropic hypernetted chain (HNC) approximation is used) only qualitative agreement with simulation is obtained in regimes where the local ion density is high and the contributions from ion-ion correlations at short range are very important. Otherwise, both the anisotropic HNC and RHNC approximations give equally good results for the systems investigated. Some methodological questions for the RHNC calculations are discussed.

Density profiles and anisotropic pair correlation functions have been calculated for a Lennard-Jones fluid in a narrow slit with attractive walls, using integral equation theory. Representative examples of these functions are presented graphically in full detail. The force between the walls as a function of the slit width for such a system is strongly oscillatory. Several aspects of the mechanism of this force are understood from a careful examination of the density profile and other one-particle properties, but an even more detailed picture is obtained by studying the pair distribution functions. We also present plots of the direct pair correlation function, the structure of which is found to be very simple. For the current system, even when the slit is narrow, this function is qualitatively similar to that of the bulk phase, but the quantitative differences can be considerable.

Density profiles for inhomogeneous dense Lennard-Jones fluids in narrow planar slits are calculated using various integral-equation closures for the anisotropic pair distribution functions. Very good agreement with simulation studies is obtained for the Zerah-Hansen (ZH) closure and a variant of the modified hypernetted chain (MHNC) closure suggested here while the Percus-Yevick (PY), the soft-core mean spherical approximation (SMSA) and, in particular, the hypernetted chain (HNC) closures give inferior results. Various properties of the fluid as functions of the slit width are calculated in the ZH approximation, using closure parameters optimized for the bulk phase. The mean particle number per unit area virtually coincides with the values from grand canonical ensemble simulations. The net pressure between the walls, which is more difficult to calculate accurately, agrees well with the simulation result. The agreement can probably be further improved by fully optimizing the ZH closure for the inhomogeneous system.

A simplified procedure for SCF Xα SW calculations on molecular systems, that can be divided into interacting units, is presented. The calculations are carried out on one part of the system at a time, iterating between interacting parts until self-consistency is attained. By exploiting the local molecular symmetry of each component part, the calculations can be further simplified, and only moderate amounts of computer time are required. The standard SCF Xα SW computer program has been modified to perform these calculations. Results for a water trimer are presented as a simple illustration of the method.