Reformulation of the Ornstein-Zernike relation for a homogeneous isotropic fluid of spherical symmetry.

A reformulation of the Ornstein-Zernike equation for a homogeneous isotropic fluid composed of m species, with spherical symmetry, is formally derived. Based on a factorization of matrices of composed functions, this reformulation provides an interesting new set of functions. As a test to this reformulation, the resulting equations are solved for a binary mixture of hard spheres and compared to those obtained from the standard solution of the Ornstein-Zernike equation and with molecular dynamics simulations.

Long-range forces and charge inversions in model charged colloidal dispersions at finite concentration.

In charged colloidal dispersion systems the interest is in finding their stability conditions, phase transitions, and transport properties, either in bulk or confinement, among other physicochemical quantities, for which the knowledge of the dispersions' molecular structure and the associated macroion-macroion forces is crucial. To investigate these phenomena simple models have been proposed. Most of the theoretical and simulation studies on charged particles suspensions are at infinite dilution conditions. Hence, these studies have been focused on the electrolyte structure around one or two isolated central particle(s), where phenomena as charge reversal, charge inversion and surface charge amplification have been shown to be relevant. However, experimental studies at finite volume fraction exhibit interesting phenomenology which imply very long-range correlations. A simple, yet useful, model is the Colloidal Primitive Model, in which the colloidal dispersion is modeled as a mixture of size (and charge) asymmetrical hard spheres, at finite volume fraction. In this paper we review recent integral equations solutions for this model, where very long-range attractive-repulsive forces, as well as new long-range, giant charge inversions are reported. The calculated macroions radial distribution functions, charge distributions, and macroion-macroion forces are qualitatively consistent with existing experimental results, and Monte Carlo and molecular dynamics simulations.

Outsized Amplitude-Modulated Structure of Very-Long-Range Charge Inversions in Model Colloidal Dispersions.

Most theoretical and simulation studies on charged suspensions are at infinite dilution and are focused on the electrolyte structure around one or two isolated particles. Some classic experimental studies with latex particle solutions exhibit interesting phenomenology which imply very-long-range correlations. Here, we apply an integral equation theory to a model charged macroion suspension, at finite volume fraction, and find an amplitude-modulated charge inversion structure, with outsized amplitudes and of very-long-range extension. These inversions are different from the standard charge inversions in that they occur at finite macroions' volume fraction, far away from the central macroion, are outsized, and increase, not decrease, with increasing particle charge and distance to the central particle, which is indicative of long-range correlations. We find our results to be in agreement with our Monte Carlo simulations and qualitatively consistent with existing experimental results.

Entropy Driven Self-Assembly in Charged Lock-Key Particles.

In this work we study the lock-key model successfully used in supramolecular chemistry and particles self-assembly and gain further insight into the infinite diluted limit of the lock and key, depletant mediated, effective attraction. We discuss the depletant forces and entropy approaches to self-assembly and give details on the different contributions to the net force for a charged lock and key pair immersed in a solvent plus a primitive model electrolyte. We show a strong correlation of the force components behavior and the underlying processes of co-ion and solvent release from the cavity. In addition, we put into context the universal behavior observed for the energy-distance curves when changing the lock and key to solvent size ratio. Basically, we now show that this behavior is not always achieved and depends on the particular system geometry. Finally, we present a qualitative good agreement with experiments when changing the electrolyte concentration, valence, and cavity-key size ratio.

Modified colloidal primitive model as a homogeneous surface charge distribution: ζ-potential.

An integral equations theory is derived and applied to a modified colloidal primitive model (MCPM), for finite concentration colloidal dispersions. In MCPM, the charge on the colloidal particle is assumed to be smeared on its surface. We find important quantitative and qualitative differences of the ζ-potential, induced charge, and the colloid-colloid electric effective force, calculated in the MCPM, with those obtained from the colloidal primitive model (CPM), where the colloidal charge is assumed to be in the center of the particle, in spite of the fact that, due to Gauss's law, both models have the same particle distribution function. In particular, for the same parameters, while the ζ-potential is positive in MCPM, is negative in the CPM, implying opposite electrophoretic mobilities, µ. An inverse µ has been theoretically predicted in the past, for infinite dilution colloidal dispersions. The MCPM could be a better model for some colloidal particles. In both models, the CPM and the MCPM, it is found a very long-range colloid-colloid correlation, in accordance with previous Monte Carlo simulations. The electrostatic, as well as entropic, like-charged colloid-colloid forces are oscillatory, implying a long-range attraction.

Statistical mechanics approach to lock-key supramolecular chemistry interactions.

In the supramolecular chemistry field, intuitive concepts such as molecular complementarity and molecular recognition are used to explain the mechanism of lock-key associations. However, these concepts lack a precise definition, and consequently this mechanism is not well defined and understood. Here we address the physical basis of this mechanism, based on formal statistical mechanics, through Monte Carlo simulation and compare our results with recent experimental data for charged or uncharged lock-key colloids. We find that, given the size range of the molecules involved in these associations, the entropy contribution, driven by the solvent, rules the interaction, over that of the enthalpy. A universal behavior for the uncharged lock-key association is found. Based on our results, we propose a supramolecular chemistry definition.

Polarity inversion of ζ-potential in concentrated colloidal dispersions.

A concentrated colloidal dispersion is studied by applying an integral equations theory to the colloidal primitive model fluid. Important effects, attributed to large size and charge and to the finite concentration of colloidal particles, are found. We observe a polarity inversion of ζ-potential for concentrated colloidal dispersions, while it is not present for a single colloidal particle at infinite dilution. An excellent qualitative agreement between our theoretical predictions and our computer simulations is observed.

Overcharging and charge reversal in the electrical double layer around the point of zero charge.

The ionic adsorption around a weakly charged spherical colloid, immersed in size-asymmetric 1:1 and 2:2 salts, is studied. We use the primitive model (PM) of an electrolyte to perform Monte Carlo simulations as well as theoretical calculations by means of the hypernetted chain/mean spherical approximation (HNC/MSA) and the unequal-radius modified Gouy-Chapman (URMGC) integral equations. Structural quantities such as the radial distribution functions, the integrated charge, and the mean electrostatic potential are reported. Our Monte Carlo "experiments" evidence that near the point of zero charge, the smallest ionic species is preferentially adsorbed onto the macroparticle, independently of the sign of the charge carried by this tiniest electrolytic component, giving rise to the appearance of the phenomena of charge reversal (CR) and overcharging (OC). Accordingly, colloidal CR, due to an excessive attachment of counterions, is observed when the macroion is slightly charged and the coions are larger than the counterions. In the opposite situation, i.e., if the counterions are larger than the coions, the central macroion acquires additional like-charge (coions) and hence becomes "overcharged," a feature theoretically predicted in the past [F. Jiménez-Angeles and M. Lozada-Cassou, J. Phys. Chem. B 108, 7286 (2004)]. In other words, here we present the first simulation data on OC in the PM electrical double layer, showing that close to the point of zero charge, this novel effect surges as a consequence of the ionic size asymmetry. We also find that the HNC/MSA theory captures well the CR and OC phenomena exhibited by the computer experiments, especially as the macroion's charge increases. On the contrary, even if URMGC also displays CR and OC, its predictions do not compare favorably with the Monte Carlo data, evidencing that the inclusion of hard-core correlations in Monte Carlo and HNC/MSA enhances and extends those effects. We explain our findings in terms of the energy-entropy balance. In the field of electrophoresis, it has been generally agreed that the charge of a colloid in motion is partially decreased by counterion adsorption. Depending on the location of the macroion's slipping surface, the OC results of this paper could imply an increase in the expected electrophoretic mobility. These observations aware about the interpretation of electrokinetic measurements using the standard Poisson-Boltzmann approximation beyond its validity region.

Electrokinetic properties of monovalent electrolytes confined in charged nanopores: effect of geometry and ionic short-range correlations.

The electrokinetic properties (such as capillary conductance, electroviscosity, and the streaming potential) are obtained for a restricted primitive model electrolyte confined in a slitlike nanopore made up of two infinite parallel plates and in a cylindrical cavity of infinite extension. The hypernetted chain/mean spherical approximation (HNC/MSA) is used to obtain the equilibrium ionic concentration profiles inside the pores, which in turn are used to calculate the electrokinetic properties via linear hydrodynamic equations. Our results are compared with those obtained via the classical Poisson-Boltzmann (PB) theory. Important quantitative and qualitative effects, attributed to geometry and to the proper consideration of short-range correlations by HNC/MSA, are discussed.

Stability mechanisms for plate-like nanoparticles immersed in a macroion dispersion.

An integral equation theory and Monte Carlo simulations are applied to study a model macroion solution confined between two parallel plates immersed in a 1:1 electrolyte and the macroions' counterions. We analyze the cases in which plates are: (a) uncharged; (b) when they are like-charged to the macroions; (c) when they are oppositely charged to the macroions. For all cases a long range oscillatory behavior of the induced charge density between the plates is found (implying an overcompensation/undercompensation of the plates' charge density) and a correlation between the confined and outside fluids. The behavior of the force is discussed in terms of the macroion and ion structure inside and outside the plates. A good agreement is found between theoretical and simulation results.

On the regimes of charge reversal.

Charge reversal of the planar electrical double layer is studied by means of a well known integral equation theory. By a numerical analysis, a diagram is constructed with the onset points of charge reversal in the space of the fundamental variables of the system. Within this diagram, two regimes of charge reversal are identified, which are referred to as oscillatory and nonoscillatory. We found that these two regimes can be distinguished through a simple formula. Furthermore, a symmetry between electrostatic and size correlations in charge reversal is exhibited. Agreement of our results with other theories and molecular simulations data is discussed.

Van der waals-like isotherms in a confined electrolyte by spherical and cylindrical nanopores.

Electrolytes confined by spherical, cylindrical, and slit-like charged nanopores are studied. Results for ionic distribution profiles, pressures of the confined fluid, and absorption isotherms are obtained through the hypernetted chain/mean spherical approximation (HNC/MSA) integral equations theory. In spherical and cylindrical geometries, an inward, non-monotonic behavior of the pressure is found as confinement increases, implying a negative compressibility. The pressure vs volume isotherms resemble liquid-vapor van der Waals-like phase transition diagrams. This effect is correlated with a charge separation inside a spherical pore previously reported (Phys. Rev. Lett., 79, 3656, 1997). Here, the mechanism of charge separation and negative compressibility are explored in detail. When compared with the slit-like pore pressure, important qualitative differences are found.

Electrolyte distribution around two like-charged rods: their effective attractive interaction and angular dependent charge reversal.

A simple model for two like-charged parallel rods immersed in an electrolyte solution is considered. We derived the three point extension (TPE) of the hypernetted chain/mean spherical approximation (TPE-HNC/MSA) and Poisson-Boltzmann (TPE-PB) integral equations. We numerically solve these equations and compare them to our results of Monte Carlo (MC) simulations. The effective interaction force, F(T), the charge distribution profiles, rho(el)(x,y), and the angular dependent integrated charge function, P(theta), are calculated for this system. The analysis of F(T) is carried out in terms of the electrostatic and entropic (depletion) contributions, F(E) and F(C). We studied several cases of monovalent and divalent electrolytes, for which the ionic size and concentration are varied. We find good qualitative agreement between TPE-HNC/MSA and MC in all the cases studied. The rod-rod force is found to be attractive when immersed in large size, monovalent or divalent electrolytes. In general, the TPE-PB has poor agreement with the MC. For large monovalent and divalent electrolytes, we find angular dependent charge reversal charge inversion and polarizability. We discuss the intimate relationship between this angular dependent charge reversal and rod-rod attraction.

The electrical double layer for a fully asymmetric electrolyte around a spherical colloid: an integral equation study.

The hypernetted chain/mean spherical approximation (HNC/MSA) integral equation for a totally asymmetric primitive model electrolyte around a spherical macroparticle is obtained and solved numerically in the case of size-asymmetric systems. The ensuing radial distribution functions show a very good agreement when compared to our Monte Carlo and molecular-dynamics simulations for spherical geometry and with respect to previous anisotropic reference HNC calculations in the planar limit. We report an analysis of the potential versus charge relationship, radial distribution functions, mean electrostatic potential, and cumulative reduced charge for representative examples of 1:1 and 2:2 salts with a size-asymmetry ratio of 2. Our results are collated with those of the modified Gouy-Chapman (MGC) and unequal radius modified Gouy-Chapman (URMGC) theories and with those of HNC/MSA in the restricted primitive model (RPM) to assess the importance of size-asymmetry effects. One of the most striking characteristics found is that, contrary to the general belief, away from the point of zero charge the properties of an asymmetric electrical double layer (EDL) are not those corresponding to a symmetric electrolyte with the size and charge of the counterion, i.e., counterions do not always dominate. This behavior suggests the existence of a new phenomenology in the EDL that genuinely belongs to a more realistic size-asymmetric model where steric correlations are taken into account consistently. Such novel features cannot be described by traditional mean-field theories such as MGC, URMGC, or even by enhanced formalisms, such as HNC/MSA, if they are based on the RPM.

Nanocap-shaped tin phthalocyanines: synthesis, characterization, and corrosion inhibition activity.

Thermal and microwave reactions between [PcSn(IV)Cl2] (1) and the potassium salts of eight fatty acids (2 a-h) led to cis-[(RCO2)2Sn(IV)Pc] compounds (3 a-h) in yields ranging from 54 to 90 %. Compounds 3 a-h were fully characterized by elemental analysis, spectroscopy (IR, UV/Vis, multinuclear NMR), and seven X-ray diffraction structures, whereby two different allotropes were observed in two cases. The two carboxylates in 3 have a cis anisobidentate binding mode, octacoordination of the tin atoms with square-antiprismatic geometry, and pi-electron-rich nanocap shapes. On account of the latter characteristics, 3 a-h compounds have anticorrosion properties. LPR and Tafel electrochemical methods were used to characterize the behavior of these derivatives in naturally aerated sour brine, which is a common environment in petroleum production and refinery operations. The measurement of the corrosion rate of carbon steel AISI 1018 in the presence of 3 a-h (500 ppm) gave efficiencies of 61-87 % for the inhibitor performance. Of the different derivatives examined, compounds 3 e and 3 h were the most effective corrosion inhibitor prototypes.

A new correlation effect in the Helmholtz and surface potentials of the electrical double layer.

The restricted primitive model of an electrical double layer around a spherical macroparticle is studied by using integral equation theories and Monte Carlo simulations. The resulting theoretical curves for the Helmholtz and surface potentials versus the macroparticle charge show an unexpected positive curvature when the ionic size of uni- and divalent electrolyte species is increased. This is a novel effect that is confirmed here by computer experiments. An explanation of this phenomenon is advanced in terms of the adsorption and layering of the electrolytic species and of the compactness of the diffuse double layer. It is claimed that the interplay between electrostatic and ionic size correlation effects, absent in the classical Poisson-Boltzmann view, is responsible for this singularity.

Overcharging in colloids: beyond the Poisson-Boltzmann approach.

A broad range of manufactured products and biological fluids are colliods. The ability to understand and control the processes (of scientific, technological and industrial interest) in which such colloids are involved relies upon a precise knowledge of the electrical double layer. The traditional approach to describing this ion cloud around colloidal particles has been the Gouy-Chapman model developed on the basis of the Poisson-Boltzmann equation. Since the early 1980s, however, more sophisticated theoretical treatments have revealed both quantitative and qualitative deficiencies in the Poisson-Boltzmann theory, particularly at high ionic strengths and/or high surface charge densities. This review deals with these novel approaches, which are mostly computer simulations and approximate integral equation theories based on the so-called primitive model. Special attention is paid to phenomena that cannot be accounted for by the classic theory as a result of neglecting ion size correlations, such as overcharging, namely, the counterion concentration in the immediate neighborhood of the surface is so large that the particle surface is overcompensated. Other illustrative examples are the nonmonotonic behavior of the electrostatic potential and attractive interactions between equally charged surfaces. These predictions are certainly remarkable and, on paper, they can have an effect on experimentally measurable quantities (for instance, electrophoretic mobility). Even so, these new approaches have scarcely been applied in practice. Thus a critical survey on the relevance of ion size correlation in real systems is also included. Overcharging of macroions can also be brought about by adsorption of oppositely charged polyelectrolytes. Noteworthy examples and theoretical approaches for them are also briefly reviewed.

Liquid correlation across the walls in a slit pore: effect on the wetting and drying transition.

The liquid structure next to the walls of a slit pore, immersed in a model simple liquid, is studied through a liquid theory and grand canonical Monte Carlo simulations. A liquid correlation across slit walls, of finite width, is found. This correlation modifies the structure and capillary partial wetting and drying transitions of the nonhomogeneous fluid, when close to its liquid-vapor coexistence curve.

Fluid-fluid correlation through a model charged membrane: analytical results.

We study the properties of electrical double layers separated by a charged plate of finite thickness. The nonlinear Poisson-Boltzmann equation is analytically solved for this system. It is shown that, for an unsymmetrically charged, narrow plate, the charged fluids at both sides of the plate are strongly correlated, and the local electroneutrality condition (LEC) is not satisfied. The LEC is satisfied only for an infinitely thick plate. Analytical expressions for the induced charge and mean electrostatic potential are given and analyzed. These findings could be relevant for the understanding of protein adsorption on membranes.

Primitive Model Electrophoresis.

The electrophoresis of a spherical macroion is calculated with the new primitive model electrophoresis (PME) theory, which incorporates the ionic size. The results are compared with the classical theory of Wiersema, O'Brien, and White. The PME mobility, as a function of the macroion's surface charge (sigma) or zeta potential (zeta), is found to depend on the ionic valence, radius and concentration, and macroion hydrodynamical radius (A); i.e., it is not universal with kappaA, as predicted by the classical theory. The mobility is very nonlinear as a function of zeta. This behavior is related to the nonlinear dependence of zeta, as a function of sigma, when ionic size is included in the theory. In the classical theory zeta is a monotonic function of sigma. Important quantitative and/or qualitative differences between PME and the classical theory are found. However, in the limit of zero ionic diameter, and/or low salt concentration, and low macroion charge, the new theory reduces to the classical theory. The agreement of the PME with experimental data is very good. In particular, the prediction of reversed mobility is corroborated by recent experimental data. Copyright 2001 Academic Press.