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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.
RESUMEN
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.
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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.
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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.
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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.
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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.
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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.
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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.
RESUMEN
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.