Charged Hard Sphere Model Research Articles

Surface Tension of Simple Molten Salts: Insight from a Charged Hard Sphere Model.

Surface tension of molten salts is rooted in many important phenomena in physical chemistry. We develop an analytical theory for the surface tension of molten salts, where the molten salt is described by a restricted primitive model electrolyte consisting of charged hard spheres, and surface tension is related to the formation of a cavity in the electrolyte. The integral equation theory is applied to the restricted primitive model electrolyte to derive an analytical formula of the cavity formation energy. The scaling relation of the cavity formation energy is further combined with morphological thermodynamics theory to determine the formula for surface tension. According to our formula, surface tension consists of a positive hard sphere contribution and a negative electrostatic contribution. Using the molar mass, interionic distance, density, and temperature as the input, our theory leads to a good prediction of surface tension of more than 16 molten salts at their melting point without introducing any adjustable parameters.

Kinetic theory of weakly ionized plasma and electrolyte mixtures including Onsager matrix and frequency dispersion effects

AbstractWe summarize the method of hydrodynamic approximation for weakly ionized plasmas developed with Klimontovich in 1962 and give a generalization to many—component systems using Onsagers matrix theory and including dispersion effects. We develop the conductivity theory of complex plasma and electrolyte mixtures based on the model of charged hard spheres with given non‐additive contact distances, including frequency‐dependent electric fields. These generalizations are made with the aim to allow applications to complex natural systems as atmospheric plasmas and seawater. Finally, we give as an example a numerical calculation of the single ion conductivities of a six‐component seawater model.

CALCULATION OF THE MELTING POINTS OF ALKALI HALIDES USING THE THERMODYNAMIC PERTURBATION THEORY

A model for calculating phase equilibria between a liquid and a crystal is proposed, which makes it possible to evaluate the melting points of ionic compounds. The dependence of the melting temperatures of alkali halides on the cation-anion composition can be described in terms of ionic radii and polarizabilities using thermodynamic perturbation theory for the molten phase. The chemical potential of the crystal phase contains the Born-Mayer formula for the electrostatic part of the energy and the Debye formula for the vibration contribution. The full system of equations describing the equilibrium between liquid and solid includes not only the equality of chemical potentials, but also contains the equation of state to calculate the equilibrium density of melts at the crystallization point. One more equation of the system is necessary for the self-consistent computation of the characteristic Blum’s screening parameter within the mean spherical model of the ionic mixture. On this basis, the melting points of fluorides, chlorides, bromides and iodides of lithium, sodium, potassium, rubidium and cesium have been calculated. It has been shown that the combination of the reference mean-spherical model of charged hard spheres with different diameters and the perturbation due to the charge-induced dipoles into the chemical potentials of molten salts is a good basis for quantitative agreement with experimental data on the melting temperatures within a few percent. Moreover, the regularities of the change in the melting temperatures reduced to the Coulomb energy at the maximum contact of the cation and anion, as well as depending on the difference in the ionic radii of the salts, are discussed.

Equation of State for Molten Alkali Halides by Thermodynamic Perturbation Theory.

Several variants of the equation of state (EoS) for molten alkali halides are considered using the thermodynamic perturbation theory. Most attention is focused on taking into account the charge-induced dipole (or induction) term to pressure. The model of charged hard spheres of different diameters within the mean spherical approximation is used as a reference system. The value of the extra induction contribution to the pressure is about 5-10% of the Coulomb input and, thus, leads to a better agreement between the calculation results and experimental data. It is shown that the EoS through the energy gives superior results as compared to the experimental data on molten alkali halides near their melting points. Trends in density change with the ionic radii and the polarizabilities are analyzed.

Statistical theory of individual ionic activity coefficients of electrolytes with multiple – Charged ions including seawater

Based on methods of statistical mechanics for the calculation of individual activity coefficients for electrolytic solutions we present analytical nonlinear extensions of the standard Debye - Hückel and Mean-Spherical approximations. These extensions, so - called DHX and MSX approximations, respectively, generalize the exact results from cluster theory and are given for the model of charged hard spheres with non - additive contact distances. The flexibility of the fully analytical model which is able to reflect e.g. cationic solvation effects and allows the treatment of ionic activities in a 6-component seawater model. Denoting by e the elementary charge, DHX and MSX include in the third order, e6, the Poirier effects of asymmetry of ion charges, and in the fourth order, e8, as well as in higher orders, weak association effects which are relevant for electrolytes with multivalent ions. Following the Justice method, weak association effects are treated in a semi - chemical description avoiding mass - action laws. An extrapolation of the theory of individual activities to a description of individual conductivities is proposed.

Stability of Anionic Complexes in Halide Melts of Bivalent Metals

The effect of volume variation at the possible dissociation equilibria of (MX4)2– anionic complexes in halide melts of bivalent metals are analyzed in terms of the mean-sphere approximation (MSA) of the statistical theory. Within the framework of the simplified model of charged hard spheres of different diameters and valences, the complete system of equilibrium equations is obtained, i.e., equations of the law of mass action and equations of state. This system makes possible self-correlated calculations of both the equilibrium concentration of autocomplexes and the melt density. It is shown that the simplest approximation of the complex diameter as the treble diameter of simple ions overestimates the effects of volume variations when considering dissociation. Taking into account the superposition of spheres makes it possible to describe the smoother volume variations with the temperature.

Adiabatic compressibility of an immiscible molten NaCl–AgI salt mixture

Adiabatic compressibility β of an immiscible 0.5NaCl + 0.5AgI liquid mixture in the immiscibility range is studied experimentally and theoretically using the model of charged hard spheres. The compressibility is calculated by the relationship β = 1/u2ρ studied using sound velocity u measured by a pulse method and density ρ determined by hydrostatic weighing. It is shown that the compressibility of the upper phase decreases and that of the lower phase increases when the temperature increases because of the superposition of the effects of the thermal motion of ions and the phase compositions. The temperature dependence of the difference between the compressibilities of the equilibrium phases is described using the empirical equation Δβ = (Tc–T)0.442, which is close to the mean-field theory description. The results of the model calculations adequately reproduce the experimentally observed temperature dependence of the compressibility of the coexisting phases. However, the theoretically predicted critical exponent (1/2) differs from the experimentally determined exponent by 13%. These results are discussed in terms of the nature of chemical bond in silver iodide.

Weak self-interactions of globular proteins studied by small-angle X-ray scattering and structure-based modeling.

We investigate protein-protein interactions in solution by small-angle X-ray scattering (SAXS) and theoretical modeling. The structure factor for solutions of bovine pancreatic trypsin inhibitor (BPTI), myoglobin (Mb), and intestinal fatty acid-binding protein (IFABP) is determined from SAXS measurements at multiple concentrations, from Monte Carlo simulations with a coarse-grained structure-based interaction model, and from analytic approximate solutions of two idealized colloidal interaction models without adjustable parameters. By combining these approaches, we find that the structure factor is essentially determined by hard-core and screened electrostatic interactions. Other soft short-ranged interactions (van der Waals and solvation-related) are either individually insignificant or tend to cancel out. The structure factor is also not significantly affected by charge fluctuations. For Mb and IFABP, with a small net charge and relatively symmetric charge distribution, the structure factor is well described by a hard-sphere model. For BPTI, with a larger net charge, screened electrostatic repulsion is also important, but the asymmetry of the charge distribution reduces the repulsion from that predicted by a charged hard-sphere model with the same net charge. Such charge asymmetry may also amplify the effect of shape asymmetry on the protein-protein potential of mean force.

Size asymmetric hard spheres as a convenient model for the capacitance of the electrical double layer of an ionic liquid

Even though ionic liquids are composed of nonspherical ions, it is shown here that the general features of the capacitance of an electrical double layer can be obtained using a charged hard sphere model. We have shown in our earlier studies that at high electrolyte concentrations or large magnitudes of the electrode charge density the fact that the ions have a finite size, and are not point ions, cause the capacitance near the potential of zero charge to increase and change from a minimum to a maximum as the ionic concentration is increased and to decrease as the magnitude of the electrode charge density increases. Here, we show that the asymmetry of the capacitance of an ionic liquid can be explained qualitatively by using spherical ions of different size without attempting to introduce the ionic shape in a detailed manner. This means that the general features of the capacitance of the double layer of an ionic liquid can be studied without using a complex model, although the study of the density or charge profiles of an ionic fluid would require one. However, this is often unnecessary in the analysis of many experiments.

Physico-chemical studies on the interaction of dendrimers with lipid bilayers. 1. Effect of dendrimer generation and liposome surface charge.

Studies on the interaction of different generation poly (amido amine) (PAMAM) dendrimers (2G, 4G and 6G) and liposomes of different compositions were carried out by a combined turbidity, dynamic light scattering and atomic force microscopic measurements. Liposomes comprising soy lecithin (SLC, negative surface charge), 1, 2-palmitoyl-sn-glycero-3-phosphatidylcholine (DPPC, mildly positive surface charge), 1,2-dipalmitoyl-sn-glycero-3-phospho-(1'-rac-glycerol (DPPG, negatively charged) and a biologically simulated mixture of DPPC + DPPG (7:3, M/M, negatively charged) were used as model bilayers. 30 wt% cholesterol was used in each combination as it is known to control the fluidity of membrane bilayers. Silica was used as a negatively charged hard sphere model with an aim to compare the results. Both the turbidity and hydrodynamic diameter values of all the liposomes, except DPPC, passed through maxima upon the progressive addition of PAMAM; the effect was insignificant in case of DPPC. Formation of dendriosome, a complex formed between dendrimer and liposome, resulted in the charge reversal of the negatively charged liposomes. Interaction between PAMAM and liposome was found to be governed by electrostatic as well as hydrogen bonding. Generation dependent PAMAM activity followed the order: 6G >4G>2G in terms of overall dendrimer concentration. However, interestingly, the order was reverse when PAMAM activity was considered in terms of total end group concentrations. AFM studies reveal the rupture of bilayer structure upon addition of dendrimer.

Lower Critical Solution Temperature in the Metastable Region of an Ionic Solution in a Non-Polar Solvent

Previous studies of the critical behavior of ionic solutions in nonpolar solvents showed mainly upper critical solution temperatures. Now, we report for the solution of tetra-n-butyl ammonium bromide (N4444Br) in toluene a nearly closed miscibility loop, where the lower critical solution temperature (Tc=297.75+/-0.05 K, xc=0.0270+/-5x10(-4)) is located in the region, which is metastable in respect to crystallization of the salt. The new observation is in variance to the former findings according to which the phase separation of ionic solutions in nonpolar solvents is similar to that of the model of charged hard spheres in a dielectric continuum, termed restricted primitive model (RPM), which has an upper critical solution point.

Characterization of the order-disorder transition of a charged hard-sphere model.

Monte Carlo simulations at constant pressure are used to characterize the structure of the restricted primitive model in the tetragonal-ordered solid phase. A method to estimate the location of the order-disorder transition and the densities of the coexistence phases is discussed. The results support the weakly first-order character of the transition.

The fluid–solid equilibrium for a charged hard sphere model revisited

The global phase diagram of a system of charged hard spheres, composed of positive and negative ions of the same size, is obtained by means of computer simulations. Thermodynamic integration and Einstein crystal calculations are used to determine the free energies of the different possible solid structures. In this way, the fluid–solid and solid–solid phase transitions are located. Gibbs–Duhem integration is used to trace the full coexistence curves between the different phases involved. Three different solid structures are found to be stable for the model considered; namely, a cesium chloride structure (CsCl), a substitutionally disordered close packed structure which is faced centered cubic (fcc), and a tetragonal ordered structure with a fcc arrangement of atoms if the charge of the ions is not considered. At high temperatures, freezing leads to the substitutionally disordered close packed structure. This solid structure undergoes an order–disorder transition at low temperatures transforming into the tetragonal solid. At low temperatures freezing leads to the cesium chloride structure (CsCl) which undergoes a phase transition to the tetragonal structure at high pressures. The tetragonal solid is the stable solid phase at low temperatures and high densities. In a narrow range of temperatures direct coexistence between the fluid and the tetragonal solid is observed. Three triple points are found for the model considered. The usual vapor–liquid–CsCl solid triple point occurs at T*=0.0225. In addition, a fluid-fcc disordered-tetragonal triple point is located at T*=0.245 and, finally, a fluid-CsCl-tetragonal triple point appears at T*=0.234. The results presented here can be used to test the performance of the different theoretical treatments of freezing available in the literature.

Structure and Transport Properties of a Charged Spherical Microemulsion System

Structure and transport properties of an oil-in-water microemulsion of weakly charged spherical micelles were studied experimentally using viscosity, NMR self-diffusion, and static and dynamic light scattering as well as theoretically by Brownian dynamics and Monte Carlo simulations and the Poisson−Boltzmann equation. The micelles contain decane covered by the nonionic surfactant pentaethylene glycol dodecyl ether (C12E5) and the ionic surfactant sodium dodecyl sulfate. The system has a constant surfactant-to-oil ratio, and the total volume fraction of surfactant and oil, Φ, is varied between 0.01 ≤ Φ ≤ 0.46. The micelles were made weakly charged by replacing a small fraction (0.01, 0.04, and 0.06) of the nonionic surfactant with ionic surfactant, retaining the micellar size. Comparison between self-diffusion and viscosity coefficients measured as a function of concentration showed that the system obeys the generalized Stokes−Einstein relation at lower micellar concentrations. At higher micellar concentrations, a slightly modified equation can be used upon the addition of an extra frictional factor due to stronger interactions. The collective diffusion coefficient shows a maximum as a function of the volume fraction. This result is in good agreement with predictions based on a charged hard-sphere model with hydrodynamic interactions. Other static and dynamic properties such as osmotic pressure, osmotic compressibility, and self-diffusion coefficient were obtained theoretically from simulations based on a charged-sphere model. The static and dynamic properties of the charged hard-sphere model qualitatively describe the behavior of the charged microemulsion micelles. At high volume fractions, Φ > 0.1, the agreement is quantitative, but at Φ < 0.1 the effect of the charge is smaller than what is predicted from the model.

Order-disorder transition in the solid phase of a charged hard sphere model.

We investigate the solid phases of the restricted primitive model (RPM). Monte Carlo simulations show the existence of an order-disorder transition from a substitutionally disordered face centered cubic lattice (fcc) to a new ordered fcc structure which is proposed as the ground state of the RPM at the close packing density. Our results suggest that the new phase might turn out in a new triple point in the RPM phase diagram involving three solid phases: CsCl, fcc ordered and fcc disordered structures. The order-disorder transition is also studied using the cell theory. The theory shows good agreement with the simulation results and suggests that the transition is weakly first order.

Corresponding-states approach to small-angle scattering from polydisperse ionic colloidal fluids.

Approximate scattering functions for polydisperse ionic colloidal fluids are obtained by a corresponding-states approach. This assumes that all pair correlation functions g(alpha beta)(r) of a polydisperse fluid are conformal to those of an appropriate monodisperse binary fluid (reference system) and can be generated from them by scaling transformations. The correspondence law extends to ionic fluids a scaling approximation (SA) successfully proposed for nonionic colloids in a recent paper. For the primitive model of charged hard spheres in a continuum solvent, the partial structure factors of the monodisperse binary reference system are evaluated by solving the Orstein-Zernike (OZ) integral equations coupled with an approximate closure. The SA is first tested within the mean spherical approximation (MSA) closure, which allows analytical solutions. The results are found in good overall agreement with exact MSA predictions up to relevant polidispersity. The SA is shown to be an improvement over the "decoupling approximation" extended to the ionic case. The simplicity of the SA scheme allows its application also when the OZ equations can be solved only numerically. An example is then given by using the hypernetted chain closure. Shortcomings of the SA approach, its possible use in the analysis of experimental scattering data and other related points are also briefly addressed.

Computer simulation of liquid ionic alloys and metal‐molten salt solutions

AbstractWe present a numerical study of simple models of liquid ionic alloys and metal‐molten salt solutions. The microscopic structure is modeled using the primitive model of charged hard spheres, the electronic structure is described by a right‐binding Hamiltonian including the crucial component of Madelung potential fluctuations. We discuss the nature of the nonmetal‐metal crossover as a function of composition in these systems and present a computation of thermodynamic properties within the screened mean spherical approximation.

Peculiarity of the Coulombic criticality?

A field-theoretical approach to the restricted primitive model of charged hard spheres is proposed. It uses a scalar field ϕ, similar to that of the sine-Gordon theory of Coulomb gas, but allows taking into account the hard-core interactions. We observe that near criticality the effective Landau-Ginzburg-Wilson Hamiltonian obtained has a negative ϕ 4 coefficient. A non-perturbative RG analysis of such a Hamiltonian shows that this may lead either to a first-order transition or to an Ising-like critical behavior, the partition being formed by the tricritical surface. This may explain the theoretical wavering encountered in the literature relative to the nature of the Coulombic criticality.

Critical behavior of effective potentials in colloidal suspensions within the charged hard-sphere model

An effective potential for a three-component charged hard-spheres mixture is studied. The critical behavior of the effective potential, which is interpreted as ordering tendency, is discussed. Obtained results are applied to making estimates for the lattice parameters of the polysterene-water suspension. Qualitative agreement of theoretically predicted lattice parameters with the experimental values is demonstrated.

The electronic structure of liquid silver chalcogenides: a tight-binding approach

We present a computational study of the electronic structure of the stoichiometric liquid zero-gap semiconductors , and . The geometry of the fluids is described by the primitive model of charged hard spheres; the electronic structure is modelled using a tight-binding Hamiltonian. The density of states is computed considering the Madelung potential fluctuations and the topological disorder characteristic of an ionic fluid. Only the introduction of nonzero tight-binding hopping matrix elements - equivalent to the formation of chemical bonds - induces a pseudogap between the chalcogenide conduction band and the silver valence band. The Fermi level can be located in a region of a small density of states; eigenstates at are likely to exhibit disorder-induced localization.