Modeling of Molten Salts

Models of molten salts have evolved with time and so have the inter-ionic potentials relevant to them. The restricted primitive model (RPM) considers the ions to be charged hard spheres of uniform size (radius rj) interacting through their coulomb potentials. The potential function is then  

A modification introduces a relative dielectric constant e replacing Aheq in the denominator of (3.8) [109, 110]. The restricted is removed when the cations and anions are permitted to have different sizes, r+ and r, and then the inter-ionic potential becomes similar to (3.8), but with 2r replaced by r+ + r. The hard sphere restriction is removed by the inclusion of a repulsion term [111] 

Here b is a salt-dependent parameter and denotes unit radius. To this expressitMi van der Waals interaction terms have been added [111], yielding  

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Several differing simple models of molten salts do indeed give reasonably close calculations of equilibrium properties, e.g., compressibility and surface tension. What these models do not do, however, is to quantitatively rationalize the data on the temperature dependence of conductance, viscous flow, and self-diffusion. The discovery by Nanis and Richards of the fact that simple liquids have heats of activation for all three properties given approximately by 3. lART presents a clear and challenging target for testing models of liquids. 

By using the pair potentials of one of the pioneer works in the modeling of molten salts (Woodcock and Singer) as well as the corresponding parameters in this work, calculate the equilibrium distance for Li and Cl ions j ust above the... 

The Structure of inorganic melts is, in spite of their relative simplicity, not completely understood. The earlier calculations and simple models of molten salts were built up rather on intuition. However, they were the necessary first step for more sophisticated approaches. 

In 1963 Dr. Danbk joined the Institute of Inorganic Chemistry of the Slovak Academy of Sciences in Bratislava, of which he was the director in the period 1991-1995. His main field of interest was the physical chemistry of molten salts systems in particular the study of the relations between the composition, properties, and structure of inorganic melts. He developed a method to measure the electrical conductivity of molten fluorides. He proposed the thermodynamic model of silicate melts and applied it to a number of two- and three-component silicate systems. He also developed the dissociation model of molten salts mixtures and applied it to different types of inorganic systems. More recently his work was in the field of chemical synthesis of double oxides from fused salts and the investigation of the physicochemical properties of molten systems of interest as electrolytes for the electrochemical deposition of metals from natural minerals, molybdenum, the synthesis of transition metal borides, and for aluminium production. 

CorrApp modelling of molten salt composition after 2 min contact between Fe and KCI/ZnCl2 salt at 320°C. 

Nevertheless, a model of molten salt hydrates that is widely accepted considers the hydrated cations to be single particles having a radius r = r + 2th2o of low electrical field strength [59]. Thus, in molten Ca(N03)2-4H20 the cation [Ca... 

The first chapter in the second volume of this series deals with the physical properties of a novel group of melts, the organic molten salts as applied to the testing of models of molten salt behavior. In addition, there are three chapters on the chemistry of solute species in melts. One of these chapters deals with solubilities of reactive gases in melts. Another chapter treats coordination chemistry and electronic spectroscopy of Group VIII elements in fused salts. The last chapter is concerned with recent developments in electroanalytical chemistry in molten salt systems. 

In the case of molten salts, no obvious model based on statistical mechanics is available because the absence of solvent results in very strong pair correlation effects. It will be shown that the fundamental properties of these liquids can be described by quasi-chemical models or, alternatively, by computer simulation of molecular dynamics (MD). 

The electrolyte concentration is very important when it comes to discussing mechanisms of ion transport. Molar conductivity-concentration data show conductivity behaviour characteristic of ion association, even at very low salt concentrations (0.01 mol dm ). Vibrational spectra show that by increasing the salt concentration, there is a change in the environment of the ions due to coulomb interactions. In fact, many polymer electrolyte systems are studied at concentrations greatly in excess of 1.0 mol dm (corresponding to ether oxygen to cation ratios of less than 20 1) and charge transport in such systems may have more in common with that of molten salt hydrates or coulomb fluids. However, it is unlikely that any of the models discussed here will offer a unique description of ion transport in a dynamic polymer electrolyte host. Models which have been used or developed to describe ion transport in polymer electrolytes are outlined below. 

This principle serves as the basis for a number of models of fused salt systems. Perhaps the best known of these is the Temkin model, which uses the properties of an ordered lattice to predict thermodynamic quantities for the liquid state [79]. However, certain other models that have been less successful in making quantitative predictions for fused salts may be of interest for their conceptual value in understanding room temperature ionic liquids. The interested reader can find a discussion of the early application of these models in a review by Bloom and Bockris [71], though we caution that with the exception of hole theory (discussed in Section II.C) these models are not currently in widespread use. The development of a general theoretical model accurately describing the full range of phenomena associated with molten salts remains a challenge for the field. 

Structural models for molten salts have been proposed by several authors Bockris [1-3], Stillinger [4], Zarzycki [5], Janz [6], Kleppa [7], Blander [8], and others. These structural models are based on the older theories of the liquid state, which were applied for molecular liquids, liquified gases, molten metals, etc. Some of these models will be treated in the following. 

Likewise, measurements of the density of molten salts show a volume increase of 10-25% at melting. These results lead to the conclusion that the simplest model for the ionic liquid is derived from the crystalline lattice. Hence, in the liquid, some elements of the crystalline lattice are maintained, and between these some holes are produced. The holes (larger than Schottky defects) explain the volume increase by melting and also the short range ordering. This model,... 

In mixtures of molten salts it is necessary to take into account the fact that the interaction forces are very strong and that the nearest neighbors of the cations are anions and the nearest neighbors of the anions are always cations. Therefore, random distributions of anions and cations cannot be conceived. On the basis of these considerations Temkin [18] proposed a model for ideal mixtures of molten salts which assumes the existence of two interlocking sublattices, one of cations and the other of anions. In the case of mixing of two salts, the cations mix on the cation sublattice and the anions mix on the anion sublattice. 

Figure 3 Model for F0rland s calculation of the mixing energy of molten salts [20].

Calculations taking into account the anion polarizability in AICI4 reduce the approximation associated with the simple additivity of pairwise potentiais in computational modeling (hard-sphere approximation) of molten salts. They predict new entities (e.g., AljClg) and in this respect have an advantage over earlier calculations. 

One of the models that can be used to approximately predict the properties of molten salts is called the hole model. The outstanding fact that led to this model is the large volume of fusion (10-20%) exhibited by simple salts on melting (Fig. 5.17). The basic idea of this rather artificial model is that within the liquid salt are tiny volume... 

Mathematical treatment of molten salts that supercool was first carried out by Cohen and Turnbull. The principal idea of the hole theory—that diffusion involves ions that wait for a void to turn up before jumping into it—is maintained. However, Cohen and Turnbull introduced into their model a property called thefree volume, Vf. What is meant by this free volume It is the amount of space in addition to that, Vq, filled by matter in a closely packed liquid. Cohen and Turnbull proposed that the free volume is linearly related to temperature... 

Why give these liquids special consideration Are not the concepts developed for understanding molten salts adequate for understanding molten oxides The essential features of fused salts ema-ge from models of the liquid state. Tha-e is no doubt that the fluidity of molten salts demands a model with plenty of free space, and a model based on density fluctuations that are constantly occurring in all parts of the liquid seems about the best way to think of the inside of a molten liquid. Is the same dependence on the opening up of temporary vacancies an adequate basis for explaining the behavior of the fused oxides ... 

In the Fiirth hole model for molten salts, the primary attraction is that it allows a rationalization of the empirical expression = 3.741 r p. In this model, fluctuations of the structure allow openings (holes) to occur and to exist for a short time. The mean hole size turns out to be about the size of ions in the molten salt. For the distribution function of the theory (the probability of having a hole of any size), calculate the probability of finding a hole two times the average (thereby allowing paired-vacancy diffusion), compared with that of finding the most probable hole size. 

The last chapter, which is on ionic liquids, describes the continuing evolution that is the result of the development of low-temperature molten salts and the contributions of computer modeling. The description of models of molten sihcates contains much of the original material in the first edition, for the models described there are those still used today. 

Many different mechanisms have been proposed in the literature for the agglomeration of bed particles. Viscous flow sintering of liquid silicates, reactive liquid sintering of molten salt systems, chemical reaction sintering by formation of new compounds, solid state sintering and vaporisation followed by re-condensation have been reported by several investigators Chemical equilibrium models have... 

In this study we restrict our consideration by a class of ionic liquids that can be properly described based on the classical multicomponent models of charged and neutral particles. The simplest nontrivial example is a binary mixture of positive and negative particles disposed in a medium with dielectric constant e that is widely used for the description of molten salts [4-6], More complicated cases can be related to ionic solutions being neutral multicomponent systems formed by a solute of positive and negative ions immersed in a neutral solvent. This kind of systems widely varies in complexity [7], ranging from electrolyte solutions where cations and anions have a comparable size and charge, to highly asymmetric macromolecular ionic liquids in which macroions (polymers, micelles, proteins, etc) and microscopic counterions coexist. Thus, the importance of this system in many theoretical and applied fields is out of any doubt. 

Structural studies in fused salts by means of careful and thorough high-temperature measurements of electrical conductivity, density, viscosity, and laser- Raman spectroscopy have been reviewed. Four problem areas are discussed (1) melting mechanisms of ionic compounds with large polyatomic cations, (2) salts as ultra-concentrated electrolyte solutions, (3) structural aspects and Raman spectroscopy, and (4) electrolysis of molten carbonates. The results in these areas are summarized and significant contributions to new experimental techniques for molten-salt studies are discussed.275 The physical properties and structure of molten salts have also been reviewed in terms of operational (hole, free volume, partly disordered crystal) and a priori (intermolecular potential) models.276 Electrochemistry... 

Contrary to the concept of the random mixing of ions, Fellner (1984), Fellner and Chrenkova (1987) proposed the molecular model for molten salt mixtures in which it is assumed that in an ideal molten mixture, molecules (ionic pairs) mix randomly. The model composition of the melt, i.e. the molar fractions of ionic pairs in the molten mixture, is calculated on the basis of simultaneous chemical equilibrium among the components of the mixture. For instance, in the melt of the system M1X-M2X-M2Y one can assume random mixing of the ionic pairs -X , mJ-X , mJ-Y , -X , and 2MJ-XY . 

In order to get some information on the possible structure of the given molten system from the conductivity measurement, a suitable reference state should be defined. Since conductivity is a scalar quantity, no ideal behavior is given by definition. However, there were several attempts in the literature to present a model of electrical conductivity of molten salts, which would describe satisfactorily the course of the conductivity dependence on composition. 

A new model for electrical conductivity of molten salt mixtures was introduced by Eellner (1984). This model should also define the ideal conductance of molten mixtures. 

Figure 8.1. Series (a) and parallel (b) model of the electrical conductivity of molten salt mixture.

Dissociation model of electrical conductivity of molten salt mixtures... 

The model of electrical conductivity of molten salt mixtures based on incomplete electrolytic dissociation of components was proposed by DanCk (1989). The dissociation degree of a component is affected by the presence of second component. Consequently, the dissociation degree of both components in the system is not constant, but changes with composition, affecting the concentration of the conducting particles in the electrolyte. This effect is caused by interactions of components, given by the nature of the repulsive forces between ions, determining their actual coordination sphere. 

A similar idea on the incomplete dissociation of molten salts was presented by Klemm and Schafer (1996). Their model was stimulated by a qualitative explanation of the Chemla effect made by Klemm (1984), which is the crossing over of the mobility isotherms at a certain temperature. This means that at high concentrations of a larger sized cation, its mobility is greater than that of the smaller one. This effect was first observed in the LiBr-KBr system by Mehta et al. (1969), was also observed later in many other monovalent systems, and named after one of its discoverers. 

The aim of the book is not only to present the state of the art studies on different properties of molten salt systems and their measurement, but also to present the possibilities of modeling molten salt systems, to be able to forecast the properties of an electrolyte mixture from the properties of the pure components in order to avoid experimentally demanding, and in most cases, also expensive measurements. Some direct methods of study on the structure (ionic composition) of molten electrolytes are also presented. 

Functions of hydration, 203 Furth model, in molten salt theory, 638 Fused oxides, and the structure of liquid water, 726... 

Shell models have been used successfully in a wide variety of systems. The greatest number of applications have been in the simulation of ionic materials,86-88 90 111 especially systems including alkali halides,83 oxides,85 89 91 92 112-115 and zeolites.93 94 The shell model is also commonly used for the simulation of molten salts,77 84 90 101 116-120 anj shell-type models have been developed for various molecular95-99 and polymeric species.100 121... 

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