Conformal Solution Theory Research Articles

Application of molecular dynamics computations to the conformal ionic solution theory: Thermodynamics of binary molten salt mixtures

An evaluation of the coefficient a (T,V) as defined in the equation for the excess Helmholtz free energy of mixing of binary solutions, ΔAmE=a (T,V)(λi−λj)2XiXj +..., derived from the conformal ionic solution theory is presented. This coefficient is shown to be negative and proportional to a fluctuation energy. The sign agrees with experimental calorimetric data of binary molten salt mixtures. A molecular dynamics computation of a (T,V) was made to compare theory and experiments. The calculated values are strongly dependent on the form of the repulsive contribution to the pair potentials (Tosi and Fumi model and Michielsen, Woerlee, Graaf, and Ketelaar model). Criteria for testing the repulsive part of proposed pair potentials are suggested as a result of this investigation.

Conformal solution theory for viscosity and thermal conductivity of mixtures

The first-order terms are derived in a conformal solution theory expansion for the viscosity and thermal conductivity of a fluid mixture. Provided that pairwise additivity of the intermolecular potentials is assumed, these terms can be made to vanish exactly by a suitable choice of the potential parameters and molecular mass for the reference system. A generalization of Enskog's dense gas theory to molecules with a general intermolecular potential law is used to suggest suitable combinations of potential parameters and reduced masses as expansion variables. Several sets of mixing rules are thus suggested. These are first tested for dilute gases by comparison with the Chapman-Enskog results, and the best mixing rules for gases are determined. This is followed by a comparison with experimental data for simple liquid mixtures. The general behaviour of the excess viscosity and thermal conductivity for binary mixtures as a function of the potential and mass parameters is investigated using the theory. It is shown that whereas the excess viscosity is nearly always negative or zero, the excess thermal conductivity may be positive or negative.

Entropy predictions in molten binary alkali halide mixtures

Excess entropies for all the common anion molten binary alkali halide mixtures have been predicted, for the first time, using an extension of the conformal solution theory. The calculated entropies are in good agreement with available experimental results.

Liquid NaK alloy: Triplet correlation function in the long-wavelength limit

Triplet correlation functions for liquid NaK alloy, in the long-wavelength limit, have been calculated with the partial structure factors derived by taking the square-well potential as a perturbation over the hard-sphere potential. The present structure factors generate the experimental compressibilities from the Kirkwood—Buff general formula while the compressibilities derived from the conformal solution theory structure factors are higher than the experimental ones.

Conformal ionic solution theory for additive ternary molten–ionic systems

Excess free energies of mixing (ΔAEm) for additive ternary molten ionic systems (AX–BX–CX or AX–AY–AZ) have been calculated from conformal ionic solution (CIS) theory. The CIS theory applies rigorously to ionic systems containing cations (or anions) of different size, whereas quasichemical theory, which is based on a lattice model, cannot be rigorously applied to such systems. Nevertheless, most of the terms calculated from CIS theory have counterparts in quasichemical theory except for asymmetric terms proportional to products of mole fractions of components i and j of the form X2iXj. Such asymmetric terms are known to be significant in molten salt systems. In the expression for ΔAEm calculated to third order [Eq. (20)], all of the coefficients can be evaluated from data on the subsidiary binaries. In the expression for ΔAEm calculated to fourth order [Eq. (33)], one can show that the only term which cannot be evaluated from data on the binaries is probably negligible. Thus the theory permits the calculation of properties of ternaries solely from a knowledge of properties of binaries.

Size effects, peaks in concentration fluctuations and liquidus curves of Na-Cs

Conformal solution theory applies to some binary alloys, for which the volume differences are not too large. The volume ratio r for Cs/Na=3, and the system is not conformal. A theory of the concentration fluctuations, valid for large r, is described. The liquidus curves are calculated, there is a rather flat portion around an Na concentration of 0.8, correlating with a strong peak in the concentration fluctuations around this composition. This is in agreement with observation. Na-Rb alloys and a number of other alloy systems show a similar feature, and these are briefly discussed.

ChemInform Abstract: TOPOLOGY OF LIQUIDUS PHASE DIAGRAMS OF CHARGE‐ASYMMETRIC RECIPROCAL MOLTEN SALT SYSTEMS

AbstractEs werden Gleichungen für die a priori‐Berechnung der thermodynamischen Eigenschaften von ternären reziproken Systemen geschmolzener Salze mit Ladungsasymmetrie entwickelt.

Densities and Excess Volumes of Fused Halides

Abstract Densities of molten AgBr-AX (A = Li, Na, K, Rb, Cs; X = Br or Cl), AgBr-AgCl, KBr-NaBr, KBr-CsBr, KCl-KBr, and KCl-CsBr mixtures have been measured at 0.5 mole fraction using the method of Archimedean displacement. The excess volumes of mixing are all positive, except for the AgBr-LiBr system. Attempts to relate the excess volumes of the binary AgBr-ABr systems to the second order conformal solution theory of Reiss, Katz, and Kleppa are unsuccessful, since V E is large even when the diameter difference parameter, δ12, is close to zero. However, the excess volumes of the reciprocal AgBr-ACl systems at 0.5 mole fraction are found, within experimental error, to have a linear dependence on δ12. The positive deviations from conformal solution theory which occur for the alkali halide mixtures have been interpreted in terms of non-Coulombic polarisation and van der Waals interactions.

Topology of Liquidus Phase Diagrams of Charge‐Asymmetric Reciprocal Molten Salt Systems

An empirical extension of conformal ionic solution theory is presented which describes the solution behavior of a class of reciprocal molten salt systems, the A+qA, B+qB∥C‐qC, D‐qD charge‐asymmetric systems. The thermodynamic properties of such ternary systems can be calculated from data on the standard free energy change for the metathetical reaction between the 4 pure constituents and solution data on the 4 binary subsystems. Calculated liquidus phase diagrams for the systems Na,Sr∥Cl,NO3; Na,Ba∥Cl,NO3; Li,K∥Cl,CrO4; Li,K∥Br,CrO4; and Na,Ca∥F,Cl agree well with measurements within experimental uncertainties. These systems are illustrative of a wide range of values of the thermodynamic quantities used in the calculations. The equations developed should prove useful as a test of the self‐consistency of reported phase diagrams, as a means of calculating Liquidus temperatures in experimentally inaccessible regions, and as an aid in constructing phase diagrams from a minimum number of measurements.

Corresponding-states correlation of properties of ionic melts

Aspects of the corresponding-states correlation of certain properties of ionic liquids and liquid mixtures are examined. The results of Monte-Carlo computations are used to show that an interionic potential to which corresponding-states theory can be rigorously applied is insufficiently flexible to account for details of the thermodynamic properties of molten alkali-metal salts. The specific model studied is one frequently referred to in discussions of the application of dimensional methods in the statistical mechanics of ionic salts. Use of the same idealized potential model in the case of mixtures leads to values of the excess thermodynamic properties which are consistent with the predictions of conformal solution theory but differ qualitatively from those observed experimentally. The possibility of using results obtained by computer simulation to extend the range of validity of existing corresponding-states relations is discussed and the example of ionic diffusivity is treated as an illustration.

Additive Ternary Molten Salt Systems—Calculation of Phase Diagrams from Thermodynamic Data of Lower Order Systems

Calculations of the liquidus temperatures of additive ternary molten salt systems are carried out from the conformal ionic solution theory (up to second order terms). The comparison between measured and calculated phase diagrams is made for five systems chosen according to different types of liquidus and different values of the binary interaction coefficients. For most cases, and in particular when solid solutions are not reported, the agreement between measurements and calculations is found to be very good. In the search for low melting electrolytes for electrochemical applications, these equations should prove useful in predicting the range of compositions where low liquidus temperatures are most likely.

Concentration dependence of electrical transport coefficients in conformal liquid metal alloys

Using partial structure factors aij obtained from conformal solution theory, the concentration dependence of the electrical resistivity rho and the thermoelectric parameter xi of liquid metal alloys is exhibited explicitly. The equivalent binary system Mg-Cd may be an example for which conformal solution theory can remove the discrepancy between the substitutional model of Faber and Ziman and experiment. However, nonlocal effects in the pseudopotential may also be important in this system.

The radial distribution function in fluid mixtures: Conformal solution theory and molecular dynamics results

The conformal solution approach is used to relate the distribution functions g αβ(r) for a fluid mixture to those of a pure fluid, g x(r). The procedure is to expand g αβ(r) about the corresponding function for an ideal solution, using σ αβ 3 and eαβσαβ 3 as expansion parameters; the expansion of the function y αβ(r) is also considered. Molecular dynamics results are reported for the tg αβ for argon-krypton liquid mixtures using the Lennard-Jones (12, 6) potential. These results are used to test the conformal solution expansions to first order; the g αβ expansion is found to be superior to that for y αβ for most r values of interest. The second order term in the conformal solution expansion for the Helmholtz free energy is also calculated for argon-krypton mixtures, and found to be about 10 per cent of the value of A E given by the van der Waals 1 theory.

Analytic equations of state of simple liquids and liquid mixtures

Based on the variational and perturbation theories of liquid state, at equilibrium conditions, an approximation technique is introduced through which it has been made possible the derivation of analytic relations for the thermodynamic properties of simple liquids in which the intermolecular potential can be represented by the Lennard-Jones (m-n) potential function. By the application of the hard-sphere expansion (HSE) conformal solution theory it has been possible to generalize the resulting relation of pure systems for the mixtures of simple liquids, and, consequently, analytic relations for the total and the excess thermodynamic properties of liquid mixtures are derived. For a numerical case study, the equations of state derived are applied to the systems for which the Lennard-Jones (6–12) potential function is assumed to be valid and the results are compared with the experimental values and the results of the other theories of liquids and liquid mixtures.

MOLECULAR PRINCIPLE OF CORRESPONDING STATES FOR VISCOSITY AND THERMAL CONDUCTIVITY OF FLUID MIXTURES

Abstract Conformal solution theory is developed for the viscosity and thermal conductivity of fluid mixtures. The procedure involves expanding the transport coefficient for the mixture about the value for an ideal solution, using groupings of the potential parameters and molecular mass as expansion coefficients. The parameters for the ideal solution are chosen so as to annul the first-order term in this expansion, thus encouraging rapid convergence. This yields mixing rules (similar to those of the van der Waals 1 theory for thermodynamic properties) for the potential parameters and molecular mass of the reference fluid. Reference fluid properties are obtained from pure fluid corresponding states correlations By making calculations for dilute gas mixtures and comparing with Chapman-Enskog theory, it is found that the first-order theory works well for mixtures of quite widely different energy parameters (e) and molecular masses; it is more sensitive to the size difference of the molecular components, howev...

Liquidus curves for eutectic systems

The liquidus curves of the Na-K system are calculated from conformal solution theory, the input consisting of thermodynamic data for pure Na and K, plus an interchange energy characteristic of the solution.

Correlation of a Partially Miscible Ternary System with Conformal Solution Theory

Correlation of a Partially Miscible Ternary System with Conformal Solution Theory

Conformal solution theory: generalized theory for pure fluids

Conformal solution theory is reformulated as an expansion in arbitrary functions of the usual molecular parameters. For pure fluids all coefficients are thermodynamic and the functions can be chosen to annual the second-order term. The rules derived are very simple and are shown to be accurate; they cast light on the success of mixture rules such as the van der Waals theory, and the different behaviour of expansions at constant volume and constant pressure.

The critical constants of binary mixtures of certain perfluoro-compounds with alkanes

The critical temperature T c and critical pressure p c were measured at five compositions for each of five binary mixtures formed by propane with perfluoropropane, perfluoro- n-hexane, hexafluoroacetone, hexafluorobenzene, and trifluoroacetonitrile, and the two binary mixtures of n-hexane with perfluoro- n-hexane and hexafluorobenzene, and of perfluorocyclobutane with pentene-1. The composition dependences of T c and p c calculated by means of the modified theory of conformal solutions are in satisfactory agreement with the experimental results. In particular, the unusual S-shaped curve of p c against mole fraction for C 3H 8 + CF 3CN, predicted by the theory, is confirmed by the experimental results. The peculiar properties of mixtures of fluoro-compounds with inert solvents and the deviations from the harmonic mean rule for ε 11 are discussed. Additionally, the densities of liquid (CF 3) 2CO and the densities and vapor pressures of CF 3CN were determined at reduced temperatures from about 0.6 to 1.

Statistical thermodynamics of mixtures. A new version for the theory of conformal solution

A new method for the calculation of thermodynamic properties of simple fluid mixtures constitutes an extension of the approach defined earlier as the “van der Waals” conformal solution theory. This extension is made possible by advances in the analytical representation of the thermodynamic properties of a mixture of hard spheres which permit the properties to be calculated directly, without the use of a reference fluid. A new hard-sphere excess function, defined as a property of the mixture less the value of this property for the hard-sphere mixture, is obtained by a new conformal solution theory using a single pure fluid as a reference substance. Although the reference substance properties could be experimentally measured values, this work obtains them from an analytical form of the Barker-Henderson perturbation theory.This new method improves prediction of the effects of large molecular size differences on the excess properties of the mixture. It uses the reference fluid to account for most of the temperature dependence of the cut-off parameter needed to define the molecular diameters in the direct hard-sphere mixture calculations and the calculations need only the high temperature limit of the cut-off parameters, even far below the critical temperature. The new method extends the original vdW conformal solution method to lower temperatures and provides an opening for inclusion of three-body interactions.Conventional excess mixing functions for several binary liquid mixtures calculated by the new method are compared with the predictions of other theories and with both experimental and Monte Carlo data.