Conformal Solution Theory Research Articles

Transport properties of binary Lennard-Jones mixtures: Insights from entropy scaling and conformal solution theory

The relation of transport properties and the molecular interactions in binary mixtures was studied. The self-diffusion coefficient, Maxwell–Stefan as well as Fickian mutual diffusion coefficient, shear viscosity, and thermal conductivity of liquid binary simple mixtures were therefore sampled using molecular dynamics simulations. The mixtures were described by the Lennard-Jones potential. The molecular interaction parameters were chosen such that a large variety of mixture behavior was covered. The two components had the same size parameter in all cases, but different dispersion energies. Moreover, the cross-interaction parameter used in the modified Lorentz-Berthelot combination rule was varied such that the resulting mixtures showed different types of phase behavior: ideal, high- and low-boiling azeotrope. The results are discussed using conformal solution theory as a link between the molecular interactions in the mixtures and the macroscopic properties. Moreover, the applicability of Rosenfeld’s entropy scaling is tested. Despite the important differences of the studied mixtures regarding their molecular interactions and the large pressure, temperature, and composition range considered, a practically monovariate relation of these properties with respect to the configurational entropy is observed. Yet, the quality of the approximation differs for the studied properties.

Molecular interactions at vapor-liquid interfaces: Binary mixtures of simple fluids.

Properties of vapor-liquid equilibria and planar interfaces of binary Lennard-Jones truncated and shifted mixtures were investigated with molecular dynamics simulations, density gradient theory, and conformal solution theory at constant liquid phase composition and temperature. The results elucidate the influence of the liquid phase interactions on the interfacial properties (surface tension, surface excess, interfacial thickness, and enrichment). The studied mixtures differ in the ratios of the dispersion energies of the two components ɛ_{2}/ɛ_{1} and the binary interaction parameter ξ. By varying ξ and ɛ_{2}/ɛ_{1}, a variety of types of phase behavior is covered by this paper. The dependence of the interfacial properties on the variables ξ and ɛ_{2}/ɛ_{1} reveals regularities that can be explained by conformal solution theory of the liquid phase. It is thereby shown that the interfacial properties of the mixtures are dominated by the mean liquid phase interactions whereas the vapor phase has only a minor influence.

Liquid–Vapor Equilibria in the SiCl4–A (A = SiCl4–nFn (n = 1–4) Impurity) Systems

The vapor–liquid separation factors of SiCl4–A (A = SiCl4–nFn (n = 1–4) silicon fluorochloride impurities in silicon tetrachloride have been determined experimentally at 298 K by statically balancing phases. The values obtained for the SiCl4–SiCl3F, SiCl4–SiCl2F2, SiCl4–SiClF3, and SiCl4–SiF4 systems are 4.9 ± 0.8, 8.2 ± 1.2, 29.8 ± 6.1, and 42.0 ± 7.5, respectively. In the SiCl4–SiCl3F system, the vapor–liquid separation factor has also been determined by the Rayleigh distillation method: α = 5.0. The experimental data agree with the vapor–liquid separation factors estimated in conformal solution theory using parameters of the Lennard- Jones potential.

Thermodynamic Investigation of the Eutectic Mixture of the $$\hbox {LiNO}_{3}$$ LiNO 3 – $$\hbox {NaNO}_{3}$$ NaNO 3 – $$\hbox {KNO}_{3}$$ KNO 3 – $$\hbox {Ca}(\hbox {NO}_{3})_{2}$$ Ca ( NO 3 ) 2 System

Molten nitrate salt is usually employed as heat transfer or energy storage medium in concentrating solar power systems to improve the overall efficiency of thermoelectric conversion. In the present work, the liquidus curves of the $$\hbox {LiNO}_{3}$$ – $$\hbox {NaNO}_{3}$$ – $$\hbox {KNO}_{3}$$ – $$\hbox {Ca}(\hbox {NO}_{3})_{2}$$ system is determined by conformal ionic solution theory according to the solid–liquid equilibrium state of the binary mixture. The calculated eutectic temperature of the mixture is $$93.17\,{^{\circ }}\hbox {C}$$ , which is close to the experimental value of $$93.22\,{^{\circ }}\hbox {C}$$ obtained from differential scanning calorimetry (DSC). Visualization observation experiments reveal that the quaternary eutectic mixture begins to partially melt when the temperature reaches $$50\,{^{\circ }}\hbox {C}$$ , and the degree of melting increases with temperature. The mixture is completely melted at $$\hbox {130}\,{^{\circ }}\hbox {C}$$ . The observed changes in the dissolved state at different temperatures correlate well with the DSC heat flow curve fluctuations.

The use of Ościk’s equation to describe the retention in reversed phase liquid chromatography

The Ościk’s equation based on the theory of conformal solutions was used to describe the chromatographic process in RP-HPLC. Theoretically calculated values of the logarithms of retention factors (logk) were compared with experimental values for a group of aromatic substances, i.e. alkylbenzenes, PAHs, and polar benzene derivatives. Studies were conducted using two columns: RP-18 and RP-4, as well as water-methanol and water-acetonitrile mixtures as mobile phases.The applicability of Everett’s equation to describe the composition of surface phase was also verified. For this purpose, the excess methanol adsorption isotherm on LiChrospher RP-18e, was experimentally determined.

Enthalpies of Mixing in the LaI3–MI (M = Li, Na, K, Rb, Cs) Binary Systems

The molar enthalpy of mixing (ΔmixHm) in the LaI3–MI (M = Na, K, Cs) liquid systems was measured over the whole composition range at 1060 K with a Calvet-type high temperature microcalorimeter. The mixing of two liquid components was achieved by using the “break-off ampoule technique”. The dependence of the interaction parameter on composition λ = A + Bx + Cx2 + Dx3 (x = mole fraction of LaI3) was determined. Unknown molar enthalpy of mixing (ΔmixHm) in the LaI3–LiI and LaI3–RbI liquid systems was calculated using the conformal solution theory of Davis. In all systems under investigation the enthalpies of mixing are negative except the LaI3–LiI system at LaI3-rich compositions. The minimum of enthalpy is shifted toward the alkali metal iodide-rich part and is located at the composition of x(LaI3) ≈ 0.35–0.40. Measured and calculated molar enthalpies of mixing were compared with the molar enthalpies of mixing in the LaCl3–MCl and LaBr3–MBr (M = Li, Na, K, Rb, Cs) liquid systems.

The theory of non-electrolyte solutions: an historical review

Starting with the work of van der Waals in 1873, a historical review is given of theories of non-electrolyte mixtures that are based on a well-defined Hamiltonian, and thus can be tested against molecular simulation, as well as experiment. Most of the first 100 years covered here were devoted to attempts to find a successful theory of simple mixtures, culminating in the van der Waals 1-fluid theory of conformal solutions, and perturbation theories based on a hard-sphere reference fluid. The last 40 years has seen the more rapid development of theories for fluids of more complex molecules, including strongly polar liquids, chain molecules and liquids in which molecular association is important. 1 Based on a Molecular Physics Lecture, ‘The Theory of Non-Electrolyte Solutions: A Recent History’, delivered at Imperial College London, 25 September 2009.

Thermodynamic performance of the NaNO3–NaCl–NaNO2 ternary system

Calculations of phase diagram for additive ternary molten salt system are carried out by the conformal ionic solution theory. The liquidus temperatures of the system NaNO3–NaCl–NaNO2 are determined according to different types of solid–liquid equilibrium and different values of the binary interaction coefficients. For the system NaNO3–NaCl–NaNO2, the calculated and experimental temperatures differ are very small below 673 K, but the oxidation and decomposition of the mixed salts are found when the temperature is higher than 673 K. Meanwhile, the eutectic point is obtained from calculated phase diagram and the eutectic temperature is 507 K. Thermal stability of this eutectic mixture is investigated by thermo-gravimetric analysis device. Experimental results show this kind of molten salt has a lower melting point (501.28 K), similar to solar salt (493 K). It is thermally stable at temperatures up to 819 K, and may be used up to 827 K for short periods.

Design of new molten salt thermal energy storage material for solar thermal power plant

In order to obtain molten salt with lower melting point, higher thermal stability and reduced cost relative to previously available materials, a variety of molten salt mixtures of alkali nitrates are investigated by experimental methods. However, since measurements are generally expensive and time-consuming, it is of interest to be able to predict melting point and the component of multi-component systems by using the numerical methods. In this paper, eutectic point and component of a new kind of the quaternary reciprocal system (K, Na/NO2, Cl, NO3) are determined firstly by conformal ionic solution theory. Then thermal stability of the mixtures that show a lower melting point is measured by thermogravimetric analysis device. Experimental results show the agreement between measurements and calculations is found to be very good. This kind of molten salt has a lower melting point, 140°C. It is thermally stable at temperatures up to 500°C, and may be used up to 550°C for short periods. Besides, this molten salt has a reduced cost relative to previous low-melting nitrate mixtures due to the elimination of cesium nitrate and lithium nitrate.

A conformal solution theory for the energy landscape and glass transition of mixtures

We apply conformal solution theory and extend to mixtures a recently derived equation of state for glass-forming liquids. The equation of state is based on the statistical properties of the multidimensional potential energy surface as a function of a macroscopic system’s degrees of freedom (energy landscape), and allows the calculation of an ideal glass transition locus, along which the configurational entropy vanishes. The landscape mixing approach yields an expression for the composition dependence of the mixture’s glass transition. A non-monotonic composition dependence is predicted by the theory for the glass transition of a binary Lennard–Jones mixture. The composition dependence of species diffusivities obtained by molecular dynamics simulation of this mixture is consistent with the theoretical prediction.

New Dieterici-type equations of state for fluid phase equilibria

The vapour–liquid critical properties of binary mixtures are calculated using conformal solution theory, the one-fluid model, the van der Waals and Carnahan–Starling–van der Waals equations, and a new Dieterici-type equation of state reported recently [J. Chem. Phys. 115 (2001) 371]. Comparisons with experimental data are reported for the critical properties of n-alkane mixtures ranging from methane to n-octane. A common feature of these comparisons is that the new Dieterici-type equation of state yields good prediction of the pressure–temperature critical locus without the need to use arbitrary adjustable parameters in the combining rules for mixture properties. In particular, the Dieterici-type equation correctly predicts the maximum in the pressure–temperature curve. In contrast, the van der Waals-type equations are inaccurate. Dieterici-type equations of state may have a useful rule in the prediction of fluid phase equilibria by reducing the need for adjustable parameters in the combining rules.

Global phase diagram for anisotropic binary fluid mixtures: reverse type IV behaviour

Calculations of the critical properties of anisotropic binary mixtures are reported using the hard convex body-van der Waals equation of state in conjunction with conformal solution theory and the one-fluid model. The calculations are used to determine the global phase diagram for anisotropic binary mixtures of molecules of identical size. In the absence of other influences, mixtures with a moderate degree of anisotropy between the component molecules are only observed to exhibit type I, II or III behaviour. For highly anisotropic mixtures, a new type of behaviour is observed which we describe as ‘reverse type IV’.

Excess properties of Lennard-Jones binary mixtures from computer simulation and theory

Monte Carlo simulation and theory are used to calculate the excess thermodynamic properties of binary mixtures of spherical Lennard-Jones molecules. We study the excess functions of three binary mixtures characterized by the following size and dispersive energy ratios: (1) (σ22/σ11)3 = 2 and ε22/ε11 = 2; (2) (σ22/σ11)3 = 1 and ε22/ε11 = 1/2 and (3) (σ22/σ11)3 = 1/2 and ε22/ε11 = 2. In all cases, the unlike size parameter, σ12, is kept constant and equal to the value given by the Lorentz combining rule (σ12 = (σ11 + σ22)/2). However, different unlike dispersive energy parameter values are considered through the following combining rules: (a) ε12 = (ε11ε22)1/2 (Berthelot rule); (b) ε12 = ε11 (association); and (c) ε12 = ε22 (solvation). The pressure and temperature dependence of the excess volume and excess enthalpy is studied using the NpT Monte Carlo simulation technique for all the systems considered. Additionally, the simplest conformal solution theory is used to check the adequacy of this approach in predicting the excess properties in a wide range of thermodynamic conditions and variety of binary mixtures. In particular, we have applied the van der Waals one-fluid theory to describe Lennard-Jones binary mixtures through the use of the Johnson et al. [1993, Molec. Phys., 78, 591] Helmholtz free energy. Agreement between simulation results and theoretical predictions is excellent in all cases and thermodynamic conditions considered. This work confirms the applicability of the van der Waals one-fluid theory in predicting excess thermodynamic properties of mixtures of spherical molecules. Furthermore, since binary mixtures of spherical Lennard-Jones molecules constitute the reference fluid to be used in perturbation theories for complex fluids, such as the statistical association fluid theory (SAFT), this work shows clearly the applicability of the conformal solution theory within the framework of SAFT for predicting excess functions.

Predicting miscibility gaps in reciprocal liquids

There is a strong correlation between the appearance of liquid miscibility gaps in reciprocal phases and the standard Gibbs energy of the reciprocal reaction, Δ°G. The associate solution model does not predict such a correlation but the two-sublattice model does. Physically, the critical temperature of a reciprocal miscibility gap is related to Δ°G and is also affected by the presence of short range order. The latter effect can be estimated from Δ°G using the conformal solution theory which was developed for reciprocal systems with univalent ions. In that approximation the short range order effect is described with a reciprocal parameter. The estimate of that parameter for systems with different valencies is now discussed. The calculated phase diagram may be reasonable for low values of the reciprocal parameter, relative to Δ°G, but is not satisfactory for large values because two asymmetric miscibility gaps will appear when the critical temperature has been suppressed to 3 4 of the value predicted without a reciprocal term. An alternative form of the reciprocal term is now proposed, which does not produce the splitting into two miscibility gaps.

Contributions to molten salt chemistry by Ole J. Keppa

Ole Kleppa and coworkers have accurately measured the enthalpies of mixing of a large number of binary molten salt systems. These results have also been proven to be useful in the analyses of phase diagrams and in creating a reliable database on free energies of mixing of a large number of systems. He made a general confirmation of a specific result by Hildebrand and Salstrom that excess free energies of mixing of simple binary molten salts could be represented by a simple polynomial, an important result for ionic systems with very long range ionic pair interactions. His measurements of the enthalpies of mixing of all binary alkali nitrates led to an expression which was close to that deduced from a simple model by Førland. This result also catalyzed the Conformal Ionic Solution Theory, the only theory fundamentally valid for molten salts. This theory later led to methods for accurately predicting the solution properties of multicomponent molten salt systems from data on the subsidiary binaries and the pure component salts. His measurements of binary systems with the two components having the same cation and two different anions indicated that deviations from ideality were generally very small. A theoretical extension of this conclusion to silicates and other polymeric slags led to reliable predictions of the solubilities (and sulfide capacities) of ionic compounds. Kleppa’s work has had a major influence on molten salt chemistry

A New Theoretical Approach to the Hydrogen-Bonded Fluids Based on the Conformal Solution Concept

In this work, a new generalized chemical theory of association is developed and is used to derive the distribution function of associated species formed due to hydrogen bonding in a pure associating fluid. The concepts of conformal solution theory are extended to consider the pure associating fluids, and the derived distribution function is used to obtain the conformal parameters. A general procedure is proposed for computing the parameters of any cubic equation of state based on the conformal solution theory developed in this work. As an example, the parameters of van der Waals equation of state are obtained. The PVT calculations for three associating fluids (water, ammonia, and methanol) substantiate the effectiveness of the proposed approach.

Critical Properties for Binary Mixtures of Ethane Containing Low Concentrations of n-Alkane

The critical temperature and pressure for binary mixtures of ethane containing n-alkanes (C5 to C10) at low concentrations (up to 5.2 mol %) have been determined. A visual technique was used where the observation of mixture critical opalescence followed by the appearance of a vapor−liquid meniscus in a constant volume sight gauge was observed. The absolute errors in the measurements of the mixture critical temperature and pressure were ±2 K and ±0.5 bar, respectively, with an estimated relative error of ±1.5% for the composition of the organic compounds used. The binary mixture critical temperature and pressure were estimated using a correlation based on the theory of conformal solutions and a dilute-mixture Soave−Redlich−Kwong (SRK) equation of state approach. Both methods correlated the critical mixture temperature to an absolute error of within 3 K. However, the mixture critical pressure was correlated to an absolute error of within 10 and 4 bar using the conformal solutions correlation and a dilute-mi...

Hard sphere expansion conformal solution theory with the Lennard–Jones (12-6) intermolecular potential

Modification of the hard sphere expansion conformal solution theory is presented concerning polarity of molecules, the Lennard–Jones (12-6) parameters, and mixing rules for unlike parameters. The theory was used for prediction of vapour–liquid equilibrium at constant temperature in binary, ternary and quaternary mixtures consisting of chlorobutanes and C 7 hydrocarbons. Excess molar volumes for binary systems are calculated, too.

Phase behaviour of ternary mixtures: a theoretical investigation of the critical properties of mixtures with equal size components

Conformal solution theory in conjunction with the one-fluid model and the Guggenheim equation of state are used to calculate the critical properties of binary and ternary mixtures characterised by molecules of identical size (identical h conformal parameters) but different energy parameters (different f conformal parameters). When the geometric mean combining rule is used to obtain contributions from unlike interactions, binary mixtures of equal size components generate Type I, II and III phase behaviour. The critical properties of ternary mixtures composed of binary subsystems of different phase behaviour types are examined. Results are presented at different temperatures and pressures covering both vapour–liquid and liquid–liquid equilibria. The results illustrate the diversity of phenomena exhibited by ternary mixtures and the relationship of the behaviour exhibited to the relative strength of dissimilar interactions between different pairs of molecules. A progressive transition between vapour–liquid and liquid–liquid equilibria and higher order critical phenomena are likely to be common features of the phase behaviour of ternary mixtures.

Surface‐tension prediction for liquid mixtures

AbstractEscobedo and Mansoori (1996) recently proposed a new expression, originally derived from statistical mechanics, for the surface‐tension prediction of pure fluids. The theory presented here is extended to matures of organic liquids based on the conformal solution theory of mixtures. Using the proposed equation, surface tensions of 55 binary mixtures are predicted within an overall 0.50 AAD%, which is better than other available prediction methods. The 55 binary mixtures are predicted within an overall 2.10 AAD% with a corresponding‐states version of the theory. The expressions proposed in this work are general since they have been applied to a variety of binary mixtures, and the results obtained agree well with the experimental data. The proposed model is directly applicable to multicomponent liquid mixtures.