The pair structure, free energy, and configurational overlap order parameter Q of an annealed sys... more The pair structure, free energy, and configurational overlap order parameter Q of an annealed system of two weakly coupled replicas of a supercooled "soft sphere" fluid are determined by solving the hypernetted-chain (HNC) and self-consistent Rogers-Young (RY) integral equations over a wide range of thermodynamic conditions ρ (number-density), T (temperature), and inter-replicas couplings ε12. Analysis of the resulting effective (or Landau) potential W(ρ,T; Q) and of its derivative with respect to Q confirms the existence of a "precursor transition" between weak and strong overlap phases below a critical temperature Tc well above the temperature To of the "ideal glass" transition observed in the limit ε12→0. The precursor transition is signalled by a loss of convexity of the potential W(Q) and by a concomitant discontinuity of the order parameter Q just below Tc, which crosses over to a mean-field-like van der Waals loop at lower temperatures. The HNC a...
Summary Electron-electron and electron-ion structural correlations in simple liquid metals are t... more Summary Electron-electron and electron-ion structural correlations in simple liquid metals are treated by using effective pair potentials to incorporate quantal effects into a pseudoclassical description of the electron fluid. An effective pair potential between simultaneous electron density fluctuations is first constructed from known properties of the degenerate jellium model, which are the plasmon sum rule, the Kimball-Niklasson relation and Yasuhara’s values
Accurate molecular dynamics (MD) calculations on highly asymmetric Lennard-Jones mixtures have be... more Accurate molecular dynamics (MD) calculations on highly asymmetric Lennard-Jones mixtures have been performed to check in rather extreme cases the ability of the self-consistent HMSA integral equation to predict the pair correlations in supercooled and glassy mixtures. We find that, in the supercooled region, the HMSA is a reasonable approximation for the structural properties and thermodynamic properties, but systematic deviations from MD data appear when the glass transition is approached.
ABSTRACT We investigate mixtures of hard spheres with positive non-additivity of the diameters (σ... more ABSTRACT We investigate mixtures of hard spheres with positive non-additivity of the diameters (σ12 > (σ11 + σ22)/2), which undergo phase separation at high density. Due to the simplicity of the interaction, they appear as prototype systems for studying phase separation in liquid mixtures. We performed Monte Carlo simulations with the so called Gibbs ensemble technique which allows a direct determination of the coexisting phases. We compare the coexistence curves obtained from simulation with the predictions of a very simple first order perturbative theory (MIX1). For asymmetries and non-additivities in a physically interesting range, our results confirm the fair reliability of MIX1. Thus we have used the perturbative theory to study trends in the phase behaviour of such binary systems as function of non-additivity and asymmetry.
Http Dx Doi Org 10 1080 00268976 2015 1038325, May 1, 2015
The accuracy of the Content should not be relied upon and should be independently verified with p... more The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.
The structural and thermodynamic behavior of a deeply supercooled Lennard-Jones liquid, and its r... more The structural and thermodynamic behavior of a deeply supercooled Lennard-Jones liquid, and its random first-order transition (RFOT) to an ideal glass is investigated, using a system of two weakly coupled replicas and the hypernetted chain integral equation for the pair structure of this symmetric binary system. A systematic search in the density-temperature plane points to the existence of two glass branches below a density-dependent threshold temperature. The branch of lower free energy exhibits a rapid growth of the structural overlap order parameter upon cooling and may be identified with the ideal glass phase conjectured by several authors for both spin and structural glasses. The RFOT, signaled by a sharp discontinuity of the order parameter, is predicted to be weakly first order from a thermodynamic viewpoint. The transition temperature T cr increases rapidly with density and approximately obeys a scaling relation valid for a reference system of particles interacting via a purely repulsive 1/r 18 potential.
We prove rigorously, in the general case of arbitrary potential and number of components, that if... more We prove rigorously, in the general case of arbitrary potential and number of components, that if a solution of the mean spherical approximation for simple fluids exists it is unique within the class of correlation functions corresponding to positive and bounded structure factors. The longstanding problem of the choice of the acceptable solutions of the system of nonlinear algebraic equations which arises with some methods used to derive analytical solutions is carefully examined with a particular emphasis on the factorization method for Yukawa mixtures. It is shown that a local criterion, related to the boundedness of the pair correlation functions, already suggested by Baxter but apparently ignored in the recent literature, is sufficient to select the unique (acceptable) solution of the model. A very simple and practical implementation of the method is given. The dependence of the asymptotic behaviour of the pair correlation functions on the parameters is briefly discussed.
Complex anion structures ((AlF4)-, (AlF5)2- and (AIF6)3-) coexist in liquid mixtures of alu-miniu... more Complex anion structures ((AlF4)-, (AlF5)2- and (AIF6)3-) coexist in liquid mixtures of alu-minium trifluoride and alkali fluorides in composition-dependent relative concentrations and are known to interact with the alkali counterions. We present a comparative study of the static and vibrational structures of MA1F4 molecules (with M = any alkali), with the aim of developing and testing a refined model of the ionic interactions for applications to the M-Al fluoride mixtures. We find that, whereas an edge-bridged coordination is strongly favoured for Li in LiAlF4 , edge-bridging and face-bridging of the alkali ion become energetically equivalent as one moves from Na to the heavier alkalis. This result is sensitive to the inclusion of alkali polarizability and may be interpreted as implying (for M = K, Rb or Cs) almost free relative rotations of the M+ and (AlF4)- partners at temperatures of relevance to experiment. The consistency of such a viewpoint with electron diffraction data on ...
Physica A: Statistical Mechanics and its Applications, 1984
The interfacial density profile of a classical one-component plasma confined by a hard wall is st... more The interfacial density profile of a classical one-component plasma confined by a hard wall is studied in planar and spherical geometries. The approach adapts to interfacial problems a modified hypernetted-chain approximation developed by Lado and by Rosenfeld and Ashcroft for the bulk structure of simple liquids. The specific new aim is to embody self-consistently into the theory a ``contact theorem'',
A factorization Ansatz for the three-particle direct correlation function c (3) is combined with ... more A factorization Ansatz for the three-particle direct correlation function c (3) is combined with the exact relation between c (3) and the pair function c (2) to derive a simple and tractable approximation for c (3) in dense, classical fluids. The predictions compare favorably with "exact" ...
The pair structure, free energy, and configurational overlap order parameter Q of an annealed sys... more The pair structure, free energy, and configurational overlap order parameter Q of an annealed system of two weakly coupled replicas of a supercooled "soft sphere" fluid are determined by solving the hypernetted-chain (HNC) and self-consistent Rogers-Young (RY) integral equations over a wide range of thermodynamic conditions ρ (number-density), T (temperature), and inter-replicas couplings ε12. Analysis of the resulting effective (or Landau) potential W(ρ,T; Q) and of its derivative with respect to Q confirms the existence of a "precursor transition" between weak and strong overlap phases below a critical temperature Tc well above the temperature To of the "ideal glass" transition observed in the limit ε12→0. The precursor transition is signalled by a loss of convexity of the potential W(Q) and by a concomitant discontinuity of the order parameter Q just below Tc, which crosses over to a mean-field-like van der Waals loop at lower temperatures. The HNC a...
Summary Electron-electron and electron-ion structural correlations in simple liquid metals are t... more Summary Electron-electron and electron-ion structural correlations in simple liquid metals are treated by using effective pair potentials to incorporate quantal effects into a pseudoclassical description of the electron fluid. An effective pair potential between simultaneous electron density fluctuations is first constructed from known properties of the degenerate jellium model, which are the plasmon sum rule, the Kimball-Niklasson relation and Yasuhara’s values
Accurate molecular dynamics (MD) calculations on highly asymmetric Lennard-Jones mixtures have be... more Accurate molecular dynamics (MD) calculations on highly asymmetric Lennard-Jones mixtures have been performed to check in rather extreme cases the ability of the self-consistent HMSA integral equation to predict the pair correlations in supercooled and glassy mixtures. We find that, in the supercooled region, the HMSA is a reasonable approximation for the structural properties and thermodynamic properties, but systematic deviations from MD data appear when the glass transition is approached.
ABSTRACT We investigate mixtures of hard spheres with positive non-additivity of the diameters (σ... more ABSTRACT We investigate mixtures of hard spheres with positive non-additivity of the diameters (σ12 > (σ11 + σ22)/2), which undergo phase separation at high density. Due to the simplicity of the interaction, they appear as prototype systems for studying phase separation in liquid mixtures. We performed Monte Carlo simulations with the so called Gibbs ensemble technique which allows a direct determination of the coexisting phases. We compare the coexistence curves obtained from simulation with the predictions of a very simple first order perturbative theory (MIX1). For asymmetries and non-additivities in a physically interesting range, our results confirm the fair reliability of MIX1. Thus we have used the perturbative theory to study trends in the phase behaviour of such binary systems as function of non-additivity and asymmetry.
Http Dx Doi Org 10 1080 00268976 2015 1038325, May 1, 2015
The accuracy of the Content should not be relied upon and should be independently verified with p... more The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.
The structural and thermodynamic behavior of a deeply supercooled Lennard-Jones liquid, and its r... more The structural and thermodynamic behavior of a deeply supercooled Lennard-Jones liquid, and its random first-order transition (RFOT) to an ideal glass is investigated, using a system of two weakly coupled replicas and the hypernetted chain integral equation for the pair structure of this symmetric binary system. A systematic search in the density-temperature plane points to the existence of two glass branches below a density-dependent threshold temperature. The branch of lower free energy exhibits a rapid growth of the structural overlap order parameter upon cooling and may be identified with the ideal glass phase conjectured by several authors for both spin and structural glasses. The RFOT, signaled by a sharp discontinuity of the order parameter, is predicted to be weakly first order from a thermodynamic viewpoint. The transition temperature T cr increases rapidly with density and approximately obeys a scaling relation valid for a reference system of particles interacting via a purely repulsive 1/r 18 potential.
We prove rigorously, in the general case of arbitrary potential and number of components, that if... more We prove rigorously, in the general case of arbitrary potential and number of components, that if a solution of the mean spherical approximation for simple fluids exists it is unique within the class of correlation functions corresponding to positive and bounded structure factors. The longstanding problem of the choice of the acceptable solutions of the system of nonlinear algebraic equations which arises with some methods used to derive analytical solutions is carefully examined with a particular emphasis on the factorization method for Yukawa mixtures. It is shown that a local criterion, related to the boundedness of the pair correlation functions, already suggested by Baxter but apparently ignored in the recent literature, is sufficient to select the unique (acceptable) solution of the model. A very simple and practical implementation of the method is given. The dependence of the asymptotic behaviour of the pair correlation functions on the parameters is briefly discussed.
Complex anion structures ((AlF4)-, (AlF5)2- and (AIF6)3-) coexist in liquid mixtures of alu-miniu... more Complex anion structures ((AlF4)-, (AlF5)2- and (AIF6)3-) coexist in liquid mixtures of alu-minium trifluoride and alkali fluorides in composition-dependent relative concentrations and are known to interact with the alkali counterions. We present a comparative study of the static and vibrational structures of MA1F4 molecules (with M = any alkali), with the aim of developing and testing a refined model of the ionic interactions for applications to the M-Al fluoride mixtures. We find that, whereas an edge-bridged coordination is strongly favoured for Li in LiAlF4 , edge-bridging and face-bridging of the alkali ion become energetically equivalent as one moves from Na to the heavier alkalis. This result is sensitive to the inclusion of alkali polarizability and may be interpreted as implying (for M = K, Rb or Cs) almost free relative rotations of the M+ and (AlF4)- partners at temperatures of relevance to experiment. The consistency of such a viewpoint with electron diffraction data on ...
Physica A: Statistical Mechanics and its Applications, 1984
The interfacial density profile of a classical one-component plasma confined by a hard wall is st... more The interfacial density profile of a classical one-component plasma confined by a hard wall is studied in planar and spherical geometries. The approach adapts to interfacial problems a modified hypernetted-chain approximation developed by Lado and by Rosenfeld and Ashcroft for the bulk structure of simple liquids. The specific new aim is to embody self-consistently into the theory a ``contact theorem'',
A factorization Ansatz for the three-particle direct correlation function c (3) is combined with ... more A factorization Ansatz for the three-particle direct correlation function c (3) is combined with the exact relation between c (3) and the pair function c (2) to derive a simple and tractable approximation for c (3) in dense, classical fluids. The predictions compare favorably with "exact" ...
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