Effective Liquid Approximation Research Articles

Wetting controlled phase transitions in two-dimensional systems of colloids

The phase behavior of disk colloids, embedded in a two-dimensional fluid matrix that undergoes a first-order phase transition, is studied in the complete wetting regime where the thermodynamically metastable fluid phase is stabilized at the surface of the disks. In dilute collections of disks, the tendency to minimize the extent of the fluid-fluid interface and the extent of the unfavorable wetting phase in the system gives rise to aggregation phenomena and to separation of large domains of disks that have the characteristics of bulk colloidal phases. The conditions for phase transitions among cluster gas, liquid, and solid phases of the disk colloids are determined from the corresponding values of the disk chemical potential within an analytic representation of the grand partition function for the excess energy associated with a gas of disk clusters in the low-disk-density limit. The wetting effective-interface potential is combined with the disk interaction potential in associating an internal energy with each one of the clusters. The theory can thus be applied to any type of interaction potential among disks, provided that the free energy associated with the corresponding bulk colloidal phases is available. A phase diagram is calculated explicitly for the case of hard disks on the basis of an analytical approximation for the free energy of the hard disk fluid phase and the generalized effective liquid approximation for the free energy of the hard disk solid phase.

Thermodynamic Perturbation Approach to Freezing of the Classical One-Component Plasma

Systematic investigations are made of the thermodynamic perturbation approach to freezing, which has proved successful for systems interacting through soft-core or long-ranged potentials. The classical one-component plasma (OCP) is taken as the extreme case of such systems and the investigations focus on the reference systems employed in this approach and on the approximation schemes used to treat that system. It is confirmed that good results are obtained for the freezing properties of the OCP if a system with repulsive, short-ranged potential is properly chosen as the reference system, and both this system and the remaining part due to the long-range interaction are separately treated by the modified weighted-density approximation (MWDA) using accurate input data. However, if we adopt the hard spheres as the reference system in this approach and use either the MWDA or the generalized effective-liquid approximation (GELA) for this system, we cannot get similar results unless we use the input data in the ...

Freezing of the Hard Spheres: Re-Examination of the Weighted-Density-Functional Theories

Freezing of the hard spheres is re-examined using the modified weighted-density approximation (MWDA) of Denton and Ashcroft and the generalized effective-liquid approximation (GELA) of Lutsko and Baus. It is found that one owes part of success of these theories to the use of the Percus-Yevick (PY) direct correlation function and the corresponding equation of state of uniform fluids as the input data in these theories. In fact, if one uses virtually \lq\lqexact” input data in place of the PY ones, the free energies of the solid phase are somewhat lowered and predicted freezing properties worsen. It is argued that this unfavorable feature of the MWDA and the GELA becomes much more serious when these theories are applied to the reference hard spheres in the thermodynamic perturbation approach to freezing of systems with long-ranged potentials.

Stability of the hard-sphere icosahedral quasilattice.

The stability of the hard-sphere icosahedral quasilattice is analyzed using the differential formulation of the generalized effective liquid approximation. We find that the icosahedral quasilattice is metastable with respect to the hard-sphere crystal structures. Our results agree with recent findings by McCarley and Ashcroft [Phys. Rev. B {\bf 49}, 15600 (1994)] carried out using the modified weighted density approximation.

Pressure of the hard-sphere solid.

The pressure of the face-centered cubic hard-sphere crystal is analyzed using two different density functional theories: the generalized effective liquid approximation and the modified weighted density approximation. It is shown that in both theories the dominant contribution originates from the ideal part of the variational free energy. It is argued that in the region near close packing, reliable results can only be obtained by using the real-space version of these theories.

Density-functional theory and atomistic simulation of the hard-sphere melt-solid interface.

The melt-solid interface of hard spheres is studied by atomistic simulations and density-functional theory (DFT). The Monte Carlo method is used to compute density profiles for the three most important orientations of the fcc-solid--melt interface. The interface ranges in thickness from 4d for the loosely packed (110) interface to 6d for the closely packed (111) interface, where d is the hard-sphere diameter. The planar generalized effective liquid approximation (PGELA) free energy functional, which accurately predicts solid and liquid free energies and coexistence conditions, is used in the DFT analysis of the hard-sphere melt-solid interface. Two parametrizations are compared for variations of the density in the interfacial region. The structural predictions of the interface by the Carnahan-Starling PGELA are in good agreement with the simulations. The calculations of the surface free energies show that the (110) interface has a smaller surface free energy, followed by the (100) interface and then closely by the (111) interface. These results are compared to other recent studies of the hard-sphere melt-solid interface.

Hard-sphere and hard-disk freezing from the differential formulation of the generalized effective liquid approximation.

We apply the differential formulation of the generalized effective liquid approximation to the study of hard-sphere and hard-disk freezing. We show that the thermodynamic properties of the solid phase are rather insensitive to the compressibility factor of the fluid phase used to map the solid onto the effective liquid. The solid-fluid coexistence data instead are quite dependent on the equation of state describing the fluid phase. Very accurate results, as compared with the simulation data, are obtained for both the freezing of hard spheres and hard disks.

Freezing of the classical one-component plasma: analyses of the non-perturbative density-functional theories

Recently developed non-perturbative density-functional theories of freezing are applied to the classical one-component plasma (OCP). The author considers the modified weighted-density approximation (MWDA) of Denton and Ashcroft and the generalized effective-liquid approximation (GELA) of Lutsko and Baus. It is shown that both the MWDA and the GELA completely fail to predict freezing of the classical OCP in contrast to their reasonable success for the quantum freezing of the electron jellium: the MWDA does not improve over the second-order theory (SOT) and the GELA is much worse. A semi-empirical analysis is made of how and to what extent the GELA must be modified for the classical OCP: in this analysis the SOT is used for the variational liquid-like solids and the Monte Carlo results are used for the stable (or metastable) BCC solids. It is found that the two effective liquids, which are assumed to be equivalent in the GELA, must differ by about 10 % in density from each other at the freezing point.

Isotropic-nematic transition of D-dimensional hard convex bodies within the effective-liquid approach.

Density-functional theory within the effective-liquid approximation is applied to the problem of the isotropic-nematic transition of D-dimensional hard convex bodies. It is shown that the free-energy functional factorizes into its radial and angular contributions. Due to this factorization two different versions of the self-consistent equations can be implemented, and it is shown that in D=3 they coincide with previous theories. In the present work all the formulas are worked out with a particular choice for the angular distribution: the one-order-parameter approximation. The problem of determining the excluded volume of two hard convex bodies is discussed. For hard ellipsoids the Gaussian-overlap approximation is used, whereas an exact formula is given for the excluded volume of two hard spherocylinders. For D=2 the virial coefficients of the isotropic phase as well as the transition are incorrectly predicted, due to the approximation of the direct correlation function involved. For D=3 the results are in very good agreement with simulations. Expression and data for the isotropic-nematic transition for D>3 are also provided. Extensive comparisons with the results of other theories are made throughout. The one-order-parameter approximation is proven not to alter the order of the transition. Finally, it is shown that the present approximation becomes exact in the large-D limit.

Local thermodynamic mapping for effective liquid density-functional theory.

The structural-mapping approximation introduced by Lutsko and Baus [Phys. Rev. A 41, 6647 (1990)] in the generalized effective-liquid approximation is extended to include a local thermodynamic mapping based on a spatially dependent effective density for approximating the solid phase in terms of the uniform liquid. This latter approximation, called the local generalized effective-liquid approximation (LGELA) yields excellent predictions for the free energy of hard-sphere solids and for the conditions of coexistence of a hard-sphere fcc solid with a liquid. Moreover, the predicted free energy remains single valued for calculations with more loosely packed crystalline structures, such as the diamond lattice. The spatial dependence of the weighted density makes the LGELA useful in the study of inhomogeneous solids.

Weighted-density-functional theories for the freezing of jellium.

Quantum freezing of electrons in a uniform neutralizing background (jellium) at T=0 is studied by suitable extensions of classical density-functional schemes of the weighted-density type. We give a derivation of the schemes that clarifies (i) the basic approximations behind them, and (ii) the modifications\char22{}with respect to the case of uncharged particles\char22{}arising from the long range of Coulomb interactions. In particular, we present an application to quantum freezing of the so-called weighted-density approximation (WDA) and generalized effective liquid approximation. We also consider the modified WDA, a simplified version of the WDA introduced by Denton and Ashcroft, and recently tested on the quantum freezing of Bose hard spheres. All approaches use as input thermodynamic and structural information of the uniform quantum liquid and yield a reasonable description of the freezing transition. The results of the various approximations are critically examined and compared with both the predictions of quantum Monte Carlo and of the Ramakrishnan and Yussouff second-order theory.

The generalized effective liquid approximation for the freezing of hard spheres

The generalized effective liquid approximation (GELA) to the density functional theory of classical nonuniform systems reproduces all the formal properties of the free energy and requires only the direct correlation function of the uniform system as input. In the case of the freezing of hard spheres very accurate free energies, pressures and fluid-solid coexistence data can be obtained from the GELA. The theory predicts, besides the equilibrium FCC solid, metastable BCC and SC phases also.

Freezing of soft spheres: A critical test for weighted-density-functional theories.

We study the freezing properties of systems with inverse-power and Yukawa interactions (soft spheres), using recently developed weighted-density-functional theories. We find that the modified weighted-density-functional approximation (MWDA) of Denton and Ashcroft yields results for the liquid to face-centered-cubic (fcc) structure transition that represent a significant improvement over those of earlier ``second-order'' density-functional freezing theories; however, this theory, like the earlier ones, fails to predict any liquid to body-centered-cubic (bcc) transition, even under conditions where the computer simulations indicate that this should be the equilibrium solid structure. In addition, we show that both the modified effective-liquid approximation (MELA) of Baus [J. Phys. Condens. Matter 2, 2111 (1990)] and the generalized effective-liquid approximation of Lutsko and Baus [Phys. Rev. Lett. 64, 761 (1990)], while giving excellent results for the freezing of hard spheres, fail completely to predict freezing into either fcc or bcc solid phases for soft inverse-power potentials. We also give an alternate derivation of the MWDA that makes clearer its connection to earlier theories.