Elusiveness of fluid-fluid demixing in additive hard-core mixtures

The conjecture that when an additive hard-core mixture phase separates when one of the phases is spatially ordered, well supported by considerable evidence, is in contradiction with some simulations of a binary mixture of hard cubes on cubic lattices. By extending Rosenfeld's fundamental measure theory to lattice models we show that the phase behavior of this mixture is far more complex than simulations show, exhibiting regions of stability of several smectic, columnar, and solid phases, but no fluid-fluid demixing. A comparison with the simulations show that they are, in fact, compatible with a fluid-columnar demixing transition, thus bringing this model into the same demixing scheme as the rest of additive hard-core mixtures.     

Velocity correlations and the structure of nonequilibrium hard-core fluids

A model for the pair-distribution function of nonequilibrium hard-core fluids is proposed based on a model for the effect of velocity correlations on the structure. Good agreement is found with molecular dynamics simulations of granular fluids and of sheared elastic hard spheres. It is argued that the incorporation of velocity correlations are crucial to correctly modeling atomic scale structure in nonequilibrium fluids.     

Discretization dependence of criticality in model fluids: a hard-core electrolyte

Grand-canonical simulations at various levels, zeta=5-20, of fine-lattice discretization are reported for the near-critical 1:1 hard-core electrolyte or restricted primitive model (RPM). With the aid of finite-size scaling analyses, it is shown convincingly that, contrary to recent suggestions, the universal critical behavior is independent of zeta (> or approximately 4), thus the continuum (zeta--> infinity ) RPM exhibits Ising-type (as against classical, self-avoiding walk, XY, etc.) criticality. A general consideration of lattice discretization provides effective extrapolation of the intrinsically erratic zeta dependence, yielding (T*(c),rho*(c)) approximately equal to (0.0493(3),0.075) for the zeta=infinity RPM.     

Critical parameters of hard-core Yukawa fluids within the structural theory

A purely statistical mechanical approach is proposed to account for the liquid–vapor critical point based on the mean density approximation (MDA) of the direct correlation function. The application to hard-core Yukawa (HCY) fluids facilitates the use of the series mean spherical approximation (SMSA). The location of the critical parameters for HCY fluid with variable intermolecular range is accurately calculated. Good agreement is observed with computer simulation results and with the inverse temperature expansion (ITE) predictions. The influence of the potential range on the critical parameters is demonstrated and the universality of the critical compressibility ratio is discussed. The behavior of the isochoric and isobaric heat capacities along the equilibrium line and the near vicinity of the critical point is discussed in details.     

Evidence against a three-phase point in a binary hard-core lattice model

Using Monte Carlo simulation, Van Duijneveldt and Lekkerkerker [Phys. Rev. Lett. 71, 4264 (1993)] found gas-liquid-solid behavior in a simple two-dimensional lattice model with two types of hard particles. The same model is studied here by means of numerical transfer-matrix calculations, focusing on the finite-size scaling of the gaps between the largest few eigenvalues. No evidence for a gas-liquid transition is found. We discuss the relation of the model with a solvable restricted solid-on-solid model of which the states obey the same exclusion rules. Finally, a detailed analysis of the relation with the dilute three-state Potts model strongly supports the tricritical point rather than a three-phase point.     

Phonon-lifetimes in demixing systems

The dynamics of silver-alkali halide mixed single crystals (Ag(x)Na(1-x)Br, x = 0.23, 0.35, 0.40 and 0.70) were studied by inelastic neutron scattering during the process of spinodal decomposition. Using the thermal three-axes spectrometer PUMA as well as the time-of-flight spectrometer IN5, the time evolution of phonons was observed in time-resolved, stroboscopic measurements. Complementary to the study of long wavelength acoustic phonons, as studied previously, we extended these investigations to Brillouin-zone boundary modes that are particularly sensitive to variations of the local structure. Starting from the homogeneous mixed phase the behaviour of these modes during demixing is observed in real-time. A simple dynamical model based on local structure variants helps to interpret the results. It is shown that the phonon lifetimes vary strongly during the phase separation and increase drastically during the coarsening process. Up to a critical size of precipitates of about 10 nm, zone-boundary modes are found to be strongly damped, while beyond the line widths are reduced to the experimental resolution. This finding leads to the conclusion that the typical mean free path of these modes is of the order of 10 nm, which corresponds to 20 unit cells.     

Equilibrium theory for the hard-core systems

It is found that the density expansion in the argument of the exponential function gives a fine convergence on the equation of state of the hard-sphere system. The pair distribution function and the equation of state is constructed by an intuitive kinetic theoretical method. The equation of state of the hard-core system with attractive potential is constructed semiempirically with the aid of this simple analytical result, and Kamerling-Onnes' constant of the critical point is obtained analytically.     

Exact solutions for a quantum hard-core system

Exact closed expressions have been obtained for the first three partial waves of the two-particle density matrix for a hard-core pairwise interaction.     

Circle theorem for hard-core binary lattice gases

We study the distribution of zeros in a symmetric, two-component Widom-Rowlinson lattice system (any number of dimensions). We show that for sufficiently large mean activity the system partition function cannot vanish if the magnitude of the ratio of the two (complex) activities is different from one.Supported in part by National Science Foundation Grants CHE76-11253 (to LKR) and Phy 78-15920 (to JLL), and by the Petroleum Research Foundation.     

Systematic field-theory for the hard-core one-component plasma

A continuous liquid flow in a vacuum (a liquid beam) of an aqueous solution of adenine salt containing hydrochloric acid or sodium hydroxide was irradiated with an intense pulsed IR laser at 3 μm, which is resonant to a vibrational mode related to the OH stretch vibration of H₂O. Neutral species isolated into the vacuum were ionized by a pulsed UV laser at 270 nm, and the product ions were mass-analyzed by a time-of-flight mass spectrometer. It is found that AH ₂ ^{2 + .} 2Cl^- and [A-iH] ^{i - .} iNa⁺ (i = 1-3) are isolated in the vacuum from the aqueous acidic and alkaline solutions, respectively, under irradiation of the IR laser, and undergo four-photon ionization involving decomposition and proton transfer of the intermediate species under irradiation of the UV laser. Received 1st May 2002 Published online 13 September 2002     

Lennard-Jones fluids confined in nanoscopic slits: Evidence for reentrant filling transitions

By using grand canonical and canonical ensemble Monte Carlo simulations, the structure and phase behavior of a Lennard-Jones (LJ) fluid confined between the parallel (100) planes of a face-centered cubic crystal are studied. Slit pores with a width which allows three adsorbate layers to form are used. It is shown that the filled pore consists of three commensurate layers over a wide range of the surface potential strength, while the pore-filling mechanism and the topology of the phase diagram change when the strength of this fluid-wall potential is varied. Condensation may occur in one step or via two layering-like transitions. The structure of monolayer films depends on the strength and corrugation of the surface potential, and the condensation of the middle layer may induce a reentrant first-order transition.Received: 16 January 2004, Published online: 23 March 2004PACS: 64.70.Nd Structural transitions in nanoscale materials - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 68.35.Rh Phase transitions and critical phenomena     

Fluid-solid transition in a hard-core system

We prove that a system of particles in the plane, interacting only with a certain hard-core constraint, undergoes a fluid-solid phase transition.     

Ferromagnetism in a hard-core boson model

The problem of ferromagnetism – associated with a ground state with maximal total spin – is discussed in the framework of a hard-core model, which forbids the occupancy at each site with more than one particle. It is shown that the emergence of ferromagnetism on finite square lattices crucially depends on the statistics of the particles. Fermions (electrons) lead to the well-known instabilities for finite hole densities, whereas for bosons (with spin) ferromagnetism appears to be stable for all hole densities.     

Density functional theory for general hard-core lattice gases

We put forward a general procedure to obtain an approximate free-energy density functional for any hard-core lattice gas, regardless of the shape of the particles, the underlying lattice, or the dimension of the system. The procedure is conceptually very simple and recovers effortlessly previous results for some particular systems. Also, the obtained density functionals belong to the class of fundamental measure functionals and, therefore, are always consistent through dimensional reduction. We discuss possible extensions of this method to account for attractive lattice models.     

Coexistence and criticality in size-asymmetric hard-core electrolytes

Liquid-vapor coexistence curves and critical parameters for hard-core 1:1 electrolyte models with diameter ratios lambda = sigma(-)/sigma(+) = 1 to 5.7 have been studied by fine-discretization Monte Carlo methods. Normalizing via the length scale sigma(+/-) = 1 / 2(sigma(+)+sigma(-)), relevant for the low densities in question, both T(*)(c) ( = k(B)T(c)sigma(+/-)/q(2)) and rho(*)(c) ( = rho(c)sigma(3)(+/-)) decrease rapidly (from approximately 0.05 to 0.03 and 0.08 to 0.04, respectively) as lambda increases. These trends, which unequivocally contradict current theories, are closely mirrored by results for tightly tethered dipolar dimers (with T(*)(c) lower by approximately 0%-11% and rho(*)(c) greater by 37%-12%).