Floating liquid phase in sedimenting colloid-polymer mixtures

Density functional theory and computer simulation are used to investigate sedimentation equilibria of colloid-polymer mixtures within the Asakura-Oosawa-Vrij model of hard sphere colloids and ideal polymers. When the ratio of buoyant masses of the two species is comparable to the ratio of differences in density of the coexisting bulk (colloid) gas and liquid phases, a stable "floating liquid" phase is found, i.e., a thin layer of liquid sandwiched between upper and lower gas phases. The full phase diagram of the mixture under gravity shows coexistence of this floating liquid phase with a single gas phase or a phase involving liquid-gas equilibrium; the phase coexistence lines meet at a triple point. This scenario remains valid for general asymmetric binary mixtures undergoing bulk phase separation.     

Low-and high-dimension limits of a phase separation model

We study a simple zero-temperature model for phase separation of a binary alloy, in which nearest-neighbor interchange can occur if the fraction of AB pairs is not thereby increased. We present analytic results for the one-dimensional case and numerical results for the infinite dimensionality limit on a Cayley tree. In neither limit does the final fraction of AB pairs agree with the dimension-independent result found previously ind=3, 4, 5.     

Unconventional spin-charge phase separation in a model 2D cuprate

In this work, we address a challenging problem of a competition of charge and spin orders for high-T _c cuprates within a simplified 2D spin-pseudospin model which takes into account both conventional Heisenberg Cu²⁺?Cu²⁺ antiferromagnetic spin exchange coupling (J) and the on-site (U) and intersite (V) charge correlations in the CuO₂ planes with the on-site Hilbert space reduced to only three effective charge states (nominally Cu^1+;2+;3+). We performed classical Monte Carlo calculations for large square lattices implying the mobile doped charges and focusing on a case of a small intersite repulsion V ? J. The on-site attraction (U < 0) does suppress the antiferromagnetic ordering and gives rise to a checkerboard charge order with the doped charge distributed randomly over a system in the whole temperature range. However, under the on-site repulsion (U > 0) the homogeneous ground state antiferromagnetic solutions of the doped system found in a mean-field approximation are shown to be unstable with respect to a phase separation with the charge and spin subsystems behaving like immiscible quantum liquids. Puzzlingly, with lowering the temperature one can observe two sequential phase transitions: first, an antiferromagnetic ordering in the spin subsystem diluted by randomly distributed charges, then, a charge condensation in the charge droplets. The effects are illustrated by the Monte Carlo calculations of the specific heat and longitudinal magnetic susceptibility.     

Existence of enantiomeric phase separation in a three-dimensional lattice gas model

A three-dimensional lattice gas model for enantiomeric phase separation is introduced. The enantiomeric molecules (d andl) are the two nonsuperimposable mirror images having the molecular structure C(AB)₂, where C is a tetrahedrally bonded carbon atom with one bond to each end of two AB groups. The lattice gas model consists of a body-centered cubic lattice, each site of which can be either vacant or occupied by a molecule oriented so that the A and B groups point toward neighboring lattice sites. Pairs of molecules interact with short-range, orientationally-dependent interactions. For a domain of interaction parameters, the Pirogov-Sinai extension of the Peierls argument is used to prove thatd-rich andl-rich phases exist in the model at sufficiently low temperature. For another domain of interaction parameters, at sufficiently high chemical potential there is an infinite number of ground states, each containing a racemic mixture ofd andl molecules.     

The shape of clusters on rectangular 2D lattices in a simple “phase separation” computer experiment

Phase separation of a binary “50:50 alloy” was simulated in Monte Carlo experiments played on 1D and 2D lattices at T = 0 K using the Ising model framework. $\text{S}$ = total number of bonds/total number of elements, was calculated for the evolving clusters. Surprisingly $\text{S}$/Z (Z = coordination number) is insensitive to the value of Z for Z = 2, 3, 4, 6.     

Inhomogeneity-induced second-order phase transitions in the Potts model on hierarchical lattices

Thermodynamics of the Potts model with an arbitrary number of states is analyzed for a class of hierarchical lattices of fractal dimension d > 1. In contrast to the case of crystal lattice, it is shown that all phase transitions on lattices of this type are of the second order. Critical exponents are determined, their dependence on structural parameters is examined, and scaling relations between them are established. A structural criterion for change in transition order is discussed for inhomogeneous systems. Application of the results to critical phenomena in phase transitions in dilute crystals and porous media is discussed.     

On phase separation in the spherical model of a ferromagnet: Quasiaverage approach

The spherical model of a ferromagnet is investigated in the framework of the generalized quasiaverage approach where an external field positive in one half of a square lattice and negative in the other half is used. It is shown that in addition to the well-known critical point, a second one can be produced by the field. Although the main asymptotic of the free energy is analytic at this point, the next-to-leading asymptotic possesses a singularity here, as well as at the point where the free energy per site is nonanalytic. An order parameter of the model also has singularities at both critical points. The magnetization profile is studied at different scales. It is shown that (in an appropriate regime), below the new critical temperature the magnetization profile freezes, that is, becomes temperature independent.     

The phase separation line in the two-dimensional Ising model

We prove that, at low temperature, the line of separation between the two pure phases shows large fluctuations in shape. This implies the translation invariance of the correlation functions associated with some non translation invariant boundary conditions and should be a peculiarity of the dimensionality of the model.This work has been partially supported by the Consiglio Nazionale delle Ricerche (Gruppo Nazionale per l'Analisi Funzionale): CNR(GNAFA).     

Kinetic ising model study of phase separation in binary alloys

The decomposition of binary alloys after a sudden quench below the critical temperature of unmixing is studied on a microscopic basis, using a stochastic model analog to the Kawasaki spin exchange Ising model. For interactions of long range the model reduces to the standard phenomenological equation. We relate this nonlinear equation to our recent treatment of the time-dependent Ginzburg-Landau theory, and calculate the nonequilibrium relaxation functions. For interactions of short range we present some computer simulations. As example, we treat a 55×55 square lattice, with a gradient in the chemical potential. Details are given for the relaxation process, which is a coarsening at the initial stage of the decomposition, while later the gradient produces a more macroscopic phase separation.     

Viscoelastic model of phase separation in colloidal suspensions and emulsions

We propose a simple physical model of phase separation of colloidal suspensions and emulsions, which we call the "viscoelastic model." On the basis of this model, we consider two poorly understood phenomena: (i) phase separation accompanying the formation of a transient gel, and its collapse, and (ii) shear effects on composition fluctuations and phase separation. These phenomena can be explained by "asymmetric stress division" between the components of a mixture due to their size difference; the interaction network of particles can store elastic energy, while a fluid component cannot. The importance of the bulk stress stemming from an interaction network is discussed, using a concept of self-induced elastic constraint due to connectivity. We argue that there are common features to polymer solutions, colloidal suspensions, emulsions, and possibly protein solutions. They originate from dynamic asymmetry between the components and the resulting interaction network of the slower component of a mixture, which leads to the formation of a transient gel.     

Minimal model for phase separation under slow cooling

Inducing phase separation by a sustained change of temperature often induces repeated waves of nucleation. As demonstrated in an accompanying movie, these oscillations can easily be demonstrated in the classroom by slowly cooling raw spirit (i.e., ethanol) and vegetable oil. In the present communication we suggest a minimal theoretical model predicting that they are of thermodynamic origin. Their frequency depends on the diffusion constant and ramp rate, and is not affected by the overall composition and sample geometry. Our experimental data support this model.     

Double-exchange model: phase separation versus canted spins

We study the competition between different possible ground states of the double-exchange model with strong ferromagnetic exchange interaction between itinerant electrons and local spins. Both for classical and quantum treatment of the local spins the homogeneous canted state is shown to be unstable against a phase separation. The conditions for the phase separation into the mixture of the antiferromagnetic and ferromagnetic/canted states are given. We also discuss another possible realization of the phase-separated state: ferromagnetic polarons embedded into an antiferromagnetic surrounding. The general picture of a percolated state, which emerges from these considerations, is discussed and compared with results of recent experiments on doped manganaties. Received 17 March 1999     

Excitation of phase transitions in dipole lattices

Phase transitions in hexagonal lattices with three and four rows of dipoles arising as a result of the reorientation of different sets of dipoles by the external field have been studied. The conditions of the implementation of two types of symmetric phase transitions and the asymmetric transitions, when the configurations of the system to the left and to the right of the excitation region are different, have been established. Merging of two regions of the phase transitions has been considered. Unidirectional phase transitions, in which either the left or the right phase transition front propagates from the excitation region along the lattice, have been obtained in a lattice with four rows of dipoles. The variations of the total dipole moment of the system and the energy of the dipole-dipole interaction during the phase transitions have been given.     

A model for phase separation in systems with orbital ordering

The possibility of phase separation in the substances with orbital ordering is analyzed. The additional charge carriers introduced due to doping favor the formation of nanosize inhomogeneities with the orbital structure different from that in the undoped material. The shapes and sizes of such inhomogeneities are determined.