The condensation and ordering of models of empty liquids

We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction between B patches to zero and calculate the phase diagram as the ratio between the AB and the AA interactions, ε(AB)*, varies. In line with previous work, on three-dimensional off-lattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of ε(AB)*, suggesting that the ratio of the energy scales--and the corresponding empty fluid regime--is independent of the dimensionality of the system and of the lattice structure. In addition, the model exhibits an order-disorder transition that is ferromagnetic in the re-entrant regime. The use of low-dimensional lattice models allows the simulation of sufficiently large systems to establish the nature of the liquid-vapor critical points and to describe the structure of the liquid phase in the empty fluid regime, where the size of the "voids" increases as the temperature decreases. We have found that the liquid-vapor critical point is in the 2D Ising universality class, with a scaling region that decreases rapidly as the temperature decreases. The results of simulations and theoretical analysis suggest that the line of order-disorder transitions intersects the condensation line at a multi-critical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime.     

磁性高分子链的磁性质和构象性质的Monte Carlo模拟

采用退火 (Annealing)MonteCarlo方法 ,从高温到低温顺序模拟了简立方格点上考虑最近邻Ising相互作用的磁性高分子链在不同温度的磁性质和构象性质 .磁性高分子链在低温下存在自发磁矩 ,无限长链的临界温度Tc=1 77± 0 0 5J kB.在临界温度附近 ,高分子链经历了从伸展的无规线团到紧缩球体的塌缩相变 .对链的尺寸、形状、近邻数及能量的分析表明 ,高分子链的构象性质从温度Tc=1 77开始发生较明显的变化 ,这表明高分子Ising链的相变是Ising相互作用和链节运动协同作用的结果 .     

Domain formation in membranes with quenched protein obstacles: lateral heterogeneity and the connection to universality classes

We show that lateral fluidity in membranes containing quenched protein obstacles belongs to the universality class of the two-dimensional random-field Ising model. The main feature of this class is the absence of a phase transition: there is no critical point and macroscopic domain formation does not occur. Instead there is only one phase. This phase is highly heterogeneous with a structure consisting of microdomains. The presence of quenched protein obstacles thus provides a mechanism to stabilize lipid rafts in equilibrium. Crucial for two-dimensional random-field Ising universality is that the obstacles are randomly distributed and have a preferred affinity to one of the lipid species. When these conditions are not met standard Ising or diluted Ising universality applies. In these cases a critical point does exist which then marks the onset toward macroscopic demixing.     

Liquid-crystalline ordering in two-dimensional systems with discrete symmetry

The mean-field theories of liquid-crystalline (nematic) ordering developed for three-dimensional systems are applied to describe two-dimensional systems of both geometrically anisotropic and anisotropically interacting particles. Systems with discrete symmetry (lattice models) for which long-range order is possible are considered on the base of the Landau free-energy expansion. It is shown that the Hamiltonian describing the energy of intermolecular interactions may be written in a common form for lyotropic and thermotropic systems. The mean-field theory gives a continuous phase transition (second-order phase transition) for a square lattice, whereas for a triangular lattice it gives a phase transition with latent heat (first-order phase transition) like for three-dimensional systems. These results are compared with results of the exact theories (two-dimensional Ising and Potts models). It is concluded that for realistic two-dimensional models the orientational in-plane ordering is not sharper than a second-order phase transition.     

Dielectric response of one-dimensional polar chains

We propose a theory for the dielectric constant of materials made of parallel infinite one-dimensional chains of dipoles. Each dipole is allowed to rotate in three dimensions. Monte Carlo simulations show that the Kirkwood factor of the chain grows with increasing dipole moment much faster than in the case of three-dimensional polar fluids. With increasing dipole moment or cooling the one-dimensional chain undergoes a continuous order-disorder transition to the ferroelectric phase, in which the dielectric constant is limited by the size of ferroelectric domains along the chain.     

Solution on the Bethe lattice of a hard core athermal gas with two kinds of particles

Athermal lattice gases of particles with first neighbor exclusion have been studied for a long time as simple models exhibiting a fluid-solid transition. At low concentration the particles occupy randomly both sublattices, but as the concentration is increased one of the sublattices is occupied preferentially. Here, we study a mixed lattice gas with excluded volume interactions only in the grand-canonical formalism with two kinds of particles: small ones, which occupy a single lattice site and large ones, which, when placed on a site, do not allow other particles to occupy its first neighbors also. We solve the model on a Bethe lattice of arbitrary coordination number q. In the parameter space defined by the activities of both particles, at low values of the activity of small particles (z(1)) we find a continuous transition from the fluid to the solid phase as the activity of large particles (z(2)) is increased. At higher values of z(1) the transition becomes discontinuous, both regimes are separated by a tricritical point. The critical line has a negative slope at z(1) = 0 and displays a minimum before reaching the tricritical point, so that a re-entrant behavior is observed for constant values of z(2) in the region of low density of small particles. The isobaric curves of the total density of particles as a function of the density or the activity of small particles show a minimum in the fluid phase.     

The phase behavior of two-dimensional symmetrical mixtures in a weak external field of square symmetry

Using Monte Carlo simulation methods in the grand canonical and semigrand canonical ensembles, we study the phase behavior of two-dimensional symmetrical binary mixtures of Lennard-Jones particles subjected to a weakly corrugated external field of a square symmetry. It is shown that the both vapor-liquid condensation and demixing transition in the liquid phase are not appreciably affected by a weakly corrugated external field. On the other hand, even a weakly corrugated external field considerably influences the structure of solid phases and the liquid-solid transition. In particular, the solid phases are found to exhibit uniaxially ordered distorted hexagonal structure. The triple point temperature increases with the corrugation of the external field, while the triple point density becomes lower when the surface corrugation increases. The changes in the location of the triple point are shown to lead to the changes of the phase diagram topology. It is also demonstrated that the solid phase undergoes a demixing transition, which is also very slightly affected by the weakly corrugated external potential. The demixing transition in the solid phase is shown to belong to the universality class of the Ising model.     

A theory of a curved vapor-liquid separation boundary: The lattice gas model

Molecular theory of curved vapor-liquid interphase boundaries was considered in terms of the lattice gas model. The theory uses the quasi-thermodynamic concept of curved layers of a separation boundary with a large radius. The transition from a rectangular lattice to such layers is performed by the introduction of a variable number of the nearest neighbors. The problems (1) of the transition from distributed molecular models to layer models reflecting macroscopic symmetry of the interphase boundary and (2) of a minimum linear size of the surface region to which thermodynamic approaches are applicable were considered. Equations for the quasi-equilibrium distribution of molecules at the vapor-liquid boundary in a metastable system were constructed in the quasi-chemical approximation taking into account direct correlations between the nearest interacting molecules. A metastable state is maintained by a pressure jump described by the macro-scopic Laplace equation on a separation surface inside the interphase region. Equations for local mean pressure values and normal and tangential pressure tensor components inside the interphase region were constructed. These equations were used to obtain microscopic difference mechanical equilibrium equations for curved boundaries of spherical and cylindrical drops in the metastable state. The relation between the micro-scopic difference mechanical equilibrium equations and similar differential equations and the macroscopic Laplace equation, which described pressure jump in a metastable system, was considered. Various definitions of surface tension are discussed.     

Relation of the verwey transition in magnetite to an order-disorder transition of strongly correlated electrons

The principal features of the Verwey transition in magnetite have been simulated by adopting elements of order-disorder theory. In certain limiting cases we obtain the model of Strässler and Kittel which had previously been used to rationalize the electronic and thermodynamic properties of magnetite. According to the present microscopic model the discontinuous Verwey transition in magnetite is driven by a change in a highly correlated electron system with temperature from a charge-ordered small-polaron state associated with local lattice deformations to a disordered state in which electrons resonate between Fe²⁺ and Fe³⁺ ions located on the octahedral cationic sites.     

Cooperative atomic displacements and melting at the limit of superheating

This paper shows how the melting of superheated crystals originates from the localization of thermal disorder in excited regions of the crystalline structure. Within such regions, disordered thermal motion is found to induce the formation of bulk topological defects. These consist of atoms with a number of nearest neighbors different from the equilibrium one. Such defectively coordinated atoms arrange according to pseudolinear clusters, the number and size of which depend on temperature. Characterized by high mobility, defective atoms and their nearest neighbors are seen to undergo a cooperative dynamics that can result in net atom displacements between equilibrium lattice sites.     

Space-time thermodynamics and subsystem observables in a kinetically constrained model of glassy materials

In a recent article [M. Merolle et al., Proc. Natl. Acad. Sci. U.S.A. 102, 10837 (2005)], it was argued that dynamic heterogeneity in d-dimensional glass formers is a manifestation of an order-disorder phenomenon in the d+1 dimensions of space time. By considering a dynamical analog of the free energy, evidence was found for phase coexistence between active and inactive regions of space time, and it was suggested that this phenomenon underlies the glass transition. Here we develop these ideas further by investigating in detail the one-dimensional Fredrickson-Andersen (FA) model, in which the active and inactive phases originate in the reducibility of the dynamics. We illustrate the phase coexistence by considering the distributions of mesoscopic space-time observables. We show how the analogy with phase coexistence can be strengthened by breaking microscopic reversibility in the FA model, leading to a nonequilibrium theory in the directed percolation universality class.     

Phase diagram of the TbBr(3)-RbBr binary system: thermodynamic and transport properties of the Rb(3)TbBr(6) compound

Phase equilibria in the TbBr3-RbBr binary system were established from differential scanning calorimetry (DSC) measurements. This binary system is characterized by two compounds, namely Rb3TbBr6 and RbTb2Br7, and two eutectics located at the TbBr3 mole fractions, x = 0.117 (728 K) and x = 0.449 (718 K), respectively. Rb3TbBr6 undergoes a solid-solid phase transition at 728 K and melts congruently at 1047 K with the related enthalpies 7.8 and 58.7 kJ mol(-1), respectively. RbTb2Br7 melts incongruently at 803 K. It undergoes also a solid-solid phase transition at 712 K, a temperature very close to that (718 K) of the second eutectic, and much attention was paid in evidencing and separating these transition and eutectic effects. Separate investigations of the thermodynamic and transport properties were performed on the Rb3TbBr6 compound. These heat capacity and electrical conductivity experimental results suggest an order-disorder mechanism in the alkali-metal cation sublattice whereas the TbBr6 octahedra, forming the anionic sublattice, retain their normal lattice positions.     

Simulating the collapse transition of a two-dimensional semiflexible lattice polymer

It has been revealed by mean-field theories and computer simulations that the nature of the collapse transition of a polymer is influenced by its bending stiffness epsilon(b). In two dimensions, a recent analytical work demonstrated that the collapse transition of a partially directed lattice polymer is always first order as long as epsilon(b) is positive [H. Zhou et al., Phys. Rev. Lett. 97, 158302 (2006)]. Here we employ Monte Carlo simulation to investigate systematically the effect of bending stiffness on the static properties of a two-dimensional lattice polymer. The system's phase diagram at zero force is obtained. Depending on epsilon(b) and the temperature T, the polymer can be in one of the three phases: crystal, disordered globule, or swollen coil. The crystal-globule transition is discontinuous and the globule-coil transition is continuous. At moderate or high values of epsilon(b) the intermediate globular phase disappears and the polymer has only a discontinuous crystal-coil transition. When an external force is applied, the force-induced collapse transition will either be continuous or discontinuous, depending on whether the polymer is originally in the globular or the crystal phase at zero force. The simulation results also demonstrate an interesting scaling behavior of the polymer at the force-induced globule-coil transition.     

Phase diagram and universality of the Lennard-Jones gas-liquid system

The gas-liquid phase transition of the three-dimensional Lennard-Jones particles system is studied by molecular dynamics simulations. The gas and liquid densities in the coexisting state are determined with high accuracy. The critical point is determined by the block density analysis of the Binder parameter with the aid of the law of rectilinear diameter. From the critical behavior of the gas-liquid coexisting density, the critical exponent of the order parameter is estimated to be β = 0.3285(7). Surface tension is estimated from interface broadening behavior due to capillary waves. From the critical behavior of the surface tension, the critical exponent of the correlation length is estimated to be ν = 0.63(4). The obtained values of β and ν are consistent with those of the Ising universality class.     

A universal description of a solid crystal and liquid using discrete distribution functions

The numerical implementation of a crystallization/melting theory that has two branches of isotherms for liquids and solids as in Landau’s theory within the general self-consistent theory of condensed states is discussed. Equations are based on discrete distribution functions (the lattice gas model). Molecular distributions are calculated to a quasi-chemical approximation reflecting the effects of direct correlations between interacting particles. the interaction between particles is described by the Lennard-Jones potential, while the vibrational motion of molecules is included using a modified quasi-dimer Mie model. The effect of the vibrations of atoms on lateral interactions between nearest and next nearest neighbors is considered, along with a scheme for considering the displacement of particles in a liquid that modify such lateral interactions. Examples of calculations describing a defective crystal and vapor-liquid system are given.     

A temperature-dependent order-disorder and crystallographic phase transition in a 0D Fe(II) spin crossover compound and its non-spin crossover Co(II) isomorph

The new dipyridylamino/triazine ligand DDE (N(2),N(2),N(4),N(4)-tetraethyl-N(6),N(6)-di(pyridin-2-yl)-1,3,5-triazine-2,4,6-triamine) has been incorporated into the mononuclear Fe(II) SCO compounds cis-[Fe(II)(NCSe)(2)(DDE)(2)] (1), cis-[Fe(II)(NCBH(3))(2)(DDE)(2)] (2), and cis-[Fe(II)(NCS)(2)(DDE)(2)] (3). Magnetic susceptibility measurements reveal that each of 1, 2 and 3 undergoes a complete, continuous spin transition with a T(?) of ～260 K, ～300 K and ～205 K, respectively. An analogue and isomorph of 1, cis-[Co(II)(NCSe)(2)(DDE)(2)] (4), remains high spin down to low temperatures. Variable temperature single crystal data reveal that 1 and 4 undergo a crystallographic phase transition (from orthorhombic Pbcn at high temperatures to monoclinic P2/c at low temperatures) accompanied by an order-disorder transition of ethyl moieties of the DDE ligand. In the Pbcn phase, the structures of 1 and 4 contain one crystallographically unique M(II) centre, while in the P2/c phase, 1 and 4 contain two crystallographically unique M(II) centres. Variable temperature powder X-ray diffraction experiments reveal that the crystallographic phase transition occurs at ～250 K for 1. The occurrence of the concomitant order-disorder and crystallographic phase transitions undergone by 1 and 4 is not directly apparent in their magnetic susceptibility measurements, and this is likely due to the local environment of the M(II) centres remaining largely undisturbed as the transitions occur. The compound 2 is isostructural to 1 and 4 at low temperatures.     

Freezing of parallel hard cubes with rounded edges

The freezing transition in a classical three-dimensional system of rounded hard cubes with fixed, equal orientations is studied by computer simulation and fundamental-measure density functional theory. By switching the rounding parameter s from zero to one, one can smoothly interpolate between cubes with sharp edges and hard spheres. The equilibrium phase diagram of rounded parallel hard cubes is computed as a function of their volume fraction and the rounding parameter s. The second order freezing transition known for oriented cubes at s = 0 is found to be persistent up to s = 0.65. The fluid freezes into a simple-cubic crystal which exhibits a large vacancy concentration. Upon a further increase of s, the continuous freezing is replaced by a first-order transition into either a sheared simple cubic lattice or a deformed face-centered cubic lattice with two possible unit cells: body-centered orthorhombic or base-centered monoclinic. In principle, a system of parallel cubes could be realized in experiments on colloids using advanced synthesis techniques and a combination of external fields.     

First-order phase transitions in repulsive rigid k-mers on two-dimensional lattices

In a previous paper [F. Roma?, A. J. Ramirez-Pastor, and J. L. Riccardo, Phys. Rev. B 72, 035444 (2005)], the critical behavior of repulsive rigid rods of length k (k-mers) on a square lattice at half coverage has been studied by using Monte Carlo (MC) simulations. The obtained results indicated that (1) the phase transition occurring in the system is a second-order phase transition for all adsorbate sizes k; and (2) the universality class of the transition changes from 2D Ising-type for monomers (k = 1) to an unknown universality class for k ≥ 2. In the present work, we revisit our previous results together with further numerical evidences, resulting from new extensive MC simulations based on an efficient exchange algorithm and using high-performance computational capabilities. In contrast to our previous conclusions (1) and (2), the new numerical calculations clearly support the occurrence of a first-order phase transition for k ≥ 2. In addition, a similar scenario was found for k-mers adsorbed on the triangular lattice at coverage k/(2k+1).