Phase Separation in a Bidirectional Two-Lane Asymmetric Exclusion Process

This paper studies a bidirectional two-lane asymmetric exclusion process, in which particles move in opposite direction on the two lanes. Interaction between the two lanes is implemented as follows: particle hops with rate p when there is a particle at the same site in the other lane, otherwise it hops with rate 1. It is shown that under periodic boundary conditions, a plateau will form on the fundamental diagram if p<1. This plateau corresponds to a phase separation phenomenon. We have compared the phase separation with those reported in previous works, and it is shown that the mechanism of phase separation in our model is different from previous ones. A possible phase separation mechanism is proposed, i.e., the system always tries to maximize the probability that particles could hop with rate 1. A simple mean field approximation and a 2-cluster mean field approach have been applied to calculate the steady current. It is shown that the results of the 2-cluster mean field approach are much closer to the simulations.     

Ground state phase diagram of the infinite dimensional Hubbard model: A variational study

We use the Gutzwiller variational method to study the ground state phase diagram of the infinite dimensional Hubbard model, paying special attention to features associated with the Gaussian form of the tight binding band density of states. We only consider trial states for which the validity of the Gutzwiller approximation has been proven, i.e., the paramagnetic, ferromagnetic, and two-sublattice antiferromagnetic states. We map out the phase diagram numerically, and give approximate analytic arguments to explain the behaviour in the small-U, and large-U limits. We give two versions of the phase diagram: one restricted to homogeneous phases, and another when phase separation is allowed. In the latter case, a homogeneous antiferromagnetic state is found only at exact half-filling, where the state is also insulating. Off half-filling, four different regions are found: pure paramagnetic, and ferromagnetic states, as well as antiferromagnetic-paramagnetic, and antiferromagnetic-ferromagnetic mixed phases.Dedicated to Professor W. Brenig on the occasion of his 60th birthdayResearch performed within the program of the Sonderforschungsbereich 341 supported by the Deutsche Forschungsgemeinschaft     

Colligative Properties of Solutions: II. Vanishing Concentrations

We continue our study of colligative properties of solutions initiated in ref. 1. We focus on the situations where, in a system of linear size L, the concentration and the chemical potential scale like c=ξ/L and h=b/L, respectively. We find that there exists a critical value ξt such that no phase separation occurs for ξ≤ξt while, for ξ>ξt, the two phases of the solvent coexist for an interval of values of b. Moreover, phase separation begins abruptly in the sense that a macroscopic fraction of the system suddenly freezes (or melts) forming a crystal (or droplet) of the complementary phase when b reaches a critical value. For certain values of system parameters, under “frozen” boundary conditions, phase separation also ends abruptly in the sense that the equilibrium droplet grows continuously with increasing b and then suddenly jumps in size to subsume the entire system. Our findings indicate that the onset of freezing-point depression is in fact a surface phenomenon.     

On the local structure of the phase separation line in the two-dimensional Ising system

We investigate the structure of the phase separation line between the pure phases in the two-dimensional Ising model, the liquid and vapor phase in lattice gas language, at low temperatures. The fluctuations in the location of this line are known to diverge in the thermodynamic limit, something which is also believed to happen to the continuum liquid-vapor interface in three dimensions (in the absence of the gravitational field). We show that despite this global divergence it is possible to define precisely the local structure of the phase separation line. This has a finite, exponentially small, width at low temperatures which is related by a central limit theorem⁽¹⁾ to the width of the global fluctuations on the appropriate (divergent) length scale. The latter has been computed explicitly⁽²⁾ for all temperatures below the critical temperatureT _c, where it diverges as (T _c –T)^–1/2. We also prove a Gibbs formula for the surface tension at low temperature, which relates it to the local structure of the phase separation line.Supported in part by NSF grant No. M^rPHY 78-15920 and MCS78-01885.On leave from: Departement de Physique Théorique, Université de Louvain, Belgium.     

Understanding liquid-liquid immiscibility and LCST behaviour in polymer solutions with a Wertheim TPT1 description

The aim of the work presented in this paper is to help in the understanding of the lower critical solution temperature (LCST) fluid phase behaviour exhibited by polymer solutions. It is well recognized that the LCST in polymer solutions is a consequence of density (compressibility) effects; the solvent is much more compressible than the polymer and the increasing difference in compressibility when the temperature is increased leads to a negative volume of mixing. The separate roles that the repulsive and attractive intermolecular interactions play in this regard are less well understood. In this study we use the Wertheim first-order thermodynamic perturbation theory (TPT1) [Wertheim, M. S., 1987, J. chem. Phys., 87, 7323; Chapman, W. G., Jackson, G., and Gubbins, K. E., 1988, Molec. Phys., 65, 1057] to describe the phase equilibria of model polymer solutions of hard spheres and hard-sphere chains where the diameter of the solvent and the polymeric segments are the same (symmetrical system). The thermodynamic functions (volume, enthalpy, entropy and Gibbs function) of mixing are determined to assess the possibility of a demixing instability in such a system. No fluid-fluid phase separation is found for the purely repulsive (athermal) system, regardless of the chain length of the polymer. The role of the attractive interactions is then investigated by incorporating attractive interactions at the mean-field level; the simplest system with equivalent (symmetric) solvent-solvent, solvent-polymer segment, and polymer segment-polymer segment interaction energies is examined. The attractive interactions are found to be essential in describing the liquid-liquid phase separation; LCST behaviour is found for mixtures with ‘polymer’ chains of seven segments or more. In this case we show that the phase behaviour is driven by an unfavourable (negative) entropy of mixing due to an increase in the density of the solvent on addition of small amounts of polymer. We also determine the thermodynamic properties of mixing for a system of spherical molecules of the same size with directional interactions that give rise to LCST and closed-loop behaviour. As expected the mechanism for phase separation in such systems is very different to that in polymer solutions.     

Zero and finite temperature phase diagram of the spinless fermion model in infinite dimensions

The phase diagram of the model of spinless fermions with repulsive nearest neighbour interaction is calculated analytically on a hypercubic lattice in infinite dimensions (d → ∞). In spite of its simplicity the model displays a rich phase diagram depending on the doping δ, the interaction U and the temperature T. The system can be in the homogeneous phase (HOM), the nonsegregated AB charge density wave (AB-CDW), the AB phase separation region (PS-AB/HOM; coexistence of AB-CDW and HOM), the incommensurate phase (IP) or the IP phase separation region (PS-AB/IP; coexistence of AB-CDW and IP). We identify three important values of the interaction U_IPL = 0.572 < U_IPH = 1.914 < U_IP/PS = 4.212 which distinguish four intervals of U. These imply four different types of phase diagrams. In all the three phase diagrams with U below U_IP/PS the IP appears. We propose a new general ansatz for the order parameter of this phase. A competition between the IP, the PS-AB/IP and the PS-AB/HOM is found. The relevance of our findings for the phase scenario of the Hubbard model is shown.     

Phase separation in the strongly correlated Falicov-Kimball model in infinite dimensions

Phase separation in the strongly correlated Falicov-Kimball model in infinite dimensions is examined. We show that the phase separation can occur for any values of the interaction constant J^* when the site energy of the localized electrons is equal to zero. Electron-poor regions always have homogeneous state and electron-rich regions have chessboard state for , chessboard state or homogeneous state in dependence upon temperature for 0<J ^* <0.03 and homogeneous state for J ^* =0. For J ^* =0 and T=0, phase separation (segregation) occurs at .The obtained results are exact for the Bethe lattice with infinite number of the nearest neighbours. Received 1 December 1998 and Received in final form 12 April 1999     

Flory-Huggins model of equilibrium polymerization and phase separation in the Stockmayer fluid

The competition between chain formation and phase separation in the Stockmayer fluid (SF) of dipolar particles is analyzed using a renormalized Flory-Huggins model of equilibrium polymerization. Calculated critical properties (T(c), phi(c), Z(c)) for the SF compare favorably with simulations over a wide range of the dimensionless dipolar (or "sticking") energy mu*. We find that the polymerization transition preempts phase separation for a large mu*, i.e., (mu*)2 >22.     

二元Lennard-Jones液体的相分离过程及其扩散性质的分子动力学研究

采用分子动力学(MD)模拟方法,研究了二元体系中相分离过程、粒子的扩散系数以及相分离域尺寸大小随温度的变化规律.发现,相分离域随温度的生长过程可以分为两个阶段,分别是温度比较高的快速生长阶段和低温时的稳定生长阶段;相分离体系中系统的扩散激活能不是常数,而是一个随温度变化的函数,并且当温度高于60 K时,满足关系式E(T)=a+bT^c.讨论了组元尺寸的变化对相分离过程的影响.结果表明,随两组元中某一组元 关键词： 相分离 扩散 分子动力学模拟     

Interplay of wetting and phase separation at surfaces

We review our understanding of surface-directed spinodal decomposition (SDSD), i.e., the interplay of wetting and phase separation in an unstable AB mixture placed in contact with a wetting surface. In this context, we present results for two problems, viz., SDSD in a semi-infinite geometry with a completely wet surface; and SDSD in a thin-film geometry with partially wet surfaces.     

Phase equilibria in random multiblock copolymers

A mean-field theory for domain structures in random multiblock copolymer melts is developed. We focus on the finite molecular weight effects resulting in a competition between macroscopic phase separation and microdomain formation in the system. We identify an essential parameter N ε controlling the phase behavior of the system, where N is the number of blocks per chain and ε is the composition asymmetry parameter (= the difference between the mean copolymer composition and its critical value). The phase diagram involving N ε and the reduced temperature as variables is obtained. The regions of coexistence of two or more phases are identified. We show that a superstructure formation on cooling is always pre-empted by a macroscopic phase separation of the macroscopically homogeneous (disordered) system yielding two homogeneous phases: H ₀↦H ₁ + H ₂. The third (lamellar) phase separates on further cooling. Then hexagonal and body-centred-cubic phases take over if N ε 1. As the Flory interaction parameter χ increases further, the standard transitions BCC↦HEX↦LAM take place. Received 13 July 2001     

Strongly interacting Fermi gases with density imbalance

We consider density-imbalanced Fermi gases of atoms in the strongly interacting, i.e., unitarity, regime. The Bogoliubov-de Gennes equations for a trapped superfluid are solved. They take into account the finite size of the system, as well as give rise to both phase separation and Fulde-Ferrel-Larkin-Ovchinnikov-type oscillations in the order parameter. We show how radio-frequency spectroscopy reflects the phase separation, and can provide direct evidence of the FFLO-type oscillations via observing the nodes of the order parameter.     

Variable reactivity and phase separation in patchy particle systems

ABSTRACT

Using statistical model, we study mechanisms of phase separation in a solution consisting of patchy particles, which are capable to form directed and saturated thermoreversible bonds. We focus on the impact of variable reactivity of patchy particles on the form of miscibility gap. We show that the variation of model parameters determining features of interparticle interaction makes it possible to obtain miscibility gaps of different types within the unified formalism. In particular, we uncover two different mechanisms of the formation of phase separation curves with lower critical solution temperature. The first mechanism is realised in the case of positive bonding energy; the second one can takes place when the energy of formation of two-bonded particles is lower than that for all other m-bonded ones. We conclude that the most interesting and non-trivial phase behavior is observed in the case of patchy particles with variable reactivity. Using rigorous statistical model, we uncover new mechanisms of phase separation in a solution consisting of patchy particles, which are capable to form directed and saturated thermoreversible bonds. This topic corresponds to state of the art in modern chemical physics. The results obtained shed light on interplay between features of non-isotropic interactions and phase behavior in both molecular and nanoparticle systems. We conclude that the most interesting and non-trivial phase behavior is observed in the case of patchy particles with variable reactivity.     

Multi-soliton complexes in mode-locked fiber lasers

We numerically investigate the formation of soliton pairs (bound states) in mode-locked fiber ring lasers in the normal dispersion domain. In the distributed mathematical model (complex cubic-quintic Ginzburg–Landau equation), we observe a discrete family of soliton pairs with equidistantly increasing peak separation. We show that stabilization of previously unstable bound states can be achieved when the finite relaxation time of the saturable absorber is taken into account. The domain of stability can be controlled by varying this relaxation time. Furthermore, we investigate the parameter domain where the region of stable bound states does not shrink to zero for vanishing absorber recovery time corresponding to a laser with an instantaneous saturable absorber. For a certain domain of the small-signal gain, we obtain a robust first level bound state with almost constant separation where the phase of the two pulses evolves independently. Moreover, their phase difference can evolve either periodically or chaotically depending on the small signal gain. Interestingly, higher level bound states exhibit a fundamentally different dynamics. They represent oscillating solutions with a phase difference alternating between zero and π.     

Adhesion-induced lateral phase separation in membranes

Adhesion between membranes is studied using a phenomenological model, where the inter-membrane distance is coupled to the concentration of sticker molecules on the membranes. The model applies to both adhesion of two flexible membranes and to adhesion of one flexible membrane onto a second membrane supported on a solid substrate. We mainly consider the case where the sticker molecules form bridges and adhere directly to both membranes. The calculated mean-field phase diagrams show an upward shift of the transition temperature indicating that the lateral phase separation in the membrane is enhanced due to the coupling effect. Hence the possibility of adhesion-induced lateral phase separation is predicted. For a particular choice of the parameters, the model exhibits a tricritical behavior. We also discuss the non-monotonous shape of the inter-membrane distance occurring when the lateral phase separation takes place. The inter-membrane distance relaxes to the bulk values with two symmetric overshoots. Adhesion mediated by other types of stickers is also considered. Received 12 January 2000 and Received in final form 15 May 2000     

Reaction-Induced Phase Separation and Structure Formation in Polymer Blends

The peculiarities of reaction-induced phase separation and the structure formation in semi- and full interpenetrating polymer networks and in the blends of linear polymers formed in situ are analyzed. It is shown that for most of these systems phase separation proceeds viathe spinodal decomposition mechanism resulting in the formation of interconnected spatially periodic structures. The possible ways for the structure regulation of the composites produced are considered.     

Theoretical investigation of the phase behaviour of model ternary mixtures containing n-alkanes,perfluoro-n-alkanes,and perfluoroalkylalkane diblock surfactants

We have used the hetero-SAFT-VR approach developed by McCabe and collaborators [Mol. Phys. 104, 571 (2006)] to investigate the phase equilibria of a number of binary and ternary mixtures of n-alkanes, perfluoro-n-alkanes, and perfluoroalkylalkane diblock surfactants. We focused our work on the understanding of the microscopic conditions that control the phase behaviour of these mixtures, with a particular emphasis of the effect on the liquid–liquid separation and the stabilisation of n-alkane + perfluoro-n-alkane mixtures when a diblock surfactant is added. We used very simple molecular models for n-alkanes, and perfluoro-n-alkanes that describe the molecules as chains with tangentially bonded segments with molecular parameters taken from the literature. In the particular case of semifluorinated alkanes or SFA surfactants, we used an hetero-segmented diblock chain model where the parameters for the alkyl and perfluoroalkyl segments taken from the corresponding linear alkanes and perfluoroalkanes, as shown in our previous work [J. Phys. Chem. B 111, 2856 (2007)]. Our goal was to identify the main effects on the phase behaviour when different perfluoroalkylalkane surfactants are added to mixtures of n-alkanes and perfluoro-n-alkanes. We selected the n-heptane + perfluoromethane binary mixture, and studied the changes on the phase behaviour when a symmetric (same number of alkyl and perfluoroalkyl chemical groups) or an asymmetric (different number of alkyl and perfluoroalkyl chemical groups) diblock surfactants is added to the binary mixture. We have obtained the phase diagrams of a wide range of binary and ternary mixtures at different thermodynamic conditions. We have found a variety of interesting behaviours as we modify the alkyl or/and the perfluoroalkyl chain-length of the diblock surfactants: the usual changes in the vapour–liquid phase separation, changes in the type of phase diagrams (typically from type I to type V phase behaviour according to the Scott and Konynenburg classification), azeotropy, and Bancroft points. We noted that the main effect of adding a symmetric or an asymmetric surfactant to the n-heptane + perfluoromethane mixture is to stabilise the system, i.e. to decrease the two-phase (liquid–liquid) immiscibility region of the ternary diagram as the surfactant concentration is increased. This effect becomes larger as the chain length of the surfactant is increased, which is consistent with a higher number of alkyl–alkyl and perfluoroalkyl–perfluoroalkyl favourable interactions in the mixture.     

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.     

Fluctuation conductivity in layered d-wave superconductors near critical disorder

We consider the fluctuation conductivity in the critical region of a disorder induced quantum phase transition in layered d-wave superconductors. We specifically address the fluctuation contribution to the systems conductivity in the limit of large (quasi-two-dimensional system) and small (quasi-three-dimensional system) separation between adjacent layers of the system. Both in-plane and c-axis conductivities were discussed near the point of insulator-superconductor phase transition. The value of the dynamical critical exponent, z = 2, permits a perturbative treatment of this quantum phase transition under the renormalization group approach. We discuss our results for the system conductivities in the critical region as function of temperature and disorder.Received: 10 October 2003, Published online: 23 December 2003PACS: 74.40. + k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.) - 73.43.Nq Quantum phase transitions     

A semiclassical approximation for matrix elements involving non-orthogonal bound states

We analyse the phase diagram of a lattice gas model with both condenseation and order-disorder phase transitions, when the system is confined between two walls. The gas-liquid transition is shifted into the, so called, capillary condensation. The crystallization, both from the gas and from the liquid, is also shifted from the bulk values, but the ordered structure is frustrated or enhanced depending on its commensuration with the walls separation, H. This produces a strong oscillatory dependence of the phase diagram with H.