Phase behavior of attractive and repulsive ramp fluids: integral equation and computer simulation studies

Using computer simulations and a thermodynamically self-consistent integral equation we investigate the phase behavior and thermodynamic anomalies of a fluid composed of spherical particles interacting via a two-scale ramp potential (a hard core plus a repulsive and an attractive ramp) and the corresponding purely repulsive model. Both simulation and integral equation results predict a liquid-liquid demixing when attractive forces are present, in addition to a gas-liquid transition. Furthermore, a fluid-solid transition emerges in the neighborhood of the liquid-liquid transition region, leading to a phase diagram with a somewhat complicated topology. This solidification at moderate densities is also present in the repulsive ramp fluid, but in this case inhibits the fluid-fluid separation.     

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).     

Metal–insulator transition in the Hubbard model on a triangular lattice with disorders: Renormalization group approach

A multistages block renormalization group approach to study the metal–insulator transition in the Hubbard model on a triangular lattice with hexagonal blocks is presented and implemented. A second‐order phase transition with a critical point at U/t = 12.5 is obtained (the coupling parameters U and t correspond to the repulsive charging energy and to the nearest‐neighbor exchange coupling terms, respectively). In the presence of disorder the phase diagram for the system exhibits a metallic phase, an insulating phase, and a domain‐localized phase that separates them in the Mott regime. The subtle influence of electron–electron interactions upon inverse participation rate in the Anderson regime is also investigated. The results are discussed in light of experimental evidence for arrays of metalic quantum dots and exact numerical diagonalization of the Hubbard Hamiltonian. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 360–374, 2003     

Recent study on counterion-mediated attraction between colloidal particles

Recent experimental results were reviewed. The 1D- and 2D-USAXS studies gave higher orders of Bragg diffraction for single crystals of colloidal silica particles, allowing more accurate determinations of the lattice constant, lattice symmetry, and direction. The closest interparticle spacing thus determined was confirmed to be smaller than the average spacing. The most closely packed planes ((110) planes for bcc) of negatively charged particles were found to be parallel to the likewise negatively charged capillary surface, inconsistently with the accepted double layer interaction theory but consistently with a recent experimental finding of positive adsorption. Shaking caused disruption of the single crystals but newly formed microcrystals retained the lattice constant and the preference of the (110) planes. The liquid-solid-liquid transition, a re-entrant phase transition, was found for silica particles and latex particles at given particle volume fraction and salt concentration, when the charge density of particles was varied. It was demonstrated that the purely repulsive Yukawa potential and the concept of renormalized charge cannot account for the re-entrant behavior. The Monte-Carlo simulation using the Sogami potential, which contains short-range repulsion and long-range attraction, was found to account for the fcc–bcc transition, which was earlier claimed to be explainable only by the Yukawa potential. Furthermore, the homogeneous-inhomogeneous phase transition and void formation could be accounted for by the simulation using the Sogami potential; the Yukawa potential could not reproduce the experiments. Attention was drawn to the experimental conditions in direct measurements of interparticle forces; only short interparticle distance and low charge density particles were covered, which make it practically impossible to detect the long-range counterion-mediated attraction. It is hoped that, by technical improvements, these shortcomings may be made up and quantitative argument become possible on the attraction.     

Adsorption behavior of repulsive molecules

Recently, it has been shown that adsorption of gases on solid surfaces often leads to repulsive forces between adsorbate molecules. In this paper, adsorption of molecules on a one-dimensional lattice is considered for repulsive interactions between adsorbate molecules. Exact adsorption isotherms are calculated and analyzed for finite and infinite chains of active sites (i.e., a one-dimensional lattice). Although the mathematical solution for the one-dimensional lattice is known for attractive and repulsive systems, the effects of intermolecular repulsions on adsorption behavior have not been studied in detail previously. Similarly, though the mathematics for the one-dimensional lattice has been solved for any arbitrary lattice length, the effect of finite size on adsorption isotherms for repulsive adsorbate interactions has never been examined. This paper shows that spatial confinement and strong attraction to active sites can cause compression of an adsorbed phase and that repulsive interactions between adsorbed molecules result in steps in the adsorption isotherms. For higher chemical potentials, the density increases until saturating at the lattice capacity. These steps in the adsorption isotherm have not been observed in previous studies of lattice systems. For small lattices, the adsorption behavior was found to be fundamentally different for even and odd values of lattice length. Lattices with an even number of lattice sites can have two steps in the adsorption isotherm, whereas systems with an odd number of sites only have a single step occurring at a coverage slightly greater than half the lattice capacity.     

蔗糖对MO/水立方液晶体系流变性质的影响

主要研究了蔗糖对甘油单油酸脂(monoolein, MO)/水立方液晶体系的流变学性质及其相行为的影响. 根据体系流变性质的变化和偏光显微镜照片, 得出随着蔗糖含量的增加, MO/水体系发生了由反相立方液晶到反相六角状液晶的相转变. 蔗糖与MO分子通过氢键相互作用, 减弱了两亲分子间的静电斥力. 当蔗糖含量增加到一临界值时, 体系的立方结构被破坏, 继续增加蔗糖的含量, 体系就会形成新的反相六角状液晶.     

Orientational phase transitions in solid deuterium bromide

Phase transition temperatures for solid deuterium bromide are calculated in the effective field approximation. The crystal structure is treated as a two-dimensional lattice of zig-zag chains of DBr molecules. Dipole—dipole and quadrupole-quadrupole interactions are included up to second neighbors, in addition, a repulsive field is introduced to fit the upper transition temperature.     

Structure of single and double stranded dna solutions as studied by ultracentrifugation

The osmotic pressure of dense solutions of DNA fragments in aqueous 0.2-2 M salt (NaCl, etc.) solutions were easily obtained from equilibrium ultracentrifugation data. Short, helical double stranded DNA fragment solutions showed a well defined ordering transition. The osmotic pressure of these helical solutions could be explained by the scaled particle theory of rigid sphero-cylinders. On the other hand, dense solutions of (single stranded) etheno-DNA derivatives (of about 100 nucleotides) showed no ordering phase transition. The osmotic pressure as a function of the ε-DNA concentration verifies a scaling prediction for random coils in the semi-dilute regime. Good fits to the reduced osmotic pressure are obtained by using the Kleintjens and Koningsveld modified mean field lattice gas equations of state. As inferred from the Zimm clustering function, essentially all intermolecular interactions at high ionic strength are purely repulsive.     

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.     

Clustering in the absence of attractions: density functional theory and computer simulations

We numerically investigate the formation of stable clusters of overlapping particles in certain systems interacting via purely repulsive, bounded pair potentials. In close vicinity of a first-order phase transition between a disordered and an ordered structure, clusters are encountered already in the fluid phase which then freeze into crystals with multiply occupied lattice sites. These hyper-crystals are characterized by a number of remarkable features that are in clear contradiction to our experience with harshly repulsive systems: upon compression, the lattice constant remains invariant, leading to a concomitant linear growth in the cluster population with density; further, the freezing and melting lines are to high accuracy linear in the density-temperature plane, and the conventional indicator that announces freezing, that is, the Hansen-Verlet value of the first peak of the structure factor, attains for these soft systems much higher values than for their hard-matter counterparts. Our investigations are based on the generalized exponential model of index 4 (i.e., Phi(r) approximately exp[-(r/sigma)4]). The properties of the phases involved are calculated via liquid state theory and classical density functional theory. Monte Carlo simulations for selected states confirm the theoretical results for the structural and thermodynamic properties of the system. These numerical data, in turn, fully corroborate an approximate theoretical framework that was recently put forward to explain the clustering phenomenon for systems of this kind (Likos, C. N.; Mladek, B. M.; Gottwald, D.; Kahl, G. J. Chem. Phys. 2007, 126, 224502).     

Solvent mediated interactions close to fluid-fluid phase separation: microscopic treatment of bridging in a soft-core fluid

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation, and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed "wetting" film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a "bridging" transition as the wetting films join to form a fluid bridge. The effective (solvent mediated) potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a nonzero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein-Zernike equations.     

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.     

Monte Carlo simulations of two-dimensional hard core lattice gases

Monte Carlo simulations are used to study lattice gases of particles with extended hard cores on a two-dimensional square lattice. Exclusions of one and up to five nearest neighbors (NN) are considered. These can be mapped onto hard squares of varying side length, lambda (in lattice units), tilted by some angle with respect to the original lattice. In agreement with earlier studies, the 1NN exclusion undergoes a continuous order-disorder transition in the Ising universality class. Surprisingly, we find that the lattice gas with exclusions of up to second nearest neighbors (2NN) also undergoes a continuous phase transition in the Ising universality class, while the Landau-Lifshitz theory predicts that this transition should be in the universality class of the XY model with cubic anisotropy. The lattice gas of 3NN exclusions is found to undergo a discontinuous order-disorder transition, in agreement with the earlier transfer matrix calculations and the Landau-Lifshitz theory. On the other hand, the gas of 4NN exclusions once again exhibits a continuous phase transition in the Ising universality class-contradicting the predictions of the Landau-Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase transition.     

Particle Monte Carlo simulation of string-like colloidal assembly in two and three dimensions

We simulate structural phase behavior of polymer-grafted colloidal particles by molecular Monte Carlo technique. The interparticle potential, which has a finite repulsive square-step outside a rigid core of the colloid, was previously confirmed via numerical self-consistent field calculation. This model potential is purely repulsive. We simulate these model colloids in the canonical ensemble in two and three dimensions and find that these particles containing no interparticle attraction self-assemble and align in a string-like assembly, at low temperature and high density. This string-like colloidal assembly is related to percolation phenomena. Analyzing the cluster size distribution and the average string length, we build phase diagrams and discover that the average string length diverges around the region where the melting transition line and the percolation transition line cross. This result is similar to Ising spin systems, in which the percolation transition line and the order-disorder line meet at a critical point.     

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.     

Phase behavior of linear heterogeneous trimers on a square lattice

Monte Carlo simulations in the grand canonical ensemble, the multiple-histogram analysis and finite-size scaling techniques have been used to study a phase behavior of trimer BAB on a square lattice. The systems with the same energies u(AA) = u(BB) and different strengths of interactions between unlike segments are considered. The AB-contacts are energetically unprofitable. There are two phase transitions: the first-order vapor-liquid transition and the second-order structural transition in the supercritical fluid. The phase diagram topology depends on the energy u(AB). The crossover between the tricritical point phase diagram topology and the critical end phase diagram topology is found. It is demonstrated that the transition to the ordered strip-like phase is non-universal.     

Liquid polymorphism and density anomaly in a three-dimensional associating lattice gas

The authors investigate the phase diagram of a three-dimensional associating lattice gas (ALG) model. This model combines orientational icelike interactions and "van der Waals" that might be repulsive, representing, in this case, a penalty for distortion of hydrogen bonds. These interactions can be interpreted as two competing distances, making the connection between this model and continuous isotropic soft-core potentials. The authors present Monte Carlo studies of the ALG model showing the presence of two liquid phases, two critical points, and density anomaly.     

Large attractive depletion interactions in soft repulsive-sphere binary mixtures

We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.     

Melting behavior of an idealized membrane model

The melting behavior of an idealized model giving rise to two-dimensional (2D) structures at low temperature and low density is investigated by Monte Carlo simulations. The system is made of particles carrying a spin of constant length and variable orientation, whose potential energy is the sum of a repulsive spherical pair interaction, and of a spin-spin contribution, reminiscent of but essentially different from the electrostatic dipole-dipole interaction. The simulation results show that the model phase diagram is determined by the interplay of a ferro- to paraelectric transition in the spin part and of the solid to fluid transition found in simple pair-potential models. The 2D solid melts into a three-dimensional (3D) fluid when the spin-spin interaction is weak. Strong spin-spin interactions give rise to two transitions, the first one corresponding to the melting of the 2D solid into a 2D fluid, and the second one corresponding to the crossover from a 2D to a 3D fluid. The fluid phase stable in between these two transitions provides a model for the liquid state arising in organic and biological membranes across their main transition.     

Orientational phase transition in a charge-transfer crystal: Triplet excitons as probes for lattice dynamics

The orientational phase transition in the charge-transfer (CT) crystal anthracene-TCNB (s-tetracyanobenze) is investigated by ESR and by Raman spectroscopy. ESR spectra of triplet excitons are observed and analysed with respect to orientational changes during the transition between two different phases. The data yield the mean molecular orientations fx (relative to a crystal fixed axis) as a function of temperature. Besides a gradual orientational change with temperature there is also an abrupt change (Δ fx ≈ 5° within 1 K) at the transition temperature suggesting a first order phase transition. A model is presented that uses exciton dynamics as a probe for lattice dynamics. The size of domains of equally oriented molecules is obtained as a function of temperature. The phase transition is also detected from the appearance of different phonon lines in the Raman spectra. These spectra gain their special value from a comparison with the behaviour of an order parameter fx, characterizing the phase transition.