Free energy studies of freezing in slit pores: an order-parameter approach using Monte Carlo simulation

We report a molecular simulation study of freezing transitions for simple fluids in narrow slit pores. A major stumbling block in previous studies of freezing in pores has been the lack of any method for calculating the free energy difference between the confined solid and liquid phases. Conventional thermodynamic integration methods often fail for confined systems, due to the difficulty in choosing a suitable path of integration. We use a different approach that involves calculating the Landau free energy as a function of a suitable order parameter, using the grand canonical Monte Carlo simulation method. The grand free energy for each phase can then be obtained by one-dimensional integration of the Landau free energy over the order parameter. These calculations are carried out for two types of wall—fluid interaction, a hard wall and a strongly attractive wall modelled on carbon. The grand free energy results for both cases clearly indicate a first order fluid to solid transition. In the case of the attractive carbon wall, there are three phases. Phase A corresponds to all layers having a liquid-like structure; phase B corresponds to the contact layers (the layers adjacent to the two pore walls) being frozen and the rest of the layers being fluid-like; phase C corresponds to all the layers being frozen. Our results for the angular structure function in the individual molecular layers show strong evidence of a transition from a two-dimensional liquid phase to a hexatic phase. This is followed by a transition from the hexatic to a crystal phase.     

Phase transitions between orthogonal and tilted hexatic phases

Tilt-driven phase transitions between hexatic smectic phases: SmF-HexB and reversed HexB-SmF have been studied in compounds belonging to two enaminoketone derivative homologue series. The tilt angle order parameter has been measured and its temperature dependence near the phase transition point has been described by applying mean-field model. For both phase sequences the tricritical points have been observed on phase transition lines in binary mixtures of respective materials having first and second order phase transitions between hexatic phases. Received 21 June 1999     

Melting in two dimensions—the current status

The current status of the controversy relating to melting in two dimensions is surveyed. To begin with, a review is given of the seminal work of Kosterlitz and Thouless. This is followed by a discussion of the modifications introduced by Nelson and Halperin. The search for the continuous transitions and the intermediate hexatic phase predicted by these theories is then described, covering both the laboratory as well as simulation experiments. Alternate viewpoints to thekt theory aired recently in the literature are also briefly examined. The paper concludes with an outlook for the future. Jawaharlal Nehru Fellow     

Two-step melting in two dimensions: first-order liquid-hexatic transition

Melting in two spatial dimensions, as realized in thin films or at interfaces, represents one of the most fascinating phase transitions in nature, but it remains poorly understood. Even for the fundamental hard-disk model, the melting mechanism has not been agreed upon after 50 years of studies. A recent Monte?Carlo algorithm allows us to thermalize systems large enough to access the thermodynamic regime. We show that melting in hard disks proceeds in two steps with a liquid phase, a hexatic phase, and a solid. The hexatic-solid transition is continuous while, surprisingly, the liquid-hexatic transition is of first order. This melting scenario solves one of the fundamental statistical-physics models, which is at the root of a large body of theoretical, computational, and experimental research.     

Cooperative dynamics in two dimensions

We report results from molecular dynamics simulations of cooperative motion in a quasi-two-dimensional system of colloid particles. We find that the onset of the deviation of the single-particle displacement distribution from Gaussian form starts in the liquid phase and extends, with increasing magnitude, through the hexatic phase into the crystalline phase. The time for which the deviation is maximum increases exponentially with the density. As the density increases toward the hexatic phase a third dynamical relaxation mode emerges. We argue that the collective motion is generated by superpositions of instantaneous normal mode vibrations, with lifetimes that increase with the density, along paths with strong bond-orientation correlation.     

Melting transition of a network model in two dimensions

The freezing transition of a network model for tensionless membranes confined to two dimensions is investigated by Monte Carlo simulations and scaling arguments. In this model, a freezing transition is induced by reducing the tether length. Translational and bond-orientational order parameters and elastic constants are determined as a function of the tether length. A finite-size scaling analysis is used to show that the crystal melts via successive dislocation and disclination unbinding transitions, in qualitative agreement with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young theory. The hexatic phase is found to be stable over only a very small interval of tether lengths. Received 4 June 1999 and Revised in final form 1 September 1999     

Refusing to twist: demonstration of a line hexatic phase in DNA liquid crystals

We report conclusive high resolution small angle x-ray scattering evidence that long DNA fragments form an untwisted line hexatic phase between the cholesteric and the crystalline phases. The line hexatic phase is a liquid-crystalline phase with long-range hexagonal bond-orientational order, long-range nematic order, but liquidlike, i.e., short-range, positional order. So far, it has not been seen in any other three dimensional system. By line-shape analysis of x-ray scattering data we found that positional order decreases when the line hexatic phase is compressed. We suggest that such anomalous behavior is a result of the chiral nature of DNA molecules.     

Thermodynamics and phase transitions in two-dimensional Yukawa systems

The results of numerical simulations of strongly-coupled two-dimensional dissipative Yukawa systems are presented. The thermodynamic characteristics of these systems were studied, namely the internal energy, the specific heat and the entropy. For the first time, it is discovered that the considered characteristics have two singular points on the melting line; one of these points corresponds to the first-order phase transition from crystal to the hexatic phase, and another point corresponds to the second-order phase transition from the hexatic phase to the isotropic liquid. The obtained results are compared to the existing numerical and analytical data.     

Spurious character of singularities associated with phase transitions in cylindrical pores

Phase transitions of simple fluids and binary fluid mixtures confined into long cylindrical pores are re-examined, such as capillary condensation/evaporation and wetting transitions. While a large part of the literature ignores the fact that due to the quasi-one-dimensional character of these systems a singular behavior associated with a sharp phase transition cannot occur, we pay attention to the extent in which these phase transitions are smoothed out (in relation to the magnitude of the pore cross-sectional area). We argue that the finiteness of the pore length is an important parameter which controls the physical phenomena that are observed in simulations (and presumably also experiments explaining the distinction between the apparent “pore critical temperature” and the “hysteresis critical temperature”). We illustrate our arguments with recent findings from simulations of a lattice gas/Ising system and of the Asakura-Oosawa model of colloid-polymer mixtures.     

Acoustic study of melting and freezing of mercury nanoparticles in porous glasses

The processes of melting and freezing of small mercury particles embedded in porous glasses with nanometric pore sizes are studied by an ultrasonic method for various values of the pore filling factor. The filling factor is found to have a threshold, below which the acoustic anomalies accompanying phase transitions change their character. The critical radius of mercury nanoparticles that corresponds to the zero melting temperature is estimated.     

Highly ordered hexatic phases with large spontaneous polarization

In this article the physical properties of hexatic phases of three substances MHPNBC, FOOPP and FNHPP have been studied by differential scanning calorimetry, texture observation and dielectric spectroscopy. Experimental results are discussed from the point of view of existing theories. It is interesting that two of the substances studied, the FOOPP and FNHPP, exhibit enhanced spontaneous polarization in the highly ordered SmI* phase and show a jump of the spontaneous polarization in the vicinity of the SmC*–SmI* transition. In the SmI* phase of FOOPP a very high value of spontaneous polarization of the order of 530?nC?cm^?2 was found. Based on the results obtained the macroscopic and microscopic properties of the hexatic phases are discussed.     

Behavior of the layer compression elastic modulus near,above, and below a smectic C–hexatic I critical point in binary mixtures

We present the first study of the layer compression modulus B carried out near, above and below the Smectic C–Hexatic I critical point in racemic mixtures of methylbutyl phenyl octylbiphenyl-carboxylate (8SI) and the octyloxy biphenyl analog (8OSI), at frequencies ranging from 0.2 Hz to 2 ×103 Hz. The behavior of B as a function of temperature shows a progressive evolution from a first order transition in 8SI to a continuous supercritical behavior in 8OSI. The latter is characterized by an increase in B, which appears above the transition, and which is followed by a leveling off when the temperature is decreased towards the transition. It is proposed that this behavior stems from the relaxation of the hexatic domains which are frozen in the frequency range studied. For the supercritical and near-critical compounds, B exhibits a small dip near the transition temperature, which is visible in the low frequency range only, indicating that the dynamics associated with the critical point is very slow. We also report measurements in the Crystal-J phase of the pure compounds, and show that 8SI behaves mechanically as a hexatic phase and 8OSI as a soft crystal phase.     

相变过程的格子Boltzmann方法模拟

应用Shan提出的伪势多相模型替代R-K着色模型,建立一种新的描述气液相变过程的格子Boltzmann理论模型,模拟蒸发(高密度转化为低密度)过程.改进了计算效率,且得到较好的计算结果.同时应用该模型从孔隙尺度模拟了多孔介质中的相变现象,验证了该模型模拟复杂相变问题的可行性.     

Observation of a hexatic columnar liquid crystal of polydisperse colloidal disks

We report the observation of a new type of columnar liquid crystal phase, which is formed by thin hard colloidal disks in a dense suspension. High-resolution small-angle x-ray diffraction reveals a combination of long-range bond-orientational order and short-range translational order between the columns, the hallmark of the hexatic phase. Our results imply that geometric frustration related to the size polydispersity of the particles destroys long-range translational order and therefore promotes the formation of this novel phase.     

似生物膜系统之六角液相

首度在二维溶致型层状液晶系统中，发现了液相与固相之间存在一“六角方向性”的新状态．这个状态显示了的六角长程有序与似液相的位置相关连特性之特征，而与熟知的二维融化理论所预期的现象有显著的差异．     

New hexatic liquid phase observed in lyotropic thin films

An intermediate surface hexatic phase between the liquid and the crystalline phases has been found for the first time in a lyotropic lamellar liquid-crystal system. This phase is highly unusual in that it has long-range sixfold bond-orientational order but liquidlike nearest-neighbor positional correlations, and could represent a significant departure from our current understanding of defect-mediated melting in two dimensions.     

Ordering in two dimensions: Optical textures in monolayers

Summary Optical studies of Langmuir monolayers of simple amphiphiles such as fatty acids and esters by polarized fluorescence microscopy and Brewster-angle microscopy reveal a large variety of textures including stripes, stars, and spirals that closely resemble textures observed in liquid crystals. The textures represent large-scale (>10 μm) spontaneous organization of the molecular tilt azimuth. Phase transitions within the monolayer can be directly observed by marked changes in texture, revealing a complex phase diagram. Many of the textures can be explained by a Landau-deGennes theory of tilted hexatic phases that takes into account the broken-symmetry characteristic of amphiphiles at an interface. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Capillary smectization and layering in a confined liquid crystal

Using density-functional theory, we have analyzed the phase behavior of a model liquid crystal confined between two parallel, planar surfaces (i.e., the so-called slit pore). As a result of confinement, a rich phase behavior arises. The complete liquid-crystal phase diagram of the confined fluid is mapped out as a function of wall separation and chemical potential. Strong commensuration effects in the film with respect to wall separation lead to enhanced smectic ordering, which gives capillary smectization (i.e., formation of a smectic phase in the pore), or frustrated smectic ordering, which suppresses capillary smectization. These effects also produce layering transitions. Our nonlocal density-functional-based analysis provides a unified picture of all the above phenomena.     

Boundary effects in chiral polymer hexatics

Boundary effects in liquid-crystalline phases can be large due to long-ranged orientational correlations. We show that the chiral-hexatic phase can be locked into an apparent three-dimensional N+6 phase via such effects. Simple numerical estimates suggest that the recently discovered "polymer hexatic" may actually be this locked phase.