The phase behaviour of a fluid in a slitlike pore with permeable walls

The confinement of a lattice fluid in a set of slitlike pores separated by semipermeable walls with a finite width has been studied. The walls are modelled by a square-well repulsive potential with a finite height. The thermodynamic properties and the phase behaviour of the system are evaluated by means of Monte Carlo simulations. For some states theoretical calculations have been made using a mean-field-type theory. These investigations confirm previous findings for confined Lennard-Jones fluids, obtained from a density functional approach. For intermediate and low potential barriers that separate the pores, the isotherms exhibit two hysteresis loops and the liquid-vapour coexistence curve divides into two branches describing condensation inside the pore and inside the permeable wall. These two branches are separated by a triple point. At temperatures lower than the triple point temperature, the condensation takes place instantaneously in both the pore and inside the permeable wall. It was found that when the temperature is scaled by the bulk critical temperature, the phase diagram emerging from this simple mean-field treatment is close to the phase diagram obtained from simulation.     

Structure and phase transitions in a network-forming associating Lennard-Jones fluid in a slit-like pore: a density functional approach

A study is reported of adsorption of an associating Lennard-Jones fluid with four associative sites per molecule in a slit-like pore. The density distribution of particles in the pore and thermodynamics properties are evaluated by using a density functional method. It is found that at low temperatures the fluid exhibits a set of layering transitions, followed by capillary condensation. Transitions are localized by analysing the grand canonical potential. The density profiles of particles and the distribution of unbound and differently bonded particles demonstrate changes in the structure of the fluid in the pore along the phase coexistence. The critical temperature is lower for a confined fluid, compared with the bulk counterpart. However, an increase in the energy of association increases the critical temperature. The envelope of the capillary condensation is narrower than the bulk liquid-vapour phase diagram. The dependence of the solvation force on the energy of association and on the bulk density is discussed.     

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.     

Freezing and melting of binary mixtures confined in a nanopore

This paper reports on a Grand Canonical Monte Carlo study of the freezing and melting of Lennard–Jones Ar/Kr mixtures confined in a slit pore composed of two strongly attractive structureless walls. For all molar compositions and temperatures, the pore, which has a width of 1.44?nm, accommodates two contact layers and one inner layer. Different wall/fluid interactions are considered, corresponding to pore walls that have a larger affinity for either Ar or Kr. The solid/liquid phase diagram of the confined mixture is determined and results compared with data for the bulk mixture. The structure of the confined mixture is studied using 2D order parameters and both positional g(r) and bond orientational G₆(r) pair correlation functions. It is found that in the confined solid phase, both the contact and inner layers have a hexagonal crystal structure. It is shown that the freezing temperature of the Ar/Kr confined mixture is higher than the bulk freezing point for all molar compositions. Also, it is found that the freezing temperature becomes larger as the ratio α of the wall/fluid to the fluid/fluid interactions increases, in agreement with previous simulation studies on pure substances confined in nanopores. In the case of pore walls having a stronger affinity for Kr atoms (ε _Ar/W<ε _Kr/W), it is observed that both the contact and inner layers of the confined mixture undergo, at the same temperature, a transition from the liquid phase to the crystal phase. The freezing of Ar/Kr mixtures confined between the walls having a stronger affinity for Ar (ε _Ar/W?>?ε _Kr/W) is more complex: for Kr molar concentration lower than 0.35, we observe the presence of an intermediate state between all layers being 2D hexagonal crystals and all the layers being liquid. This intermediate state consists of a crystalline contact layer and a liquid-like inner layer. It is also shown that the qualitative variations of the increase of freezing temperature with the molar composition depend on the affinity of the pore wall for the different components. These results confirm that, in addition to the parameter α the ratio of the wall/fluid interactions for the two species, η=?_Ar/W/?_Kr/W, is a key variable in determining the freezing and melting behaviour of the confined mixture.     

Phase behaviors in binary mixture of diblock copolymers confined between two parallel walls

The phase behaviors in binary mixture of diblock copolymers confined between two parallel walls are investigated by using cell dynamics simulation of the time-dependent Ginzburg-Landau theory. The morphological dependence of the wall-block interaction and the distance between walls (confinement degree) has been systematically studied, and the effect of repulsive interactions between different monomers is also discussed. It is interesting that multiple novel morphological transitions are observed by changing these factors, and various multilayered sandwich structures are formed in the mixture. Furthermore, the parametric dependence and physical reasons for the microdomain growth and orientational order transitions are discussed. From the simulation, we find that much richer morphologies can form in binary mixture of diblock copolymers than those in pure diblock copolymer. Our results provide an insight into the phase behaviors under parallel walls confinement and may provide guidance for experimentalists. This model system can also give a simple way to realize orientational order transition in soft materials through confinement.     

Stress anisotropy in liquid crystalline phases

Monte Carlo simulations of bulk liquid crystals in the isotropic, nematic and smectic phases were performed. The simulations were carried out using different box shapes. The diagonal components of the pressure tensor were calculated to verify that the system is in mechanical equilibrium. For simulations in cubic boxes it was found that the three components of the pressure tensor had the same values in the isotropic and nematic phases but they were different in the smectic phase, i.e. the system seemed to be under anisotropic stress. NVT and NPT simulations in the smectic phase were performed by allowing the box sides to fluctuate independently; in this case, the average diagonal components of the pressure tensor had the same value. Inaccurate calculation of the total pressure produces incorrect equilibrium boundaries in the phase diagram. Microphases and poorly defined layering can be found in simulations of smectic phases when they are performed on cubic boxes. Although the pressure anisotropy is relaxed out, the layering structure in smectic phases seems to depend on the initial configuration, regardless of the simulation method.     

Phase behaviors in a binary mixture of diblock copolymers confined between two parallel walls

The phase behaviors in a binary mixture of diblock copolymers confined between two parallel walls are investigated by using a cell dynamics simulation of the time-dependent Ginzburg-Landau theory.The morphological dependence of the wall-block interaction and the distance between walls(confinement degree) has been systematically studied,and the effect of repulsive interactions between different monomers is also discussed.It is interesting that multiple novel morphological transitions are observed by changing these factors,and various multilayered sandwich structures are formed in the mixture.Furthermore,the parametric dependence and physical reasons for the microdomain growth and orientational order transitions are discussed.From the simulation,we find that much richer morphologies can form in a binary mixture of diblock copolymers than those in a pure diblock copolymer.Our results provide an insight into the phase behaviors under parallel wall confinement and may provide guidance for experimentalists.This model system can also give a simple way to realize orientational order transition in soft materials through confinement.     

Capillary freezing or complete wetting of hard spheres in a planar hard slit?

Extensive simulations of a hard sphere fluid confined between two planar hard walls show the onset of crystalline layers at the walls at about 98.3% of bulk crystallization density rho(f) independent of the wall separations L(z), and is, hence, a single wall phenomenon. As the bulk density far from the wall rho(b) increases, the thickness of the crystalline film appears to increase logarithmically, with (rho(f)-rho(b)) indicating complete wetting by the hard sphere crystal of the wall-fluid interface. Increasing rho(b) further, we observe a jump in the adsorption which depends on L(z) and corresponds to capillary freezing. The formation of crystalline layers below bulk crystallization, the logarithmic growth of the crystalline film, its independence of L(z), and its clear distinction from capillary freezing lend strong evidence for complete wetting by the hard sphere crystal at the wall-fluid interface.     

Hexatic ordering in freely suspended liquid crystal films

In this paper, we report results from synchrotron X-ray scattering studies of thefluid/hexactic/solid phases and phase transitions in both very thick and very thin, freely suspended films of tilted hexatic liquid crystals. Contrary to the thick film case, the higher Fourier coefficients describing the bond orientational order are suppressed in very thin films. This suppression is consistent with a two-dimensional bond orientational order parameter, ₆, rather than the three-dimensional bond orientational order parameter found in very thick films. For a film containing twently-three (23) smectic layers we find that ₆ is two-dimensional whereas the positional order in the crystallineS _J phase is three-dimensional. We present an analysis of the thick film data in terms of the three-dimensionalXY-model and a new mean field theory model which incorporates explicitly the quasi two-dimensional nature of bulk smectic phases.     

Phase behaviour of a Lennard-Jones fluid in a pore with permeable walls of a finite thickness: a density functional approach

A confinement of a Lennard-Jones fluid in a system of slitlike pores separated by semipermeable walls of a finite width is studied. The walls are modelled by square-well repulsive potential wells. The structure of the confined fluid is investigated by means of a density functional method. For high potential barriers separating the pores, the phase behaviour of the system is similar to that for a single slitlike pore with impenetrable walls. For intermediate and low potential barriers the system shows different phase behaviour. Within some temperature range the isotherms exhibit two hysteresis loops, which characterize the condensation of the fluid in different parts of the system, namely in the pore and inside the semipermeable walls. The systems characterized by low and intermediate potential barriers exhibit the triple point, such that at temperatures below that triple point the condensation instantaneously takes place in both the pore and inside the permeable wall.     

Phase transition and some physical properties of binary mixtures of two nematogenic compounds showing induced smectic phase

The binary mixtures of nematogenic compounds 4-n-pentyl phenyl 4-n′-hexyloxy benzoate (ME6O.5) and 4-cyanophenyl 4-pentyl benzoate (CPPB) show the presence of induced smectic phase. In this article, we report the phase diagram and the results of refractive index, density, static dielectric permittivity and X-ray diffraction measurements of different binary mixtures of (ME6O.5?+?CPPB) throughout the entire composition range. The density and refractive index values have been analysed to obtain orientational order parameters. The various physical properties of the system have been discussed on the basis of the phase diagram.     

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.     

Spectral investigations of surface ordering in ultrathin molecular films

Surface molecular ordering in ultrathin molecular films is investigated. The optical transmission spectra of molecular films ranging in thickness from 2 to 13 smectic layers (6.7–43 nm) in the region of the electronic absorption bands in the smectic A phase of cyanobiphenyl CB9 are measured. The thickness and temperature dependences of the permittivity are determined. It is found that the orientational ordering of the molecules depends on the film thickness. The penetration depth of the surface molecular orientational order does not exceed two smectic layers (<7 nm). Zh. éksp. Teor. Fiz. 115, 1833–1842 (May 1999)     

Grand canonical Monte Carlo simulations of phase equilibria of pure silicon tetrachloride and its binary mixture with carbon dioxide

Grand canonical histogram-reweighting Monte Carlo simulations were used to obtain the phase behaviour of pure silicon tetrachloride and its binary mixture with carbon dioxide. Two new potential models for pure silicon tetrachloride were developed and parametrized to the vapour-liquid coexistence properties. The first model, with one exponential-6 site and fixed electrostatic charges on atoms, does not adequately reproduce the experimental phase behaviour due to its inability to represent orientational anisotropy in the liquid phase. The second potential model, with five exponential-6 sites for the repulsive and dispersive interactions plus partial charges, accurately reproduces experimental saturated liquid and vapour densities as well as vapour pressures and the second virial coefficient for pure silicon tetrachloride. This model was used in simulations of the phase behaviour of the binary mixture carbon dioxide-silicon tetrachloride. Two sets of combining rules (Lorentz-Berthelot and Kong [1973, J. chem. Phys., 59, 2464]) were used to obtain unlike-pair potential parameters. For the binary system, the predicted phase diagram is in good agreement with experiment when the Kong combining rules are used. The Lorentz-Berthelot rules significantly overestimate the solubility of carbon dioxide in silicon tetrachloride.     

Nanorings in planar confinement: the role of repulsive surfaces on the formation of lacuna smectics

ABSTRACT

We study the structure and liquid-crystalline phase behaviour of a model of confined non-convex circular soft-repulsive nanorings in a planar slit geometry using molecular-dynamics simulation. The separation distance between the structureless parallel soft-repulsive walls is made large enough to allow for the formation of a distinct bulk phase in the central region of the box which is in coexistence with the adsorbed fluid thus allowing the analysis of single-wall effects. As the density of the particles is increased, the fluid adsorbs (wets) onto the planar surfaces leading to the formation of well-defined smectic-A layers with a spacing proportional to the diameter of the rings. An analysis of the nematic order parameter at distances perpendicular to the surface reveals that the particles in each layer exhibit anti-nematic behaviour and planar (edge-on) anchoring relative to the short symmetry axis of the rings. This behaviour is in stark contrast to the behaviour observed in convex disc-like particles that have the tendency to form nematic (discotic) structures with homeotropic (face-on) anchoring. The smectic phases formed by nanorings in the bulk and under confinement are characterised by the formation of low-density layered liquid-crystalline states with large voids, referred to here as lacuna smectic phases. In contrast to what is typically found for confined liquid-crystalline systems involving convex particles, no apparent biaxiality is found for nanorings in planar confinement. We argue that formation of the low-density lacuna smectic layers with planar anchoring is a consequence of the non-convex shape of the circular rings that allow for interpenetration between the particles as observed for nanorings under bulk conditions [C. Avendaño, G. Jackson, E.A. Müller and F.A. Escobedo, Proc. Natl. Acad. Sci. U.S.A. 113, 9699 (2016); H.H. Wensink and C. Avendaño, Phys. Rev. E 94, 062704 (2016)].     

Phase equilibra in binary Lennard-Jones mixtures: phase diagram simulation

A three-box version of the Gibbs ensemble Monte Carlo method was used to determine the phase diagram type of several binary mixtures of one-centre Lennard-Jones particles. The method can be used to establish a direct link between the intermolecular potential modelling the interactions in a given system and its fluid phase diagram, without the knowledge of the corresponding equation of state governing its ρVT behaviour. As an example of the application of the method, closed-loop behaviour in an isotropic system could be found using a set of Lennard-Jones parameters exhibiting a cross-interaction diameter with a negative deviation from the Lorentz—Berthelot combination rule.     

A molecular dynamics study of carbon dioxide in water: diffusion,structure and thermodynamics

Atomistic simulations are reported of a model of CO₂ in water. CO₂ is modelled by partial charges and Lennard-Jones interaction sites on each atom; the SPC/E model for water is used. Good agreement with experiment is found for the translational diffusion constants. The variation of the dynamics with the potential parameter was investigated. As expected, the orientational correlation times increase as the magnitude of the quadrupole moment is increased, but the translational diffusion constants are found to be surprisingly insensitive to the magnitude of the CO₂ quadrupole moment. The translational friction coefficient was resolved into electrostatic, Lennard-Jones and cross-terms; the Lennard-Jones contribution is found to be the largest. Varying the Lennard-Jones size parameter affects both translational and reorientational motion. In order to try to understand these results further, the variation of solvation free energy was investigated and the solvent structure around carbon dioxide was examined as the electrostatic and Lennard-Jones parameters were changed. The temperature dependence of the self-diffusion constant of pure SPC/E water was determined.     

Langevin dynamics simulations of phase separation in a one-component system

Langevin dynamics computer simulations have been performed for a two-dimensional Lennard-Jones fluid quenched into the coexistence region of its liquid-vapor phase diagram. For late stages of the phase-separation process, the average radius of the liquid clusters is found to grow proportional to (time)^1/4. This growth law is analyzed theoretically and compared to recent molecular dynamics and Monte Carlo results. Details of the different simulation methods are critically discussed.     

Influence of pressure on the electric-field-induced phase transitions in liquid crystals

Within the framework of Landau-de-Gennes formulation, we analyse the effect of pressure on electric-field-induced phase transitions in a liquid crystal which shows spontaneously an isotropic-smectic A transition. Inferring from the experimental pressure dependences on the layer spacing in smectic A phase, as well as the nematic-smectic A metastable temperature T^*_AN, we incorporated the pressure dependence in the free energy through (the surface energy term) and the coupling between the quadrupolar nematic ordering Q_ij and the smectic order parameter ψ. From the S-T phase diagram, we found that the stability of field-induced nematic phase increases with pressure, whereas the discontinuity of the transition decreases. Also, the region where paranematic phase transits directly to smectic A phase increases with pressure.     

First inelastic neutron scattering studies on thin free standing polymer films

Intermolecular coupling plays an important role in determining the dynamics and the mobility of polymeric and non-polymeric glass-formers. The breadth of the dispersion is an indicator of the intermolecular coupling strength. The coupling model relates intermolecular coupling through the breadth of the dispersion to the dynamics of bulk glass-formers. When a glass-former is confined in nanometer pores or in thin films and if there is absence of chemical and physical interactions with the wall, intermolecular coupling is reduced, resulting in an increase of mobility. The coupling model is used to account for such changes of relaxation time of 1) ortho-terphenyl and poly(dimethyl siloxane) confined in nanometer pores, 2) polymer thin film confined between two impenetrable walls from Monte Carlo simulation, and 3) polymer film confined by perfectly smooth and purely repulsive potential acting on the repeat units from molecular-dynamics simulation. The model continues to explain the opposite effects observed when there is an increase of intermolecular coupling due to the presence of chemical or physical interaction with the walls.Received: 1 January 2003, Published online: 8 October 2003PACS: 64.70.Pf Glass transitions - 68.60.Bs Mechanical and acoustical properties - 36.20.-r Macromolecules and polymer molecules