Chirality-induced phase transitions in some liquid crystalline binary mixtures

Novel binary mixtures have been prepared between an optically active antiferroelectric liquid crystal, (S)-4-(1-methylheptyloxycarbonyl)phenyl 4'-octyloxy-biphenyl-4-carboxylate, and an optically active twin liquid crystal, (R)-3-methyladipic acid bis[4-(5-octyl-2-(pyrimidinyl)phenyl] ester, and the liquid crystalline properties investigated. The stability of each liquid crystal phase was found to decrease by mixing these two liquid crystalline materials. Furthermore, a phase diagram between these compounds showed a clear discontinuity in phase sequences. These results indicate that the liquid crystal phases are different in nature between these materials. The mixture consisting of the antiferroelectric material (40 per cent) and the twin material (60 per cent) shows an unusual liquid crystal phase, where the texture is similar to that reported for the twist grain boundary (TGB) phase. Related binary mixtures have been prepared between optically active or racemic materials, where the chirality of the system is expected to be altered systematically. The TGB phase was found to be induced only in the mixture between the optically active materials. Two kinds of effect on the appearance of the TGB phase, i.e. a strong helical structure induced by the optically active twin liquid crystal and a decrease of the smectic layer strength achieved by mixing between two types of liquid crystalline materials, are discussed.     

Monte Carlo study of four dimensional binary hard hypersphere mixtures

A multithreaded Monte Carlo code was used to study the properties of binary mixtures of hard hyperspheres in four dimensions. The ratios of the diameters of the hyperspheres examined were 0.4, 0.5, 0.6, and 0.8. Many total densities of the binary mixtures were investigated. The pair correlation functions and the equations of state were determined and compared with other simulation results and theoretical predictions. At lower diameter ratios the pair correlation functions of the mixture agree with the pair correlation function of a one component fluid at an appropriately scaled density. The theoretical results for the equation of state compare well to the Monte Carlo calculations for all but the highest densities studied.     

Determination of surface tension in binary mixtures using transition-matrix Monte Carlo

We present a methodology based on grand-canonical transition-matrix Monte Carlo and finite-size scaling analysis to calculate surface tensions in binary mixtures. In particular, mixture transition-matrix Monte Carlo is first used to calculate apparent, system-size-dependent free-energy barriers separating coexisting fluid phases. Finite-size scaling is then used to extrapolate these values to the infinitely large system limit to determine the true thermodynamic surface tension. A key distinction of the methodology is that it yields the entire isothermal surface-tension curve for a binary mixture in a relatively small number of simulations. We demonstrate the utility of the method by calculating surface-tension curves for three binary Lennard-Jones mixtures. While we have only examined the surface tension of simple fluids in this work, the method is general and can be extended to molecular fluids as well as to determine interfacial tensions of liquid-liquid interfaces.     

Crystal nucleation in binary hard sphere mixtures: a Monte Carlo simulation study

We present calculations of the nucleation barrier during crystallization in binary hard sphere mixtures under moderate degrees of supercooling using Monte Carlo simulations in the isothermal-isobaric semigrand ensemble in conjunction with an umbrella sampling technique. We study both additive and negatively nonadditive binary hard sphere systems. The solid-fluid phase diagrams of such systems show a rich variety of behavior, ranging from simple spindle shapes to the appearance of azeotropes and eutectics to the appearance of substitutionally ordered solid phase compounds. We investigate the effect of these types of phase behavior upon the nucleation barrier and the structure of the critical nucleus. We find that the underlying phase diagram has a significant effect on the mechanism of crystal nucleation. Our calculations indicate that fractionation of the species upon crystallization increases the difficulty of crystallization of fluid mixtures and in the absence of fractionation (azeotropic conditions) the nucleation barrier is comparable to pure fluids. We also calculate the barrier to nucleation of a substitutionally ordered compound solid. In such systems, which also show solid-solid phase separation, we find that the phase that nucleates is the one whose equilibrium composition is closer to the composition of the fluid phase.     

Determination of fluid-phase behavior using transition-matrix Monte Carlo: binary Lennard-Jones mixtures

We present a novel computational methodology for determining fluid-phase equilibria in binary mixtures. The method is based on a combination of highly efficient transition-matrix Monte Carlo and histogram reweighting. In particular, a directed grand-canonical transition-matrix Monte Carlo scheme is used to calculate the particle-number probability distribution, after which histogram reweighting is used as a postprocessing procedure to determine the conditions of phase equilibria. To validate the methodology, we have applied it to a number of model binary Lennard-Jones systems known to exhibit nontrivial fluid-phase behavior. Although we have focused on monatomic fluids in this work, the method presented here is general and can be easily extended to more complex molecular fluids. Finally, an important feature of this method is the capability to predict the entire fluid-phase diagram of a binary mixture at fixed temperature in a single simulation.     

Adsorption of binary mixtures on two-dimensional surfaces: theory and Monte Carlo simulations

The adsorption of binary mixtures on square lattices is studied by combining theoretical modeling and Monte Carlo (MC) simulations in grand canonical ensemble. The adsorption thermodynamics is analyzed through the total and partial isotherms. Two theoretical models have been used in the present study: (i) the first, which we called cluster approximation (CA), is based on exact calculations of configurations on finite cells. An efficient algorithm allows us to calculate the detailed structure of the configuration space for \(m = l \times l \) cells; and (ii) the second is a generalization of the classical quasi-chemical approximation (QCA) in which the adsorbate is a binary mixture of species \(a\) and \(b\) . Adsorbate–adsorbate lateral interactions are incorporated in the context of the two mentioned approximations. Results from CA and QCA are compared with MC simulations. Close agreement between simulated and theoretical data supports the validity of the theoretical models to describe the adsorption of mixed gases on two-dimensional surfaces.     

Histogram Monte Carlo simulation on phase transitions in single‐polymer systems

Applying the histogram Monte Carlo simulation method and the bond‐fluctuation model, various phase transitions in single‐polymer systems were investigated. The critical transition temperature (Θ point) in the coil‐globule collapse transition of a macromolecular chain is accurately determined. Finite‐size scaling results near the transition point are verified. The first‐order transition associated with the freezing/crystallization of a polymer at a temperature below the Θ point is also observed. The free energy profiles associated with these two transitions are explicitly computed. Furthermore, the unfolding phase transition associated with stretching a collapsed polymer chain is investigated. The free energy profile associated with the transition is explicitly computed. Results on the energy cumulants and free energy profiles provide direct evidences for the first‐order nature of the unfolding phase transition.     

Monte Carlo simulations of phase transitions and adsorption isotherm discontinuities on surface compression

Low temperature, Grand Canonical Monte Carlo simulations were used to study the adsorption of fluid layers on cubic, hexagonal, and atomically smooth substrates to determine the effects of registry and surface compression on the system. The size of the fluid molecules was fixed to be 20% larger than the substrate molecules in order to observe the transition from an expanded to commensurate and finally to an incommensurate monolayer. For relatively weak fluid-substrate interactions, the cubic system underwent a first-order phase transition. As the strength of the fluid-substrate interactions increased, the molecules became fixed at commensurate locations and the transition from low density to commensurate packing became continuous. The strong fluid-substrate interactions lead to the development of a kink in the adsorption isotherm that showed the increased stability of the commensurate phase. This kink became more pronounced as the system temperature was decreased. The hexagonal system showed less dramatic results due to a decrease in the substrate well depth of the relative to the cubic system. The system did experience a first-order phase transition for a weak fluid-substrate interactions and the transition became much more gradual as the fluid-substrate interaction increased. The molecules became fixed to commensurate substrate locations, but the surface was not corrugated sufficiently to have a stable commensurate phase. The atomically smooth substrate showed the first-order phase transition expected of a low temperature system with no effects of registry.     

On the fluid phase behaviour of fluid binary mixtures using the Yukawa fluid molecular model

By expanding Ginoza’s mean spherical approximation (MSA) results in an inverse-temperature expansion, Henderson et al. obtained explicit results for the thermodynamic functions of a pure Yukawa fluid. We have recently published explicit results for the coefficients in an inverse-temperature expansion of the thermodynamic functions for the MSA for mixtures of Yukawa fluids. Attention is drawn to the fact that the MSA in the Ginoza formulation, does not always yield a convergent solution. The expansion used in this paper will always yield a result. In this work we present our investigations of the fluid phase diagram of Yukawa binary mixtures by considering an expansion of the MSA Helmholtz free energy up to the fifth order of the inverse-temperature expansion. The calculated fluid phase diagrams for Yukawa binary mixtures are similar to those of real mixtures.     

A new method of semigrand canonical ensemble to calculate first-order phase transitions for binary mixtures

First-order phase transitions of binary mixtures at the given pressure (P) and temperature (T) are studied by taking into account the composition fluctuations. Isothermal-isobaric semigrand canonical ensemble is adopted to find the relations among the total number of molecules, the composition fluctuations and Gibbs free energy density. By combining two identical subsystems of mixtures successively, the free energy density is transformed until being stable and its linear segments represent phase transitions. A new method is developed to calculate the phase equilibriums of binary mixtures. The method handles multiple types and number of phase equilibriums at single time and its solutions are physically justified. One example is shown for calculating the phase diagram of binary Lennard-Jones mixture. It demonstrates that the fluctuations of the total number of molecules in mixtures are fundamental behind phase transitions and the van der Waals loops in Gibbs free energy are reasonable.     

Wetting transitions of asymmetric binary polymer mixtures

We examine the effect on surface-wetting phase transitions in polymer mixtures when the degrees of polymerization of the two components are different. It has been demonstrated by Schmidt and Binder (J. Phys. (Paris) 46 , 1631 (1985)) that in a symmetric polymer mixture a second-order wetting transition occurs if the wall-polymer interaction f(ϕ₀) has a negative curvature f″(ϕ₀), where ϕ₀ is the surface volume fraction of the polymer component preferred by the wall. We found that in an asymmetric mixture this is not necessarily the case.     

Monte Carlo phase diagram for diblock copolymer melts

A partial phase diagram is constructed for diblock copolymer melts using lattice-based Monte Carlo simulations. This is done by locating the order-disorder transition (ODT) with the aid of a recently proposed order parameter and identifying the ordered phase over a wide range of copolymer compositions (0.2相似文献   

An efficient sampling algorithm for variational Monte Carlo

We propose a new algorithm for sampling the N-body density mid R:Psi(R)mid R:(2)R(3N)mid R:Psimid R:(2) in the variational Monte Carlo framework. This algorithm is based upon a modified Ricci-Ciccotti discretization of the Langevin dynamics in the phase space (R,P) improved by a Metropolis-Hastings accept/reject step. We show through some representative numerical examples (lithium, fluorine, and copper atoms and phenol molecule) that this algorithm is superior to the standard sampling algorithm based on the biased random walk (importance sampling).     

Kinetic Monte Carlo study of binary diffusion in silicalite

We report a Kinetic Monte Carlo (KMC) study of the diffusion of linear n-hexane (nC6) and 2,2-dimethylbutane (22DMB) mixture in zeolite silicalite. We first investigated the loading dependences of single component self- and corrected diffusivities of nC6 at 300 K. Anisotropic transition rates are implemented to account for the distribution of the molecules within the zeolite framework. Repulsive guest-guest interactions are modeled using the parameter introduced by Reed and Ehrlich (Surf. Sci. 102:588–601, 1981). The results are in good agreement with recent experimental Quasi Elastic Neutron Scattering data of Jobic et al. (J. Phys. Chem. B 110:2195–2201, 2006), although the influence of the adsorption isotherm inflection is not reproduced. The binary diffusion study of nC6/22DMB mixtures was performed by implementing the nC6 transition rates used for the single component study while 22DMB molecules propagate via intersection-intersection hops. This KMC model allows for different saturation capacities and accounts for interactions between molecules by introducing f _ij parameters. Results show the large impact of guest-guest interactions between nC6 and 22DMB on both self- and corrected diffusivities of the two components. Molecule-size effects are found to be predominant near 22DMB saturation capacity. Acceleration/deceleration effects already described in the literature are confirmed.     

Freezing line of the Lennard-Jones fluid: a phase switch Monte Carlo study

We report a phase switch Monte Carlo (PSMC) method study of the freezing line of the Lennard-Jones (LJ) fluid. Our work generalizes to soft potentials the original application of the method to hard-sphere freezing and builds on a previous PSMC study of the LJ system by Errington [J. Chem. Phys. 120, 3130 (2004)]. The latter work is extended by tracing a large section of the Lennard-Jones freezing curve, the results of which we compare with a previous Gibbs-Duhem integration study. Additionally, we provide new background material regarding the statistical-mechanical basis of the PSMC method and extensive implementation details.     

Equations for describing liquid-vapor phase equilibria in binary mixtures

Three forms of equations for describing experimental data on liquid and vapor pressures, depending on temperature and composition at phase equilibria in binary mixtures, are proposed and evaluated. It is determined that the form of equation depends on the relationship between the temperature of a mixture and the critical temperatures of the components of the mixture. Exact data on the phase equilibria in nitrogenoxygen, nitrogen-argon, and oxygen-argon mixtures [1] are approximated to assess the effectiveness of the equations’ forms. It is found that the equations also allow us to determine the phase composition at a given temperature and pressure and temperatures of phases at a given pressure and composition.     

Solvent dependence of charge-transfer transitions in binary aqueous mixtures

Summary Charge-transfer transitions of Ru(bipy) ₃ ²⁺ , Fe(bipy) ₃ ²⁺ , Fe(CN) ₆ ^3- , and free bipy (bipy=2,2-bipyridine) are solvent dependent. Evidence is presented that dielectric continuum theory provides a reasonable basis for interpreting medium effects on the electronic transition energies in binary solvent mixtures as well as in pure solvents.     

FTIR of liquid crystals. Organization and phase transitions in binary mixtures of nonylcyanobiphenyl and phenyl-cyclohexanecarboxylate

The FTIR spectra of the isotropic and mesomorphic N, S_Ad, S_A1, S_B and S_G phases of 4-n-nonyl-4'-cyanobiphenyl (9CB), 4-n-pentylphenyl-trans-4'-n-pentylcyclohexane-1-carboxylate (5H5) and their binary mixtures have been recorded and analysed. Changes in absorbance related to spontaneous reorientation of the molecules at the phase transitions have been observed and assigned to the orientation of the transition dipoles of typical vibrations. The results are discussed in terms of the phase diagram obtained by D.S.C. and by optical microscopy.     

Pattern formation in phase separating binary mixtures

We experimentally investigate the interplay of thermodynamics with hydrodynamics during phase separation of (quasi-) binary mixtures. Well defined patterns emerge while slowly crossing the cloud point curve. Depending on the material parameters of the experimental system, two distinct scenarios are observed. In quasi-binary mixtures of methanol-hexane patterns appear before macroscopic phase separation sets in. In course of time the patterns turn faint while the overall turbidity of the sample increases until the mixtures become completely turbid. We attribute this pattern formation to a latent heat induced instability resembling a Rayleigh-Bénard instability. This is confirmed by calorimetric data and an estimate of its Rayleigh number. Mixtures of C(4)E(1)-water doped with decane phase separate under heating. After passing the cloud point curve these mixtures first become homogenously turbid. While clearing up, pattern formation is observed. We attribute this type of pattern formation to an interfacial tension induced Bénard-Marangoni instability. The occurrence of the two scenarios is supported by the relevant dimensionless numbers.