Andrew J. Masters

Biaxial Nematic Order in the Hard-boomerang Fluid

Abstract We consider a fluid of hard boomerangs, each composed of two hard spherocylinders joined at their ends at an angle ψ. The resulting particle is nonconvex and biaxial. The occurence of nematic order in such a system has been investigated using Straleys theory, which is a simplificaton of Onsagers second-virial treatment of long hard rods, and by bifurcation analysis. The excluded volume of two hard boomerangs has been approximated by the sum of excluded volumes of pairs of constituent spherocylinders, and the angle-dependent second-virial coefficient has been replaced by a low-order interpolating function. At the so-called Landau point, ψ Landau ≈ 107.4°, the fluid undergoes a continuous transition from the isotropic to a biaxial nematic (B) phase. For ψ ≠ ψLandau ordering is via a first-order transition into a rod-like uniaxial nematic phase (N +) if ψ > ψLandau, or a plate-like uniaxial nematic (N−) phase if ψ < ψLandau. The B phase is separated from the N+ and N− phases by two lines of contin...

Theory and computer simulation of bent-core molecules

Fluids of hard bent-core molecules have been studied using theory and computer simulation. The molecules are composed of two hard spherocylinders, with length-to-breadth ratio L/D, joined by their ends at an angle 180°−γ. For L/D=2 and γ=0,10,20°, the simulations show isotropic, nematic, smectic, and solid phases. For L/D=2 and γ=30°, only isotropic, nematic, and solid phases are in evidence, which suggests that there is a nematic-smectic-solid triple point at an angle in the range 20°<γ<30°. In all of the orientationally ordered fluid phases the order is purely uniaxial. For γ=10° and 20°, at the studied densities, the solid is also uniaxially ordered, whilst for γ=30° the solid layers are biaxially ordered. For L/D=2 and γ=60° and 90° we find no spontaneous orientational ordering. This is shown to be due to the interlocking of dimer pairs which precludes alignment. We find similar results for L/D=9.5 and γ=72°, where an isotropic-biaxial nematic transition is predicted by Onsager theory. Simulations in ...

Monte Carlo simulation of F−(H2O)4 using an ab initio potential

We present results concerning the structure and energetics of the cluster F−(H2O)4 at 0 K, using high quality ab initio methods, and at a temperature of 300 K, using an ab initio Monte Carlo simulation. At 0 K, we find the global energy minimum corresponds to three waters solvating the fluoride ion and with the fourth water in an outer hydration shell, hydrogen bonding to the other water molecules. Structures involving four waters hydrogen bonding to the fluoride are, however, of only slightly higher energy. At 300 K, the simulation results indicate that the fluoride is mostly to be found within a tetrahedron of solvating water molecules. The cluster is mobile, however, and a wide variety of structures are sampled.

Long-time tails in angular momentum correlations

We compare computer simulation results for the angular velocity autocorrelation function (AVACF) of a colloidal particle with theoretical predictions. We consider both spherical and nonspherical particles in two and three dimensions. The theoretical prediction for the long‐time decay of the AVACF in three dimensions is well known, here we also give the two‐dimensional result, along with a sketch of how it was derived. For spherical particles we find excellent agreement between the simulations results and theoretical predictions in both two and three dimensions. We also find that the same expressions apply to the nonspherical particles when the particles have had time to undergo a significant angular displacement. This observation is again in agreement with theory.

Computer simulation of a twisted nematic liquid crystal

We have performed the first computer simulation of a twisted nematic liquid crystal using non-spherical hard particles in modified periodic boundary conditions. The director profiles are stable, suggesting that the technique may usefully complement conventional simulations of unperturbed liquid crystals. We make preliminary calculations of the twist elastic constant K 2 by measurement of intermolecular torques: the results are in moderately good agreement with those obtained from fluctuation expressions.

Liquid crystal formation in a system of fused hard spheres

The Monte Carlo method is used to study three systems of fused hard spheres with length-to-width ratios ranging from 3·5 to 5·2. Spontaneous nematic alignment is observed only for the most elongated molecules. The isotropic data are compared with a theoretical expression due to Boublik and are fitted by a y expansion in each case. Site-site distribution functions and Legendre coefficients of the total angular distribution function are reported for a representative state point in the nematic phase. These are discussed in relation to the equivalent functions for a system of parallel fused spheres. It is found that the single-particle angular distribution function is represented well by f(γ) = A exp (- κ cos2 γ) + c. The Frank elastic constants are estimated and are in the expected range. At higher densities there is evidence for a smectic phase.

Monte-Carlo integration for virial coefficients re-visited: hard convex bodies, spheres with a square-well potential and mixtures of hard spheres

Techniques to adapt the hit-and-miss Monte-Carlo numerical integration are proposed with the aim to determine virial coefficients up to eighth order in fluids of hard convex bodies, hard spheres with an attractive square-well potential and a two-component mixture of hard spheres. These algorithms make use of look-up tables of all the blocks contributing to the coefficients. Each type of block is represented in the tables by several entries. These correspond to all possible topologically equivalent graphs that can be generated by the Monte-Carlo process. This rendered the Monte-Carlo method statistically more efficient. In the case of a two-component system the look-up tables had to have representations of blocks having two sorts of vertices. The reported data are: improved values of the seventh and eighth virial coefficients for hard spheres, the sixth, seventh and eighth coefficients of spheroids, spherocylinders and cutspheres, fifth virial coefficient of spheres with a square-well potential of relative range 1.25; 1.5; 1.75 and 2.0 and the partial contributions of the sixth virial coefficient for a mixture of hard spheres with the size ratio 0.1.

A molecular theory of Stokes–Einstein behavior. I. Translational Brownian motion

By using the Mori generalized Langevin equation an expression for the velocity autocorrelation function of a Brownian particle is obtained. By an appropriate choice of the potential of interaction between the particle and the fluid molecules the frequency dependent friction coefficient reduces to the value found when the slip boundary condition is applied in a hydrodynamic calculation; a different choice gives almost exactly the stick value. The reasons why the previous ’’mode‐coupling’’ calculations give an incorrect form for the friction coefficient are discussed.

Equation of state of hard and Weeks–Chandler–Anderson hyperspheres in four and five dimensions

The fifth and sixth virial coefficient for hard hyperspheres in four and five dimensions has been computed using Monte Carlo techniques. It is found that B5/B24 has values 0.035 63±0.000 07 and 0.012 87±0.000 06 and that B6/B25 has values 0.007 691±0.000 028 and 0.000 942±0.000 027 in four and five dimensions, respectively. These values are used to investigate the equation of state of hard and Weeks–Chandler–Anderson (WCA) hyperspheres in four and five dimensions. Molecular dynamics simulations are performed for WCA hyperspheres. When compared to the molecular dynamics calculations, it is found that both the hard hypersphere and WCA equations of state are well described by a variety of theoretical approaches as long as the density is in the low-to-moderate regime. At the highest fluid densities studied, the Luban–Michels procedure provides the best accuracy for hard hyperspheres. The WCA prescription for the scaling of the reference system to a hard hypersphere one is a very good approximation in the flui...

Exploring reaction pathways with transition path and umbrella sampling: Application to methyl maltoside

The transition path sampling (TPS) method is a powerful approach to study chemical reactions or transitional properties on complex potential energy landscapes. One of the main advantages of the method over potential of mean force methods is that reaction rates can be directly accessed without knowledge of the exact reaction coordinate. We have investigated the complementary nature of these two differing approaches, comparing transition path sampling with the weighted histogram analysis method to study a conformational change in a small model system. In this case study, the transition paths for a transition between two rotational conformers of a model disaccharide molecule, methyl beta-D-maltoside, were compared with a free energy surface constrained by the two commonly used glycosidic (phi,psi) torsional angles. The TPS method revealed a reaction channel that was not apparent from the potential of mean force method, and the suitability of phi and psi as reaction coordinates to describe the isomerization in vacuo was confirmed by examination of the transition path ensemble. Using both transition state theory and transition path sampling methods, the transition rate was estimated. We have estimated a characteristic time between transitions of approximately 160 ns for this rare isomerization event between the two conformations of the carbohydrate. We conclude that transition path sampling can extract subtle information about the dynamics not apparent from the potential of mean force method. However, in calculating the reaction rate, the transition path sampling method required 27.5 times the computational effort than was needed by the potential of mean force method.