Monte Carlo study of dipolar and quadrupolar hard prolate spherocylinders

Monte Carlo simulations of hard prolate spherocylinders (HPSs) with embedded dipole or quadrupole moment are reported for two elongations (L?=?0.5 and 1) and several values of the packing fraction. The MC values of the residual internal and Helmholtz energy and compressibility factor were determined. Our work represents the first simulation study of dipolar HPSs focused on the determination of the thermodynamic properties. In the case of quadrupolar HPSs, our results enlarge the range of state conditions for which the simulation data are available. The obtained MC data were used for a test of the perturbation theory of polar non-spherical molecule fluids. In order to evaluate the perturbation contributions containing the two-particle integrals, the values of the shape integrals (evaluated recently for dipolar and quadrupolar hard prolate spherocylinders) were employed and we were allowed to avoid the use of the similarity between Kihara and Gaussian overlap models. Fair agreement between the simulation data and the theoretical predictions was reached.     

Critical properties of non-spherical molecule fluids from the virial expansion

Critical constants of pure fluids (as important reference data in constructing vapour-liquid phase diagrams and basic input of various estimation methods) were determined for systems of non-spherical Kihara molecules; values of the critical temperature, density, compression factor and pressure of fluids composed of prolate and oblate molecules were evaluated from the fourth-order virial expansion. The second and third virial coefficients of the Kihara molecules were determined by applying the recently proposed method in which the effect of molecular core geometry and functional dependence of a pair interaction on the surface-surface distance are factorized and the former contribution determined from a formula for the corresponding hard convex body virial coefficient. The virial expansion for non-spherical Kihara molecules is applied to determine the critical constants of n-alkanes (methane to octane) and cyclic hydrocarbons (cyclopentane, cyclohexane, benzene and naphthalene); a fair agreement with experimental data was found.     

Gibbs ensemble simulation of the vapour-liquid equilibrium of square well spherocylinders

Gibbs ensemble Monte Carlo simulations have been performed for systems of square-well spherocylinders of different length-to-breadth ratio. The results are used to test a recent perturbation theory proposed for this kind of system. In addition, the results are compared to similar simulations performed for a Kihara fluid of elongated molecules. An unexpected good agreement is found for the coexistence thermodynamic and structural properties of both model fluids, hence suggesting that the hard spherocylinder plus square-well interaction should be considered as a reference potential for a perturbative treatment of more complex fluid models.     

Vapour–liquid equilibrium of fluids composed by oblate molecules

Gibbs ensemble Monte Carlo simulations are performed to obtain the vapour–liquid equilibrium of oblate-like fluids interacting through the Kihara intermolecular potential. Results confirm the validity of a perturbation theory for Kihara fluids, whose accuracy for prolate fluids was tested some years ago. As in the case of hard ellipsoids, the symmetry of the phase diagram of oblate and prolate models is analysed. An interesting relation of Boyle temperature and critical parameters with molecular volume is found for the considered models. As a particular application, this relation allows the prediction of some thermodynamic properties of a new promising biofuel 2,5dimethylfuran.     

Critical properties of non-spherical molecule fluids from virial expansion

For systems of Kihara molecules with circular cores, the values of the reduced critical constants were determined from the fourth-order virial expansion as functions of the core diameter/thickness ratio. From expressions for the reduced functions both for the oblate and prolate shapes, the values of critical constants of four cyclic hydrocarbons and four branched alkanes were evaluated and compared with the experimental data and values obtained from the perturbation theory.     

Hard body fluids again: Virial coefficients and equations of state

The table of the virial coefficientsB ₂ throughB ₄ of all hard body fluid models considered so far has been completed by calculating the missing coefficients. Applicability of these coefficients to predicting the thermodynamic behaviour of dense hard body fluids is assessed and certain discrepancies in the data for oblate spherocylinders are found. It is shown that by combining the Padé approximant with an appropriate analytic expression an accurate 3-parameter equation of state results.     

Demixing and nematic behaviour of oblate hard spherocylinders and hard spheres mixtures: Monte Carlo simulation and Parsons–Lee theory

Parsons–Lee approach is formulated for the isotropic–nematic transition in a binary mixture of oblate hard spherocylinders and hard spheres. Results for the phase coexistence and for the equation of state in both phases for fluids with different relative size and composition ranges are presented. The predicted behaviour is in agreement with Monte Carlo simulations in a qualitative fashion. The study serves to provide a rational view of how to control key aspects of the behaviour of these binary nematogenic colloidal systems. This behaviour can be tuned with an appropriate choice of the relative size and molar fractions of the depleting particles. In general, the mixture of discotic and spherical particles is stable against demixing up to very high packing fractions. We explore in detail the narrow geometrical range where demixing is predicted to be possible in the isotropic phase. The influence of molecular crowding effects on the stability of the mixture when spherical molecules are added to a system of discotic colloids is also studied.     

Second virial coefficient of homonuclear two-centre Lennard-Jones molecules

A semiempirical expression based on numerical values of the second virial coefficient of the two-centre Lennard-Jones molecules and on the theoretical expression for hard dumbells is given. The resulting expression possesses the form developed formerly for the second virial coefficient of the Kihara non-spherical molecules and reproduces fairly well the correct limits at high temperatures. It allows the prediction of the second virial coefficient at reduced temperatures T*≧0·5.     

Computer simulation study of a flexible-rigid-flexible model for liquid crystals

Small molecules that form liquid crystals typically consist of a rigid core with flexible tails on one end or on both ends. To date, most computer simulation studies have used completely rigid models such as hard spherocylinders: cylinders, characterized by their length/diameter ratio L/D, with hemispherical end caps. We have studied a model consisting of spherocylinders with L/D = 4, with a flexible tail attached to each end. The tails are ‘ideal’ in the sense that they have no volume. Using Monte Carlo simulations the phase behaviour of this model was studied and, for comparison, the behaviour of hard spherocylinders with L/D = 4 without tails was studied as well. The addition of the tails is found to stabilize the smectic-A phase at a lower pressure, and the nematic phase disappears. In the smectic-A and crystal phases, the smectic layers are further apart when tails are added. The structure of the layers and the smectic-A–crystal transition pressure change only a little. For both models close to melting the crystal consists of ordered layers, but there is almost no correlation between particle positions in neighbouring layers. In fact, the layer coupling is so weak that in a long simulation the layers are found to glide over each other. As the pressure is increased the crystal gradually becomes more ordered and the crystalline layers ultimately ‘lock’ into place.     

An equation of state for hard convex body chains

The thermodynamic perturbation theory of hard sphere chains is generalized to derive an equation of state for hard convex body chains. The hard convex body chain equation of state contains two parameters that are related directly and rigorously to the geometry of the hard convex body. The compressibility factors and second virial coefficients of chains composed of prolate spherocylinders, oblate spherocylinders and doublecones are calculated and compared with hard sphere chain calculations. The comparison indicates that the nature of the hard convex body has a profound influence on the properties of the chain.     

Mixtures of hard spherocylinders and hard spheres

Monte Carlo simulations have been performed for equimolar mixtures of hard prolate spherocylinders of length: breadth ratio 2:1 and hard spheres, in the fluid region. Two systems have been studied. In the first the breadth of the spherocylinder was equal to the hard sphere diameter, and in the second system both components were of equal molecular volume.

The compressibility factor, PV/NkT, has been obtained for both mixtures at four reduced densities (packing fractions) from 0·20 to 0·45. The results have been compared with the predictions of several analytical equations appropriate to mixtures of hard convex molecules, and an equation due to Pavlicek et al. was found to be very accurate. The results have been used to calculate the excess volumes of mixing at constant pressure, in an attempt to establish the relative importance of the effects of differences in molecular volume and shape on the thermodynamic properties.

The structural properties of the mixtures have also been investigated by calculating pair distribution functions for the three types of pair interactions present in these mixtures.     

Smectic phases in hard particle mixtures: Koda's theory

Mixtures of parallel linear particles and spheres tend to demix upon compression. The linear species usually concentrates in regular layers, thus forming a smectic phase. With increasing concentration of spheres this ‘smectic demixing’ transition occurs at ever lower packing densities. For the specific case of hard spherocylinders and spheres Koda et al. [T. Koda, M. Numajiri, S. Ikeda, J. Phys. Jap., 65, 3551 (1996)] have explained the layering effect in terms of a second virial approximation to the free energy. We extend this approach from spherocylinders to other linear particles, namely fused spheres, ellipsoids and sphero-ellipsoids.     

The correlations in a star molecule fluid. Integral equation theory and Monte Carlo study

The structure of a starlike molecule (SLM) fluid with four arms of different length is studied by applying the associative Percus–Yevick integral equation (IE) theory and canonical Monte Carlo (MC) simulations. In the IE study the SLM fluid is modelled by a fluid of hard spheres with four associative sites on each sphere while the MC has been performed for a freely-joined tangent hard sphere fluid. The total radial distribution functions have been calculated in both approaches for different volume fraction regimes and different arm lengths. It is shown that the associative IE theory predicts the structure of SLM fluid best for relatively long arms and at high densities. Additionally, the dependence of the SLM centre–centre correlations on the functionality and fluid particle density has been analysed using the MC results.     

Computer simulations of soft repulsive spherocylinders

Computer simulations of systems of soft repulsive spherocylinders (SRS) of aspect ratio (L/D) equal to 4 have been carried out using the parallel molecular dynamics program GBMOLDD. At sufficiently high densities the system forms stable nematic and smectic-A liquid crystalline phases. Results are presented for a series of seven isochores in the NVE ensemble, and for isobars at T? = kT/?= 0.5, 1.0, 1.5 in the NpT ensemble.     

Perturbation theory for fluids of rod-like molecules interacting via the Kihara potential

For systems of molecules interacting via the Kihara core potential a first-order perturbation theory is proposed. As a reference system soft convex bodies are employed with interactions given by the entire repulsive part of the original pair potential (i.e. for surface-to-surface distances smaller than that of the potential minimum). Their equilibrium behaviour is interpreted on the basis of the representative hard convex bodies-parallel convex bodies to the assumed cores with temperature-dependent thickness. The shape of the distribution function was approximated by the Verlet-Weis form. Theoretical expressions were used for the determination of the thermodynamic functions of the Kihara-molecule systems at several reduced temperatures and compared with experimental data for nitrogen.     

Equation of State for Parallel Rigid Spherocylinders

The pair distribution function of monodisperse rigid spherocylinders is calculated by Shinomoto’s method, which was originally proposed for hard spheres. The equation of state is derived by two different routes: Shinomoto’s original route, in which a hard wall is introduced to estimate the pressure exerted on it, and the virial route. The pressure from Shinomoto’s original route is valid only when the length-to-width ratio is less than or equal to 0.25 (i.e., when the spherocylinders are nearly spherical). The virial equation of state is shown to agree very well with the results of numerical simulations of spherocylinders with length-to-width ratio greater than or equal to 2.     

Sixth,seventh and eighth virial coefficients of the Lennard-Jones model

We report values of the virial coefficients B _n of the Lennard-Jones (LJ) model, as computed by the Mayer Sampling Monte Carlo method. For n = 4 and 5, values are reported for 103 temperatures T = 0.62 to 40.0 (in LJ units); for n = 6, 31 values are reported for T = 0.625 to 20.0; for n = 7, 15 values are reported from T = 0.625 to 10; and for n = 8, four values are reported from T = 0.75 to 10. Data are used to estimate the location of the LJ critical point, and the critical temperature estimated this way is given to within 0.8% of the established value, while the critical density is too low by 10%. Data derived from the virial equation of state (VEOS) are compared to pressures and internal energies calculated by Monte Carlo simulation. Simulations of systems ranging from 125 to 30,000 particles are extrapolated to infinite system size, and it is shown that the VEOS–when applied at densities where the series has reached convergence–provides results closer to the infinite-system values than obtained by any of the finite-system simulations. For n = 6, convergence of VEOS (within a 1% tolerance) is obtained for densities up to the spinodal for subcritical temperatures and up to ρ = 0.4 (in LJ units) in the vicinity of the critical temperature; the range of applicability of VEOS increases with temperature, reaching for example densities of 0.65 for T = 5.0 and 0.8 for T = 8.0 when truncated at n = 6.