S. Lago

Isotropic-nematic transition of hard polar and nonpolar molecules

A new theory to study isotropic‐nematic transition is proposed. This theory requires a good knowledge of the thermodynamic properties of the isotropic phase. It allows to study nematic formation in systems possessing attractive forces. We determine isotropic‐nematic equilibria for a number of hard linear models as hard spherocylinders, hard ellipsoids, and hard tangent spheres in a linear configuration. The theory predicts quite nicely the transitions when compared to simulation results. We also study the effect of an ideal dipole or quadrupole on nematic formation. Dipolar or quadrupolar forces favor the presence of a nematic phase although the effect is moderate. However, for large multipole moments no stable nematic phase was found.

A fast algorithm to evaluate the shortest distance between rods

Abstract We present a fast algorithm to evaluate the shortest distance between rods of either the same or different length. The presented algorithm speeds up considerably the evaluation of the shortest distance with respect to other previously reported algorithms. As an application, this algorithm has allowed a fast development of the statistical mechanics of molecular fluids interacting through potentials depending on the shortest distance as, e.g. the Kihara model. The reported algorithm has proved to be very useful to study the liquid state either by simulation (Monte Carlo or Molecular Dynamics) or by perturbation theory and to obtain thermodynamic properties of Kihara-like fluids.

Virial coefficients and equation of state of hard alkane models

The virial coefficients up to the fifth of hard conformers of alkanes have been evaluated numerically. The conformers were selected by using the rotational isomeric state approximation. The effect of branching and length of the chain on the anisotropy of alkanes is discussed and a relation between the nonsphericity parameter α and the acentric factor ω for this kind of molecule is proposed. We modified the equation of state for tangent hard spheres first proposed by Wertheim [M. S. Wertheim, J. Chem. Phys. 87, 7323, (1987)] to allow for overlapping of the constituting hard spheres. This modified version predicts with high accuracy the virial coefficient of the hard conformers of alkanes. Moreover comparison of this equation of state with simulation results of repulsive models of n‐alkanes reveals very good agreement. The effect of condensed phase effect on the conformational equilibria of n‐alkanes up to n‐octane is analyzed.

Reaction field simulations of the vapor-liquid equilibria of dipolar fluids: Does the reaction field dielectric constant affect the coexistence properties?

Abstract Vapor-liquid equilibria of two Stockmayer fluids have been obtained by computer simulations in the Gibbs ensemble. The long-range dipolar interactions have been considered within the reaction field geometry. Two different criteria for the reaction field dielectric constant, (ϵ rf , have been applied. It is shown that ϵ rf does not significantly affect either the coexistence properties or the structure of coexisting phases for the simulated systems.

Structure and thermodynamics of the dipolar hard sphere fluid from the reference‐hypernetted chain equation with minimized free energy

The reference‐hypernetted chain equation, generalized to molecular fluids, is optimized by choosing the reference system so as to minimize the free energy. This procedure, which assures a significant improvement in the internal thermodynamic consistency of the theory, is here applied to a fluid of dipolar hard spheres, using both the complete dipolar potential and one with a reaction field (RF) truncation. We confirm that a recent reformulation of the relation between the dielectric constant e and the mean square dipole moment for the RF geometry indeed brings e for the truncated potential into reasonably good agreement with the infinite‐range values, but that the important correlation functions nevertheless differ qualitatively in their long‐range behavior. The method of solving the molecular integral equation, developed earlier, can be applied to other multipolar potentials, or alternatively, to molecules with distributed point charges.

Potential parameters of methyl and methylene obtained from second virial coefficients of n-alkanes

The second virial coefficients of a number of n-alkanes (from butane to hexadecane) have been evaluated by using the Rotational Isomeric State model. Methyl and methylene groups have been modelled as Lennard-Jones (12 – 6) interaction sites centered on the position of the carbon atoms. Equal size has been assigned to the methyl and methylene groups but differences in the well-depth of the potential were considered. We have chosen the values of the potential well-depths of methyl and methylene group to fit the second virial coefficient of several n-alkanes in a range of about 300 K. The agreement with experimental results is good. Then, it is shown that a simple site-site potential model is able to reproduce the second virial coefficient of several n-alkanes in a wide range of temperatures.

Extension of the optimized RHNC equation to multicomponent liquids

We have extended the optimized reference‐hypernetted chain formalism to multicomponent liquids. The reference system is constructed from a mixed hard spheres fluid with additive diameters whose structural and thermodynamic properties have been conveniently parametrized. The theory is applied to binary liquid mixtures interacting through a repulsive Lennard‐Jones potential as well as the complete Lennard‐Jones potential; calculated results are in excellent agreement with those of numerical simulations.

Computer simulation of vapor–liquid equilibria of linear quadrupolar fluids. Departures from the principle of corresponding states

Vapor–liquid equilibria of different quadrupolar linear Kihara fluids have been studied, by using the Gibbs ensemble Monte Carlo technique. Coexistence curves for fluids with elongations L*=L/σ=0.3, 0.6, and 0.8 and different quadrupoles are given. We analyze the effect of quadrupole moment on critical properties. Quadrupole moment increases the critical temperature, pressure, and density. The magnitude of the increase depends on both anisotropy and quadrupole moment. A new way of reducing the quadrupole is proposed, so that the variation of critical properties due to the quadrupole follows a universal behavior. Quadrupole provokes deviations from the principle of corresponding states. A broadening of the coexistence curve is observed due to the quadrupole. The quadrupole moment increases the slope of the vapor pressure curve vs temperature inverse. Simulation data are used to describe vapor–liquid equilibria of carbon dioxide. Good agreement between simulation and experiment is achieved.

Linear hard sphere models Virial coefficients and equation of state

Virial coefficients of tangent hard spheres in a linear configuration have been determined numerically. Trends of the virial coefficients with the molecular anisotropy are similar to those of other linear models, such as hard spherocylinders or hard ellipsoids. Theoretical predictions of virial coefficients from different equations of state of hard body fluids are compared with the numerical results. None of them provides a completely satisfactory description of the lower virial coefficients when the anisotropy of the molecule is large. We propose a new method to build up an equation of state of hard linear models (prolate or oblate) from the knowledge of the first five virial coefficients. The equation of state obtained in this way provides a very good description of the equation of state of hard linear fluids at low, medium and high anisotropies.

Solution of the Percus–Yevick equation for hard spherocylinders. I. The entire pair correlation function

The Percus–Yevick equation for hard spherocylinders has been numerically solved using a recent algorithm to calculate the shortest distances between rods proposed by ourselves. The equation is solved for four different reduced densities to η=0.3879 and length‐to‐breadth ratio L*=1.0. Comparison with available Monte Carlo results for some selected orientations shows moderate agreement. Dependence of the pair correlation function and direct correlation function on mutual orientations and density are analyzed for these orientations. We found that none of the current approximations used in perturbation theories or in simplified integral equations can give even a qualitative description of the behavior of correlation functions for the above elongation L*.