Tomáš Boublík

Third virial coefficient and the hard convex body equation of state

A modified equation of state of hard convex body fluids is proposed in which the ratio of the third virial coefficients is employed as the second parameter (in addition to the parameter of non-sphericity α); the resulting equation of state yields the dependence of the compressibility factor on density for hard convex body fluids with a considerable variety of shapes within the error estimates of the simulation data. The third virial coefficients of hard convex bodies of one type are expressed in terms of parameters α and τ; the proposed expressions discern between convex bodies of different shapes with the same values of α (e.g. prolate and oblate ellipsoids of revolution) and enable accurate determination of the third virial coefficients in a broad range of non-sphericities.

Self-consistent equations of state for hard body mixtures

The self-consistency (S-C) constraints on the solute chemical potential and equation of state are stated and employed to find corrections to thermodynamic functions in the colloidal limit for the most often used equations of state. It is shown that the S-C approach and Hendersons expression for the contact radial distribution functions yield the same correction term in the case of the Boublik—Mansoori—Carnahan—Starling—Leland (BMCSL) equation of state for hard spheres. For hard sphere (and hard convex body) mixtures a new variant of the equation of state and Helmholtz energy is proposed that fulfils better the self-consistency constraints than the frequently used equations. It is shown that the correction term for Δμ 2 in hard convex body mixtures described by improved scaled particle theory differs from that for BMCSL only by the non-sphericity parameter. For the Kolafa—Boublik and modified scaled particle theory versions the correction terms are more complex.

The second virial coefficient of polar rod-like molecules

Abstract New method is proposed to determine thermodynamic functions of systems whose molecules interact via the non-spherical Kihara + electrostatic ( ES ) pair potentials. The second virial coefficient is studied for hard sphero-cylinders or rod-like Kihara molecules with permanent dipoles or quadrupoles embedded in centers of the molecules. Alternative definition of the hard convex body pair potential allows to factorize the many-fold integrals (in the expansion for the electrostatic forces) into a simple integral over center–center (cc) distance and a shape integral over orientational coordinates only. The latter integral was determined for permanent dipole–dipole, quadrupole–quadrupole and dipole–quadrupole interactions and its dependence on the reduced length was expressed in the form of Pade approximant. For pure polar hard sphero-cylinders and polar Kihara molecules the pseudo-experimental data were determined for a series of the reduced lengths and reduced values of the dipole or quadrupole moments and used to test the proposed method. The method is then successfully used to correlate the experimental second virial coefficient of 1,1,1-trifluoroethane and 1,1,1,2-tetrafluoroethane.

Simulations in ternary hard sphere mixtures

Abstract The Monte Carlo method was used to determine the compression factors and radial distribution functions (rdf) of ternary hard-sphere mixtures with hard-sphere diameters σ A =1, σ B =0.6, σ C =0.3 at several packing fractions ( y =0.35, 0.40 and 0.45) and mole fractions ( x A = x B = x C =1/3 or x A =1/6, x B =1/3, x C =1/2). The obtained values of the compression factor were employed to test the equations of state of hard-sphere mixtures. Fair agreement was found in all the cases. Also the obtained contact values of rdfs, g ij ( σ ij ), compare well with the theoretical values. Simulation results for the dependence of the rdfs on distance were compared with values determined from a simple relation devised recently for calculation of g ij ( x ) in ternary and multi-component systems. In all the cases, a satisfactory agreement was found for distances close to the contact values. Larger deviations were found in the range of distances close to the first minimum of g ij . The magnitude of deviations increases with the increasing differences between σ ij and σ A . In the case of considerably different values of σ ij and σ A , the proposed theoretical method overestimates g ij for x ≥ x min .

Combining rule for interaction energies of the (CO)2, (N2)2 and CO-N2 complexes

The relationship between interaction energies of the most stable structures of the (CO)2, (N2)2 and CO-N2 complexes is investigated using the supermolecule CCSD(T) and MP4 methods and aug-cc-pVXZ (X = D,T,Q) basis sets extended by a set of midbond functions centred in the middle of the intermolecular bond. A simple combining rule for interaction energies of this triad of clusters is proposed.

Critical properties of non-spherical molecule fluids from the 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.

CLUSTER INTEGRALS OF CONVEX MOLECULE SYSTEMS

Cluster integrals assigned to particles interacting via the Kihara non-spherical potential are studied theoretically. An exact formula is derived which allows one to consider the effect of molecular shape separately from the effect of soft interactions. Employing the proposed formalism, the cluster integrals are analysed. The approach is applied to determine the third virial coefficient and an efficient computational method is developed. The third virial coefficient was calculated for a combination of molecules with hard cores of prolate spher-ocylindrical- and spherical shapes interacting via the square-well, triangle-well and 12-6 pair potentials. Comparison with numerical results obtained by Monte Carlo integration is made and fair agreement is found.

Systems of oblate molecules. Monte Carlo study

Monte Carlo (MC) simulations were performed for systems of hard oblate spherocylinders with breadth-to-height ratios φ = 0.5–3.5 and packing fractions y = 0.25–0.45 and for Kihara oblate molecule systems of φ = 1 at reduced temperatures T* = 0.75 and 1.0 and y = 0.05–0.45. The compression factors and the dependence of the average correlation functions on the shortest surface-to-surface distance were determined for the case of hard oblate spherocylinders and the compression factors, residual internal energies and average correlation functions for the case of the generalized Kihara molecule systems. In addition, values of the third virial coefficient of the hard oblate spherocylinders were evaluated in the range of φ = 1–3. Results of the MC simulations for the hard oblate spherocylinders compare well with the available data in the literature and theoretical values; thermodynamic functions of the Kihara molecule systems were determined from the second-order perturbation theory. They agree well with our MC values at lower densities and higher reduced temperatures.

The third cross virial coefficient of hard convex bodies

Third cross virial coefficients of different combinations of hard prolate spherocylinders, hard oblate spherocylinders and hard spheres were calculated employing a simple Monte Carlo method. Obtained results were compared with a semiempirical relation proposed by one of the present authors. Two semiempirical relations devised recently for pure fluids were extended to yield the cross third virial coefficients. Satisfactory agreement was found in the case of moderately non-spherical bodies. For higher non-sphericities, theoretical values differ from Monte Carlo values up to 7%. Considerable regularities were found in series of one combination with an increase of the parameters L and/or D.

Perturbation theory for fluids of non-spherical polarizable dipolar molecules

Wertheims renormalized thermodynamic perturbation theory is extended to systems of the polarizable dipolar Kihara molecules and applied to the polarizable dipolar two-centre Lennard-Jones (LJ) fluid. In the third-order perturbation theory, the thermodynamic properties of the reference two-centre LJ fluids are evaluated via the thermodynamic functions of the corresponding system of the Kihara rod-like molecules. For the molecular distribution function of the Kihara fluid the function of the corresponding Gaussian overlap model is substituted. From the second- and third-order perturbation terms (determined for the permanent dipole moment and constant isotropic polarizability) the Pade approximant is formulated and its derivative used for the determination of the value of the effective dipole moment. The final value of the effective dipole moment is used to evaluate the electrostatic contributions to the residual Helmholtz energy, pressure and internal energy. For the given value of the permanent dipole mom...