Force field parameters used in classical molecular simulations can be estimated from quantum mechanical calculations or spectroscopic measurements. This especially applies to bonded interactions such as bond-stretching, bond-bending, and torsional interactions. However, it is difficult and computational expensive to obtain accurate parameters describing the nonbonded van der Waals interactions from quantum mechanics. In many studies, these parameters are adjusted to reproduce experimental data, such as vapor-liquid equilibria (VLE) data. Adjusting these force field parameters to VLE data is currently a cumbersome and computationally expensive task. The reason is that the result of a calculation of the vapor-liquid equilibria depends on the van der Waals interactions of all atom types in the system, therefore requiring many time-consuming iterations. In this work, we use an analytical equation of state, the perturbed chain statistical associating fluid theory (PC-SAFT), to predict the results of molecular simulations for VLE. The analytical PC-SAFT equation of state is used to approximate the objective function f(p) as a function of the array of force field parameters p. The objective function is here for example defined as the deviations of vapor pressure, enthalpy of vaporization and liquid density data, with respect to experimental data. The parameters are optimized using the analytical PC-SAFT equation of state, which is orders of magnitude quicker to calculate than molecular simulation. The solution is an excellent approximation of the real objective function, so that the resulting method requires only very few molecular simulation runs to converge. The method is here illustrated by optimizing transferable Lennard-Jones parameters for the n-alkane series. Optimizing four force field parameters p = (ε(CH(2))(CH(2)), ε(CH(3))(CH(3)), σ(CH(2))(CH(2)), σ(CH(3))(CH(3))) we obtain excellent agreement of coexisting densities, vapor pressure and caloric properties within only 2 -3 molecular simulation runs.
Onsager-like theories are commonly used to describe the phase behavior of nematic (only orientationally ordered) liquid crystals. A key ingredient in such theories is the orientation-dependent excluded volume of two molecules. Although for hard convex molecular models this is generally known in analytical form, for more realistic molecular models that incorporate intramolecular flexibility, one has to rely on approximations or on computationally expensive Monte Carlo techniques. In this work, we provide a general correlation for the excluded volume of tangent hard-sphere chains of arbitrary chain length and flexibility. The flexibility is introduced by means of the rod-coil model. The resulting correlation is of simple analytical form and accurately covers a wide range of pure component excluded volume data obtained from Monte Carlo simulations of two-chain molecules. The extension to mixtures follows naturally by applying simple combining rules for the parameters involved. The results for mixtures are also in good agreement with data from Monte Carlo simulations. We have expressed the excluded volume as a second order power series in sin (γ ), where γ is the angle between the molecular axes. Such a representation is appealing since the solution of the Onsager Helmholtz energy functional usually involves an expansion of the excluded volume in Legendre coefficients. Both for pure components and mixtures, the correlation reduces to an exact expression in the limit of completely linear chains. The expression for mixtures, as derived in this work, is thereby an exact extension of the pure component result of Williamson and Jackson [Mol. Phys. 86, 819-836 (1995)].
The liquid crystal phase behavior of linear and partially flexible hard-sphere chain fluids and the solubility of hard spheres in hard-sphere chain fluids are studied by constant pressure Monte Carlo simulations. An extensive study on the phase behavior of linear fluids with a length of 7,8,9,10,11,12,13,14,15, and 20 beads is carried out. The phase behavior of partially flexible fluids with a total length of 8, 10, 14, and 15 beads and with different lengths for the linear part is also determined. A precise description of the reduced pressure and of the packing fraction change at the isotropicnematic coexistence was achieved by performing long simulation runs. For linear fluids, a maximum in the isotropic to nematic packing fraction change is observed for a chain length of 15 beads. The infinite dilution solubility of hard spheres in linear and partially flexible hard-sphere chain fluids is calculated by the Widom test-particle insertion method. To identify the effect of chain connectivity and molecular anisotropy on free volume, solubility is expressed relative to that of hard spheres in a hard sphere fluid at same packing fraction as relative Henry's law constants. A linear relationship between relative Henry's law constants and packing fraction is observed for all linear fluids. Furthermore, this linearity is independent of liquid crystal ordering and seems to be independent of chain length for linear chains of 10 beads and longer. The same linear relationship was observed for the solubility of hard spheres in nematic forming partially flexible fluids for packing fractions up to a value slightly higher than the nematic packing fraction at the isotropic-nematic coexistence. At higher packing fractions, the small flexibility of these fluids seems to improve solubility in comparison with the linear fluids. © 2013 AIP Publishing LLC. [http://dx
The Helmholtz energy of a fluid interacting by a Lennard-Jones pair potential is expanded in a perturbation series. Both the methods of Barker-Henderson (BH) and of Weeks-Chandler-Andersen (WCA) are evaluated for the division of the intermolecular potential into reference and perturbation parts. The first four perturbation terms are evaluated for various densities and temperatures (in the ranges ρ=0-1.5 and T=0.5-12) using Monte Carlo simulations in the canonical ensemble. The simulation results are used to test several approximate theoretical methods for describing perturbation terms or for developing an approximate infinite order perturbation series. Additionally, the simulations serve as a basis for developing fully analytical third order BH and WCA perturbation theories. The development of analytical theories allows (1) a careful comparison between the BH and WCA formalisms, and (2) a systematic examination of the effect of higher-order perturbation terms on calculated thermodynamic properties of fluids. Properties included in the comparison are supercritical thermodynamic properties (pressure, internal energy, and chemical potential), vapor-liquid phase equilibria, second virial coefficients, and heat capacities. For all properties studied, we find a systematically improved description upon using a higher-order perturbation theory. A result of particular relevance is that a third order perturbation theory is capable of providing a quantitative description of second virial coefficients to temperatures as low as the triple-point of the Lennard-Jones fluid. We find no reason to prefer the WCA formalism over the BH formalism.
An extension of Onsager's second virial theory is developed to describe the isotropic-nematic phase transition of tangent hard-sphere chain fluids. Flexibility is introduced by the rod-coil model. The effect of chain-flexibility on the second virial coefficient is described using an accurate, analytical approximation for the orientation-dependent pair-excluded volume. The use of this approximation allows for an analytical treatment of intramolecular flexibility by using a single pure-component parameter. Two approaches to approximate the effect of the higher virial coefficients are considered, i.e., the Vega-Lago rescaling and Scaled Particle Theory (SPT). The Onsager trial function is employed to describe the orientational distribution function. Theoretical predictions for the equation of state and orientational order parameter are tested against the results from Monte Carlo (MC) simulations. For linear chains of length 9 and longer, theoretical results are in excellent agreement with MC data. For smaller chain lengths, small errors introduced by the approximation of the higher virial coefficients become apparent, leading to a small under-and overestimation of the pressure and density difference at the phase transition, respectively. For rod-coil fluids of reasonable rigidity, a quantitative comparison between theory and MC simulations is obtained. For more flexible chains, however, both the Vega-Lago rescaling and SPT lead to a small underestimation of the location of the phase transition. © 2013 AIP Publishing LLC. [http://dx
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