Kihara Fluids Research Articles

Monte Carlo simulations and molecular discrete perturbation theory of multipolar oblate Kihara fluids

The vapor-liquid coexistence of oblate Kihara fluids embedding both point dipole or quadrupole moments has been determined within the framework of the Gibbs ensemble Monte Carlo method and predicted by the molecular discrete perturbation theory. For dipolar models, we explored both axial and non-axial orientations of the dipole moment with respect to the molecular axis. The discrepancies between theoretical and simulations results are discussed in terms of both the reliability of the approximations in which the free energy terms in the perturbation expansion for molecular fluids are based and of the aggregation features found in the structural distribution functions of the liquid phases close to the coexistence boundary, more prominent for highly anisotropic fluids. As a last output of the study, we found a non-monotonous behavior of the critical properties for dipolar models that seems to be wedded to that structuring/aggregation effects, mostly induced by the strongly oriented multipolar interactions.

Critical temperature shift modeling of confined fluids using pore-size-dependent energy parameter of potential function

The behavior and critical properties of fluids confined in nanoscale porous media differ from those of bulk fluids. This is well known as critical shift phenomenon or pore proximity effect among researchers. Fundamentals of critical shift modeling commenced with developing equations of state (EOS) based on the Lennard–Jones (L–J) potential function. Although these methods have provided somewhat passable predictions of pore critical properties, none represented a breakthrough in basic modeling. In this study, a cubic EOS is derived in the presence of adsorption for Kihara fluids, whose attractive term is a function of temperature. Accordingly, the critical temperature shift is modeled, and a new adjustment method is established in which, despite previous works, the bulk critical conditions of fluids are reliably met with a thermodynamic basis and not based on simplistic manipulations. Then, based on the fact that the macroscopic and microscopic theories of corresponding states are related, an innovative idea is developed in which the energy parameter of the potential function varies with regard to changes in pore size, and is not taken as a constant. Based on 94 available data points of critical shift reports, it is observed that despite L–J, the Kihara potential has sufficient flexibility to properly fit the variable energy parameters, and provide valid predictions of phase behavior and critical properties of fluids. Finally, the application of the proposed model is examined by predicting the vapor–liquid equilibrium properties of a ternary system that reduced the error of the L–J model by more than 6%.

Thermodynamics of multipolar Kihara fluids. Results from Monte Carlo simulations and molecular discrete perturbation theory

We present a systematic study of the vapor–liquid equilibria of prolate Kihara fluids embedding both dipole and quadrupole moments Monte Carlo simulations and perturbation theory methods. The agreement between both approaches is good and allows to shed light on some general features of molecular models whose distribution of charge can be modeled as a dipole plus a quadrupole moments. The validation of the equation of state does lead as a byproduct to a rapid, uncommon, and powerful instrument able to widen the frontiers of perturbation theory for molecular fluids and their mixtures.

Liquid crystal phase diagram of soft repulsive rods and its mapping on the hard repulsive reference fluid

The liquid crystal phase diagram of the soft repulsive Kihara fluid has been characterised by means of Monte Carlo simulations, for a selection of elongations of the rod-like particles (L*= 2–7) and over a broad range of temperatures (T *= 1–50). Three qualitatively different regimes of liquid crystalline behaviour are described that are related to the emergence of isotropic–nematic–smectic and isotropic–smectic–solid triple points above specific rod elongations. A mapping of the soft repulsive fluids on hardrepulsive fluids of effective elongation depending on L* and T * is evaluated. Such mapping provides a correct qualitative description of the role of temperature on the liquid crystal phases, and provides a fairly accurate prediction of equations of states and radial functions within the isotropic, nematic and smectic phases. Nevertheless, in comparison to the simulation results, the mapping underestimates the temperature of the isotropic–nematic–smectic triple point, while it overestimates that of the isotropic–smectic–solid one. These results should guide the use of reference hard-body systems to describe the behaviour of soft liquid crystalline materials.

Perturbation theory for non-spherical fluids based on discretization of the interactions

An extension of the discrete perturbation theory [A. L. Benavides and A. Gil-Villegas, Mol. Phys. 97(12), 1225 (1999)] accounting for non-spherical interactions is presented. An analytical expression for the Helmholtz free energy for an equivalent discrete potential is given as a function of density, temperature, and intermolecular parameters with implicit shape dependence. The presented procedure is suitable for the description of the thermodynamics of general intermolecular potential models of arbitrary shape. The overlap and dispersion forces are represented by a discrete potential formed by a sequence of square-well and square-shoulders potentials of shape-dependent widths. By varying the intermolecular parameters through their geometrical dependence, some illustrative cases of square-well spherocylinders and Kihara fluids are considered, and their vapor-liquid phase diagrams are tested against available simulation data. It is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the Monte Carlo data for the selected potentials, except near the critical region.

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.

A novel orientation-dependent potential model for prolate mesogens

An intermolecular potential is introduced for the study of molecular mesogenic fluids. The model combines distinct features of the well-known Gay-Berne and Kihara potentials by incorporating dispersive interactions dependent on the relative pair orientation to a spherocylinder molecular core. Results of a Monte Carlo simulation study focused on the liquid crystal phases exhibited by the model fluid are presented. For the chosen potential parameters, molecular aspect ratio L*=5 and temperatures T*=2, 3, and 5, isotropic, nematic, smectic-A, and hexatic phases are found. The location of the phase boundaries as well as the equation of state of the fluid and further thermodynamical and structural parameters are discussed and contrasted to the Kihara fluid. In comparison to this latter fluid, the model induces the formation of ordered liquid crystalline phases at lower packing fractions and it favors, in particular, the appearance of layered hexatic ordering as a consequence of the greater attractive interaction assigned to the parallel side-to-side molecular pair configurations. The results contribute to the evaluation of the role of specific interaction energies in the mesogenic behavior of prolate molecular liquids in dense environments.

Liquid crystal behavior of the Kihara fluid.

The liquid crystal phases of the Kihara fluid have been studied in computer simulations. The work focuses on the isotropic-nematic-smectic-A triple point region, especially relevant for the understanding of the properties and the design of real mesogens with specific phase diagrams. The Kihara interaction resembles more appropriately than other related models, the shape of elongated polymers and biomolecules, and a closer assertion is provided for the role of the configurational entropy and the dispersive interactions in the behavior of such molecules in dense phases or under macromolecular crowding conditions.

Influence of charge distribution on the thermophysical and dynamical properties of polar linear molecules

Gibbs ensemble Monte Carlo and molecular dynamics simulations were used to study thermophysical and dynamical properties of Kihara fluids consisting of linear molecules with dipolar symmetry. Two models differing in the electrostatic part of the intermolecular potential have been considered. The first one is an ideal dipole (ID) model where electrostatic interactions are modeled as point dipoles placed on the molecular center of mass, and the second one is a discrete charge (DC) model with single positive and negative charges placed at opposite ends of the molecules. The magnitude of the charges and the distance between them were chosen to reproduce the dipole moment of the ID model. In addition, an effective ionic strength for the DC model has been defined. Simulations were performed at several densities and temperatures in a wide range of molecular lengths and at three dipole moments. For all the systems, vapor–liquid equilibrium, thermodynamic, and structural properties, autocorrelation functions, correlation times, and transport properties such as diffusion, shear viscosity, and thermal conductivity have been obtained and analyzed. The results of the present study are in agreement with those found in previous works and they confirm that, although differences between the DC model and the ID model are small for the lower molecular lengths, they become more pronounced at higher molecular lengths. Finally, the influence of the effective ionic strength on the different properties of the system is discussed.

Application of Kihara potential model to real non-spherical fluids

The calculation of radial distribution function (RDF) of Kihara rigid core fluids is performed using the sequential–analytic (S–A) method and the effect of reduced rigid core diameter on the shape of RDF is demonstrated. A theoretical equation of state for Kihara fluid is presented and used to calculate its reduced critical properties. It has been shown that the critical compressibility factor of a Kihara fluid is solely determined by its reduced rigid core diameter, and hence the critical compressibility factor of any real fluids can be reproduced through adjusting the value of reduced rigid core diameter. Instead of regression of virial coefficient or viscosity data of dilute gases, it is suggested to determine the parameters of Kihara potential model by matching the critical properties of corresponding substances. It has been shown that the Kihara parameters determined by matching critical properties can be used to predict the properties of both dilute and dense fluids while those determined by fitting dilute gas properties cannot.

Coexistence properties of higher n-alkanes modelled as Kihara fluids: Gibbs ensemble simulations

The coexistence vapour–liquid properties of higher n-alkanes of large anisotropy (pentane, decane, and pentadecane) modelled by rod-like Kihara fluids were determined using Gibbs-ensemble (GE) and extended Gibbs ensemble (EGE) Monte Carlo simulations. We found that for dense, low temperature states the EGE becomes more accurate and efficient than GE. Comparison of the simulation results with those of a second-order perturbation theory shows that, surprisingly, the theory performs reasonably well for models of large elongations (pentadecane) but disagrees considerably for the model of pentane.

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.

Perturbation theory for fluids of non-spherical polarizable dipolar molecules

Wertheim's 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 Padé 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 moment the thermodynamic functions depend both on polarizability and elongation of the model considered (and on temperature and density). Fair agreement of the theoretical results with simulation data for the polarizable Stockmayer and polarizable dipolar 2cLJ fluids was found.

Monte Carlo simulations of dipolar and quadrupolar linear Kihara fluids. A test of thermodynamic perturbation theory

Several simulations of dipolar and quadrupolar linear Kihara fluids using the Monte Carlo method in the canonical ensemble have been performed. Pressure and internal energy have been directly determined from simulations and Helmholtz free energy using thermodynamic integration. Simulations were carried out for fluids of fixed elongation at two different densities and several values of temperature and dipolar or quadrupolar moment for each density. Results are compared with the perturbation theory developed by Boublík for this same type of fluid and good agreement between simulated and theoretical values was obtained especially for quadrupole fluids. Simulations are also used to obtain the liquid structure giving the first few coefficients of the expansion of pair correlation functions in terms of spherical harmonics. Estimations of the triple point temperature to critical temperature ratio are given for some dipole and quadrupole linear fluids. The stability range of the liquid phase of these substances is shortly discussed and an analysis about the opposite roles of the dipole moment and the molecular elongation on this stability is also given.

Monte Carlo simulations of dipolar and quadrupolar linear Kihara fluids. A test of thermodynamic perturbation theory

Several simulations of dipolar and quadrupolar linear Kihara fluids using the Monte Carlo method in the canonical ensemble have been performed. Pressure and internal energy have been directly determined from simulations and Helmholtz free energy using thermodynamic integration. Simulations were carried out for fluids of fixed elongation at two different densities and several values of temperature and dipolar or quadrupolar moment for each density. Results are compared with the perturbation theory developed by Boublík for this same type of fluid and good agreement between simulated and theoretical values was obtained especially for quadrupole fluids. Simulations are also used to obtain the liquid structure giving the first few coefficients of the expansion of pair correlation functions in terms of spherical harmonics. Estimations of the triple point temperature to critical temperature ratio are given for some dipole and quadrupole linear fluids. The stability range of the liquid phase of these substances is shortly discussed and an analysis about the opposite roles of the dipole moment and the molecular elongation on this stability is also given.

Nonequilibrium properties of linear polar Kihara fluids from molecular dynamics. Results for models and for liquid acetonitrile

Molecular dynamics simulations for polar Kihara fluids are reported for linear models of different lengths at several dipole and quadrupole values and at three different thermodynamic states. Two of these states are close to the vapor–liquid equilibrium curve and the third one is at the same density as the first and at the same temperature as the second. Self-correlation functions and translational and orientational times are calculated and analyzed. Transport properties, diffusion, thermal conductivity, and shear viscosity are also reported and discussed in terms of multipolar forces. Correlation terms are used to calculate band broadening in different kinds of molecular spectra. Finally, it is shown how it is possible to discriminate between two models of acetonitrile that fit equilibrium properties equally well by using dynamic properties.

Dynamical properties and transport coefficients of Kihara linear fluids

Transport properties of spherical and linear molecules modeled by the Kihara potential are studied by molecular dynamics simulations. Diffusion coefficients, shear viscosities, and thermal conductivities are calculated for a wide range of the fluid region and for several elongations. The corresponding individual and collective correlation functions are discussed along with angular velocity and reorientational correlation functions. Relaxation times and simple models relevant to orientational motion are also studied. The results obtained are discussed in a corresponding states framework, using previous Gibbs ensemble Monte Carlo data for the liquid–vapor equilibria of the models. In this way, the role of elongation can be studied. It is found that in most of the liquid region, the diffusion coefficient is weakly dependent on elongation. On the other hand, both viscosity and thermal conductivity are found to decrease with elongation. The dependence of transport coefficients on density and temperature is also discussed. On testing the Stokes–Einstein relation, it was observed that, unlike previous findings for hard spheres, stick boundary conditions perform just as good as slip boundary conditions for the Lennard-Jones fluid and the low-elongated Kihara fluid.

Liquid-Vapor Equilibria of Polar Fluids from a van der Waals-like Theory

A van der Waals-like theory of quadrupolar and dipolar linear fluids is presented. The reference system consists of a hard polar fluid, and attractive forces are considered through the mean field approximation. The effect of polar forces on liquid-vapor equilibria and on critical properties is analyzed for a number of molecular elongations. Trends as predicted by the theory are compared with computer simulations of linear polar fluids, and good agreement is found. Polar forces increase the critical temperature and acentric factor of a fluid. Quadrupole moment increases the critical density of a fluid. However, high dipole moments decrease critical densities. Deviations from the principle of corresponding states are analyzed. Polar forces and molecular elongation provoke a broadening of the coexistence curve and an increase of the slope of the vapor pressure curve when reduced by their critical magnitudes. The presented treatment, being quite simple, describes most of the main features of vapor-liquid equilibria of linear polar fluids. I. Introduction It is a century now since van der Waals proposed his equation of state.' A consequence of this equation is that all fluids follow the same equation of state when reduced by their critical magnitudes. That constitutes the principle of corresponding states which was later formulated on a molecular basis.* Although this principle holds quite well for spherical and almost spherical molecules, important deviations were found for molecules having a nonspherical shape or presenting a multipole (dipole or quadrupole) moment. Early attempts to account for these deviations from statistical mechanics grounds were form~lated.~.~ They were especially successful in the description of the effect of polar forces on spherical-shaped modek5 The past two decades were quite active in developing an understanding of the role of molecular shape on phase equilibria. van der Waals-like theories? perturbation theories,7-l0 or even computer simulation' ' have provided a clear understanding of the role of molecular shape on phase equilibria. The situation is less satisfactory for nonspherical polar fluids although some recent progress should be mentioned. Integral equations are now being solved for a number of linear polar models,'* and progress in the field through this line may be anticipated. Perturbation theories have recently been developed for linear polar fluids, and the consequences have not completely been explored yet.13-17 Simultaneously, a number of simulation studies concerning dipolar and quadrupolar linear fluids have been perf~rmed.'~J~ Quite recently, it has become possible to easily obtain liquid-vapor equilibria by computer simulation through the so-called Gibbs ensemble methodology.2o This new route is just being explored. In fact, Dubey et a1.*' have presented simulation results for linear dipolar fluids, and we have recently performed a very comprehensive simulation study of quadrupolar linear Kihara fluids.22 A similar study for a quadrupolar two-center Lennard-Jones model has recently been performed by using the NFT+ test particle method.23 These studies can be considered as examples of what may be learned in the near future on vapor-liquid equilibria of linear polar fluids.

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.

First-order radial distribution functions based on the mean spherical approximation for square-well, Lennard-Jones, and Kihara fluids

Following the assumption of the mean spherical approximation, analytical expressions of the first-order radial distribution function are obtained for the square-well, Lennard-Jones, and Kihara potentials with a hard core through a complex-plane analysis. The developed expression yields good agreement with the available computer simulation data for the radial distribution function of the Lennard-Jones fluid.