Surface tension correlation for pure polar fluids by a new molecular model and SRK equation of state

In this work, a new model based on molecular thermodynamic was presented to correlate the surface tension of pure polar liquids. This model was developed based on the Davis theory. According to this theory, the surface tension is defined as a function of radial distribution function (RDF) and potential function (PF) as well. The proposed model includes three additive terms; hard sphere, dispersion and polar interactions. The RDF of Kolafa equation of state and Dirac delta function as a PF were used for hard sphere interaction. The RDF expression of Xu and Hu was considered for both dispersion and polar interactions. The presented model has two adjustable parameters, size and energy, which were obtained by optimization of an objective function for each pure fluid. This proposed approach was used for 19 pure polar fluids divided into 6 groups; organic acids, alcohols, ketones, ethers, aldehydes, and water. The average absolute deviation percent (AAD%) obtained for 19 fluids are 0.74. Also the surface tension of these 19 fluids was calculated by the use of SRK EOS and Sugden empirical formula in two cases. In case 1, Sugden's Parachor was calculated from Hugill and van Welsenes correlation and in case 2, it was obtained by optimization of an objective function for each component. The values of AAD% are 43.544 and 2.281 for cases 1 and 2, respectively. These results show the new model, which includes two adjustable parameters, can correlate the surface tension of the pure polar liquids with a high accuracy.     

A new equation of state for polar and nonpolar pure fluids

Chung, T.H., Khan, M.M., Lee, L.L. and Starling, K.E., 1984. A new equation of state for polar and nonpolar pure fluids. Fluid Phase Equilibria, 17: 351–372A new equation of state based on the concept of perturbation theory and the hard-convex-body equation of state has been developed successfully for nonpolar compounds. The equation can predict the thermodynamic properties (density, enthalpy departure and vapor pressure) of a wide range of pure fluids from small, spherical (argon-like) molecules to large, structurally complex molecules. For nonpolar compounds, the equation employs three parameters: the shape, size and energy parameters. For normal paraffins, the size parameter (hard-core volume) is related to the measurable van der Waals volume given by Bondi. For most other compounds, it is related to the critical volume. The shape-parameter values reflect the structure and degree of acentricity of the compound of interest. The equation has been extended to polar and associating compounds by using the mean-potential model. For polar compounds, a fourth parameter is required. The equation has been tested extensively for polar (dipolar and quadrupolar) and hydrogen-bonding compounds. The applicability of this equation for such a wide variety of substances provides an important first step in the development of a composition-dependent equation of state for mixtures.     

An interaction site model integral equation study of molecular fluids explicitly considering the molecular orientation

We implemented an interaction site model integral equation for rigid molecules based on a density-functional theory where the molecular orientation is explicitly considered. In this implementation of the integral equation, multiple integral of the degree of freedom of the molecular orientation is performed using efficient quadrature methods, so that the site-site pair correlation functions are evaluated exactly in the limit of low density. We apply this method to Cl(2), HCl, and H(2)O molecular fluids that have been investigated by several integral equation studies using various models. The site-site pair correlation functions obtained from the integral equation are in good agreement with the one from a simulation of these molecules. Rotational invariant coefficients, which characterize the microscopic structure of molecular fluids, are determined from the integral equation and the simulation in order to investigate the accuracy of the integral equation.     

An integral equation theory for inhomogeneous molecular fluids: the reference interaction site model approach

An integral equation theory which is applicable to inhomogeneous molecular liquids is proposed. The "inhomogeneous reference interaction site model (RISM)" equation derived here is a natural extension of the RISM equation to inhomogeneous systems. This theory makes it possible to calculate the pair correlation function between two molecules which are located at different density regions. We also propose approximations concerning the closure relation and the intramolecular susceptibility of inhomogeneous molecular liquids. As a preliminary application of the theory, the hydration structure around an ion is investigated. Lithium, sodium, and potassium cations are chosen as the solute. Using the Percus trick, the local density of solvent around an ion is expressed in terms of the solute-solvent pair correlation function calculated from the RISM theory. We then analyze the hydration structure around an ion through the triplet correlation function which is defined with the inhomogeneous pair correlation function and the local density of the solvent. The results of the triplet correlation functions for cations indicate that the thermal fluctuation of the hydration shell is closely related to the size of the solute ion. The triplet correlation function from the present theory is also compared with that from the Kirkwood superposition approximation, which substitutes the inhomogeneous pair correlation by the homogeneous one. For the lithium ion, the behavior of the triplet correlation functions from the present theory shows marked differences from the one calculated within the Kirkwood approximation.     

Transient molecular dynamics simulations of liquid viscosity for nonpolar and polar fluids

A transient molecular dynamics (TMD) method for obtaining fluid viscosity is extended to multisite, force-field models of both nonpolar and polar liquids. The method overlays a sinusoidal velocity profile over the peculiar particle velocities and then records the transient decay of the velocity profile. The viscosity is obtained by regression of the solution of the momentum equation with an appropriate constitutive equation and initial and boundary conditions corresponding to those used in the simulation. The transient velocity decays observed appeared to include both relaxation and retardation effects. The Jeffreys viscoelastic model was found to model accurately the transient responses obtained for multisite models for n-butane, isobutane, n-hexane, water, methanol, and 1-hexanol. TMD viscosities obtained for saturated liquids over a wide range of densities agreed well for the polar fluids, both with nonequilibrium molecular dynamics (NEMD) results using the same force-field models and with correlations based on experimental data. Viscosities obtained for the nonpolar fluids agreed well with the experimental and NEMD results at low to moderate densities, but underpredicted experimental values at higher densities where shear-thinning effects and viscous heating may impact the TMD simulations.     

Thermodynamic properties of polar fluids from a perturbed-dipolar-hard-sphere equation of state

Based on theoretical results for a system of hard spheres with dipoles, a new equation of state is applied to the correlation of thermodynamic properties for four fluids: argon, ammonia, water and acetonitrile. The reference system has the same dependence on density as that given by the Carnahan-Starling equation, but the coefficients are now functions of temperature through the reduced dipole moment. These coefficients are chosen to match the Padé approximant developed by Rushbrooke, Stell and Hoye for the Helmholtz energy of dipolar hard spheres. The reference system proposed here shows a phase transition for reduced dipole moments greater than 1.9. A simple, empirical perturbation term is added to the reference system to account for induction and dispersion forces. For polar fluids, the equation gives results significantly better than those obtained from conventional cubic equations of state, when using the same limited experimental data for determining equation-of-state parameters.     

An extended saturated liquid density equation

The recently developed saturated liquid density correlation of Iglesias-Silva and Hall for halogenated paraffins is extended to other classes of compounds involving paraffins, cycloparaffins, olefins, diolefins, cyclic-olefins, aromatics, alcohols, ethers, liquefied inorganic gases, and others. The two adjustable parameters of the correlation are optimized and reported for 126 compounds. The average error for 5377 experimental data points was 0.27%. The correlation is extended to multicomponent mixtures. A set of mixing rules is proposed. The correlation with this set of mixing rules is used to predict the saturated liquid density of 86 multicomponent systems consisting of LNG, heavy hydrocarbons, CO₂, H₂S, alcohols and halogenated paraffins. The average of error for 1378 experimental data points was 1.03% with 0 bias with respect to experimental data. These values compare well with the values from well-known correlations. For polar compounds or multicomponent systems containing polar compounds, the computation of saturated liquid density by this correlation shows superiority with respect to the other correlations.     

SSOZ-HNC and SSOZ-PY integral equation studies of the structure of three-site polar fluids

Structure factors and site-site distribution functions for models of liquid carbon disulphide (CS₂) and acetonitrile (CH₃CN) are obtained by using the site-site Ornstein-Zernike (SSOZ) integral equation with the Percus-Yevick (PY) and the hypernetted chain (HNC) closures. The calculated structure factors are found to be in good agreement with the neutron and X-ray diffraction data as well as with the simulation data. The site charges have a significant effect on the distribution functions but not on the structure factors of both the systems. There is very good qualitative agreement between the calculated distribution functions and the results from computer simulations. Distinctive shoulders found in the simulation results for the first peaks of the C-N and CH₃-CH₃ distribution functions are enhanced in the calculations using the integral equations.     

An approach for extending van der waals equations of state for polar,hydrogen bonding fluids applied to the soave equation of state

A method is developed for extending van der Waals type equations of state to highly polar, hydrogen bonding fluids. The method uses the acentric factor of the hydrocarbon homolog as the shape parameter and an empirical polar parameter incorporated into a closed form, temperature dependent polar correction term. When the method is applied to the Soave equation of state, a three-parameter equation of state results which reduces to the Soave equation for non-polar fluids, yet fits vapor pressures for polar fluids much better than the original equation. Furthermore, unlike other extensions applicable to polar fluids, the polar parameters obtained do seem to be related to the expected strength of polar interactions for different classes of compounds.     

An extended correlation for second virial coefficients of associated and quantum fluids

The empirical correlation developed in a previous paper is extended to hydrogen bonding and quantum pure compounds. The calculations of the second virial coefficients only require additional parameters, the reduced dipole moment for the associated compounds (alcohols, amines, water) and reduced de Broglie wavelength for the quantum compounds (H₂, D₂, T₂, ³He, He, Ne). The results agree well with experimental data.     

Perturbed chain-statistical associating fluid theory extended to dipolar and quadrupolar molecular fluids

The perturbed chain statistical associating fluid theory (PC-SAFT) is extended to polar molecular fluids, namely dipolar and quadrupolar fluids. The extension is based on the perturbation theory for polar fluids by Stell and co-workers. Appropriate expressions are proposed for dipole-dipole, quadrupole-quadrupole, and dipole-quadrupole interactions. Furthermore, induced dipole interactions are calculated explicitly in the model. The new polar PC-SAFT model is relatively complex; for this purpose, a truncated polar PC-SAFT model is proposed using only the leading term in the polynomial expansion for polar interactions. The new model is used for the calculation of thermodynamic properties of various quadrupolar pure fluids. In all cases, the agreement between experimental data and model predictions is very good.     

13C NMR studies of molecular relaxation processes in polar fluids

A study of the dynamical molecular structure of a dilute polar fluid is reported, in which ¹³C spin-lattice relaxation times of decanol in deuterated cyclohexane are presented for the individual carbon atoms, and the results are discussed in the context of viscosity data of decanol in alkane systems. The two techniques provide complementary information about the mobility of the alcohol chains and the onset of multimer formation, which is also pertinent to the dynamics of electron solvation in the same systems.     

Ion-induced nucleation in polar one-component fluids

We present a Ginzburg-Landau theory of ion-induced nucleation in a gas phase of polar one-component fluids, where a liquid droplet grows with an ion at its center. By calculating the density profile around an ion, we show that the solvation free energy is larger in gas than in liquid at the same temperature on the coexistence curve. This difference much reduces the nucleation barrier in a metastable gas.     

Application of the CPA equation of state to reservoir fluids in presence of water and polar chemicals

The complex phase equilibrium between reservoir fluids and associating compounds like water, methanol and glycols has become more and more important as the increasing global energy demand pushes the oil industry to target reservoirs with extreme or complicated conditions, such as deep or offshore reservoirs. Conventional equation of state (EoS) with classical mixing rules cannot satisfactorily predict or even correlate the phase equilibrium of those systems. A promising model for such systems is the Cubic-Plus-Association (CPA) EoS, which has been successfully applied to well-defined systems containing associating compounds. In this work, a set of correlations was proposed to calculate the CPA model parameters for the narrow cuts in ill-defined C₇₊ fractions. The correlations were then combined with either the characterization method of Pedersen et al. or that of Whitson et al. to extend CPA to reservoir fluids in presence of water and polar chemical such as methanol and monoethylene glycol. With a minimum number of adjustable parameters from binary pairs, satisfactory results have been obtained for different types of phase equilibria in reservoir fluid systems and several relevant model multicomponent systems. In addition, modeling of mutual solubility between light hydrocarbons and water is also addressed.     

An extended formula of site-site Smoluchowski-Vlasov equation for electrolyte solution and infinitely dilute solution

Solvation dynamics is one of the central subjects in solution chemistry. Site-site Smoluchowski-Vlasov (SSSV) equation is a diffusion equation for molecular liquid to analytically calculate the van Hove time correlation function. However, the application has been limited to simple solvent system such as liquid water because of the difficulty in solving the equation. In this study, an extended treatment of SSSV equation is proposed, which is applicable to a wide range of solution systems including mixed solution, electrolyte solution, and infinitely dilute solution. The present treatment realizes computation of the dynamics in LiCl aqueous solution, NaCl aqueous solution, and infinitely dilute aqueous solution of Li(+) and Cs(+) at the molecular level.     

Perturbation theory for the radial distribution function for simple polar fluids

The radial distribution function for a fluid whose molecules interact according to the Stockmayer potential was calculated by means of thermodynamic perturbation theory using two different approximations for the perturbation term and was compared with computer simulation results. The approximation based on the Percus-Yevick equation was found to be in much better agreement with the simulations than was the “simplified superposition approximation” to the perturbation term.     

Effective central potentials for molecular fluids

A recent suggestion by Lebowitz and Percus that the median intermolecular potential may serve as a simple temperature-independent effective central potential is tested against virial inversion data for the site-site Lennard-Jones potential obtained by Smith and Tindell. Excellent agreement is found even when the anisotropy in the potential is large. Second virial coefficients computed from the effective potential reproduce the true values to a high degree of accuracy.     

Dielectric permittivity profiles of confined polar fluids

The dielectric response of a simple model of a polar fluid near neutral interfaces is examined by a combination of linear response theory and extensive molecular dynamics simulations. Fluctuation expressions for a local permittivity tensor epsilon(r) are derived for planar and spherical geometries, based on the assumption of a purely local relationship between polarization and electric field. While the longitudinal component of epsilon exhibits strong oscillations on the molecular scale near interfaces, the transverse component becomes ill defined and unphysical, indicating nonlocality in the dielectric response. Both components go over to the correct bulk permittivity beyond a few molecular diameters. Upon approaching interfaces from the bulk, the permittivity tends to increase, rather than decrease as commonly assumed, and this behavior is confirmed for a simple model of water near a hydrophobic surface. An unexpected finding of the present analysis is the formation of "electrostatic double layers" signaled by a dramatic overscreening of an externally applied field inside the polar fluid close to an interface. The local electric field is of opposite sign to the external field and of significantly larger amplitude within the first layer of polar molecules.     

Bulk modulus for some simple molecular fluids

The bulk modulus B of several molecular fluids composed of rigid molecules has been calculated from p-p-T data obtained with a high-pressure vibrating tube densitometer. The data of all the substances studied, including Ar, can be described by a single master curve when plotted versus the reduced density *, in agreement with the predictions of the Gubbins-Gray perturbation theory for fluids with the same reference system. Combination of p-p-T and C_v data with the virial theorem has allowed the calculation of the exponent characterizing the repulsive branch of the intermolecular potential n. The different values of n suggest that different reference systems should be used for each substance, in contradiction with the conclusions obtained from the B versus * curves. This indicates that p-p-T data are less sensitive to the details of the intermolecular potential than their combination with other thermal properties like C_v, internal energy or residual entropy.