Square-well Chain Fluids Research Articles

Equation of state with quantum effects for square-well chain fluid with variable range

Equation of state with quantum effects for square-well chain fluid with variable range

Experimental Determination and Modeling of Density, Viscosity, and Surface Tension for Sulfolane + Ethyl Acetate and + n-Propyl Acetate

The density, viscosity, and surface tension for the binary mixtures of sulfolane + ethyl acetate and + n-propyl acetate were measured at the atmospheric pressure and temperature ranging from 308.15 to 328.15 K. The linear equation and Andrade model were successfully used to correlate the experimental density and viscosity, respectively. On the basis of the experimental data, the viscosity energy barrier and the surface entropy/enthalpy were further obtained. The calculation of the molecular interaction energy using the Dmol3 module in Materials Studio software shows that the interaction energy in sulfolane + ethyl acetate is slightly greater than one in sulfolane + n-propyl acetate, which is consistent with the experimental observation. In addition, each experimental property of density, viscosity, and surface tension can well be reproduced by the square-well chain fluid with variable range (SWCF-VR) equation of state with one different binary adjustable parameter.

Phase Equilibria of Polydisperse Square-Well Chain Fluid Confined in Random Porous Media: TPT of Wertheim and Scaled Particle Theory.

Extension of Wertheim's thermodynamic perturbation theory and its combination with scaled particle theory is proposed and applied to study the liquid-gas phase behavior of polydisperse hard-sphere square-well chain fluid confined in the random porous media. Thermodynamic properties of the reference system, represented by the hard-sphere square-well fluid in the matrix, are calculated using corresponding extension of the second-order Barker-Henderson perturbation theory. We study effects of polydispersity and confinement on the phase behavior of the system. While polydispersity causes increase of the region of phase coexistence due to the critical temperature increase, confinement decreases the values of both critical temperature and critical density making the region of phase coexistence smaller. This effect is enhanced with the increase of the size ratio of the fluid and matrix particles. The increase of the average chain length at fixed values of polydispersity and matrix density shifts the critical point to a higher temperature and a slightly lower density.

The role of higher-order terms in perturbation approaches to the monomer and bonding contributions in a SAFT-type equation of state for square-well chain fluids

ABSTRACTA perturbation theory for square-well chain fluids is developed within the scheme of the (generalised) Wertheim thermodynamic perturbation theory. The theory is based on the Pavlyukhin parametrisations [Y. T. Pavlyukhin, J. Struct. Chem. 53, 476 (2012)] of their simulation data for the first four perturbation terms in the high temperature expansion of the Helmholtz free energy of square-well monomer fluids combined with a second-order perturbation theory for the contact value of the radial distribution function of the square-well monomer fluid that enters into bonding contribution. To obtain the latter perturbation terms, we have performed computer simulations in the hard-sphere reference system. The importance of the perturbation terms beyond the second-order one for the monomer fluid and of the approximations of different orders in the bonding contribution for the chain fluids in the predicted equation of state, excess energy and liquid–vapour coexistence densities is analysed.

Density functional theory for the selective adsorption of small molecules on a surface modified with polymer brushes

A density functional method based on weighted density approximation is extended to study the selective adsorption of small molecules on a surface modified with end-grafted square-well chains. The excess part of the Helmholtz free energy functional is divided into two components: the hard sphere repulsion and the square-well attraction. The equation of state for hard sphere chain fluids developed by Liu et al. is used to calculate the repulsive part of the excess Helmholtz free energy functional, and the equation of state for square-well chain fluid with variable range developed by Li et al. is employed to calculate the attractive part. With this theoretical model, we examine the physical properties of the grafted polymer and the selective adsorption of small molecules on the modified surface.

Equation of state of square-well chain fluid with variable range for CO<sub>2</sub> + physical absorption solvent

采用变阱宽方阱链流体(SWCF-VR)状态方程关联了CO 2 在几种常规物理吸收溶剂中的溶解度数据, 得到了二元交互作用参数, 建立了二元交互作用参数与温度的关联式. 结果表明, 采用一个二元交互作用参数, SWCF-VR 方程均能很好地描述CO 2 在常规流体中的溶解度, 尤其能满意再现甲醇低温洗工艺中CO 2 -甲醇的相行为. 利用建立的二元交互作用参数与温度的关联式, 可将SWCF-VR 状态方程拓展应用于预测二元系统气液两相的密度以及CO 2 -物理吸收溶剂多元系统的气液平衡.

Capturing Thermodynamic Behavior of Ionic Liquid Systems: Correlations with the SWCF-VR Equation

An equation of state for square-well chain fluids with variable well-width range (SWCF-VR EoS) [Li et al. Fluid Phase Equilib.2009, 276, 57] was applied to ionic liquid (IL) systems. ILs were treat...

Modeling pVT Properties and Vapor-Liquid Equilibrium of Ionic Liquids Using Cubic-plus-association Equation of State

Combining Peng-Robinson (PR) equation of state (EoS) with an association model derived from shield-sticky method (SSM) by Liu et al., a new cubic-plus-association (CPA) EoS is proposed to describe the thermodynamic properties of pure ionic liquids (ILs) and their mixtures. The new molecular parameters for 25 ILs are obtained by fitting the experimental density data over a wide temperature and pressure range, and the overall average deviation is 0.22%. The model parameter b for homologous ILs shows a good linear relationship with their molecular mass, so the number of model parameters is reduced effectively. Using one temperature-independent binary adjustable parameter k ij , satisfactory correlations of vapor-liquid equilibria (VLE) for binary mixtures of ILs + non-associating solvents and + associating solvents are obtained with the overall average deviation of vapor pressure 2.91% and 7.01%, respectively. In addition, VLE results for ILs + non-associating mixtures from CPA, lattice-fluid (LF) and square-well chain fluids with variable range (SWCF-VR) EoSs are compared.

A new simple analytical expression for the average site–site radial distribution function of hard sphere chain fluid

A new simple analytical expression for the first coordination shell (1 ≤ x ≤ 2) of the average site–site intermolecular radial distribution function (ASSIRDF) of freely jointed tangent hard sphere chain fluid (FJTHSC) is proposed. The proposed expression is a polynomial expansion of packing fraction. The dependence of each polynomial coefficient on the radial coordinate and segment number is described by a polynomial expansion of nonlinear base function and a simple relation proposed by Liu and Hu, respectively. The coefficients involved in the expression of ASSIRDF are optimized by fitting the numerical values of Percus–Yevick (PY) integral equation theory of Chiew. The proposed expression of ASSIRDF is applied to an analytical perturbative equation of state (EOS) in order to modify it and improve its accuracy in predicting the compressibility factor and vapor–liquid equilibria of freely jointed tangent square-well chain (FJTSWC) fluids of variable well-widths (1 ≤ λ ≤ 2). The predicted results are in good agreement with the simulation data and also compared with that of other well-known equations of state.

Modeling of Surface Tension and Viscosity for Non-electrolyte Systems by Means of the Equation of State for Square-well Chain Fluids with Variable Interaction Range

The equation of state (EOS) for square-well chain fluid with variable range (SWCF-VR) developed in our previous work based on statistical mechanical theory for chemical association is employed for the correlations of surface tension and viscosity of common fluids and ionic liquids (ILs). A model of surface tension for multi-component mixtures is presented by combining the SWCF-VR EOS and the scaled particle theory and used to produce the surface tension of binary and ternary mixtures. The predicted surface tensions are in excellent agreement with the experimental data with an overall average absolute relative deviation (AAD) of 0.36%. A method for the calculation of dynamic viscosity of common fluids and ILs at high pressure is presented by combining Eyring's rate theory of viscosity and the SWCF-VR EOS. The calculated viscosities are in good agreement with the experimental data with the overall AAD of 1.44% for 14 fluids in 84 cases. The salient feature is that the molecular parameters used in these models are self-consistent and can be applied to calculate different thermodynamic properties such as pVT, vapor-liquid equilibrium, caloric properties, surface tension, and viscosity.

Modeling of the Thermodynamic Properties of Aqueous Ionic Liquid Solutions with an Equation of State for Square-Well Chain Fluid with Variable Range

A new thermodynamic model based on an equation of state for square-well chain fluid with variable range (SWCF-VR) is proposed to describe the thermodynamic properties of aqueous solutions of ionic liquids. In this approach the electrostatic interactions are characterized via the mean spherical approximation and the ionic associations between the cations and anions of the ionic liquid are considered through the shield-sticky approach. The liquid densities, osmotic coefficients, and vapor pressures of aqueous solutions of nine ionic liquids (ILs) containing [Cxmim][Br] (x = 2, ..., 6), [C4mim][BF4] and [Cxmim][MSO4] (x = 1, 3, 4) have been modeled with the new model. Two ionic parameters for each anion and three for each cation of the ionic liquids were adjusted to experimental liquid densities and osmotic coefficients, and the corresponding average deviations are only 0.87% and 2.49%, respectively. Using the same ionic parameters, the vapor pressures of ionic liquid solutions are accurately predicted. The ...

A new simple analytic equation of state for square-well chain fluids with variable width, 1.1 < λ < 2, based on perturbation theory and an analytic representation of the hard-sphere radial distribution function g HS(r)

A new, simple and analytic perturbation theory equation of state for square-well chain fluids of variable well width (1.1 < λ < 2) is proposed. It is based on the recently developed, infinite-order Barker and Henderson perturbation theory for the thermodynamic properties of the reference monomer square-well fluid [J. Chem. Phys. 124 (2006) 154505], the statistical associating fluid theory to account for chain formation, and the new analytical expression of the radial distribution function of hard spheres developed by Sun in terms of a polynomial expansion of nonlinear base functions [Can. J. Phys. 83 (2005) 55]. The various integrals appearing in the theory are then simply evaluated in closed form. The compressibility factor and the internal energy thus obtained are in overall good agreement with existing computer simulation data for dimer, 4-mer, 8-mer and 16-mer square-well chain fluids at different well-width. Moreover the compressibility factors also compare favorably with those obtained from six other square-well chain fluids equations of state.

Representation of Phase Behavior of Ionic Liquids Using the Equation of State for Square-well Chain Fluids with Variable Range

An equation of state (EOS) for square-well chain fluids with variable range (SWCF-VR) developed based on statistical mechanics for chemical association was employed for the calculations of pressure-volume-temperature ( pVT) and phase equilibrium of pure ionic liquids (ILs) and their mixtures. The new molecular parameters for 23 ILs were obtained by fitting their experimental density data over a wide temperature and pressure ranges. The molecular parameters of ILs composed of homologous organic cation and an identical anion such as [C x mim][NTf 2] are good linear with respect to their molecular weight, indicating that the molecular parameters of homologous substances, subsequently pVT and vapor-liquid equilibria vapor-liquid equilibria (VLE) can be predicted using the generalized parameter when no experimental data were available. The new set of parameters were satisfactorily used for calculations of the property of solvent and ILs mixture and the solubility of gas in various ILs at low pressure only using one temperature-independent binary interaction parameter.

A new analytical perturbed equation of state for hard chain fluids with attractive potentials of variable range

A completely analytical perturbation theory equation of state for hard chain fluids is derived. The derived equation of state can represent the thermodynamic properties of many kinds of hard chain fluids such as the square-well chain and Yukawa chain fluid, by varying of its parameters. The predicted results are in good agreement with both the molecular simulation data and the well-known equations of state. In this paper the hard chain molecules are modelled as a pearl necklace of freely jointed spheres that interact via site–site intermolecular potential. Our first- and second-order perturbation terms are based on the Barker–Henderson local compressibility approximation and Gulati–Hall’s perturbation theory, respectively. To obtain the perturbation terms, we do not require knowledge of site–site radial distribution function of the reference hard chain fluid, which is obtained from molecular dynamic simulation, or any explicit mathematical form of it. This perturbation method yields a simple and general analytical expression for each thermodynamic property of hard chain fluids. The most important feature of this equation of state is that it has no adjustable parameters and in some regions in which there is no simulation data for such fluids, such equation may be used to predict the needed data.

Equation of State for the Vapor−Liquid Equilibria of Binary Systems Containing Imidazolium-Based Ionic Liquids

The vapor−liquid equilibria of binary systems containing imidazolium-based ionic liquids (ILs) have been investigated using an equation of state (EOS) for the heteronuclear square-well chain fluids (hetero-SWCFs). ILs are represented by “diblock compounds”, with the alkyl group as one block and the imidazolium ring−anion pair as the other block. Model parameters of the imidazolium ring−anion block are obtained by fitting the experimental pressure−volume−temperature (pVT) data of ILs, and they are combined with those of the alkyl block from our previous work to correlate and predict the molar volumes of homologous imidazolium ILs, with the average deviations of 0.62% and 3.24%, respectively. Vapor−liquid equilibria (VLE) of 22 binary systems that contain imidazolium ILs and solvents are correlated, with an average deviation of 5.38%. The results reveal that the imidazolium ILs can be regarded as diblock compounds fairly well and the hetero-SWCF−EOS is well-suited for calculation of their thermophysical pro...

Phase behavior of dipolar fluids from a modified statistical associating fluid theory for potentials of variable range

A statistical associating fluid theory for potentials of variable range to model dipolar fluids is presented. The new theory, termed the SAFT-VR+D equation (the statistical associating fluid theory for potentials of variable range plus dipole), explicitly accounts for dipolar interactions and their effect on the structure of the fluid. This is achieved through the use of the generalized mean spherical approximation (GMSA) to describe a reference fluid of dipolar square-well segments. Isothermal-isobaric and Gibbs ensemble Monte Carlo simulations have been performed in order to test the new theoretical approach. Predictions for the thermodynamic properties and phase behavior of dipolar square-well monomer and chain fluids, in which one or more segments are dipolar, are considered and compared with new computer simulation data. The results show that the equation of state in general provides a good description of the phase behavior of dipolar monomer and chain fluids. Some deviations are seen between the simulation data and theoretical predictions for monomer fluids with large dipole moments and for molecules composed of segments with dipoles in different orientations. This is addressed through the replacement of the GMSA by the linearized exponential approximation.

Studies on the density profiles of square-well chain fluid confined in a slit pore by density functional theory

The density profiles of square-well chain fluid confined in two planar walls are calculated using density-functional theory based on the weighted-density appro ximation of Yethiraj. The free energy functional of the system consists of an id eal part and excess part. We obtain the excess part by the equation of state of corresponding uniform system combined with the weighted-density approximation. We adopted respectively the equations of state based on cavity correlation fun ction and the statistically associating fluid theory. The calculated density pro files are compared with the corresponding Monte Carlo simulation data at differe nt chain lengths, temperatures, volume fractions and different attractions of t he wall. For a square-well chain fluid confined in two hard planar walls, result s from both equations of state are in good agreement with that of the Monte Car lo simulations at high temperature and high volume fraction. Both results devia te from the Monte Carlo result at low temperature and low volume fraction. The density profile in hard wall slit pore calculated from the equation of state of SAFT-VR is in better agreement with the available simulation data than that fro m the equation of state developed by Liu et al. We find that the equation of st ate has significant influence on theoretical prediction. For the walls with attr active forces, predictions from both equations of state deviate from the simula tion data. This deviation results from the increasing non-uniformity of the flu ids. Therefore, more suitable weighted-density function is needed to improve the density-functional theory.

Square-well chain molecules: a semi-empirical equation of state and Monte Carlo simulation data

A semi-empirical equation of state was developed for square-well chain fluids on the basis of Monte Carlo (MC) simulation data. The equation was formed by combining terms describing non-bonded square-well segments, hard-sphere chain formation, and a perturbation term describing the square-well contribution to chain formation. The functional dependence on the chain length is the same as that derived in the statistical associating fluid theory (SAFT). Extensive isobaric–isothermal MC simulations were performed for the dimer, 4-mer, 8-mer, and 16-mer square-well fluids at temperatures below or near the critical point. The new equation satisfactorily represents the volumetric properties of square-well chain fluids, up to and including the 100-mer, which was the longest chain length studied. Additionally, the new model accurately reproduces the phase envelopes of the dimer and 4-mer fluids, however, it underestimates the vapor pressures for 8-mer’s and above.

Calculating thermodynamic properties from perturbation theory: Part III. The mixtures of square-well chain fluid

A completely analytic perturbation theory has been developed to calculate the Helmholtz energy, compressibility factor, internal energy and constant-volume heat capacity for square-well chain fluid mixtures. This theory is based on the improved Barker–Henderson macroscopic compressibility (mc) approximation proposed by Zhang, the first-order perturbation theory of Wertheim in which Zhang’s analytic monomer radial distribution function as the function of temperature and monomer density is used, and a simple mixing rule similar to that of Hino–Prausnitz. The validity of the perturbation theory is evaluated by comparing the calculated compressibility factor, internal energy and constant-volume heat capacity for the freely jointed square-well chain mixtures from the theory to MC simulation data. The results show that the theory predicts results in good agreement with simulation results.

Calculating thermodynamic properties from perturbation theory: II. An analytic representation for the square-well chain fluid

An analytic representation of thermodynamic properties of the freely jointed square-well chain fluid is developed based on the thermodynamic perturbation theory of Barker–Henderson, Zhang and Weitheim. By using a real function expression for the radial distribution function and incorporating structural information for square-well monomer of TPT1 model, an analytic expression for the Helmholtz energy of square-well chain fluid is expanded from Zhang’s analytic expressions for thermodynamic properties of square-well monomer. The expression leads to good predictions of the compressibility factor, residual internal energy and constant-volume heat capacity for 4-mer, 8-mer and 16-mer square-well fluids when compared with the Monte Carlo (MC) simulation results. The incorporating structural information for square-well dimer of TPT-D model is also calculated. To obtain the constant-volume heat capacity needed, NVT MC simulations were performed.