The extension of coordination number model by using the local composition theory: mixtures

The extension of a new coordination number model to mixture is presented in this work. Extended model agrees well with the Monte Carlo (MC) simulation results for square-well (SW) mixture fluids and shows better results compared with other models. To test our model, we compare the compressibility factors from various models for SW fluids at different λ values and for SW fluid mixtures at λ=1.5. Although our model is obtained by fitting simulation data at λ=1.5, it shows better results for the different λ values than other coordination number model. Compared with the compressibility factors of various binary mixtures of SW fluids calculated from other models, this model presents better results. Because our model considers the temperature dependency importantly by using the total site number, it predicts coordination number and compressibility factor well in the wide temperature range and enables one to derive an equation of state (EOS) through integration of the coordination number equation.     

Theoretical prediction of the coordination number, local composition, and pressure-volume-temperature properties of square-well and square-shoulder fluids

By assuming a Boltzmann distribution for the molecular equilibrium between local and bulk environments, a general model is derived for the prediction of coordination numbers and local compositions of square-well and square-shoulder fluids. The model has no empirical parameter fitted from the data of square-well and square-shoulder fluids, but is valid from the low-density limit to the high-density limit. The applicable width of well or shoulder covers the commonly used range varying from 1.0 to 2.0. The model can accurately predict the coordination numbers of pure square-well and square-shoulder fluids, so the equation of state derived from it is superior to other equations of state based on the existing coordination number models. The model also accurately predicts the local compositions of mixtures in wide ranges of density and size ratio (1.0-8.0), as well as the configuration energy of lattice gases and highly nonideal lattice mixtures. It is remarkable that the model correctly predicts temperature-dependent coordination numbers and local compositions for both equal- and unequal-sized mixtures at close packing, which cannot be predicted by the existing coordination number models. Our derivation demonstrates that the energy parameters in local composition models should represent the potential difference of a molecule between the local and bulk environments, not the pair-interaction potential, and depend on the system conditions and different kinds of pair-interaction parameters. This result is very useful for the development of local composition and activity coefficient models and the mixing rules of equations of state.     

How "sticky" are short-range square-well fluids?

The aim of this work is to investigate to what extent the structural properties of a short-range square-well (SW) fluid of range lambda at a given packing fraction eta and reduced temperature T* = kBT/epsilon can be represented by those of a sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective stickiness parameter tau(T*,lambda). Such an equivalence cannot hold for the radial distribution function g(r) since this function has a delta singularity at contact (r = sigma) in the SHS case, while it has a jump discontinuity at r = lambda sigma in the SW case. Therefore, the equivalence is explored with the cavity function y(r), i.e., we assume that [formula: see text]. Optimization of the agreement between y(SW) and y(SHS) to first order in density suggests the choice tau(T*,lambda) = [12(e(1/T* - 1)(lambda - 1)](-1). We have performed Monte Carlo (MC) simulations of the SW fluid for lambda = 1.05, 1.02, and 1.01 at several densities and temperatures T* such that tau(T*,lambda) = 0.13, 0.2, and 0.5. The resulting cavity functions have been compared with MC data of SHS fluids obtained by Miller and Frenkel[J. Phys.: Condens. Matter 16, S4901 (2004)]. Although, at given values of eta and tau, some local discrepancies between y(SW) and y(SHS) exist (especially for lambda = 1.05), the SW data converge smoothly toward the SHS values as lambda-1 decreases. In fact, precursors of the singularities of y(SHS) at certain distances due to geometrical arrangements are clearly observed in y(SW). The approximate mapping y(SW)-->y(SHS) is exploited to estimate the internal energy and structure factor of the SW fluid from those of the SHS fluid. Taking for y(SHS) the solution of the Percus-Yevick equation as well as the rational-function approximation, the radial distribution function g(r) of the SW fluid is theoretically estimated and a good agreement with our MC simulations is found. Finally, a similar study is carried out for short-range SW fluid mixtures.     

Equations of state for pure and mixture square-well fluids. II. Equations of state

New coordination number models for square-well (SW) fluids are incorporated with the generalized van der Waals partition function to develop equations of state for both pure and mixture SW fluids. The equations of state have been extensively tested with the Monte Carlo simulation data, of which three sets (18 data points) for the pure SW fluids are produced in this work. The results show that, without any parameters, our model reasonably describes not only the PVT behaviors but also the second and third virial coefficients of the model fluids. In addition, a comprehensive comparison has been made between our models and the other equations of state derived from the Lee-Chao and Lee-Sandler coordination number correlations.     

Solvent density inhomogeneities and solvation free energies in supercritical diatomic fluids: a density functional approach

Density functional theory is used to explore the solvation properties of a spherical solute immersed in a supercritical diatomic fluid. The solute is modeled as a hard core Yukawa particle surrounded by a diatomic Lennard-Jones fluid represented by two fused tangent spheres using an interaction site approximation. The authors' approach is particularly suitable for thoroughly exploring the effect of different interaction parameters, such as solute-solvent interaction strength and range, solvent-solvent long-range interactions, and particle size, on the local solvent structure and the solvation free energy under supercritical conditions. Their results indicate that the behavior of the local coordination number in homonuclear diatomic fluids follows trends similar to those reported in previous studies for monatomic fluids. The local density augmentation is particularly sensitive to changes in solute size and is affected to a lesser degree by variations in the solute-solvent interaction strength and range. The associated solvation free energies exhibit a nonmonotonous behavior as a function of density for systems with weak solute-solvent interactions. The authors' results suggest that solute-solvent interaction anisotropies have a major influence on the nature and extent of local solvent density inhomogeneities and on the value of the solvation free energies in supercritical solutions of heteronuclear molecules.     

Vapor-liquid equilibria simulation and an equation of state contribution for dipole-quadrupole interactions

A systematic investigation on vapor-liquid equilibria (VLEs) of dipolar and quadrupolar fluids is carried out by molecular simulation to develop a new Helmholtz energy contribution for equations of state (EOSs). Twelve two-center Lennard-Jones plus point dipole and point quadrupole model fluids (2CLJDQ) are studied for different reduced dipolar moments micro*2=6 or 12, reduced quadrupolar moments Q*2=2 or 4 and reduced elongations L*=0, 0.505, or 1. Temperatures cover a wide range from about 55% to 95% of the critical temperature of each fluid. The NpT+test particle method is used for the calculation of vapor pressure, saturated densities, and saturated enthalpies. Critical data and the acentric factor are obtained from fits to the simulation data. On the basis of this data, an EOS contribution for the dipole-quadrupole cross-interactions of nonspherical molecules is developed. The expression is based on a third-order perturbation theory, and the model constants are adjusted to the present 2CLJDQ simulation results. When applied to mixtures, the model is found to be in excellent agreement with results from simulation and experiment. The new EOS contribution is also compatible with segment-based EOS, such as the various forms of the statistical associating fluid theory EOS.     

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR)

An accurate prediction of phase behavior at conditions far and close to criticality cannot be accomplished by mean-field based theories that do not incorporate long-range density fluctuations. A treatment based on renormalization-group (RG) theory as developed by White and co-workers has proven to be very successful in improving the predictions of the critical region with different equations of state. The basis of the method is an iterative procedure to account for contributions to the free energy of density fluctuations of increasing wavelengths. The RG method has been combined with a number of versions of the statistical associating fluid theory (SAFT), by implementing White's earliest ideas with the improvements of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters: a cutoff wavelength L for density fluctuations and an average gradient of the wavelet function Φ. In this work, the SAFT-VR (variable range) equation of state is extended with a similar crossover treatment which, however, follows closely the most recent improvements introduced by White. The interpretation of White's latter developments allows us to establish a straightforward method which enables Φ to be evaluated; only the cutoff wavelength L then needs to be adjusted. The approach used here begins with an initial free energy incorporating only contributions from short-wavelength fluctuations, which are treated locally. The contribution from long-wavelength fluctuations is incorporated through an iterative procedure based on attractive interactions which incorporate the structure of the fluid following the ideas of perturbation theories and using a mapping that allows integration of the radial distribution function. Good agreement close and far from the critical region is obtained using a unique fitted parameter L that can be easily related to the range of the potential. In this way the thermodynamic properties of a square-well (SW) fluid are given by the same number of independent intermolecular model parameters as in the classical equation. Far from the critical region the approach provides the correct limiting behavior reducing to the classical equation (SAFT-VR). In the critical region the β critical exponent is calculated and is found to take values close to the universal value. In SAFT-VR the free energy of an associating chain fluid is obtained following the thermodynamic perturbation theory of Wertheim from the knowledge of the free energy and radial distribution function of a reference monomer fluid. By determining L for SW fluids of varying well width a unique equation of state is obtained for chain and associating systems without further adjustment of critical parameters. We use computer simulation data of the phase behavior of chain and associating SW fluids to test the accuracy of the new equation.     

Theory and computer simulation of the coordination number of square-well fluids of variable width

Computer simulations have been performed to determine the coordination number of square-well (SW) fluids for wide ranges of densities, temperatures, and potential widths. These data are used to test the performance of a new coordination number model derived on the basis of the quasi-chemical approximation. The model presents a considerable improvement over other previously reported theoretical models based on similar grounds.     

微孔中简单流体粘度的分子动力学模拟及关联模型

用分子动力学模拟计算了微孔介质中流体氩在不同温度、不同密度和不同孔径下的剪切粘度.并根据Chapman-Enskog关于硬球流体传递性质的理论以及Heyes的关于Lennard-Jones流体粘度的表达式,提出了两个描述微孔介质中流体粘度的模型,该模型可以计算微孔中流体氩在不同状态下的粘度值.通过与计算机模拟值的比较,证明这两个微孔流体粘度模型是可用的.     

Helmholtz energy,extended corresponding states and local composition model for fluid mixtures

We present a model for the calculation of mixture properties. This model is based on the mixture residual Helmholtz energy given by the sum of two terms: one is the residual Helmholtz energy calculated by an extended corresponding states (ECS) model while the other is a correction term. The ECS model is based on methane as the reference fluid and shape factors that carry out the scaling of properties between the fluid of interest and the reference fluid. These shape factors are given by correlations in terms of reduced temperature and density. The application to mixtures is carried out with the one-fluid van der Waals mixture model. The correction term is temperature- and density-dependent as is given by a local composition mixing rule. Local compositions were calculated from a coordination number model based on lattice gas theory. With respect to binary-mixture properties, densities were calculated with an average absolute deviation (AAD) of 0.12%; speeds of sound were calculated with an AAD of 0.16% and bubble pressures were calculated with an AAD of 1.77%. Also, natural gas densities were calculated with AAD of 0.03% and natural gas speeds of sound were calculated with AAD of 0.049%. All these results are very satisfactory when compared with those obtained by modern mixture models.     

Monte Carlo simulations of thermodynamic and structural properties of Mie(14,7) fluids

The vapor-liquid phase envelope of Mie(14,7) fluids is determined by the Gibbs ensemble Monte Carlo (MC) simulation technique. The NVT-MC simulation method is then utilized to compute the equation of state and the pair correlation function over a wide range of densities and temperatures. The effective diameters are calculated via the virial minimization method and the results are applied as the repulsion-attraction splitting distance within the generic van der Waals (GvdW) theory to compute the mean free volume. The density and temperature dependence of these parameters are studied and discussed. The results for the effective diameter, and the GvdW parameters are fitted to analytical functions of density and temperature. An examination of the results for the fluid phase equilibria of argon shows excellent agreement with empirical data for the densities of the coexisting phases, the vapor pressure, and the critical point. The computed free volumes are used to compute the diffusion coefficient of argon and the results are compared with experimental data.     

Structural properties of a model system with effective interparticle interaction potential applicable in modeling of complex fluids

We report grand canonical ensemble Monte Carlo (MC) simulation and theoretical studies of the structural properties of a model system described by an effective interparticle interaction potential, which incorporates basic interaction terms used in modeling of various complex fluids composed of mesoscopic particles dispersed in a solvent bath. The MC results for the bulk radial distribution function are employed to test the validity of the hard-sphere bridge function in combination with a modified hypernetted chain approximation (MHNC) in closing the Ornstein-Zernike (OZ) integral equation, while the MC data for the density profiles in different inhomogeneous environments are used to assess the validity of the third-order+second-order perturbation density functional theory (DFT). We found satisfactory agreement between the results predicted by the pure theories and simulation data, which classifies the proposed theoretical approaches as convenient tools for the investigation of complex fluids. The present investigation indicates that the bridge function approximation and density functional approximation, which are traditionally used for the study of neutral atomic fluids, also perform well for complex fluids only on condition that the underlying effective potentials include a highly repulsive core as an ingredient.     

Statistical-mechanical theory of rheology: Lennard-Jones fluids

The generalized Boltzmann equation for simple dense fluids gives rise to the stress tensor evolution equation as a constitutive equation of generalized hydrodynamics for fluids far removed from equilibrium. It is possible to derive a formula for the non-Newtonian shear viscosity of the simple fluid from the stress tensor evolution equation in a suitable flow configuration. The non-Newtonian viscosity formula derived is applied to calculate the non-Newtonian viscosity as a function of the shear rate by means of statistical mechanics in the case of the Lennard-Jones fluid. For that purpose we have used the density-fluctuation theory for the Newtonian viscosity, the modified free volume theory for the self-diffusion coefficient, and the generic van der Waals equation of state to compute the mean free volume appearing in the modified free volume theory. Monte Carlo simulations are used to calculate the pair-correlation function appearing in the generic van der Waals equation of state and shear viscosity formula. To validate the Newtonian viscosity formula obtained we first have examined the density and temperature dependences of the shear viscosity in both subcritical and supercritical regions and compared them with molecular-dynamic simulation results. With the Newtonian shear viscosity and thermodynamic quantities so computed we then have calculated the shear rate dependence of the non-Newtonian shear viscosity and compared it with molecular-dynamics simulation results. The non-Newtonian viscosity formula is a universal function of the product of reduced shear rate (gamma*) times reduced relaxation time (taue*) that is independent of the material parameters, suggesting a possibility of the existence of rheological corresponding states of reduced density, temperature, and shear rate. When the simulation data are reduced appropriately and plotted against taue*gamma* they are found clustered around the reduced (universal) non-Newtonian viscosity formula. Thus we now have a molecular theory of non-Newtonian shear viscosity for the Lennard-Jones fluid, which can be implemented with a Monte Carlo simulation method for the pair-correlation function.     

A Singlet-RISM theory for solid/liquid interfaces Part I: uncharged walls

We present a novel integral equation method for the calculation of fluid structure in the vicinity of a plane impenetrable wall. The theory is based on the well-known RISM equation and is capable of dealing with arbitrary interaction site model (ISM) fluids at a solid/liquid interface. In conjunction with several closure approximations, the equations are solved numerically and wall-fluid site density distributions as well as charge density, field, and potential profiles are calculated for pure water and aqueous electrolyte solutions with varying concentrations adjacent to an uncharged soft wall. The results show reasonable agreement with corresponding computer simulation data.     

Fluids in nanospaces: molecular simulation studies to find out key mechanisms for engineering

We have analyzed various phenomena that occur in nanopores, focusing on elucidating their key mechanisms, to advance the effective engineering use of nanoporous materials. As ideal experimental systems, molecular simulations can effectively provide information at the molecular level that leads to mechanistic insight. In this short review, several of our recent results are presented. The first topic is the critical point depression of Lennard-Jones fluid in silica slit pores due to finite size effects, studied by our original Monte Carlo (MC) technique. We demonstrate that the first layers of adsorbed molecules in contact with the pore walls act as a “fluid wall” and impose extra finite size effects on the fluid confined in the central portion of the pore. We next present a new kernel for pore size distribution (PSD) analysis, based entirely on molecular simulation, which consists of local isotherms for nitrogen adsorption in carbon slit pores at 77 K. The kernel is obtained by combining grand canonical Monte Carlo (GCMC) method and open pore cell MC method that was developed in the previous study. We show that overall trends of the PSDs of activated carbons calculated with our new kernel and with conventional kernel from non-local density functional theory are nearly the same; however, apparent difference can be seen between them. As the third topic, we apply a free energy analysis method with the aid of GCMC simulations to investigate the gating behavior observed in a porous coordination polymer, and propose a mechanism for the adsorption-induced structural transition based on both the theory of equilibrium and kinetics. Finally, we construct an atomistic silica pore model that mimics MCM-41, which has atomic-level surface roughness, and perform molecular simulations to understand the mechanism of capillary condensation with hysteresis. We calculate the work required for the gas–liquid transition from the simulation data, and show that the adsorption branch with hysteresis for MCM-41 arise from spontaneous capillary condensation from a metastable state.     

Resummed thermodynamic perturbation theory for central force associating potential. Multi-patch models

A resummed thermodynamic perturbation theory for associating fluids with multiply bondable central force associating potential is extended for the fluid with multiple number of multiply bondable associating sites. We consider a multi-patch hard-sphere model for associating fluids. The model is represented by the hard-sphere fluid system with several spherical attractive patches on the surface of each hard sphere. Resummation is carried out to account for blocking effects, i.e., when the bonding of a particle restricts (blocks) its ability to bond with other particles. Closed form analytical expressions for thermodynamical properties (Helmholtz free energy, pressure, internal energy, and chemical potential) of the models with arbitrary number of doubly bondable patches at all degrees of the blockage are presented. In the limiting case of total blockage, when the patches become only singly bondable, our theory reduces to Wertheim's thermodynamic perturbation theory (TPT) for polymerizing fluids. To validate the accuracy of the theory we compare to exact values, for the thermodynamical properties of the system, as determined by Monte Carlo computer simulations. In addition we compare the fraction of multiply bonded particles at different values of the density and temperature. In general, predictions of the present theory are in good agreement with values for the model calculated using Monte Carlo simulations, i.e., the accuracy of our theory in the case of the models with multiply bondable sites is similar to that of Wertheim's TPT in the case of the models with singly bondable sites.     

Virial coefficients and inversion curve of simple and associating fluids

Free energy simulation method is applied to calculate the virial coefficients of square-well (SW) fluids of variable well-width and square-well based dimer forming associating fluids. In this approach, Monte Carlo sampling is performed on a number of molecules equal to the order of integral, and configurations are weighted according to the absolute value of the integrand. An umbrella-sampling average yields the value of the cluster integral in reference to a known integral. By using this technique, we determine the virial coefficients up to B₆ for SW fluid with variable potential range from λ = 1.25 to λ = 3.0 and model associating fluids with different association strengths: ?_af = 0.0, 8.0, 16.0 and 22.0. These calculated values for SW fluids are in good agreement with the literature. We examine these coefficients in the context of the virial equation of state (VEOS) of SW fluids. VEOS up to B₄ or up to B₆ describes the PVT behavior along the saturated vapor line better than the series that includes B₅. We used these coefficients to find the critical properties of SW fluids and compared with the literature values. Boyle temperature is also determined and is found to increase with the increase in the well-extent and associating strength. We also report Joule–Thomson inversion curve for Lennard–Jones fluid and SW fluids using different truncated VEOS and compared with that predicted from established EOS.     

双流体高聚物配位溶液理论——纯物质的状态方程及其应用

以Ｆｌｏｒｙ局部组合型囚胞理论为雏形，引进空穴数，建立了更符合流体特性的双流体高聚物配位统计模型，以配位分数和局部位分数替代原局部组成中面积接触分数和局部面积接触分数概念，用拟化学近似处理局部配位分数，导出纯物质的状态方程，并应用于聚丙烯（ＰＰ）、聚丁烯－１（ＰＢＴ）、聚苯乙烯（ＰＳ）三个体系的关联，取得了良好的关联精度，根据ＰＰ和ＰＢＴ的链节结构与空穴数的关系，预言了高聚物的链节结构和空穴数与聚     

Description of self-diffusion coefficients of gases,liquids and fluids at high pressure based on molecular simulation data

The purpose of this work is to evaluate the potential of modeling the self-diffusion coefficient (SDC) of real fluids in all fluid states based on Lennard–Jones analytical relationships involving the SDC, the temperature, the density and the pressure. For that, we generated an equation of state (EOS) that interrelates the self-diffusion coefficient, the temperature and the density of the Lennard–Jones (LJ) fluid. We fit the parameters of such LJ–SDC–EOS using recent wide ranging molecular simulation data for the LJ fluid. We also used in this work a LJ pressure–density–temperature EOS that we combined with the LJ–SDC–EOS to make possible the calculation of LJ–SDC values from given temperature and pressure. Both EOSs are written in terms of LJ dimensionless variables, which are defined in terms of the LJ parameters ɛ and σ. These parameters are meaningful at molecular level. By combining both EOSs, we generated LJ corresponding states charts which make possible to conclude that the LJ fluid captures the observed behavioral patterns of the self-diffusion coefficient of real fluids over a wide range of conditions. In this work, we also performed predictions of the SDC of real fluids in all fluid states. For that, we assumed that a given real fluid behaves as a Lennard–Jones fluid which exactly matches the experimental critical temperature T_c and the experimental critical pressure P_c of the real fluid. Such an assumption implies average true prediction errors of the order of 10% for vapors, light supercritical fluids, some dense supercritical fluids and some liquids. These results make possible to conclude that it is worthwhile to use the LJ fluid reference as a basis to model the self-diffusion coefficient of real fluids, over a wide range of conditions, without resorting to non-LJ correlations for the density–temperature–pressure relationship. The database considered here contains more than 1000 experimental data points. The database practical reduced temperature range is from 0.53 to 2.4, and the practical reduced pressure range is from 0 to 68.4.     

Towards the development of theoretically correct liquid activity coefficient models

We propose a general approach for developing liquid activity coefficient models based on the concept of local composition that satisfy at least two important physical conditions: (1) the total number of neighboring molecules around one molecule of species A must be a constant at any temperature for all possible mixture compositions, and (2) the number of pairs between any two species A–B determined from the local composition of B around A must be the same as that of A around B. Most commonly used liquid activity coefficient models (such as UNIQUAC) satisfy condition (1) but fail to meet condition (2), and thus are considered as fundamentally flawed. We propose a general formulation for the local composition equation containing a symmetric function of species A and B which ensures condition (2) be always satisfied. We show that the composition and temperature dependence of the symmetric functions can be completely obtained from condition (1), resulting in a new class of excess Gibbs free energy models. It is found that such a model can quantitatively reproduce the results of Monte Carlo simulation for various types of lattice fluids, while conventional models are merely qualitative. Furthermore, such a model is more accurate than the UNIQUAC model in correlating experimental data, especially in the dilute regime. Therefore, models developed based on this approach are theoretically sound and potentially applicable to a broader range of conditions.