A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT

A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.     

On the solvation force of water-like fluid models with square-well attraction and site–site association in slit-like pores: density functional approach

The solvation force of the water-like fluid models with square-well attraction and site–site chemical association confined to slit-like pores has been explored. Theoretical procedure is based on the application of the density functional approach with mean-field approximation for the attractive interparticle interactions. The chemical association effects are treated by using the first-order thermodynamic perturbation theory of Wertheim. Trends of behaviour of the solvation force are put in correspondence with the distribution of molecules in the pores and with the average density of the adsorbate. Moreover, the distribution of non-bonded species on pore width is described. The influence of the width of the square-well and of the gas–solid attraction is discussed. A comparison of theoretical predictions with computer simulations results for water models in slit-like pores is performed.     

简单流体和烷烃表面张力的梯度理论模型

利用比容平移修正后的Peng-Robinson状态方程和密度梯度理论建立了简单流体和烷烃的表面张力的理论模型,并提出了适合于这一类纯物质的作用因子通用关联式。对3种简单流体和21种烷烃的表面张力的计算结果表明, 利用新的作用因子关联式结合梯度理论模型能在广泛温度范围内高精度地再现纯物质的表面张力,总的平均绝对偏差为 0．19 mN·m-1,计算精度可以满足工程应用的需要。     

On the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids

It is shown that the variational principle for the grand potential of a nonuniform fluid as a functional of the singlet density yields the potential distribution theory for the equilibrium density. We derive the explicit form that the functional takes for a system of hard rods, and propose an approximate one for hard spheres. Attractive interactions are also considered in mean-field approximation. In all cases the pair direct correlation function of the nonuniform system is obtained and the density gradient expansion of the free energy is investigated.     

The effects of interaction range,porosity and molecular association on the phase equilibrium of a fluid confined in a disordered porous media

Grand-canonical transition-matrix Monte Carlo (GC-TMMC) is employed to analyse the effects of range of interaction, packing fraction and molecular association on phase coexistence properties of square-well (SW) based fluids in disordered pores. The nature of the phase equilibria were studied inside a repulsive disordered porous media with packing fractions, η _m = 0.05 and 0.10. Three values of the SW attractive well range parameter were studied: λ = 1.5, 1.75, and 2.0. Coexistence number probability distribution reflects the signature of the disordered structure of the porous matrix. Yet, no multiple fluid–fluid transition was observed. The effect of strength of molecular association on coexistence densities, density profile, saturation pressure, and monomer fraction for the SW based dimerizing fluids inside a repulsive disordered media is reported. Association is found to increase as the packing fraction of the matrix increase. Critical properties of these confined fluids are calculated via a rectilinear diameter approach. Fractional shift in the critical temperature linearly decreases with the increase in the attractive well width for non-associating fluids. The rate of decrease in the critical temperature shift increases with the increase in packing fraction. Associating sites are found to suppress the shift in the critical temperature.     

Investigation of vapour--liquid nucleation properties for spherical and chain-like fluids by density functional theory

The excess Helmholtz free energy functional for nonpolar chain-like molecules is formulated in terms of a weighted density approximation （WDA） for short-range interactions and a Weaks Chandler Andersen （WCA） approximation and a Barker Henderson （BH） theory for long-range attraction. Within the framework of density functional theory （DFT）, vapour liquid interracial properties including density profile and surface tension, and vapour-liquid nucleation properties including density profile, work of formation and number of particles are investigated for spherical and chain- like molecules. The obtained vapour liquid surface tension and the number of particles in critical nucleus for Lennard- Jones （L J） fluids are consistent with the simulation results. The influences of supersaturation, temperature and chain length on vapour liquid nucleation properties are discussed.[第一段]     

平行板间方势阱偶极流体的结构性质研究

在密度泛函理论(DFT)框架下, 应用改进的基本度量理论(MFMT)表达硬球作用对自由能泛函的贡献, 根据统计力学理论结合加权密度近似(WDA)表达偶极作用对自由能泛函的贡献,得到了方势阱偶极流体在平行板间的密度分布表达式, 计算了偶极流体在两平行板间的密度分布, 并探讨了方势阱深度和宽度对体系密度分布的影响. 此外, 通过体系密度分布, 进一步分析了方势阱宽度和深度以及板间尺度与溶剂化力的关系.     

平行板间方势阱偶极流体的结构性质研究

在密度泛函理论(DFT)框架下, 应用改进的基本度量理论(MFMT)表达硬球作用对自由能泛函的贡献, 根据统计力学理论结合加权密度近似(WDA)表达偶极作用对自由能泛函的贡献,得到了方势阱偶极流体在平行板间的密度分布表达式, 计算了偶极流体在两平行板间的密度分布, 并探讨了方势阱深度和宽度对体系密度分布的影响. 此外, 通过体系密度分布, 进一步分析了方势阱宽度和深度以及板间尺度与溶剂化力的关系.     

Nonlinear Kelvin–Helmholtz instability of magnetized surface waves on a subsonic gas–viscous potential liquid interface

A nonlinear stability analysis, of magnetic fluids, was carried out for interfacial waves between a subsonic inviscid gas and viscous streaming liquid when a normal constant magnetic field is present. The viscosity term in the problem was carried out using the viscous potential theory. The nonlinear analysis results nonlinear partial differential equations, for different cases, using multiple scales method. Using the modulation concept, we have discussed different numerical examples to show the effects of the system parameters on criteria of the interfacial waves (in)stability.     

Overlapping Associating Fluids with Directional Bonds in a Bulk and Near a Hard Wall: Monte Carlo Study

Two models have been used in these Monte Carlo simulations: the original model with an angular-dependent associative interaction and a model with an angular-averaged potential, which is better suited for simulation and computationaly more efficient. We show that in the homogeneous case under the same conditions, both models yield a nearly identical interparticle structure, but with a slightly different degree of dimerization. This causes differences between these models in the local density distribution of monomers and dimers when an inhomogeneity is present, though the resulting local total density distribution is found to be the same. The theoretical predictions based on Wertheim's theory of association are always closer to the simulation data for the model with the angular-averaged potential.     

Revisiting finite-scale Navier–Stokes theory: Order-of-magnitude results,new critical values,and connections to Stokesian fluids

We return to Ref. [7] and present, as well as note the implications stemming from, a rigorous order-of-magnitude-based derivation of the governing system considered therein. The system in question models the ‘piston problem’ for the case of a viscous, but thermally non-conducting, gas with constant transport coefficients under the generalization of the Navier–Stokes (NS) equations known as the finite-scale Navier–Stokes (FSNS) equations. Our analysis also provides a rigorous derivation of the FSNS system considered in Ref. [12], highlights links between FSNS theory and Stokesian fluids, and examines the possible applicability of generalizations of the perfect gas law to finite-scale theory. We conclude with a brief discussion regarding new critical values of the averaging length scale.     

电流变液系统流动的渐近估计

根据电流变液中球形颗粒的运动模型，研究了颗粒质量很小时，电流变液中颗粒运动的渐近状态，利用微分不等式理论，给出了相应运动的渐近估计. 关键词： 电流变液 微分不等式理论 渐近估计     

Zero-frequency elastic moduli of uniform fluids

A statistical mechanical treatment of equilibrium elasticity of a uniform fluid phase based on density functional theory is presented. Bulk expressions for the stress tensor and the zero-frequency elastic moduli tensor involving the direct correlation function are found.     

The theory of non-electrolyte solutions: an historical review

Starting with the work of van der Waals in 1873, a historical review is given of theories of non-electrolyte mixtures that are based on a well-defined Hamiltonian, and thus can be tested against molecular simulation, as well as experiment. Most of the first 100 years covered here were devoted to attempts to find a successful theory of simple mixtures, culminating in the van der Waals 1-fluid theory of conformal solutions, and perturbation theories based on a hard-sphere reference fluid. The last 40 years has seen the more rapid development of theories for fluids of more complex molecules, including strongly polar liquids, chain molecules and liquids in which molecular association is important.     

A three-component model on the structure of colloidal solution with size-asymmetric electrolytes

ABSTRACT

A three-component model on the structure of colloidal solution with size asymmetric electrolytes is attempted here using density functional theory and Monte Carlo simulation. The solvent is represented as an individual component along with that as a dielectric continuum. The theory uses a weighted density approximation for the hard-sphere contribution to the free energy, whereas the ionic contribution is evaluated through a perturbation expansion around the bulk density. The theory is found to reproduce the simulation data quite well for a wide range of parametric conditions. The present study reflects the importance of the presence of the solvent in determining the structural behaviour of spherical double layers.     

The critical supersaturations predicted by nucleation theory

A general set of equations is derived for calculating the supersaturation required to obtain a given rate of nucleation. This set is general enough to encompass all the present theories, the classical theory, the Lothe-Pound theory, the Reiss-Katz-Cohen theory, a recent theory by H. Reiss, and any other theory which includes a size-dependent correction to the classical theory. Comparison of these predictions is made for various substances.     

Molecular mean field theory for liquid water

Attractive bonding interactions between molecules typically have inherent conservation laws which influence the statistical properties of such systems in terms of corresponding sum rules. We have considered lattice water as an example, and we have enunciated the consequences of the sum rule through a general computational procedure called molecular mean field theory. Fluctuations about the mean field are computed and many of the liquid properties have been deduced and compared with Monte Carlo simulation, molecular dynamics, and experimental results. Large correlation lengths are seen to be a consequence of the sum rule in the liquid phase. Long-range Coulomb interactions are shown to have minor effects on our results.     

Lattice density functional theory for confined Ising fluids: comparison between different functional approximations in slit pore

ABSTRACT

In this paper, Lafuente and Cuesta's cluster density functional theory (CDFT) and lattice mean field approximation (LMFA) are formulated and compared within the framework of lattice density functional theory (LDFT). As a comparison, an LDFT based on our previous work on nonrandom correction to LMFA is also developed, where local density approximation is adopted on the correction. The numerical results of density distributions of an Ising fluid confined in a slit pore obtained from Monte Carlo simulation are used to check these functional approximations. Due to rational treatment on the coupling between site-excluding entropic effect and contact-attracting enthalpic effect by CDFT with Bethe-Peierls approximation (named as BPA-CDFT for short), the improvement of BPA-CDFT beyond LMFA is checked as expected. And it is interesting that our LDFT has a comparative accuracy with BPA-CDFT. Apparent differences between the profiles such as solvation force, excess adsorption quantity and interfacial tension from LMFA and non-LMFAs are found in our calculations. We also discuss some possible theoretical extensions of BPA-CDFT.     

Theory and simulation of chain molecules with multiple bonding sites in an associating solvent

Although polyethylene oxide (PEO) is soluble in water, polymethylene oxide (PMO) is not, even though PMO has more association sites. Some suggest this is due to orientation effects in the water hydrogen-bond network. A simulation and theory study of the effect of bonding site density on thermodynamic properties and extent of bonding of a linear flexible chain in a hydrogen-bonding solvent is performed. Predictions from Wertheim's theory are compared against simulation results. Thermodynamic properties and extent of bonding were obtained. The solvent molecules are modeled as hard spheres with four association sites in a tetrahedral arrangement. The chains are flexible and consist of six tangent segments of hard spheres with bonding sites that interact with the solvent molecules. A solvent molecule can also form a bond with a second solvent molecule. The association interaction is modeled with an orientation-dependent square-well. The total number of bonding sites on each chain is varied and the effects studied. This is another test of the theory for the case of mixtures of associating molecules of different sizes. The Metropolis Monte Carlo technique was chosen to perform simulations in the canonical and isothermal–isobaric ensembles. Good agreement was found between theory and simulation.