Sedimentation equilibrium of colloidal suspensions in a planar pore based on density functional theory and the hard-core attractive Yukawa model

The sedimentation equilibrium of colloidal suspensions modeled by hard-core attractive Yukawa (HCAY) fluids in a planar pore is studied. The density profile of the HCAY fluid in a gravitational field and its distribution between the pore and uniform phases are investigated by a density functional theory (DFT) approach, which results from employing a recently proposed parameter-free version of the Lagrangian theorem-based density functional approximation (Zhou, S. Phys. Lett. A 2003, 319, 279) for hard-sphere fluids to the hard-core part of the HCAY fluid, and the second-order functional perturbation expansion approximation to the tail part as was done in a recent partitioned density functional approximation (Zhou, S. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2003, 68, 061201). The resultant DFT approach is, thus, the first adjustable parameter-free DFT for HCAY fluids. The validity of the present DFT for HCAY fluids of reduced range parameter z(red) = 1.8 under various external potentials is established in the first of the papers cited previously. The present DFT for HCAY fluids can predict the radial distribution function for the bulk HCAY fluid accurately in the colloidal limit (large value of z(red)), and in the hard-sphere limit, its prediction for the density profile of the hard-sphere fluid in a gravitational field is in very good agreement with the existing simulation data. The dependence of the density profile and distribution coefficient on the magnitude of the interparticle attraction, gravitational field, and degree of confinement is investigated in detail by the present DFT approach. Intuitive and qualitative analyses are also compared with the quantitative DFT calculational results.     

Further test of third order + second-order perturbation DFT approach: hard core repulsive Yukawa fluid subjected to diverse external fields

Grand canonical Monte Carlo simulation is used to investigate density profiles of hard-core repulsive Yukawa (HCRY) model fluid under the influence of various external fields and radial distribution function (RDF) of the bulk HCRY system. The aim of these extensive simulations is to provide exact data for purely repulsive interaction potential against which the validity of a third order + second-order perturbation DFT approach can be tested. It is found that a semiempirical parametrized bridge function due to Malijevsky and Labik performs very well for the RDF of the bulk HCRY fluid. Incorporation of a bulk second-order direct correlation function (DCF) of the HCRY fluid based on the Malijevsky-Labik bridge function into the third order + second-order perturbation DFT approach yields the resulting theoretical predictions for the density profiles of inhomogeneous HCRY fluid that are in a very good agreement with the simulation data, an exception being somewhat larger deviations appearing for the structure of the fluid around the center of a hard spherical cavity. Both theory and simulation predict layering transition and gas-liquid coexistence phenomena occurring with the HCRY model fluid under confined conditions. For the case of an inverse sixth-power repulsive potential under the influence of a flat stationary wall defined by an inverse twelfth-power repulsive potential, the present third order + second-order perturbation DFT approach is found to be superior to several existing weighted density approximations (WDA) and partitioned WDA.     

Is perturbation DFT approach applicable to purely repulsive fluids?

A recently proposed third order + second order perturbation density functional theory (DFT) approach is tested for the validity and applicability to purely repulsive model fluids subjected to various external fields. Hard core repulsive Yukawa potential, point particle Yukawa potential, and inverse power potential are employed as sample models. Theoretical DFT results are compared with the corresponding simulation data obtained by grand canonical ensemble Monte Carlo simulation. This comparison indicates that the third order + second order perturbation DFT approach is suitable for these purely repulsive fluids only on condition of high accuracy of the imported bulk second order direct correlation function (DCF). However, in this case the origin of the successful performance somewhat differs from that observed for the mean field approximation applied to van der Waals fluids. In the present case it originates from the observation that the bulk second order DCF is strongly dependent on the density argument for the hard-core part, while for the distances exceeding the core dimension this dependence is considerably weaker.     

How to extend hard sphere density functional approximation to nonuniform nonhard sphere fluids: applicable to both subcritical and supercritical temperature regions

A methodology for the formulation of density functional approximation (DFA) for nonuniform nonhard sphere fluids is proposed by following the spirit of a partitioned density functional approximation [Zhou, Phys. Rev. E 68, 061201 (2003)] and mapping the hard core part onto an effective hard sphere whose high order part of the functional perturbation expansion is treated by existing hard sphere DFAs. The resultant density functional theory (DFT) formalism only needs a second order direct correlation function and pressure of the corresponding coexistence bulk fluid as inputs and therefore can be applicable to both supercritical and subcritical temperature cases. As an example, an adjustable parameter-free version of a recently proposed Lagrangian theorem-based DFA is imported into the present methodology; the resultant DFA is applied to Lennard-Jones fluid under the influence of external fields due to a single hard wall, two hard walls separated by a small distance, a large hard sphere, and a spherical cavity with a hard wall. By comparing theoretical predictions with previous simulation data and those recently supplied for coexistence bulk fluid situated at "dangerous" regions, it was found that the present DFA can predict subtle structure change of the density profile and therefore is the most accurate among all existing DFT approaches. A detailed discussion is given as to why so excellent DFA for nonhard sphere fluids can be drawn forth from the present methodology and how the present methodology differs from previous ones. The methodology can be universal, i.e., it can be combined with any other hard sphere DFAs to construct DFA for other nonhard sphere fluids with a repulsive core.     

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.     

Phase behavior of colloids and proteins in aqueous suspensions: Theory and computer simulations

The fluid phase behavior of colloidal suspensions with short-range attractive interactions is studied by means of Monte Carlo computer simulations and two theoretical approximations, namely, the discrete perturbation theory and the so-called self-consistent Ornstein-Zernike approximation. The suspensions are modeled as hard-core attractive Yukawa (HCAY) and Asakura-Oosawa (AO) fluids. A detailed comparison of the liquid-vapor phase diagrams obtained through different routes is presented. We confirm Noro-Frenkel's extended law of scaling according to which the properties of a short-ranged fluid at a given temperature and density are independent of the detailed form of the interaction, but just depend on the value of the second virial coefficient. By mapping the HCAY and AO fluids onto an equivalent square-well fluid of appropriate range at the critical point we show that the critical temperature as a function of the effective range is independent of the interaction potential, i.e., all curves fall in a master curve. Our findings are corroborated with recent experimental data for lysozyme proteins.     

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.     

A hybrid method for predicting the microstructure of polymers with complex architecture: combination of single-chain simulation with density functional theory

A hybrid method is proposed to investigate the microstructure of various polymeric fluids confined between two parallel surfaces. The hybrid method combines a single-chain Monte Carlo (MC) simulation for the ideal-gas part of the Helmholtz energy and a density functional theory (DFT) for the excess part that arises from nonbonded intersegment interactions. The latter consists of a modified fundamental measure theory for excluded-volume effect, the first-order thermodynamics perturbation theory for chain connectivity, and a mean-field approximation for the van der Waals attraction. In comparison with a conventional DFT, the hybrid method avoids calculation of the time-consuming recursive functions and is directly applicable to polymers with arbitrary molecular architecture. Its numerical performance has been validated by extensive comparisons with MC data for the density distributions of totally flexible, semiflexible, or rigid polymers and those with starlike architecture. Special attention is also given to the formation of a nematic monolayer by rigid molecules laying perpendicular to a planar surface. The hybrid method predicts the surface pressure versus surface coverage in good agreement with experiment.     

Microstructure and self-assembly of inhomogeneous rigid rodlike chains between two neutral surfaces: A hybrid density functional approach

We use a hybrid density functional approach to investigate the microstructure and self-assembly of inhomogeneous rigid rodlike chains between two neutral surfaces, i.e., two hard walls. In the calculation, the rodlike molecule is modeled as a rigid rod linearly connected by the tangent sphere beads. The hybrid method combines a single-chain Monte Carlo (MC) simulation for the ideal-gas part of Helmholtz energy and a DFT approach for the excess Helmholtz energy. The DFT approach includes a modified fundamental measure theory for the excluded-volume effect, the first order thermodynamics perturbation theory for chain connectivity, and the mean field approximation for the van der Waals attraction. We investigate the effect of the chain length (i.e., aspect ratio) of the rodlike molecule and the separation between two surfaces on the microstructure and self-assembly of inhomogeneous rigid rodlike chains. For the athermal systems, the rodlike chain fluids present a smaller partitioning coefficient compared to the flexible chain fluids. For the thermal systems, lamellar thin films formed by the rigid rodlike molecules perpendicular to the neutral surface are observed. The effects of the head-head interaction and the separation on the self-assembly of the rodlike chain fluids in the slit are investigated.     

Modified PT-LJ-SAFT Density Functional Theory: I. Prediction of surface properties and phase equilibria of non-associating fluids

A new modified version of a Perturbation Density Functional Theory (PT-DFT) based on the Statistical Association Fluid Theory (SAFT) with a Lennard–Jones interaction potential is proposed to model the vapor–liquid phase equilibrium and to predict the interfacial behavior of non-associating hydrocarbon fluids. In the interaction model for the Helmholtz free energy functional the molecules are separated into m spherical segments interacting via a Lennard–Jones potential. The segments form chains of tangent spheres. In the perturbation approximation to Density Functional Theory the interaction potential is split according to WCA and the attractive term to the free energy functional consists of a suitable modification of the perturbation expression. This modification to PT-DFT yields surface tensions for the Lennard–Jones sphere fluid (m = 1.0) which are in perfect agreement with simulation data.The new PT-DFT model combines the high flexibility of the SAFT free energy functional with a modified density functional approach that enables to perform accurate calculations of interfacial properties. To take into account the contributions to surface tension resulting from mesoscale thermal fluctuations a semiempirical model is proposed that allows to correct the microscopic intrinsic surface tension.The model is used to describe the phase equilibrium of lower alkanes and aromatics. The results demonstrate the capability to fit vapor–liquid equilibrium data and to predict very accurately the surface properties of these fluids within the uncertainties of the experimental data.     

修正的格子空间的密度泛函理论在狭缝中的应用

对描述单原子分子溶液在狭缝中的吸附现象的格子空间的密度泛函理论 (LDFT, lattice density functional theory)进行了修正, 在系统Helmholtz函数的推导中引入了平均场近似校正和Gibbs-Helmholtz方程. 对比Monte Carlo (MC)模拟结果, 发现LDFT理论对吸附分子在狭缝中的吸附浓度分布的预测与模拟数据有较大的偏差, 而修正模型的结果与模拟数据吻合较好 .随着体相浓度的变化,分子在狭缝中具有多级吸附行为, 具体表现为在特定体相浓度区, 对相同的体相浓度,狭缝中同时存在不同的分子浓度分布, 而在Gibbs等温线上可以明显看出多级吸附的性质. 对比修正前后的结果发现,两者均可以预测多级吸附行为, 但仍存在着较大的差异.     

First-order mean-spherical approximation for interfacial phenomena: a unified method from bulk-phase equilibria study

The recently proposed first-order mean-spherical approximation (FMSA) [Y. Tang, J. Chem. Phys. 121, 10605 (2004)] for inhomogeneous fluids is extended to the study of interfacial phenomena. Computation is performed for the Lennard-Jones fluid, in which all phase equilibria properties and direct correlation function for density-functional theory are developed consistently and systematically from FMSA. Three functional methods, including fundamental measure theory for the repulsive force, local-density approximation, and square-gradient approximation, are applied in this interfacial investigation. Comparisons with the latest computer simulation data indicate that FMSA is satisfactory in predicting surface tension, density profile, as well as relevant phase equilibria. Furthermore, this work strongly suggests that FMSA is very capable of unifying homogeneous and inhomogeneous fluids, as well as those behaviors outside and inside the critical region within one framework.     

Effect of attractions on the structure of polymer solutions confined between surfaces: a density functional approach

A density functional theory is presented to study the effect of attractions on the structure of polymer solutions confined between surfaces. The polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres, both having Yukawa-type attractions and the mixture being confined between attractive Yukawa-type surfaces. The present theory treats the ideal gas free energy functional exactly and uses weighted density approximation for the hard chain and hard sphere contributions to the excess free energy functional. The attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions on the density profiles of the polymer and the solvent molecules are found to agree quite well with the Monte Carlo simulation results for varying densities, chain lengths, wall separations, and different sets of interaction potentials.     

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.     

Preferential interaction between DNA and small ions in mixed-size counterion systems: Monte Carlo simulation and density functional study

Competitive binding between counterions around DNA molecule is characterized using the preferential interaction coefficient of individual ion in single and mixed electrolyte solutions. The canonical Monte Carlo (MC) simulation, nonlinear Poisson-Boltzmann (PB) equation, and density functional theory (DFT) proposed in our previous work [Wang, Yu, Gao, and Luo, J. Chem. Phys. 123, 234904 (2005)] are utilized to calculate the preferential interaction coefficients. The MC simulations and theoretical results show that for single electrolyte around DNA, the preferential interaction coefficient of electrolyte decreases as the cation size is increased, indicating that the larger cation has less accumulation ability in the vicinity of DNA. For the mixed electrolyte solution, it is found that cation diameter has a significant effect on the competitive ability while anion diameter has a negligible effect. It proves that the preferential interaction coefficients of all ions decrease as the total ionic concentration is increased. The DFT generally has better performance than the PB equation does when compared to the MC simulation data. The DFT behaves quite well for the real ionic solutions such as the KCl-NaCl-H2O, NaCl-CaCl2-H2O, and CaCl2-MgCl2-H2O systems.     

Effect of attractive interactions on the structure of polymer melts confined between surfaces: a density-functional approach

A density-functional theory is presented to study the structure of polymers, having attractive interactions, confined between attractive surfaces. The theory treats the ideal-gas free-energy functional exactly and uses weighted density approximation for the hard-chain contribution to the excess free-energy functional. The bulk interactions of freely jointed hard spheres are obtained from generalized Flory equation of state and the attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions are found to be in quite good agreement with the Monte Carlo simulation results for varying densities, chain lengths, and different interaction potentials. The results confirm important implications of using different approximations for the hard-sphere and attractive interactions.     

Software Package: An Advanced Theoretical Tool for Inhomogeneous Fluids(Atif)

In spite of the impending flattening of Moore’s law,the complexity and size of the systems we are interested in keep on increasing.This challenges the computer simulation tools due to the expensive computational cost.Fortunately,advanced theoretical methods can be considered as alternatives to accurately and efficiently capture the structural and thermodynamic properties of complex inhomogeneous fluids.In the last decades,classical density functional theory(cDFT)has proven to be a sophisticated,robust,and efficient approach for studying complex inhomogeneous fluids.In this work,we present a pedagogical introduction to a broadly accessible open-source density functional theory software package named"an advanced theoretical tool for inhomogeneous fluids"(Atif)and of the underlying theory.To demonstrate Atif,we take three cases as examples using a typical laptop computer:(i)electric double-layer of asymmetric electrolytes;(ii)adsorptions of sequencedefined semiflexible polyelectrolytes on an oppositely charged surface;and(iii)interactions between surfaces mediated by polyelectrolytes.We believe that this pedagogical introduction will lower the barrier to entry to the use of Atif by experimental as well as theoretical groups.A companion website,which provides all of the relevant sources including codes and examples,is attached.     

Free energy density functional for adsorption of fluids in nanopores

A classical free energy density functional, which is isomorphic to a usual effective hard sphere model + mean field approximation for tail contribution, is proposed for treatment of real fluids in inhomogeneous states. In the framework of the classical density functional theory (DFT), the present functional is applied to two representative model fluids, namely, a Lennard-Jones fluid and a hard core attractive Yukawa fluid, subject to influence of various external fields. A comprehensive comparison with simulation results and a detailed analysis show that the present functional holds simultaneously all of the desirable properties inherent in an excellent functional, such as high accuracy, computational simplicity, consistency with a hard wall sum rule, nonrecourse to use of adjustable parameter(s) and weighted densities, reproduction of bulk second-order direct correlation function (DCF) in bulk limit, and applicability to subcritical fluid phenomena.     

Prediction of global vapor-liquid equilibria for mixtures containing polar and associating components with improved renormalization group theory

Our recently improved renormalization group (RG) theory is further reformulated within the context of density functional theory. To improve the theory for polar and associating fluids, an explicit and complete expression of the theory is derived in which the density fluctuation is expanded up to the third-order term instead of the original second-order term. A new predictive equation of state based on the first-order mean spherical approximation statistical associating fluid theory (FMSA-SAFT) and the newly improved RG theory is proposed for systems containing polar and associating fluids. The calculated results for both pure fluids and mixtures are in good agreement with experimental data both inside and outside the critical region. This work demonstrates that the RG theory incorporated with the solution of FMSA is a promising route for accurately describing the global phase behavior of complex fluids and mixtures.