How critical fluctuations influence adsorption properties of a van der Waals fluid onto a spherical colloidal particle

A recently proposed 3rd-order thermodynamic perturbation theory (TPT) is extended to its 5th-order version and non-uniform counterpart by supplementing with density functional theory (DFT) and a number of ansatzs for a bulk 2nd-order direct correlation function (DCF). Employment of the ansatzs DCF enables the resultant non-uniform formalism devoid of any adjustable parameter and free from numerically solving an Ornstein–Zernike integral equation theory. Density profiles calculated by the present non-uniform formalism for a hard core attractive Yukawa (HCAY) fluid near a spherical geometry are favorably compared with corresponding simulation data available in literature, and are more accurate than those based on a previous 3rd + 2nd-order perturbation DFT. The non-uniform 5th-order TPT is employed to investigate adsorption of the HCAY fluid onto a colloidal particle; it is disclosed that a depletion adsorption can be induced when the coexistence bulk fluid is situated in neighborhood of a critical point or near a bulk vapor–liquid coexistence gaseous phase or liquid phase density. A physical interpretation is given for such depletion adsorption and for its connection with parameters of the potential under consideration, which is ascribed to critical density fluctuations existing within a wide region of the bulk diagram. For a large spherical external potential inducing wetting transition, it is found that only round wetting transition is found instead of 1st-order pre-wetting transition in the case of a planar wall external potential, and the wetting transition temperature increases relative to that for the planar wall external potential. The present theoretical results for wetting transitions are supported by previous investigation based on thermodynamic considerations and a phenomenological Landau mean field theory, and are also in conformity with the present qualitative physical interpretation.     

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.     

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.     

Extending the simple weighted density approximation for a hard-sphere fluid to a Lennard-Jones fluid II. Application

A simple weighted density approximation (SWDA) was extended to nonuniform Lennard-Jones fluids by following the spirit of a partitioned density function theory [S. Zhou, Phys. Rev. E 68 (2003) 061201] and mapping the hard-core part onto an effective hard-sphere fluid whose higher order terms beyond the second order of the functional perturbation expansion are treated by the SWDA. The resultant DFT formalism performs well for Lennard-Jones fluids under the influence of diverse external fields. With the present DFT formalism, we investigate in detail the structure and adsorption properties of a low-density LJ gas in a spherical cavity with a wall consisting of hard-sphere or LJ particles. It was found that when the cavity wall exerts an attractive external potential on the LJ particles in the cavity, the excess adsorption decreases as the temperature increases, while when the cavity wall exerts a hard repulsive external potential on the LJ particles in the cavity, the excess adsorption increases as the temperature increases.     

Non-hard sphere thermodynamic perturbation theory

A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established.     

Solid phase thermodynamic perturbation theory: test and application to multiple solid phases

A simple procedure for the determination of hard sphere (HS) solid phase radial distribution function (rdf) is proposed, which, thanks to its physical foundation, allows for extension to other crystal structures besides the fcc structure. The validity of the procedure is confirmed by comparing (1) the predicted HS solid phase rdf's with corresponding simulation data and (2) the predicted non-HS solid phase Helmholtz free energy by the present solid phase first-order thermodynamic perturbation theory (TPT) whose numerical implementation depends on the HS solid phase rdf's as input, with the corresponding predictions also by the first-order TPT but the required HS solid phase rdf is given by an "exact" empirical simulation-fitted formula. The present solid phase first-order TPT predicts isostructural fcc-fcc transition of a hard core attractive Yukawa fluid, in very satisfactory agreement with the corresponding simulation data and is far more accurate than a recent thermodynamically consistent density functional perturbation theory. The present solid phase first-order TPT is employed to investigate multiple solid phases. It is found that a short-ranged potential, even if it is continuous and differentiable or is superimposed over a long-ranged potential, is sufficient to induce the multiple solid phases. When the potential range is short enough, not only isostructural fcc-fcc transition but also isostructural bcc-bcc transition, simple cubic (sc)-sc transition, or even fcc-bcc, fcc-sc, and bcc-sc transitions can be induced. Even triple point involving three solid phases becomes possible. The multiple solid phases can be stable or metastable depending on the potential parameters.     

球腔中氢键流体的吸附-解吸附转变:表面调控研究

集中讨论了球形微腔表面对腔中氢键流体相态结构的调控机制. 为了揭示微腔表面对腔中氢键流体相平衡的影响, 首先根据吸附-解吸附原理并利用经典流体的密度泛函理论计算了微腔中氢键流体的平衡密度分布, 进而通过吸附-解吸附等温线及巨势等温线绘制出体系的相图. 在此基础上, 重点考察了球腔尺寸、 表面作用强度和作用力程对氢键流体毛细凝聚及层化转变的影响. 结果表明, 这些因素可以有效地调控体系毛细凝聚和层化转变的临界约化温度、 临界密度和相区大小等特征, 从而阐明了表面调控的主要机制. 研究结果为设计相关吸附材料提供了理论参考.     

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.     

Performance evaluation of third-order thermodynamic perturbation theory and comparison with existing liquid state theories

To evaluate the performance of a recently proposed third-order thermodynamic perturbation theory (TPT), we employ the third TPT for calculation of thermodynamic properties such as compressibility factor, internal energy, excess chemical potential, gas-liquid coexistence curve, and critical properties of several fluids. By comparing the third-order TPT results with corresponding simulation data available in literature and supplied in the present report and theoretical results from several other theoretical approaches, one concludes that the third-order TPT is, in general, more accurate than other approaches such as Barker-Henderson second-order TPT using a macroscopic compressibility approximation (MCA-TPT), self-consistent Ornstein-Zernike approach, Monte Carlo perturbation theory, and a specially devised equation of state. Specifically, the third-order TPT can predict quantitatively a double critical phenomena of gas-liquid transition and a low-density liquid (LDL)-high-density liquid (HDL) transition associated with a soft core (SC) potential fluid very satisfactorily, but the predictions for the LDL-HDL transition based on the second-order MCA-TPT are quantitatively very bad or qualitatively incorrect. The failure of the second-order MCA-TPT for the SC fluid can be ascribed to the facts that for the SC potential the second-order and third-order terms of the perturbation expansion are not small quantities and that the second-order term is underestimated by the MCA. It is concluded that the present third-order version of the TPT is reliable for varying model fluids.     

Yukawa流体的相平衡和界面张力研究

应用二阶微扰理论, Duh-Mier-Y-Teran状态方程和在平均球近似(mean spherical approximation, MSA)的基础上获得的直接相关函数, 建立了适用于均匀流体和非均匀流体的状态方程. 结合此状态方程, 重整化群理论(renormalization group theory, RG)和密度泛函理论(density functional theory, DFT), 分别研究了Yukawa流体的相平衡和界面张力. 结果与分子模拟数据吻合良好.     

Phase behavior of density-dependent pair potentials

Phase diagram is calculated by a recently proposed third-order thermodynamic perturbation theory (TPT) for fluid phase and a recently proposed first-order TPT for solid phases; the underlying interparticle potential consists of a hard sphere repulsion and a perturbation tail of an attractive inverse power law type or Yukawa type whose range varies with bulk densities. It is found that besides usual phase transitions associated with density-independent potentials, the density dependence of the perturbation tail evokes some additional novel phase transitions including isostructural solid-solid transition and liquid-liquid transition. Novel triple points are also exhibited which includes stable fluid (vapor or liquid)-face-centered cubic(fcc)-fcc and liquid-liquid-fcc, metastable liquid-body-centered cubic(bcc)-bcc. It also is found that the phase diagram sensitively depends on the density dependence and the concrete mathematical form of the underlying potentials. Some of the disclosed novel transitions has been observed experimentally in complex fluids and molecular liquids, while others still remain to be experimentally verified.     

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.     

Solvation effects for polymers at an interface: a hybrid self-consistent field-density functional theory approach

Using polyatomic density functional theory of Kierlik and Rosinberg, we show that Wertheim's thermodynamic perturbation theory (TPT) incorporates solvation effects in a systematic, although simplified form. We derive two approximate solvation potentials, which require the knowledge of the correlation function in the reference unbonded fluid only. The theoretical predictions are tested against many-chain Monte Carlo simulations for moderate chain lengths. The predictions of the end-to-end distance in the bulk are in a reasonable agreement with simulations for the TPT(M-1) approximation, while the simpler TPT2_e approximation leads to the solvation potential that is shorter ranged and considerably less accurate. The resulting conformations are used in the subsequent self-consistent field theory calculations of hard-sphere polymers at a hard wall. While the incorporation of the solvation effects has little impact on the density profiles, the predictions of the components of the end-to-end distance vector as a function of the distance to the wall are much improved.     

Hard-sphere perturbation theory for a model of liquid Ga

Investigating thermodynamic properties of a model for liquid Ga, we have extended the application of the hard-sphere (HS) perturbation theory to an interatomic pair potential that possesses a soft repulsive core and a long-range oscillatory part. The model is interesting for displaying a discontinuous jump on the main-peak position of the radial distribution function at some critical density. At densities less than this critical value, the effective HS diameter of the model, estimated by the variational HS perturbation theory, has a substantial reduction with increasing density. Thus, the density dependence of the packing fraction of the HS reference fluid has an anomalous behavior, with a negative slope, within a density region below the critical density. By adding a correction term originally proposed by Mon to remedy the inherent deficiency of the HS perturbation theory, the extended Mansoori-Canfield/Rasaiah-Stell theory [J. Chem. Phys. 120, 4844 (2004)] very accurately predicts the Helmholtz free energy and entropy of the model, including an excess entropy anomaly. Almost occurring in the same density region, the excess entropy anomaly is found to be associated with the anomalous packing faction of the HS fluid.     

Density functional theory study on the structure and capillary phase transition of a polymer melt in a slitlike pore: effect of attraction

A density functional theory is proposed to investigate the effects of polymer monomer-monomer and monomer-wall attractions on the density profile, chain configuration, and equilibrium capillary phase transition of a freely jointed multi-Yukawa fluid confined in a slitlike pore. The excess Helmholtz energy functional is constructed by using the modified fundamental measure theory, Wertheim's first-order thermodynamic perturbation theory, and Rosenfeld's perturbative method, in which the bulk radial distribution function and direct correlation function of hard-core multi-Yukawa monomers are obtained from the first-order mean spherical approximation. Comparisons of density profiles and bond orientation correlation functions of inhomogeneous chain fluids predicted from the present theory with the simulation data show that the present theory is very accurate, superior to the previous theory. The present theory predicts that the polymer monomer-monomer attraction lowers the strength of oscillations for density profiles and bond orientation correlation functions and makes the excess adsorption more negative. It is interesting to find that the equilibrium capillary phase transition of the polymeric fluid in the hard slitlike pore occurs at a higher chemical potential than in bulk condition, but as the attraction of the pore wall is increased sufficiently, the chemical potential for equilibrium capillary phase transition becomes lower than that for bulk vapor-liquid equilibrium.     

AaDd型氢键流体的统计理论（V）：球形微腔中的相平衡

利用密度泛函理论并结合改进的基本度量理论研究了球形微腔中AaDd型氢键流体的相态结构．首先,根据氢键流体在球腔中的吸附一脱附等温线以及相应的巨势等温线获得不同条件下氢键流体的相图．在此基础上,重点讨论了氢键作用、球腔尺寸以及腔壁与流体之间的相互作用等因素对氢键流体相平衡特征的影响．结果表明,流体层化转变和毛细凝聚的临界温度、临界密度和临界相区域等相态特征与这些因素密切相关．研究结果可为进一步揭示几何约束下氢键流体的相平衡及聚集态结构提供可能的理论线索．     

Nonanalytic curvature contributions to solvation free energies: influence of drying

We investigate the solvation of a hard spherical cavity, of radius R, immersed in a fluid for which the interparticle forces are short ranged. For thermodynamic states lying close to the liquid binodal, where the chemical potential deviation deltamu is identical with mu-muco(T) is very small and positive, complete wetting by gas (drying) occurs and two regimes of interfacial behavior can be identified. These are characterized by the length scale Rc=2gamma(gl)infinity/(Deltarhodeltamu), where gamma(gl)infinity is the planar gas-liquid surface tension and Deltarho is the difference in coexisting densities at temperature T. For R>Rc, the interfacial free energy and the density profile of the fluid near the hard wall can be expanded in powers of the curvature R(-1), in keeping with the analysis of Stillinger and Cotter [J. Chem. Phys. 55, 3449 (1971)]. In the other regime, R0, of the work of formation of a hard spherical cavity and of the Gibbs adsorption and the fluid density at contact with the wall. Our analysis, which is based on an effective interfacial Hamiltonian combined with exact statistical mechanical sum rules, is confirmed fully by the results of microscopic density functional calculations for a square-well fluid. We discuss the repercussions of our results for solvation phenomena, emphasizing that nonanalytic behavior equivalent to that we find for complete drying in solvophobic systems will also arise in the case of complete wetting, i.e. when liquid films are adsorbed on the surface of large (colloidal) particles or at curved substrates. We reassess various results in the important but neglected Stillinger-Cotter paper, where drying was not considered explicitly, in the light of our present analysis.     

高分子链在球内表面上的吸附/排空转变

应用自洽场理论(SCFT)研究了受限于球内的高分子溶液的结构,重点关注高分子链在受限壁附近的行为.根据自洽场理论数值计算结果,讨论了球半径、高分子与球限制壁的相互作用、高分子平均浓度等因素对球内高分子浓度分布的影响.从高分子浓度分布和吸附/排空层厚度可以发现,在一定的条件下,受限的高分子在受限壁上会发生吸附/排空转变.吸附/排空转变与受限球大小、高分子链长和平均浓度,以及高分子链与受限壁之间相互作用都有关系.理论预测发生吸附/排空转变时的高分子与球限制壁的临界相互作用参数与链长的倒数成线性关系,且斜率与球半径有关.限制球越小,要发生吸附/排空转变,需要高分子与球之间有更大的临界吸引能.     

Structure and adsorption of a hard-core multi-Yukawa fluid confined in a slitlike pore: grand canonical Monte Carlo simulation and density functional study

Because of the increasing interest in studying the phenomenon exhibited by charge-stabilized colloidal suspensions in confining geometry, we present a density functional theory (DFT) for a hard-core multi-Yukawa fluid. The excess Helmholtz free-energy functional is constructed by using the modified fundamental measure theory and Rosenfeld's perturbative method, in which the bulk direct correlation function is obtained from the first-order mean spherical approximation. To validate the established theory, grand canonical ensemble Monte Carlo (GCMC) simulations are carried out to determine the density profiles and surface excesses of multi-Yukawa fluid in a slitlike pore. Comparisons of the theoretical results with the GCMC data suggest that the present DFT gives very accurate density profiles and surface excesses of multi-Yukawa fluid in the slitlike pore as well as the radial distribution functions of the bulk fluid. Both the DFT and the GCMC simulations predict the depletion of the multi-Yukawa fluid near a nonattractive wall, while the mean-field theory fails to describe this depletion in some cases. Because the simple form of the direct correlation function is used, the present DFT is computationally as efficient as the mean-field theory, but reproduces the simulation data much better than the mean-field theory.