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.     

Structures and adsorption of binary hard-core Yukawa mixtures in a slitlike pore: grand canonical Monte Carlo simulation and density-functional study

The grand canonical ensemble Monte Carlo simulation and density-functional theory are applied to calculate the structures, local mole fractions, and adsorption isotherms of binary hard-core Yukawa mixtures in a slitlike pore as well as the radial distribution functions of bulk mixtures. The excess Helmholtz energy functional is a combination of the modified fundamental measure theory of Yu and Wu [J. Chem. Phys. 117, 10156 (2002)] for the hard-core contribution and a corrected mean-field theory for the attractive contribution. A comparison of the theoretical results with the results from the Monte Carlo simulations shows that the corrected theory improves the density profiles of binary hard-core Yukawa mixtures in the vicinity of contact over the original mean-field theory. Both the present corrected theory and the simulations suggest that depletion and desorption occur at low temperature, and the local segregation can be observed in most cases. For binary mixtures in the hard slitlike pore, the present corrected theory predicts more accurate surface excesses than the original one does, while in the case of the attractive pore, no improvement is found in the prediction of a surface excess of the smaller molecule.     

Density profiles and solvation forces for a Yukawa fluid in a slit pore

The effect of varying wall-particle and particle-particle interactions on the density profiles near a single wall and the solvation forces between two walls immersed in a fluid of particles is investigated by grand canonical Monte Carlo simulations. Attractive and repulsive particle-particle and particle-wall interactions are modeled by a versatile hard-core Yukawa form. These simulation results are compared to theoretical calculations using the hypernetted chain integral equation technique, as well as with fundamental measure density functional theory (DFT), where particle-particle interactions are either treated as a first order perturbation using the radial distribution function or else with a DFT based on the direct-correlation function. All three theoretical approaches reproduce the main trends fairly well, but exhibit inconsistent accuracy, particularly for attractive particle-particle interactions. We show that the wall-particle and particle-particle attractions can couple together to induce a nonlinear enhancement of the adsorption and a related "repulsion through attraction" effect for the effective wall-wall forces. We also investigate the phenomenon of bridging, where an attractive wall-particle interaction induces strongly attractive solvation forces.     

Thermodynamic and structural properties of repulsive hard-core Yukawa fluid: integral equation theory, perturbation theory and Monte Carlo simulations

The thermodynamic and structural properties of purely repulsive hard-core Yukawa particles in the fluid state are determined through Monte Carlo simulation and modeled using perturbation theory and integral equation theory in the mean spherical approximation (MSA). Systems of particles with Yukawa screening lengths of 1.8, 3.0, and 5.0 are examined with results compared to variations of MSA and perturbation theory. Thermodynamic properties were predicted well by both theories in the fluid region up to the fluid-solid phase boundary. Further, we found that a simplified exponential version of the MSA is the most accurate at predicting radial distribution function at contact. Radial distribution function of repulsive hard-core Yukawa particles are also reported. The results show that methods based on MSA and perturbation theory that are typically applied to the attractive hard-core Yukawa potential can also be extended to the purely repulsive hard-core Yukawa potential.     

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.     

Structures and correlation functions of multicomponent and polydisperse hard-sphere mixtures from a density functional theory

The structures of nonuniform binary hard-sphere mixtures and the correlation functions of uniform ternary hard-sphere mixtures were studied using a modified fundamental-measure theory based on the weight functions of Rosenfeld [Rosenfeld, Phys. Rev. Lett. 63, 980 (1989)] and Boublik-Mansoori-Carnahan-Starling-Leland equation of state [Boublik, J. Chem. Phys. 53, 471 (1970); Mansoori et al., J. Chem. Phys. 54, 1523 (1971)]. The theoretical predictions agreed very well with the molecular simulations for the overall density profiles, the local compositions, and the radial distribution functions of uniform as well as inhomogeneous hard-sphere mixtures. The density functional theory was further extended to represent the structure of a polydisperse hard-sphere fluid near a hard wall. Excellent agreement was also achieved between theory and Monte Carlo simulations. The density functional theory predicted oscillatory size segregations near a hard wall for a polydisperse hard-sphere fluid of a uniform size distribution.     

基于密度泛函理论研究二元排斥Yukawa流体的表面结构性质

基于自由能密度泛函理论(DFT)考察了二元排斥Yukawa (HCRY)流体在不同外场下的密度分布. 基于微扰理论, 体系的Helmholtz自由能泛函采用硬球排斥部分和长程色散部分贡献之和, 其中Kierlik和Rosinberg的加权密度近似(WDA)被用来计算硬球排斥部分, 而色散部分采用平均场理论(MFT)进行描述. 为了验证DFT计算结果的合理性, 研究中采用巨正则Monte Carlo(GCMC)模拟计算了在不同主体相密度、硬核直径和位能参数比的条件下二元HCRY混合流体的密度分布. 结果表明, 该DFT计算结果与GCMC模拟值吻合良好.     

Thermodynamic and structural properties of mixed colloids represented by a hard-core two-Yukawa mixture model fluid: Monte Carlo simulations and an analytical theory

The interaction between colloidal particles is well represented by a hard-core two-Yukawa potential. In order to assess the accuracy of theoretical predictions for the thermodynamic and structural properties of mixed colloids, standard Monte Carlo simulations are carried out for the hard-core two-Yukawa mixtures. In the simulations, one range parameter in the two-Yukawa potential is taken as 1.8 or 2.8647, and another is taken as 4, 8, or 13.5485. Both attractive and repulsive dominant cases of the potential outside the hard core are considered. The effects of temperature, density, composition, size and energy parameter ratios on internal energy, compressibility factor, and radial distribution function are investigated extensively. Theoretical calculations are performed in the framework of analytical solution for the Ornstein-Zernike equation with the first-order mean spherical approximation (FMSA). Our analysis shows that the FMSA is very accurate for the prediction of the compressibility factor of the hard-core two-Yukawa mixtures at all conditions studied. The FMSA generally predicts accurate internal energy, but overestimates the internal energy of the systems at lower temperatures. Furthermore, we found that a simplified exponential version of the FMSA predicts fairly good radial distribution function at contact for the mixed two-Yukawa fluids. The comparison of the theoretical compressibility factor with that from the Monte Carlo simulations suggests that the FMSA can be used to investigate the fluid-fluid equilibria of hard-core two-Yukawa mixtures.     

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.     

Depletion potentials in colloidal mixtures of hard spheres and rods

The depletion potential between a hard sphere and a planar hard wall, or two hard spheres, imposed by suspended rigid spherocylindrical rods is computed by the acceptance ratio method through the application of Monte Carlo simulation. The accurate results and ideal-gas approximation results of the depletion potential are determined with the acceptance ratio method in our simulations. For comparison, the depletion potentials are also studied by using both the density functional theory and Derjaguin approximations. The density profile as a function of positions and orientations of rods, used in the density functional theory, is calculated by Monte Carlo simulation. The potential obtained by the acceptance ratio method is in good agreement with that of density functional theory under the ideal-gas approximation. The comparison between our results and those of other theories suggests that the acceptance ratio method is the only efficient method used to compute the depletion potential induced by nonspherical colloids with the volume fraction beyond the ideal-gas approximation.     

The structural properties of a two-Yukawa fluid: Simulation and analytical results

Standard Monte Carlo simulations are carried out to assess the accuracy of theoretical predictions for the structural properties of a model fluid interacting through a hard-core two-Yukawa potential composed of a short-range attractive well next to a hard repulsive core, followed by a smooth, long-range repulsive tail. Theoretical calculations are performed in the framework provided by the Ornstein-Zernike equation, solved either analytically with the mean spherical approximation (MSA) or iteratively with the hypernetted-chain (HNC) closure. Our analysis shows that both theories are generally accurate in a thermodynamic region corresponding to a dense vapor phase around the critical point. For a suitable choice of potential parameters, namely, when the attractive well is deep and/or large enough, the static structure factor displays a secondary low-Q peak. In this case HNC predictions closely follow the simulation results, whereas MSA results progressively worsen the more pronounced this low-Q peak is. We discuss the appearance of such a peak, also experimentally observed in colloidal suspensions and protein solutions, in terms of the formation of equilibrium clusters in the homogeneous fluid.     

Interfacial colloidal sedimentation equilibrium. I. Intensity based confocal microscopy

This paper reports confocal microscopy measurements of inhomogeneous colloidal sedimentation equilibrium profiles near planar wall surfaces for conditions when colloid dimensions are comparable to the characteristic gravitational length scale. The intensity based confocal method developed in this work enables real-space measurements of one-dimensional density profiles of Brownian colloids without identifying many single colloid centers in large imaging volumes. Measured sedimentation equilibrium profiles for single-phase interfacial fluids and for coexisting inhomogeneous fluid and solid phases are in agreement with a perturbation theory and Monte Carlo simulations within the local density approximation. Monte Carlo simulated colloid scale density profiles display some minor differences with confocal images in terms of microstructural transitions involving the onset of interfacial crystallization and the precise elevation of the fluid-solid interface. These discrepancies are attributed to polydispersity unaccounted for in the analyses, sensitivity of the perturbation theory to the effective hard sphere size, and the influence of ensemble, system size, and box shape in Monte Carlo simulations involving anisotropic/inhomogeneous solids. Successful demonstration of intensity based confocal microscopy provides a basis for future measurements of three-dimensional colloidal interactions, dynamics, and structure near surfaces.     

Local structure and thermodynamics of a core-softened potential fluid: theory and simulation.

Phase behavior and structural properties of homogeneous and inhomogeneous core-softened (CS) fluid consisting of particles interacting via the potential, which combines the hard-core repulsion and double attractive well interaction, are investigated. The vapour-liquid coexistence curves and critical points for various interaction ranges of the potential are determined by discrete molecular dynamics simulations to provide guidance for the choice of the bulk density and potential parameters for the study of homogeneous and inhomogeneous structures. Spatial correlations in the homogeneous CS system are studied by the Ornstein-Zernike integral equation in combination with the modified hypernetted chain (MHNC) approximation. The local structure of CS fluid subjected to diverse external fields maintaining the equilibrium with the bulk CS fluid are studied on the basis of a recently proposed third order+second order perturbation density functional approximation (DFA). The accuracy of DFA predictions is tested against the results of a grand canonical ensemble Monte Carlo simulation. Reasonable agreement between the results of both methods proves that the DFA theory applied in this work is a convenient theoretical tool for the investigation of the CS fluid, which is practically applicable for modeling numerous real systems.     

The behavior of fluids near solutes: a density functional theory and computer simulation study

The density distribution of solvent near a solute particle is studied using density functional theory and Monte Carlo simulation. The fluid atoms interact with each other via a hard sphere plus Yukawa potential, and interact with the solute via a hard sphere potential. For small solute sizes, the solvent displays liquidlike ordering near the particle. When the solute become larger, a drying transition is observed at state points near the coexistence conditions of the solvent. These predictions are similar to those of a recent theory for the hydrophobic effect by Lum, Chandler, and Weeks [J. Phys. Chem. 103, 4570 (1999)], although a comparison with simulations shows that the theory of this work is quantitatively more accurate. The connection between density functional methods and the LCW approach is also established.     

Density and chain conformation profiles of square-well chains confined in a slit by density-functional theory

Density and chain conformation profiles of square-well chains between two parallel walls were studied by using density-functional theory. The free energy of square-well chains is separated into two contributions: the hard-sphere repulsion and the attraction. The Heaviside function is used as the weighting function for both of the two parts. The equation of state of Hu et al. is used to calculate the excess free energy of the repulsive part. The equation of state of statistical associating fluid theory for chain molecules with attractive potentials of variable range [A. Gil-Villegas et al. J. Chem. Phys. 106, 4168 (1997)] is used to calculate the excess free energy of the attractive part. Because the wall is inaccessible to a mass center of a longer chain, there exists a sharp fall in the distribution of end-to-end distance near the wall as the chain length increases. When the average density of the system is not too low, the prediction of this work is in good agreement with computer simulation results for the density profiles and the chain conformation over a wide range of chain length, temperature, and attraction strength of the walls. However, when the average density and the temperature are very low, the prediction deviates to a certain degree from the computer simulation results for molecules with long chain length. A more accurate functional approximation is needed.     

Anomalous potentials from inverse analyses of interfacial polydisperse attractive colloidal fluids

This paper investigates effects of using monodisperse inverse analyses to extract particle-particle and particle-surface potentials from simulated interfacial colloidal fluids of polydisperse attractive particles. Effects of polydispersity are investigated as functions of particle concentration and attractive well depth and range for van der Waals and depletion potentials. Forward Monte Carlo simulations are used to generate particle distribution functions for polydisperse interfacial colloidal fluids from which inverted potentials are obtained using an inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method. Attractive potentials are successfully recovered for monodisperse colloidal fluids, but polydispersity that is unaccounted for in inverse analyses produces (1) apparent softening of strong forces, (2) anomalous repulsive and attractive interactions, and (3) aphysical particle overlaps. This investigation provides insights into the role of polydispersity in altering the equilibrium structure and corresponding inverted potentials of attractive colloidal fluids near surfaces. These findings should assist the design and interpretation of optical microscopy experiments involving interfacial colloidal fluids similar to the simulated experiments reported here.     

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.     

Compressible or incompressible blend of interacting monodisperse linear polymers near a surface

We consider a lattice model of a mixture of repulsive, attractive, or neutral monodisperse linear polymers of two species, A and B, with a third monomeric species C, which may be taken to represent free volume. The mixture is confined between two hard, parallel plates of variable separation whose interactions with A and C may be attractive, repulsive, or neutral, and may be different from each other. The interactions with A and C are all that are required to completely specify the effect of each surface on all three components. We numerically study various density profiles as we move away from the surface, by using the recursive method of Gujrati and Chhajer [J. Chem. Phys. 106, 5599 (1997)] that has already been previously applied to study polydisperse solutions and blends next to surfaces. The resulting density profiles show the oscillations that are seen in Monte Carlo simulations and the enrichment of the smaller species at a neutral surface. The method is computationally ultrafast and can be carried out on a personal computer (PC), even in the incompressible case, when Monte Carlo simulations are not feasible. The calculations of density profiles usually take less than 20 min on a PC.     

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.