Investigation of excess adsorption, solvation force, and plate-fluid interfacial tension for Lennard-Jones fluid confined in slit pores

The excess Helmholtz free energy functional is formulated in terms of a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)] for a short ranged repulsion and a first-order mean-spherical approximation theory [Y. P. Tang, J. Chem. Phys. 118, 4140 (2003)] for a long ranged attraction. Within the framework of the density functional theory, the density profile, excess adsorption, solvation force, and plate-fluid interfacial tension of a Lennard-Jones fluid confined in slit pores are predicted, and the results agree well with the simulation data. The phase equilibria inside the slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal, and the plate-fluid interfacial tensions at equilibrium states are predicted consequently.     

受限于纳米狭缝中的四缔合Lennard-Lones流体的相平衡和界面张力研究

分别用改进的基础测量理论和平均球近似理论表达短程作用和长程作用对四缔合Lennard-Jones流体的过剩自由能的贡献. 在密度函泛理论的框架下, 研究了平均密度等温线, 密度分布, 未缔合分子在平衡汽相和液相中的分布, 相平衡以及平衡时的界面张力等热力学性质. 分析了缔合能量, 流体-固体作用和孔宽对受限于纳米狭缝中的四缔合Lennard-Jones流体相行为的影响.     

用密度泛函理论研究Lennard-Jones 流体在狭缝中的相平衡

用改进的基础度量理论(modified fundamental measure theory, MFMT)和密度Taylor展开分别表达过剩自由能中的短程作用和色散作用. 流体分子与狭缝壁之间的相互作用以10-4-3势能函数表达. 由巨势最小原理确定Lennard-Jones (LJ)流体在狭缝中的密度分布和过剩吸附量, 所得结果与分子模拟数据吻合良好. 根据平衡时两相温度, 化学势及巨势相等, 计算了LJ流体在狭缝中的相平衡.     

Prediction of phase behavior of nanoconfined Lennard-Jones fluids with density functional theory based on the first-order mean spherical approximation

The recently proposed first-order mean spherical approximation (FMSA) [Y. Tang, J. Chem. Phys. 121, 10605 (2004)] for inhomogeneous fluids is extended to study the phase behavior of nanoconfined Lennard-Jones fluids, which is consistent with the phase equilibria calculation of the corresponding bulk fluid. With a combination of fundamental measure theory, FMSA provides Helmholtz free energy and direct correlation function to formulate density functional theory, which implementation is as easy as the mean-field theory. Following previous success in predicting density profiles inside slit pores, this work is focused specially on the vapor-liquid equilibrium of the Lennard-Jones fluids inside these pores. It is found that outside the critical region FMSA predicts well the equilibrium diagram of slit pores with the sizes of 5.0, 7.5, and 10 molecular diameters by comparing with available computer simulation data. As a quantitative method, FMSA can be treated as an extension from its bulk calculation, while the mean-field theory is only qualitative, as its bulk version.     

Surface tension of chain molecules through a combination of the gradient theory with the CPA EoS

Despite the interest in systems containing non-associating compounds such as alkanes and fluoroalkanes or associating compounds like alkanols, their vapor–liquid interfaces have received little quantitative attention. Aiming at modeling the interfacial tensions of several families of chain molecules, a combination of the density gradient theory of fluid interfaces with the Cubic-Plus-Association (CPA) equation of state was developed. The density gradient theory is based on the phase equilibria of the fluid phases separated by the interface, for what an adequate equation of state is required.     

Structure and phase behavior of a confined nanodroplet composed of the flexible chain molecules

A polymer density functional theory has been employed for investigating the structure and phase behaviors of the chain polymer, which is modelled as the tangentially connected sphere chain with an attractive interaction, inside the nanosized pores. The excess free energy of the chain polymer has been approximated as the modified fundamental measure-theory for the hard spheres, the Wertheim's first-order perturbation for the chain connectivity, and the mean-field approximation for the van der Waals contribution. For the value of the chemical potential corresponding to a stable liquid phase in the bulk system and a metastable vapor phase, the flexible chain molecules undergo the liquid-vapor transition as the pore size is reduced; the vapor is the stable phase at small volume, whereas the liquid is the stable phase at large volume. The wide liquid-vapor coexistence curve, which explains the wide range of metastable liquid-vapor states, is observed at low temperature. The increase of temperature and decrease of pore size result in a narrowing of liquid-vapor coexistence curves. The increase of chain length leads to a shift of the liquid-vapor coexistence curve towards lower values of chemical potential. The coexistence curves for the confined phase diagram are contained within the corresponding bulk liquid-vapor coexistence curve. The equilibrium capillary phase transition occurs at a higher chemical potential than in the bulk phase.     

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.     

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.     

Theory of repulsive charged colloids in slit-pores

Using classical density functional theory (DFT) we analyze the structure of the density profiles and solvation pressures of negatively charged colloids confined in slit pores. The considered model, which was already successfully employed to study a real colloidal (silica) suspension [S. H. L. Klapp et al., Phys. Rev. Lett. 100, 118303 (2008)], involves only the macroions which interact via the effective Derjaguin-Landau-Verwey-Overbeek (DLVO) potential supplemented by a hard core interaction. The solvent enters implicitly via the screening length of the DLVO interaction. The free energy functional describing the colloidal suspension consists of a hard sphere contribution obtained from fundamental measure theory and a long range contribution which is treated using two types of approximations. One of them is the mean field approximation (MFA) and the remaining is based on Rosenfeld's perturbative method for constructing the Helmholtz energy functional. These theoretical calculations are carried out at different bulk densities and wall separations to compare finally to grand canonical Monte Carlo simulations. We also consider the impact of charged walls. Our results show that the perturbative DFT method yields generally qualitatively consistent and, for some systems, also quantitatively reliable results. In MFA, on the other hand, the neglect of charge-induced correlations leads to a breakdown of this approach in a broad range of densities.     

Phase Equilibria of Hydrogen Bonding Fluid in a Slit Pore with Broken Symmetry

Phase equilibria of hydrogen bonding (HB) fluid confined in a slit pore with broken symmetry were investigated by the density functional theory incorporated with modified fundamental measure theory, where the symmetry breaking originated from the distinct interactions between fluid molecules and two walls of the slit pore. In terms of adsorption-desorption isotherms and the corresponding grand potentials, phase diagrams of HB fluid under various conditions are presented. Furthermore, through phase coexistences of laying transition and capillary condensation, the effects of HB interaction, pore width, fluid-pore interaction and the broken symmetry on the phase equilibrium properties are addressed. It is shown that these factors can give rise to apparent influences on the phase equilibria of confined HB fluid because of the competition between intermolecular interaction and fluid-pore interaction. Interestingly, a significant influence of broken symmetry of the slit pore is found, and thus the symmetry breaking can provide a new way to regulate the phase behavior of various confined fluids.     

Density functional theory for semiflexible and cyclic polyatomic fluids

The effects of bond angle and chain stiffness on the structures of semiflexible polyatomic fluids are investigated by incorporating the bending potential into a density functional theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 2368 (2002)] that combines a modified fundamental measure theory for the excluded-volume effects and the first-order thermodynamics perturbation theory for the chain connectivity. The refined density functional theory faithfully reproduces the density profiles and conformational properties of a variety of triatomic fluids near a hard wall in which extensive Monte Carlo simulation data are available. In particular, the theory is able to capture the structures of rigid cyclic trimers where all segments are identical. The variation of local density profiles with respect to the chain length of confined polyatomic fluids is also explored. For quadratomic fluids confined in slit pores, the density profile of the middle segments exhibits novel double peaks that are absent in a fully flexible chain model. In addition, the density functional theory is applied to predicting the conformational properties and adsorption behavior of heterogeneous triatomic fluids of type "ABB" mimicking surfactant molecules. The competition between surface adsorption and self-association of trimers consisting of surface active and self-binding "A" segments and neutral "B" segment is explored.     

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.     

Critical behavior in microemulsions

Interactions in dispersions have been studied using light scattering techniques applied to microemulsions. In these systems, hard sphere interactions are dominant. The remaining interactions (van der Waals, etc.) are usually attractive and short-ranged and can be treated as perturbations. However, close to phase transitions where the microemulsion separates into two other microemulsions, the attractive part of the potential becomes large and behaves as if long range interactions were present; the characteristics of the scattered light can also be interpreted by assuming that the system is close to a critical consolute point. The low interfacial tensions (measured between the two microemulsions in equilibrium using surface light scattering techniques) and the large interfacial thicknesses (deduced from optical reflectivity) are consistent with the picture in terms of critical phenomena.     

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-functional theory and Monte Carlo simulation for the surface structure and correlation functions of freely jointed Lennard-Jones polymeric fluids

We present a nonlocal density-functional theory of polymeric fluids consisting of freely jointed Lennard-Jones chains with explicit consideration of the segment size, van der Waals attraction, and structural correlations due to chain connectivity. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the short-ranged repulsion and the first-order thermodynamic perturbation theory for chain connectivity. The contribution of the long-ranged attraction to the Helmholtz energy functional is taken into account using a quadratic density expansion with the direct correlation function obtained from the first-order mean-spherical approximation. The numerical performance of the density-functional theory is compared well with the simulation results from this work as well as those from the literature for the segment-level density profiles and correlation functions of Lennard-Jones chains in slit pores, near isolated nanoparticles, or in bulk.     

Density functional theory of liquid crystals and surface anchoring: hard Gaussian overlap-sphere and hard Gaussian overlap-surface potentials

This article applies the density functional theory to confined liquid crystals, comprised of ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The extended restricted orientation model proposed by Moradi and co-workers [J. Phys.: Condens. Matter 17, 5625 (2005)] is used to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the optimized sum of Percus-Yevick and Roth DCF for hard spheres; the anisotropy introduced by means of the closest approach parameter, the expression proposed by Marko [Physica B 392, 242 (2007)] for DCF of HGO, and hard ellipsoids were used. In this study we extend an our previous work [Phys. Rev. E 72, 061706 (2005)] on the anchoring behavior of hard particle liquid crystal model, by studying the effect of changing the particle-substrate contact function instead of hard needle-wall potentials. We use the two particle-surface potentials: the HGO-sphere and the HGO-surface potentials. The average number density and order parameter profiles of a confined HGO fluid are obtained using the two particle-wall potentials. For bulk isotropic liquid, the results are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 71, 021705 (2005)]. Also, for the bulk nematic phase, the theory gives the correct density profile and order parameter between the walls.     

AB2型聚合物流体的表面结构性质

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)表达聚合作用对自由能泛函的贡献, 建立了描述AB2型聚合物流体的化学势, 得到了聚合物流体在硬球颗粒表面的密度分布表达式, 计算了聚合物流体在硬球颗粒表面附近的密度分布, 并探讨了体积分数、聚合程度和硬球颗粒尺度对体系密度分布的影响. 此外, 通过体系密度分布, 进一步分析了体积分数、聚合程度和硬球颗粒尺度与剩余吸附的关系.     

Effect of surface active sites on adsorption of associating chain molecules in pores: A Monte Carlo study

This work describes the adsorption behavior of associating and non-associating chains and their mixtures in pores with activated surfaces. The systems are studied using Gibbs ensemble Monte Carlo molecular simulations. Fluid molecules are modeled as freely jointed Lennard-Jones chains. Associating chains have, additionally, an associating square-well site placed in an end sphere. The pores are modeled as regular slit pores via an integrated Lennard-Jones potential (10-4-3); activation is achieved by placing specific association sites protruding from the surface. Two different solid-fluid interaction parameters are used, one of which corresponds roughly to alkanes on graphite, the other being a much weaker interaction. Adsorption isotherms are presented for several different cases: associating and non-associating chains confined within both neutral and activated walls. Mixtures of associating and non-associating chains are also considered. The effects of pore size, temperature and chain length are quantified. Selectivities obtained are in the range of those seen in adsorption experiments of alkane-alkanol mixtures.