Density functional theory of size-dependent surface tension of Lennard-Jones fluid droplets using a double well type Helmholtz free energy functional

A double well type Helmholtz free energy density functional and a model density profile for a two phase vapor-liquid system are used to obtain the size-dependent interfacial properties of the vapor-liquid interface at coexistence condition along the lines of van der Waals and Cahn and Hilliard density functional formalism of the interface. The surface tension, temperature-density curve, density profile, and thickness of the interface of Lennard-Jones fluid droplet-vapor equilibrium, as predicted in this work are reported. The planar interfacial properties, obtained from consideration of large radius of the liquid drop, are in good agreement with the results of other earlier theories and experiments. The same free energy model has been tested by solving the equations numerically, and the results compare well with those from the use of model density profile.     

Nucleation in cylindrical capillaries

We use a local density functional theory in the square gradient approximation to explore the properties of critical nuclei for the liquid-vapor transition of van der Waals fluids in cylindrical capillaries. The proposed model allows us to investigate the effect of pore size, surface field, and supersaturation on the behavior of the system. Our calculations predict the existence of at least three different pathways for the nucleation of droplets and bubbles in these confined fluids: axisymmetric annular bumps and lenses, and asymmetric droplets. The morphological transition between these different structures is driven by the existence of states of zero compressibility in the capillary. We show that the classical capillarity theory provides surprisingly accurate predictions for the work of formation of critical nuclei in cylindrical pores when line tension contributions to the free energy are taken into account.     

Properties of argon liquid-vapor interface

The short-wave cutoff boundary of the capillary wave spectrum is established. Effective thickness L _b of the “bare” density profile in the interfacial layer is calculated according to experimental data on the ellipticity ratio of reflected light. The free parameters of the extended van der Waals theory of capillarity are determined. The positions of the equimolecular dividing surface and tension surface are calculated, as well as the temperature dependence of the Tolman parameter.     

Metastable extension of the liquid-vapor phase equilibrium curve and surface tension

The method of molecular dynamics has been used to calculate the parameters of liquid-vapor phase equilibrium and the surface tension in a two-phase system of 4096 Lennard-Jones particles. Calculations have been made in a range from the triple point to near-critical temperature and also at temperatures below the triple point corresponding to the metastable equilibrium of a supercooled liquid and supersaturated vapor. To determine the surface tension, along with a mechanical approach a thermodynamic one has been used as well. The latter was based on calculation of the excess internal energy of an interfacial layer. It has been shown that in accuracy the thermodynamic approach is as good as the more sophisticated mechanical one. Low-temperature asymptotics of the phase-equilibrium curve and also of liquid and vapor spinodals have been considered in the Lennard-Jones and the van der Waals models. The behavior of the surface tension and the excess internal energy of an interfacial layer at T-->0 is discussed.     

Free energy partitioning analysis of the driving forces that determine ion density profiles near the water liquid-vapor interface

Free energy partitioning analysis is employed to explore the driving forces for ions interacting with the water liquid-vapor interface using recently optimized point charge models for the ions and SPC/E water. The Na(+) and I(-) ions are examined as an example kosmotrope/chaotrope pair. The absolute hydration free energy is partitioned into cavity formation, attractive van der Waals, local electrostatic, and far-field electrostatic contributions. We first compute the bulk hydration free energy of the ions, followed by the free energy to insert the ions at the center of a water slab. Shifts of the ion free energies occur in the slab geometry consistent with the SPC/E surface potential of the water liquid-vapor interface. Then the free energy profiles are examined for ion passage from the slab center to the dividing surface. The profiles show that, for the large chaotropic I(-) ion, the relatively flat total free energy profile results from the near cancellation of several large contributions. The far-field electrostatic part of the free energy, largely due to the water liquid-vapor interface potential, has an important effect on ion distributions near the surface in the classical model. We conclude, however, that the individual forms of the local and far-field electrostatic contributions are expected to be model dependent when comparing classical and quantum results. The substantial attractive cavity free energy contribution for the larger I(-) ion suggests that there is a hydrophobic component important for chaotropic ion interactions with the interface.     

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.     

Generalized van der Waals Theory of Interfaces in Simple Fluid Mixtures

An efficient implementation of the generalized van der Waals theory of fluids is presented for the calculation of surface tension in simple fluid mixtures. While detailed correlation analysis is avoided the dominant binding energy contribution and the negative contribution due to the nonlocal entropy are accounted for in the free energy density functional by simple physical approximations of the type originally introduced by van der Waals. Efficient computation is achieved by the use of a single-parameter optimization of a tanh-shaped profile representing the total density as well as the composition variation across the interface. This simple profile nevertheless incorporates the expected adsorption to the interface of the volatile component. Application is made to argon/krypton mixtures represented by Lennard-Jones potentials and Lorentz-Berthelot combining rules. Surface tension predictions compare well with both experimental observations and computer simulation results which also indicated close agreement in particle density profiles, especially if the Berthelot rule is amended with a binary interaction parameter slightly (3%) less than unity. Copyright 2001 Academic Press.     

Adsorption of square and rectangular plate-like molecules on a planar surface

A mean-field statistical thermodynamic analysis of monolayer adsorption of rigid square and rectangular plate-like molecules on a homogeneous planar surface is developed. The analysis is simplified by only considering facewise and edgewise modes of adsorption in restricted orthogonal orientations parallel to the surface. The free energy density, adsorbate population distribution and surface spreading pressure are obtained as a function of adsorbate density and compared for square plate molecules using three different sequences of adsorbate molecule placement on the surface to evaluate the configurational degeneracy. It is found that edgewise adsorbed molecules can be anisotropically ordered if the edge length of square and rectangular plate-like molecules exceeds three length units in the absence of anisotropic dispersion interactions. If intermolecular dispersion interactions are present and of sufficient strength, the spreading pressure-density isotherms can exhibit one or two van der Waals loops for square plate molecules with three van der Waals loops possible for rectangular plate adsorbate molecules. The phase transitions for the adsorbed monolayer corresponding to the appearance of these van der Waals loops are discussed.     

Mechanism of hydrodynamic separation of biological objects in microchannel devices

In this study, the separation mechanism employed in hydrodynamic chromatography in microchannel devices is analyzed. The main purpose of this work is to provide a methodology to develop a predictive model for hydrodynamic chromatography for biological macromolecules in microchannels and to assess the importance of various phenomenological coefficients. A theoretical model for the hydrodynamic chromatography of particles in a microchannel is investigated herein. A fully developed concentration profile for non-reactive particles in a microchannel was obtained to elucidate the hydrodynamic chromatography of these particles. The external forces acting on the particles considered in this model include the van der Waals attractive force, double-layer force as well as the gravitational force. The surface forces, such as van der Waals attractive force as well as the double-layer repulsive force, can either enhance or hinder the average velocity of the macromolecular particles. The average velocity of the particles decreases with the molecular radius because the van der Waals attractive force increases the concentration of the particles near the channel surface, which is the low-velocity region. The transport velocity of the particles is dominated by the gravity and the higher density enlarges the effect caused by gravity.     

On the nonpolar hydration free energy of proteins: surface area and continuum solvent models for the solute-solvent interaction energy

Implicit solvent hydration free energy models are an important component of most modern computational methods aimed at protein structure prediction, binding affinity prediction, and modeling of conformational equilibria. The nonpolar component of the hydration free energy, consisting of a repulsive cavity term and an attractive van der Waals solute-solvent interaction term, is often modeled using estimators based on the solvent exposed solute surface area. In this paper, we analyze the accuracy of linear surface area models for predicting the van der Waals solute-solvent interaction energies of native and non-native protein conformations, peptides and small molecules, and the desolvation penalty of protein-protein and protein-ligand binding complexes. The target values are obtained from explicit solvent simulations and from a continuum solvent van der Waals interaction energy model. The results indicate that the standard surface area model, while useful on a coarse-grained scale, may not be accurate or transferable enough for high resolution modeling studies of protein folding and binding. The continuum model constructed in the course of this study provides one path for the development of a computationally efficient implicit solvent nonpolar hydration free energy estimator suitable for high-resolution structural and thermodynamic modeling of biological macromolecules.     

Re-entrant phase behavior for systems with competition between phase separation and self-assembly

In patchy particle systems where there is a competition between the self-assembly of finite clusters and liquid-vapor phase separation, re-entrant phase behavior can be observed, with the system passing from a monomeric vapor phase to a region of liquid-vapor phase coexistence and then to a vapor phase of clusters as the temperature is decreased at constant density. Here, we present a classical statistical mechanical approach to the determination of the complete phase diagram of such a system. We model the system as a van der Waals fluid, but one where the monomers can assemble into monodisperse clusters that have no attractive interactions with any of the other species. The resulting phase diagrams show a clear region of re-entrance. However, for the most physically reasonable parameter values of the model, this behavior is restricted to a certain range of density, with phase separation still persisting at high densities.     

Wettability study of surface modified silica aerogels with different silylating agents

In wettability study, surface free energy interactions are of crucial importance for silica aerogels in which absorption of organic liquids and transportation of chemicals carried out for chemical and biotechnological applications. In present study, we have used Lifshitz–van der Waals/acid–base approach for calculation of surface free energy of aerogel sample. We have investigated that the surface free energy values of aerogels are 45.95, 51.42 and 45.69 mJ/m² by modifying their surfaces using 7 % chlorotrimethylsilane (TMCS), dimethyldichlorosilane (DMDCS) and hexamethyldisilazane (HMDZ) silylating reagents with solvent, respectively. The alcogels were prepared by two step acid–base catalyzed process where the molar ratio of precursors tetraethoxysilane:methanol:oxalic acid:NH₄OH:NH₄F was kept at optimal value of 1:16.5:0.71:0.58:0.60:0.98, respectively. To modify gel surfaces, TMCS, DMDCS and HMDZ concentration have been varied from 5 to 12 % and such alcogels were dried at ambient pressure. The aerogels have been characterized by fourier transform infrared spectroscopy, scanning electron microscopy, thermo-gravimetric and differential thermal analysis and Wetting properties of silica aerogel surfaces was studied by contact angle measurements. The surface chemical composition of DMDCS modified silica aerogels was studied by using X-ray photoelectron spectroscopy. As there is not any direct method, we have used Lifshitz–van der Waals/acid–base approach which gives, polar and non-polar components of aerogels surface free energy.     

Communication: Length scale dependent oil-water energy fluctuations

Interfacial fluctuations in the cohesive (van der Waals) interaction energy of spherical oil-drops with water provide evidence of a length scale dependent transition from linear to non-linear response behavior. For sub-nanometer oil-drop sizes, energy fluctuations are found to be independent of the van der Waals coupling strength, while nanometer (and larger) size oil drops experience highly non-linear energy fluctuations. The latter behavior is linked to enhanced hydrophobic density fluctuations and the emergence of entropic contributions to oil-water cohesive interaction free energies.     

A van der waals theory with quartic density gradients

Functional methods show that biphasic mixtures of rods and solvent have interfacial free energies quartic in the density gradient in contrast to the quadratic van der Waals theory. The result is novel because there is more than one order parameter and because the coupling is via the distribution functions.     

Adsorption of benzene on coinage metals: a theoretical analysis using wavefunction-based methods

The interaction of benzene with a Ag(111) surface has been determined using reliable ab initio electronic structure calculations. The results are compared to a recent detailed analysis of the interaction of benzene with copper and gold surfaces, thus making it possible to derive a consistent picture for the electronic structure changes encountered when benzene is brought into contact with the densely packed coinage metal surfaces. To avoid the problems encountered when the presently most frequently employed computational approach, density functional theory (DFT), is applied to adsorbate systems where dispersion (or van der Waals) forces contribute substantially, we use a wavefunction-based approach. In this approach, the weak van der Waals interactions, which are dominated by correlation effects, are described using second-order perturbation theory. The surface dipole moment and the work function changes induced upon adsorption are also discussed.     

Interfacial tension and wetting in colloid-polymer mixtures

We calculate the interfacial tension and the wetting behavior in phase separated colloid-polymer mixtures both for ideal and excluded volume interacting polymers. Within the recently developed extension of the free volume theory to include polymer interactions the interfacial tension of the free interface is calculated by adding a van der Waals squared gradient term. The wetting behavior at a hard wall is calculated following a Cahn-Fisher-Nakanishi approach taking the one- and two-body colloid-wall interactions into account. Comparing results for interacting polymers with those for ideal polymers we find that for interacting polymers the interfacial tension does not increase as steeply as a function of the gas-liquid colloid density difference. Furthermore, the wetting transition shifts to higher polymer concentrations, even to above the triple line. The predictions for both the interfacial tension and the wetting are compared to recent experiments.     

The standard free energy of surfactant adsorption at air/water and oil/water interfaces: Theoretical vs. empirical approaches

The standard free energy of surfactant adsorption represents the work of transfer of a surfactant molecule from the bulk of solution to an infinitely diluted adsorption layer. This quantity can be determined by non-linear fits of surface-tension isotherms with the help of a theoretical model of adsorption. Here, the models of Frumkin, van der Waals and Helfand-Frisch-Lebowitz are applied, and the results are compared. Irrespective of the differences between these models, they give close values for the standard free energy. The results from the theoretical approach are compared with those from the most popular empirical approach. The latter gives values of the standard free energy, which are considerably different from the respective true values, with c.a. 10 kJ/mol for nonionic surfactants, and with c.a. 20 kJ/mol for ionic surfactants. These differences are due to contributions from interactions between the molecules in dense adsorption layers. It is concluded that the true values of the standard free energy can be determined with the help of an appropriate theoretical model. For the processed sets of data, the van der Waals model gives the best results, especially for the determination of the standard adsorption enthalpy and entropy from the temperature dependence of surface tension. The results can be useful for the development of a unified approach to the thermodynamic characterization of surfactants.     

Lateral capillary forces between solid bodies on liquid surface: a lattice Boltzmann study

When two solid bodies are placed on the surface of a dense liquid under gravitation, they deform the liquid surface to experience a lateral capillary force between themselves that can be attractive and repulsive, depending on the wettabilities and weights of the bodies. In the present study, the lateral capillary force between two square bodies at a liquid-vapor interface has been examined using numerical simulations based on a two-dimensional two-phase lattice Boltzmann (LB) method. The particular situations were simulated, where every body was vertically constrained and had the fixed triple points at its upper or lower corners. Here, the triple point indicates the place at which vapor, liquid, and solid phases meet. The interaction force between these two bodies was calculated as a function of the separation distance, the interfacial tension, and the gravitational acceleration. The simulation results agree well with the analytical expression of the lateral capillary interaction, indicating that our LB method can reproduce the interaction force between two bodies of various wettabilities at a liquid-vapor interface in mechanical equilibrium.     

用DVR方法研究Ar-HF和Ar-DF的振转光谱

本文用离散变量表示(DVR)方法研究了Ar-HF和Ar-DF体系的振转光谱。对这两个体系的已观测到的振转能级, 用DVR方法得到的计算值与实验结果十分吻合, 误差一般小于0.1cm^-^1, 最大偏差为0.24cm^-^1对Ar-HF的(1113)态。该研究结果与Hutson等用耦合孔道法得到的计算结果基本一致, 但对(3210)振动能级和对(3002)-(3110)态的能级分裂值, 本文计算结果更接近观测值。