Depletion interactions between colloidal particles in polymer solutions: density functional approach

A density functional theory for colloid–polymer mixtures based on the weighted-density approximation has been developed to investigate the depletion effects acting between two colloids immersed in a bath of polymers and the depletion effects for a colloid near a planar hard wall. The theoretical results for the polymer-induced depletion interactions and the local polymer density distributions are in good agreement with the computer simulations. The calculation shows that the depletion interaction for a colloid near a planar hard wall is much stronger than that between two colloids in a polymer solution because of the strong confinement effect. The behaviour of the depletion interactions has been analysed as a function of the polymer density, the polymer chain length, and the colloid/polymer size ratio. Strong depletion effects appear in short-chain systems and with large colloid/polymer size ratios.     

Towards a microscopic theory of wetting by ionic solutions. I. Surface properties of the semi-primitive model

As a first step towards a density functional theory (DFT) of wetting by ionic solutions we examine the density profiles of ions and solvent molecules confined near a charged wall, or between two walls, and the corresponding interfacial properties, including adsorption, surface tension, solvation force and electrostatic properties, within the semi-primitive model (SPM) of solutions made up of hard sphere solvent particles and charged hard spheres. Both monovalent and divalent cations with species-dependent diameters are considered. The density functional includes the best available Rosenfeld hard-sphere functional, as well as mean-field and Coulomb correlation contributions. The simpler mean-field functional is found to be adequate, at least for monovalent ions. The size differences lead to an interesting ‘fine structure’ of the density and charge density profiles. Cohesive interactions between all species are shown to lead to significant changes in the density profiles.     

Behavior of a wetting phase near a solid boundary: vapor near a weakly attractive surface

Density profiles of a LJ vapor near a weakly attractive surface with long-range fluid wall potential was studied along the pore coexistence curve. There are two localized density maxima near the pore wall: the first one is caused by localization of the molecules in the minimum of the fluid-wall potential, and the second one reflects adsorption of molecules at the first layer at higher densities. In addition, a third, weak density maximum is observed close to the critical temperature due to the competition between the long-range attractive tail of the fluid-wall potential and the effect of missing neighbors. This maximum separates the region of a gradual density depletion toward the surface due to the missing neighbor effect and the adsorption region further from the surface, where the density gradually increases toward the surface due to the attractive fluid-wall potential. When approaching the bulk critical temperature, this maximum moves away from the surface due to the divergence of the bulk correlation length. Applicability of various equations to describe the vapor density profiles is examined. Excess adsorption of vapor at low temperatures turns into excess depletion at higher temperatures. The crossover temperature increases with increasing pore size and strengthening fluid-wall interaction. The problems of the theory of the surface critical behavior of Ising models in a case of a non vanishing surface field and its mapping on a fluid is discussed.     

Nematic order in small systems: measuring the elastic and wall-anchoring constants in vibrofluidized granular rods

We investigate nematic order in vibrated granular rods confined to a small quasi-2D container less than 10 rod lengths in diameter. As rod density ρ increases, patterning shifts from bipolar to uniform alignment. We find that a continuum liquid crystal free energy functional captures key patterning features down to almost the particle size. By fitting theory to experiments, we estimate the relative values of bend and splay elastic constants and wall anchoring. We find that splay is softer than bend for all ρ and rod lengths tested, while the ratio of the average elastic constant to wall anchoring increases with ρ.     

Critical assessment of effective interfacial potentials based on a density functional theory for wetting phenomena on curved substrates

In this Letter we examine an effective interfacial Hamiltonian approach for wetting phenomena based on two different density approximations in the framework of a density functional theory. The system under consideration is an attractive spherical wall subject to adsorption by a metastable liquid. We argue that, contrary to a planar geometry, in the spherical case the popular sharp-kink approximation leads to a considerable disagreement for the film thickness with numerical results obtained from density functional theory. We show that the deviation originates from the inaccuracy of the predicted liquid-gas surface tension. We further demonstrate that the prediction can be substantially improved when a soft-interface approximation is adopted, such that the liquid-gas interface is approximated by a smooth monotonic function.     

纳米通道内气体剪切流动的分子动力学模拟

采用分子动力学模拟方法研究了表面力场对纳米通道内气体剪切流动的影响规律.结果显示通道内的气体流动分为两个区域:受壁面力场影响的近壁区域和不受壁面力场影响的主流区域.近壁区域内,气体流动特性和气体动力学理论预测差别很大,密度和速度急剧增大并出现峰值,正应力变化剧烈且各向异性,剪切应力在距壁面一个分子直径处出现突变.主流区域的气体流动特性与气体动力学理论预测相符合,该区域内的密度、正应力与剪切应力均为恒定值,速度分布亦符合应力-应变的线性响应关系.不同通道高度及密度下,近壁区域的归一化密度、速度及应力分布一致,表明近壁区域的气体流动特性仅由壁面力场所决定.随着壁面对气体分子势能作用的增强,气体分子在近壁区域的密度和速度随之增大,直至形成吸附层,导致速度滑移消失.通过剪切应力与切向动量适应系数(TMAC)的关系,得到不同壁面势能作用下的TMAC值,结果表明壁面对气体分子的势能作用越强,气体分子越容易在壁面发生漫反射.     

Theory of the interface between a classical plasma and a hard wall

The interfacial density profile of a classical one-component plasma confined by a hard wall is studied in planar and spherical geometries. The approach adapts to interfacial problems a modified hypernetted-chain approximation developed by Lado and by Rosenfeld and Ashcroft for the bulk structure of simple liquids. The specific new aim is to embody self-consistently into the theory a “contact theorem”, fixing the plasma density at the wall through an equilibrium condition which involves the electrical potential drop across the interface and the bulk pressure. The theory is brought into fully quantitative contact with computer simulation data for a plasma confined in a spherical cavity of large but finite radius. It is also shown that the interfacial potential at the point of zero charge is accurately reproduced by suitably combining the contact theorem with relevant bulk properties in a simple, approximate representation of the interfacial charge density profile.     

A unified wall function for compressible turbulence modelling

Turbulence modelling near the wall often requires a high mesh density clustered around the wall and the first cells adjacent to the wall to be placed in the viscous sublayer. As a result, the numerical stability is constrained by the smallest cell size and hence requires high computational overhead. In the present study, a unified wall function is developed which is valid for viscous sublayer, buffer sublayer and inertial sublayer, as well as including effects of compressibility, heat transfer and pressure gradient. The resulting wall function applies to compressible turbulence modelling for both isothermal and adiabatic wall boundary conditions with the non-zero pressure gradient. Two simple wall function algorithms are implemented for practical computation of isothermal and adiabatic wall boundary conditions. The numerical results show that the wall function evaluates the wall shear stress and turbulent quantities of wall adjacent cells at wide range of non-dimensional wall distance and alleviate the number and size of cells required.     

The diffusion of hydrogen monomers on hole-doped graphitic lattices: over-barrier transition and quantum tunneling

The diffusion of hydrogen and deuterium monomers on hole-doped graphene (a planar graphitic lattice), the outside wall and the inside wall of hole-doped (6, 0) single-walled carbon nanotubes (a curved graphitic lattice) was investigated using density functional theory and density functional perturbation theory. The jump frequencies for the over-barrier transition and phonon-assisted quantum tunneling were calculated by transition state theory and small-polaron theory, respectively. The effects of the local curvature of the surface and the hole doping on the thermodynamic and kinetic properties of a hydrogen monomer on these graphitic lattices are discussed. Our results demonstrate that it is sufficient to judge the diffusional mobility of a hydrogen monomer on graphitic lattices from just the over-barrier transition, no matter how much it is curved and hole doped, while the quantum tunneling can be safely neglected because it is significantly suppressed by the covalent bonding of hydrogen with the graphitic lattice.     

A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT

A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.     

Kinetics of domain wall pinning in an incommensurate Pb overlayer on a Cu(110) surface

We have used grazing incidence X-ray scattering to study the kinetics of domain wall pinning during the transition between an incommensurate phase and a domain wall glass phase. The growth of both domain wall density and domain size are described by power-laws. The results are discussed in the context of recent theoretical models of growth.     

Neutron depolarization study on the magnetic correlation length of nickel ferrite with different packing densities

The magnetic correlation length of a mixed nickel ferrite powder was studied by a newly commissioned depolarized neutron beamline at the W3 port of Tsing Hua Open Pool Reactor (THOR). In this work, Ni ferrite powder samples with different packing densities were studied. The magnetic correlation lengths of the sample were observed to be 2 μm at virgin state and about 3.1 μm at remanent state from the packing density of 20–60%. This magnetic domain size is smaller than particle size. No significant change of domain size at this packing density implies the domain wall motion is hindered by the porosity effectively up to at least 60% of packing density.     

Density functional study on the pressure profile of the inhomogeneous fluid mixture

By using the statistical mechanics, the pressure tensor for the multi component fluid mixture is derived. With the help of the classical density functional theory, profiles of the pressure components are calculated, and the influence of the total volume fraction, ratio of volume fraction, and size asymmetry on the pressure are studied. In addition, our results show that for the mixture confined in the hard cavity, the pressure shows a discontinuity near the cavity wall. However, in the soft cavity condition, the discontinuity disappears.     

Surface-induced first-order transition in athermal polymer-nanoparticle blends

We investigate the phase behavior of athermal polymer-nanoparticle blends near a substrate. We apply a recent fluids density functional theory of Tripathi and Chapman to a simple model of the blend as a mixture of hard spheres and freely jointed hard chains, near a hard wall. We find that there is a first-order phase transition in which the nanoparticles expel the polymer from the surface to form a monolayer. The nanoparticle transition density depends on the length of the polymer and the overall bulk density of the system. The effect is due both to packing entropy effects related to size asymmetry between the components and to the polymer configurational entropy. The simplicity of the system allows us to understand the so-called "entropic-push" observed in experiments.     

A correlation-hole approach to the electric double layer with counter-ions only

ABSTRACT

We study a classical system of identically charged counter-ions near a planar wall carrying a uniform surface charge density. The equilibrium statistical mechanics of the system depends on a single dimensionless coupling parameter. A new self-consistent theory of the correlation-hole type is proposed which leads to a modified Poisson–Boltzmann integral equation for the density profile, convenient for analytical progress and straightforward to solve numerically. The exact density profiles are recovered in the limits of weak and strong couplings. In contrast to previous theoretical attempts of the test-charge family, the density profiles fulfil the contact-value theorem at all values of the coupling constant and exhibit the mean-field decay at asymptotically large distances from the wall, as expected. We furthermore show that the density corrections at large couplings exhibit the proper dependence on coupling parameter and distance to the charged wall. The numerical results for intermediate values of the coupling provide accurate density profiles which are in good agreement with those obtained by Monte Carlo simulations. The crossover to mean-field behaviour at large distance is studied in detail.     

Raman theory of quantum wires. Evidence of ripples in Raman spectra of thin wall Si nanotubes

In the present paper we develop for the first time a general theory calculating the Raman spectrum of a quantum wire, using the phonon modes active in the wire. No Raman theory is at present available for quantum wires. In fact, to date only phenomenological models with arbitrary parameters, or unidimensional approaches have been published specifically for quantum dots. In our approach the confinement effects due to the reduced size are introduced directly by means of the Heisenberg Uncertainty Principle. The present theory, applied to silicon nanowires, permits the evaluation of Raman frequency shift and linewidth broadening as a function of the size. The results obtained by this model for Si nanowires are in close agreement with the few experimental data available in the literature. The model also shows evidence of ripples in the Raman spectra of thin wall Si nanotubes. This theory can be applied as well to any semiconductor of known phonon branches.     

Associating fluids with four bonding sites against a hard wall: density functional theory

We present two new perturbation density functional theories to investigate non-uniform fluids of associating molecules. Each fluid molecule is modelled as a spherical hard core with four highly anisotropic square well sites placed in tetrahedral symmetry on the hard core surface. In one theory we apply the weighting from Tarazona's hard sphere density functional theory to Wertheim's bulk first-order perturbation theory. The other theory uses the inhomogeneous form of Wertheim's theory as a perturbation to Tarazona's hard-sphere density functional theory. Each theory approaches Tarazona's theory in the limit of zero association. We compare results from theory and simulation for density profiles, fraction of monomers, and adsorption of an associating fluid against a hard, smooth wall over a range of temperatures and densities. The non-uniform fluid theory which uses Tarazona's weighting of Wertheim's theory in the bulk is in good agreement with computer simulation results.     

Temperature variation of bubble domains in Dy0.3Tm0.7FeO3 mixed orthoferrite

Bubble domain structure in Dy_0.3Tm_0.7FeO₃ mixed orthoferrite was studied between room temperature and 480 K using the Faraday effect. Temperature dependence of the magnetization and domain wall energy density has been determined. Starting from the molecular field theory and one-ion theory of magnetocrystalline anisotropy, expressions describing a temperature dependence of the domain wall energy density in orthoferrites have been derived. In the expression for magnetocrystalline energy, uniaxial as well as cubic anisotropy have been accounted for.     

超临界CO_2在岩石孔隙内流动状态的分子模拟

本文采用分子模拟的方法研究了地质封存条件下超临界CO_2在镁橄榄石孔隙内的流动,分析了孔隙尺寸、温度、压强对超临界CO_2的密度分布和流动速度的影响.研究结果表明,只有当孔隙尺寸大于5.0 nm时,超临界CO_2分子在岩石孔隙内的流动才符合Poiseuille流动;同时,超临界CO_2分子在岩石近壁面存在1.5 nm的密度震荡,当孔隙尺寸小于15 nm时,密度振荡现象会影响CO_2分子在岩石孔隙内的平均密度;升高温度、降低压强的方法可以减小密度震荡的第一峰值,减弱岩石壁面与CO_2的相互作用,使得CO_2的流动速度增加.     

On surface properties of a weakly-coupled classical one-component plasma: The size effect in finite systems

The surface properties of a weakly coupled classical one-component plasma of finite size are calculated exactly within the Poisson-Boltzmann (PB) approximation scheme. It is found that the ion density profile and the surface energy for a spherical system show strong size dependence. The surface energy also strongly depends on the position of the hard wall introduced for achieving an appropriate equilibrium ion configuration. These results indicate that the recent Monte Carlo simulation data for a spherical system must be interpreted, at least in the weak-coupling regime, as including substantial size effects and cannot be directly compared with the theoretical calculations for the planar surface. For a slab, on the other hand, such size effects are found to be very small if the hard wall is placed at sufficiently distant position from the surface. The dominant contribution to the surface energy which is omitted in the PB approximation is also estimated by the perturbation calculations.