Perturbation theory of polar hard Gaussian overlap fluid mixtures

A perturbation theory of polar hard Gaussian overlap fluid mixture is discussed. Explicit analytic expressions for the second and third varial coefficients are given. Numerical results are estimated for the thermodynamic properties of quadrupolar hard Gaussian overlap fluid and fluid mixture. It is found that the excess free energy and internal energy depend on concentrationsc ₁,c ₂, molecular diameter ratioR, shape parameterK and the quadrupole momentsQ*₁,Q*₂.     

The solvation and hydrophobic interaction of non-polar molecules in water in the approximation of interatomic potentials: The Monte Carlo method

The problem of calculating thermodynamic functions of solvation and hydrophobic interaction of non-polar molecules in water is considered, and the functions of ‘switched off’ interaction which allow one to compare calculated and experimental data are introduced and discussed. Expressions for the free energies, entropies and internal energies of solvation and hydrophobic interaction are deduced by statistical mechanics, and the possibility of computing these quantities from information about interatomic potential functions is considered. An application of the Monte Carlo method with the Boltzmann transition probabilities between the states of a Markov chain has allowed us to evaluate configuration integrals and thermodynamic functions of solvation and hydrophobic interaction. For solvation, the calculated values are in good agreement with the experimental data if the periodic boundary conditions are observed, and in moderate agreement should these be neglected. For hydrophobic interaction, the plot of F _HI(R ₁₂) is built and the potentials of average force for two methane molecules, as well as two hard spheres, is evaluated.     

Linear and non-linear theories of solvation forces in fluids

From an exact expression for the free energy of a non-uniform classical fluid, due to Saam and Ebner, a closure is used to develop a non-linear theory for the density and solvation force between two planar walls. In the linear limit these expressions reduce to ones used successfully elsewhere. Numerical solution of the equations for a hard sphere fluid shows that while the density profiles predicted by the two theories are markedly different, the solvation forces are similar.     

Solvation forces in fluids

Using a formalism derived by us in an earlier paper we obtain the density profile and solvation force between two identical hard plates separated by a fluid characterized by (i) an Orstein-Zernike correlation function and (ii) a Percus-Yevick sticky sphere correlation function. Example (i) yields an exponential or hyperbolic density profile characterized by a correlation length ξ that diverges at the critical point as (T-T_c )^-v . The corresponding force is weak and attractive following an exponential law at large separations. Example (ii) yields an attractive force in the vicinity of the critical region and an oscillatory force at higher densities and/or higher temperatures which can significantly modify forces between colloid particles.     

The energy injection into a fluid by stochastic volume forces and random stirring forces

The wavenumber spectrum of the stationary energy injection rate into an incompressible fluid described by the Navier-Stokes equations is evaluated for some simple realizations of stochastic volume as well as stirring forces. A general relation between energy injection, fluid's response, and force correlations is derived which was previously shown to be particularly simple for Gaussian distributed forces with white noise frequency spectrum. For two kinds of such model volume forces the energy injection rates are calculated: Fluid volume elements of variable size around randomly chosen positions are forced in one model centralsymmetrically in the other one anti-symmetrically under inversion with various force density profiles. The circumstances under which both models display an energy injection rate k ^–1 into a bandd k around the wavenumberk are discussed. As a simple realization of stochastic stirring forces externally moved hard spheres immersed in the fluid are considered. The equation of motion and energy balance for the velocity field of the combined system is discussed. The spectral distribution of energy injection by stirring is shown to be that of a volume force model.     

On the solvation force of water-like fluid models with square-well attraction and site–site association in slit-like pores: density functional approach

The solvation force of the water-like fluid models with square-well attraction and site–site chemical association confined to slit-like pores has been explored. Theoretical procedure is based on the application of the density functional approach with mean-field approximation for the attractive interparticle interactions. The chemical association effects are treated by using the first-order thermodynamic perturbation theory of Wertheim. Trends of behaviour of the solvation force are put in correspondence with the distribution of molecules in the pores and with the average density of the adsorbate. Moreover, the distribution of non-bonded species on pore width is described. The influence of the width of the square-well and of the gas–solid attraction is discussed. A comparison of theoretical predictions with computer simulations results for water models in slit-like pores is performed.     

Lattice Boltzmann simulation of the dispersion of aggregated Brownian particles under shear flows

The deformation and breakup processes of a particle-cluster aggregate under shear flows are investigated by the two-phase lattice Boltzmann method. In the simulation the particle is modeled by a hard droplet with large viscosity and strong surface tension. The van der Waals attraction force is taken into account for the interaction between the particles. Also, the Brownian motion is considered for nano-particles. Two important dimensionless parameters are introduced in order to classify calculated results. One is the ratio of fluid force to the maximum inter-particle force, Y, and the other is the Péclet number which is the ratio of the rate of diffusion by a shear flow to the rate of diffusion by Brownian motion. It is found that Y is the key factor in dispersion and that the Brownian motion retards the dispersion.     

Diffusion within a near-critical nanopore fluid

Results are presented for grand canonical Monte Carlo (GCMC) and both equilibrium and non-equilibrium molecular dynamics simulations (EMD and NEMD) conducted over a range of densities and temperatures that span the two-phase coexistence and supercritical regions for a pure fluid adsorbed within a model crystalline nanopore. The GCMC simulations provided the low temperature coexistence points for the open pore fluid and were used to locate the capillary critical temperature for the system. The equilibrium configurational states obtained from these simulations were then used as input data for the EMD simulations in which the self-diffusion coefficients were computed using the Einstein equation. NEMD colour diffusion simulations were also conducted to validate the use of a system averaged Einstein analysis for this inhomogeneous fluid. In all cases excellent agreement was observed between the equilibrium (linear response theory) predictions for the diffusivities and non-equilibrium colour diffusivities. The simulation results are also compared with a recently published quasi-hydrodynamic theory of Pozhar and Gubbins (Pozhar, L. A., and Gubbins, K. E., 1993, J. Chem. Phys., 99, 8970; 1997, Phys. Rev. E, 56, 5367.). The model fluid and the nature of the fluid wall interactions employed conform to the decomposition of the particle–particle interaction potential explicitly used by Pozhar and Gubbins. The local self-diffusivity was calculated from the local fluid–fluid and fluid wall hard core collision frequencies. While this theory provides reasonable results at moderate pore fluid densities, poor agreement is observed in the low density limit.     

Quasi-2D and prewetting transitions of square-well fluids on a square-well substrate

Molecular simulation methodologies are employed to study the first-order transition of variable square-well (SW) fluids on a wide range of weak attractive surfaces. Surface phase diagram of SW fluids of attractive well diameter λ _ff = 1.5, 1.75, 2.0 on a smooth, structureless surface modelled by a SW potential is reported via grand-canonical transition-matrix Monte Carlo (GC-TMMC) and histogram reweighting techniques. Fluids with λ _ff = 1.5 and 1.75 show quasi-2D vapour–liquid phase transition; on the other hand, prewetting transition is visible for a SW fluid with larger well-extent λ _ff = 2.0. The prewetting line, its length, and closeness to the bulk saturation curve are found to depend strongly on the nature of the fluid–fluid and fluid–wall interaction potentials. Boundary tension of surface coexistence films is calculated by two methods. First, the finite size scaling approach of Binder is used to evaluate the boundary tension via GC-TMMC. Second, the results of the boundary tension are verified by virtue of its relation to the pressure tensor components, which are calculated using a NVT-Monte Carlo approach. The results from the two methods are in good agreement. Boundary tension is found to increase with the increase in the wall–fluid interaction range for the quasi-2D system; conversely, boundary tension for thin–thick film, at prewetting transition, decreases with the increase in the wall–fluid interaction range.     

The Laplace transform of the MSA pair distribution functions between macroions in an ion-dipole fluid

The Laplace transform is obtained for the pair distribution function between a pair of ions, an ion and a macroion, and a pair of macroions in an ion-dipole fluid. This fluid is a simplified model of an electrolyte with a discrete model of solvent (hard spheres with embedded point dipoles). From these results, an expression for the solvation force between macroions is obtained. This result consists of the classical DLVO result plus a series of corrections.     

Effective interaction between two giant spheres suspended in a size polydisperse hard-sphere fluid

Analytic expressions for the Laplace transform of the interaction energy and force between two exceedingly large hard spheres at infinite dilution in a polydisperse hard-sphere suspending fluid are presented. The equations are based on the Percus–Yevick approximation for the many-component suspending fluid, supplemented by the hypernetted chain approximation for the correlation function of the suspended spheres. By applying the Derjaguin approximation, the energy and force results for two spheres are related to the energy per unit area and the disjoining pressure between two flat walls suspended in a polydisperse fluid. Numerical results for the representative Schultz distributions of the diameters of the species comprising the suspending fluid are presented and discussed.     

Palladium‐catalyzed cyclization of 2‐alkynyl‐N‐ethanoyl anilines to indoles: synthesis,structural, spectroscopic,and mechanistic study

This study reports a facial regio‐selective synthesis of 2‐alkyl‐N‐ethanoyl indoles from substituted‐N‐ethanoyl anilines employing palladium (II) chloride, which acts as a cyclization catalyst. The mechanistic trait of palladium‐based cyclization is also explored by employing density functional theory. In a two‐step mechanism, the palladium, which attaches to the ethylene carbons, promotes the proton transfer and cyclization. The gas‐phase barrier height of the first transition state is 37 kcal/mol, indicating the rate‐determining step of this reaction. Incorporating acetonitrile through the solvation model on density solvation model reduces the barrier height to 31 kcal/mol. In the presence of solvent, the electron‐releasing (–CH₃) group has a greater influence on the reduction of the barrier height compared with the electron‐withdrawing group (–Cl). These results further confirm that solvent plays an important role on palladium‐catalyzed proton transfer and cyclization. For unveiling structural, spectroscopic, and photophysical properties, experimental and computational studies are also performed. Thermodynamic analysis discloses that these reactions are exothermic. The highest occupied molecular orbital?lowest unoccupied molecular orbital gap (4.9–5.0 eV) confirms that these compounds are more chemically reactive than indole. The calculated UV–Vis spectra by time‐dependent density functional theory exhibit strong peaks at 290, 246, and 232 nm, in good agreement with the experimental results. Moreover, experimental and computed ¹H and ¹³C NMR chemical shifts of the indole derivatives are well correlated. Copyright © 2015 John Wiley & Sons, Ltd.     

Role of molecular interactions and end chain length on the photosensitivity of liquid crystalline alkyl cyanobiphenyl dimers – UV absorption-based approach through DFT calculations

In this paper, the photosensitivity of liquid crystalline alkyl cyanobiphenyl (nCB: n = 6, 7; n is the number of carbon atoms in the alkyl chain) dimers has been presented through density functional theory (DFT) calculations. The nCB structures have been optimized using the Becke, three-parameter, Lee–Yang–Parr hybrid functional with the 6-31+G (d) basis set using the crystallographic geometry as input. The electronic structures of the dimer molecules have been computed using the optimized geometries. The spectra of the dimer molecules have been calculated by employing the DFT method. The excited states have been calculated via configuration interaction singles with the semi-empirical Hamiltonian Zerner intermediate neglect of differential overlap. The influence of molecular interactions and the end chain length on ultraviolet absorption spectral characteristics and the photosensitivity of the compounds has been discussed. These results offer a hint for the protection of various optical devices from the intense light induced damages, and to model photosensitivity.     

The correlations in a star molecule fluid. Integral equation theory and Monte Carlo study

The structure of a starlike molecule (SLM) fluid with four arms of different length is studied by applying the associative Percus–Yevick integral equation (IE) theory and canonical Monte Carlo (MC) simulations. In the IE study the SLM fluid is modelled by a fluid of hard spheres with four associative sites on each sphere while the MC has been performed for a freely-joined tangent hard sphere fluid. The total radial distribution functions have been calculated in both approaches for different volume fraction regimes and different arm lengths. It is shown that the associative IE theory predicts the structure of SLM fluid best for relatively long arms and at high densities. Additionally, the dependence of the SLM centre–centre correlations on the functionality and fluid particle density has been analysed using the MC results.     

Density Profiles in a Classical Coulomb Fluid Near a Dielectric Wall. I. Mean-Field Scheme

The equilibrium density profiles in a classical multicomponent plasma near a hard wall made with a dielectric material characterized by a relative dielectric constant ∈_w are studied from the first Born–Green–Yvon (BGY) equation combined with Poisson equation in a regime where Coulomb coupling is weak inside the fluid. In order to prevent the collapse between charges with opposite signs or between each charge and its dielectric image inside the wall when ∈_w>1, hard-core repulsions are added to the Coulomb pair interaction. The charge-image interaction cannot be treated perturbatively and the density profiles vary very fast in the vicinity of the wall when ∈_w≠1. The formal solution of the associated inhomogeneous Debye–Hückel equations will be given in Paper II, together with a systematic fugacity expansion which allows to retrieve the results obtained from the truncated BGY hierarchy. In the present paper the exact density profiles are calculated analytically up to first order in the coupling parameter. The expressions show the interplay between three effects: the geometric repulsion from the impenetrable wall; the electrostatic effective attraction (∈_w>1) or repulsion (∈_w<1) due to its dielectric response; and the Coulomb interaction between each charge and the potential drop created by the electric layer which appears as soon as the system is not symmetric. We exhibit how the charge density profile evolves between a structure with two oppositely-charged layers and a three-layer organization when ∈_w varies. (The case of two ideally conducting walls will be displayed elsewhere).     

约束条件下胶球间排空力的研究

用MonteCarlo方法对处于两平行硬板约束下三个浓度的大小胶球系统进行了模拟,通过对大胶球表面小胶球密度的统计,由密度积分公式获得了大胶球所受的排空力.研究结果显示,因为平行硬板的存在或当改变两平行硬板的距离时,同浓度下,排空力在硬板距离小的时候最明显;三个浓度中,浓度高的,排空力受硬板距离影响最大;有硬板约束比无该约束的时候,排空力效果更显著.     

纳米通道滑移流动的分子动力学模拟研究

本文采用非平衡分子动力学方法对平板纳米通道滑移流动进行了非平衡分子动力学模拟,获得了不同壁面势能和不同温度时流体的速度分布及密度分布。研究结果表明滑移速度在很大程度上决定于流体温度和壁面吸引力作用强度的大小。由于不同壁面吸引力时流体的密度分布受温度的影响规律不同,使得不同壁面吸引力时流体的滑移速度受温度影响规律也不一致。而且,流体结构受壁面流速的影响要受到壁面势能的制约。     

Exciton eigenstates and biexciton interaction energies in a spherical core/shell semiconductor hetero-nano structure

The exciton eigenstates and biexciton interaction energies in a spherical core–shell hetero-nano structure in the type II and the quasi-type II carrier localization regimes have been analyzed. For the analysis, we have evaluated the electron–hole overlap integral, the binding energy of exciton ground state, and the interaction energy of bi-exciton ground state in the structure. In the evaluation, the first order perturbation approach has been employed, where the direct Coulomb interaction energy, the surface polarization energy and the dielectric solvation energy are included. Our results show that the exciton eigenenergies and exciton–exciton interaction energy strongly depend on the choice of materials on which both the dielectric constants and the electron and hole effective masses rely.