Vapour-to-Liquid Nucleation in Associating Lennard-Jones Fluids with Multiple Association Sites

The excess Helmholtz free energy functional for associating Lennard-Jones （L J） fluid is formulated in terms of a weighted density approximation for short-ranged interactions and a Weeks-Chandler-Andersen approximation for long-range attraction. Within the framework of density functional theory, phase equilibria, vapour-liquid surface tension and vapour-liquid nucleation properties including the density profile, work of formation, excess number of particles and critical supersaturation are investigated for associating LJ fluids with different numbers of association sites （M =1,2, 3, 4） per particle. The influences of association energy and association sites on phase equilibria, surface tension and vapour-liquid nucleation properties are discussed.     

Nucleation for Lennard-Jones Fluid by Density Functional Theory

A non-mean field density functional theory is employed to investigate the vapour-liquid nucleation. The excess Helmholtz free energy functional is formulated in terms of a local density approximation for short ranged repulsion and a density-gradient expansion for long-ranged attractions. An analytical expression for the direct correlation function of a Lennard-Jones fluid is utilized to take into account the effect of long-ranged attractions on intermolecular correlations. With the predicted bulk properties and surface tension as input, the nucleation properties including density profile, work of formation and number of particles at the reduced temperatures T^* = 0.694 and 0.741 are investigated. The obtained number of particles in the critical nucleus agrees well with the simulation data.     

Density functional study of the pressure tensor for inhomogeneous Lennard—Jones fluids

Based on classical density functional theory,an expression of the pressure tensor for inhomogeneous fluids is presented.This takes into account greater correlation between particles,especially for systems that are geometrically confined or involve an interface.The density and pressure components of Lennard-Jones fluids confined in hard and softened nano-cavities are calculated.A comparison between the results of this work and IK expression suggests that the agreement depends on temperature.The interfacial tension for hard sphere fluids agrees well with the Monte Carlo result when the bulk density is not too large.The results of the solid-fluid interfacial tension for Lennard-Jones fluids demonstrate that different types of external potentials modulate the interfacial tension in different manners.     

Investigation of vapour--liquid nucleation properties for spherical and chain-like fluids by density functional theory

The excess Helmholtz free energy functional for nonpolar chain-like molecules is formulated in terms of a weighted density approximation （WDA） for short-range interactions and a Weaks Chandler Andersen （WCA） approximation and a Barker Henderson （BH） theory for long-range attraction. Within the framework of density functional theory （DFT）, vapour liquid interracial properties including density profile and surface tension, and vapour-liquid nucleation properties including density profile, work of formation and number of particles are investigated for spherical and chain- like molecules. The obtained vapour liquid surface tension and the number of particles in critical nucleus for Lennard- Jones （L J） fluids are consistent with the simulation results. The influences of supersaturation, temperature and chain length on vapour liquid nucleation properties are discussed.[第一段]     

First-principles investigation of the electronic, elastic and thermodynamic properties of VC under high pressure

An investigation of the electronic,elastic and thermodynamic properties of VC under high pressure has been conducted using first-principles calculations based on density functional theory (DFT) with the plane-wave basis set,as implemented in the CASTEP code. At elevated pressures,VC is predicted to undergo a structural transition from a relatively open NaCl-type structure to a more dense CsCl-type one. The predicted transition pressure is 520 GPa. The elastic constant,Debye temperature and heat capacity each as a function of pressure and/or temperature of VC are presented for the first time.     

Density Functional Approach Based on Numerically Obtained Bridge Functional

The ornstein-zenike equation is solved with the Rogers-Young approximation for bulk hard sphere fluid and Lennard-Jones fluid for several state points.Then the resulted bulk fluid radial distribution function combined with the test particle method is employed to determine numerically the function relationship of bridge functional as a function of indirect correlation function.It is found that all of the calculated points from different phase space state points for a same type of fluid collapse onto a same smooth curve.Then the numerically obtained curve is used to substitute the analytic expression of the bridge functional as a function of indirect correlation function required in the methodology [J.Chem.Phys,112(2000)8079] to determine the density distribution of non-uniform hard sphere fluid and Lennard-Jones fluid.The good agreement of theoretical predictions with the computer simulation data is obtained.The present numerical procedure incroporates the knowledge of bulk fluid radial distribution function into the constructing of the density functional approximation and makes the original methodology more accurate and more filexible for various interaction potential fluid.     

Augmented Kierlik--Rosinberg Fundamental Measure Functional and Extension of Fundamental Measure Functional to Inhomogeneous Non-hard Sphere Fluids

From point of view of weighted density procedure, it is guessed that a Percus-Yevick （PY） compressibility excess free energy density, appearing in the Kierlik Rosinberg type fundamental measure functional （KR-FMF） and expressed in terms of scaled particle variables, can be substituted by a corresponding expression dictated by a more accurate Mansoori Carnahan-Starling Leland （MCSL） equation of state, while retaining the original weighting functions; it is numerically indicated that the resultant undesirable non-self-consistency between the PY type weighting function and MCSL type excess free energy density had no bad effect on the performance of the resultant augmented KR-ffMF which, on the one hand, preserves the exact low-density limit of the original KR-FMF and holds a high degree of pressure self-consistency, on the other hand, improves significantly, as expected, the predictions of density profile of hard sphere fluid at single hard wall contact location and its vicinity, and of the bulk hard sphere second order direct correlation function （DCF）, obtained from functional differentiation. The FMF is made applicable to inhomogeneous non-hard sphere fluids by supplementing a functional perturbation expansion approximation truncated at the lowest order with summation of higher order terms beyond the lowest term calculated by the FMF for an effective hard sphere fluid; the resultant extended FMF only needs second order DCF and pressure of the fluid considered at coexistence state as inputs, consequently is applicable whether the considered temperature is above critical point or below critical point. The extended MCSL-augmented KR-FMF is found to be endowed with an excellent performance for predictions of density profile and surface tension by comparing the present predictions of these two quantities with available computer simulation data for inhomogeneous hard core attractive Yukawa fluid and Lennard-3ones fluid.     

Thermodynamic Properties of Hard-Sphere Fluid under Confined Condition Based on Bridge Density Function

Based on the functional integral procedure, a recently proposed bridge density function [J. Chem. Phys. 112 (2000) 8079] is developed to calculate global thermodynamic properties of non-uniform fluids. The resulting surface tension of a hard wall-hard sphere interface as a function of the bulk hard sphere fluid density is in good agreement with the available simulation data. The proposed numerical procedure from the approximation of non-uniform first-order direct correlation function to a non-uniform system with excess Helmholtz free energy is of fundamental importance for phase behaviour under the confined condition due to the fact that many available simple approximations in classical density functional theory are for non-uniform first-order direct correlation function.     

Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid

A systematic methodology is proposed to deal with the weighted density approximation version of classical density functional theory by employing the knowledge of radial distribution function of bulk fluid.The present methodology results from the concept of universality of the free energy density functional combined with the test particle method.It is shown that the new method is very accurate for the predictions of density distribution of a hard sphere fluid at different confining geometries.The physical foundation of the present methodology is also applied to the quantum density functional theory.     

Functional Counterpart of Lagrangian Theorem and Perturbative Density Functional Theory：a Forgotten Idea

In this Letter,we truncate the functional expansion of the non-uniform first-order direct correlation function (DCF) around the bulk density at the lowest order.But the truncation is performed formally and exactly by making use of functional counterpart of the Lagrangian theorem of differential calculus.Consequently the expansion coefficient,i.e.the uniform second-order DCF,is replaced by its non-uniform counterpart whose density argument is an appropriate mixture of calculated density distribution and the bulk density with a mixing parameter determined by a hard-wall sum rule.The non-uniform second-order DCF is then approximated by the uniform second-order DCF with an appropriate weighted density as its density argument.The present formally exact truncated functional expansion predicts the density distribution in good agreement with simulation data for hard sphere and Lennard-Jones fluid exerted by an external field.     

Thermoelasticity of CaO from first principles

The thermoelastic properties of CaO over a wide range of pressure and temperature are studied using density functional theory in the generalized gradient approximation. The transition pressure taken from the enthalpy calculations is 66.7GPa for CaO, which accords with the experimental result very well. The athermal elastic moduli of the two phases of CaO are calculated as a function of pressure up to 200GPa. The calculated results are in excellent agreement with existing experimental data at ambient pressure and compared favourably with other pseudopotential predictions over the pressure regime studied. It is also found that the degree of the anisotropy rapidly decreases with pressure increasing in the B1 phase, whereas it strongly increases as the pressure increases in the B2 phase. The thermodynamic properties of the B1 phase of CaO are predicted using the quasi-harmonic Debye model; the heat capacity and entropy are consistent with other previous results at zero pressure.     

Nuclear Level Density and Thermodynamic Functions for Nuclei with Static Deformation

The level densities of even-odd and even-even isotopes^161,162Dy,^166Er and ^171,172Yb were calculated using microscopic theory of interacting fermions and compared with experiments.It is found that the data can be well reproduced with level density formalism for nuclei with static deformation.The nuclear temperature as well as the reproduced with level density formalism for nuclei with static deformation.The nuclear temperature as well as the entropy of nuclear system as a function of excitation energy has been extracted from the BCS theory.It is shown that the entropy exhibits an S-formed shape as a function of excitation energy.This is interpreted as a phase transition.Procedure of treating the even-odd and even-even nuclear systems has been presented and discussed.     

A Self-Consistent Theory for the Inter-and Intramolecuiar Correlation Functions of a Hard-Sphere-Yukawa-Chain Fluids

An extended test-particle method is used to predict the inter- and intramolecular correlation functions of freely jointed hard-sphere-Yukawa-chain fluids by calculating the segmental density distributions around a fixed segment. The underlying density functional theory for chain fluids is based on a modified fundamental measure theory for the hard-sphere repulsive and a mean-field approximation for attraction between different segments. The calculated intra- and inter-molecular distribution functions agree well with the results from Monte Carlo simulations, better than those from alternative approaches.     

Estimation of Plasma Density by Surface Plasmons for Surface-Wave Plasmas

An estimation method of plasma density based on surface plasmons theory for surface-wave plasmas is proposed. The number of standing-wave is obtained directly from the discharge image, and the propagation constant is calculated with the trim size of the apparatus in this method, then plasma density can be determined with the value of 9.1 × 10^17m^-3. Plasma density is measured using a Langmuir probe, the value is 8.1 × 10^17m^-3 which is very close to the predicted value of surface plasmons theory. Numerical simulation is used to check the number of standing-wave by the finite-difference time-domain （FDTD） method also. All results are compatible both of theoretical analysis and experimental measurement.     

Modified Eyring viscosity equation and calculation of activation energy based on the liquid quasi-lattice model

Viscosity is an important physical parameter of fluid,and the Eyring viscosity equation is a popular viscosity theory.Based on the Eyring reaction rate equation and Boltzmann statistical theory,and including the probabilities of creating a hole in liquid and the transition to the neighboring hole,a modified Eyring viscosity equation was proposed.According to the structural characteristics of short-range order,liquid is treated as a quasi-lattice structure in a small region.The activation energy,which is the minimum energy needed for the molecule to jump to its neighboring hole because of the restriction of other molecules around it,was analytically calculated from an intermolecular Lennard-Jones potential function and a Stockmayer potential function.The viscosity values of 37 kinds of typical liquids at 25°C and the dependence of viscosity of three kinds of liquids on temperatures were calculated with this modified viscosity equation,and the calculated results agree with the experimental values to some extent.This work not only enriches the understanding of the mechanism of liquid viscosity,but also could provide some theoretical guides for the relevant studies and applications.     

Characterization of Phase Transition in Heisenberg Fluids from Density Functional Theory

The phase transition of Heisenberg fluid has been investigated with the density functional theory in mean-field approximation （MF）. The matrix of the second derivatives of the grand canonical potential Ω with respect to the particle density fluctuations and the magnetization fluctuations has been investigated and diagonalized. The smallest eigenvalue being 0 signalizes the phase instability and the related eigenvector characterizes this phase transition. We find a Curie line where the order parameter is pure magnetization and a spinodal where the order parameter is a mixture of particle density and magnetization. Along the spinodal, the character of phase instability changes continuously from predominant condensation to predominant ferromagnetic phase transition with the decrease of total density. The spinodal meets the Curie line at the critical endpoint with the reduced density p＊=pσ3=0.224 and the reduced temperature T＊ =kT/ε=1.87 （σ is the diameter of Heisenberg hard sphere and e is the coupling constant）.     

Effective Depletion Potential of Colloidal Spheres

A new semianalytical method, which is a combination of the density functional theory with Rosenfeld density functional and the Ornstein-Zernike equation, is proposed for the calculation of the effective depletion potentials between a pair of big spheres immersed in a small hard sphere fluid. The calculated results are almost identical to the integral equation method with the Percus-Yevick approximation, and are also in agreement well with the Monte Garlo simulation results.     

Strain-induced insulator–metal transition in ferroelectric BaTiO_3(001) surface:First-principles study

The electronic properties of TiO_2-terminated BaTiO_3(001) surface subjected to biaxial strain have been studied using first-principles calculations based on density functional theory. The Ti ions are always inward shifted either at compressive or tension strains, while the inward shift of the Ba ions occurs only for high compressive strain, implying an enhanced electric dipole moment in the case of high compressive strain. In particular, an insulator–metal transition is predicted at a compressive biaxial strain of 0.0475. These changes present a very interesting possibility for engineering the electronic properties of ferroelectric BaTiO_3(001) surface.     

First Principles Study of Adsorption and Reaction of CO on SrTiO3 （100） Surface： the Role of Surface Oxygen Vacancies

The adsorption and reaction of CO on SrTiO3 （100） surface with and without surface oxygen vacancy are investigated by the first-principles calculation based on the density functional theory. The calculated results reveal that the oxygen vacancy site prefers to the activation of the C-O bond. The adsorption energies increase to 1.0855 and 0.3245eV for defect-CO and defect-OC orientations, respectively. Particularly the C-O bond is elongated by about 0.1285 ？ in the defect-OC orientation compared with that in the Ti-OC one without surface oxygen vacancies. There is predominantly a chemisorption mechanism between the CO molecule and the surface in the defect-CO orientation.     

Inner Structure of Boiling Nucleus and Interfacial Energy Between Nucleus and Bulk Liquid

A model of two-region structure of a nucleus is proposed to describe nucleus evolution.The interracial tension between bulk liquid phase and nucleus is dependent on the density gradient in the transition region and varies with the structure change of the transition region.With the interracial tension calculated using this model,the predicted nucleation rate is very close to the experimental measurement.Furthermore,this model and associated analysis provide solid theoretical evidence to clarify the definition of nucleation rate and understand the nucleation phenomenon with insight into the physical nature.