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.     

A simulation study of the effects of adsorbent energy on the diffusion of molecules in slit pores: 1 commensurate slit widths

Equilibrium molecular dynamics simulation has been used to study the self-diffusion coefficients (from correlation of the molecular velocity) and the collective, or centre of mass diffusion coefficients (from correlation of the streaming velocity) of a Lennard-Jones fluid in model slit pores. The slit widths were chosen to be integer multiples of the Lennard-Jones adsorbate diameter, and therefore are close to being commensurate with layered adsorbate structures. Slits of reduced width H* = 3 and 5 were examined at a reduced temperature of T* = 1.0. The adsorbate densities ranged from 0.3 to 0.9 in reduced units. The adsorbent adsorbate interaction was modelled as a simple potential with inverse 4th power attraction plus hard wall repulsion, and systems with reduced parameter u₀* ranging from ?5 to +5 were studied. Molecule-wall scattering was represented by a diffuse reflection algorithm. The density distributions show strong layering in the attractive system, but this is absent in the most repulsive slits, except at very high densities. Self-diffusion is only weakly dependent on u₀* and slit width at high densities, but a strong dependence on u₀* appears at low densities. The collective diffusion coefficient is less easy to calculate with high accuracy; nevertheless, it is clear that there is a strong dependence of this property on u₀* Trajectory plots show zones in which the particles are more or less strongly localized, but undergo irregular oscillatory motion corresponding to regions of high density in the single-particle distributions.     

Thermal conductivity of fluids with steeply repulsive potentials

We consider the thermal conductivity of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, φ(r) = ε(σ/r)ⁿ. The time correlation function for the heat flux, C_λ(t), and the time average, C_λ(0) are calculated numerically by molecular dynamics simulations, and accurate expressions for these are also derived for the SRP fluid. We show, by molecular dynamics simulations, that close to the hard-sphere limit this time correlation function has the same analytic form as for the shear and pressure correlation functions for the shear and bulk viscosity, i.e. C_λ(t)/C_λ(0) = 1 ?T* (nt*)² + 0((nt*)⁴), where T* = k _B T/ε, is the reduced temperature, k _B is Boltzmann's constant and t* = (ε/σ²)^1/2 t is the reduced time. The thermal conductivity for the limiting case of hard spheres is numerically very close to that given by the traditional Enskog relation. At low densities the normalized relaxation times are typically largest for the thermal conductivity, followed by shear and then bulk viscosity. Close to the maximum fluid density, the latter two increase rapidly with density (especially for the shear) but continue a monotonic decline for the thermal conductivity. This reflects the relative insensitivity of the thermal conductivity to the approach to the fluid-solid phase boundary.     

Temperature Distributions Across the Plasma Layer of Planar Low Pressure Microwave Plasmas — A Comparative Investigation by Optical Emission Spectroscopy

Nowadays low temperature non-equilibrium plasmas received considerable attention in very different fields of plasma processing. The subject of the present paper is the comparative measurement of neutral gas temperature and optical excitation temperature to analyze the temperature distributions across the plasma layer of H₂ non-equilibrium plasmas (p = 0.2 – 1.5 kPa) with small admixtures of hydrocarbons in a novel planar microwave plasma source (2.45 GHz) used for plasmachemical deposition purposes by means of optical emission spectroscopy. Typical microwave power flux densities into the plasma lie within a range of 2 W cm^?2 to 20 W cm^?2. Results of neutral gas temperature measurements derived from H_α line Doppler profiles are compared with rotational temperatures of H₂ and N₂ molecules. The neutral gas temperature (800–1700 K) corresponds to the rotational temperature of the H₂ molecules (Fulcher band, R 0–0 branch) but shows a more distinct spatial gradient. The rotational temperature of admixtured N₂ molecules (2000–3000 K) is much more higher although Boltzmann distribution was ensured. The spatially resolved measured excitation temperature (1–3 eV) determined with the help of line intensity ratios of admixtured Ar well agrees with Langmuir probe measurements. The reported measurements as a whole demonstrate the feasibility of comparative investigations of different optically determined temperatures for expressive characterization of low pressure microwave plasmas.     

空气放电非平衡等离子体的模拟计算

 基于空气放电非平衡等离子体动力学,对空气放电进行了数值计算,分析了放电后等离子体中的主要粒子（N₂(v6),N₂(A3),O₂(a1),O和O₃）数密度随起始温度、电子数密度和约化场强的变化趋势。计算结果表明,随着初始温度的升高,空气放电产生的粒子数密度增加。温度为300 K时,放电产生的O原子数密度最大值约为4.90×⁷ cm^-3,而当温度升高到400 K和500 K时,O原子数密度的最大值则相应地增加到5.2×10¹⁰ cm^-3和5.51×10¹⁰ cm^-3。约化场强的影响与温度类似,其中氮气的振动激发态N₂(v6)数密度随约化场强的变化幅度不明显。电子数密度增加,粒子数密度大幅增加,氮分子的激发态N₂(A3)粒子数密度与电子数密度保持严格的线性关系。     

Transport coefficients of hard sphere fluids

New calculations have been made of the self-diffusion coefficient D, the shear viscosity η_s, the bulk viscosity η_b and thermal conductivity λ of the hard sphere fluid, using molecular dynamics (MD) computer simulation. A newly developed hard sphere MD scheme was used to model the hard sphere fluid over a wide range up to the glass transition (～0.57 packing fraction). System sizes of up to 32 000 hard spheres were considered. This set of transport coefficient data was combined with others taken from the literature to test a number of previously proposed analytical formulae for these quantities together with some new ones given here. Only the self-diffusion coefficient showed any substantial N dependence for N < 500 at equilibrium fluid densities (ε 0.494). D increased with N, especially at intermediate densities in the range ε ～ 0.3–0.35. The expression for the packing fraction dependence of D proposed by Speedy, R. J., 1987, Molec. Phys., 62, 509 was shown to fit these data well for N ～ 500 particle systems. We found that the packing fraction ε dependence of the two viscosities and thermal conductivity, generically denoted by X, were represented well by the simple formula X/X ₀ = 1/[1 ? (ε/ε₁)]^m within the equilibrium fluid range 0 > ε > 0.493. This formula has two disposable parameters, ε and m, and X ₀ is the value of the property X in the limit of zero density. This expression has the same form as the Krieger-Dougherty formula (Kreiger, I. M., 1972, Adv. Colloid. Interface Sci., 3, 111) which is used widely in the colloid literature to represent the packing fraction dependence of the Newtonian shear viscosity of monodisperse colloidal near-hard spheres. Of course, in the present case, X _o was the dilute gas transport coefficient of the pure liquid rather than the solvent viscosity. It was not possible to fit the transport coefficient normalized by their Enskog values with such a simple expression because these ratios are typically of order unity until quite high packing fractions and then diverge rapidly at higher values over a relatively narrow density range. At the maximum equilibrium fluid packing fraction ε = 0.494 for both the hard sphere fluid and the corresponding colloidal case a very similar value was found for η_s/η_o ?30–40, suggesting that the ‘crowding’ effects and their consequences for the dynamics in this region of the phase diagram in the two types of liquid have much in common. For the hard sphere by MD, D_o/D ～ 11 at the same packing fraction, possibly indicating the contribution from ‘hydrodynamic enhancement’ of this transport coefficient, which is largely absent for the shear viscosity. Interestingly the comparable ratio for hard sphere colloids is the same.     

Structure,thermodynamic and transport properties of imidazolium-based bis(trifluoromethylsulfonyl)imide ionic liquids from molecular dynamics simulations

Molecular dynamics (MD) simulations have been performed in order to investigate the properties of [C _n mim⁺][Tf₂N^?] (n?=?4,?8,?12) ionic liquids (ILs) in a wide temperature range (298.15?498.15?K) and at atmospheric pressure (1 bar). A previously developed methodology for the calculation of the charge distribution that incorporates ab initio quantum mechanical calculations based on density functional theory (DFT) was used to calculate the partial charges for the classical molecular simulations. The wide range of time scales that characterize the segmental dynamics of these ILs, especially at low temperatures, required very long MD simulations, on the order of several tens of nanoseconds, to calculate the thermodynamic (density, thermal expansion, isothermal compressibility), structural (radial distribution functions between the centers of mass of ions and between individual sites, radial-angular distribution functions) and dynamic (relaxation times of the reorientation of the bonds and the torsion angles, self-diffusion coefficients, shear viscosity) properties. The influence of the temperature and the cation's alkyl chain length on the above-mentioned properties was thoroughly investigated. The calculated thermodynamic (primary and derivative) and structural properties are in good agreement with the experimental data, while the extremely sluggish dynamics of the ILs under study renders the calculation of their transport properties a very complicated and challenging task, especially at low temperatures.     

Generic van der Waals equation of state for polymers, modified free volume theory, and the self-diffusion coefficient of polymeric liquids

In this paper, a molecular theory of self-diffusion coefficient is developed for polymeric liquids (melts) on the basis of the integral equation theory for site-site pair correlation functions, the generic van der Waals equation of state, and the modified free volume theory of diffusion. The integral equations supply the pair correlation functions necessary for the generic van der Waals equation of state, which in turn makes it possible to calculate the self-diffusion coefficient on the basis of the modified free volume theory of diffusion. A random distribution is assumed for minimum free volumes for monomers along the chain in the melt. More specifically, a stretched exponential is taken for the distribution function. If the exponents of the distribution function for minimum free volumes for monomers are chosen suitably for linear polymer melts of N monomers, the N dependence of the self-diffusion coefficient is N⁻¹ for the small values of N, an exponent predicted by the Rouse theory, whereas in the range of 2.3?lnN?4.5 the N dependence smoothly crosses over to N⁻², which is reminiscent of the exponent by the reptation theory. However, for lnN?4.5 the N dependence of the self-diffusion coefficient differs from N⁻², but gives an N dependence, N^−2−δ(0<δ<1), consistent with experiment on polymer melts in the range. For polyethylene δ≈0.48 for the parameters chosen for the stretched exponential. Because the stretched exponential function contains undetermined parameters, the N dependence of diffusion becomes semiempirical, but once the parameters are chosen such that the N dependence of D can be successfully given for a polymer melt, the temperature dependence of the self-diffusion coefficient can be well predicted in comparison with experiment. The theory is satisfactorily tested against experimental and simulation data on the temperature dependence of D for polyethylene and polystyrene melts.     

Phonon relaxation and heat conduction in one-dimensional Fermiben Pastaben Ulam β lattices by molecular dynamics simulations

The phonon relaxation and heat conduction in one-dimensional Fermi-Pasta-Ulam (FPU) β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence of the FPU β lattice, is first calculated from the energy autocorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. We find that the relaxation rate as a function of wave number k is proportional to k^1.688, which leads to a N^0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415. Our results confirm the N^2/5 divergence in one-dimensional FPU β lattices. The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices. We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions. It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.     

The self-diffusion coefficient in the gas phase at moderate densities,obtained by computer simulations

The self-diffusion coefficient for Lennard-Jones molecules has been determined by molecular dynamics for densities up to the critical one and for temperatures ranging from T = 1.3∈/k to T = 5.56∈/k. At low density, the results are in a good agreement with the theoretical predictions; at elevated densities agreement with the available experimental results is found, although the scarcity of experimental data prevents a general comparison between real systems and the molecular dynamical calculations.Additional computations with different pair-potentials lead to results which throw some doubts on the reliability of the so-called Modified Enskog Theory.     

Investigation of the mass dependence of self-diffusion coefficients by molecular dynamics calculations: binary and ternary isotopic mixtures of atoms

Extensive molecular dynamics calculations have been used to study for the first time systematically the dependence of the self-diffusion coefficients D_i (i = 1, 2, 3) in binary and ternary atomic isotopic mixtures on the particle mass ratios m*₂ = m ₂/m ₁ and m*₃ = m ₃/m ₁ at different reduced temperatures T* and reduced particle number densities n*, using a Lennard-Jones 12-6 potential and a hard-soft-spheres potential. In addition, the dependence of D_i values of binary mixtures on the mole fraction x ₁ = 1—x ₂ was also investigated for some thermodynamic states. The calculated values of D_i can be represented quantitatively by exponential estimates of the form D_i = D* _i (m*₂)^ex _i in the case of binary mixtures and D_i = D ⁰ _i (m*₂)^{ex _i} (m ₃)^{ext _i} in the case of ternary mixtures. D ⁰ _i are the self-diffusion coefficients in reference mixtures of mass ratios m*₂ = m*₃ = 1. The dependence of the exponents ex _i (m*₂, T*, n*, x ₁) of binary mixtures on m*₂, T*, n*, and x ₁ and the dependence of the exponents ext _i (m*₂, m*₃, n*) of equimolar ternary mixtures at T* = 1.8 on the exponents ex _i of the constituent binary mixtures and on m*₂, m*₃, and n* are discussed.     

应用链式硬球模型计算流体的自扩散系数

将链式硬球模型流体方程用于计算实际高密度流体的自扩散系数,并与流体的试验数据或模拟数据相比较。使用该方程计算碳链长度在150以下压力在200MPa以下;平均温度在100K以上时,非极性自扩散系数的平均绝对偏差多为5％左右。     

Development of a united-atom force field for 1-ethyl-3-methylimidazolium tetracyanoborate ionic liquid

Three united-atom (UA) force fields are presented for the ionic liquid 1-ethyl-3-methylimidazolium tetracyanoborate, abbreviated as [EMIM]⁺[B(CN)₄]^?. The atomistic charges were calculated based on the restrained electrostatic potential (RESP) of the isolated ions (abbreviated as force field 1, FF-1) and the ensemble averaged RESP (EA-RESP) method from the most stable ion pair configurations obtained by MP2/6-31G*+ calculations (abbreviated as FF-2 and FF-3). Non-electrostatic parameters for both ions were taken from the literature and Lennard–Jones parameters for the [B(CN)₄]^? anion were fitted in two different ways to reproduce the experimental liquid density. Molecular dynamics (MD) simulations were performed over a wide temperature range to identify the effect of the electrostatic and non-electrostatic potential on the liquid density and on transport properties such as self-diffusion coefficient and viscosity. Predicted liquid densities for the three parameter sets deviate less than 0.5% from experimental data. The molecular mobility with FF-2 and FF-3 using reduced charge sets is appreciably faster than that obtained with FF-1. FF-3 presents a refined non-electrostatic potential that leads to a notable improvement in both transport properties when compared to experimental data.     

Experimental verification of a zero-dimensional model of the kinetics of XeCl* discharges by XeCl*(B)-, XeCl*(C)-, and Xe2Cl*-density measurements

Absolutely calibrated emission spectroscopy has been used to determine the particle number densities of XeCl^*(B), XeCl^*(C), and Xe₂Cl^* in a small scale Ne/Xe/HCl discharge with well-defined current and voltage pulses for a wide range of parameters. The measured particle number densities could be reproduced quite well by numerical model calculations using the rate-coefficient values of Quiñones et al. [1] for the quenching of XeCl^*(B,C) by Ne, Xe, and 2Xe, but 3.0 × 10^–31 cm⁶/s for the formation of Xe₂Cl^* by (Ne + Xe)-quenching. For the electron quenching, we recommend a rate coefficient value of 3.2 × 10^–8 cm³/s. From the equilibrium ratio of the particle number densities of XeCl^*(C) and XeCl^*(B), the energy separation between these states has been estimated to be 72 ± 33 cm^–1 with the B state placed above the C state.     

Investigation of the mass dependence of self-diffusion coefficients by molecular dynamics calculations: comparison with the Enskog theory

The dependence of the Enskog self-diffusion coefficients D_i,E on mass ratios m_i* = m_i/m₁ in hard sphere mixtures is described by exponential expressions of the form D_i,E = D⁰ _i,E(m*₂)eX_i,E in the case of binary mixtures and D_i,E = D⁰ _iE (m*₂)eX_i,E(m*₃)eXt_i,E in the case of ternary mixtures. D⁰ _i,E are the self-diffusion coefficients in reference mixtures with m*₂ = m*₃ = 1. ex_i,E (i = 1,2) and ext_i,E (i = 1,2,3) are the so called Enskog exponents of binary and ternary mixtures, respectively. Their dependence on particle mass and diameter, mole fraction, density and temperature is discussed and compared with corresponding results of molecular dynamics calculations.     

Short-range order structure and free volume distribution in liquid bismuth: X-ray diffraction and computer simulations studies

ABSTRACT

The structure of liquid bismuth was studied by X-ray diffraction and computer simulation methods. The contraction of the atomic structure within the first coordination sphere in the temperature interval of 575-1225?K is reported. The temperature dependencies of the coordination numbers and of the free volume are analysed. On the basis of the temperature dependencies of the free volume, the temperature dependencies of viscosity and the self-diffusion coefficient were calculated to be in the ranges from 1.17 to 0.86?mPa?s and from 2.18 × 10^?9 to 5.44 × 10^?9?m²/s, respectively. The free volume – extracted results are in fair agreement with the experimental data and with the results obtained in the molecular dynamics simulations.     

Electronic structure of silicon nitride according to ab initio quantum-chemical calculations and experimental data

Charge transfer ΔQ = 0.35e at the Si-N bond in silicon nitride is determined experimentally using photoelectron spectroscopy, and the ionic formula of silicon nitride Si₃^+1.4N₄^−1.05 is derived. The electronic structure of α-Si₃N₄ is studied ab initio using the density functional method. The results of calculations (partial density of states) are compared with experimental data on X-ray emission spectroscopy of amorphous Si₃N₄. The electronic structure of the valence band of amorphous Si₃N₄ is studied using synchrotron radiation at different excitation energies. The electron and hole effective masses m _e ^* ≈ m _h ^* ≈ 0.5m _e are estimated theoretically. The calculated values correspond to experimental results on injection of electrons and holes into silicon nitride.     

Density studies across the smectic G-nematic and nematic-lsotropic transitions

The densities of N(p-n-pentyloxy benzylidene) p-ethylaniline and N(p-n-hexyloxy benzylidene) p-ethylaniline are measured as a function of temperature from the isotropic liquid to the smectic G phase. Both the compounds exhibit enantiotropic smectic G and nematic liquid crystalline phases. The changes in density across the phase transformations and the thermal expansion coefficient confirm the order of the transitions as of first order. The particular importance of the smectic G to nematic transformation is apparent from the density jump across the transition. An estimate of the pressure dependence of the isotropic-nematic transition temperature is found to be in reasonable accord with the literature data.     

Measurement of D* mesons in jets from p + p collisions at ?s \sqrt s = 200 GeV

We report the measurement of charged D* mesons in jets produced in proton-proton collisions at a center of mass energy $ \sqrt s $ \sqrt s = 200 GeV with the STAR experiment at RHIC. The production rate is found to be N(D*⁺ + D*⁻)/N (jet) = 0.015 ± 0.008 (stat) ± 0.007 (sys) for D* mesons with fractional momenta 0.2 < z < 0.5 in jets with 11.5 GeV mean transverse energy. This rate is consistent with perturbative QCD evalulation of gluon splitting into a pair of charm quarks and subsequent hadronization.     

The reaction πN → ππN in a meson-exchange approach

A resonance model for two-pion production in the pion-nucleon reaction is developed that includes information obtained in the analysis of pion-nucleon scattering in a meson-exchange model. The baryonic resonances Δ(1232), N^*(1440), N^*(1520), N^*(1535), and N^*(1650) are included. The model reproduces the total cross-sections up to kinetic energies of the incident pion of 400MeV and obtains the shapes of the differential cross-sections in reasonable agreement with the data.