Momentum transfer analysis in Lennard-Jones fluids

The transfer of momentum of a test particle to its neighbours is investigated in Lennard-Jones fluids by computer experiments at different densities.     

Critical properties of homopolymer fluids studied by a Lennard-Jones statistical associating fluid theory

A Lennard-Jones statistical associating fluid theory, the soft-SAFT equation of state, is used to study the dependence of the critical properties on chain length for pure polymers. The critical constants of chains up to 10⁶ monomer units are predicted. The main advantage of these calculations, versus others found in the literature, is the fact that the equation is able to accurately predict experimental data available only for short chain lengths and, at the same time, it is able to predict the critical properties in the infinite chain length scaling regime, without any further assumptions. The equation gives quantitative agreement with experimental and Monte Carlo simulation data for normal alkanes. For very long chains, the equation predicts mean-field scaling behaviour, as expected. Moreover, taking advantage of the linearity of the molecular volumes and dispersive energies with the chain molecular weight, a value of 1/5 is found for the critical compressibility factor of an infinitely long n-alkane chain. It is demonstrated that this is not contradictory to Wertheim's theory.     

The optical properties of liquid metals

Measurements of the dielectric constant, ε₁ + iε₂, have been made on liquid mercury, cadmium, lead and bismuth by a polarimetric method for a range of wavelengths in the visible region. Special attention has been paid to the problem of surface conditions and the final results are believed to be truly representative of the bulk properties of the liquids. The values for the absorption, ωε₂, are found to be consistently higher than those calculated from the free electron Drude theory. This is equivalent to the results of previous workers that a best fit to the Drude equations requires an effective number of electrons slightly greater than the number of valence electrons. Sum rule arguments show that this is to be expected when coupling with the core states is properly taken into account.

Measurements on mercury-bismuth alloys are also reported.     

Chemical potentials and phase equilibria of Lennard-Jones chain fluids

Computer simulations (molecular dynamics) were performed for ensembles of flexible tangent Lennard-Jones chains consisting of n sites (n = 1, 2, 4, 8, and 16). From these simulations, the orthobaric liquid and vapour densities were calculated not only with the traditional method of simulating a liquid film in coexistence with vapour, but also using the rigorous thermodynamic condition of satisfying the chemical potential equality between the phases in equilibrium. The agreement with literature data, as far as such exist, is excellent.     

Structural properties of low-density liquid alkali metals

The static structure factors of liquid alkali metals have been modelled at temperatures close to their melting points and a few higher temperatures using the reverse Monte Carlo (RMC) method. The positions of 5000 atoms in a box, with full periodicity, were altered until the experimental diffraction data of the structure factor agrees with the associated model structure factor within the errors. The model generated is then analysed. The position of the first peak of the pair distribution function g(r) does not show any significant temperature dependence and the mean bond lengths can be approximated within an interval of 3.6–5.3 Å, 4.5–6.6 Å, 4.8–6.7 Å and 5.1–7.3 Å for Na, K, Rb and Cs respectively. The cosine bond distributions show similar trend with the flattening up of the first peak with increase in temperature. In addition, the coordination numbers of these liquid metals are high due to the presence of non-covalent bonding between them. On the average, we surmise that the coordination number decreases with increase in temperature     

A self-consistent approach for modelling the interfacial properties and phase diagrams of Yukawa,Lennard-Jones and square-well fluids

A self-consistent density-functional approach is presented for describing the phase behaviour and interfacial tensions of van der Waals fluids represented by the hard-core Yukawa (HCY), Lennard-Jones (LJ) and square-well (SW) potentials. The excess Helmholtz energy functional is formulated in terms of a modified fundamental measure theory (MFMT) for the short-ranged repulsion and a density-gradient expansion for the van der Waals attractions. Analytical expressions for the direct correlation functions of uniform fluids are utilized to take into account the effect of van der Waals’ attraction on intermolecular correlations. For bulk phases, the density functional theory is reduced to an equation of state (EOS) that provides accurate saturation pressures and vapour–liquid phase diagrams. Near the critical region, the long-range fluctuations can be corrected by using the renormalization group (RG) theory. With the same set of molecular parameters, the theory also yields satisfactory surface tensions and interfacial density profiles at all relevant temperatures.     

Direct and indirect correlations in low density supercritical Lennard-Jones fluids

We have carried out a detailed comparison of the direct and indirect correlation functions obtained from canonical molecular dynamics (NVT-MD) simulation of supercritical Lennard-Jones fluids to the results obtained by solving the Ornstein-Zernike equation with the approximate Duh-Henderson (DH) closure. The variations of equilibrium correlations are studied as functions of density at two supercritical isotherms near and away from the critical point. The direct and indirect correlations predicted using the DH closure provides a very good agreement with our simulation results at low densities. However, a marked deviation is observed at higher densities. These results are correlated to the discrepancies between the density and temperature dependence of the underlying bridge function. The implication of these results on the calculation of chemical potential and the Krichevskii parameter is also presented.     

The electron transport properties of pure liquid metals

Progress in the theory of the electrical conductivity and other ordinary transport properties of liquid metals since 1961 is reviewed. After a brief account of the basic nearly-free-electron diffraction formula, the quantitative comparison of this formula with experiment is discussed.

For the alkali metals, the agreement is adequate, given the uncertainty of the pseudopotentials, although there is controversy about the calculation of the temperature coefficient of ρ _L. To explain the observed volume dependence of ρ _L, and the thermoelectric power, it also seems necessary to allow for the variation of the pseudopotential with the positions of the Fermi level and the core levels relative to the bottom of the conduction band.

Quantitative results for the noble and polyvalent metals are meagre, and although calculations of ρ _L for Al and Zn are in excellent agreement with experiment there may be other cases where the basic formula is not adequate. The general question of the structure and convergence of the perturbation series for ρ _L is discussed, and it is suggested that corrections for higher order terms can be minimized by making the pseudopotential as near as possible to the t-matrix of an ion.

The anomalous properties of Hg are then discussed, in the light of the work of Mott (1966). In this connection it is shown that Edwards' formula (1962) for ρ _L, in which the Fermi velocity, v _F, is taken to be that of a free electron, ?k _F/m, despite deviations from the free-electron curve for ?(k), can be derived by using the expectation value of the current operator in place of e v _F in the Boltzmann equation. This modification of the elementary theory allows the Hall constant of a liquid metal to deviate from 1/nec, as found experimentally.     

Pair and singlet diffusion in a Lennard-Jones liquid

Inspired by the experimental work of Richter et al. [1], we have investigated the dynamic behaviour of pairs of particles of a Lennard-Jones liquid for four different thermodynamic states. The short and long time behaviour of dynamic correlation functions of pairs are studied and directly compared with that of single particle correlation functions. Only those relating to singlet and pair diffusion are treated.

A list of the correlation functions considered in this work is presented in the table of the Appendix.

The main results are the following:

• (i)the mean square displacement of pairs of particles departs only slightly from that of single particles (doubled);

• (ii)for long times, the mean square displacement of pairs is significantly reduced when pairs from only the first coordination shell are considered;

• (iii)in the short time region the mean square displacment of pairs resembles that of single atoms, however that of pairs being initially closer than the mean separation of particles in the liquid exhibits a small tendency to lie above the doubled one of single particles.

Our results, obtained by extensive molecular dynamics (MD) calculations, are in quantitative disagreement with results generated by other authors [3, 4], and the findings of Posch et al. [6] could not be confirmed in detail by our work.     

超临界Lennard-Jones流体结构特性分子动力学研究

研究超临界流体在不同压力和温度的结构特征有助于深刻理解并有效利用超临界流体.本文采用分子动力学方法模拟超临界压力、拟临界温度附近流体的结构及密度波动曲线的排列熵,分析状态参数变化的影响.结果表明,定压下,径向分布函数随温度升高,第一峰值位置逐渐向右移动,但右移幅度随着压力偏离临界点距离的增大而减弱,近临界压力时,出现峰值最高点的工况和等温压缩系数的极值点位置一致,压力增大,该现象消失.低压力拟临界点时易出现面积大、相对集中且分布稳定的高/低密度区,无明显嵌套现象.静态结构因子存在一定发散行为,发散的最大值和等温压缩系数极值点所处工况符合.低压力时密度时间序列的波动幅度最大,类周期现象较明显.在分子间势能、等温压缩系数和热运动效应的共同作用下,当压力(P)为1.1倍的临界压力(Pc)时,排列熵在0.99倍的拟临界温度(Tpc)达到最小值,P = 1.3Pc和1.5Pc时,最小排列熵与等温压缩系数的最大值工况点保持一致,压力继续增大,各模拟工况密度和排列熵的波动减弱,流体均匀性增强.     

Lennard-Jones binary fluids: A comparative study between the molecular dynamics and Monte Carlo descriptions of their structural properties

Molecular dynamics and Monte Carlo techniques are employed for the study of binary Lennard-Jones fluids. Systematic comparisons between the predictions of both techniques are discussed, with particular emphasis on the dependency of the structural properties with respect to temperature and Lennard-Jones potential parameters.     

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.     

Analytic properties of the Ishida-Yonezawa approximation for liquid and amorphous metals

We generally examine the analytic properties of the Ishida-Yonezawa approximation for the tight binding single s-band model. A sufficient condition is derived on which a solution satisfies the physical conditions; (1) sum rule, (2) reality, (3) definiteness, (4) analyticity, (5) boundary condition and (6) uniqueness.     

Relations between lattice dynamics of simple metals and liquid state properties

The actual interaction between ions in a metal is divided into the direct interaction of the ion cores and the ion-electron-ion interaction. The ion-electron-ion interaction is treated according to the Hartree-Fock approximation modified by a screened exchange potential. Since until now the bare ion potential is not known very accurately, the observed phonon frequencies were used to determine a model pseudopotential with the least squares method. Using this model pseudopotential the electronic band structure, the density of states as well as the electrical resistivity of molten Na, K, Al and Pb were calculated.     

Theory of the liquid-vapour interface of a binary mixture of Lennard-Jones fluids

We present results of calculations of the equilibrium surface tension and density profiles for the liquid-vapour interface of a binary mixture of Lennard-Jones 12-6 fluids. The calculations are based on a density-functional theory for the Helmholtz free energy of the inhomogeneous mixture. This is a ‘microscopic’ generalization of the van der Waals-Cahn-Hilliard theory for the interface of a binary mixture.

Our calculations cover the full range of liquid-vapour coexistence and the whole range of concentration. We find a correlation between the excess surface tension of the mixture and the surface segregation (adsorption) of the species with the lower surface tension. The ways in which segregation and excess surface tension depend on the Lennard-Jones parameters of the pure components are briefly discussed. Our results for the excess surface tension of mixtures of Ar and N₂ and Ar and CH₄ are compared with experiment; the agreement is reasonable.     

The dispersion relation of the dynamic structure factor of one-dimensional Lennard-Jones fluids

A molecular dynamics computer simulation of a one-dimensional repulsive Lennard-Jones system shows that “gaps” exist in the dispersion relation of the dynamic structure factor.     

Influence of dispersive long-range interactions on properties of vapour–liquid equilibria and interfaces of binary Lennard-Jones mixtures

The influence of dispersive long-range interactions on properties of vapour–liquid equilibria and interfaces of six binary Lennard-Jones (LJ) mixtures was studied by molecular dynamics (MD) simulations and density gradient theory (DGT). The mixtures were investigated at a constant temperature T, at which the low-boiling component, which is the same in all mixtures, is subcritical. Two different high-boiling components were considered: one is subcritical, the other is supercritical at T. Furthermore, the unlike dispersive interaction was varied such that mixtures with three different types of phase behaviour were obtained: ideal, low-boiling azeotrope, and high-boiling azeotrope. In a first series of simulations, the full LJ potential was used to describe these mixtures. To assess the influence of the long-range interactions, these results were compared with simulations carried out with the LJ truncated and shifted (LJTS) potential applying the corresponding states principle. The dispersive long-range interactions have a significant influence on the surface tension and the interfacial thickness of the studied mixtures, whereas the relative adsorption and the enrichment are hardly affected. Furthermore, the influence of the long-range interactions on Henry's law constants and the phase envelopes of the vapour–liquid equilibrium was investigated. The long-range interactions have practically no influence on the composition dependency of the investigated mixture properties.