我们使用分子动力学模拟结果的粘性二元Lennard-Jones混合物检查势能和维里之间的相关性。根据最近的一项提议[U。R.佩德森等等，Phys. Rev. Lett. 100，015701（2008）]，发现两个量的波动是强相关的，表现出比例常数γ，在数值上等于分子间势函数的逆幂律近似的斜率的三分之一。相关性在更高的密度下更强，其中原子间的分离在逆幂律近似更准确的范围内。这些相同的液体符合其动力学的热力学标度，标度指数等于Gamma。因此，能量和压力之间的强相关性和热力学标度的属性都反映了一个潜在的逆幂律表示捕捉有趣的功能，致密，高粘度液体的动力学的能力。
英文摘要：
We use molecular dynamics simulation results on viscous binary Lennard-Jones mixtures to examine the correlation between the potential energy and the virial. In accord with a recent proposal [U. R. Pedersen et. al. Phys. Rev. Lett. 100, 015701 (2008)], the fluctuations in the two quantities are found to be strongly correlated, exhibiting a proportionality constant, Gamma, numerically equal to one-third the slope of an inverse power law approximation to the intermolecular potential function. The correlation is stronger at higher densities, where interatomic separations are in the range where the inverse power law approximation is more accurate. These same liquids conform to thermodynamic scaling of their dynamics, with the scaling exponent equal to Gamma. Thus, the properties of strong correlation between energy and pressure and thermodynamic scaling both reflect the ability of an inverse power law representation of the potential to capture interesting features of the dynamics of dense, highly viscous liquids.
Liquids displaying strong virial-potential energy correlations conform to an approximate density scaling of their structural and dynamical observables. This scaling property does not extend to the entire phase diagram, in general. The validity of the scaling can be quantified by a correlation coefficient. In this work a simple scheme to predict the correlation coefficient and the density-scaling exponent is presented. Although this scheme is exact only in the dilute gas regime or in high dimension d, a comparison with results from molecular dynamics simulations in d = 1 to 4 shows that it repr…
It is demonstrated that the crossover between gas- and liquid-like regions on the phase diagram of the Lennard-Jones system occurs at a fixed value of the density divided by its value at the freezing point, $ρ/ρ_{\rm fr}\simeq 0.35$. This definition is consistent with other definitions proposed recently. As a result a very simple practical expression for the gas-to-liquid crossover line emerges.
How universal is the Lindemann criteria in melting of Lennard-Jones polydisperse solids?
通常认为，当结晶固体颗粒的均方位移（MSD）超过阈值时发生熔融。这被称为林德曼标准，由林德曼于1910年首次提出。然而，Chakravarty等人证明了这种常识是不充分的，因为当压力也允许沿着相图的共存线变化时，熔融时的MSD可能是温度依赖性的[Chakravarty C，Debenedetti PG和Stillinger F H 2007 J.Chem.Phys.126 204508]。本文通过对二维和三维多分散Lennard-Jones固体的广泛的分子动力学模拟表明，在熔融时，粒度分布的小极限和大极限上的颗粒表现出显著不同的林德曼比。尽管MSD中存在所有分散体，但发现在尺寸分散度为5-10%时，熔融在两个维度上都是一级的。
Longitudinal and transverse sound velocities of Lennard-Jones systems are calculated at the liquid-solid coexistence using the additivity principle. The results are shown to agree well with the ``exact'' values obtained from their relations to excess energy and pressure. Some consequences, in particular, in the context of the Lindemann's melting rule and Stokes-Einstein relation between the self-diffusion and viscosity coefficients are discussed. Comparison with available experimental data on the sound velocities of solid argon at melting conditions is provided.
讨论了一维链平衡态中断裂和团簇的定义。解析表达式获得预期的集群长度，$\langle K \rangle$，作为温度和压力的函数，在一个一维的Lennard-Jones链。这些表达式进行了比较，从分子动力学模拟的结果。发现$\langle K \rangle$随$β= 1/k_BT$和压力呈指数增加，$P$与文献中以前的结果一致。说明了一种使用$\langle K \rangle (β, P)$生成Lennard-Jones链的“相图”的方法。讨论了Lennard-Jones链中热输运研究的一些意义。
Solvent-mediated interactions emerge from complex mechanisms that depend on the solute structure, its wetting properties and the nature of the liquid. While numerous studies have focused on the two first influences, here, we compare results from water and Lennard-Jones liquid in order to reveal to what extent solvent-mediated interactions are universal with respect to the nature of the liquid. Besides the influence of the liquid, results were obtained with classical density functional theory and brute-force molecular dynamics simulations which allows us to contrast these two numerical techniqu…
In a recent paper [S. Khrapak, Molecules {\bf 25}, 3498 (2000)] the longitudinal and transverse sound velocities of conventional Lennard-Jones systems at the liquid-solid coexistence were calculated. It was shown that the sound velocities remain almost invariant along the liquid-solid coexistence boundary lines and that their magnitudes are comparable with those of repulsive soft sphere and hard sphere models at the fluid-solid phase transition. This implies that attraction does not affect the magnitude of sound velocities at the fluid-solid phase transition. This paper provides further eviden…
It is demonstrated that properly reduced transport coefficients (self-diffusion, shear viscosity, and thermal conductivity) of Lennard-Jones fluids along isotherms exhibit quasi-universal scaling on the density divided by its value at the freezing point. Moreover, this scaling is closely related to the density scaling of transport coefficients of hard-sphere fluids. The Stokes-Einstein relation without the hydrodynamic diameter is valid in the dense fluid regime. The lower density boundary of its validity can serve as a practical demarcation line between gas-like and liquid-like regimes.
This paper studies physical aging by computer simulations of a 2:1 Kob-Andersen binary Lennard-Jones mixture, a system that is less prone to crystallization than the standard 4:1 composition. Starting from thermal-equilibrium states, the time evolution of the following four quantities is monitored following up and down jumps in temperature: the potential energy, the virial, the average squared force, and the Laplacian of the potential energy. Despite the fact that significantly larger temperature jumps are studied here than in previous experiments, to a good approximation all four quantities c…
Unlike crystalline solids or ideal gases, transport properties remain difficult to describe from a microscopic point of view in liquids, whose dynamics result from complex energetic and entropic contributions at the atomic scale. Two scenarios are generally proposed: one represents the dynamics in a fluid as a series of energy barrier crossings, leading to Arrhenius-like laws, while the other assumes that atoms rearrange themselves by collisions, as exemplified by the free volume model. To assess the validity of these two views, we computed, using molecular dynamics simulations, the transport …
The binary Kob-Andersen (KA) Lennard-Jones mixture is the standard model for computational studies of viscous liquids and the glass transition. For very long simulations the viscous KA system crystallizes, however, by phase separating into a pure A particle phase forming an FCC crystal. We present the thermodynamic phase diagram for KA-type mixtures consisting of up to 50\% small (B) particles showing, in particular, that the melting temperature of the standard KA system at liquid density $1.2$ is $1.028(3)$ in A particle Lennard-Jones units. At large B particle concentrations the system cryst…
The shear viscosity of a Lennard-Jones fluid is obtained by stochastic dissipative molecular dynamics (SDMD) simulations. A generic constraint to the equations of motion is given that reduces the sensitivity of the shear viscosity to the value of the the fluctuation-dissipation or thermostat parameter. At high shear rates the shear viscosity becomes dependent on the size of the system, and corrections to the equipartition kinetic temperature arise. At constant kinetic temperature the shear viscosity is shown to decrease with increasing shear rate.
It is difficult to derive the solid-fluid transition theoretically from microscopic models, although this phenomenon itself has been investigated for a long time. We previously constructed an exactly-solvable model with the solid-fluid transition. This model resembles the infinite-range (or mean-field) model in spin systems in some points, hence it can be called a "mean-field model" of the solid-fluid transition. In the present paper, we construct a "mean-field approximation" of the solid-fluid transition by using the "mean-field model" introduced in our previous study, and tries to describe t…
The phase diagram of the prototypical two-dimensional Lennard-Jones system, while extensively investigated, is still debated. In particular, there are controversial results in the literature as concern the existence of the hexatic phase and the melting scenario. Here, we study the phase behaviour of 2D LJ particles via large-scale numerical simulations. We demonstrate that at high temperature, when the attraction in the potential plays a minor role, melting occurs via a continuous solid-hexatic transition followed by a first-order hexatic-fluid transition. As the temperature decreases, the den…
