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Register a new userDensity-scaling exponents and virial potential-energy correlation coefficients for the (2n,n) Lennard-Jones system
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This paper investigates the relation between the density-scaling exponent $gamma$ and the virial potential-energy correlation coefficient $R$ at several thermodynamic state points in three dimensions for the generalized $(2n,n)$ Lennard-Jones (LJ) system for $n=4, 9, 12, 18$, as well as for the standard $n=6$ LJ system in two, three, and four dimensions. The state points studied include many low-density states at which the virial potential-energy correlations are not strong. For these state points we find the roughly linear relation $gammacong 3nR/d$ in $d$ dimensions. This result is discussed in light of the approximate extended inverse power law description of generalized LJ potentials [N. P. Bailey et al., J. Chem. Phys. 129, 184508 (2008)]. In the plot of $gamma$ versus $R$ there is in all cases a transition around $Rapprox 0.9$, above which $gamma$ starts to decrease as $R$ approaches unity. This is consistent with the fact that $gammarightarrow 2n/d$ for $Rrightarrow 1$, a limit that is approached at high densities and/or temperatures at which the repulsive $r^{-2n}$ term dominates the physics.
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It is well known that elastic effects can cause surface instability. In this paper, we analyze a one-dimensional discrete system which can reveal pattern formation mechanism resembling the step-bunching phenomena for epitaxial growth on vicinal surfaces. The surface steps are subject to long-range pairwise interactions taking the form of a general Lennard--Jones (LJ) type potential. It is characterized by two exponents $m$ and $n$ describing the singular and decaying behaviors of the interacting potential at small and large distances, and henceforth are called generalized LJ $(m,n)$ potential. We provide a systematic analysis of the asymptotic properties of the step configurations and the value of the minimum energy, in particular, their dependence on $m$ and $n$ and an additional parameter $alpha$ indicating the interaction range. Our results show that there is a phase transition between the bunching and non-bunching regimes. Moreover, some of our statements are applicable for any critical points of the energy, not necessarily minimizers. This work extends the technique and results of [Luo et al, SIAM MMS, 2016] which concentrates on the case of LJ (0,2) potential (originated from the elastic force monopole and dipole interactions between the steps). As a by-product, our result also leads to the well-known fact that the classical LJ (6,12) potential does not demonstrate step-bunching type phenomena.
We calculate the density of states of a binary Lennard-Jones glass using a recently proposed Monte Carlo algorithm. Unlike traditional molecular simulation approaches, the algorithm samples distinct configurations according to self-consistent estimates of the density of states, thereby giving rise to uniform internal-energy histograms. The method is applied to simulate the equilibrium, low-temperature thermodynamic properties of a widely studied glass former consisting of a binary mixture of Lennard-Jones particles. We show how a density-of-states algorithm can be combined with particle identity swaps and configurational bias techniques to study that system. Results are presented for the energy and entropy below the mode coupling temperature.
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 conform to the single-parameter-aging scenario derived and validated for small jumps in experiments [Hecksher et al., J. Chem. Phys. 142, 241103 (2015)]. As a further confirmation of single-parameter aging with a common material time for the different quantities monitored, their relaxing parts are found to be almost identical for all temperature jumps.
We numerically investigated the connection between isobaric fragility and the properties of high-order stationary points of the potential energy surface in different supercooled Lennard-Jones mixtures. The increase of effective activation energies upon supercooling appears to be driven by the increase of average potential energy barriers measured by the energy dependence of the fraction of unstable modes. Such an increase is sharper, the more fragile is the mixture. Correlations between fragility and other properties of high-order stationary points, including the vibrational density of states and the localization features of unstable modes, are also discussed.
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