We investigate the calorimetric liquid-glass transition by performing simulations of a binary Lennard-Jones mixture in one through four dimensions. Starting at a high temperature, the systems are cooled to T=0 and heated back to the ergodic liquid state at constant rates. Glass transitions are observed in two, three and four dimensions as a hysteresis between the cooling and heating curves. This hysteresis appears in the energy and pressure diagrams, and the scanning-rate dependence of the area and height of the hysteresis can be described by power laws. The one dimensional system does not experience a glass transition but its specific heat curve resembles the shape of the $D\geq 2$ results in the supercooled liquid regime above the glass transition. As $D$ increases, the radial distribution functions reflect reduced geometric constraints. Nearest-neighbor distances become smaller with increasing $D$ due to interactions between nearest and next-nearest neighbors. Simulation data for the glasses are compared with crystal and melting data obtained with a Lennard-Jones system with only one type of particle and we find that with increasing $D$ crystallization becomes increasingly more difficult.
This is a Reply to the Comment of Muessel and Rieger cond-mat/9804063 to out paper on ``Aging Effects in a Lennerd-Jones Glass''. We show that the scaling function proposed by Muessel and Rieger does not lead to a satisfactory scaling of our aging data.
We study the liquid-glass transition of the Lennard-Jones binary mixture introduced by Kob and Andersen from a thermodynamic point of view. By means of the replica approach, translating the problem in the study of a molecular liquid, we study the phase transition due to the entropy crisis and we find that the Kauzmann's temperature $\tk$ is $\sim 0.32$. At the end we compare analytical predictions with numerical results.
In a recent letter [PRL 78 (1997) 4581] Kob and Barrat reported results of their molecular dynamics simulation of the non-equilibrium dynamics of a binary Lennard-Jones glass. They propose an aging scenario in this system that is close to a t/t_w scaling behavior. In this comment we present new results and show that a different aging scenario, known under the name activated dynamics scaling [i.e. log((t+t_w)/tau)/log(t_w/tau)], describes the aging regime of this kind of glassy systems much better.
In two recent interesting letters evidence was presented for the existence of a growing dynamic correlation length when we approach the glass transition from the liquid phase (a similar divergence is present also in the off-equilibrium dynamics below $T_c$). Here we would like to point out that this phenomenon can be easily predicted using the replica approach.
By using extensive Molecular Dynamics simulations, we have determined the violation of the fluctuation-dissipation theorem in a Lennard-Jones liquid quenched to low temperatures. For this we have calculated $X(C)$, the ratio between a one particle time-correlation function $C$ and the associated response function. Our results are best fitted by assuming that $X(C)$ is a discontinuous, piecewise constant function. This is similar to what is found in spin systems with one step replica symmetry breaking. This strengthen the conjecture of a similarity between the phase space structure of structura…
Molecular dynamics simulations are used to generate an ensemble of saddles of the potential energy of a Lennard-Jones liquid. Classifying all extrema by their potential energy u and number of unstable directions k, a well defined relation k(u) is revealed. The degree of instability of typical stationary points vanishes at a threshold potential energy, which lies above the energy of the lowest glassy minima of the system. The energies of the inherent states, as obtained by the Stillinger-Weber method, approach the threshold energy at a temperature close to the mode-coupling transition temperatu…
We report the results of calculation of diffusion coefficients for Lennard-Jones liquids, based on the idea of time-scale invariance of relaxation processes in liquids. The results were compared with the molecular dynamics data for Lennard-Jones system and a good agreement of our theory with these data over a wide range of densities and temperatures was obtained. By calculations of the non-Markovity parameter we have estimated numerically statistical memory effects of diffusion in detail.
We report on numerical procedures for, and preliminary results on the search for, tunnelling centres in Lennard-Jones clusters, seen as simple model systems of glasses. Several of the double-well potentials identified are good candidates to give rise to two-level systems. The role of boundary effects, and the application of the semiclassical WKB approximation in multidimensional spaces for the calculation of the ground state splitting are discussed.
We present the results of a large scale molecular dynamics computer simulation study in which we investigate whether a supercooled Lennard-Jones liquid exhibits dynamical heterogeneities. We evaluate the non-Gaussian parameter for the self part of the van Hove correlation function and use it to identify ``mobile'' particles. We find that these particles form clusters whose size grows with decreasing temperature. We also find that the relaxation time of the mobile particles is significantly shorter than that of the bulk, and that this difference increases with decreasing temperature.
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…
It is established that liquid metals exhibit surface layering at the liquid-vapor interface, while dielectric simple systems, like those interacting through Lennard-Jones potentials, show a monotonic decay from the liquid density to that of the vapor. First principles molecular dynamics simulations of the liquid-vapor interface of several liquid metals (Li, Na, K, Rb, Cs, Mg, Ba, Al, Tl and Si), and the Na$_3$K$_7$ alloy near their triple points have been performed in order to study the atomic motion at the interface, mainly at the outer layer. Comparison with results of classical molecular dy…
The potential energy surface (PES) of Lennard-Jones clusters is investigated using the activation-relaxation technique (ART). This method defines events in the configurational energy landscape as a two-step process: (a) a configuration is first activated from a local minimum to a nearby saddle-point and (b) is then relaxed to a new minimum. Although ART has been applied with success to a wide range of materials such as a-Si, a-SiO2 and binary Lennard-Jones glasses, questions remain regarding the biases of the technique. We address some of these questions in a detailed study of ART-generated ev…
We present a quantitative comparison at equivalent thermodynamical conditions of bulk and confined dynamical properties of a Lennard Jones binary mixture upon supercooling. Both systems had been previously found to display a behavior in agreement with the Mode Coupling theory of the evolution of glassy dynamics. Differences and analogies of behavior are discussed focusing in particular on the role of hopping in reducing spatially correlated dynamics in the confined system with respect to the bulk.
We investigate a binary Lennard-Jones mixture with molecular dynamics simulations. We consider first a system cooled linearly in time with the cooling rate gamma. By varying gamma over almost four decades we study the influence of the cooling rate on the glass transition and on the resulting glass. We find for all investigated quantities a cooling rate dependence; with decreasing cooling rate the system falls out of equilibrium at decreasing temperatures, reaches lower enthalpies and obtains increasing local order. Next we study the dynamics of the melting process by investigating the most imm…
We use the results derived in the framework of the replica approach to study the liquid-glass thermodynamic transition. The main results are rederived without using replicas and applied to the study of the Lennard-Jones binary mixture introduced by Kob and Andersen. We find that there is a phase transition due to the entropy crisis. We compute both analytically and numerically the value of the phase transition point $T_{K}$ and the specific heat in the low temperature phase.
The potential energy landscape in the Kob-Andersen Lennard-Jones binary mixture model has been studied carefully from liquid down to the supercooled regime, from T =2 down to T =0.46. One thousand of independent configurations along the time evolution have been examined at each investigated temperature. From the starting configuration we searched the nearest saddle (or quasi-saddle) and minimum of the potential energy. The vibrational densities of states for the starting and the two derived configurations have been evaluated. Besides the number of negative eigenvalues of saddle, other quantiti…
The off-equilibrium dynamics of a monatomic Lennard-Jones glass is investigated after sudden isothermal density jumps (crunch) from well equilibrated liquid configurations towards the glassy state. The generalized fluctuation-dissipation relation has been studied and the temperature dependence of the violation factor m is found in agreement with the one step replica symmetry breaking scenario, i.e. at low temperature m(T) is found proportional to T up to an off-equilibrium effective temperature T_eff, where m(T_eff)=1. We report T_eff as a function of the density and compare it with the glass …
Using the activation-relaxation technique (ART), we study the nature of relaxation events in a binary Lennard-Jones system above and below the glass transition temperature (T_g). ART generates trajectories with almost identical efficiency at all temperature, thus avoiding the exponential slowing down below T_g and providing extensive sampling everywhere. Comparing these runs, we find that the number of atoms involved in an event decreases strongly with temperature. In particular, while in the supercooled liquid activated events are collective, involving on average thirty atoms or more, events …
We analyze one thousand independent equilibrium trajectories of a system of 155 Lennard Jones particles to separate in a model-free approach the role of temperature and the role of the explored potential energy landscape basin depth in the particle dynamics. We show that the diffusion coefficient $D$ can be estimated as a sum over over contributions of the sampled basins, establishing a connection between thermodynamics and dynamics in the potential energy landscape framework. We provide evidence that the observed non-linearity in the relation between local diffusion and basin depth is respons…
Properties of local minima as a function of density are studied in a binary Lennard-Jones system for kinetic equipartition temperatures $T=1.0$ (normal liquid), 0.5 (supercooled liquid), and 0.4 (glass), in reduced units. The number of different local minima sampled, energy, pressure, normal mode angular frequencies, mean distance between all pairs of local minima and partial radial distribution functions are presented. In agreement with previous studies by Sastry [Phys. Rev. Lett. {\bf 85}, 590 (2000)] a limiting density is found at $ρ_l=1.06$ with negative pressure, below which the local str…
The properties of higher-index saddle points have been invoked in recent theories of the dynamics of supercooled liquids. Here we examine in detail a mapping of configurations to saddle points using minimization of $|\nabla E|^2$, which has been used in previous work to support these theories. The examples we consider are a two-dimensional model energy surface and binary Lennard-Jones liquids and solids. A shortcoming of the mapping is its failure to divide the potential energy surface into basins of attraction surrounding saddle points, because there are many minima of $|\nabla E|^2$ that do …
