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Extensive molecular dynamics simulations are performed on a glass-forming Lennard-Jones mixture to determine the nature of the cooperative motions occurring in this model fragile liquid. We observe stringlike cooperative molecular motion ("strings") at temperatures well above the glass transition. The mean length of the strings increases upon cooling, and the string length distribution is found to be nearly exponential. [S0031-9007(98)05583-5] PACS numbers: 61.20.Lc, 61.43.Fs, 64.70.Pf The concept of cooperative molecular motion [1,2] is commonly invoked to rationalize dramatic changes in the transport properties of liquids as they are cooled toward their glass transition [3]. In the heuristic Adam and Gibbs model [1] of supercooled liquids, relaxation occurs through "cooperatively rearranging regions" which grow with decreasing temperature. A more rigorous treatment of collective motion in liquids by Zwanzig and Nossal emphasizes the occurrence of momentum density excitations whose lifetime grows as the temperature is lowered [4]. Modecoupling theory (MCT) [5] attributes the slowing down of particle motion at low temperatures to "backflow" collective particle motion which eventually causes a structural arrest of the liquid dynamics. However, there has been no direct experimental observation of these kinds of cooperative motion.Computer simulations offer advantages over experiments on real liquids for the investigation of collective particle motion. In molecular dynamics the position and velocity of all the particles are known at all times. As a consequence, correlation functions quantifying the motion of particular subsets of particles can be readily determined. Recent experiments [6,7] and simulations [8,9] have identified dynamical heterogeneity in supercooled liquids and spin glasses [10]. It is natural to suppose that cooperative motion might be associated with this dynamical heterogeneity. A well studied Lennard-Jones (LJ) system, recently introduced to study the dynamics of simple supercooled liquids, provides a particularly good model to test for cooperative motion, since its properties have been well characterized [11] and evidence for dynamical heterogeneity has already been identified for this model [9].In this Letter, we test whether cooperative molecular motion occurs in this model fragile glass-forming liquid. We find that molecular motion indeed becomes increasingly collective upon cooling. However, the regions involved in this motion are not compact, as usually supposed [1,12], but instead form stringlike structures. The average string length increases with decreasing temperature, and the string length distribution is nearly exponential.We performed extensive molecular dynamics simulations of a three dimensional binary mixture (80:20) of 8000 LJ particles where the interaction parameters [13] are chosen to prevent demixing and crystallization [11]. Ten temperatures T between 0.550 and 0.451 above the fitted mode-coupling temperature T c ഠ 0.431 [11] are studied. We emphasize that this temperatu...

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.Recent NMR experiments have shown that the relaxation in supercooled liquids is not homogeneous, i.e. that there are regions in space in which the relaxation of the particles is significantly faster (or slower) than the average relaxation of the system [1]. Subsequently, this result has been supported by optical spectroscopy, forced Rayleigh scattering and further NMR experiments [2]. However, these types of experiments are unable to determine the nature of these "dynamical heterogeneities," and consequently details such as size are

We investigate, for two water models displaying a liquid-liquid critical point, the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquidliquid critical point. We find a correlation between the dynamic crossover and the locus of specific heat maxima C P max (''Widom line'') emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesized liquid-liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between C P max and dynamic crossover is not limited to the case of water, a hydrogen bond network-forming liquid, but is a more general feature of crossing the Widom line. Specifically, we also study the Jagla potential, a spherically symmetric two-scale potential known to possess a liquid-liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions. By definition, in a first-order phase transition, thermodynamic state functions such as density and enthalpy H change discontinuously as we cool the system along a path crossing the equilibrium coexistence line (Fig. 1a, path ␤). However, in a real experiment, this discontinuous change may not occur at the coexistence line because a substance can remain in a supercooled metastable phase until a limit of stability (a spinodal) is reached (1) (Fig. 1b, path ␤).If the system is cooled isobarically along a path above the critical pressure P c (Fig. 1b, path ␣), the state functions continuously change from the values characteristic of a high-temperature phase (gas) to those characteristic of a low-temperature phase (liquid). The thermodynamic response functions, which are the derivatives of the state functions with respect to temperature (e.g., isobaric heat capacity C P ϭ (ѨH͞ѨT) P ), have maxima at temperatures denoted T max (P). Remarkably, these maxima are still prominent far above the critical pressure (2-5), and the values of the response functions at T max (P) (e.g., C P max ) diverge as the critical point is approached. The lines of the maxima for different response functions asymptotically approach one another as the critical point is approached, because all response functions become expressible in terms of the correlation length. This asymptotic line is sometimes called the ''Widom line'' and is often regarded as an extension of the coexistence line into the ''one-phase region.'' If the system is cooled at constant pressure P 0 , and P 0 is not too far from the critical pressure P c , then there are two classes of behavior possible. (i) If P 0 Ͼ P c (path ␣), then experimentally measured quantities will change dramatically but continuously in the vicinity of the Widom line (with huge fluctuations as measured by, e.g., C P ). (ii) If P 0 Ͻ P c (path ␤), experimentally measured quantities will change discontinuously if the coexistence line is actually seen. However, ...