Stringlike Cooperative Motion in a Supercooled Liquid

Abstract

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...

Local polymer dynamics under strong connectivity constraints: The dendrimer case

“…Associations of the temporal scale t * at which the NGP peaks with the time scale for collective motion responsible for the ␣-relaxation process have already been noticed in different glass-forming systems. Studies in supercooled liquids 13,19,22 demonstrated the relation of t * with the lifetime of the dynamic heterogeneities and the cooperative motion necessary for the release of the particles from their cage, which characterizes the early stages of ␣-relaxation. In linear polymer models it was shown 6,9 that NGP peaks in the late-␤/early-␣ regime, while t * was found to follow a similar temperature dependence with that of the ␣-relaxation ͑see Ref.…”

“…9,16 Instead of the free diffusion realized in simple unassociated liquids, a subdiffusive behavior is observed in monomer motion due to bonding, before final diffusion sets in. 4,6,9,16 Close examination of the motional mechanisms at this time and length scales in different kinds of glass-forming systems 9,20,22,23 revealed the key role of mobility-correlated subregions in the realization of cooperative motion. In the case of polymers chain connectivity may provide alternative routes, not present in simple liquids, for short range spatially correlated dynamics.…”

“…[27][28][29][30][31] These attributes may essentially "filter out" certain dynamic features met either in liquids or linear polymers allowing a better assessment of the relative importance of each factor. For instance, in both of these glass-forming systems, regions of low or high mobility may fluctuate through the sample in a finite time scale, promoting specific mechanisms for cooperative particle rearrangements ͑e.g., stringlike particle/monomer clusters 9,22 ͒ that are expected to be suppressed in dendrimers. Identification and monitoring of regions possessing distinct mobilities rely on a proper selection of subensembles of "fast" and "slow" moving units, for the definition of which various approaches have been followed so far.…”

Dynamical Heterogeneity and Jamming in Glass-Forming Liquids

“…We also find that force chains do not play the same role as force chains in granular materials, but may indicate a difference in the evolution of the local environment of particles with different mobility. We also discuss a possible relationship between force chains found here and the development of string-like motion found in other glass-forming liquids [2,3]. …”

“…[2,27,47,48,49,50,51,52], several approaches -including calculation of a displacement-displacement correlation function, identification of clusters of mobile particles, and calculation of a four-point time-dependent density correlation function -predicted and demonstrated the importance of spatially heterogeneous dynamics in supercooled liquids using a rigorous statistical mechanical analysis. In particular, using the four-point time-dependent density correlation function formalism, we found dynamical correlation lengths of regions of localized and delocalized particles which suggests a picture of fluctuating domains of temporarily localized and delocalized particles, as suggested by Stillinger and Hodgedon [53].…”