Spatially Heterogeneous Dynamics and the Adam−Gibbs Relation in the Dzugutov Liquid

Abstract

We perform molecular dynamics simulations of a one-component glass-forming liquid and use the inherent structure formalism to test the predictions of the Adam-Gibbs (AG) theory and to explore the possible connection between these predictions and spatially heterogeneous dynamics. We calculate the temperature dependence of the average potential energy of the equilibrium liquid and show that it obeys the RosenfeldTarazona T 3/5 law for low temperature T, while the average inherent structure energy is found to be inversely proportional to temperature at low T, consistent with a Gaussian distribution of potential energy minima. We investigate the shape of the basins around the local minima in configuration space via the average basin vibrational frequency and show that the basins become slightly broader upon cooling. We evaluate the configurational entropy S conf , a measure of the multiplicity of potential energy minima sampled by the system, and test the validity of the AG relation between S conf and the bulk dynamics. We quantify the dynamically heterogeneous motion by analyzing the motion of particles that are mobile on short and intermediate time scales relative to the characteristic bulk relaxation time. These mobile particles move in one-dimensional "strings", and these strings form clusters with a well-defined average cluster size. The AG approach predicts that the minimum size of cooperatively rearranging regions (CRR) of molecules is inversely proportional to S conf , and recently (Phys. Rev. Lett. 2003, 90, 085506) it has been shown that the mobile-particle clusters are consistent with the CRR envisaged by Adam and Gibbs. We test the possibility that the mobile-particle strings, rather than clusters, may describe the CRR of the Adam-Gibbs approach. We find that the strings also follow a nearly inverse relation with S conf . We further show that the logarithm of the time when the strings and clusters are maximum, which occurs in the late--relaxation regime of the intermediate scattering function, follows a linear relationship with 1/TS conf , in agreement with the AG prediction for the relationship between the configurational entropy and the characteristic time for the liquid to undergo a transition to a new configuration. Since strings are the basic elements of the clusters, we propose that strings are a more appropriate measure of the minimum size of a CRR that leads to configurational transitions. That the cluster size also has an inverse relationship with S conf may be a consequence of the fact that the clusters are composed of strings.

Quantitative relations between cooperative motion, emergent elasticity, and free volume in model glass-forming polymer materials

“…Simulation has led the way in defining the existence and precise nature of cooperative motion in cooled liquids. In particular, several studies have established that the activation freeenergy barrier ΔG for structural relaxation is proportional to the average length of string-like clusters involving particle exchange motion (20,21,(34)(35)(36)(37)41). These well-defined string clusters provide a concrete realization of the CRRs.…”

Interfacial mobility scale determines the scale of collective motion and relaxation rate in polymer films

“…In particular, those monomers with the greatest mobility tend to cluster and subsets within these clusters move collectively in a string-like manner, observed both in computer simulations 23,26,[37][38][39][40][41][42][43] and colloidal experiments [44][45][46][47] . Significantly, several publications [25][26][27]48 indicate that the string size may offer a molecular realization of CRR. Therefore, we aim to test whether the interfacial scale might be reflective of this scale of cooperative motion.…”

String model for the dynamics of glass-forming liquids

“…[18][19][20][21] The proportionality between the average string length L and G(T) was found to hold even when the fragility of the GF fluid was varied over a broad range in a model polymera) Electronic mail: fstarr@wesleyan.edu nanoparticle composite. 19,21 Additionally, this relation between G and L can account for the dynamical changes in supported polymer films having variable thickness, substrate roughness, stiffness, and polymer-substrate interaction strength.…”