Role of Structure and Entropy in Determining Differences in Dynamics for Glass Formers with Different Interaction Potentials

Abstract

We present a study of two model liquids with different interaction potentials, exhibiting similar structure but significantly different dynamics at low temperatures. By evaluating the configurational entropy, we show that the differences in the dynamics of these systems can be understood in terms of their thermodynamic differences. Analyzing their structure, we demonstrate that differences in pair correlation functions between the two systems, through their contribution to the entropy, dominate the differences in their dynamics, and indeed overestimate the differences. Including the contribution of higher order structural correlations to the entropy leads to smaller estimates for the relaxation times, as well as smaller differences between the two studied systems.Many approaches towards understanding the dynamical behavior of liquids attempt to predict dynamics in terms of static structural correlations [1,2], often focussing on two-body correlation functions. In turn, it has been argued that the short range, repulsive interactions have a dominant role in determining the pair correlation function, with the attractions making a perturbative contribution. Such an approach was shown to be effective in predicting the pair correlation function for dense liquids interacting via. the Lennard-Jones (LJ) potential, by Weeks, Chandler and Andersen, who treated the LJ potential as a sum of a repulsive part (referred to subsequently as the WCA potential) and the attractive part [3]. If such a treatment carries over to the analysis of dynamics, the expectation would be that liquids with LJ and the corresponding WCA interactions should have similar dynamics. However, in a series of recent papers, Bertheir and Tarjus have shown that model liquids with LJ and WCA interactions, exhibiting fairly similar structure, exhibit dramatically different dynamics, characterized by a structural relaxation time, at low temperatures [4][5][6][7]. In order to analyze this "non-perturbative" effect of the attractive forces on the dynamics, Berthier and Tarjus studied a number of "microscopic" approaches to predict the dynamics, based on knowledge of the static pair correlations. They conclude that the approaches they analyze are unsuccessful in capturing the differences in dynamics between the LJ and WCA systems. Dyre and co-workers [8][9][10] have argued that the origins of these observations are not specifically in the inclusion or neglect of attractive interactions [10], but factors such as the inclusion of interactions of all first shell neighbors [8], and the presence or absence of scaling between systems/state points compared [9]. In particular, Pedersen and Dyre [9] identify a purely repulsive inverse-power-law (IPL) potential that has dynamics that can be mapped to the LJ case studied by Bertheir and Tarjus. These observations notwithstanding, the inability to capture the differences between the LJ and WCA system highlighted by Berthier and Tarjus by predictive approaches to dynamics remains an open issue. In this regard, it has been s...

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