University of Cambridge > > Theoretical Chemistry Informal Seminars > Role of Pair and Higher Order Correlations in Entropy and Dynamics of Glass Forming Systems

Role of Pair and Higher Order Correlations in Entropy and Dynamics of Glass Forming Systems

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We present a study of two model liquids, Lennard Jones (LJ) and its repulsive counter part (WCA), exhibiting similar structure but significantly different dynamics at low temperatures [1]. The observation raises questions about the role of structure and thermodynamics in determining the dynamics. The well known Adam-Gibbs (AG) relation, τ(T) = τ_o exp (A/TS_c), expresses relaxation times τ in terms of a thermodynamic quantity, the configurational entropy S_c. By evaluating S_c, we show that the AG relationship quantitatively captures the differences in the dynamics between the LJ and WCA systems thus predicting that the differences in the dynamics of these systems can be understood in terms of their thermodynamic differences [2]. In order to analyze the independent role of pair and many body correlations we re-express the AG relation in terms of pair configurational entropy S_c2 and residual multiparticle entropy, ∆S, and show that although the pair contribution diverges at higher temperatures reminiscent of the well known mode coupling theory (MCT) behaviour, they capture the corresponding differences in τ(T) of the two systems [2]. Thus similar structures of the two systems predict different S_c2 values, indicating a strong sensitivity of the later to changes in the former [2]. However, as expected the pair entropy is not enough to explain the correct dynamics and the residual multiparticle entropy arising from many body correlation is essential. But an interesting observation is that the ∆S, speeds up the dynamics at low temperatures, which is at odds with the notion that stronger multiparticle correlations are responsible for the stronger temperature dependence of the relaxation times [2]. We further show that the AG theory which is based on activation dynamics can completely describe the MCT power law behavior in the region where the latter is found to be valid [3]. Since the configurational entropy has a finite value at the MCT transition temperature, T_c, the AG relation is not expected to predict any avoided transition in this regime. Our study reveals that although Sc is finite, Sc2 vanishes at T_K2 and in the MCT regime provides a dominant contribution to the total configuratonal entropy. We further find that T_K2 ≃ T_c , thus concluding that the avoided transition at T_c observed in the AG relation is due to the vanishing of S_c2 [3].

References [1] L. Berthier and G. Tarjus, Phys. Rev. Lett. 103,170601 (2009). [2] A. Banerjee, S. Sengupta, S. Sastry and S. M. Bhattacharyya , Phys. Rev. Lett. 113, 225701 (2014). [3] M. K. Nandi, A. Banerjee, S. Sengupta, S. Sastry and S. M. Bhattacharyya (to be submitted).

This talk is part of the Theoretical Chemistry Informal Seminars series.

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