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1 Phys. Rev. E 79, 031501 (2009) Quantitative theory of a time-correlation function in a one-component glass-forming liquid with anisotropic potential Edan Lerner, Itamar Procaccia, and Ido Regev Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel Received 8 September 2008; revised 30 November 2008; published 10 March 2009 The Shintani-Tanaka model is a glass-forming system whose constituents interact via an anisotropic potential depending on the angle of a unit vector carried by each particle. The decay of time-correlation functions of the unit vectors exhibits the characteristics of generic relaxation functions during glass transitions. In particular it exhibits a stretched exponential form, with the stretching index depending strongly on the temperature. We construct a quantitative theory of this correlation function by analyzing all the physical processes that contribute to it, separating a rotational from a translational decay channel. These channels exhibit different relaxation times, each with its own temperature dependence. Interestingly, the separate decay function of each of these processes is a temperature-independent function, and is shown to scale (exhibit data collapse) at different temperatures. Taken together with temperature-dependent weights determined a priori by statistical mechanics this allows one to generate the observed correlation function in quantitative agreement with simulations at different temperatures. This underlines the danger of concluding anything about glassy relaxation functions without detailed physical scrutiny. 2 PNAS Growing length and time scales in glass-forming liquids Smarajit Karmakara, Chandan Dasguptaa,b,1 and Srikanth Sastryb Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved January 9, 2009 (received for review November 6, 2008) Abstract The glass transition, whereby liquids transform into amorphous solids at low temperatures, is a subject of intense research despite decades of investigation. Explaining the enormous increase in relaxation times of a liquid upon supercooling is essential for understanding the glass transition. Although many theories, such as the Adam–Gibbs theory, have sought to relate growing relaxation times to length scales associated with spatial correlations in liquid structure or motion of molecules, the role of length scales in glassy dynamics is not well established. Recent studies of spatially correlated rearrangements of molecules leading to structural relaxation, termed “spatially heterogeneous dynamics,” provide fresh impetus in this direction. A powerful approach to extract length scales in critical phenomena is finite-size scaling, wherein a system is studied for sizes traversing the length scales of interest. We perform finite-size scaling for a realistic glass-former, using computer simulations, to evaluate the length scale associated with spatially heterogeneous dynamics, which grows as temperature decreases. However, relaxation times that also grow with decreasing temperature do not exhibit standard finite-size scaling with this length. We show that relaxation times are instead determined, for all studied system sizes and temperatures, by configurational entropy, in accordance with the Adam–Gibbs relation, but in disagreement with theoretical expectations based on spin-glass models that configurational entropy is not relevant at temperatures substantially above the critical temperature of mode-coupling theory. Our results provide new insights into the dynamics of glass-forming liquids and pose serious challenges to existing theoretical descriptions. Keywords: correlation length dynamic heterogeneity finite-size scaling glass transition relaxation time [ Last edited by hslining on 2009-9-21 at 23:29 ] |
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