School on glass formers and glasses
Sarika Maitra Bhattacharyya Lectures

15 January, 2010

Bridging the gap between mode coupling theory and random first order transition theory

Abstract

In the lecture I will first briefly discuss the success and failure of mode coupling theory (MCT) in describing the dynamics in supercooled liquids. The MCT is known to breakdown at the temperature, T0c, where the landscape properties first show a change [1]. The region between T0c and the glass transition temperature Tg is known as the crossover region. In this region the dynamics is known to change from continuous diffusive motion to discontinuous activated hopping motion. However, the exact mechanism of this transition is not well understood. Both experiments and simulation studies have shown that MCT like dynamics follows even below T0c [2]. To understand the dynamics in this cross-over region we have to go beyond the mode coupling theory. The activated dynamics is a many body interaction which is not possible to describe under the present MCT scheme. However, the random first order transition (RFOT) theory which essentially states that high entropy liquid states nucleate within a glassy medium can provide us the rate of these nucleation processes which lead to the activation events [3]. I will discuss the RFOT theory and how it can provide us the estimate of the activated events. The unified theory combines the mode coupling theory (MCT) and random first order transition (RFOT) theory to describe the supercooled liquid dynamics over a wide range of temperature, including the cross-over regime [4,5,6]. I will discuss the unified theory and how both continuous and activate dynamics can be described under a common framework. Once I describe the unified theory I will discuss its success in describing and predicting the dynamics in the crossover regime.

References and suggested reading

  1. Y. Brumer , D. R. Reichman, Phys. Rev. E 69 041202-1, (2004).
  2. W. Kob, M. Nauroth, F. Sciortino, J Non-Cryst Solids 307-310, 181 (2002).
  3. V. Lubchenko and P. G. Wolynes, J. Chem. Phys. 119, 9088 (2003).; 
    X. Xia and P. G Wolynes, Phys. Rev. Lett. 86, 5526 (2001); 
    X. Xia and P. G. Wolynes Proc. Natl. Acad. Sci. U. S. A. 97, 2990 (2000)
  4. S. M. Bhattacharyya, B. Bagchi, P. G. Wolynes, Phys. Rev. E 72 031509, (2005)
  5. S. M. Bhattacharyya, B. Bagchi, P. G. Wolynes, http://arxiv.org/abs/cond-mat/0702435 (2007)
  6. S. M. Bhattacharyya, B. Bagchi, P. G. Wolynes, Proc. Natl. Acad. Sci. U. S. A. 105, 16077 (2008)