Approach to the glass transition studied by higher order correlation functions

Abstract

We present a theoretical framework based on a higher order density correlation function, analogous to that used to investigate spin glasses, to describe dynamical heterogeneities in simulated glass-forming liquids. These higher order correlation functions are a four-point, time-dependent density correlation function g4(r,t) and a corresponding ‘structure factor’ S4(q,t) which measure the spatial correlations between the local liquid density at two points in space, each at two different times. g4(r,t) and S4(q,t) were extensively studied via molecular dynamics simulations of a binary Lennard-Jones mixture approaching the mode coupling temperature from above in Franz et al (1999 Phil. Mag. B 79 1827), Donati et al (2002 J. Non-Cryst. Solids 307 215), Glotzer et al (2000 J. Chem. Phys. 112 509), Lacević et al (2002 Phys. Rev. E 66 030101), Lacević et al (2003 J. Chem. Phys. submitted) and Lacević (2003 Dissertation The Johns Hopkins University). Here, we examine the contribution to g4(r,t), S4(q,t) and the corresponding dynamical correlation length, as well as the corresponding order parameter Q(t) and generalized susceptibility χ4(t), from localized particles. We show that the dynamical correlation length ξ4SS(t) of localized particles has a maximum as a function of time t, and the value of the maximum of ξ4SS(t) increases steadily in the temperature range approaching the mode coupling temperature from above.