Correlation of nonexponentiality with dynamic heterogeneity from four-point dynamic susceptibility chi(4)(t) and its approximation chi(T)(t)

Various properties of vitrifying liquids are correlated with the dispersity of the dynamics, the latter reflected in the magnitude of the nonexponentiality parameter, beta(K), describing the distribution of relaxation times. These properties include the mean relaxation time, tau(alpha), the fragility, and the dynamic crossover. The correlations with beta(K) are observed in both experimental data and the results from molecular dynamics simulations on Lennard-Jones (LJ) type systems. Another, rather obvious property to correlate with beta(K) is the dynamic heterogeneity, which can be quantified from the number of molecules, N-c, dynamically correlated over a time span tau(alpha). For a given LJ system, N-c can be rigorously calculated and we find that it does indeed correlate with beta(K) over a range of thermodynamic conditions. However, the analysis of experimental data for a broad range of real materials, wherein an approximation is required to obtain N-c, reveals the absence of any relationship between N-c and beta(K) among different materials. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3481355]