Anomalous diffusion and stretched exponentials in heterogeneous glass-forming liquids: low-temperature behavior.
We propose a model of a heterogeneous glass-forming liquid and compute the low-temperature behavior of a tagged molecule moving within it. This model exhibits stretched-exponential decay of the wave-number-dependent, self-intermediate scattering function in the limit of long times. At temperatures close to the glass transition, where the heterogeneities are much larger in extent than the molecular spacing, the time dependence of the scattering function crosses over from stretched-exponential decay with an index b=1/2 at large wave numbers to normal, diffusive behavior with b=1 at small wave numbers. There is a clear separation between early-stage, cage-breaking beta relaxation and late-stage alpha relaxation. The spatial representation of the scattering function exhibits an anomalously broad exponential (non-Gaussian) tail for sufficiently large values of the molecular displacement at all finite times.
Langer
J S
JS
Department of Physics, University of California, Santa Barbara, California 93106-9530, USA.
Mukhopadhyay
Swagatam
S