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The origin of stretched exponential relaxation in supercooled glass-formingliquids is one of the central questions regarding the anomalous dynamics ofthese fluids. The dominant explanation for this phenomenon has long been theproposition that spatial averaging over a heterogeneous distribution of locallyexponential relaxation processes leads to stretching. Here we performsimulations of model polymeric and small-molecule glass-formers in theisoconfigurational ensemble to show that stretching instead emerges from acombination of spatial averaging and locally nonexponential relaxation. Resultsindicate that localities in the fluid exhibiting faster-than-average relaxationtend to exhibit locally stretched relaxation, whereas slower-than-averagerelaxing domains exhibit compressed exponential relaxation. We show that localstretching is predicted by loose local caging, as measured by the Debye-Wallerfactor, and vice versa. This phenomenology in the local relaxation ofin-equilibrium glasses parallels the dynamics of out of equilibrium under-denseand over-dense glasses, which likewise exhibit an asymmetry in their degree ofstretching vs compression. On the basis of these results, we hypothesize thatlocal stretching and compression in equilibrium glass-forming liquids resultsfrom evolution of particle mobilities over a single local relaxation time, withslower particles tending towards acceleration and vice versa. In addition toproviding new insight into the origins of stretched relaxation, these resultshave implications for the interpretation of stretching exponents as measuredvia metrologies such as dielectric spectroscopy: measured stretching exponentscannot universally be interpreted as a direct measure of the breadth of anunderlying distribution of relaxation times.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

The microscopic origins of stretched exponential relaxation in two model  glass-forming liquids as probed by simulations in the isoconfigurational  ensemble