Does a Growing Static Length Scale Control the Glass Transition?

Several theories of the glass transition propose that the structural relaxation time ${\tau }_{\alpha }$ is controlled by a growing static length scale $\xi$ that is determined by the free energy landscape but not by the local dynamic rules governing its exploration. We argue, based on recent simulations using particle-radius-swap dynamics, that only a modest factor in the increase in ${\tau }_{\alpha }$ on approach to the glass transition may stem from the growth of a static length, with a vastly larger contribution attributable, instead, to a slowdown of local dynamics. This reinforces arguments that we base on the observed strong coupling of particle diffusion and density fluctuations in real glasses.

Figure 1

Left panel: schematic of the free energy landscape $F(\{\mathbf{r}\})$ for models where the dominant kinetic barriers $E_{\mathrm{coll}}$ are collective, and appear on a length scale $\xi$. Local barriers $E_{\mathrm{el}}$ are much smaller than $E_{\mathrm{coll}}$. In this scenario, introducing swap moves in the dynamic rules should have little effect on structural relaxation, since it leaves $E_{\mathrm{coll}}$ unchanged; also, there should be a very large decoupling between particle diffusion (that can occur by permuting particles, which requires overcoming local barriers only) and relaxation of density fluctuations (for which collective barriers must be overcome). Both predictions appear to be contradicted by observations, suggesting that local barriers dominate the slowdown (right panel). (In this case, the definition of $E_{\mathrm{coll}}$ and $\xi$ may become somewhat arbitrary).