The shapes of cooperatively rearranging regions in glass-forming liquids

The cooperative rearrangement of groups of many molecules has long been thought to underlie the dramatic slowing of liquid dynamics on cooling towards the glassy state. For instance, there exists experimental evidence for cooperatively rearranging regions (CRRs) on the nanometre length scale near the glass transition. The random first-order transition (RFOT) theory of glasses predicts that, near the glass-transition temperature, these regions are compact, but computer simulations and experiments on colloids suggest CRRs are string-like. Here, we present a microscopic theory within the framework of RFOT, which unites the two situations. We show that the shapes of CRRs in glassy liquids should change from being compact at low temperatures to fractal or 'stringy' as the dynamical crossover temperature from activated to collisional transport is approached from below. This theory predicts a correlation of the ratio of the dynamical crossover temperature to the laboratory glass-transition temperature, and the heat-capacity discontinuity at the glass transition. The predicted correlation quantitatively agrees with experimental results for 21 materials.