The shapes of cooperatively rearranging regions in glass-forming liquids

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Abstract

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.

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Figure 1: The shape of CRRs at Tg and Tc.
Figure 2: Predictions for the crossover temperatures.
Figure 3: Free-energy contours for the fuzzy-sphere model.
Figure 4: Predicted and experimental viscosity.
Figure 5: Shape characteristics for the fuzzy sphere.
Figure 6: Radial dimensions of the fuzzy sphere.

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Acknowledgements

Work at UCSD was supported by NSF grant CHE0317017. J.S. was supported by the Ames Laboratory, operated for the US Department of Energy by Iowa State University under Contract No. W-7405-Eng-82 (J.S.). We would also like to acknowledge K. Schmidt-Rohr for helpful comments.

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Correspondence to Jacob D. Stevenson or Peter G. Wolynes.

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