Numerical determination of the exponents controlling the relationship between time, length, and temperature in glass-forming liquids

The Journal of Chemical Physics
Chiara CammarotaP Verrocchio

Abstract

There is a certain consensus that the very fast growth of the relaxation time tau occurring in glass-forming liquids on lowering the temperature must be due to the thermally activated rearrangement of correlated regions of growing size. Even though measuring the size of these regions has defied scientists for a while, there is indeed recent evidence of a growing correlation length xi in glass formers. If we use Arrhenius law and make the mild assumption that the free-energy barrier to rearrangement scales as some power psi of the size of the correlated regions, we obtain a relationship between time and length, T log tau approximately xi(psi). According to both the Adam-Gibbs and the random first order theory the correlation length grows as xi approximately (T-T(k))(-1/(d-theta)), even though the two theories disagree on the value of theta. Therefore, the super-Arrhenius growth of the relaxation time with the temperature is regulated by the two exponents psi and theta through the relationship T log tau approximately (T-T(k))(-psi/(d-theta)). Despite a few theoretical speculations, up to now there has been no experimental determination of these two exponents. Here we measure them numerically in a model glass former, finding psi=1...Continue Reading

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Citations

May 25, 2012·Proceedings of the National Academy of Sciences of the United States of America·Chiara Cammarota, Giulio Biroli
Apr 6, 2013·The Journal of Chemical Physics·Giulio Biroli, Juan P Garrahan
Apr 6, 2013·The Journal of Chemical Physics·Chiara Cammarota, Giulio Biroli
Jun 7, 2012·The Journal of Chemical Physics·Andrea CavagnaPaolo Verrocchio
Apr 6, 2013·The Journal of Chemical Physics·Giacomo GradenigoPaolo Verrocchio
Jul 28, 2016·The Journal of Chemical Physics·Atreyee BanerjeeSarika Maitra Bhattacharyya
Jul 28, 2016·The Journal of Chemical Physics·Saurish ChakrabartyChandan Dasgupta
Jul 5, 2018·Journal of Physics. Condensed Matter : an Institute of Physics Journal·C Patrick RoyallJoshua Robinson
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Jan 16, 2017·The Journal of Chemical Physics·Yuan-Chao HuWei-Hua Wang
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Nov 5, 2013·Physical Review Letters·Giulio BiroliItamar Procaccia
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