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

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Numerical determination of the exponents controlling the relationship between time, length and temperature in glass-forming liquids (Articolo in rivista) (literal)

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Alternative label

Chiara Cammarota (1); Andrea Cavagna (2); Giacomo Gradenigo (3); Tomas S. Grigera (4); Paolo Verrocchio (3) (2009)
Numerical determination of the exponents controlling the relationship between time, length and temperature in glass-forming liquids
in The Journal of chemical physics
(literal)

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Chiara Cammarota (1); Andrea Cavagna (2); Giacomo Gradenigo (3); Tomas S. Grigera (4); Paolo Verrocchio (3) (literal)

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(1) Dipartimento di Fisica, 'Sapienza' Università di Roma, and Center for Statistical Mechanics and Complexity (SMC), CNR - INFM, Piazzale Aldo Moro 5, 00185 Roma, Italy (2) Center for Statistical Mechanics and Complexity (SMC), CNR - INFM and Istituto Sistemi Complessi (ISC), CNR, via dei Taurini 19, 00185 Roma, Italy (3) Dipartimento di Fisica and SOFT, Università di Trento, via Sommarive 14, 38050 Trento, Italy (4) Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA - CCT La Plata) and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, c.c. 16, suc. 4, 1900 La Plata, Argentina and CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina (literal)

Titolo

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

Abstract

There is a certain consensus that the very fast growth of the relaxation time ? 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 ? in glass formers. If we use Arrhenius law and make the mild assumption that the free-energy barrier to rearrangement scales as some power ? of the size of the correlated regions, we obtain a relationship between time and length, T log ? ? ??. According to both the AdamGibbs and the random first order theory the correlation length grows as ? ? (T-Tk)-1/(d-?), even though the two theories disagree on the value of ?. Therefore, the super-Arrhenius growth of the relaxation time with the temperature is regulated by the two exponents ? and ? through the relationship T log ? ? (T-Tk)-?/(d-?). 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 ? = 1 and ? = 2. Surprisingly, even though the values we found disagree with most previous theoretical suggestions, they give back the well-known VFT law for the relaxation time, T log ? ? (T-Tk)-1. (literal)

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