There is a certain consensus that the very fast growth of the relaxation time τ 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 ψ of the size of the correlated regions, we obtain a relationship between time and length, T log τ∼ ψ. According to both the Adam-Gibbs and the random first order theory the correlation length grows as ∼ (T- Tk) -1/(d-θ), even though the two theories disagree on the value of θ. Therefore, the super-Arrhenius growth of the relaxation time with the temperature is regulated by the two exponents ψ and θ through the relationship T log τ∼ (T- Tk)-ψ/(d-θ). 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 ψ=1 and θ=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 τ∼ (T- T k)-1. © 2009 American Institute of Physics.

Numerical determination of the exponents controlling the relationship between time, length, and temperature in glass-forming liquids / Cammarota, C.; Cavagna, A.; Gradenigo, G.; Grigera, T. S.; Verrocchio, P.. - In: THE JOURNAL OF CHEMICAL PHYSICS. - ISSN 0021-9606. - 131:19(2009), p. 194901. [10.1063/1.3257739]

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

Cammarota C.;Cavagna A.;Gradenigo G.;Grigera T. S.;Verrocchio P.
2009

Abstract

There is a certain consensus that the very fast growth of the relaxation time τ 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 ψ of the size of the correlated regions, we obtain a relationship between time and length, T log τ∼ ψ. According to both the Adam-Gibbs and the random first order theory the correlation length grows as ∼ (T- Tk) -1/(d-θ), even though the two theories disagree on the value of θ. Therefore, the super-Arrhenius growth of the relaxation time with the temperature is regulated by the two exponents ψ and θ through the relationship T log τ∼ (T- Tk)-ψ/(d-θ). 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 ψ=1 and θ=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 τ∼ (T- T k)-1. © 2009 American Institute of Physics.
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/1472321
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? 6
  • Scopus 50
  • ???jsp.display-item.citation.isi??? 49
social impact