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

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, $T\log \tau \sim {\xi }^{\psi }$. According to both the Adam-Gibbs and the Random First Order theory the correlation length grows as $\xi \sim (T-T_k{)}^{-1/(d-\theta )}$, 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 $T\log \tau \sim (T-T_k{)}^{-\psi /(d-\theta )}$. 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 $\psi =1$ and $\theta =2$. 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, $T\log \tau \sim (T-T_k{)}^{-1}$.

9 pages, 8 figures

References in corpus (2)

• Mosaic multi-state scenario vs. one-state description of supercooled liquids
• Analytic determination of dynamical and mosaic length scales in a Kac glass model

Cited by in corpus (39)

• Theoretical perspective on the glass transition and amorphous materials
• Perspective: The Glass Transition
• Models and algorithms for the next generation of glass transition studies
• The Relationship of Dynamical Heterogeneity to the Adam-Gibbs and Random First-Order Transition Theories of Glass Formation
• Ideal Glass Transitions by Random Pinning
• Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling
• Perspective: Configurational entropy of glass-forming liquids
• Dynamic heterogeneity in a glass forming fluid: susceptibility, structure factor and correlation length
• The role of structure and entropy in determining differences in dynamics for glass formers with different interaction potentials
• A phase-separation perspective on dynamic heterogeneities in glass-forming liquids
• Does the Adam-Gibbs relation hold in simulated supercooled liquids?
• Comparison of Static Length-Scales Characterizing the Glass Transition
• The race to the bottom: approaching the ideal glass?
• Evidence for a disordered critical point in a glass-forming liquid
• The Adam-Gibbs relation for glass-forming liquids in 2, 3 and 4 dimensions
• Random Pinning Glass Transition: Hallmarks, Mean-Field Theory and Renormalization Group Analysis
• Dynamic relaxation of a liquid cavity under amorphous boundary conditions
• Evidence of growing spatial correlations during the aging of glassy glycerol
• Locally favoured structures and dynamic length scales in a simple glass-former
• Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel
• Renormalization group analysis of the random first order transition
• Static and dynamical properties of a hard-disk fluid confined to a narrow channel
• Understanding the Dynamics of Glass-forming Liquids with Random Pinning within the Random First Order Transition Theory
• Surface tension fluctuations and a new spinodal point in glass-forming liquids
• Effect of total and pair configurational entropy in determining dynamics of supercooled liquids over a range of densities
• Growing Surface Tension of Amorphous-Amorphous Interfaces on Approaching the Colloidal Glass Transition
• Random-Field Ising like effective theory of the glass transition: I Mean-Field Models
• Static correlations functions and domain walls in glass-forming liquids: the case of a sandwich geometry
• Unifying different interpretations of the nonlinear response in glass-forming liquids
• A general fluctuation-response relation for noise variations and its application to driven hydrodynamic experiments
• Fluctuations and Shape of Cooperative Rearranging Regions in Glass-Forming Liquids
• The Devil is in the details: Pentagonal bipyramids and dynamic arrest
• Collective relaxation dynamics in a three-dimensional lattice glass model
• Third and Fifth Harmonic Responses in Viscous Liquids
• Analysis of the anomalous mean field like properties of Gaussian core model in terms of entropy
• Configurational Entropy of Self Propelled Glass Formers
• Amorphous Order & Non-linear Susceptibilities in Glassy Materials
• Is the glassy dynamics same in 2D as in 3D? The Adam Gibbs relation test
• Static self-induced heterogeneity in glass-forming liquids: Overlap as a microscope