Length scales in glass-forming liquids and related systems: a review

Abstract

The central problem in the study of glass-forming liquids and other glassy systems is the understanding of the complex structural relaxation and rapid growth of relaxation times seen on approaching the glass transition. A central conceptual question is whether one can identify one or more growing length scale(s) associated with this behavior. Given the diversity of molecular glass-formers and a vast body of experimental, computational and theoretical work addressing glassy behavior, a number of ideas and observations pertaining to growing length scales have been presented over the past few decades, but there is as yet no consensus view on this question. In this review, we will summarize the salient results and the state of our understanding of length scales associated with dynamical slow down. After a review of slow dynamics and the glass transition, pertinent theories of the glass transition will be summarized and a survey of ideas relating to length scales in glassy systems will be presented. A number of studies have focused on the emergence of preferred packing arrangements and discussed their role in glassy dynamics. More recently, a central object of attention has been the study of spatially correlated, heterogeneous dynamics and the associated length scale, studied in computer simulations and theoretical analysis such as inhomogeneous mode coupling theory. A number of static length scales have been proposed and studied recently, such as the mosaic length scale discussed in the random first-order transition theory and the related point-to-set correlation length. We will discuss these, elaborating on key results, along with a critical appraisal of the state of the art. Finally we will discuss length scales in driven soft matter, granular fluids and amorphous solids, and give a brief description of length scales in aging systems. Possible relations of these length scales with those in glass-forming liquids will be discussed.

Dynamics of Molecular Crystals by Means of 1H NMR Relaxometry: Dynamical Heterogeneity versus Homogenous Motion

“…As already stated in the Introduction, the Cole–Davidson form of a spectral density represents a stretched exponential correlation function . This form of correlation functions is predicted by the mode coupling theory for liquids of high viscosity and glass‐forming systems (amorphous solids) as a result of molecular interactions described, for instance, by the Lennard–Jones potential . These predictions have experimentally been confirmed for numerous liquids and molecular glasses .…”

“…[17] This form of correlation functions is predicted by the mode coupling theory [29] for liquids of high viscosity and glass-forming systems (amorphous solids) as ar esult of molecular interactions described, for instance, by the Lennard-Jones potential. [30] These predictions have experimentally been confirmed for numerous liquids and molecular glasses. [9] The correlation function describes heterogeneous dynamics with ad istribution of correlation times mathematically expressed in ref.…”

Understanding the dynamics of glass-forming liquids with random pinning within the random first order transition theory

“…In Ref. [29], it was shown that the length scale obtained via the methods mentioned above for three dimensional systems completely explains the finite size effects seen in the relaxation time τ α for all temperatures including high temperatures. So, for the two dimensional systems, we employed the method of finite-size scaling of τ α [30] to obtain the static length scales as the eigenvalue method and PTS methods involve much larger computational efforts to obtain the length scale.…”

Suppressed density of states in self-generated Coulomb glasses

“…The resulting supercooled liquid displays an exponential increase of its viscosity. As such, glasses are inherently nonequilibrium states of matter, even though on any reasonable experimental timescale the material appears to be static [1][2][3][4].…”