The shapes of cooperatively rearranging regions in glass-forming liquids

Abstract

The shapes of cooperatively rearranging regions in glassy liquids change from being compact at low temperatures to fractal or "stringy" as the dynamical crossover temperature from activated to collisional transport is approached from below. We present a quantitative microscopic treatment of this change of morphology within the framework of the random first order transition theory of glasses. We predict a correlation of the ratio of the dynamical crossover temperature to the laboratory glass transition temperature, and the heat capacity discontinuity at the glass transition, ∆Cp. The predicted correlation agrees with experimental results for the 21 materials compiled by Novikov and Sokolov.Our increased ability to visualize and experimentally probe supercooled liquids on the nanometer length scale has explicitly revealed the presence of cooperatively rearranging regions 1,2,3,4,5,6,7,8,9,10 (CRR's). The cooperative rearrangement of groups of many molecules has long been thought to underlie the dramatic slowing of liquid dynamics upon cooling and could also explain the non-exponential time dependence of relaxation in glassy liquids. Activated transitions of regions of growing size were postulated in the venerable Adam-Gibbs argument for the glass transition 11 . To move, a region, in the AG view, must have a minimum of two distinct conformational states. Natural as this suggestion is, the sizes predicted from literally applying this notion are far too small to explain laboratory observations. The minimal AG cluster would have only two particles since the measured entropy per particle is of order 1k B at the glass transition.A distinct approach, the random first order transition (RFOT) theory of glasses, is based on a secure statistical mechanical formulation at the mean field level 12,13,14,15,16,17,18,19 but also goes beyond mean field theory to explain the non-exponential, non-Arrhenius dynamics of supercooled liquids through the existence of compact, dynamically reconfiguring regions ("entropic droplets") 20,21,22 whose predicted size is, in contrast to the Adam-Gibbs bound, very much consistent with what has been measured (125-200 molecules), using both scanning microscopy 1,8 and NMR techniques 7,9 , at temperatures near to T g .Computer simulations 3,23,24 and light microscopy studies of colloidal glasses 10 , however, have revealed dynamically reconfiguring regions that are not compact and contain fewer particles. Some investigators describe these regions as "fractal 6 " while others use the term "strings 3 " to characterize them. It has been suggested that such "stringy" excitations should be taken as the fundamental objects in the theory of glass transitions. As we will show, the fractal nature of the dynamically reconfiguring regions in the relatively high temperature regime probed in current computer simulations follows naturally from RFOT theory. To be precise, RFOT theory predicts the shape of the reconfiguring regions changes from compact to fractal as the system is heated from low temperatures, chara...

Thermodynamic signature of growing amorphous order in glass-forming liquids

“…This behaviour is also expected within the RFOT scenario that predicts a vanishing surface tension at the mode-coupling transition T MC , which behaves as a spinodal point. Coherent amorphous order droplets should therefore be fractal around T MC and compact below 30 , which suggests an increase of the effective value of ν as T decreases. A first-principles RFOT computation of q c (R) for the model we simulated would be very instrumental to clarify this issue.…”

Route to calculate the length scale for the glass transition in polymers

“…This value means that CRR possess a compact shape growing in three directions. This hypothesis has been rationalized within the framework of the random first order transition theory [10]. Very recent molecular dynamics simulations in a Lennard-Jones liquid, performed taking into account the motion of all particles [11], also suggest that the structural rearrangement involves the motion of compact regions.…”

Transport properties of glass-forming liquids suggest that dynamic crossover temperature is as important as the glass transition temperature

“…There is a growing body of evidence that, upon cooling, a liquid does not become a glass in a spatially homogeneous fashion (15)(16)(17)(18)(19). The system becomes increasingly spatially correlated due to the growing of characteristic length and time scales of dynamically correlated regions of space as T decreases (9,15,(20)(21)(22)(23)(24). For example, there is an explicit dependence of the α-relaxation time τ on the typical length scale ξ, τ ¼ exp½μξðTÞ∕T , where μ represents a typical free energy per unit length (9).…”