Enhanced cooperativity below the caging temperature of glass-forming liquids

– The utility of a cooperative length scale for describing the dynamics of small molecule glass-formers is shown. Molecular Dynamics and Monte Carlo simulations reveal a distribution of cooperatively moving fractal events below the temperature TA at which dynamics become caged. Guided by these results, four straightforward methods emerge to recognize TA in experimental data and quantify the length scale that grows on cooling below TA. This length scale is consistent with 4-D NMR experiments which are sensitive to the slow moving population. Many liquids either cannot crystallize or crystallize sufficiently slowly that they vitrify below their glass transition temperature Tg. A fundamental understanding of glass formation is still lacking because it has not been firmly established whether the pronounced slowing down is simply kinetic in origin or there is an underlying thermodynamic character [1–6]. This letter shows that there is a natural length scale for cooperative motion that grows as the glass transition is approached. The 1965 model of Adam and Gibbs [1] suggests that there should be cooperative motion in glass-forming liquids. The size ξ of the cooperative volume is related to the configurational entropy of the liquid Sc. At temperatures T , sufficiently above Tg, where the relaxation time τα, and the viscosity η, vary as τα ∼ η/T ∼ exp [E/kBT ], all molecules undergo independent local Brownian movements without signs of cooperativity. As temperature is lowered, the density of the liquid gradually increases and Brownian motion becomes hindered, as neighboring particles block each others attempts to move. This crowding leads to cooperative dynamics [5–9], active for all T below the caging temperature TA. The onset of cooperativity is also accompanied by the observed ‘caging effect’ in the mean-square displacement of a particle between the ballistic and self-diffusive regimes, and a reduction in Sc, causing ξ to grow. These changes result in a progressively stronger temperature dependence of η and τα at lower temperatures. (∗) E-mail: [email protected]