Growing range of correlated motion in a polymer melt on cooling towards the glass transition

Many liquids cooled to low temperatures form glasses (amorphous solids) ins tead of crystals. As the glass transition is approached, molecules become l ocalized and relaxation times increase by many orders of magnitude(1). Many features of this 'slowing down' are reasonably well described(2) by the mo de-coupling theory of supercooled liquids(3). The ideal form of this theory predicts a dynamical critical temperature T-c at which the molecules becom e permanently trapped in the 'cage' formed by their neighbours, and vitrifi cation occurs. Although there is no sharp transition, because molecules do eventually escape their cage, its signature can still be observed in real a nd simulated liquids. Unlike conventional critical phenomena (such as the b ehaviour at the liquid-gas critical point), the mode-coupling transition is not accompanied by a diverging static correlation length. But simulation(4 -10) and experiment(11,12) show that liquids are dynamically heterogeneous, suggesting the possibility of a relevant 'dynamical' length scale characte rizing the glass transition. Here we use computer simulations to investigat e a melt of short, unentangled polymer chains over a range of temperatures for which the mode-coupling theory remains valid. We find that although den sity fluctuations remain short-ranged, spatial correlations between monomer displacements become long-ranged as T-c is approached on cooling. In this way, we identify a growing dynamical correlation length, and a correspondin g order parameter, associated with the glass transition. This finding sugge sts a possible connection between well established concepts in critical phe nomena and the dynamics of glass-forming liquids.