Mobile-particle clusters in supercooled liquids become increasingly noncompact as spatial dimension increases

Dynamical heterogeneity has been directly associated with mobile-particle clusters (MPCs) composed of subclusters undergoing cooperative particle exchange in the form of string-like rearrangements. These string-like clusters are of interest since their growth upon cooling closely parallels that of the hypothetical "cooperatively rearranging regions” (CRR) of Adam and Gibbs. Stevenson et al. [Nat. Phys. 2, 268 (2006)] have argued that the structure of the CRR inferred from random first order transition theory should change from fractal at high temperatures to compact at temperatures below the onset temperature for the low temperature regime of glass-formation, where relaxation and diffusion become landscape-dominated. This argument implies that if strings indeed correspond to the CRR, they should undergo a transition from a random-coil-like state to a globular compact state as temperature decreases. Our molecular-dynamics results for supercooled liquids in spatial dimensions 2 ≤ d ≤ 6, however, indicate that neither the smaller MPCs nor the strings show any tendency to become geometrically compact at low temperatures. We also generalize earlier observations by Starr et al. [J. Chem. Phys. 138, 12A541 (2013)] by finding that the geometrical structures of both MPCs and strings are consistent with dynamic clusters that self-assemble into branched and linear equilibrium polymers (with excluded volume interactions) throughout this range of d.