Relations between the sub-molecula and the cooperative scales in the molecular dynamics of the glass-forming liquids

Abstract The molecules of the supercooled liquids in the cooperative molecular dynamics are partitioning to specific dynamic units, known as “beads”. The beads have been defined as the smallest units, forming the heat capacity of the supercooled liquids. The beads appear as a sub-molecular scale in the dynamics of the glass-forming liquids. In the Adam-Gibbs theory the number of molecules, rearranging simultaneously, has been defined as the size of the cooperative rearranging region and these regions form the second larger molecular scale in molecular dynamics. Due to a noticeable discrepancy in estimating the number of beads in the molecules by the empirical rules as well as by theoretical models the relations between these two scales are not well known. Recently, a new thermodynamic method for estimating the number of the beads in the molecules and a rule for the examination of their temperature dependence have been suggested. By these methods 48 low-molecular supercooled liquids are investigated and the relations between these two molecular scales and the structure of the molecules have been found. The estimated number of configuration beads is compared with the number of the structural units (the chemical groups, the ions and the atoms), with the assigned number by the empirical rules and with the ones calculated, based on a Lennar-Jones model of the random first order transition theory. A constant and two kinds of temperature dependence of the number of the beads in the molecules of different liquids have been revealed. A molecular basis, forming the fragility of the supercooled liquids, has been found. From the results obtained, the investigated liquids are classified in several groups following the logical line in the formation of the beads.