Lindemann-like size-independent glass-transition criterion for polymers

It is well known that the intrinsic melting mechanism is independent of crystal size according to Lindemannʹs melting criterion. In order to probe whether the glass transition mechanism is also size-independent, segment dynamics of free-standing polystyrene (PS) films is determined by considering the temperature- and thickness-dependent number of styrene segments Nα(T,D) in the cooperative rearranging region (CRR). Under the help of Adams–Gibbs glass transition theory and molecular dynamics simulation, Nα(T,D) function is established and it decreases as D decreases or T increases. However, Nα[Tg(D),D] at the glass transition temperature Tg(D) is size-independent, which is consistent with the simulation results obtained by Donthʹs method. Meanwhile, its relative temperature function Nα{[T − Tg(D)]/Tg(D)} is also size-independent. Therefore, Nα[Tg(D),D] function as a criterion for glass transition, which describes the physical nature of the glass transition, is similar to the vibrational amplitude in Lindemannʹs melting criterion.