Small characteristic length at the glass transition cooperativity onset

TLDR: In this article, a fluctuation theory approach to a cooperativity onset of the dynamic glass transition is described, and the experimental indications can analytically be reproduced by means of a Landau order parameter expansion adapted to dominance of fluctuation in a free volume approach.

Abstract: A fluctuation theory approach to a cooperativity onset of the dynamic glass transition is described. Recent dielectric and heat capacity spectroscopy (HCS) experiments for several random copolymers of n-butyl methacrylate with styrene indicate a steep linear increase of relaxation intensities (Δe, ΔCp) and of square root of cooperativity (Nα 1/2 ) as function of temperature below the onset. A quasi continuous description is derived from kinetic molecular randomness. This description can be applied to small cooperativity near the onset. The experimental indications can analytically be reproduced by means of a Landau order parameter expansion adapted to dominance of fluctuation in a free volume approach to the dynamic glass transition. An important parameter of the approach is the minimal cooperativity of order Nα min 1. The sharp onset obtained in the extrapolation is associated with the construction of a large conditionality raster. Far below the onset, the size of cooperativity at the glass temperature is theoretically estimated to be of order N α (Tg) 100 molecules. A new interpretation of the WLF asymptote 1g Ω is suggested.