Distribution of Free Volume in a Glass

Kinetic plots for the ring closure reaction for 8-bromo-2,2 -dimethyl-6-nitro-l -phenyl-(2H-[l]benzospiropyran-2,2 -indoline) in PMMA at (1) 17 °C, (2) 30.2 °C and (3) 42.0 °C. 

The longer time kinetics has to allow for the free volume being created next to the molecule to allow for the ring closure. To describe the process it is necessary to allow for there to be a distribution of free volume in the system and this is best described by a distribution function Z p) which has the form 

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