J. Phys. I France
Volume 7, Numéro 4, April 1997
Page(s) 581 - 598
DOI: 10.1051/jp1:1997177
J. Phys. I France 7 (1997) 581-598

Small Characteristic Length at the Glass Transition Cooperativity Onset

E. Donth, S. Kahle, J. Korus and M. Beiner

Universität Halle, Fachbereich Physik, 06099 Halle (Saale), Germany

(Received 24 June 1996, revised 8 November 1996, accepted 23 December 1996)

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 ( $\Delta_\varepsilon,\;\Delta C_{\rm p}$) and of square root of cooperativity $(N_\alpha^{1/2})$ as function of temperature below the onset. A quasi continuous description is derived from kinetic molelcular 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 $N_\alpha^{\rm min}\approx 1$. 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 $N_\alpha(T_{\rm g})\approx 100$ molecules. A new interpretation of the WLF asymptote lg $\Omega$ is suggested.

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