Vogel-Fulcher law of glass viscosity: A new approach
arXiv:cond-mat/0407688
Abstract
Starting with an expression, due originally to Einstein, for the shear viscosity \textit{$η$}(\textit{$δÏ$}) of a liquid having a small fraction \textit{$δÏ$}by volume of solid particulate matter suspended in it at random, we derive an effective-medium viscosity \textit{$η$}(\textit{$Ï$}) for arbitrary \textit{$Ï$} which is precisely of the Vogel-Fulcher form. An essential point of the derivation is the incorporation of the excluded-volume effect at each turn of the iteration \textit{$Ï$}$_{n + 1 =}$\textit{$Ï$}$_{n}$\textit{+$δÏ$}. The model is frankly mechanical, but applicable directly to soft matter like a dense suspension of microspheres in a liquid as function of the number density. Extension to a glass forming supercooled liquid is plausible inasmuch as the latter may be modelled statistically as a mixture of rigid, solid-like regions (\textit{$Ï$}) and floppy, liquid-like regions (1-\textit{$Ï$}), for \textit{$Ï$} increasing monotonically with supercooling.
5 pages, 1 figure