Vogel-Fulcher law of glass viscosity: A new approach
Abstract
Starting with an expression, due originally to Einstein, for the shear viscosity η(δϕ) of a liquid having a small fraction δϕby volume of solid particulate matter suspended in it at random, we derive an effective-medium viscosity η(ϕ) for arbitrary ϕ 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 ϕn + 1 =ϕn+δϕ. 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 (ϕ) and floppy, liquid-like regions (1-ϕ), for ϕ increasing monotonically with supercooling.
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