Glycerol is a glass-forming liquid with

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Solid State Physics, Ch Solids without a lattice: glasses and quasicrystals

Problem

T_g = 190\,\mathrm{K}

, defined by

\eta(T_g) = 10^{12}\,\mathrm{Pa\,s}

. A separate viscometry measurement gives

\eta = 10^{10.64}\,\mathrm{Pa\,s}

T = 195\,\mathrm{K}

. ((a)) Using these two points, estimate the fragility index

m = \left.\dfrac{{\rm d}\log_{10}\eta}{{\rm d}(T_g/T)}\right|_{T_g}

by a finite difference, and say whether glycerol behaves as a strong or a fragile liquid, comparing your value with

m\approx20

for silica and

m\approx81

for o-terphenyl. ((b)) Using the relation between

m

and the shift of

T_g

per decade of cooling rate, predict the shift in

T_g

produced by cooling six decades faster.

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