Abstract
Different equations have been proposed for estimating the glass transition temperature of amorphous mixtures. All such expressions lack a term to account for the effect of the entropy of mixing on the glass transition. An entropy based analysis for the glass transition of amorphous mixtures is presented. The treatment yields an explicit mixing term in the expression for the glass transition temperature of a mixture. The obtained expression reduces to the Couchman-Karasz equation in the limiting case where the contribution of the entropy of mixing approaches zero. Equivalent expressions are obtained for the glass transition temperature of a mixture of two glass formers as for the effect of a plasticizing liquid diluent on the glass transition temperature of an amorphous material.
Highlights
A number of expressions have been proposed for estimating the glass transition temperature (Tg) of amorphous mixtures [1,2,3,4,5]
Entropy 2008, 10 eq where Tgm represent the glass transition temperature of the mixture predicted by the equation of interest, the subscripts 1 and 2 denote components 1 and 2, respectively, φ represents the concentration, expressed as either mole (x) or weight (w) fraction, and k is a parameter whose physical interpretation depends on the underlying physical model of the particular equation used
This is noteworthy considering that entropy plays a defining role in glass formation [6, 7]. It follows that the same shortcoming extends to any expression of the form of Equation 1, proposed for the prediction of the glass transition temperature of amorphous mixtures
Summary
A number of expressions have been proposed for estimating the glass transition temperature (Tg) of amorphous mixtures [1,2,3,4,5]. This is noteworthy considering that entropy plays a defining role in glass formation [6, 7]. It follows that the same shortcoming extends to any expression of the form of Equation 1, proposed for the prediction of the glass transition temperature of amorphous mixtures. The question of the entropy of mixing and the glass transition of mixtures has been discussed in the literature [4, 8, 9]. An explicit relationship between the entropy of mixing and the glass transition of amorphous mixtures is still lacking
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