Entropy of Mixing and the Glass Transition of Amorphous Mixtures

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.

Thermal properties in strong hydrogen bonding systems composed of poly(vinyl alcohol), polyethyleneimine, and graphene oxide

“…So, the strengthened hydrogen bonding produced by mixing may induce a decrease of the configurational entropy in the blend at melt state. This may lead to the abnormal increase of T g s. Pinal [22] has extended the classical thermodynamic approach of Couchman-Karasz to a hydrogen bonding system and has obtained following expression. (2) where T gm is the glass transition temperature of the mixture obtained experimentally, T CK is defined in Eq.…”

“…DC pi is the difference in the heat capacity of the liquid and the heat capacity of the glass forms of component i. Molar volumes of the repeating unit of PEI (V 1u = 36.11 cm 3 /mol) and PVA (V 2u = 32.28 cm 3 /mol) were bonding itself is exothermic. Pinal [22] have extended the classical thermodynamic approach of Couchman and Karasz [42] to the hydrogen bonding system, and reached the conclusion that the abnormal increase of T g is due to the negative entropy of mixing. Either case, the negative entropy of mixing or endothermic enthalpy of mixing is certainly abnormal behavior induced by strong hydrogen bonding.…”

“…Hydrogen bonding in polymer blends has been of interest to polymer scientists for several decades [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. One major characteristic in such systems is the large positive deviation of glass transition temperature (T g ) from conventional mixing rules [22,23,26,35].…”

“…One major characteristic in such systems is the large positive deviation of glass transition temperature (T g ) from conventional mixing rules [22,23,26,35]. It is well known that miscible binary blends exhibit a single T g between the T g s of their individual component polymers.…”

Experimental evidence for excess entropy discontinuities in glass-forming solutions

“…Albeit this effect might be small in many compatible polymer systems, it could change T g in multi-component mixtures as shown here considerably. In a different approach, Pinal 33 interprets the deviation from the Couchman-Karasz equation as "a result of the liquidaccessible configurational entropy of mixing," which is the part of the configurational entropy that gets consumed upon cooling until glass transition occurs.…”