Mixing free volume

It is of interest to return to the values of x,(see Table 6)i The values shown are the times necessary to reach half the total relaxation between the plastic and the rubbery states, shown in log form. The differences in t of a factor of 10 are also an indication of the extent of molecular mixing free volume changes. Hence indirectly, they bear on the trend of impact strengths noted. 

The sum of these expressions represents the entropy of mixing. The result obtained by substituting for the free volumes from Eqs. (13), (14), and (15), is identical with Eq. (10). According to this simple derivation, the terms appearing in Eq. (10) represent contributions to the entropy which originate in the greater spatial freedom of the molecules in the solution. By a simple extension of the derivation to a mixture of polymer species, Eq. (12) may be obtained. 

Deters (14) vibromilled a blend of cellulose and cellulose triacetate. The acetic acid content of cellulose acetate decreased with grinding time (40 h) while that of the cellulose increased, suggesting the formation of a block or graft copolymer or of an esterification reaction by acetic acid developed by mechanical reaction. Baramboim (/5) dissolved separately in CO polystyrene, poly(methyl methacrylate), and poly(vinyl acetate). After mixing equal volumes of solutions of equivalent polymer concentration, the solvent was evaporated at 50° C under vacuum and the resultant product ball-milled. The examination of the ball-milled products showed the formation of free radicals which copolymerized. 

A very interesting approach to the theoretical prediction of the limit value A a Tg was developed in 49. As a result of a thermodynamic consideration of mixing macromolecules with holes and taking into account the free-volume concept, it was shown that... 

The concept of free volume varies on how it is defined and used, but is generally acknowledged to be related to the degree of thermal expansion of the molecules. When liquids with different free volumes are mixed, that difference contributes to the excess functions (Prausnitz et al., 1986). The definition of free volume used by Bondi (1968) is the difference between the hard sphere or hard core volume of the molecule (Vw= van der Waals volume) and the molar volume, V ... 

Figure 7. Local volume fractions of the monomers for two configurations of chains which end up at Z and z-i, respectively (a) simple addition of the volume fractions of the brushes (b) configuration that minimizes the Flory— Huggins mixing free energy for the conditions mentioned in the text.

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