Thermal specific free volume

According to Ferry12 the free-volume per cm of substance, i. e. the fractional free-volume /, is hard to define exactly and should be regarded as merely a useful semi quantitative concept. Specifically, the thermal expansion coefficients of liquids for the most part reflect the increase in fractional free-volume only a small part is connected with the anharmonic dependence of potential energy or interatomic and intermoleeular distances. 

Crosslinking has no specific direct effect on thermal degradation crosslinks can be either weak points (e.g., tertiary carbons in polyester or anhydride-cured epoxies) or thermostable structural units (e.g., trisubstituted aromatic rings in phenolics, certain epoxies, or certain thermostable polymers). Indirect effects can be observed essentially above Tg crosslinking reduces free volume and thus decreases 02 diffusivity. It also prevents melting, which can be favorable in burning contexts. 

If an amorphoiis polymer is cooled it will usually attempt to crystallize, but because of the high internal viscosity of the medium it is often precluded from packing into its lowest energy conformation. At 0 K, the lack of thermal excitation prevents the occurrence of most photochemical reactions. As the temperature is increased, the specific volume of the polymer will also increase as a result of forming "free volume", that is, space vdiich is not occupied by hard-shell dimensions of the atoms comprising the polymeric structure. The amount of free volume will depend to a certain extent on the previous thermal history. As free volume increases along with thermal excitation, various kinds of molecular motions will be observed in the polymer vdiich can be detected by I ysical measurements. 

In contrast to Vf, the specific volume V in the glassy state of the polymer exhibits a larger slope than above Tg, which is due to the thermal contraction of Vocc ( occ,g O.Sag). The agreement of the slope dVld vh) fl-om the phenomenological relation Eq. (11.6) with dVf/d vh) from Eq. (11.5) above Tg we consider as evidence that o-Ps detects precisely the free volume calculated fl om S-S hole theory. The larger slope of dVld vh) below Tg supports the conclusion from the S-S equation of state calculation that Vocc shows here, as distinct from above Tg, a certain thermal expansion. 

If the free volume shows a linear expansion with the temperature, Vf = Ef(T- T ), where Ef=dVf IdT is its specific thermal expansivity and Tq < Tg is the temperature where the (linearly extrapolated) free volume disappears, one obtains from Eq. (11.7) the well-known Vogel-Fulcher-Tammann-Hesse (VFTH) equation [Vogel, 1921 Fulcher, 1925 Tammann and Hesse, 1926] ... 

The question arises as to what is the origin of stabilizing NLO dipole moments in T-polymer and T-polymer 2. One possibility is that the free volume of the polymer matrix provides the free space where the aligned dipole moment can be thermally reoriented. The densities of T-polymer and T-polymer 2 are larger than those of L-polymer and L-polymer 2 as shown in Table III. The larger densities of T-polymer and T-polymer 2 imply smaller free volumes. The free volume Vf can be estimated from the experimentally obtained specific volume V (the reciprocal value of measured density) and the zero point molar volume Vq,... 

The free volume theory originated some years later than the lubricity and the gel theories, when the evolution of different properties of polymers as a function of temperature, specific volume, thermal expansion coefficients, or viscosity was attempted to be explained.The relationships between these properties and some variables corresponding to polymer stracture, such as molecular weight or terminal groups content, the presence of another monomer and, of course, the presence of plasticizers, was also explained. For plasticized polymers the theory attempted to explain the diminution of the glass transition temperature with the plasticizer content. This theory is a contribution of different authors, but it was postulated by Fox and Floiy. The theory is still being used to explain some properties of plasticized polymers, i.e., viscoelastic properties. ... 

---