Doolittle expression, glass transition

The three most important factors in the equation are the viscosity and the thermodynamic parameters G and Gm- The viscosity can be approximated between the liquidus temperature, Tuq, and the liquid-+glass transition temperature, Tg, by a Doolittle expression involving the relative free volume (Ramachandrarao et al. 1977) while G can be calculated using the relationship... 

These authors were the first FGSE workers to make extensive use of the concept of free volume 42,44) and its effect on transport in polymer systems. That theory asserts that amorphous materials (liquids, polymers) above their glass transition temperature T contain unoccupied volume randomly distributed and in parcels of sufficient size to permit jumps of small molecules — and of polymer jumping segments — to take place. Since liquids have a fractional free volume fdil typically greater than that, f, of polymers, the diffusion rate both of diluent molecules and (uncrosslinked and unentangled) polymer molecules should increase with increasing diluent volume fraction vdi,. The Fujita-Doolittle expression 43) describes this effect quantitatively for the diluent diffusion ... 

Free Volume Theory. Free volume theory suggests that the glass transition temperature is observed for polymers when their viscosity approaches that of their liquid state. Following a derivation based on the Doolittle expression for polymer viscosity (r ) as a function of free volume (Eisenberg, 1984)... 

This is similar to the Doolittle expression for viscosity. It is further assumed that near the glass transition ... 

The appearance of the glass transition results from the reduction of molecular mobility as the temperature falls, slowing the collapse of free volume. We now introduce the concept that the mobility at any temperature depends primarily on the free volume remaining, so that the rates of both bulk and shear deformations can be advantageously expressed in terms of Vf rather than T as the independent variable. This principle was applied long ago to the shear viscosity of simple liquids by Batchinski, and more recently by Doolittle with an empirical equation which was found to represent with high accuracy viscosities of ordinary liquids of low... 

The free volume theories state that the glass transition is characterized by an iso-free volume state, i.e. they consider that the glass temperature is the temperature at which the polymers have a certain universal free volume. The starting point of the theory is that the internal mobility of the system expressed as viscosity is related to the fractional free volume. This empirical relationship is referred to as the Doolittle equation. It is a consequence of the universal William-Landel-Ferry (WLF) equation and the Doolittle equation that the glass transition is indeed an iso-free volume state. The WLF equation, expressed in general terms, is ... 

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