Free volume models superpositioning

Time-temperature superpositioning was originally derived from free volume models, which assume that the rates of molecular motions are governed by the available unoccupied space. Early studies of molecular liquids led to the Doolittle equation, relating the viscosity to the fractional free volume, f =V /(V - Vo), where V is the specific volume and Vo is the occupied volume normalized by the mass) (Doolittle and Doolittle, 1957 Cohen and Turnbull,... 

Trapping of particles A by B is described as earlier in terms of the black sphere model (3.2.16). A model of particle reproduction by division (8.2.6) along with a simplification of integral terms has also the following advantage. Creation of particles, as it was shown in Chapter 7 leads usually to the problem of the proper account of free volume available for particles A the superposition approximation is valid here only for small dimensionless particle concentrations. In our treatment of the reproduction this problem does not arise since prey animals A appear near other A s which are outside the... 

The fundamental concept of the material clock or reduced time is similar to the principle described above in the discussion of time-temperature superposition. In the mechanical constitutive models, however, the change in the stress or deformation induces a shift in the material relaxation time. The fact that the time depends on the state of stress (or strain) or on its history leads to additional non-linearities in behavior from what is expected with, eg, the K-BKZ model. Physical explanations for the shifting material time are often based on free-volume ideas that are often invoked to explain time-temperature superposition. In addition, entropy changes have been invoked as have stress-activated processes. 

Low values of the heat of water absorption can be obtained. These values smaller than the liquefaction energy may result from the superposition of an endothermal mechanism breaking of some bonds (4), further cristallization of the polymers (5), expansion of the macromolecules with change of volume. For this last case, which does not correspond to an expansion mechanism described by the Flory model one has to take into account the enthalpy and free energy of expansion (6,7) or the internal pressure due to the polymer (8). 

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