Iso free volume state

Lipatov, Y. S. The Iso-Free-Volume State and Glass Transition in Amorphous Polymers New Development of the Theory. Vol. 26, pp. 63 —104. 

The Iso-Free-Volume State and Glass Transitions in Amorphous Polymers ... 

The Iso-Free-Volume State at the Glass-Transition Point.77... 

As early as 1950 Fox and Fiery19 put forward the idea that the glass temperature corresponds to the iso-free-volume state. This hypothesis was developed by other authors20 21 and has won wide acceptance. It has been used with minor modifications as the basis for a number of sophisticated theories of the glass-transition... 

On the basis of many experimental data Kanig concluded that the fractional free-volume at Te as usually determined is not a constant, and therefore it is desirable to introduce additional characteristics of the iso-free-volume state. Such characteristics may be represented by the values given by Eq. (54) relating to glass temperature, iPfi and ip 2. In this case it follows that... 

The theory predicts an iso-free-volume state at T , which is equal to T0 of the Vogel equation, but an examination of the calculated values of /g does not indicate that Tg is an iso-free-volume state. 

In addition, in polymeric compositions, i.e. in filled polymers, as a rule a broadening of the relaxation spectra takes place81. All these characteristics are closely associated with molecular parameters and free-volume, therefore it is interesting to consider how structural changes, induced in the same polymer by the action of the solid surface, may influence the applicability of the free-volume concept and the approach to such systems via the iso-free-volume state. In 82 the applicability of the... 

In the case under consideration different physical structures were realized due to the formation of the polymer network in the surface layers the filler surface, as usually happens in filled systems. As is known79, this induces considerable changes in the structure of the material. It is also possible that in these conditions a more defective network structure is formed. These results show that even the purely physical factors influencing the formation of the polymer network in the interface lead to such changes in the relaxation behavior and fractional free-volume that they cannot be described within the framework of the concept of the iso-free-volume state. It is of great importance that such a model has been devised for a polymer system that is heterogeneous yet chemically identical. 

Everything discussed in the present paper shows that the free-volume concept, although very useful from the qualitative point of view, cannot be used for the quantitative description of many properties of polymer systems. This is especially clear when we consider glass-transition phenomena using the idea of the iso-free-volume state. Many experimental data, discussed above, show that this concept cannot be applied even to polymer materials having the same chemical nature but a different physical structure. From the experimental results Goldstein104 had already concluded that the concept of free-volume cannot be correct. These conclusions were carefully discussed later105. ... 

For polystyrene, D = 83 SOOg.mol i, which means that beyond a mass of approximately D, the temperature T is fixed - (T ) = 49.7 0.3°C.Therefore, in the entangled region, the free volume fraction is constant at a given temperature and the iso-free volume state merges into the isothermal state. 

From the vertical shift factor of the master curve, we are able to describe the mass dependence of the zero-shear viscosity in the iso-free volume state which is directly connected to the radius of gyration of the chains. In the molten state, it is generally assumed that the chains exhibit a Gaussian conformation and therefore the viscosity should be proportional to the molecular weight. 

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