Iso free volume

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

It was also noted by Farrington and co-workers that the chemical nature of the end-groups may have a substantial effect on the viscosity of bulk dendrimers, even under iso-free volume conditions [49]. This seems consistent with the establishment of interdendrimer interactions and supramolecular organization at rest in the bulk state. However, as in most other areas of dendrimer rheology, more data are desirable before definite conclusions can be drawn. 

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... 

K i being a constant independent of other material properties (iso-free-volume concept of Tg). 

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... 

It is understood that this equation should correspond to the empirical SB equation if K were a constant, i.e. if ip, in accordance with iso-free-volume theory were a constant value and parameter a the same for all polymers. 

In the light of the above results the concept of iso-free-volume at Tg cannot be considered proved, and indeed, it is in contradiction with many experimental data. This is why some authors41,44 have developed new ideas according to which liquids and polymers at Tg are in a state of isoviscosity (isoviscous state), not necessarily in the free-volume state. In connection with this we should like to note that some improvements to the SB rule were proposed55 in the form ... 

The expressions in brackets are the expansivities above and below Tg. The constant K3 is a function of bond type in chains and is really constant for every class of polymers. The physical interpretation of this equation may be consistent with the iso-free-volume concept. However, we believe that the introduction of this equality is in practise a denial of the concept. There are also other arguments against this concept. Kastner56 found, for example, that dielectric losses diminish during the isothermal volume contraction, which indicates a dependence of relaxation times on free-volume. However, if we assume that relaxation time depends exclusively on free-volume, the calculated reduction factor differs from the experimental one. 

To prove the concept of iso-free-volume, some attempts were made to determine /g directly from experiment. In 60 free-volume was determined from the difference in specific volume of a polymer in bulk and in solution. It was found... 

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. 

From the point of view of the applicability of the iso-free-volume concept, it is of great interest to test it for some systems more complicated than simple polymeric liquids, despite the fact that, as we have already shown, this concept has failed in many cases even for simple polymers. The more complicated cases considered are compositions and polymeric blends and alloys. 

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. ... 

Figure I 1.7. Variation of viscoelastic scaling factors with gas content for PS-C02 and PDMS-C02 systems. Lower scaling factor values for PS-C02 system, compared with PDMS-C02 system, are due to the closer proximity of the experimental temperatures to Tg of the pure polymer. The top curve displaying results for iso-free volume dilution of high-Mw polystyrene by low-Af polystyrene represents the effect on viscosity of volumetric dilution of high-Mw chains. Viscosity reductions for polymer-gas systems are significantly lower than the iso-free volume dilution curve, indicating that viscosity reduction is primarily due to free volume contributed by dissolved gas.

A simplified version of the free volume theory, considering that Tg is an iso-free volume point and that the free volume absorbed by one crosslink is independent of the crosslink density, leads to (Fox et al., 1955) ... 

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