The Free Volume in Amorphous Polymers

The glass transition phenomenon has been the object of many molecular theories, that of Ferry [29], further developed by Bueche [30], on the free volume concept being widely accepted in the polymer field. The volume occupied by a chain of amorphous polymer consists partly of free space, i.e., the volume excluded by the movements of segments about their equilibrium position. As shown in Fig. 1.8, the temperature coefficient for the polymer volume at constant pressure dV dT)p is higher for the viscoelastic state (curve b) than for the glassy state (curve a), and it changes abruptly at Tg this is the mathematical definition of the glass transition temperature. It can also be defined as the 

Effect of tricresyl phosphate on the brittle-tough temperature Jb) of plasticized PVC (wi = weight fraction of the plasticizer) [27]. 

V phenyl salicylate tricresyl phosphate o methyl salicylate Q nitrobenzene A chloroform X methyl acetate ethyl acetate ° benzene toluene 

Lowering of the glass transition temperature (Tg) of polystyrene by different plasticizers (wi = weight fraction of plasticizer) [31,32]. 

This simple relation is in very good agreement with the experimental results at high polymer concentration shown in Fig. 1.10 and can be used to predict the effect of a given low-molecular-weight plasticizer on Tg of a concentrated polymer-plasticizer system, provided Tg is known, this quantity being much more difficult to determine than Tg.  

---

In summary, it is clear that the o-Ps lifetime determined via the PALS technique provides accurate information on the apparent mean size of the nanoholes, which comprise the free volume in amorphous polymers. It also seems well established (see Chapter 11) that provided that the noise level in the PALS spectrum is sufficiently reduced, the distribution of o-Ps lifetimes can be obtained, which generates information regarding nanohole-size distribution. Concerns have been raised about the utility of the o-Ps intensity, I3, to characterize the number density of nanoholes and hence the fractional free volume via Eq. (12.2), because the value of I3 can be influenced significantly by the presence of species that inhibit or enhance positronium formation. We feel that we can utilize I3 values to evaluate fl actional free volumes via Eq. (12.2), provided either that the sample is rejuvenated by heating above Tg prior to measurement, and/or experiment indicates that the value of I3 remains constant within experimental error, during the time of exposure to the positron source. 

The correlation between the ionic migration and the local segmental motion of polymer chains may be subjected to closer examination. According to the free volume theory, the free volume in amorphous polymers that occurs above 7g increases in accordance with the temperature difference T — [23]. Because of the enlarged free volume above T, the polymer chain becomes locally mobile. The mode of the micro-Brownian motion is considered to be cooperative, involving several repeat units of the polymer chains. The dielectric relaxation time for the backbone motion of PPO and... 

---