Frozen free volume

Fig. 3.26 Equilibrium and frozen free volumes of a polymer in the vicinity of the glass transition temperature.

Solid body. In amorphous systems, calculate the hole fraction in the vitreous state, h = h P and then the pressure and composition dependencies of the frozen free-volume fraction, FF = FF(P, w). The semicrystalline systems must be treated as supercooled liquids (described by the S-S equation of state) comprising dispersed crystals, described by the Midha-Nanda-Simha-Jain equation of state [see Eqs. (6.32) to (6.34)]. 

Many physical properties change in the vicinity of Tg (it is really a region), the most prominent being the dynamic ones. A transition between two dynamic states occurs in the amorphous phase—between the "glassy" state, wherein the mobility of chain fragments is frozen (frozen "free volume") and the elastic state wherein the chain mobility increases upon the rise of temperature (the free volume increases and viscosity decreases, respectively). (Free volume is defined as the difference between the volume of the liquid phase and the extrapolated value at absolute zero temperature.) It is customary to define the transition (TJ when a fraction of frozen free volume of 2.5% appears, and stays constant at lower temperatures. There is no "real" solidification, however, but a frozen liquid. The rate of the measurement (or the fre-... 

The existence of T (or other transitions) is associated with the rotation of side groups or other well defined fragments of the mer, thus releasing some additional frozen free volume at temperatures below Tg. It is obvious, that the various transition temperatures have a paramount effect on the polymer performance. Aroxmd Tg many parameters are drastically changing, such as... 

The viscosity dependence of intramolecular excimer formation is complex. As in the case of molecular rotors (Section 8.2), most of the experimental observations can be interpreted in terms of free volume. However, compared to molecular rotors, the free volume fraction measured by intramolecular excimers is smaller. The volume swept out during the conformational change required for excimer formation is in fact larger, and consequently these probes do not respond in frozen media or polymers below the glass transition temperature. 

In a series of papers, Diphant has been used to probe the microviscous properties of various polymer oils, and free volume parameters have been extracted. 4,88 90) In a comparative study of Excimer and TICT probes, it could be shown that the response of these probes is frozen out at lower temperatures, as can be expected from the large reaction volume necessary, whereas the TICT reaction still shows sizable rates at these high-viscosity conditions. (26) Moreover, this study also showed that the free volume fraction measured by the TICT probes is larger than that measured by Excimer probes. 

Later Kanig took into account the temperature dependence of the fractional free-volume, calculated according to his equations. Below Tg, as temperature decreases, sPfl increases as a result of a decrease in expansion volume at frozen hole volume. Above Tg, pn increases due to the sharp rise in hole volume. At Te the value ip i is at its minimum. From the condition d [Pg.75]

For a fixed strain rate, a comparison of Eq. (74) and experimental data [51, 52] of miscible blends is shown in Fig. 32. Curves 1 and 2 represent, respectively, the PPO/PS blends in compression, and the PPO/PS-pCIS blends in tension.Table 2 lists the three parameters fjf2, CK, and A/f2 used in curves 1 and 2. The unique feature here is the presence of a maximum yield (or strength) for 0 <

nonequilibrium interaction (A < 0). Such phenomenon does not occur in incompatible blends or composite systems. Table 2 also reveals that the frozen-in free volume fractions which are equal to 0.0243 and 0.0211 for polystyrene and for PPO, respectively. These are reasonable values for polymers in the glassy state. In the search for strong blends, we prefer to have —A/f2 > 1, and a larger difference between the yield stresses of blending polymers. 

The free spaces where Ps can form and o-Ps can have a reasonably long lifetime may be extrinsic defects, as just illustrated, or intrinsic defects, such as created when heating a pure solid compound. More generally, they may correspond to the natural voids present in any solid matrix (e.g., "free volume" in polymers, treated elsewhere in this book). Ps can be formed not only in molecular solids, including frozen liquids, but also in a number of ionic solids, even when the open spaces are rather small. For example, Ps is formed in such a highly packed lattice as KC1 [44, 45] where the largest space available corresponds to the tetrahedral sites circumscribed by 4 Cf anions, with a radius of only 0.0845 nm, resulting in an o-Ps lifetime of about 0.65 ns. 

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