Frozen free-volume fraction

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)]. 

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. 

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. 

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-... 

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]

The kinetics of spiropyran and azobenzene photoisomerization deviate from first order when these dyes are entrapped in a solid matrix below Tg.24-34 This behavior has been attributed to the presence of a distribution of free volume within the matrix, as shown in Table 3.11 .35 When the probe is located in sites of free volume Vf greater than the critical volume for isomerization Vfc, the reaction proceeds at the same rate as in solution. For sites of Vf < Vfc, the reaction is retarded, since it becomes controlled by the matrix molecular motions. At low temperature, the local molecular motions are frozen and fluctuations of local free volume become increasingly small as the temperature decreases. Consequently the fraction of sites where Vf < Vk increases. 

As shown in Figure 2.1, the frozen fraction of the free volume, FF = FF(Tp, follows the same dependence whether T changes are caused by the polymeric chemical structure or imposed pressure. The observed, general dependence follows the relation ... 

Figure 2.1. Frozen fraction of free volume vs. glass transition temperature. Full triangles — values for different polymers at ambient pressures [Simha and Wilson, 1973], Squares — PS data at pressures P = 0 - 400 MPa (data [Rehage, 1980] calculations [Utracki and Simha, 1997]).

From the fundamental point of view, the glass transition reflects a change in the molecular mobility upon cooling, and it is associated with freezing of a portion of the free volume. However, the frozen fraction depends on the absolute value of T — as its absolute value increases more... 

Free volume frozen fraction, FF 131-132,137,187 Free volume lattice model 128-132,138-142... 

FIGURE 6.7 Free-volume frozen fraction versus pressure for three PS samples differently vitrified 1, the standard isothermal method of dilatometric tests 2, isobaricaUy cooling from about Tg + 30°C to ambient, then reheating, increasing P, and so on 3, isobaricaUy heating from 30 to 240°C in 170 temperature-steps at each level of pressure. (From Utracki... 

The simplified procedure starts with computation of the characteristic P, 1, V parameters from the PVT data at T> Tg. Next, from Eqs. (14.2) and (14.3), the fictitious hole fraction in the glassy state at T < Tg and P (a prime indicates an independent variable in the vitreous state) is calculated as /lextrapoi = ( P )-Subsequently, from the PVT data at T < Tg, using Eq. (14.2), the hole fraction in the glassy state, hgu = h(T, P ), is computed. Thus, for the same set of T, P, the hole fractions that the melt would have, /lextrapoi, and the factual one, /igiass > extrapoi, are determined. From the isobaric values of h versus T, the frozen fraction of free volume is calculated as [McKinney and Simha, 1974]... 

FIGURE 14.19 Pressure dependence of the free-volume frozen fraction for PS and its PNC. 

In the vitreous region the V versus T slope depends on P and the MMT content for PS resins it is positive, but as P and the clay content increase, its value decreases toward negative. In consequence, the apparent free-volume frozen fraction, FFt, changes from about 0.6 for PS to 1.6 for PNC-17 at 160MPa. The value of FF at ambient pressure, FF/>=o.i, and its first derivative with respect to P also show local extrema at the concentration of free PS disappearance, Wmax-... 

By comparing the sorption and transport behavior of small molecules in an as-cast, disordered, isotropic sample with those of an annealed, ordered, frozen liquid crystalline sample, the effect of axial ordering on sorption and transport properties may be determined unambiguously. Moreover, the influence of axial ordering on other properties (e.g. density, fractional free volume, glass transition temperature, and free volume accessible to orthoPositronium) may be determined. 

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