Primary transition

Figure Bl.15.2. The state energies and eorresponding eigenfiinetions (l igh-field labels) as a fiinetion of the applied magnetie field Bq for a system of spin S = 1 and B z, shown for D>0 and E O. The two primary transitions (A Mg= l) are indieated for a eonstant frequeney speetnim. Note that, beeause E O, the state energies vary nonlinearly with Bq at low Bq.

Because the p value is positive, negatively charged carbon ions are considered to be the primary transition state complex (TSC). The TSC will dissociate to a substituted phenol radical and a stable anion. It may also be neutralized by the toluene, resulting in the addition of a proton, H+ (Arai and Dorfman, 1964) therefore, eaq is considered to interact with the ir-orbital of the ring as in electrophilic substitution rather than to affect electron distribution and polarizability of a certain substituent. 

Oefor -motion Hookian Glassy Secondary transition Primary transition Highly elastic rubbery Flow... 

Lowering the frequency shifts the temperature of a transition to a lower temperature (Fig. 6). At one time, it was suggested that multiple frequencies could be used, and the Tg should then be determined by extrapolation to 0 Hz. This was never really accepted as it represented a fairly large increase in testing time for a small improvement in accuracy. For most polymer systems, for very precise measurements, one uses a DSC. Different types of transitions also have different frequency dependencies. If one looks at the slope of the temperature dependence of transitions against frequency, one sees that in many cases that the primary transitions like and Tg have a different dependence on frequency than the lower temperature transitions. In fact, the activation energies are different for ot, (3, and y transitions because of the different motions required and the transitions can be sorted by this approach. ... 

For example, in the case of sulfonated styrene ionomers (34), the peak height of primary transition is much higher than that of secondary transition below the critical concentration, while the hight of secondary transition peak exceeds that of primary transition peak above the critical concentration. 

While the water sensitivity of the 3 peak is generally agreed on, contradictory evidence exists in regard to the a peak. Preliminary evidence from Yeo and Eisenberg (31) suggests that the a peak in Nafion acid might be insensitive to moisture content since water is, by and large, incompatible with the fluorocarbon backbone. However, a very recent study (40), as mentioned before, presents evidence of a definite shift to lower temperature of the primary transitions of Nafion acid and its sodium salt on immersion in water, relative to those obtained in the dry state. 

Figure 3-21. Comparison between master curve of polystyrene and predictions of the modified Rouse theory in the primary transition region.

Another major discrepancy between theory and experiment is exemplified in Figure 3-21. In this figure, the predicted relaxation according to the Rouse theory is compared with an experimental result for polystyrene in the primary transition region. It is clear that polystyrene undergoes its glass-to-rubber... 

Figure 3-22. Relaxation in the primary transition region considering varying numbers of relaxing elements. The elements in the transition region in each case is z - pc.

Solution The mechanical properties of polymers depend on time and temperature. The time dependence is usually expressed as a frequency dependence, which to a first approximation is related to time by 2jt 1) = 1/t where X> is the frequency. The combined dependence of molecular processes of viscoelastic materials on frequency and temperature can be described by an activation energy E, . Ej, is about 100 kcal/mol and 10 kcal/mol for primary and secondary transitions, respectively. This implies that the relaxation processes associated with the molecular motions shift to higher temperatures at higher frequencies however, the secondary transition shifts more than the primary transition. Therefore, if tests are conducted at high frequencies, the resolution between the energy absorption peaks for primary and secondary transitions that are close to each other is poor. Thus, in this case, the P and a peaks, which are relatively distinct at 0.1 Hz, merge at 50 Hz, and there is a shift in the peak to higher temperatures. 

A glass transition occurs for an amorphous polymer when the slope of a plot of specific volume changes abruptly with rise of temperature. The slope itself (the thermal expansion coefficient a), a = [llY] dV/dT, shows a step-change at Tg. A crystalline polymer also shows a transition at the same temperature, due to its amorphous phase. (It will be explained later that only semi-crystallinity may exist and there are almost always amorphous domains.) In the case of a crystalline polymer, however, a primary transition temperature, T, exists, signified by an abrupt change in volume. The specific volume of the crystalline polymer is always lower than that of the equivalent amorphous one because its more compact stmcture increases the density. 

The most common form is the nematic, a bimdle of parallel, long, rodlike molecules. Additional cooling to the primary transition temperature, T leads to solidification into a solid crystalline phase (small crystallites). In the region between Tj and T , a liquid of very low viscosity prevails, in contrast to the high melt viscosity. The aromatic polyesters have high heat distortion temperatures (HDT). Vectra, composed of para-hydroxy-benzoic acid (PHBA) and para-hydroxy-naphtoic acid (PHNA), has an HDT of 180 C-240 C. Xy-dar, composed of PHBA, tera-phthalic acid and biphenol, has an even higher HDT of 260 C-350 C. 

Semicompatible IPN s, on the other hand, exhibit one broad transition (see Figure 8.13). This broad transition may be considered to result from an extensive overlap of the two primary transitions, or, more probably, of transitions of all possible compositions that can contribute independent... 

The area of sub-T or higher-order transitions has been heavily studied [42], as these transitions have been associated with mechanical properties. These transitions can sometimes be seen by DSC and TMA, but they are normally too weak or too broad for determination by these methods. DMA, DEA, and similar techniques are usually required [43]. Some authors have also called these types of transitions [44] second-order transitions to differentiate them from the primary transitions of and Tg, which involve large sections of the main chains. Boyer reviewed the Tp in 1968 [45] and pointed out that while a correlation often exists, the Tp is not always an indicator of toughness. Bershtein [46] reported that this transition can be considered the activation barrier for solid-phase reactions, deformation, flow or creep,... 

In addition, there is one primary transition, usually called the glass transition . 

TABLE 14.1 Primary Transition Temperatures of Selected PLA Copolymers... 

Polymers can also be classified as crystalline, semi-crystalline or amorphous polymers depending on their degree of crystallinity. A crystal is basically an orderly arrangement of atoms in space. Polymers that are able to crystallize imder suitable temperature conditions are called crystalline pol)mers. The primary transition temperature, when a crystalline pol)mer transforms from a solid to a liquid, is the melting temperature designated T . 

The temperature of the midpoint of the primary transition can be roughly specified by the inflection in G (not the point where G 10 dynes/cm as in Chapter 12) or the maximum in tan h or A. Such transition midpoint temperatures have been determined for numerous crystalline polymers, 42,43,46,48-55 nd some are summarized in Table 16-1. (The midpoint temperature Tm should not be confused with the melting point.) Comparison with Table 12-11 indicates that these midpoint temperatures are slightly higher for partially crystalline polymers than for amorphous polymers of the same or similar chemical composition. There is in some cases a perceptible increase ixiTm with degree of crystallinity. It will be recalled that in loaded rubbers, also, the filler increases Tm slightly (Section C4 of Chapter 12). 

An example is shown in Fig. 18-17, where v and attenuation (= 8.686a) at 2 X 10 Hz are plotted against temperature for polyfvinyl acetate), as reported by Thurn and Wolf. Three zones of dispersion are apparent. The one at 93 C undoubtedly represents the primary transition from glasslike to rubberlike consistency, in which o drops by about 50% because of the virtual disappearance of the jG term in equation 13 as it becomes smaller than K by several orders of magnitude. But... 

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