Loss maximum

In the first case, that is with dipoles integral with the main chain, in the absence of an electric field the dipoles will be randomly disposed but will be fixed by the disposition of the main chain atoms. On application of an electric field complete dipole orientation is not possible because of spatial requirements imposed by the chain structure. Furthermore in the polymeric system the different molecules are coiled in different ways and the time for orientation will be dependent on the particular disposition. Thus whereas simple polar molecules have a sharply defined power loss maxima the power loss-frequency curve of polar polymers is broad, due to the dispersion of orientation times. 

Equation (13) also allows to describe the T vs. vd dependence when Ta is replaced by T and Top by T y, i.e. by a hypothetical temperature of the /3d process at vd = 0. The resulting constant k d is a mere characteristic of the curvature of this dependence and cannot be assigned the original physical meaning because there is no process and no corresponding rise in the expansion coefficient for dry PHEMA. It can be seen from Table 2 that T y and k d are dependent on the type of diluent which evidences the role of polymer-diluent interactions. It should be emphasized that is not a characteristic of the polymer itself but of a pair polymer-diluent. This result has also been corroborated for the opposite type of systems, i.e. for different polymers swollen with the same diluent, namely, water. The temperature location of the water-induced /3d loss maxima and its variation with the water concentration clearly depend on the polymer composition (cf. Figs. 13,16-20). 

It has been mentioned in the section on viscoelasticity that dielectric loss maxima are sometimes observed at the same temperatures and... 

Figures 3-5 that the dielectric relaxation again reveals only a single a relaxation for the mixtures. These are, however, noticeably broader than the a relaxation of the pure polymers. The temperatures of the loss maxima, when plotted (Figure 7) as a function of wu the weight fraction of PPO in the mixtures, do not display the smooth monotonic increase in T0 vs. Wi that was shown by both the Vibron and the DSC results. Instead, there is a pronounced increase in Tg above = 0.5 to give a sigmoid curve for this relation. Some reservations should be attached to this observation inasmuch as data for only three polyblend compositions are available nevertheless a qualitatively similar phenomenon is observed in the analysis of the intensity of the y peak (below). Further, if only the stronger maxima in the dynamical mechanical data are considered— i.e.y if the secondary peaks and shoulders which led to the identification of two phases are omitted—then a similar sigmoid curve is found. The significance of this observation is discussed later.

The y Relaxation. In common with many other polymers (8) both PPO and PS display significant loss maxima below room temperature at the frequencies under consideration. Whereas the process responsible for the a loss is at least qualitatively understood in terms of a main chain relaxation associated with the glass transition, y losses can often only tentatively be attributed to specific mechanisms. In PPO, for example, it does not seem unreasonable to propose that the y loss is associated with librations in the two pendant methyl groups this view is somewhat reinforced by the observation that in the dielectric measurements the relaxational strengths of the y and a loss processes are comparable. As the latter can be well interpreted (6) in terms of a dipolar relaxation of the main chain in which the entire dipolar contributions arise from the methyl groupings, it seems plausible to assume that the same dipoles are responsible for the y loss mechanism. In polystyrene there is a similar... 

Figure 8. Loss maxima as a function of reciprocal temperature for dynamical mechanical open squares] and dielectric loss [filled circles] measurements of a and y peaks. The numbers correspond to the composition, wt % of FFO, in...

The present dielectric results show that for corresponding frequencies the temperatures of the y loss maxima for pure PPO and PS are extremely close. At 100 Hz, for example, these occur at —116° and —119°C, respectively. Further, the temperature but not intensity of the PPO y peak is somewhat sensitive to sample preparation and could be shifted upwards by 5°-10° by increasing the annealing temperature from 180° to 210 °C. Even though annealing was conducted in vacuo, this indicates the possibility of the y peaks arising at least in part from polar species introduced as a result of oxidation. As has already been observed, the dynamic mechanical y loss peaks are uniformly weak, but as far as can be observed, the peak temperatures again are consistent with the dielectric data. 

Because the y loss maxima of the constituent polymers are so close in temperature, we would not expect to find any change in this parameter in the mixtures, and indeed none was observed. The maxima in pure PPO are somewhat stronger than in PS at 1 kHz, the c"max are 2.5 X 10 3 and 9 X 10"4, respectively. Consequently, it is not unexpected also to find a uniform change in the c"max values for the mixtures roughly proportional to the respective compositions. More information, however, can be obtained by considering the relaxational strengths themselves—i.e., of the areas under the loss peaks. The values of eR — were obtained from the following equation (10) ... 

Dynamic viscoelastic and stress-optical measurements are reported for blends of crosslinked random copolymers of butadiene and styrene prepared by anionic polymerization. Binary blends in which the components differ in composition by at least 20 percentage units give 2 resolvable loss maxima, indicative of a two-phase domain structure. Multiple transitions are also observed in multicomponent blends. AU blends display an elevation of the stress-optical coefficient relative to simple copolymers of equivalent over-all composition. This elevation is shown to be consistent with a multiphase structure in which the domains have different elastic moduli. The different moduli arise from increased reactivity of the peroxide crosslinking agent used toward components of higher butadiene content. 

Comparison of the positions of the loss maxima leads to some interesting observations. In all binary blends, which differ by more than 20 percentage units in component composition, the E" maxima occur within a few degrees of their position in the components. The maxima in tan 8... 

Column 9 identifies corresponding loss maxima of the components (C) with those observed in the blend (B). 

It is difficult to assess to what extent the imperfect fits obtained by the equivalent models are the result of partial miscibility. This is because the models do predict minor shifts in the loss maxima, which are in the same direction as the shifts expected from partial miscibility. Thus the major cause of the deviations may well be the inability of the models to describe a complex morphology with a single adjustable parameter. 

The dynamic mechanical properties of four 2,6-T-2P samples containing from 19 to 43 wt% hard segments are summarized in Figure 10. A low temperature s relaxation is apparent at about — 70°C for all compositions examined. The transition temperatures of these loss maxima and the associated activation energies are given in Table III. A second process, the c relaxation, can be noted as a shoulder on the high temperature side of the 8-loss maximum. The conclusion of this relaxation is marked by a change in slope of the loss modulus vs. temperature plots... 

FIG. 13.26 Arrhenius plot for the loss maxima of poly(cylohexyl methacrylate) (PCHMA), poly(cyclohexyl acrylate) (PCHA) and cyclohexanol (CHOH).The maxima are obtained from tan <5 vs. Tcurves. From Heijboer (1972). 

Relaxations observed in polymers show broader dispersion curves and lower loss maxima than those predicted by the Debye model, and the (s" s ) curve falls inside the semicircle. This led Cole and Cole (1941) to suggest the following semi-empirical equation for dielectric relaxations in polymers ... 

A value E 12.4 1.5kcal mole" was obtained. Since this value Is comparable with the values of energy barriers to rotation observed for aromatic ketones (measured In a polystyrene matrix) which also show loss maxima around SxlO Hz, It Is... 

As a consequence, a system containing particles of different shape will exhibit a sequence of loss maxima, centered at frequencies lower than that at which occurs the maximum loss for spheres. 

Figure 5. Transition temperatures from loss maxima (1 Hz) for the blends of Fig. 7 as a function of wt % ionomer. Open triangles ionic transition temperatures from loss nKxiuli...

Polyethylene samples were also exposed to conditions which created 0.4% clustered water and dielectric data taken at low temperatures on the samples. The same loss maximum noted In polycarbonate and polysulfone near -100 C at 1 kHz was also noted In polyethylene. A special polyethylene sample was molded around a PTFE sheet. The PTFE was removed and replaced with distilled water. This sample was equivalent to a thin water layer between polyethylene sheets. The dielectric behavior of this sample was quantitatively equivalent to that of the polyethylene containing spherical clusters of water if the difference in geometry of the water phase is taken into account. Figure 7 shows the logarithm of the frequency of loss maxima due to water clusters versus reciprocal temperature for polyethylene, polycarbonate, poly(vlnyl acetate and polysulfone. The polysulfone data from Allen are shown for comparison and It Is seen that the data can be Interpreted as a single mechanism with an activation energy of 7 kcal/ mole. 

Figure 7. Dielectric loss maxima due to clustered water in various host polymers...

Figure 9. PVAc dielectric beta transition loss maxima vs 1/T as a function of...

A mat of nylon 6 crystals from 0.05% glycerol solution exhibits (42) loss maxima at 150°, 230°, and 410°K. (102 c.p.s.). The lower two maxima are similar to those found for melt-formed samples. The major maximum at 410°K. is 60° higher than the major loss peak for melt-formed samples and is therefore believed to be caused by a different mechanism. Other nylon 6 samples show (42) a loss modulus shoulder at 470°K. (102 c.p.s.) near the melting point, and therefore the motion responsible is believed to take place in the crystalline regions, while the 410°K. peak is ascribed to motion in a metastable crystalline phase made up of a mixture of the a and 7 forms (42). 

At least two T minima and two loss maxima are apparent in Figure 2, indicating the existence of at least three different mechanisms. Nonexpotential magnetization decay curves, decomposable into two parts each associated with a separate T value, were observed for P4MP1 crystals from 77°-170°K. The occurrence of two spin-lattice relaxation mechanisms at... 

A reproducible base-line drawing procedure and a kind of peak deconvolution procedure is necessary to determine the area of this rubber loss maximum and that of the original PP relaxation maxima. A computerised deconvolution program for the separation of overlapping DMA loss maxima was described by... 

Measuring the dielectric loss maxima as a function of the temperature at a number of discrete frequencies provides the data for an Arrhenius plot i.e. ln( ) versus 1/T(max.). According to equation 5.14 and w(max.).r =1, an experimental activation energy value can be calculated from the slope of this curve ... 

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