Retardation spectra reduced

Reduced retardation spectra, Lp, calculated from the creep compliance Jpit/ar) curves shown in Fig. 18, are presented logarithmically in Fig. 19 as a function of the logarithm of the reduced retardation time, ijax. The chosen reference temperatures bring the short time spectral contributions together, showing the similarity between the networks of different chain density. The... 

FIGURE 5.14 The logarithm of the reduced retardation spectrum, Lp, shown as function of the logarithm of the reduced retardation time, A./uj , for the three urethane-end linked polybutadiene elastomers, (o) TB-1, ( ) TB-2, ( )TB-3. The response has been reduced to corresponding state temperatures of 74°C, 0°C, and 17°C, respectively, for the primary softening transition. 

Fig. 2.27. Recoverable-compliance, Ji(t), data of PPMS 5000 at temperatures -32.2°C ( ), -35.0°C U),-38.6°C (t),-40.0°C ( ), -41.1 °C (x), -42.6 °C n, -44.5 °C ( ), -45.2 °C (V), -46.9 °C (A), and -50 °C (o). The data taken at different temperatures have been shifted horizontally along the log t axis by a temperature-dependent shift factor log ut in order to superpose the curves at the short-time end with the data for -35.0 °C. The inset shows the retardation spectrum, L, as a function of the reduced retardation time X with reference temperature To = -35.0 °C, which was obtained numerically from J lf) data.

Fig. 2.31. The logarithm of the retardation spectrum L of poly(methyl methacrylate) as a function of the logarithm of the reduced retardation time r/ar. The solid curve was calculated from the reduced Jr(t) curve obtained from creep data taken at lower temperatures (14.4-34.7 °C) and longer times (10° s < r < 10 s) and shifted to 13.1° C. The dashed line was calculated from the dynamic compliances obtained by Williams and Ferry at higher temperatures and frequencies To was chosen to be 10.8 °C. From [217] by permission.

FIG. 3-7. Retardation spectrum for a styrene-butadiene rubber (curve Vll of Fig. 3-4), reduced to 2S°C and plotted linearly against log t to illustrate partial integration by equation 33 to determine Js 1.13 X 10" cm /dyne. 

FIG. 13-6. Logarithmic plot of retardation spectrum reduced to -30 C for poly(cis-isoprene) with molecular weight 1.75 X 10 (dotted curve) and 3.95 X 10 (solid curve). (Nemoto, Odani, and Ku-rata. ) Reproduced with permission from Macromolecules, 5,531 (1972). Copyright by The American Chemical Society. 

FIG. 13-16, Retardation spectrum of conventional poly(methyl methacrylate) with = 7.6 X 10 reduced to 120 C. (Plazek, Tan, and O Rourke. ) Reproduced, by permission, from Plazek/Rourke, Rheol. Acta, 13, 367 (1974), Stcinkopff Verlag, Darmstadt. 

FIG. 15-3. Recoverable shear creep compliance and retardation spectrum of l 3 5-tri-a-naphthyl benzene, reduced to 64.2°C from measurements at that temperature and above (open circles) and at four other temperatures as indicated. (Points for spectrum calculated in several different ways.) (Plazek and Magill. )... 

FIG. 15-9. Loss tangent for secondary relaxation mechanism in poly(<7clohexyl methacrylate), reduced to —60 C from data of Heijboer measured from —90 to —42 C. Open circles, from torsion G"IG ) closed circles, from flexure ( "/ ). Dashed line is prediction from a single-line retardation spectrum with constants adjusted to make the maximum coincide dotted line, loss tangent of poly(methyl methacrylate) from Fig. 15-6 adjusted to same location of maximum on frequency scale. 

Figure 5.7 Storage and loss moduli versus reduced frequency for poly(vinyl acetate) with a very narrow MWD as calculated from creep data using the retardation spectrum as an intermediary (logarithmic scales). It was not possible to achieve superposition over the entire range of frequencies, and two shift factors were used to deal with data in high and low-frequency zones.The reference temperature is 60 °C. All the relaxation zones are clearly exhibited. From Plazek [31].

Figure 5.10 Retardation spectrum of the poly(vinyl acetate) of Figs. 5.7 and 5.8 versus reduced time (logarithmic scales). The slope is 1/3 in the glassy region reflecting Andrade creep.The plateau zone is between the two peaks, the second of which marks the start of the terminal zone. It was not possible to obtain superposition using a single reference temperature, and different values were used in short and long-time zones.This is reflected in the difference between the curves obtained with = 35 X (dashed line) and with 60 X (points). From Plazek [31].

The infrared ellipsometer is a combination of a Fourier-transform spectrometer (FTS) with a photometric ellipsometer. One of the two polarizers (the analyzer) is moved step by step in four or more azimuths, because the spectrum must be constant during the scan of the FTS. From these spectra, the tanf and cosd spectra are calculated. In this instance only A is determined in the range 0-180°, with severely reduced accuracy in the neighborhood of 0° and 180°. This problem can be overcome by using a retarder (compensator) with a phase shift of approximately 90° for a second measurement -cosd and sind are thereby measured independently with the full A information [4.315]. 

The function Q(o-) is similar to the slit function which distorts lines in spectra collected on dispersion instruments. Q(instrument line shape and can be varied by changing the maximim optical retardation L or by changing the form of a(8). Figure 3 shows several choices for the apodization function and the resulting instrument line shape for each. It can be seen that the width of the instrument line shape is proportional to 1/L. Thus, the larger the optical retardation, the narrower the spectral lines become. For the case where a(8) = 1 for all 8 between 0 and L, the narrowest lines are achieved, but the side-lobes or "ringing" are most severe. When many absorption or emission lines in a spectrim are convolved with this instrument line shape, the spectrum can become difficult to interpret. Therefore, a compromise is usually reached between an apodization function a(8) which produces narrow spectral lines and one which reduces the side-lobes. 

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