Poly frequency

An analogous variation of frequency of the nonnal inodes occurs in poly atomics. 

The analogous coupling between the antisyimnetric stretch and bend is forbidden in the H2O Hamiltonian because of syimnetry.) The 2 1 resonance is known as a Femii resonance after its introduction [ ] in molecular spectroscopy. The 2 1 resonance is often very prominent in spectra, especially between stretch and bend modes, which often have approximate 2 1 frequency ratios. The 2 1 couplmg leaves unchanged as a poly ad number the sum ... 

Figure 3.16 Some experimental dynamic components, (a) Storage and loss compliance of crystalline polytetrafluoroethylene measured at different frequencies. [Data from E. R. Fitzgerald, J. Chem. Phys. 27 1 180 (1957).] (b) Storage modulus and loss tangent of poly(methyl acrylate) and poly(methyl methacrylate) measured at different temperatures. (Reprinted with permission from J. Heijboer in D. J. Meier (Ed.), Molecular Basis of Transitions and Relaxations, Gordon and Breach, New York, 1978.)...

The time-temperature superpositioning principle was applied f to the maximum in dielectric loss factors measured on poly(vinyl acetate). Data collected at different temperatures were shifted to match at Tg = 28 C. The shift factors for the frequency (in hertz) at the maximum were found to obey the WLF equation in the following form log co + 6.9 = [ 19.6(T -28)]/[42 (T - 28)]. Estimate the fractional free volume at Tg and a. for the free volume from these data. Recalling from Chap. 3 that the loss factor for the mechanical properties occurs at cor = 1, estimate the relaxation time for poly(vinyl acetate) at 40 and 28.5 C. 

Electrical Properties. AH polyolefins have low dielectric constants and can be used as insulators in particular, PMP has the lowest dielectric constant among all synthetic resins. As a result, PMP has excellent dielectric properties and alow dielectric loss factor, surpassing those of other polyolefin resins and polytetrafluoroethylene (Teflon). These properties remain nearly constant over a wide temperature range. The dielectric characteristics of poly(vinylcyclohexane) are especially attractive its dielectric loss remains constant between —180 and 160°C, which makes it a prospective high frequency dielectric material of high thermal stabiUty. 

When dipoles are directly attached to the chain their movement will obviously depend on the ability of chain segments to move. Thus the dipole polarisation effect will be much less below the glass transition temperature, than above it Figure 6.4). For this reason unplasticised PVC, poly(ethylene terephthalate) and the bis-phenol A polycarbonates are better high-frequency insulators at room temperature, which is below the glass temperature of each of these polymers, than would be expected in polymers of similar polarity but with the polar groups in the side chains. 

In the case of polymer molecules where the dipoles are not directly attached to the main chain, segmental movement of the chain is not essential for dipole polarisation and dipole movement is possible at temperatures below the glass transition temperature. Such materials are less effective as electrical insulators at temperatures in the glassy range. With many of these polymers, e.g., poly(methyl methacrylate), there are two or more maxima in the power factor-temperature curve for a given frequency. The presence of two such maxima is due to the different orientation times of the dipoles with and without associated segmental motion of the main chain. 

Poly(vinyl chloride) has a good resistance to hydrocarbons but some plasticisers, particularly the less polar ones such as dibutyl sebacate, are extracted by materials such as iso-octane. The polymer is also resistant to most aqueous solutions, including those of alkalis and dilute mineral acids. Below the second order transition temperature, poly(vinyl chloride) compounds are reasonably good electrical insulators over a wide range of frequencies but above the second order transition temperature their value as an insulator is limited to low-frequency applications. The more plasticiser present, the lower the volume resistivity. 

Poly(methyl methacrylate) is a good electrical insulator for low-frequency work, but is inferior to such polymers as polyethylene and polystyrene, particularly at high frequencies. The influence of temperature and frequency on the dielectric constant is shown in Figure 15.9. 

Although it is a polar polymer, its electrical insulating properties at room temperature are good even at high frequencies owing to the fact that since room temperature is well below the transition temperature dipole orientation is severely restricted. Some data on the crystallinity of poly(ethylene terephthalate) are presented in Table 25.5. 

Fig. 7. Voigt model analysis of (a) lateral contact stiffness and (b) the response time, t, for a silicon nitride tip vs. poly(vinylethylene) as a function of frequency and polymer aging times. Reprinted with permission from ref [71].

Fig. 10. Concentration dependence of a modulus in the region of low-frequency plateau (i.e. yield stress , measured by a dynamic modulus). Dispersion medium poly (butadiene) with M = 1.35 x 105 (7), silicone oil (2) polybutadiene with M = 1 x I04 (3). The points are taken from Ref. [6], The straight line through these points is drawn by the author of the present paper. In the original work the points are connected by a curve in another manner...

Fig. 14. Amplitude dependences (y0 is the amplitude of cyclic deformations) of the elastic modulus for frequency a) = 63 s 1 13% dispersion of acetylene carbon black in low- (/) and high-molecular (2) poly(isobutylene)s...

FIGURE 5.17 Temperature versus G —the shear storage modulus at a frequency of 1.6 Hz for diblock copolymer poly(ethylene propylene)-poly(ethylethylene) (PEP-PEE). The order-disorder transition (ODT) calculated to be 291°C 1°C. (From Rosedale, J.H. and Bates, F.S., Macromolecules, 23, 2329, 1990. With permission of American Chemical Society.)... 

In our tip-enhanced near-field CARS microscopy, two mode-locked pulsed lasers (pulse duration 5ps, spectral width 4cm ) were used for excitation of CARS polarization [21]. The sample was a DNA network nanostructure of poly(dA-dT)-poly(dA-dT) [24]. The frequency difference of the two excitation lasers (cOi — CO2) was set at 1337 cm, corresponding to the ring stretching mode of diazole. After the on-resonant imaging, CO2 was changed such that the frequency difference corresponded to none of the Raman-active vibration of the sample ( off-resonant ). The CARS images at the on- and off- resonant frequencies are illustrated in Figure 2.8a and b, respectively. 

Kitajima and Tolman have provided estimates of the relative electron-donating properties of poly(pyrazolyl)borato ligands based upon comparisons of the observed p(CO) stretching frequencies of sev-... 

If the stacking faults occur only rarely (say, every 105 layers on average), the result is a polysynthetic twinned crystal (cf. Fig. 18.8, p. 223). Depending on the frequency of the stacking faults, there is a smooth transition between crystals with stacking faults and poly synthetic twinning. 

The dynamic viscoelasticity of particulate gels of silicone gel and lightly doped poly-p-phenylene (PPP) particles has been studied under ac excitation [55]. The influence of the dielectric constant of the PPP particles has been investigated in detail. It is well known that the dielectric constant varies with the frequency of the applied field, the content of doping, or the measured temperature. In Fig. 11 is displayed the relationship between an increase in shear modulus induced by ac excitation of 0.4kV/mm and the dielectric constant of PPP particles, which was varied by changing the frequency of the applied field. AG increases with s2 and then reaches a constant value. Although the composite gel of PPP particles has dc conductivity, the viscoelastic behavior of the gel in an electric field is qualitatively explained by the model in Sect. 4.2.1, in which the effect of dc conductivity is neglected. 

The random coil amide I VCD pattern is exacdy the same shape, but smaller in amplitude and shifted in frequency from the pattern characteristic of poly-L-proline II (PLP II) which is a left-handed 3ihelix of trans peptides (Kobrinskaya et al., 1988 Dukor and Keiderling, 1991 Dukor et al., 1991 Dukor and Keiderling, 1996 Keiderling et al., 1999b). This... 

In one example, the Tics of the non-crystalline methyl, methine and methylene carbons of iPP, 70% crystalline, were compared at room temperature with those of model atactic poly(propylene), hydrogenated poly(2-methyl-l,3-pentadiene) [163]. It was found that, within the experimental error, the Tic values of each of the carbons were the same in both polymers. The conclusion can then be reached that the fast segmental motion, at or near the Larmor frequency of... 

Here m is the mode order (m — 1,3,5. .., usually 1 for polyethylenes), c the velocity of light, p the density of the vibrating sequence (density of pure crystal) and E the Young s modulus in the chain direction. The LAM band has been observed in many polymers and has been widely used in structural studies of polyethylenes [94—99,266], as well as other semi-crystalline polymers, such as poly (ethylene oxide) [267], poly(methylene oxide) [268,269] and isotactic poly(propylene) [270,271], The distribution of crystalline thickness can be obtained from the width of the LAM mode, corrected by temperature and frequency factors [272,273] as ... 

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