Temperature band width

The damping behavior of polymers can be altered to optimize either the temperature span covered or the damping effectiveness for particular temperatures. The area under the loss modulus temperature curve tends to be constant for some polymer combination, which has been expressed by the empirical "temperature band width law" of Oberst (2) ... 

Since then, the vibrational spectrum of Ss has been the subject of several studies (Raman [79, 95-100], infrared [101, 102]). However, because of the large number of vibrations in the crystal it is obvious that a full assignment would only be successful if an oriented single-crystal is studied at different polarizations in order to deconvolute the crystal components with respect to their symmetry. Polarized Raman spectra of samples at about 300 K have been reported by Ozin [103] and by Arthur and Mackenzie [104]. In Figs. 2 and 3 examples of polarized Raman and FTIR spectra of a-Ss at room temperature are shown. If the sample is exposed to low temperatures the band-widths can enormously be reduced (from several wavenumbers down to less than 0.1-1 cm ) permitting further improvements in the assignment. 

P 42] Typically, a flow rate of 150 pi min was used [71]. A 0.1 M furan solution containing 0.1 M NaCl04 and 5 mM NaBr was used as reaction medium. Reaction was carried out at room temperature. Interdigitated band electrodes with 100 pm wide gaps and 500 pm band widths were tested in a 800 pm deep Perspex micro reactor. 

Temperature congruence for the double layer on rutile in the presence of the indicated concentrations of KN03. Between 5 and 50° C all data coincide within the band width. 

Little is known about the fluorescence of the chla spectral forms. It was recently suggested, on the basis of gaussian curve analysis combined with band calculations, that each of the spectral forms of PSII antenna has a separate emission, with Stokes shifts between 2nm and 3nm [133]. These values are much smaller than those for chla in non-polar solvents (6-8 nm). This is due to the narrow band widths of the spectral forms, as the shift is determined by the absorption band width for thermally relaxed excited states [157]. The fluorescence rate constants are expected to be rather similar for the different forms as their gaussian band widths are similar [71], It is thought that the fluorescence yields are also probably rather similar as the emission of the sj tral forms is closely approximated by a Boltzmann distribution at room temperature for both LHCII and total PSII antenna [71, 133]. 

Finally we note some other properties of these allowed transitions of the lanthanide ions. From Table 1 it becomes clear that in general the 4f—5d bands have a smaller band width than the c.t. transitions, typical values being 1000 and 2000 cm-i, respectively. In this connection it is interesting to find that at low temperatures the 4f- -5d absorption and emission bands often show a distinct and extended vibrational fine structure [Ce3+ (25), Tb + (25), Eu2+ (14, 26), Yb2+ (27)], whereas c.t. transitions do not. From this it seems probable that in the excited c.t. state the interaction between the lanthanide ion and its surroundings is stronger than in the excited 4f 5d state. This is not imexpected. As far... 

As the intensity of summation bands do not depend on Boltzmann factors, most of the extra frequencies mentioned in the last two paragraphs will persist at least to some degree at low temperatures, i.e. they will contribute to a temperature independent residual band width. 

These various consequences parallel closely the analogous ones of the fluctuation and frequency modulation theories. There is, however, one important point of difference between the classical and quantum viewpoints which does not seem to have been emphasized previously, namely that transitions from the lowest level of the ground state can occur to several levels of the upper curve. This means that even at very low temperatures, when all the molecules are initially in this lowest energy level, a band of considerable breadth with frequencies rXH + m>(XH Y) will still persist. The temperature independent residual band width is a direct result of the perturbations of the system (in particular the finite change in the distance rxymin) caused by the absorption of a large quantum of radiation of frequency vXH. The same type of explanation may apply to other vibrational bands which remain of finite width at low temperatures the occurrence of such bands have been the cause of considerable discussion [34]. 

Equipment. The spectra were recorded on a Beckman IR12 spectrometer in the absorbance mode, with low amplifier gain and slit widths smaller than 1.6 of the half-band width of the OH or OD bands. Under these conditions the apparent optical density of the OH bands could be reproduced within 0.5%. To avoid errors from sample emission at temperatures higher than 100°C, the spectra were scanned with the chopper between sample and detector disconnected. 

At this point it is suitable to summarize the discussion by tabulating the intensities found for bands of different types. This is done in Table 4. In principle, the molar extinction coefficient, e, is not a good measure of band intensity. However, for transition metal compounds at any rate, the band widths for spin-allowed bands at ambient temperatures are mostly of the order of 2000 cm-1. With this fact in mind, it has become the custom to use s as a rough measure of band intensity, and to facilitate comparisons of that type the values of e associated with the varying types of transition are included in Table 4. 

Very recently, Bailey and Richards (23) have shown that a high degree of sensitivity for adsorbed species can be achieved by measuring the absorption of infrared radiation on a thin sample cooled to liquid helium temperature. The optical arrangement used in these studies is shown in Figure 10. The modulated beam produced by the interferometer is introduced into the UHV sample chamber and reflected off a thin slice of monocrystalline alumina covered on one side by a 1000 k film of nickel or copper. Radiation absorbed by the sample is detected by a doped germanium resistance thermometer. The minimum absorbed power detected by this device when operated at liquid helium temperature is 5 x 10 14 W for a 1 Hz band width. With this sensitivity absorbtivities of 10"4 could be measured. 

Self diffusion coefficients can be obtained from the rate of diffusion of isotopically labeled solvent molecules as well as from nuclear magnetic resonance band widths. The self-diffusion coefficient of water at 25°C is D= 2.27 x 10-5 cm2 s 1, and that of heavy water, D20, is 1.87 x 10-5 cm2 s 1. Values for many solvents at 25 °C, in 10-5 cm2 s 1, are shown in Table 3.9. The diffusion coefficient for all solvents depends strongly on the temperature, similarly to the viscosity, following an Arrhenius-type expression D=Ad exp( AEq/RT). In fact, for solvents that can be described as being globular (see above), the Stokes-Einstein expression holds ... 

Eq. (1) is used to find the d-band width (6.5 eV) once the other parameters of the band shape are determined. Similarly, Eq. (2) is used to determine the s-band width (12.9 eV) of a free-electron density of states symmetric in energy about the middle of the band. The d-band density of states, Nj(E). rises sharply at the lower band edge to about 1.5 states/eV atom then falls off to 0.47 states/eV atom near the middle. With the general shape of Nj. (E) and Ns(E) given, the critical magnitude of Nd( q ), the chemical potential in d-orbital, is determined from the observed linear part of the low-temperature specific heat as follows ... 

The photocatalytic activity of MgO, too, is considered to be caused by surface hydroxyl groups. This is shown in an investigation of the hydrogen-deuterium exchange at room temperature 78>. Monochromatic light was used in the range between 1800 and 4000 A and with a band width of 96 A. The reaction is treat-... 

Pressed pellets of BaTiC>3 were sintered in a platinum dish for six hours at 900°C in a controlled partial pressure of oxygen. The samples were quenched to room temperature, and the spectra recorded on a four-slit double-monochromator Raman spectrophotometer. An Ar+ laser with excitation at 514.5 nm was the source. The spectra were recorded at room temperature. Figure 4-30 shows the spectrum of BaTiC>3 whose Ba/Ti ratio is equal to 0.9999. The Raman spectrum is sensitive to the Ba/Ti ratio and theoxygen non-stoichiometry. The half-band width is variable as well as the intensity ratio of the 525 and 713 cm-1 bands. The ratio (I525/713) is at a minimum at the composition of 0.9999, and this can be observed in Fig. 4-31, which shows a plot of the intensity ratio (I525//713) vs. the Ba/Ti composition. 

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