Frequency domain regime

For spin-f nuclei, dipolar interactions may be modulated by intramolecular (DF, reorientation etc.) and/or intermolecular (TD) processes. In general, the intra- and inter-molecular processes can produce quite different Tj frequency dispersion curves. In practice, NMR field cycling experiments are often needed to extend the frequency domain from those employed in conventional spectrometers to a lower frequency range (i.e., the kHz regime) for unambiguous separation (and identification) of different relaxation mechanisms. The proton spin relaxation by anisotropic TD in various mesophases has been considered by Zumer and Vilfan.131 133,159 In the nematic phase, Zumer and Vilfan found the following expression for T ... 

The dipole response in real time gives access to the response in frequency domain by Fourier transfrom D (a)), from which one can extract the strength function S(n>) = cA b yf and the power spectrum P( ) = I)(a/) 2. The strength function is the more suited quantity in the linear regime, where it can be related to the photoabsorption cross section [31], while the power spectrum better applies for spectral analysis in the non linear regime [24],... 

We shall conclude this chapter with a few speculative remarks on possible future developments of nonlinear IR spectroscopy on peptides and proteins. Up to now, we have demonstrated a detailed relationship between the known structure of a few model peptides and the excitonic system of coupled amide I vibrations and have proven the correctness of the excitonic coupling model (at least in principle). We have demonstrated two realizations of 2D-IR spectroscopy a frequency domain (incoherent) technique (Section IV.C) and a form of semi-impulsive method (Section IV.E), which from the experimental viewpoint is extremely simple. Other 2D methods, proposed recently by Mukamel and coworkers (47), would not pose any additional experimental difficulty. In the case of NMR, time domain Fourier transform (FT) methods have proven to be more sensitive by far as a result of the multiplex advantage, which compensates for the small population differences of spin transitions at room temperature. It was recently demonstrated that FT methods are just as advantageous in the infrared regime, although one has to measure electric fields rather than intensities, which cannot be done directly by an electric field detector but requires heterodyned echoes or spectral interferometry (146). Future work will have to explore which experimental technique is most powerful and reliable. 

Generally PSAs are well known for their very viscoelastic behavior, which is necessary for them to function properly. It was therefore important to characterize first the effect of the presence of diblocks on the linear viscoelastic behavior. Since a comprehensive study on the effect of the triblock/diblock ratio on the linear viscoelastic properties of block copolymer blends has recently been reported [46], we characterized the linear viscoelastic properties of our PSA only at room temperature and down to frequencies of about 0.01 Hz. Within this frequency range all adhesives have a very similar behavior in terms of elasticity, as can be seen in Fig. 22.10. The differences appear at low frequency, a regime where the free iso-prene end of the diblock chain is able to relax. This relaxation process is analogous to the relaxation of an arm of a star-like polymer [47], and causes G to drop to a lower plateau modulus, the level of which is only controlled by the density of triblock chains actually bridging two styrene domains [46]. 

For /g < / , as prescribed previously, it is not difficult to verify that the above description in the time domain is in accord with the frequency-domain results presented previously. Since the relationship between the pulse width Tand the minimum bandwidth of the final filter is governed by the Fourier transform property TB i [7.70], (7.135) for the noise power in this regime may be written as... 

The investigation of this type of the Prederiks transition is very useful for practical applications, because the domains discussed result in a parasitic scattering effect in nematics with two-frequency addressing regimes [2]. 

Discrepancies between numerical values of the estimated damping coefficients is shown in Table I. The frequency domain approach invariably produced an indication of strong cross-coupling terms which was not confirmed either by the time-domain results or by direct observation of the damper ring response. The authors believe that the squeeze-film was probably over-excited during the frequency domain tests and consequently driven out of the linear regime. The presence of significant nonlinear stiffness effects in the squeeze-film could account for the discrepancies which have been observed. 

FIG U RE 5.14 The impedance spectra of the CCL with an ideal oxygen transport in (a) normal Tafel, (b) and (c) double Tafel regimes for the indicated values of the dimensionless cell current densityy o, with (c) the high-frequency domain (linear branch) of the spectra in (b). Parameters for the calculations are listed in the second (PEFC) column of Table 5.6. 

Fig. 4—Retardation as a function of voltage. The continuing reorientation of the structure (left side) with increasing voltage results in an ever increasing retardation, i.e., birefringence. The retardation A0 continues to increase unless another electro-optic regime ensues viz, below the dielectric relaxation frequency, domains, and above, chevron distorions (M. Hareng, et al ).

If the diffusion coefficients along the three axes are sufficiently different from each other (Di > D2 > D3), the different regimes corresponding to Eqs. (8) can be observed, according to the frequency domains. Explicit forms of these typical regimes are given in Table 5.1. The shape of /(w) is shown in Fig. 5.1. 

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