Frequency response spectra

Crystals of microporous materials must be formed into pellets of siutable dimensions, porosity and mechanical strength, or be formed into a membrane on the surface of support materials when used in practice. Such composite pellets or membranes offer a bidispersed porous structure, with macro-or mesopores between the crystals and micropores permeating the crystals. The overall rate of the transport in such systems depends on the interplay of various processes occurring within the pellets or membranes. Jordi and Do [24,46] have developed a general theoretical model and seven relevant degenerate models to analyse the frequency response spectra of a system containing bidispersed pore structure materials for slab, cylindrical and spherical macro- and micropore geometry. Sun et al. [47] also reported the theoretical models of the FR for non-isothermal adsorption in biporous sorbents. 

A fundamental advantage of the frequency response method is its ability to yield information concerning the distribution of molecular mobilities. For example, a bimodal distribution of diffusivites, which is difficult to detect by conventional sorption measurements, leads to two different resonances [49], Moreover, from an analysis of the frequency response spectrum it is even possible to monitor molecular diffusion in combination with chemical reactions [45]. As in conventional sorption experiments, however, the intrusion of heat effects limits the information provided by this technique for fast adsorption-desorption processes [50]. 

It has been demonstrated that EIS can serve as a standard analytical diagnostic tool in the evaluation and characterization of fuel cells. Scientists and engineers have now realized that the entire frequency response spectrum can provide useful data on non-Faradaic mechanisms, water management, ohmic losses, and the ionic conductivity of proton exchange membranes. EIS can help to identify contributors to PEMFC performance. It also provides useful information for fuel cell optimization and for down-selection of the most appropriate operating conditions. In addition, EIS can assist in identifying problems or predicting the likelihood of failure within fuel cell components. 

The most complete and unambiguous characterization of the response of an AW device is always obtained from a complete frequency response spectrum, including all four S parameters. In addition, there are cases, particularly for fairly complex interactions between the AW and a surface film, in which the nature of the response might never be understood without this important tool. There are several important reasons, however, not to attempt the measurement of an entire... 

In the frequency response method, first applied to the study of zeolitic diffusion by Yasuda [29] and further developed by Rees and coworkers [2,30-33], the volume of a system containing a widely dispersed sample of adsorbent, under a known pressure of sorbate, is subjected to a periodic (usually sinusoidal) perturbation. If there is no mass transfer or if mass transfer is infinitely rapid so that gas-solid mass-transfer equilibrium is always maintained, the pressure in the system should follow the volume perturbation with no phase difference. The effect of a finite resistance to mass transfer is to cause a phase shift so that the pressure response lags behind the volume perturbation. Measuring the in-phase and out-of-phase responses over a range of frequencies yields the characteristic frequency response spectrum, which may be matched to the spectrum derived from the theoretical model in order to determine the time constant of the mass-transfer process. As with other methods the response may be influenced by heat-transfer resistance, so to obtain reliable results, it is essential to carry out sufficient experimental checks to eliminate such effects or to allow for them in the theoretical model. The form of the frequency response spectrum depends on the nature of the dominant mass-transfer resistance and can therefore be helpful in distinguishing between diffusion-controlled and surface-resistance-controlled processes. 

Ground acceleration This is the time history of ground acceleration as a result of an earthquake, where multiple frequency excitation predominates (Figure 14.12(b). A ground response spectrum (GRS) can be derived from this history. 

Floor acceleration This is the time history of acceleration of a partictilar floor nr structure caused by a given ground acceleration (Figure 14.16). It may have an amplified narrow band spectrum due to structural filtration, where single frequency excitation and resonance may predominate, depending upon the dynamic characteristics of the structure. A floor response spectrum (FR.S). as shown in Figure 14.18, can be derived from this history. Consideration of GRS or FRS will depend upon the location of the object under test. 

Photomultipliers are used as detectors in the single-channel instruments. GaAs cathode tubes give a flat frequency response over the visible spectrum to 800 nm in the near IR. Contemporary Raman spectrometers use computers for instrument control, and data collection and storage, and permit versatile displays. 

The time resolution of the instrument determines the wavenumber-dependent sensitivity of the Fourier-transformed, frequency-domain spectrum. A typical response of our spectrometer is 23 fs, and a Gaussian function having a half width... 

In the time-domain detection of the vibrational coherence, the high-wavenumber limit of the spectral range is determined by the time width of the pump and probe pulses. Actually, the highest-wavenumber band identified in the time-domain fourth-order coherent Raman spectrum is the phonon band of Ti02 at 826 cm. Direct observation of a frequency-domain spectrum is free from the high-wavenum-ber limit. On the other hand, the narrow-bandwidth, picosecond light pulse will be less intense than the femtosecond pulse that is used in the time-domain method and may cause a problem in detecting weak fourth-order responses. 

The strong point of SFG is that the process is forbidden in centrosymmetric media (i.e. media with an inversion center). Therefore it occurs only at interfaces, where the sum-frequency response forms within a region of typically one nanometer thickness. Hence, neither the bulk of the catalyst nor the molecules in the gas phase contribute to the SFG spectrum. 

Multi-channel compression systems divide the speech spectrum into several frequency bands, and provide a compression amplifier for each band. The compression may be independent in each of the bands, or the compression control signals and/or gains may be cross-linked. Independent syllabic compression has not been found to offer any consistent advantage over linear amplification [Braida et al., 1979][Lippmann et al., 1981][Walker et al., 1984], One problem in multi-channel compression systems has been the unwanted phase and amplitude interactions that can occur in the filters used for frequency analysis/synthesis [Walker et al., 1984] and which can give unwanted peaks or notches in the system frequency response as the gains change in each channel. 

Diffuse Reflectance Spectroscopy Instead of analyzing the frequency response of the fight to extract chemical information as is done in reflectance-mode absorption spectroscopy, diffuse reflectance spectroscopy extracts the bulk absorption and scattering coefficients by fitting the spectrum to a particular model.76... 

Because digital filtering can produce a brick wall frequency response, any peak that falls outside the spectral window is removed completely and will not alias. This can be a problem if you set the spectral window too narrow You will never be aware of the peaks you miss. If you accidentally set the spectral window to include nothing but noise, you will get just that in the spectrum nothing but noise The good news is that if we are only interested in a small part of the ID spectrum, we can cut out the rest of the spectrum using the digital filter. For example, in a 2D N-1 HSQC spectrum of a protein, we are only... 

For an idealized material with a single absorption frequency, the connection between absorption spectrum and imaginary-frequency response looks like Fig. LI. 8. 

The advantage of network analysers is the possibility of impedance measurement near resonance with evaluation of the parameters R, L, C and C0 and test of the equivalent electrical circuit. However frequency response and network analysers are relatively slow with 1-10 s per measurement in typical experiments. A new generation of faster instruments has come to the market like the HP E5100 Network Analyzer with 40 (is per point in the impedance spectrum which allows us to obtain the impedance of the system in less than 10 ms. 

The interference between different vibrations (including those of different molecules) resulting from the coherent nature of the experiment makes the analysis of VSFS spectra considerably more complicated than that of spectra recorded with linear spectroscopic techniques. However, this complexity can be exploited to provide orientational information if a complete analysis of the VSF spectrum is employed taking into account the phase relationships of the contributing vibrational modes to the sum-frequency response [15,16]. In the analysis it is possible to constrain the average orientation of the molecules at the surface by relating the macroscopic second-order susceptibility, Xs g of the system to the molecular hyperpolaiizabilities, of the individual... 

Examples of the frequency response of the resonance spectra for various a-Si H films are shown in Fig. 2.18 (Reimer, Vaughan and Knights, 1980). The line is broadened by the short lifetime of proton spin orientation. There are two distinct components to the spectrum, corresponding to fast and slowly relaxing states, with line widths of... 

For comparison, the frequency response of a two-port SAW resonator is shown in Figure 6.11 (page 364). Note that it resembles the response of the delay line, with the addition of a sharp spike, where the insertion loss is considerably lower, at the center of the pass band. The similarity of the delay line and resonator frequency responses is a consequence of both devices using the same transducer pattern, while the spiked region of much lower insertion loss is a result of the ridge-reflector array utilized to set up a standing wave. Unlike the highest point of the delay-line spectrum, there is no 6-dB theoretical insertion loss limit for the peak of the resonator spectrum — loss can approach 0 dB. 

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