Surface frequency response method

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. 

Yasuda, Y. and Saeki, M., Kinetic details of a gas-surface systems hy the frequency response method, J. Phys. Chem., 82, 74-80, 1978. 

Yasuda, Y., Frequency response method for investigation of gas/surface dynamic phenomena. Heterogeneous Chem. Rev., 1, 103-124, 1994. 

Cycled Feed. The qualitative interpretation of responses to steps and pulses is often possible, but the quantitative exploitation of the data requires the numerical integration of nonlinear differential equations incorporated into a program for the search for the best parameters. A sinusoidal variation of a feed component concentration around a steady state value can be analyzed by the well developed methods of linear analysis if the relative amplitudes of the responses are under about 0.1. The application of these ideas to a modulated molecular beam was developed by Jones et al. ( 7) in 1972. A number of simple sequences of linear steps produces frequency responses shown in Fig. 7 (7). Here e is the ratio of product to reactant amplitude, n is the sticking probability, w is the forcing frequency, and k is the desorption rate constant for the product. For the series process k- is the rate constant of the surface reaction, and for the branched process P is the fraction reacting through path 1 and desorbing with a rate constant k. This method has recently been applied to the decomposition of hydrazine on Ir(lll) by Merrill and Sawin (35). 

Recently there has been a growing emphasis on the use of transient methods to study the mechanism and kinetics of catalytic reactions (16, 17, 18). These transient studies gained new impetus with the introduction of computer-controlled catalytic converters for automobile emission control (19) in this large-scale catalytic process the composition of the feedstream is oscillated as a result of a feedback control scheme, and the frequency response characteristics of the catalyst appear to play an important role (20). Preliminary studies (e.g., 15) indicate that the transient response of these catalysts is dominated by the relaxation of surface events, and thus it is necessary to use fast-response, surface-sensitive techniques in order to understand the catalyst s behavior under transient conditions. 

Ultrasound-based sensors for metal-coated fiber optic measurements based on interferometric determination of the displacement using a Michelson interferometer have also been designed. The input acoustic field can be detected by using two reference methods, namely (a) time-delay spectroscopy with a calibrated hydrophone (a hydrophone with known frequency response determining the sound pressure, the input displacement being obtained by simple algebra) and (b) the interferometric foil technique (the displacement of a metallized foil situated at the surface of the fluid measured by the interferometer used for fibre tip measurements). The frequency dependence of the transfer function compared well with the theoretical models [51]. 

Abstract Theoretical, experimental principles and the applications of the frequency response (FR) method for determining the diffusivities in microporous and bidispersed porous solid materials have been reviewed. Diffusivities of hydrocarbons and some other sorbates in microporous crystals and related pellets measured using the FR technique are presented, and the FR data are analysed to demonstrate the identification of the FR spectra. These results display the ability of the FR method to discriminate multi-kinetic mechanisms, including a surface resistance or surface barrier occurring simultaneously in the systems, which are difficult to be determined using other microscopic or macroscopic methods. The FR measurements also showed that the diffusivity of a system depends significantly on the subtle differences in molecular shape and size of sorbates in various... 

Electrochemical Impedance Spectroscopy (EIS) is a powerful nondestructive method to characterize biomaterials. Electrode materials, solution resistance, elec-trode/electrolyte interface impedance, charge transfer resistance, and surface rough-ness/double layer capacitance can be measured and their frequency response properties can be determined in a fast frequency scan. 

EIS has been applied extensively to the analysis of the corrosion mechanism of iron and other metals in aqueous solutions. To characterize a given corrosion process, it is practically advisable to obtain a full AC frequency scan of the system, including sufficient low-frequency response and small amplitude voltage perturbation with cyclic voltammetry, before acquiring the response data such as current, voltage, and polarization resistance Most corrosion kinetics studies have been done on uniformly corroding surfaces where the dissolution of the metal is uniform all over the surface in contact with the electrolyte [43]. Localized corrosion and stress corrosion cracking can also be analyzed by impedance methods such as local EIS (Section 13-4). 

The sensing methods summarized thus far are intended for absorption detection of molecules in the ambient, but molecules (or indeed thin films) on the microresonator surface can also be detected. In particular, if the surface is covered to such an extent that the optical energy absorbed heats the microresonator, the resulting thermal bistability in the frequency-scan response can be used to determine the absorption and/or thickness of the thin-film coating. This and surface characterization by measurement of the thermal accommodation coefficient were described in Sect. 5.5. These methods offer quite precise measurement, provided that certain reasonable and easily implemented assumptions are satisfied. 

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