Frequency response measurements diffusion

The evidence for several types of adsorption (four types plus an ultra-slow exponential due perhaps to internal oxygen diffusion) was sufficiently strong to justify study of the hydrogen-supported nickel system by actual frequency response measurement. 

Frequency Response Measurements of Diffusion in Microporous Materials... 

FREQUENCY-RESPONSE MEASUREMENTS OF DIFFUSION OF SORBATES IN ZEOLITES... 

Rees, L.V.C. and Shen, D., Frequency-response measurements of diffusion of xenon in silicalite-1. J. Chem. Soc., Faraday Trans., 86, 3687 3692, 1990. 

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]. 

The different behaviours of gas diffusion electrodes with different catalyst loadings were studied by Paganin et al. [4], EIS measurements of 0.5 and 1 cm2 single cells were conducted with H2/02 (air) as fuel/oxidant. In their measurements, a Solartron 1250 frequency response analyzer and a 1286 electrochemical interface were employed. The amplitude of the AC signal was 10 mV and the frequency range was typically from 10 mHz to 10 kHz. Representative EIS results are shown in Figures 6.1 and 6.2. 

On the basis of this model one expects that if the spatial period of the grating pattern being recorded is increased, the achievable index modulation will drop off when the period becomes larger than the distance over which monomer can diffuse in the time before the fixing exposure. The experimental spatial-frequency response curve in Fig. 18 shows this expected low-spatial-frequency cutoff (37). Measured rates of monomer diffusion in polymer films are also consistent with the basic diffusion model (38). 

Fig. 18. Self-diffusion coefficients of benzene in NaX at 458 K PFG NMR, O (97) and (92) (JENS, A (13) deduced from NMR lineshape analysis, (10). Comparison with nonequilibrium measurements T, sorption uptake with piezometric control (93) , zero-length column method (96) o, frequency-response and single-step frequency-response technique (98). The region of the results of gravimetric measurements with different specimens (92) is indicated by the hatched areas. Asterisked symbols represent data obtained by extrapolation from lower temperatures with an activation energy confirmed by NMR measurements.

There are macroscopic (uptake measurements, liquid chromatography, isotopic-transient experiments, and frequency response techniques), and microscopic techniques (nuclear magnetic resonance, NMR and quasielastic neutron spectrometry, QENS) to measure the gas diffusivities through zeolites. The macroscopic methods are characterized by the fact that diffusion occurs as the result of an applied concentration gradient on the other hand, the microscopic methods render self-diffusion of gases in the absence of a concentration gradient [67]. 

Hopefully, this work will encourage further research on how to capitalize state-of-the-art modeling techniques and high-frequency meteorological measurements to improve our real-time ability in response to atmospheric releases of hazardous materials from an industrial accident or terrorist act. An urgent and challenging issue that needs to be addressed is diffusion model validation. Without comprehensive validation, even a well-designed prediction system cannot be accepted for operational application. 

Frequency response methods have been found useful in both theoretical and experimental analysis of gas mixing in fluidized beds. Experiments in a fluidized-bed reactor related to mixing theory were made by Bamstone and Harriott 24). Testin and Stuart have measured diffusion coefficients in gas-solid adsorption studies 25). 

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. 

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... 

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