Piezometric uptake

In contrast with the results obtained in this laboratory, the piezometric uptake rate data of Bulow et al. (25,26) lie very much closer to the NMR data. It should, however, be noted that the corrections introduced to account for valve effects and other extraneous factors were very large, thus inevitably reducing the confidence level. 

H-n.m.r. [71], quasi-elastic neutron scattering [72], frequency response [73] and piezometric sorption uptake [34]. On the other hand, theself-consistency of data reported in [4,39,66,67] suggests further analysis of phenomena, probably interfered with bothithe samples and the experimental techniques used. 

Conventionally, molecular uptake is recorded gravi-metrically [18-20]. Alternatively, for a limited supply of adsorbate, molecular uptake may also be calculated from a knowledge of the time dependence of the pressure (piezometric method [21, 22]) or composition of the gas phase. Changing the sorbate pressure by a step change of the gas volume has proved to be a very efficient method for following fast sorption processes (single step method [23, 24]). The sorption uptake may also be measured volumctrically by mans of a gas burette arrangement [25]. 

Sorption Rates in Batch Systems. Direct measurement of the uptake rate by gravimetric, volumetric, or piezometric methods is widely used as a means of measuring intraparticle diffusivities. Diffusive transport within a particle may be represented by the Fickian diffusion equation, which, in spherical coordinates, takes the form... 

In Fig. 18 the self-diffusivities obtained by different experimental techniques are compared. It appears that in both the absolute values and the trends in the concentration dependence, the QENS data, the PFG NMR results, and the data derived from sophisticated uptake experiments using the piezometric or single-step frequency-response techniques agree. Nevertheless, disagreement with some sorption results has to be stated. Additional information on the molecular reorientation of benzene in zeolite X has been obtained by QENS and NMR lineshape analysis. 

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.

It is the first time in the present paper that the uptake curves from a piezometric apparatus have been simulated by the solution of the Volterra integral equation [9,10] which reflects in detail the interaction of the sorption kinetics with the apparatus. This approach enabled us to get kinetic data with a high accuracy. 

The intracrystalline diffusivities of the hydrocarbons were measured under the conditions of the temperature range of 373-773 K and the pressure range of 0-1.33 kPa by the constant volume method [9]. The apparatus and the procedure are the same as employed by Hashimoto et al. [4,5]. Change in the total pressure caused by adsorption was recorded by use of a piezometric sensor with a transducer, the response of which is first enough to measure accurately the pressure change. To eliminate the influence of several factors (such as mass conductivity between the sorbate and the pressure sensor) on the pressure change, the blank tests were conducted without zeolites. Comparing these data obtained with those with zeolites, an uptake curve of the amount adsorbed was obtained. 

The piezometric method involves following the pressure response in a dosing cell connected to an uptake cell containing a sample of the adsorbent. According to the results reported in the hterature, the piezometric method can be used to accurately measure intracrystalline diffusivities for fast diffusing and strongly adsorbed species such as benzene on NaX [15,16]. Furthermore, it is also claimed to provide the required accuracy needed to study combined intracrystalline processes such as diffusion and first-order reaction [17]. 

Fig. 4 Theoretical piezometric response curves for a the dosing cell and b the uptake cell, calculated from Eqs. 6-9 with y = 8 = 0.01 and various values of parameter w. The curves corresponding to equilibrium control are shown by heavier lines. From Brandani [23] with permission...

We conclude that the piezometric technique is capable of yielding reliable diffusivity data provided that the pressures are monitored in the uptake cell and the limitations imposed by the time constant of the valve and finite heat dissipation rates are respected. For strongly adsorbed species theses restrictions limit the applicability to relatively slow processes (half times of at least several seconds). For weakly adsorbed species somewhat faster diffusion processes can be measured. A detailed assessment of the range of validity of this method, as a function of the system variables, has been presented by Schumacher and Karge [19]. In reviewing earlier reported piezometric diffusivity data, the values derived from measuring only the pressure in the dosing cell should not be accepted without further detailed analysis. 

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