Piezometric sorption

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. 

In both gravimetric and piezometric experiments it is generally desirable to make the measurement over a small differential concentration change in order to ensure that the assumption of system linearity is fulfilled. Under these conditions the transient sorption curve (expressed as fractional approach to equilibrium) should be independent of either the step size or direction (adsorption or desorption). Varying the step size and direction thus provides a simple and sensitive experimental test for system linearity. 

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