Sorption uptake-rate curves

Fig. 7 Sorption uptake-rate curves ofbenzene in 50 mg of NaX (cf. [65]) at 440 K and 2.0 Torr. and denote adsorption and desorption processes, respectively. The continuous line is obtained from Eq. 26 with a fractional uptake of 0.6 and D = 4.9 x 10 m s" Note 1 Torr = 133.33 Pa...

Sorption uptake rate curves of ben ne in silicalite-1 (0 x) and HZSM-5 ( 0,+) at 395 K, 0.826 foir. (0>0) denote adsorption processes and (x,- ) denote desorption processes. Lines were calculated using the solution for diffusion in a sphere for silicalite and a cylinder for HZSM-5 from a well-stined solution of limited volume with fractional uptakes of 0.46 and 0.33, respectively (see eqn. (7)). 

The rate of uptake slows down considerably as p decreases, p affects the slopes of both the initial and the later portions of the uptake curve. This shows that uptake rate is very sensitive to the adsorbate loading and the heat of sorption. For a Langmurian system, p may be written as ... 

The apparent simplicity of this approach is, however, deceptive. For measurement of intracrystalline diffusion the method works well when diffusion is relatively slow (large crystals and/or low diffusivity), but when sorption rates are rapid the uptake rate may be controlled by extracrystalline diffusion (through the interstices of the adsorbent bed) and/or by heat transfer. The intrusion of such effects is not always obvious from the shape of the uptake curve, but it may generally be detected by changing the sample quantity and/or the sample configuration. It is in principle possible to allow for such effects in the mathematical model used to interpret the uptake curves (Fig. 2), and indeed the modeling of nonisothermal systems has been studied in considerable detail [8-12]. However, any such intrusion will obviously diminish the accuracy and confidence with which the intracrystalline diffusivities can be determined. 

The most widely used unsteady state method for determining diffusivities in porous solids involves measuring the rate of adsorption or desorption when the sample is subjected to a well defined change in the concentration or pressure of sorbate. The experimental methods differ mainly in the choice of the initial and boundary conditions and the means by which progress towards the new position of equilibrium is followed. The diffusivities are found by matching the experimental transient sorption curve to the solution of Fick s second law. Detailed presentations of the relevant formulae may be found in the literature [1, 2, 12, 15-17]. For spherical particles of radius R, for example, the fractional uptake after a pressure step obeys the relation... 

The initial deviation of the observed rate from the ideal curve complicates calculation of D from the half-time of sorption or desorption since it would be difficult to locate the start of the ideal diflEusion process. However, D values obtained in this manner should still prove useful in assessing the eflFects of various treatments on the same substrate (e.g., skin) since the relative error attributable to the initial non-equilibrium conditions in the sample chamber will be the same. When D is calculated in this way and the start of the diflEusion process is referenced to t = 0 (i.e. the time required to achieve 50% uptake or loss is referenced to... 

Considering the mechanisms of sorption discussed in Section II, e.g. surface precipitation or formation of new phases involving the adsorbent and the adsorbate, the above kinetic model is not sufficient to describe isotope exchange in all relevant systems, although most experimental kinetic curves can be reproduced by proper adjustment of parameters (effective D in the solid and in the liquid film, rate constants of surface reactions) within the discussed above model. Spectroscopic studies (Section I and II) suggest that the uptake of adsorbate is often due to simultaneous formation of surface complex and surface precipitation. Single F t) curve based on the radioactivity of the solution is not sufficient to describe sorption kinetics in such systems. 

If the surface is first saturated with a monolayer of protein exposed to steady-state concentration cQ, and then is exposed to a second treatment at concentration 2c0, a second front emerges. The second profile represents the situation where no net protein is adsorbed and thus, in principle, is representative of the diffusion-shifted flow pattern of the nonadsorbed protein. Figure 7 shows both the initial (cQ) and second (2c0) fronts and the subtraction curve which is very close to the ideal step function. If the data are interpreted as solution-borne molecules passing over an inert surface, then (a) adsorption must be essentially instantaneous and (b) the surface must become covered by exhausting the concentration of solute at the front as it moves down the column. The slope of the difference profile should represent the rate of uptake of material on the column, and that is essentially infinite on the time scale of the experiment. The point of inflection of the subtracted front indicates the slowing of the sorption process due to filling of sites on the surface. 

Metal-ion uptake in a dynamic system Sorption experiments in a dynamic system were carried out using a glass column (length 10 cm, internal diameter 1.2 cm) filled with 1.0 g resin. The resin was washed with distilled-deionized water (10 bed volumes), then a solution containing 40 ppm Cu was passed through at a flow rate of 3 mLmin . For determination of the breakthrough curve, the eluate from the column was collected in 50 mL fractions and the copper cation concentration was determined by atomic absorption spectroscopy. 

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