Desorption curve

A somewhat subtle point of difficulty is the following. Adsorption isotherms are quite often entirely reversible in that adsorption and desorption curves are identical. On the other hand, the solid will not generally be an equilibrium crystal and, in fact, will often have quite a heterogeneous surface. The quantities ys and ysv are therefore not very well defined as separate quantities. It seems preferable to regard t, which is well defined in the case of reversible adsorption, as simply the change in interfacial free energy and to leave its further identification to treatments accepted as modelistic. 

A numerical solution of this equation for a constant surface concentration (infinite fluid volume) is given by Garg and Ruthven [Chem. Eng. ScL, 27, 417 (1972)]. The solution depends on the value of A. = n i — n )/ n — n ). Because of the effect of adsorbate concentration on the effective diffusivity, for large concentration steps adsorption is faster than desorption, while for small concentration steps, when D, can be taken to he essentially constant, adsorption and desorption curves are mirror images of each other as predicted by Eq. (16-96) see Ruthven, gen. refs., p. 175. 

Fig. 10. Purging (desorption) curves for the N-butane in a one liter canister...

When the temperature of the analyzed sample is increased continuously and in a known way, the experimental data on desorption can serve to estimate the apparent values of parameters characteristic for the desorption process. To this end, the most simple Arrhenius model for activated processes is usually used, with obvious modifications due to the planar nature of the desorption process. Sometimes, more refined models accounting for the surface mobility of adsorbed species or other specific points are applied. The Arrhenius model is to a large extent merely formal and involves three effective (apparent) parameters the activation energy of desorption, the preexponential factor, and the order of the rate-determining step in desorption. As will be dealt with in Section II. B, the experimental arrangement is usually such that the primary records reproduce essentially either the desorbed amount or the actual rate of desorption. After due correction, the output readings are converted into a desorption curve which may represent either the dependence of the desorbed amount on the temperature or, preferably, the dependence of the desorption rate on the temperature. In principle, there are two approaches to the treatment of the desorption curves. 

In most cases the authors prefer the second way of treatment of the desorption data, which is analytic in its nature the Arrhenius equation, whose parameters are assumed to be constant, is solved either in a closed form or numerically. The resulting quantities determining the location, height, and shape of a maximum on the desorption curve are analyzed and expressed whenever possible, in at least approximately linear form, and then compared with the experimental results. A simple analytical expression of the time-temperature function is essential for this kind of treatment. 

The flash desorption technique is applied usually in ultrahigh vacuum conditions. Then all the mentioned contributions to S and F should be accounted for in the evaluation of the experimental desorption curves. The effect of Sw on the results of desorption measurements is discussed in... 

A different approach consists of stepwise changing the adsorbent temperature and keeping it constant at each of the prefixed values Tx, Ts,. . ., Tn for a certain time interval (e.g. 10 sec), thereby yielding the so-called step desorption spectra s(81-85). The advantage of this method lies in a long interval (in terms of the flash desorption technique) for which the individual temperatures Ti are kept constant so that possible surface rearrangements can take place (81-83). Furthermore, an exact evaluation of the rate constant kd is amenable as well as a better resolution of superimposed peaks on a desorption curve (see Section VI). What is questionable is how closely an instantaneous change in the adsorbent temperature can be attained. This method has been rarely used as yet. 

Fiq. 4. Conditions for resolution of two adjacent peaks on a desorption curve according to Carter (88). Tm and Tm are the temperatures at maximum desorption rate for the first and second peak, respectively. T and T are the temperatures at maximum desorption rate for the first and second peak, respectively. Te and Te are the temperatures at 1/e = 37 per cent of the maximum desorption rate for the first and second peak, respectively. 

The required distribution of initial populations ntu can be obtained in the following manner (32). Let us consider a system with Ed mi = 20 kcal/ mole and Ed max = 45 kcal/mole. Assuming that kd = 1013 sec-1 and x = 1, we can calculate theoretical desorption rates dnai/dt for Ed = 20, 21, 22,..., 45 kcal/mole as a function of nBOi. With increasing temperature, 25 values of dnjdt are measured at temperatures corresponding to Ed of 20, 21, 22,. . ., 45 kcal/mole. Since the total desorption rate at any moment must be equal to the sum of the individual desorption processes, we obtain 25 linear equations. Their solution permits the computation of the initial populations of the surface sites in the energy spectrum considered, i.e. the function n,oi(Edi). From the form of this function, desorption processes can be determined which exhibit a substantial effect on the experimental desorption curve. 

Let us consider that Ed corresponding to a peak on the desorption curve is coverage dependent, while kd (and thus the adsorption entropy) remains constant. (For the variability of kd see Section II.A.) When seeking the required function Ed (6) we refer to Eq. (8) in which the term exp (— Edf RT) exhibits the greatest variability. A set of experimental curves of the desorption rate with different initial populations n,B must be available. When plotting ln(— dn,/dt) — x ln(n ) vs 1/T, we obtain the function Ed(ne) from the slope, for the selected n, as has been dealt with in Section V. In the first approximation which is reasonable for a number of actual cases, let us take a simple linear variation of Ed with n ... 

In the Dynamic method a flow of He is passed over the sample at 77 K. A small amount of N2 is introduced into the He stream. The gas stream coming from the sample is monitored using mass spectroscopy. N2 is only detected after a monolayer is formed. The N2 supply is then switched off and the desorption curve plotted. Integration of this curve gives the information required for the BET equation. 

Adsorbed carbon monoxide on platinum formed at 455 mV in H2S04 presents a thermal desorption spectrum as shown in Fig. 2.4b. As in the case of CO adsorption from the gas phase, the desorption curve for m/e = 28 exhibits two peaks, one near 450 K for the weakly adsorbed CO and the other at 530 K for the strongly adsorbed CO species. The H2 signal remains at the ground level. A slight increase in C02 concentration compared to the blank is observed, which could be due to a surface reaction with ions of the electrolyte. Small amounts of S02 (m/e = 64) are also observed. 

Both reduced absorption and desorption curves have a linear region extending up to a MJM value of 0.6. Should D be an increasing function of Ci, this linear region can be further extended. 

The reduced absorption and desorption curves do not depend on the thickness of the polymer film. 

If D is an increasing function of Ci, the reduced absorption curve always lies above the desorption curve. The divergence becomes more significant when the dependence of D on c, becomes stronger the difference will disappear if D is a constant. 

Various anomalous diffusional behaviors have been observed and documented for both sorption and permeation experiments. Detailed discussions of these anomalies can be found elsewhere [12,35,36], Here only a brief summary of major findings is given. First, for the sorption anomaly, it has been observed that the reduced sorption curve has a distinctive thickness dependence. In this case, the reduced absorption and desorption curves obtained at various thick-... 

A procedure for characterizing the rates of the volume change of gels has not been uniformly adopted. Often, the kinetics are simply presented as empirical sorption/desorption curves without quantitative analysis. In other cases, only the time required for a sample of given dimensions to reach a certain percentage of equilibrium is cited. One means of reducing sorption/desorption curves to empirical parameters is to fit the first 60% of the sorption curve to the empirical expression [119,141]... 

This solution is valid for the initially linear portion of the sorption (or desorption) curve when MtIM is plotted against the square root of time. These equations also demonstrate that for Fickian processes the sorption time scales with the square of the dimension. Thus, to confirm Fickian diffusion rigorously, a plot of MJM vs. Vt/T should be made for samples of different thicknesses a single master curve should be obtained. If the data for samples of different thicknesses do not overlap despite transport exponents of 0.5, the transport is designated pseudo-Fickian. ... 

Figure 3 Adsorption and desorption curves for the sorption of radon on coconut based charcoal. (Jebackumar, 1985).

Examination of Figures 2 to 4 clearly indicates flow enhancement of the desorption as seen by the substantial decreases in adsorbance once flow is applied. The overall trend of the desorption curves for the three molecular weight samples is similar and is characterized by a fairly rapid initial desorption followed by an approach to steady state. The desorption rate increases with the velocity gradient whereas the steady state adsorbance decreases as the flow is increased. 

Figure 2. Desorption curves of PS-4 at various velocity gradients ( + ) 2600 sec-1 ( A ) 5200 sec-1 ...

Fig.9. Loading and breakthrough curves Fig. 10. Purging (desorption) curves for the in a one liter canister, 40 g/hr N-butane N-butane in a one liter canister feed rate...

Figure 10. Effects of internal and external transport resistances on the computed step-response of CO desorption. Curve A corresponds to our experimental conditions. Key A, km — 60 cm/s, Deff = 0.0246 cms/s B, km —r oo, Def, = 0.0246 cm2/s and C,km- oo, Delt oo.

The thermal desorption curve following the reaction of ethylene or propylene with 0 shows no substantial products in the gas up to 450 °C, and at that temperature CH is the primary product (19). These results suggest the following reactions, using ethylene as an example ... 

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