Desorption equilibrium

Taking i m = 0, we obtain an equation for the desorption process alone, i.e. for the case where the rate of readsorption is negligible. On the other hand, if only the last term in the brackets is considered, one has the equation for the equilibrium desorption. 

From Pm still further information about the parameters of the desorption process can be obtained. To this end, Eq. (8) must be solved. The solution, however, is accessible only in the case of desorption alone. If the contribution of the second term in Eq. (8) is appreciable, it is necessary to insert for P from Eq. (13). Thus, nonlinear differential equations result even for the most simple cases (x = 1, or the equilibrium desorption), which can be solved by numerical methods only or by iterative methods provided the second term in Eq. (8) is small. 

The near-equilibrium desorption in a closed system (dP/dt dn,/dt) was used in practice, for example, by Procop and Volter (45h) and by Dawson and Peng (98). 

The associative adsorption of NO is supported by several infrared studies (12-14) Spectra of NO adsorbed on reduced Rh show an intense band at 1660-1740 cm- - and a weaker band at 1830 cm-- -. These features are associated with NO adsorbed as NO -and N0a, respectively. If the surface is partially oxidized, a third band is observed at 1910 cm- -, associated with N0 +. During steady-state reduction of NO by H2, only the NOa form of adsorbed NO is observed (10). The reversibility of NO aasorbtion into this state has been examined by Savatsky and Bell (14). Their work shows that at temperatures above 293 K, equilibrium desorption occurs when a stream of argon is passed over a Rh/Si02 catalyst bearing preadsorbed NO. 

Although adsorption and desorption together establish an adsorption equilibrium, desorption has received relatively little experimental attention. 

Figure 2. Capillary hysteresis of nitrogen in cylindrical pores at 77 K. Equilibrium desorption (black squares) and spinodal condensation (open squares) pressures predicted by the NLDFT in comparison with the results of Cohan s equation (the BJH method) for spherical (crosses and line) and cylindrical (line) meniscus.

To calculate the pore size distributions we have constructed two kernels of theoretical isotherms in cylindrical channels corresponding to the metastable adsorption and equilibrium desorption branches. These kernels were employed for calculating pore size distributions from experimental isotherms following the deconvolution procedure described elsewhere [21, 24] In Figs 6-7 we present the pore size distributions of the enlarged MCM-41 samples [2-4] calculated from the experimental desorption branches by means of the desorption kernel and the pore size distributions calculated from the experimental adsorption branches by means of the adsorption kernel The pore size distributions obtained from the desorption and adsorption branches practically coincide, which confirms that the NLDFT quantitatively describes both branches on the adsorption-desorption isotherm. 

It was clear that an equilibrium desorption time of more than 100 h is required for 1,3-DCB. Accordingly, three triplicate samples each of the PPI soil at three different initial soil concentrations were kept well-mixed with 40 ml of distilled water for 180 h. The desorption isotherm thus obtained is plotted in Fig. 6. It is clear that this desorption isotherm indicates that a portion of the compound remains bound to the soil. The linear isotherm representing this would consist of (i) a reversible portion obeying the conventional linear isotherm, Wrev= KSWCW, where Wrev is the soil concentration (pg/g), Ksw is the partition coefficient (1/g), and Cw is the aqueous phase concentration (pg/1), and (ii) a desorption... 

Desorption is the reverse of the sorption process. If the pesticide is removed from solution that is in equilibrium with the sorbed pesticide, pesticide desorbs from the soil surface to reestabUsh the initial equilibrium. Desorption replenishes pesticide in the soil solution as it dissipates by degradation or transport processes. Sorption/desorption therefore is the process that controls the overall fate of a pesticide in the environment. It accomplishes this by controlling the amount of pesticide in solution at any one rime that is available for plant uptake, degradation or decomposition, volatilization, and leaching. A number of reviews are available that describe in detail the sorption process (31—33) desorption, however, has been much less studied. 

Conceptually, the solvent extraction process involves contacting the contaminated sludge with a solvent so that some of the PCB sorbed on the sludge will be desorbed. At long contacting times an equilibrium partitioning of the PCB between the sludge and the solvent phases (henceforth desorption equilibrium) will be obtained. Batch extraction experiments were performed to establish the equilibrium desorption charasteristics. 

By contacting different amounts of sludge and fresh solvent, and allowing equilibrium to establish, information on equilibrium desorption characteristics was gathered. Obviously, increasing the solvent mass to sludge mass ratio (R) will result in an increase in the amount of PCB extracted. It was found that 50% of all extractable PCB desorbed for R approximately equal to 2, whereas 90% of the PCB was removed if R was approximately 5. Similar conclusions were reached for both solvents. 

Earlier, we have made the following general conclusions regarding the capillary condensation in cylindrical pores [7], The reversible isotherms in sufficiently narrow pores and the desorption branches of hysteretic isotherms in wider pores correspond to the equilibrium transitions predicted by the NLDFT. The adsorption branches of hysteretic isotherms lie inside the theoretical hysteresis loop. The metastable states on the theoretical desorption branch are not observed. These conclusions were made based on analyses of limited experimental data on reference MCM-41 materials with pores of diameter < 5nm. Sayari et al. [8-10] have recently synthesized enlarged MCM-41 samples with pore diameters from 5 to 10 nm. The Nj isotherms on these samples are presented in Figs. 3-6 in comparison with the theoretical loops for cylindrical pores of average size, formed by the metastable adsorption branch and the equilibrium desorption branch. The experimental and theoretical hysteresis loops are in a perfect qualitative agreement. 

Figure 9.4 Comparison of pore diameters obtained from capillary hysteresis of nitrogen in cylindrical pores at 77.4 K. Equilibrium desorption and spinodal condensation pressures predicted by the NLDFT method in comparison with the resuits of the BJH method. (Reprinted with permission from A. V. Neimark and P. 1. Ravikovitch., Microporous Mesoporous Mater. 2001, 44-45, 697. Copyright 2(X)1 Elsevier.)...

Equilibrium radical desorption The equilibrium desorption of a radical takes into account the different solubility of the radicals between the polymer particles and the aqueous phase. The rate coefficient of equilibrium radical desorption (ko ) can be related to the simple radical desorption rate coefficient by ... 

Model (a) For the thermal desorption type, equilibrium desorption... 

Recall that these two results are valid for nondispersive equilibrium desorption of a bed, initially saturated throughout at a level of C°2 by a mobile phase without any solute species, when Langmuir adsorption isotherm characterizes the adsorption equilibrium between the solute in the mobile phase and the adsorbent. 

Using these techniques hygroscopic materials can be characterised by increased water sorption at high RH values. The experimental method can be extended to examine the mechanism of the water sorption process. At 90% RH, the target RH is then taken down to 0% RH so that each equilibrium desorption step mirrors the adsorption steps. The mass change associated with water sorption onto hygroscopic materials should be equal for the adsorption and desorption at any given RH. The quantity of water taken up by each step is... 

Evaluation of such equilibrium desorption experiments is very straightforward. The force-extension trace is fitted by a sigmoid function to yield the plateau force and length (Figure 7). The detachment process at the plateau end shows a finite detachment slope, which represents the cantilever force constant once the cantilever has a finite stiffness, and the detachment is on a considerably faster timescale than the pulling, which is generally the case (see Figure 4(d)). 

Slippery case. Low friction force, that is, high lateral mobility, means that a polymer can immediately follow the rip motion. The equilibrium desorption is not altered by friction, resulting in a flat plateau during lateral pulling (Figure 10(b), blue). In this case, molecular dynamics simulation predict a water depletion layer in the vicinity of hydrophobic substrates where the polymer can slide on. ° A subcase is low but detectable friction force. In this case, the polymer does not follow the tip motion immediately. This causes an angle between normal to substrate and polymer. Only once the force exerted by the tip in a lateral direction... 

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