Threshold pressure for adsorption

The effects of the pore size and pore geometry are best illustrated by Table IV. Table IV lists the threshold pressure for adsorption in different ... 

Threshold Pressure for Adsorption in Different Pore Sizes and Shapes N2 on Carbon at 77 K Po = 1 atm... 

Table 2.4. Theoretical threshold pressure for adsorption in different pore sizes and shapes...

Comparing eq.(3.9-l la) for adsorption to eq.(3.9-l lb) for desorption, we obtain the following relationship between the threshold pressure for condensation and that for evaporation for a zero contact angle... 

We now know that for each pore of radius r, there exists a threshold pressure for condensation and a threshold pressure for evaporation. This important point now can be used to determine the pore size and its distribution. During the adsorption cycle the filling of pore with adsorbate is in a radial fashion, and hence the rise in the amount adsorbed versus pressure is gradual. After the pore is filled, and when the pressure is reduced the liquid in the pore will remain until the pressure in the gas phase reaches the evaporation pressure governed by eq. (3.9-1 lb) at which the liquid will instantaneously evaporate, leaving only the adsorbed layer behind. As the pressure is reduced further the amount adsorbed will decrease and the relationship between the amount adsorbed and the pressure is dictated by the equilibrium between the two phases (for example the BET equation). 

Experimental observation of such a trend in lEJ would be a strong indication that the threshold phenomenon is real. Fig. 76 shows the results of nitrogen adsorption on the above-mentioned oxides most of which were reported by Fuller and Thompson [17]. (H2O is for water pre-covered oxides and CO is for partially oxidized carbon.) The value for E of oxides is plotted as a function of the enthalpy of their formation. Since the threshold pressures for some of the oxides are too low to be measured directly, Xc values are obtained from the % theory equation. It is apparent that the correlation does exist as predicted. Although not claimed, due to the question of stoichiometry to be used for the cleaved solid surface, this figure shows a linear relationship between the energies of the threshold and the enthalpies of formations. For the intersection at = 0, the value for E should be... 

Gil et al. [21] present data which seem to evidence a threshold pressure for N2 adsorption. This observation was for nitrogen adsorption on microporous carbon. What is important about this data is that the threshold pressure is obvious even when looking at the data from the point of view of Henry s law. Fig. 77 illustrates this quite well. This plot illustrates that the threshold pressure is not an artifact of the transformation to the x plot. In this figure the threshold pressure appears to be at about 1.0X10 whereas, a x plot indicates it to be about 1.2X 10 P/Ps-... 

The results of the adsorption Ar on Teflon shown in Fig. 78 are in the untransformed form to illustrate the shape of the isotherm. The data for this figure are given in Table 24 to show the precision and accuracy that is obtainable with the instrumentation described. In this form, even with a high threshold pressure, the presence of a threshold pressure for most experiments, especially the volumetric type, would be missed. The zero pressure recording, however, is very obvious with the instruments described. This value is well within any conceivable error by a factor of 10 The flat portion of the pressure curve is more evident in the x plot. This plot is shown... 

Cohan s quantitative analysis in 1938 was based on the suggestion of Foster (1932, 1934) that the hysteresis in adsorption is due to the delay in forming a meniscus in the capillary. For adsorption, this is occurred by radial filling, rather than vertical filling as in the case of desorption. When condensation of the first layer occurs, the effective radius r decreases, causing further condensation at a fixed reduced pressure P/Pq. This means that a pore of radius r, corresponding to the threshold reduced pressure P/Pq, will be filled instantaneously. 

We shall present this approach in two separate parts. In the first part, we shall study the system of water adsorption onto activated carbon, and in the second part we shall deal with a general adsorption system. The reason for this distinction is that in the case of water adsorption on activated carbon, water does not fill the pore at pressures lower than a threshold pressure. At threshold pressure, the pore is instantaneously filled with water. 

In this section, to satisfy the disproof of Henry s law several instances of the observed are presented. This has indeed been reported in the literature by others. With the adsorption of water on NaCl reported by Peters and Ewing [18,19] the threshold pressure is very clear, confirmed by both the isotherm and by infrared. In their investigation of the microporosity of Y-zeolites for which very low-pressure measurements were needed Guo et al. [20] reveal threshold pressures along with the reported oscillating adsorption. The oscillations are undoubtedly due to a variety of effect but one of these could be change in E. ... 

Low-pressure hysteresis is not confined to Type I isotherms, however, and is frequently superimposed on the conventional hysteresis loop of the Type IV isotherm. In the region below the shoulder of the hysteresis loop the desorption branch runs parallel to the adsorption curve, as in Fig. 4.26, and in Fig. 4.2S(fi) and (d). It is usually found that the low-pressure hysteresis does not appear unless the desorption run commences from a relative pressure which is above some threshold value. In the study of butane adsorbed on powdered graphite referred to in Fig. 3.23, for example, the isotherm was reversible so long as the relative pressure was confined to the branch below the shoulder F. 

The threshold level of a substance can be decreased by the presence of less sensori-cally active substances. In a mixture of ethanol, ethylacetate, ethyleneglycol mono-ethylether and toluene, the odor threshold level of ethyl acetate was reduced to half and in the case of cookies a factor of 5 decrease was observed. A reason for this finding may be the adsorption process taking place in the solid food. Compared to the solution processes in the complete food, the influence of other components on the ethyl acetate partition coefficient during a simple adsorption on the surface is likely to be larger. The repulsion of ethyl acetate from the surface increases its partial pressure over the food. 

Let us summarise the conditions of formation of a microscopic foam film in order to serve the in vivo situation. These are film radius r from 100 to 400 pm capillary pressure pa = 0.3 - 2.5-102 Pa electrolyte (NaCl) concentration Ce 0.1 mol dm 3, ensuring formation of black films (see Section 3.4) and close to the physiological electrolyte concentration sufficient time for surfactant adsorption at both film surfaces. Under such conditions it is possible also to study the suitable dependences for foam films and to use parameters related to formation and stability of black foam films, including bilayer films (see Section 3.4.4). For example, the threshold concentration C, is a very important parameter to characterise stability and is based on the hole-nucleation theory of bilayer stability of Kashchiev-Exerowa. As discussed in Section 3.4.4, the main reason for the stability of amphiphile bilayers are the short-range interactions between the first neighbour molecules in lateral and normal direction with respect to the film plane. The binding energy Q of a lipid molecule in the foam bilayer has been estimated in Section 11.2. 

Experimental results of water vapor adsorption. Helium relative permeability, Pr, and water vapor permeability, Pe, for the two alumina pellets are presented in figures 6a and 6b, for water relative pressures up to unity. As the amount of water adsorbed starts to rapidly increase with P/Po, due to capillary condensation, a significant increase of its permeability may also be observed due to the resulting capillary enhancement of flow. At a certain value of P/Po where Vs is close to unity, all pores of the membrane are in the capillary condensation regime and thus follow the capillary enhanced type of flux. At this point water vapor permeability reaches its maximum value while, helium relative permeability decreases rapidly and falls to zero well below the point of saturation. This may be attributed, according to percolation theory, to the fact that in a simple cubic lattice, if -75% of the pores are blocked by capillary condensate, the system has reached its percolation threshold and helium... 

MCM-41 and HMS materials show adsorption at a pressure lower than the threshold at 0.43 p/p°. In this region it is difficult to evaluate the pore size with classical method based on the Kelvin equation, because both micropore filling and capillary condensation can occur. Instead DFT (silica model) permits a better evaluation of pore size distribution in this region, observing a very narrow pore size distribution for lVICM-41 (Figure 6, curve b)... 

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