Adsorption isotherms shapes

The preceding set of equation is valid only for Langmuir adsorption isotherms, and numerical simulation must be used to obtain the flow rates for other adsorption isotherm shapes or for multicomponent mixtures. 

In the present theory of van der Waals adsorption, the multilayer starts below the pressure P and builds up with increasing pressure, and the capillaries are not filled up even for pressures greater than this condensation pressure P, which contradicts the capillary condensation. This means that the multilayer theory based on van der Waals adsorption has an upper limit in the pressure range. Despite this limitation, the van der Waals theory puts all five types of adsorption isotherm shape into one framework, that is it can deal with unimolecular adsorption (Langmuir), multilayer adsorption (BET) and enhanced adsorption in capillaries (BDDT). 

The nitrogen adsorption isotherm shape changes slightly for silicas modified by pyrolysis T< 1000 K) of different organics independent of the type of oxide matrices in comparison with that for pristine silicas (Figure 4.5). 

Figure 4.8. The lUPAC classification of adsorption isotherm shapes (Sing etal., 1985)...

Adsorption measurements should preferably be supplemented by microcalorimetry, such as immersion and flow-microcalorimetry (see Figure 4.8. The lUPAC classification of adsorption isotherm shapes see also Figure 8.4). These techniques give additional information about the nature of surfaces of the adsorbent and the mode or mechanism of adsorption. 

When calcium is used in the preparation of activated carbons it is found that the adsorption capacity increases in both carbon series with the extent of burn-off. However changes in the porosity of the activated carbons with burn-off differ considerably in the presence of calcium, mainly for CO, activation. Figure 1 (a and b) for carbon A and Figure 2 (a and b) for carbon B show the remarkable effect of the catalyzed carbon-CO, activation. The adsorption isotherms shapes are very different from those found for the uncatalyzed activation. Isotherms are a combination of type I and II in contrast to the well defined type I isotherms obtained for the uncatalyzed CO, activation. Carbon A2 and B2 behave differently (Figure 1 b and 2b) probably due to their different initial porosity and calcium contents. In any case, catalytic activation in CO, gives rise to a noticeable development of mesoporosity and, as a result, a much wider pore size distribution. Mercury porosimetry. Figure 3 (a and b), show the very different pore size distributions obtained by catalytic activation with calcium mesoporosity development is very noticeable in agreement with the N, adsorption data. 

Carbon C-IIl has a slight higher micropore volume with a wider pore entrances than C-l and C-ll which is equally accessible to both N2 and CO2. Its N2 adsorption isotherm shape (.see Figure 2) indicates that in addition to micropores there is a well developed mesoporosity which gives rise to an important slope of the isotherm plateau. 

Figure 10.4. Basic adsorption isotherm shapes for vapors on solids below critical temperature of the adsorbate.

The adsorption isotherm corresponding to Eq. X-51 is of the shape shown in Fig. X-1, that is, it cannot explain contact angle phenomena. The ability of a liquid him to coexist with bulk liquid in a contact angle situation suggests that the him structure has been modihed by the solid and is different from that of the liquid, and in an enmirical way, this modihed structure corresponds to an effective vapor pressure F , F representing the vapor pressure that bulk liquid would have were its structure that of the... 

Adsorption isotherms are by no means all of the Langmuir type as to shape, and Brunauer [34] considered that there are five principal forms, as illustrated in Fig. XVII-7. TVpe I is the Langmuir type, roughly characterized by a monotonic approach to a limiting adsorption at presumably corresponds to a complete monolayer. Type II is very common in the case of physical adsorption... 

Desiccants. A soHd desiccant is simply an adsorbent which has a high affinity and capacity for adsorption of moisture so that it can be used for selective adsorption of moisture from a gas (or Hquid) stream. The main requkements for an efficient desiccant are therefore a highly polar surface and a high specific area (small pores). The most widely used desiccants (qv) are siHca gel, activated alumina, and the aluminum rich zeoHtes (4A or 13X). The equiHbrium adsorption isotherms for moisture on these materials have characteristically different shapes (Fig. 3), making them suitable for different appHcations. 

Many models have been proposed for adsorption and ion exchange equilibria. The most important factor in selecting a model from an engineering standpoint is to have an accurate mathematical description over the entire range of process conditions. It is usually fairly easy to obtain correcl capacities at selected points, but isotherm shape over the entire range is often a critical concern for a regenerable process. 

The basic measurement of adsorption is the amount adsorbed v, which usually is given in units of cm of gas adsorbed per gram of adsorbent. Usually this quantity is measured at constant temperature as a function of pressure p (in mm Hg), and hence is termed an isotherm. Isobars and isosteres also can be measured, but have little practical utility. It has been found that isotherms of many types exist, but the five basic isotherm shapes are shown in Figure 1, where />ois the vapor pressure. 

Fig. 17 shows the adsorption isotherms of all (undimerized and dimerized) particles. Except for a very fast increase of adsorption connected with filling of the first adlayer, the adsorption isotherm for the system A3 is quite smooth. The step at p/k T 0.28 corresponds to building up of the multilayer structure. The most significant change in the shape of the adsorption isotherm for the system 10, in comparison with the system A3, is the presence of a jump discontinuity at p/k T = 0.0099. Inspection of the density profiles attributes this jump to the prewetting transition in the... 

Motivated by a puzzling shape of the coexistence line, Kierlik et al. [27] have investigated the model with Lennard-Jones attractive forces between fluid particles as well as matrix particles and have shown that the mean spherical approximation (MSA) for the ROZ equations provides a qualitatively similar behavior to the MFA for adsorption isotherms. It has been shown, however, that the optimized random phase (ORPA) approximation (the MSA represents a particular case of this theory), if supplemented by the contribution of the second and third virial coefficients, yields a peculiar coexistence curve. It exhibits much more similarity to trends observed in... 

As with the Langmuir adsorption isotherm, which in shape closely resembles Michaelis-Menten type biochemical kinetics, the two notable features of such reactions are the location parameter of the curve along the concentration axis (the value of Km or the magnitude of the coupling efficiency factor) and the maximal rate of the reaction (Vmax). In generic terms, Michaelis-Menten reactions can be written in the form... 

Knox and Piper (13) assumed that the majority of the adsorption isotherms were, indeed, Langmuir in form and then postulated that all the peaks that were mass overloaded would be approximately triangular in shape. As a consequence, Knox and Piper proposed that mass overload could be treated in a similar manner to volume overload. Whether all solute/stationary phase isotherms are Langmuir in type is a moot point and the assumption should be taken with some caution. Knox and Piper then suggested that the best compromise was to utilize about half the maximum sample volume as defined by equation (15), which would then reduce the distance between the peaks by half. They then recommended that the concentration of the solute should be increased until dispersion due to mass overload just caused the two peaks to touch. 

The adsorption of a component j in a given system depends on temperature T and on the component s concentration, Cyj, in the bulk phase. The overall adsorption equation can be written as Aj =f(T, Cyj). The relation between adsorption and the adsorbate s bulk concentration (or pressure, in the case of gases) at constant temperature is called the adsorption isotherm the relation between adsorption and temperature at constant concentration is called the adsorption isobar. From the shape of the adsorption isotherms, the adsorption behavior can be interpreted. In the case of monolayer adsorption, the isotherms are usually written in the form 9 =f(Cyj). (The subscript j is dropped in what follows.)... 

There are several isotherm models for which the isotherm shapes and peak prohles are very similar to that for the anti-Langmuir case. One of these models was devised by Fowler and Guggenheim [2], and it assumes ideal adsorption on a set of localized active sites with weak interactions among the molecules adsorbed on the neighboring active sites. It also assumes that the energy of interactions between the two adsorbed molecules is so small that the principle of random distribution of the adsorbed molecules on the adsorbent surface is not significandy affected. For the liquid-solid equilibria, the Fowler-Guggenheim isotherm has been empirically extended, and it is written as ... 

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