Isothenn types

Truly reversible Type V isotherms are quite rare. It is significant that the example reported by Dubinin (1980) was obtained on a low bum-off (5.7%) carbon, which was certainly ultramicroporous. It was pointed out that with an activated carbon obtained by 20% bum-off, the hysteresis extended over virtually the whole range of pore filling - the water isothenn then having a very similar appearance to that of the Carbosieve isotherm in Figure 9.26. 

Amphiphilic behaviour at an air-water interface was studied using monolayer experiments. Surface pressure-area isothenns were recorded for PS-rfe dr-(NH2) with = 1-16. The formed monolayers were also investigated with a Brewster angle microscope (BAM) [53], which made it possible to investigate the type of structures that are formed in the monolayer. The results are shown in Figure 15. 

Figure 6, The induction period, of the aiitocatalytic reaction, of 2 cm of a high explosive of the tiue AC type confined in the closed cell and subjected to the isothermal storage test performed at a T, on the low temperature side, recorded for the time, At, from the insertion of the cell into the isothennal storage testing device till the start of the autocaialylic reaction of the high explosive at the T,.

In any event, it is clear that it is the self-heating process, in the early stages, of a chemical of the TD type, having an arbitrary shape and an arbitrary size, placed in the atmosphere under isothennal conditions, and not the induction... 

SUiircdse type uptake curve lO c uptake at pH 5 and uptake a( pH 6- ) Linear Jog-log adsorption isothenns at constant pH, slope I 17 kJ/mol... 

Problems in Choice of a Reactor. When a process engineer is faced with the problem of designing a commercial or semicommercial unit, he must first choose the reactor to be used. The type of reactor (tube, tower, or tank), the type of operation (batch, continuous, recycle, or once-through), and the means of temperature control (isothennal or adiabatic) may depend on the type of reaction involved. In order to choose the best reactor and method of operation, the specific type of reacting system must be considered. 

The BET isotherm plots for the Cr(VI)/Sn02 catalyst (Figure 4) show that tlie isotherm for uncalcined catalyst is typical for adsorption onto a microporous solid (type 1 isotherm). This form of isotherm is retained after calcination at 300°C, but after calcination at higher temperatures the isotherm changed drastically in form. Calcination at 1000°C resulted in an isothenn characteristic of a type III non-porous solid. Whilst after calcination at 600°C the material exhibited intermediate behaviour and was mesoporous. 

In the same figure, for comparison, the isotherm obtained for tlie Alumina support after heat treatment at 500°C is shown. The isotherm was of Type IV, corresponding to a mesoporous material i.e. having pores between 1 and 25nm pore radii. The pore size distribution, calculated using the BJH [12] method on the desorption branch of the isothenn, indicated that the majority of the mesopores in this material had a radius of 3mn. 

In conclusion, tlie maximum adsoiption capacity should be measmed in fixed-bed experiments under dynamic conditions, and if models aie applicable, diffusion coefficients should be also deteniiined in fixed-bed appaiams. Due to the fact tliat the equilibrium isotheniis requue extended data series and thus are time-consuming experiments, the latter are quite difficult to be conducted in fixed-bed reactors and from this point of view, it is more practical to evaluated equilibrium isothams in batch reactor systems. Then, it is known that when applying fixed-bed models using an equilibrium isothenn obtained in batch-type experiments, the equilibrium discrepancy (if it exists) can be compensated by a different estimate for the solid diffusion coefficient (Inglezakis and Grigoropoulu, 2003 Weber and Wang, 1987). 

There are several types of comparative plots such as the t-plot [69-72], tts-plot [12, 13, 17, 27] and 6-plot [73], which differ only in the way of presenting the standard adsorption isotherm measured on the reference solid. In the case of the 0-plot, the standard isothenn is... 

Eq.(2) together widi Eq.(3) describe isodierms not only for supercritical, but also for subcritical if the isothenns ow type-I feature. It was shown recendy [22] that diis model woiks well for the isodierms distributed densety around the critical temperature as shown... 

FIGURE 2.18 A typical Type II isothenn showing Point A and Point B. (Gregg, S.J. and Sing, K.S.W., m Adsorption, Surface Area, and Porosity, Acad. Press Inc. London, 1982. With permission.)... 

FIGURE 4.2 Schematic plot of a type II isothenn from lUPAC classification (Sing 1985) as a function of pressure (a) and the logarithm of pressure (b). The dashed fine shows the point of monolayer saturation, and the dotted line marks the point of the adsorbate vapor pressure. In (c), a schematic drawing of the (ideal) situation is shown multilayer adsorption takes place, but the adsorbate-surface interaction is stronger than adsorbate-adsorbate interaction, thus the first layer forms preferentially to multilayer growth. 

VI This type of isotherm is attributed to several possibilities the most likely being, if the temperature is below the adsorptive triple point, that the adsorbate is more Uke a solid forming a structured layer, i.e. epitaxial growth. Other possible explanations include multiple pore sizes. If the steps are at the low-pressure portion of the isotherm, then the steps may be due to two or more distinct energies of adsorption. If the steps are at the high pressure part of the isothenn, then the steps might be due to sharp steps on the adsorbate surface... 

The BET equation includes isotherms of types 1. 2 and 3 but not types 4 and 5. Brunauer et al. [28] derived a new isothenn equation to cover all five types. The BET equation has also been derived by statistical reasoning by several authors [16]. 

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