Isotherm shape influence

The influence of temperature can be seen on Figs. 8-9. The storage capability is increasing for lower temperatures. Figure 9 compares the behaviour of the adsorption isotherms at different temperature levels for two of the more promising samples steam activated Busofit-M8 and wood-based carbon WAC 3-00 . The shape of the isotherms in the two cases is dissimilar. The isotherms for the 77 and 153 K exhibit a classical type 1 isotherm shape indicating a microporous material. The isotherms at room temperature exhibit a much less pronounced curvature (more like type II isotherm). As is seen from plots (Fig. 9) experimental data fit the calculated adsorption values (Dubinin-Radushkevich equation) with an error sufficient for practical purposes. 

Figure 5. Effectiveness factor rj as a function of the Thiele modulus for different pellet shapes. Influence of intraparticle diffusion on the effective reaction rate (isothermal, first order, irreversible reaction).

These considerations have their consequences regarding the interpretation of experimental data should it be done in terms of isotherms or in equations of state Preferably both should be considered, but when specific features are under study a choice may have to be made. For instance, surface heterogeneity shows up very strongly in the shapes of the Isotherms (sec. 1.7) but very little in the equation of state in the model case of local Langmuir isotherms without lateral interaction heterogeneity is not seen at all in the equation of state (because the energy is not considered and the entropy not affected) whereas the isotherm shape is dramatically Influenced. On the other hand, for homogeneous model surfaces equations of state may be more suited to observe subtle distinctions in lateral mobility or lateral interaction. 

The mobile-phase composition in chromatography is important because (1) it determines the thermodynamic properties of the separation, and (2) it may effect the mobile-phase viscosity and thus the operating pressure. The thermodynamic properties are characterized by the adsorption isotherm. The adsorption isotherm directly influences the shape and rate of migration of the individual components of the feed and thus the degree of separation. How strongly the mobile-phase composition effects the adsorption isotherm needs to be ascertained for each separation problem experimentally. This can be done by measuring the individual band profiles at various compositions or by measuring the... 

The ideal model should be applied to get information about the thermodynamic behavior of a chromatographic column. Through work by Lapidus and Amundson (1952) and van Deemter et al. (1956) in the case of linear isotherms and by Glueckauf (1947, 1949) for nonlinear isotherms, considerable progress was made in understanding the influences of the isotherm shape on the elution profile. This work was later expanded to a comprehensive theory due to improved mathematics. Major contributions come from the application of nonlinear wave theory and the method of characteristics by Helfferich et al. (1970, 1996) and Rhee et al. (1970, 1986, 1989), who made analytical solutions available for Eqs. 6.41 and 6.42 for multi-component Langmuir isotherms. 

Interactions between adjacent adsorbed molecules (3) exist for almost all real adsorption systems. For gas-solid adsorption these interactions make an important contribution to isotherm shape and in systems where adsorbent-adsorbate interactions are comparatively the interactions between adjacent adsorbed molecules may play a dottunant role (e.g., type 111 isotherm of Fig. 3-6)1 In liquid-solid adsorptidh the interactions between adsorbed molecules are generally much leSS ihiportant than in gas-solid adsorption, insofar as their influence oh. isotherm shape is concerned. Similar interactions exist in the nonadsorbed phase and largely cancel the net contribution to adsorption energy of interactions between adsorbed molecules. Occasionally, this cancellation may be incomplete, and interactions between adsorbate molecules can then make an important contribution to adsorption in liquid-solid systems (e.g. basic eluent effect in Section 8-3B). 

Already, through work by Glueckauf and Coates (1947) and Glueckauf (1949) considerable progress has been made in understanding the influences of the isotherm shapes on the shapes of elution profile for nonlinear isotherms. 

Also the aggregation number has a direct influence on the isotherm shape, however, for n > 20 it becomes also independent of n. If the critical adsorption Fc is sufficiently large, the curves exhibit a characteristic kink which indicates the formation of clusters in the adsorption layer. 

Very few attempts have been made to investigate the influence of porosity on the course of adsorption from solution. Recent work in this laboratory has shown that in favourable cases it is possible to extend the application of the OCg-method for the analysis of solute isotherms. The analysis gave a clear indication of the effect of primary micropore filling in distorting the isotherm shape when applied to certain L-type isotherms (e.g. of iodine and salicylic acid adsorption by activated charcoals), but difficulties were encountered when the non-porous reference material gave H-shaped or S-shaped isotherms (i.e. either very high or very low affinity). 

Nucleation catalysts also have a strong influence on the overall crystallization kinetics, as is demonstrated in the experimental isotherms illustrated in Figs. 9.69 and 9.70 for poly(caprolactam) (238) and poly(ethylene terephthalate) (253) respectively. The isotherms for poly(ethylene terephthalate) are for a fixed crystallization temperature with different types of nucleation catalyst at the indicated weight percent. In all cases the isotherm shapes are similar to one another. There is an enhancement of the crystallization rate that is also found with other catalysts for... 

This section is concerned with analyses of simultaneous reaction and mass transfer within porous catalysts under isothermal conditions. Several factors that influence the final equation for the catalyst effectiveness factor are discussed in the various subsections. The factors considered include different mathematical models of the catalyst pore structure, the gross catalyst geometry (i.e., its apparent shape), and the rate expression for the surface reaction. 

On the other hand, changes of subphase pH have no considerable influence on the shape of then -A curves of lecithins, since they do not contain movable protons. This is different in the case of cephalins (e.g. (7)), where the isotherms at high pH s are considerably broadened (34). 

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