Characteristic adsorption curve

The curve of Fig. XVII-15 is essentially a characteristic curve of the Polanyi theory, but in the form plotted in might better be called a characteristic isotherm. Furthermore, as would be expected from the Polanyi theory, if the data for a given adsorbate are plotted with RTln P/f ) as the abscissa instead of just ln(P/P ), then a nearly invariant shape is obtained for different temperatures. The plot might then be called the characteristic adsorption curve. 

Fig 9. Characteristic adsorption curves ftn- nitrc en on active carbons at 77 K... 

If the characteristic adsorption curve shows temperature invariance, as it is often observed for microporous carbons, the first term in Eq. (32) is equal zero. An experimental application of Eq. (32) and (33) for active carbons was reported in ref. [108]. 

Thus, the curves =f(W) should be temperature-independent for a given gas. Since this curve characterizes the given adsorbate-adsorbent system, it is called the characteristic adsorption curve for a given adsorbent. The characteristic curve is the same for all temperatures and, hence, a unique characteristic of a given adsorbent-adsorbate system. 

The experimental verification of the Polanyi potential theory can be carried out by calculating the characteristic curve from one experimental isotherm and in determining from the characteristic curve the adsorption isotherms at any other temperature. It is essential that the basic isotherm used for obtaining the characteristic adsorption curve should cover the whole range of values and followed with great accuracy. 

Experimental verification of the Polanyi theory deals with the calculation of the characteristic adsorption curve by means of an experimental isotherm and hence determination of the isotherms at different temperatures. The first practical examinations of the potential theory of adsorption carried out by Titoff [137] and Berenyi [138] showed the good agreement with experiment. 

Dubinin and his co-workers [156-158] as well as Radushkevich [159] found that the characteristic adsorption curve is related to the porous structure of the adsorbent. Radushkevich [159] proved theoretically the equations of the characteristic adsorption curves for the two extreme types of adsorbents with narrow and wide pores. Based on this Dubinin proposed the expression known in literature as the Dubinin-Radushkevich (DR) isotherm equation [136]. 

The underpotentlal deposition of lead has been examined on LEED-characterized single crystal silver surfaces with 0.1 M HF as the electrolyte using a special ultra-high vacuum-electrolyte transfer system. Each of the low index surfaces has a characteristic voltammetry curve with multiple adsorption and desorption UPD peaks. 

The relationship between the over-potential and Ig U will deviate from the Tafel linear area due to the medium affecting the diffusion layer. The effect will gradually disappear and the polarization curves separate each other obviously when the potential is far from zero electric charge potential. This is the reason that COj and Ca(OH) ions have some surfactant action compared with OH ion to form characteristic adsorption more easily and to bring about the change of the capacitance of the double electric charge layer. 

The adsorption isotherms obtained for various detergents showed a characteristic feature that an equilibrium value was obtained when the concentration of detergent was over critical micelle concentration (CMC). The adsorption was higher at 40°C than at 20°C. However, the shapes of the adsorption curves was the same (Birdi, 2002). 

The adsorption curve of cadmium ions as a function of pH on metal oxide surfaces is characteristic for such systems, and is called the adsorption edge. The adsorption of cadmium increases with increasing pH, and is almost complete (-100%) at high pH. The adsorption edge shifts with an increase in the initial concentration of Cd2+ ions towards higher pH values. The adsorption of cadmium cations causes an increase of the t, potential, with an increase of total concentration of these ions in the system. 

It should be noted that irrespective of complexity of a system, its component composition and properties, the principle of formation of porosity of adsorbents found for binary mixtures holds for more complicated systems too. The only difference is final results, i.e., the shape of the Vg composition curves that is different from those of the adsorption curves of samples synthesized from binary systems. Several explanations can be suggested for this difference but the main reason is sorption characteristics of the components, which can be identical, slightly or substantially different from one another. As reported... 

Several simulation runs were carried out to gain insight into the effect of bead design parameters on the adsorption characteristics of immobilized adsorbent beads. The physical parameters (rate constant, diffusivity etc.) for the simulation studies were determined from experimental data on the adsorption of cycloheximide, a low molecular weight antibiotic, onto XAD-4 non-ionic polymeric resin (10.11) (Table I). The fit between the model and the experimentally determined adsorption curves is quite good (Figure 3). 

The removal of Zn(II) by adsorption onto HCO in ammoniacal solutions is illustrated in Fig. 20. The data around pH 6-7 do not follow the characteristic sigmoidal curve, with the percent removal decreasing sharply followed by an immediate sharp increase. The data are modeled as two distinct curves (see Sec. VI) to highlight the probable cause of this apparent deviation from normal adsorption behavior. Curve 1 represents the removal assuming that a coprecipitation mechanism is operating. Curve 2 represents the removal assuming that an adsorption mechanism is operating. 

The latter mechanism, on the other hand, accounts for the peak characteristic of the second adsorption curve. A lowering of the proton concentration in solution would favour the dissociation of the surface SiOH... 

Having calculated the curve characteristic for a given temperature it is possible to determine adsorption isotherms at other temperatures. The Polanyi potential theory does not give a definite equation of adsorption isotherm which, to some extent, replaces the characteristic adsorption equation. 

The validity and the usability of the potential theory for prediction of the multicomponent adsorption are tested on the data on binary adsorption. The first set of data is taken from Ref 102. The data on adsorption of four different hydrocarbons on the same adsorbate at 298 K were correlated by means of five fitting parameters four characteristic adsorption energies , and one adsorbate capacity xq common to all four substances. The results of correlation presented in Fig. 22 indicate good agreement of calculated curves with experimental data. 

Fig. 25 shows adsorption curves for five binary mixtures of the four components above. The characteristic adsorption energies are taken from the correlation of individual adsorption isotherms with a common value of xg. A good quantitative agreement between experimental data and calculated curves is observed, except for the methane-ethane mixture, for which the agreement is slightly worse. The qualitative agreement is also excellent. For example, the ethane-propylene and methane-ethylene curves almost coincide and intersect at low molar... 

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