Isotherms by Shape

Classification of Isotherms by Shape Representative isotherms are shown in Fig. 16-5, as classified by Brunauer and coworkers. 

In calculations of pore size from the Type IV isotherm by use of the Kelvin equation, the region of the isotherm involved is the hysteresis loop, since it is here that capillary condensation is occurring. Consequently there are two values of relative pressure for a given uptake, and the question presents itself as to what is the significance of each of the two values of r which would result from insertion of the two different values of relative pressure into Equation (3.20). Any answer to this question calls for a discussion of the origin of hysteresis, and this must be based on actual models of pore shape, since a purely thermodynamic approach cannot account for two positions of apparent equilibrium. 

The S-shaped isotherm has an initial slope that increases with increasing equilibrium solute concentration and has two causes. Giles et al. (1974) attributed the S-shape to cooperative adsorption due to solute-solute interactions. These interactions stabilized the solute at the solid surface, and therefore the first adsorbed molecules enhance the adsorption of the next solute molecules. At high concentration, when the sites of the solid surface are saturated with solute the slope of adsorption isotherm start to decrease again. Sposito (1984) explained the S-shaped isotherm by a competing reaction within the solution. Solution ligands compete with surface... 

A similar argument holds for the influence of the peak shape on the separation criterion. In the non-linear part of the distribution isotherm, the shape of the peak will be a function of the injected quantity. Hence, once again, the location of the optimum may be affected by the composition of the sample. Also, the effect of column dimensions on the peak shape may be hard to predict, and the peak shape may to a large extent be determined by the characteristics of the instrument, rather than of the column. Therefore, if the composition (or the concentration) of the sample can be expected to vary considerably, and if it is desirable that the result of an optimization process can be extrapolated to different columns (of the same type) and to different instruments, then it is advisable to use criteria that are not affected by the relative peak areas, nor by the shape of the peaks. 

The adsorption isotherm starts at a low relative pressure. At a certcdn minimum pressure, the smallest pores will be filled with liquid nitrogen. As the pressure is increased still further, larger pores will be filled and near the saturation pressure, all the pores are filled. The total pore volume is determined by the quantity of gas adsorbed near the saturation pressure. Desorption occurs when the pressure is decreased from the saturation pressure. The majority of physisorption isotherms may be grouped into six types [9]. Due to capillary condensation, many mesoporous systems exhibit a distinct adsorption-desorption behaviour which leads to characteristic hysteresis loops (Type IV and V isotherms) whose shape is related to pore shape. Type I isotherms, characterised by a plateau at high partial pressure, are characteristic of microporous samples. A typical isotherm, representative of a mesoporous sample is given in Fig. 4.6, with a schematic representation of the adsorption steps. 

The new capillary condensation theory, if essentially valid, claims that the shape of isotherms measured up to saturation, that is, x = PjP = 1, is determined by the pore size distribution of porous bodies, and so any theory to explain sorption isotherms by thermodynamic or kinetic mechanisms becomes meaningless except with respect to the formation of monolayer adsorption. Therefore an important problem in sorption is to investigate the pore structure of sorbent specimens, which are easily varied by varying the conditions of their preparation, and to elucidate the pore structure in relation to the material properties. 

We note that the theoretical isotherms exhibit quite different shapes when the radius of elementary particles and the packing type are changed as shown in Figs. 2 and 3. Therefore in later works we could easily obtain suitable experimental isotherms by choosing proper values of and and the type of packing by a trial-and-error method, in order to satisfy the experimental observations. 

In studies of surfactant adsorption at the solid-aqueous solution interface one uncovers interesting features related to the shape of adsorption isotherms in the region corresponding to high surfactant concentrations [15]. Let us discuss the shape of the adsorption isotherm by describing the adsorption in the whole range of surfactant concentrations (from x = 0 to x = 1) from a solution containing infinitely miscible components. To do so, let s compare the surfactant concentration at the surface, x(s), and in the bulk, x. 

One interesting feature of the dynamic model is that it generates adsorption isotherms which are similar to experimentally observed isotherms. The shape of the isotherm is determined by the size of the "surface denaturation" time constant s, and a2/a,. The isotherms may have shapes normally... 

The isothermal S-shaped cure-time curves are represented by two exponentials joined together at c = c, the rate of cure being continuous across the junction. 

Fig. 5 ws the CH4 isotherms measured at 77 K on NTR, LIM, CFC and AC-C03 samples and displayed in a logarithm scale in order to magnify the adsorption range for relative pressure bdow 0.1. Both isotherm step shape and position at F/Pg = 0.5) are different BET and Dubinin theories show, that lower the position of the step, lower the adsorption energy of the adsorbent (2 and respectively). Obviously, the position values are lower for micropotous adsorbents (NTR, LIM, AC-C03) than that of CFC. Isotherm shapes of the mictopcnous adsorbents are dorninated by the absolute pore width and geometry [12]. 

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