S-Shaped excess isotherms

In the case of S-shaped excess isotherms, the value of the adsorption azeotropic composition xf is known. At the azeotropic point nf" = 0 therefore, Xi = Xu according to Eq. (1). Since x = n /n the adsorption capacity can be divided into two terms with the help of the equations [14-16]... 

In this chapter we give a parallel analysis of the liquid sorption excess isotherms and adsorption exchange enthalpy isotherms of benzene-n-heptane and methanol-benzene mixtures on adsorbents with polar and apolar surfaces. Systems with U- or S-shaped excess isotherms were selected. Our aim is to examine the presence and character of a connection between adsorption excess and enthalpy isotherms for the various isotherm types [36],... 

An excess isotherm determined in a methanol-benzene mixture on silica gel is U-shaped. If, however, the silica surface is modified by octadecyldimethylchloro-silane (silica gel Cig) in methanol-benzene mixtures, an S-shaped excess isotherm is obtained, the azeotropic point of which is x, = 0.615 (Fig. 8a). When the displacement process is started from benzene, it can be seen that up to a molar fraction of Xi = 0.6 the incorporation of methanol into the adsorption layer results in a change in enthalpy of about 7.35 J/g. However, the displacement of benzene is not yet complete up to the azeotropic point the adsorption layer will also contain benzene. A common characteristic of the two isotherms presented in Fig. 8 is that the isotherm nf = /(xj) is linear in a very wide range of composi-... 

For S-shaped excess isotherms (Schay-Nagy types IV and V [46-49]), < )i is nearly constant in a relatively wide concentration range, and at o(n) = Q (j)S = ( ja j adsorption azeotropic composition, appears. In this case the value of A ,// changes very little in the middle section of the enthalpy isotherm, where ( )5 is constant then at the azeotropic composition a maximum... 

FIG. 11 Classification of immersional wetting enthalpy isotherms (a) U-shaped excess isotherm, with corresponding enthalpy of irmnersion isotherm, (b) S-shaped excess isotherm, with corresponding enthalpy of immersion isotherm. 

When alcohol-benzene mixtures are adsorbed on adsorbents with low surface energies, S-shaped excess isotherms are measured [17-19,32,33]. When changes in enthalpy accompanying the adsorption displacement process are examined in these systems, the integral exchange enthalpy isotherms usually do not increase monotonously but possess a backward section. After... 

The solubility of several penetrants in PTMSP indicate relevant differences between polar and non-polar components. In particular, for the alcohols, unusual S shaped solubility isotherms are observed which cannot be explained by the dual mode model. Variations of solubility with temperature were also considered in this work, and the mixing enthalpy for n-pentane, n-hexane, ethanol and methanol in PTMSP was calculated. Significant negative mixing enthalpies were measured in all cases, and absolute values of the excess enthalpy of the sorption is much higher for the alkanes than for the alcohols. 

Figure 5.13. The two basic shapes of reduced surface excess (or composite ) isotherms over the whole concentration range S-shape (S) or inverted U-shape (U). Thick line axes (zero in bottom left) represent the isotherms for component 2. Thin line axes (zero in top right) represent the isotherms for component 1.

Figure 5.14. Typical shapes of surface excess isotherms from dilute solutions (Langmuir or L-shape, S-shape, stepwise (SW)).

Figure 2.8. Classification of excess isotherms for binary solutions, (a) (inverse) U-shape (b) (toppled) S-shape (c) linear.

The surface excess isotherm for adsorption of bulk water (0 < Xi < 1) from a binary liquid mixture can be U (water selectively adsorbed at all values of Xi) or S (water not selectively adsorbed at aU values of xi) shaped [20], Figure 8 shows an example of U shaped isotherm for adsorption of water-alcohol binary mixture on Alcoa H-152 alumina... 

Different types of adsorption excess isotherms (U- and S-shaped functions) naturally yield different free enthalpy functions A21G = /(Xi), the course of which is characteristic of the minimum energy of wetting at the solid/liquid interface, a parameter diagnostic of the stability of the disperse system. 

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