Surface excess isotherm

Fig. XI-10. Isotherm of composition change or surface excess isotherm for the adsorption of (1) benzene and (2) n-heptane on Graphon. (From Ref. 141.)...

Figure 6.11 Composite (surface excess) isotherms for the adsorption of (a) benzene from solution in methanol on to charcoal177 and (b) chloroform from solution in carbon tetrachloride on to charcoal178 (By courtesy of (a) American Chemical Society, (b) Journal of the Chemical Society)...

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

Since the reduced and relative surface excess isotherms convey composite information on the adsorption of the two components, there is a strong incentive to determine the individual (or separate ) isotherms, i.e. the adsorbed amount n (or ) versus concentration, mole fraction or mass fraction. It will be recalled that this implies some assumptions about the thickness, composition and structure of the adsorbed layer, and therefore is not to be recommended for reporting adsorption from solution data in a standard form. Indeed, this second step is already part of the theoretical interpretation of the adsorption mechanisms. 

A second, more analytical, consequence of 12.1.1) is that the change in bulk composition is not only the consequence of the disappearance of. say A from a mixture of A and B, but is also due to the desorption of B. When an isotherm is measured on the basis of depletion of component A in solution, l.e. when is measured, the resulting Isotherm is not an individual isotherm, relating to the Interfaclal properties of A only, but a surface excess (formally called composite) isotherm, relating to the Interfacial properties of A and B. There is no thermodynamic way to decompose such surface excess isotherms into the two individual ones, although there are situations where this can be done with reasonable model assumptions. 

Before further discussing the thermodynamics and model analyses of surface excess isotherms, let us look at some typical shapes, as shown in fig. 2.8. TYpes (a) and (b) are the most common. Schay and Nagy ) distinguish more types by... 

The more complex the individual isotherms, the more complicated is the surface excess Isotherm. The simple situation of n = 0 and n° = const, leads to... 

Models, methods and examples of decomposing surface excess Isotherms into their constituent parts will be discussed in sec. 2.4. 

In which the l.h.s, is the operational surface excess, telling us by how much the mole fraction of 2 In the adsorbate exceeds that in the liquid. According to (2.3.81 this is (one of) the measured surface excess Isotherms, if plotted as a function of x. 

Figure 2.23. Extrapolation of linear parts of surface excess isotherms. Dotted curve sketch of the individual isotherm for substance 2 in type a.

Basically the Issue is that [4.2.1] reflects a surface excess isotherm, as already encountered in the adsorption of binary mixtures on solid surfaces (secs. II.2.3 and 4). Adsorption of the one component cannot be effected without depletion from the surface of the other, and because splitting these two processes is Inoperational, thermodynamics tells us that only the two adsorptions together are measurable ). 

The solution of the dividing plane problem is that the adsorptions are not referred to a zero value of one of the two components, but that Tj " cmd are introduced where is the surface excess of 1 per unit cirea over the amoimt of 1 in a reference system of uniform composition with Xj = (1 - x) and x =x. This is the excess that is measured in surface excess isotherms and which determines the surface tension. The definitions are... 

Figure 4.3. Surface excess Isotherms according to (4.2.12]. For conditions see the text. K Is the exchange constant. The curves correspond to the drawn ones in fig. 11.2.11, after normalization.

Figure 4.6. Surface excess isotherms (top) ind surface tension (bottom) of a binary mixture of an r-mer and a monomer. z°K(r]l z = 5.

Figure 4.10. Surface excess isotherms of linear alkanes (he), with different chain length n, in mixtures with benzene. Temperature 30°C. (Redrawn from Schmidt and Clever, loc. cit.)...

The set of surface excess isotherms cannot be used to derive individual isotherms eq. [4.2.3b) contains two unknowns. So an additional assumption is needed. The authors took + r A = 1 (results not shown). Equation [4.2.26] might be an alternative. Anedyses like the one leading to fig. 4.10 can of course be extended to all literature data available. 

The specific surface excess isotherms for binary liquid mixtures benzene + n-heptane and benzene + 2-propanol were measured by static immersion method [8] The concentrations of equilibrium solutions were determined using HP 5890 gas chromatograph from Hewlett-Packard. The initial mixtures over the whole concentration range served for detector calibration, The surface excess of a given component was calculated from the relation ... 

Earlier investigations presented in the papers [4,14] suggest a higher selectivity of adsorption in respect to preferentially adsorbed component for adsorbents containing narrower mesopores. Similar effect should be expected for microporous materials In order to study the influence of porosity type on adsorption from liquids the measurements of specific surface excess isotherms were performed for binary liquid mixtures benzene + n-heptane / carbon AC-2 and AC-4 benzene + 2-propanol / carbon AC-2 and AC-4. 

Numerous analytical models have also been developed for binary liquid phase surface excess isotherms. A model equation that accounts for adsorbate size differences, bulk liquid phase nonideality, as well as a simplified description of adsorbent heterogeneity is given below ... 

Fig. 5 Binary surface excess isotherms for adsorption of liquid mixtures (A) benzene (1) + cyclohexane (2) on silica gel and (B) pyridine (1) + -heptane (2) on silica gel and alumina.

The thermodynamic property to quantify the heat effects for ad(de)sorption of a liquid mixture is the heat of immersion. Fig. 7 shows examples of heat of immersion of binary benzene-cycloxane mixtures on two activated carbons at 30°The corresponding surface excess isotherms are U-shaped (e.g., see Fig. 5A). Benzene is the more selectively adsorbed species. The... 

The surface excess isotherm [nj(xi)] of trace water (xi 1) from a mixture on activated alumina can have types I and IV shapes analogous to those for adsorption of pure water vapour [20,21],... 

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... 

The effect of temperature on the surface excess isotherms of water from liquid mixtures on the aluminas is generally much less pronounced than those for adsorption from vapours [26]. 

Analytical mathematical models describing (a) the propagation of constant pattern MTZ and (b) the desorption profiles under local equilibrium conditions in packed columns for ad(de)sorption of bulk binary liquid mixtures having an U shaped surface excess isotherm and obeying SELDF kinetic mechanism are available [27]. 

Surface Excess Isotherm A function relating, at constant temperature and pressure, the relative adsorption, reduced adsorption, or similar surface excess quantity to the concentration of component in the equilibrium bulk phase. 

Kxpcrimcntal data for adsorption from solution are usually expressed as specific reduced surface excess isotherms, sometimes called composite isotherms, in which n()Ax, /m is plotted as a function... 

Despite the above-mentioned problem, numerous works have been published to micromodel adsorbent heterogeneity by assuming that the adsorbent comprises a patchwise distribution of homogeneous sites of different isosteric heats of adsorption [23], According to this concept, the overall surface excess isotherm of a pure gas i on a heterogeneous adsorbent ( f ) is given by... 

It should be noted here that aU models of Tables 3 and 4 were originally developed by using the actual amount adsorbed ( f) as the base variable. We adapted them to describe the actually measured surface excess variable (nD as functions of P, T, and because they describe the experimental surface excess isotherm data very well. 

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