Energy of immersion

Some experimental techniques are to be preferred for the accurate determination of integral quantities (e.g. from energy of immersion data or a calorimetric experiment in which the adsorptive is introduced in one step to give the required coverage), while others are more suitable for providing high-resolution differential quantities (e.g. a continuous manometric procedure). It is always preferable experimentally to determine the differential quantity directly, since its derivation from the integral molar quantity often results in the loss of information. 

Condensable vapours pose problems with the other methods. Some of these difficulties (e.g. temperature gradients and spurious condensation) can be avoided by the measurement of energies of immersion. 

Figure 5.1. Dependence of the energy of immersion on the initial coverage of the solid surface ( H and V stands for Harkins and Jura procedure ).

The maximum energy of immersion, which we designate A i/0, is liberated when the vacuum-solid interface is replaced by the liquid-solid interface. Thus, for the immersion of an outgassed adsorbent of surface area A, we obtain ... 

When area A is already covered with a physisorbed layer at surface excess concentration r (i.e. n jA), the energy of immersion becomes... 

Finally, when the adsorbed layer is thick enough to behave as a liquid Him, the energy of immersion, A Unm f/1, which corresponds to the disappearance of the liquid-gas interface, is simply ... 

The above equations are all based on the internal energy. Similar equations can be written with the enthalpy since the surface excess enthalpy and energy are identical in the Gibbs representation when 1 =0 (Harkins and Boyd, 1942). Therefore the various energies of immersion defined by Equations (5.6)—(5.8) are all virtually equal to the corresponding enthalpies of immersion, i.e. (A inmH°, AimmHr and Ah 1), thus ... 

Figure 5.2. Relation between energy of immersion and net molar integral energy of adsorption /iV -u1)-...

The second step, which takes place in the calorimeter, gives rise to an energy of immersion A Imm Ur which is of course smaller than A iram U° and directly depends on r, i.e. on the pre-coverage. 

It thus becomes possible to assess the net molar integral energy of adsorption (u° - ux) from the difference between the energy of immersion of the outgassed adsorbent and that of the adsorbent with a pre-adsorbed surface excess concentration, as was originally pointed out by Hill (1949). 

Figure 5.3. Relation between energies of immersion, separation and adhesion.

The following three main routes are available to assess the wettability. The first method is dependent on the measurement of contact angles, while the second and third make use of energy of immersion and adsorption isotherm data. 

Assessment of wettability from the energy of immersion. Since it is equal in magnitude to the Helmholtz free energy of immersion per unit area (cf. Equation (5.32)), the wettability can be written as ... 

In fact, the validity of Equation (5.38) is supported by the observation by Robert (1967) that the energies of immersion of carbon blacks in a number of hydrocarbons of the same family (e.g. n-alkanes from 7 to 16 carbon atoms) could be ranked exactly in the same order as the adsorbability of these hydrocarbons. 

In principle, to carry out immersion microcalorimetry, one simply needs a powder, a liquid and a microcalorimeter. Nevertheless, it was early realized that the heat effects involved are small and the sources of errors and uncertainties numerous. Many attempts have been made to improve immersion microcalorimetric techniques. Before commenting on this type of experiment, we describe the equipment and procedure which has been found by Rouquerol and co-workers to be of particular value for energy of immersion measurements (Partyka et al., 1979). 

Calculation of correction terms and, finally, of the energy of immersion. 

It should be kept in mind that any change in surface area, surface chemistry, or microporosity will result in a change in the energy of immersion. Because immersion calorimetry is quantitative and sensitive, and because the technique is not too difficult to apply in its simplest form, it can be used for quality testing. The preliminary outgassing requires the same care as for a BET measurement, but, from an operational standpoint, energy of immersion measurements are probably less demanding than gas adsorption measurements. 

This was the basis of the approach by Chessick et al. (1954, 1955) and Zettlemoyer etal. (1958), which involved the use of a series of immersion liquids such as butyl derivatives differing only in their polar groups 1-butanol, 2-butanol, butanal, 1-aminobutane, 1-chlorobutane, butanoic acid. With the polar surfaces studied (rutile, CaF2, Aerosil, alumina), an approximately linear relation was found between the energy of immersion and the dipole moment. The slope gave directly the average field strength (for instance, 820 V//rm 1 on a rutile titanium (tv) oxide) and the... 

Another modification easily assessed by immersion microcalorimetry is the change in hydrophobicity of a surface, e.g. by oxidizing a graphitized carbon surface. The energy of immersion in water was shown to increase almost linearly with decrease in hydrophobicity (Young et al., 1954) and the energies of immersion of hydrophobic and hydrophilic patches were estimated to be 31 and 730 J m-2, respectively (Healy et ah, 1955). 

The change in nature of the oxidized surface can be followed with immersion liquids other than water. By increasing the oxygen content of a carbon black (Le. Spheron 6) up to 12%, Robert and Brusset (1965) obtained an increase of the energy of immersion in methanol from 140 to as much as 390 mJ nT2 (practically the same ratio as that observed with water), whereas the energy of immersion in n-hexadecane remained nearly constant, around 100 mJ m-2. 

Figure 5.8. Various types of energy of immersion isotherms (after Zettlemoyer, 1965).

When a set of immersion liquids is used, with an appropriate range of molecular sizes and shapes (i.e. flat, like aromatic molecules, or bulky), the energy of immersion is directly dependent on the extent of the molecular penetration into the porous network. This was shown for example by Atkinson et al. (1982) on microporosity and by Denoyel et al. (1993). 

As we have already seen, it is not difficult to undertake accurate energy of immersion measurements provided that the microcalorimetric technique is carefully selected and that certain precautions are taken. It was pointed out by Chessick (1962) that it is deceptively easy to obtain heat of wetting data, but the results will be of very little scientific value unless steps are taken to ensure that the adsorbent and the liquid have been properly prepared and that the conditions of the experiment meet well-defined thermodynamic requirements. 

Immersion calorimetry provides a very useful means of assessing the total surface area of a microporous carbon (Denoyel et al., 1993). The basic principle of this method is that there is a direct relation between the energy of immersion and the total area of the microporous material. Indeed, for the two model cases of slit-shaped and cylindrical micropores, the predicted maximum enhancement of the adsorption potential (as compared with that of the flat surface of same nature) is 2.0 and 3.68, respectively (Everett and Powl, 1976). These values are remarkably similar to the increased surface area occupied by a molecule in the narrowest possible slit-shaped and cylindrical pores (i.e. 2.0 in a slit and 3.63 in a cylinder). To apply the method we... 

From the viewpoint of the areal energy of immersion, the behaviour of micro-porous and external solid surfaces is identical. 

The first stage is usually a simple comparison of the specific energies of immersion. In the absence of a relatively large external surface area, the energies are controlled by the nature of the microporous network (see for instance Stoeckli and Ballerini, 1991, or Rodriguez-Reinoso et al., 1997). 

For a more detailed evaluation of the microporosity, one must be able to interpret the energy of immersion data. At present, there are two procedures favoured by different investigators. 

The first procedure is based on the Dubinin-Stoeckli principles of volume filling (see Section 4.4.4). The energy of immersion A l/ is related to the micropore volume W0(d) and the characteristic energy Eq for a given micropore size and immersion liquid (Bansal et al., 1988) by the expression ... 

The second procedure directly relates the energy of immersion A, U to the micropore surface area a(mic), as described in Section 6.5.2. As we saw, very simply ... 

Immersion of dry samples in liquids of different molecular size This method is designed to take advantage of molecular sieving. The basic data are simply in the form of a curve of the specific energy of immersion versus the molecular size of the immersion liquid. This provides immediate information on the micropore size distribution. For room-temperature experiments one can use the liquids listed in Table 8.1, which are well suited for the study of carbons. Because of the various ways of expressing the critical dimension of a molecular probe or its molecular size , one must be careful to use a consistent set of data (hence the two separate lists in Table 8.1). Again, one can process the microcalori-metric data to compare either the micropore volumes accessible to the various molecules (see Stoeckli et a ., 1996), or the micropore surface areas, as illustrated in Figure 8.5. 

Most carbon blacks have a low affinity for water, i.e. they are hydrophobic. However, the level of hydrophobicity is reduced by the presence of chemisorbed oxygen and certain functional groups (Walker and Janov) 1968 Bradley et al., 1995). The relative extents of the polar and hydrophobic areas of carton blacks have been studied by various methods (Boehm, 1994), including energy of immersion measurements (Barton and Harrison, 1975) and by liquid flow calorimetry (Groszek,... 

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