Homotattic Surface

The interpretation of adsorption isotherms in terms of a surface displaying a symmetrical (Gaussian) distribution of adsorptive potentials to the adsorbate has been successfully applied to a number of systems but marked exceptions have been found, particularly with crystals that were selected as likely to have completely homotattic surfaces. These exceptional adsorption isotherms are readily interpreted, however, as the result of a sum of two, or occasionally three, distinctly different Gaussian distributions, presumably deriving from the same number of surface constituents. Among these constituents the expected homotattic substrate, which is associated with a particular crystal face, can always be identified. 

The adsorbent was chosen purposefully as one likely to give a near-homotattic surface, because of the hexagonal layer-lattice structure of the crystal the surface constituent of low heterogeneity is therefore identified with the basal plane of... 

Ross and Boyd (II) prepared crystals of sodium chloride in which both the 100 and the HI surfaces were developed the adsorption isotherm of ethane at 90.1° K gave evidence of two type 2—i.e., near-homotattic—surfaces, as well as showing the initial knee, which is evidence of a type 1 surface. This isotherm is shown in Figure 4, which also includes for comparison an ethane isotherm measured at the same temperature for a sodium chloride adsorbent that had only 100 faces developed the pressure characteristic of the phase transition of ethane on the homotattic 190 surface of sodium chloride at 90.1° K shows on both isotherms as the location of a discontinuity at p = 4.5 X 10-3 mm. the homotattic ill portion of the surface is responsible for the convex shape (with respect to the pressure axis) of the isotherm beyond the knee, though the rise is not suffi-... 

The surface field of a near-homotattic surface can be estimated from the observed value of the two-dimensional critical temperature aTc. According to de Boer (4),... 

When a molecule is adsorbed, the process is accompanied by a liberation of heat that can be measured calorimetrically. The experimentally measured heat can be related to a thermodynamic quantity, the differential heat of adsorption, by relationships that depend on the specifics of the calorimeter used [1, Ch. III]. The differential heat of adsorption, on a homotattic surface at any isotherm... 

In these early efforts, the goal was to find an analytical description of Q p) using a specific theoretical model for adsorption on a homotattic surface and an assumed distribution function. An alternative way to use Eq. (9) is to assume the form of both Q p) and q p.. T o) and thence derive the distribution function/(6 o) by inversion. That this can be done and that a unique solution exists for ( Uq) was demonstrated rigorously by Sips [12]. To describe the experimental isotherm. Sips chose for Q p) an empirical equation of the form... 

Homotattic Surface. A microscopically uniform and homogeneous surface. This includes ideal crystal surfaces where the adsorption potential energy, U t, x) is a periodic function of t, e.g. the ideal (100) surface of sodium chloride or an ideal basal surface plane of graphitized carbon black. 

Intrinsic Heterogeneity. That periodic surface heterogeneity possessed by a single homotattic surface. 

Residual Heterogeneity. A term used when describing a patchwise heterogeneous surface it is that heterogeneity that cannot be ascribed to homotattic surfaces and is generally caused by impurities and defects on the surface. 

Table 4.3 Two-Dimensional Equations of State and Adsorption Isotherms on Homotattic Surfaces...

We shall consider the most frequent homotattic patch of surface and Equation 8 in the following substitutions ... 

Adsorption on heterogeneous surfaces is conveniently described in terms of ideal adsorption i.e., a process described by one or the other model described in the scheme of section 3.1.) on a surface characterized by an adsorption-energy distribution function ipiq), where ip q)dq respresents the fraction of surface with adsorption energy between q and q 4- d. This picture is usually referred to as homotattic patch approximation. 

Patch. An area of a surface that is either energetically unisorptic or homotattic. 

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