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Extension of acid/base theories to solids
The surface of a metal oxide consists of ordered arrays of acid-base centres. The cationic metal centres act as Lewis acid sites while the anionic oxygen centres act as Lewis bases. Surface Hydroxyl groups are able to serve as Brønsted acid or base sites as they are able to give up or accept a proton. The surface of most metal oxides will be, to some extent, hydroxylated under normal conditions when water vapor is present. The strength and the amount of Lewis And Brønsted acid-base sites will determine the catalytic activity of many metal oxides. Due to this there is a great need to develop standard methods for the characterization of the strength, concentration, and distribution of surface acid-base sites.

The concepts of Lewis acid-base theory and Brønsted-Lowry acid-base theory may be applied to surfaces, however there is no general theory that serves to determine surface acidity or basicity. The qualitative treatment of Brønsted acid base theory is based on the thermodynamic equilibrium constant (Ka) of acid-base reactions between individual molecules in homogeneous systems. This treatment requires measurement of equilibrium concentrations of reactants and products. The presence of two phases also provides a problem for the quantitative acid-base determination of solids. When an acid or base is adsorbed on to an oxide surface it will perturb neighbouring acid-base sites. This perturbation will inevitably influence the relaxation of the surface and make it impossible to have acid-base reactions at the surface which only involve a single surface site.

Structural relation to surface acidity/basicity
For metal oxides acidity and basicity are dependent on the charge and the radius of the metal ions as well as the character of the metal oxygen bond. The bond between oxygen and the metal is influenced by the coordination of the metal cations and the oxygen anions as well as the filling of the metal d-orbitals. The surface coordination is controled by the face that is exposed and by the surface relaxation. Structral defects can greatly contribute to the acidity or basicity as sites of high unsaturation can occur from oxygen or metal ion vacancies.

Indicator Method
Adsorption of an indicator molecule was first proposed by Hammett for ordering the strength of solid acids and bases. This technique is only applicable to surface Brønsted sites on metal oxides. According to Hammett, the strength of a Brønsted surface site can be determined by the Hammett acidity function,

$$ H_o = pK_{BH^+} -log \frac{[BH^+]}{[B]} $$

where B is the basic indicator molecule. The concentration of Brønsted acid sites can be determined by titrating a suspension of the oxide with an acid/base indicator present. However, this method is subject to many problems. For instence only Bronsted acid sites can be quantified with this method. Metal oxide surfaces can have both Brønsted and Lewis acid sites present at the same time which leads to a nonspecific interaction between the oxide and the indicator. Also, as outlined in the theory section, the perturbation of neighboring sites upon adsorption of indicator molecules compromises the integrity of this model.

IR determination of adsorbed probe molecules
The adsorption of a very weakly basic or acidic probe molecule can serve to give a picture of Brønsted and Lewis acid-base sites. Infared spectroscopy of surface sites and adsorbed molecules can then be used to monitor the change in the vibrational frequencies upon adsorption. A very weakly acidic probe molecule can be used to minimize disturbing neighboring sites so that a more accurate measure of surface acidity or basicity can be obtained. A variety of probe molecules can be used including: ammonia, pyridine, acetonitrile, carbon monoxide, and carbon dioxide.

Calorimetric and Thermal Desorption
Two promising methods for the description of the acid-base properties of metal oxides are Calorimetric measurements of adsorption enthalpies and Temperature Programed desorption. The measurement of the heat of adsorption of basic or acidic probe molecules can give a description of acidic and basic sites on metal oxide surfaces. Temperature programed desorption provides information about acid-base properties by saturating the surface with a probe molecule and measuring the amount that desorbes from the surface as a function of temperature. The calorimetric method provides a quantitative thermodynamic scale of acetate properties by measuring the heat of adsorption. Calorimetric methods can be considered to give a measure of the total acidity or basicity as it is not descriminate to either Lewis or Brønsted sites. However, when differential heats of adsorption are combined with other techniques, such as IR spectroscopy, the nature and distribution of acid-base adsorption sites can be obtained. .

ZrO2
Zirconia exists in the monoclinic, tetragonal or cubic crystal system depending on the temperature. The surface acidity and bascity of the oxide is dependent on which phase is present and which crystal face is showing. The surfaces of Zerconia have hydroxyl groups, which can act as Brønsted acids or bases, and coordination-unsaturated Zr4+O2- acid base pairs which contribute to its overall acid-base properties. Adsorption studies have shown that monoclinic zirconia is more basic than tetragonal, as it forms stronger bonds with CO2. Adsorption of CO shows that the tetragonal phase has more acidic Lewis acid sites than the monoclinic phase, but that it has a lower concentration of Lewis acid sites.