A study was carried out on the synthesis of ethyl tert-butyl ether from ethanol and 2-methylpropene on silica gel samples modified by the addition of ZrO 2 and Al 2 O 3 . A decrease in the turnover frequency (TOF) of the reaction is observed with increasing acidity of surface of the modified silica gels. A relationship was found between the TOF of the reaction and the fractal dimension of the catalyst. The TOF of the reaction decreases with increasing fractal dimension of the catalyst.Key words: silica gel, fractal dimension, synthesis of ethyl tert-butyl ether, acidity, turnover frequency.Some of the most important factors determining catalytic properties of a material are the chemical nature of the active sites and the surface morphology. Catalysts, as a rule, have irregular structure, which is difficult to describe quantitatively. A fractal approach has recently begun to be used for the quantitative description of catalyst morphology [1]. In particular, the structural sensitivity of heterogeneous catalytic reactions may be due to change in the fractal dimension of the catalyst [1]. It has also been shown that the fractal dimension may affect the rate of heterogeneous catalytic reactions [1]. Conversion and selectivity for such reactions as the oxidation of formaldehyde on Pt/TiO 2 [2], petroleum reforming on PtRe/Al 2 O 3 [3], and the hydrodesulfurization of thiophene on MoP-Al 2 O 3 [4] depend on the fractal dimension of the catalyst. In previous work [5], we have shown that change in the preexponential factor of the rate constant of an oxidation-reduction reaction results from change in the fractal dimension of the catalyst.The fractal approach, as a rule, is used to examine oxidation-reduction reactions. However, it is often difficult in such processes to relate the catalytic activity to the active surface sites. The nature of the active surface sites can be examined more concretely in reactions proceeding through an acid-base interaction. In this case, the activity of the catalysts is determined by the acid or basic surface sites, whose concentration may be established rather exactly using reported methods [6]. The clear understanding of the nature of the active sites makes the examination of acid-base reactions a promising and interesting area for the application of the fractal approach. Hence, in the present work, we extended the fractal approach for analyzing acid-base catalysis processes. 328One such acid-base reaction is the synthesis of ethyl tert-butyl ether (ETBE) from ethanol and 2-methylpropene in the presence of acid catalysts [7]:Side-reactions may include the dimerization of 2-methylpropene to give diisobutylene, the dehydration of ethanol to give diethyl ether, and the hydration of 2-methylpropene by water present in the starting raw material to give 2-methylpropan-1-ol.The rate of the reaction leading to ETBE depends significantly on the chemical nature and type of acid-base catalyst used. Such catalysts may be ion-exchange resins, aluminas, oxides, and zeolites [7]. In our previous work [8]...

The textural and fractal characteristics of the nanopowders of yttrium-stabilized zirconium dioxide, produced by heat treatment under various conditions, were studied by analyzing the adsorption isotherms of nitrogen. It was shown that the specific surface area and the total volume of the pores decrease with increase in the calcination temperature while the surface fractal dimensionality remains practically unchanged.

The effect of fractal dimension of zirconium dioxide on its catalytic properties in the oxidation of CO has been studied. The interconnection between the pre-exponential factor of the reaction rate constant and the fractal dimension of the catalyst has been established. It has been shown that the pre-exponential factor decreases with an increase in the mass fractal dimension.Key words: zirconium dioxide, fractal dimension, oxidation of CO, activation energy, pre-exponential factor.In recent times the theory of fractals and its application to various chemical processes has undergone great development [1]. The interest of physical chemists in fractals is explained by the fact that one of the basic objects of investigation are systems in which a key role is played by the state of the boundaries between phases. Among such systems is heterogeneous catalysis which is determined not only by the chemical nature of the catalyst but also it structure. As a rule heterogeneous catalysts are characterized by complex irregular structures which are sufficiently effectively described by the use of fractal geometry [2]. The basic characteristic of fractal systems is their fractal dimension which can be determined with the help of various methods such as adsorption [3], small angle dispersion (SAXS and SANS) [4], porometry [5], electron microscopy [6], etc. Fractal approaches are used for the analysis of the regularity of the processes of heterogeneous catalytic reactions [2]. It has been shown that the fractal dimension affects the rate of heterogeneous catalytic reactions. A large number of studies are connected with computer modeling of reactions on fractals [1]. For such reactions as the oxidation of formaldehyde on Pt/TiO 2 [7], hydrogenization of carbazole on Mo 2 N [8], reforming of naphtha on PtRe/Al 2 O 3 [9], and the hydrodesulfuration of thiophene on MoP-Al 2 O 3 [10], it has been established that conversion and selectivity depends on the fractal dimension of the catalyst. Despite the considerable number of studies in this field, the interconnection between the fractalness of catalysts and the rate of reactions occurring on the surface remains insufficiently studied.The present study is concerned with the establishment of the influence of the morphology of the surface of nano-sized zirconium dioxide, expressed by means of fractal geometry, on its catalytic properties in the oxidation of carbon monoxide.Zirconium dioxide powder, stabilized with 3.4 mole % of Y 2 O 3 , was prepared by chemical deposition method as described elsewhere [11]. Samples were prepared from the powder obtained by calcination at 400 (1), 500 (2), 600 (3), 700 (4), 800 (5), and 900°C (6) for 1 h.Analysis of structures of the powder samples was carried out by small angle diffractometers simultaneously from Siemens (Germany), Anton Paar and Necus-Braun (Austria) with a Kratki small angle camera by thermostatting the samples from 0 to 70°C with a precision of ±0.1°C [11]. The structural-dispersion characteristics of the powder samples (mean size of th...