Boreskov Institute of Catalysis of the Siberian Branch of Russian ...

OP-I-25EFFECT OF CATALYST FRACTAL DIMENSION ON THE RATECONSTANT OF HETEROGENEOUS CATALYTIC REACTIONPeter Strizhak, Andrij Tripolsky, Tanya GurnykL.V. Pysarzhevsky Institute of Phisical Chemistry, Ukrainian National Academy of Sciences,Kyiv, Prosp. Nauky 31, 03028, Ukraine, E-mail: pstrizhak@hotmail.comIn present study we develop a theoretical approach, which reveals a relation between thecatalyst fractal dimension and the rate constant. Based on the fractal approach [1] we derivethe following dependence between pre-exponential factor of the reaction rate constant andcatalyst fractal dimension:− 1⎛ ⎛ ⎞D − 2 ⎞⎜ ⎜ r0⎟ F rm ⎟ln k 0 = A − BD = − 1 − ⎜ ⎟F A B⋅⎜⎜ r ⎟ d⎟⎝ m ⎠⎝⎠(1)where = ln k + 2 ln⎛ R ,⎞ ⎛ ⎞A0 ⎜ ⎟ B = lnR⎝ r⎜R⎟0 ⎠ ⎝ r 0 ⎠, k o is the experimental value of the pre-exponentialfactor, k 0R is a size independent fraction of the pre-exponential factor, r m gives the mostprobable radius of particles of active component which is obtained from the probabilitydistribution function of active component, d gives particle size of an active componentobtained from the study of specific adsorption of probe molecules with characteristic linearsize r 0 .On the other hand, we show the following relation between activation energy, E, andfractal dimension:ln(E-E 0 ) = ln(πε) + D F ln(R/r) (2)where Е 0 gives activation energy of activated complex on isolated active site, R gives theradius of disturbed area of the surface, r is the radius of adsorbed molecule (active site), εgives reorganization energy of one atom or molecule of the surface, D F is the surface fractaldimension.Hence, the rate constant of heterogeneous catalytic reaction may be expressed by thefollowing equation:⎛⎜D − EF 2⎛ r0⎞ ⎜k = k0 R ⎜ ⎟ exp ⎜ −⎝ r ⎠ ⎜⎝0+⎛ R ⎞π ⎜ ⎟⎝ r ⎠RTD F⎞ε ⎟⎟⎟⎟⎠We performed an experimental study to verify eq.1 and eq.2. We study the carbonmonooxide oxidation on silica, alumina, zeolite and acetone hydrogenation over dispersedmetals. The fractal dimension was determined applying the FHH (Frenkel–Halsey–Hill)(3)73