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

PP-I-2LATERAL INTERACTIONS, FINITE MOBILITY ANDMULTIPLICITY OF STEADY STATES FOR LANGMUIR –HINSHELWOOD MECHANISM. MONTE CARLO ANDTRANSFER-MATRIX TECHNIQUESJu.A. Brizhanskaja*, L.V. Brizhanskii*, A.V. Myshlyavtsev* , **, M.D. Myshlyavtseva**Omsk State Technical University, Omsk, Russia**Institute of Hydrocarbons Processing SB RAS, Omsk, RussiaThe simplest model for CO oxidation on platinum surface is the well known three stepsLangmuir-Hinshelwood mechanismA 2+ 2Z ↔ 2AZ; B + Z ↔ BZ; AZ + BZ → AB + 2Z,(1)where AZ and BZ are the adsorbed species on the catalyst Z, and A 2 , B and AB the gas phasesubstances. The conventional mean-field (MF) kinetic equations can be written as [1]A( 1−x − y)( 1−x − y)−22⎪⎧dx / dt = 2k1P− 2k−x − k xy2 1 3⎨, (2)⎪⎩ dy / dt = k2PBk−2y − k3xywhere x and y are the adsorbate coverages, P and the reactant pressures, and k , k 1,k , −1 k−2 3, k the rate constants for adsorption, desorption and reaction, respectively; t is time.For simplicity we are going to consider the case of irreversible adsorption (= 0). Forsome parameter sets there exists the domain of the multiplicity of the steady states in theplane( lg P , lg P )2ABA 2PB2k , − 1k−2. This domain contains only two internal steady states. The simplest MFequations (2) ignore the non-ideality of surface rate processes. We considered earlier the MFequations incorporating the adsorbate-adsorbate lateral interactions via the coveragedependence of the rate constants. It is known that in the frameworks of the lattice gas modeland the transition state theory there are the exact expressions for the rate constants. Weconsidered a lattice gas model as a model of adsorbed overlayer. Two kind of adsorbedspecies can occupy lattice sites of a square lattice. We take into account only nearest-neighborlateral interactions. Within the framework of our model the exact analytical expressions of theright hand parts of equations (1) are absent and hence we should use an approximatetechnique. It is well known, that the one of the most effective approach is the transfer matrixmethod. Using the latter approach one can solve the problem of deriving expressions for therate constants as functions of concentration. Experience shows that the transfer matrixtechnique yields very good results. It was shown that the number of the internal steady statescan be equal to arbitrary integer number. We have studied numerically twenty seven models214