Analytical expression of concentrations of adsorbed CO molecules, O atoms and oxide oxygen

Chinnasamy Thangapandi, Lakshmanan Rajendran

Department of Mathematics, The Madura College, Madurai, India;.

DOI: 10.4236/ns.2013.53045                

Abstract

A mathematical model of the oscillatory regimes of CO oxidation over plantinum-group metal catalysts are discussed. The model is based on nonstationary diffusion equation containing a nonlinear term related to Michaelis-Menten kinetics of the enzymatic reaction. This paper presents the analytical and numerical solution of the system of non-linear differential equations. Here the Homotopy perturbation method (HPM) is used to find out the analytical expressions of the concentration of CO molecules, O atom and oxide oxygen respectively. A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical and numerical results is observed.

Keywords

Oscillatory Dynamics; Reaction-Diffusion; Boundary Value Problems; Homotopy Perturbation Method

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Hugo, P. and Jakubith, M. (1972) Dynamic behavior and kinetics of carbon monoxide-oxidation at the platinum catalyst. Chemie Ingenieur Technik, 44, 383-387. doi:10.1002/cite.330440608
[2]	Beusch, H., Fieguth, P. and Wicke, E. (1972) Kinetically and thermally induced instabilities in reaction behavior of individual catalyst particles. Chemie Ingenieur Technik, 44, 445-451. doi:10.1002/cite.330440702
[3]	Kurkina, E.S. and Semendyaeva, N.L. (2005) Oscillatory dynamics of co oxidation on platinum-group metal catalysts. Kinetics and Catalysis, 46, 453-463. doi:10.1007/s10975-005-0098-4
[4]	Sales, B.C., Turner, J.E. and Maple, M.B. (1982) Oscillatory oxidation of CO over Pt, Pd and Ir catalysts: Theory. Surface Science, 114, 381-394. doi:10.1016/0039-6028(82)90692-6
[5]	Eigenberger, G. (1978) Steady state multiplicity of the kinetic model of CO oxidation reaction. Chemical Engineering Science, 33, 1255-1263. doi:10.1016/0009-2509(78)85091-X
[6]	Bykov, V.I., Yablonskii, G.S. and Elokhin, V.I. (1981) Steady state multiplicity of the kinetic model of CO oxidation reaction. Surface Science Letters, 107, 334-338.
[7]	Yablonskii, G.S., Bykov, V.I. and Elokhin, V.I. (1984) Kinetics of model reactions of heterogeneous catalysis. Nauka, Novosibirsk. (in Russian)
[8]	Slin’ko, M.M. and Slin’ko, M.G. (1982) Rate oscillations in heterogeneous catalyzed reactions. Kinetics and Catalysis, 23, 1421.
[9]	Makeev, A.G. and Semendyaeva, N.L. (1996) A note on g-derivative and g-integral. Tatra Mountains Mathematical Publications, 8, 76.
[10]	Slinko, M.M., Kurkina, E.S., Liauw, M.A. and Jaeger, N.J. (1999) Mathematical modeling of complex oscillatory phenomena during CO oxidation over Pd zeolite catalysts. Journal of Chemical Physics, 111, 8105-8114. doi:10.1063/1.480144
[11]	Peskov, N.V., Slinko, M.M. and Jaeger, N.I. (2002) Stochastic model of reaction rate oscillations in the CO oxidation on nm-sized palladium particles. Journal of Chemical Physics, 116, 2098-2106. doi:10.1063/1.1429234
[12]	Zhdanov, V.P. (2002) Monte carlo simulations of oscillations, chaos and pattern formation in heterogeneous catalytic reactions. Surface Science Reports, 45, 231-326. doi:10.1016/S0167-5729(01)00023-1
[13]	Latkin, E.I., Elokhin, V.I. and Gorodetskii, V.V. (2001) Monte carlo model of oscillatory CO oxidation having regard to the change of catalytic properties due to the adsorbate-induced Pt(1 0 0) structural transformation. Journal of Molecular Catalysis A: Chemical, 166, 23-30. doi:10.1016/S1381-1169(00)00468-4
[14]	Elokhin V.I. and Latkin E.I. (1995) Statistic lattice model of oscillating and wave phenomena over the catalyst surface during CO oxidation. Doklady Akademii Nauk, 344, 56-61. (in Russian)
[15]	Elokhin, V.I., Latkin, E.I., Matveev, A.V. and Gorodetskii, V.V. (2003) Application of statistical lattice models to the analysis of oscillatory and auto wave processes on the reaction of carbon monoxide oxidation over platinum and palladium surfaces. Kinetics and Catalysis, 44, 672-700. doi:10.1023/A:1026106509151
[16]	Haario, H. and Seidman, T.I. (1994) Reaction and diffusion at a gas/liquid interface, II. SIAM Journal on Mathematical Analysis, 25, 1069-1084. doi:10.1137/S0036141092234712
[17]	He, J.H. (1999) Homotopy perturbation technique. Computer Methods in Applied Mechanics and Engineering, 178, 257-262. doi:10.1016/S0045-7825(99)00018-3
[18]	He, J. H. (2000) A coupling method of homotopy technique and a perturbation technique for non-linear problems. Computer Methods in Applied Mechanics and Engineering, 35, 37-43. doi:10.1016/S0020-7462(98)00085-7
[19]	He, J.-H. (2003) Homotopy perturbation method: A new nonlinear analytical technique. Applied Mathematics and Computation, 135, 73-79. doi:10.1016/S0096-3003(01)00312-5
[20]	He, J.-H. (2006) Homotopy perturbation method for solving boundary value problems. Physics Letters A, 350, 87- 88. doi:10.1016/j.physleta.2005.10.005
[21]	He, J.-H. (2006) Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B, 20, 1141-1199. doi:10.1142/S0217979206033796
[22]	Kalachev, L.V. and Seidman, T.I. (2003) Singular perturbation analysis of a stationary diffusion/reaction system exhibiting a corner-type behavior in the interval interior. Journal of Mathematical Analysis and Applications, 288, 722-743. doi:10.1016/j.jmaa.2003.09.024
[23]	Li, S.J. and Liu, Y.X. (2006) An improved approach to nonlinear dynamical system identification using pid neural networks. International Journal of Nonlinear Sciences and Numerical Simulation, 7, 177-182.
[24]	Loghambal, S. and Rajendran, L. (2010) Mathematical modeling of diffusion and kinetics of amperometric immobilized enzyme electrodes. Electrochim Acta, 55, 5230-5238. doi:10.1016/j.electacta.2010.04.050
[25]	Meena, A. and Rajendran, L. (2010) Mathematical modeling of amperometric and potentiometric biosensors and system of non-linear equations—Homotopy perturbation approach. Journal of Electroanalytical Chemistry, 644, 50-59. doi:10.1016/j.jelechem.2010.03.027
[26]	Anitha, S., Subbiah, A., Subramaniam S. and Rajendran, L. (2011) Analytical solution of amperometric enzymatic reactions based on Homotopy perturbation method. Electrochimica Acta, 56, 3345-3352. doi:10.1016/j.electacta.2011.01.014
[27]	Ananthaswamy, V. and Rajendran, L. (2012) Analytical solution of two-point non linear boundary value problems in a porous catalyst particles. International Journal of Mathematical Archieve, 3, 810-821.
[28]	Baronas, R., Ivanauskas, F. Kulys, J. (2010) Mathematical modelling of biosensors: An Introduction for chemists and mathematicians. Springer, Dordrecht, Heidelberg, London, New York.