Analytical expression of non steady-state concentration profiles at planar electrode for the CE mechanism

ABSTRACT

The analytical solutions of the non-steady-state concentrations of species at a planar microelectrode are presented. These simple new approximate expressions of concentrations are valid for all values of time and possible values of rate constants. Analytical equations are given to describe the current when the homogeneous equilibrium position lies heavily in favour of the electroinactive species. Working surfaces are presented for the variation of limiting current with a homogeneous kinetic parameter and equilibrium constant. Moreover, in this work we employ the Homotopy perturbation method to solve the boundary value problem.

The analytical solutions of the non-steady-state concentrations of species at a planar microelectrode are presented. These simple new approximate expressions of concentrations are valid for all values of time and possible values of rate constants. Analytical equations are given to describe the current when the homogeneous equilibrium position lies heavily in favour of the electroinactive species. Working surfaces are presented for the variation of limiting current with a homogeneous kinetic parameter and equilibrium constant. Moreover, in this work we employ the Homotopy perturbation method to solve the boundary value problem.

Cite this paper

PonRani, V. and Rajendren, L. (2010) Analytical expression of non steady-state concentration profiles at planar electrode for the CE mechanism.*Natural Science*, **2**, 1318-1325. doi: 10.4236/ns.2010.211160.

PonRani, V. and Rajendren, L. (2010) Analytical expression of non steady-state concentration profiles at planar electrode for the CE mechanism.

References

[1] Fleischmann, M., Pons, S., Rolison, D. and Schmit, P.P. (1987) Ultra microelectrodes. Data Systems & Technology, Inc., Morganton, NC.

[2] Oldham, K.B. (1991) Steady-state microelectrode voltammetry as a route tohomogeneous kinetics. Journal of Electroanalytical Chemistry, 313, 225-236.

[3] Lavagnini, I., Pastore, P. and Magno, F. (1993) Digital simulation of steady-state and non-steady state voltommetric responses for electrochemical reactions occurring at an invalid microdisc electrode: Application to ECirr , CE first-order reactions. Journal of Electroanalytical Chemistry, 358, 193-200.

[4] Fleischmann, M., Pletcher, D., Denuault, G., Daschbach, J. and Pons, S. (1989) The behaviour of microdisk and microring electrodes predictions of the chronoamperometric response of microdisks and of the steady state for CE and EC catalytic reactions by application of Neumann’s integral theorem. Journal of Electroanalytical Chemistry, 263, 225-236.

[5] Streeter, I. and Compton, R.G. (2008) Numerical simulation of the limiting current for the CE mechanism. Journal of Electroanalytical Chemistry, 615, 154-158.

[6] Ghori, Q.K., Ahmed, M. and Siddiqui, A.M. (2007) Application of He’s Homotopy Perturbation Method to Sumudu Transform. International Journal of Nonlinear Sciences and Numerical Simulation, 8, 179-184.

[7] Ozis, T. and Yildirim, A. (2007) Numerical Simulation of Chua’s Circuit Oriented to Circuit Synthesis. International Journal of Nonlinear Sciences and Numerical Simulation, 8, 243- 248.

[8] Li, S.J. and Liu, Y.X. (2006) A Multi-component Matrix Loop Algebra and its Application. International Journal of Nonlinear Sciences and Numerical Simulation, 7, 177- 182.

[9] Mousa, M.M. and Ragab, S.F. (2008) Soliton switching in fiber coupler with periodically modulated dispersion, coupling constant dispersion and cubic quintic nonlinearity. Zeitschrift für Naturforschung, 63 140-144.

[10] He, J.H. (1999) Homotopy perturbation technique. Computer Methods in Applied Mechanics and Engineering, 178, 257-262.

[11] He, J.H. (2003) Homotopy perturbation method: a new nonlinear analytical technique. Applied Mathematics and Computation, 135, 73-79.

[12] He, J.H. (2003) A Simple perturbation approach to blasius equation. Applied Mathematics and Computation, 140, 217-222.

[13] He, J.H. (2006) Homotopy perturbation method for solving boundary value problems. Physics Letters A, 350, 87-88.

[14] Golbabai, A. and Keramati, B. (2008) Modified homotopy perturbation method for solving Fredholm integral equations. Chaos solitons Fractals, 37, 1528.

[15] Ghasemi, M., Kajani, M.T. and Babolian, E. (2007) Numerical solutions of the nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method. Journal of Applied Mathematics and Computing, 188, 446-449.

[16] Biazar, J. and Ghazvini, H. (2009) He’s homotopy perturbation method for solving system of volterra integral equations of the second kind. Chaos solitons fractals, 39, 770.

[17] Odibat, Z. and Momani, S. (2007) A reliable treatment of homotopy perturbation method Klein-Gordon equations. Physics Letters A, 365, 351-357.

[18] Chowdhury, M.S.H. and Hashim, I. (2007) Solutions of time-dependent Emden-Fowler type equations by homotopy perturbation method. Physics Letters A, 368, 305-313.

[19] He, J.H. (2006) Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B, 20, 1141-1199.

[20] Donald, A.P. (2010) Homotopy perturbation method and the natural convection flow of a third grade fluid through a circular tube. Nonlinear Science Letters A, 1, 43-52.

[21] Ganji, D.D. and Rafei, M. (2006) Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method. Physics Letters A, 356, 131-137.

[22] He, J.H. (2008) A elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. International Journal of Modern Physics B, 22, 3487-3578.

[1] Fleischmann, M., Pons, S., Rolison, D. and Schmit, P.P. (1987) Ultra microelectrodes. Data Systems & Technology, Inc., Morganton, NC.

[2] Oldham, K.B. (1991) Steady-state microelectrode voltammetry as a route tohomogeneous kinetics. Journal of Electroanalytical Chemistry, 313, 225-236.

[3] Lavagnini, I., Pastore, P. and Magno, F. (1993) Digital simulation of steady-state and non-steady state voltommetric responses for electrochemical reactions occurring at an invalid microdisc electrode: Application to ECirr , CE first-order reactions. Journal of Electroanalytical Chemistry, 358, 193-200.

[4] Fleischmann, M., Pletcher, D., Denuault, G., Daschbach, J. and Pons, S. (1989) The behaviour of microdisk and microring electrodes predictions of the chronoamperometric response of microdisks and of the steady state for CE and EC catalytic reactions by application of Neumann’s integral theorem. Journal of Electroanalytical Chemistry, 263, 225-236.

[5] Streeter, I. and Compton, R.G. (2008) Numerical simulation of the limiting current for the CE mechanism. Journal of Electroanalytical Chemistry, 615, 154-158.

[6] Ghori, Q.K., Ahmed, M. and Siddiqui, A.M. (2007) Application of He’s Homotopy Perturbation Method to Sumudu Transform. International Journal of Nonlinear Sciences and Numerical Simulation, 8, 179-184.

[7] Ozis, T. and Yildirim, A. (2007) Numerical Simulation of Chua’s Circuit Oriented to Circuit Synthesis. International Journal of Nonlinear Sciences and Numerical Simulation, 8, 243- 248.

[8] Li, S.J. and Liu, Y.X. (2006) A Multi-component Matrix Loop Algebra and its Application. International Journal of Nonlinear Sciences and Numerical Simulation, 7, 177- 182.

[9] Mousa, M.M. and Ragab, S.F. (2008) Soliton switching in fiber coupler with periodically modulated dispersion, coupling constant dispersion and cubic quintic nonlinearity. Zeitschrift für Naturforschung, 63 140-144.

[10] He, J.H. (1999) Homotopy perturbation technique. Computer Methods in Applied Mechanics and Engineering, 178, 257-262.

[11] He, J.H. (2003) Homotopy perturbation method: a new nonlinear analytical technique. Applied Mathematics and Computation, 135, 73-79.

[12] He, J.H. (2003) A Simple perturbation approach to blasius equation. Applied Mathematics and Computation, 140, 217-222.

[13] He, J.H. (2006) Homotopy perturbation method for solving boundary value problems. Physics Letters A, 350, 87-88.

[14] Golbabai, A. and Keramati, B. (2008) Modified homotopy perturbation method for solving Fredholm integral equations. Chaos solitons Fractals, 37, 1528.

[15] Ghasemi, M., Kajani, M.T. and Babolian, E. (2007) Numerical solutions of the nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method. Journal of Applied Mathematics and Computing, 188, 446-449.

[16] Biazar, J. and Ghazvini, H. (2009) He’s homotopy perturbation method for solving system of volterra integral equations of the second kind. Chaos solitons fractals, 39, 770.

[17] Odibat, Z. and Momani, S. (2007) A reliable treatment of homotopy perturbation method Klein-Gordon equations. Physics Letters A, 365, 351-357.

[18] Chowdhury, M.S.H. and Hashim, I. (2007) Solutions of time-dependent Emden-Fowler type equations by homotopy perturbation method. Physics Letters A, 368, 305-313.

[19] He, J.H. (2006) Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B, 20, 1141-1199.

[20] Donald, A.P. (2010) Homotopy perturbation method and the natural convection flow of a third grade fluid through a circular tube. Nonlinear Science Letters A, 1, 43-52.

[21] Ganji, D.D. and Rafei, M. (2006) Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method. Physics Letters A, 356, 131-137.

[22] He, J.H. (2008) A elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. International Journal of Modern Physics B, 22, 3487-3578.