武汉大学电化学课件 陈胜利 Chaper 5 -Electrode process with complex mechanism.ppt

Chapter 5,Electrode Processes With Complex Mechanisms,In the foregoing sections, we have assumed that the interfacial reactions proceed through a simple one-step charge transfer mechanism,In reality, a reaction may undergo a complex mechanism containing a number of steps. And it is rather unrealistic that two or more electrons can tunnel through the solid/liquid interfaces simultaneously.,Possible processes involved in an electrode reaction,Oad,O,Rad,R,O,R,ne,Preceding Chemical reactions,Following Chemical reactions,Electrode,Charge transfer,Adsorption,Desorption,May occurs in a number of elementary steps,The electrode reaction proceed through a multi-step of electron transfer mechanism,The overall reaction: O + ne,R may have a mechanism as following,O + ne,O (net results of steps preceding rds),O + e,R (rds- rate determining step ),kc,ka,R + n e,R (net results of steps following rds),The current-potential characteristic can be written as,If we assume that the steps preceding to and following the rds are under equilibrium,The current-potential characteristic then becomes,The current-potential characteristic for a one-step multi-electron transfer process:,O + ne,R,kc,ka,The electrode reactions with coupled homogeneous chemical reactions,Some electrode reactions have mechanisms in which the interfacial electron transfer does not occur directly between the electrode and the initial reactants, or the immediate result of the interfacial electron transfer is not the final products. Instead, the charge transfer processes involve some reaction intermediates that form from (or transform to) initial reactants (or final products) through pure chemical reactions in the electrolyte solution,Reaction-diffusion equation:,The electrode reactions coupled with a preceding homogeneous chemical reactions (CE mechanism),General equations under steady-state,If we assume that,then,Where,We can re-write the reaction-diffusion equations for O and O as follows,The above two equations can be solved with boundary conditions:,x = 0:,x d:,The resultant solutions are,Case 1-No concentration polarization of O. Since the concentration of O is very low and is negligible comparing to O, the profile of ct is mainly affected by cO. No concentration polarization of O means there is little concentration polarization of the total concentration, i.e., cts cOs ctb cOb, thus,iLk - kinetic limiting current density, the limiting current density when no concentration polarization of O occurs,Then,For Diffusion controlled electrode processes:,Case 2-There is concentration polarization of O. We have to use the general solutions about the concentration profiles.,Since the concentration of O is very low and is negligible comparing to O, the profile of ct is mainly affected by cO , i.e., cts cOs , thus, the concentration profiles of O and O can be expressed as,we know that,So,Considering that: Kb=1-Kf 1 and cts cOs,As cOs 0 :,We can re-arrange the above equation into the following form,and,Thus, we can use steady-state methods such as microelectrode methods, hydrodynamic methods like RDE to investigate the electrode reactions with CE mechanism.,Then,If an electrode reaction has a CE mechanism and the equilibrium of the interfacial electron transfer step remains maintained (Nernst system), the steady-state current-potential characteristic always has the form similar to that in a diffusion-controlled simple electron transfer reaction. That is, a limiting current plateau is always seen when the overpotential beyond certain value and the current-potential curves can be fitted into the following equation,From the values of j1/2 and iL, kinetic rate constants may be obtained.,The electrode reaction coupled with following homogeneous chemical reactions (EC mechanism),General equations under steady-state,boundary conditions:,x = 0:,x d:,The resultant solutions are,If large amounts of R is initially present in the solution, But R is initially absent, the concentration polarization of R is negligible,So,If the interfacial electron transfer is a Nernst system, then,Assuming that there is no concentration polarization of O, replacing cRs with the current expression above leads to,i .e.,The electrode reaction coupled with a parallel homogeneous chemical reaction (homogeneous catalysis),At the applied electrode potentials, only the redox couple O/R can exchange electrons with the electrode. The electrochemical transformation between the redox couple XO /XR is unfavorable due to either thermodynamic or kinetic barrier. But a homogeneous reaction between these two redox couples can occurs in the solution,Os,Rs,ne,Ob,Rb,x,XOs+,+ XRs,+ XRb,XOb+,redox couple O/R are called mediators,If the concentration of the XO and XR in the solution is very high, they will have little concentration polarization during the electrode reaction, their concentration item can be integrated into the kinetics constant of kpf and kpb respectively. At steady-state, we have the following equations,The boundary conditions are:,The resultant solutions are:,For Nernst electrode system,Considering that kpf kpb,The electrode reactions involving surface adsorption steps,Oad,Rad,O,R,ne,Electrode,Charge transfer,Adsorption,Desorption,The electrode reactions with preceding adsorption steps,The mass balance equations at steady-state:,x = 0:,x :,To solve these equations would produce the the expression for current,Simply, if there is no concentration polarization of O, we can express the current in ter