武汉大学电化学课件 陈胜利 Chaper 4 -Transient electrode processes.ppt

Chapter 4,Transient Electrode Processes,What is transient electrode processes,As an electrochemical perturbation is imposed on the electrode/solution interface and the electrode reaction proceeds, concentration gradients of reactant and product will develop and extend gradually in the solution side of electrode/electrolyte interface. Before the steady-state is reached, the local concentrations near electrode surface changes dynamically with time, i.e., ci/ t 0 The concentration change depends on the mode of the electrochemical perturbations imposed on the electrode/electrolyte interface. How to describe and express the dynamic development of the concentration gradient - c(x,t) ?,The theoretical treatment of transient mass transfer process,The time-dependent concentration-profile at electrode/electrolyte interface can be obtained by solving the Ficks second law. To do so, proper initial and boundary conditions Initially, the electrode system is under equilibrium, no reaction occurs, and no concentration gradient exists in the solution, so,Since that the concentration gradient can not extend unlimitedly, so,The boundary conditions that define the concentrations at electrode surface are required. These boundary condition should depend on the electrochemical perturbation imposed on the electrode,The transient electrode processes under a constant potential,Case 1- The electrode process is totally reversible (Nernst electrode systems: The interfacial reaction kinetics is very facile and the equilibrium is approximately maintained. The values of surface concentration will be constant under constant potential ),The resultant solution of the second Ficks law for O is,Called “error function”,If cis 0,（参考教材第三章第98100页）,The concentration profile and the development of diffusion layer,Cottrell equation,The transient electrode processes under a constant potential condition,Case 2 - The electrode process is under mixed diffusion and interfacial kinetics control when the interfacial electrode reaction rate is comparable to the diffusion rate .,Boundary condition,The diffusion equation of the Ficks second law can be solved with above boundary conditions, the semi-infinite boundary conditions and the initial conditions. The solution gives the expression of ci(x,t),ik - kinetic current density, the current density when there is no concentration polarization occurs,（Refer to: 教材第四章第150页）,At very small value of t,t,As t = 0 , i = ik,The transient electrode processes under constant current condition,The resulted concentration profiles ci(x,t) can be obtained by solving the Ficks second diffusion equation. An expression for the concentration of O at x = 0 is given as,Boundary condition,Sand Equation,Accordingly, an expression for the concentration of R at x = 0 is given as (assuming that R is initially absent, i.e., cR(x,0)=0, cRb = 0 ),How about the j t relation ?,The transient variation of electrode potential with time under constant current condition,Case 1- Nernst electrode systems,As t = t , the reactant is completely depleted, cOs = 0, the original reaction will no longer have enough rate to support the current applied, the system will switch to an alternative reaction.,The transient variation of electrode potential with time under constant current condition,Case 2 - Under mixed diffusion and interfacial kinetics control,2.1 - Irreversible electrode system (The electrode system has very small i0 value so that the the applied current density i can result in large overpotentials where the back reaction can be neglected. i ic),There is a linear relation between j and ln(1-t1/2/t1/2). The slope the of the j - ln(1-t1/2/t1/2) plot gives an value. The intercept at t = 0 can be used to calculate the value of k0,2.2 - Quasi-reversible electrode system (The electrode system has intermediate i0 value, the back reaction can not be ignored),The transient electrode processes under potentiodynamic polarization,Boundary condition,Case 1- Nernst electrode systems,The transient electrode processes under potentiodynamic polarization,Boundary condition,Case 2- The electrode process is under mixed diffusion and interfacial kinetics control.,2.1 - Irreversible electrode system (The electrode system has very small i0 value. i ic or i ia ),2.2 - Quasi-reversible electrode system,Boundary condition,A brief review about the transient process on planar electrodes,The transient electrode processes are generally treated by solving the Ficks second law with proper initial and boundary conditions,Upon switching the electrode potential from values at which no net reaction occurs to where a net reaction can take place, the current dynamically changes with time due to development of the diffusion layer. The thickness of the effective diffusion layer is,The current-time characteristic is described by the Cottrell equation,This equation says that the current decreases continuously with time until it becomes to zero due to increased thickness of the diffusion layer.,The current-time curves on a planar electrode under a constant potential:,The transient current is always larger than the steady-state current.,A potential sweep process is equivalent to a series of potential step process, the measured current value is a point on the i t curve shown in above figure. The location of this point on the i t curve depends on the scanning rate. The higher the scanning rate, the earlier the current point is measured. So the current on a i j curves increases with the potential scanning rate u. If the scanning rate is slow enough, the steady-state i j curves would be obtained.,dash line: Steady-state i j curve; solid line: transient i j curve,The transient electrode processes on a spherical electrode,When a spherical rather than a large planar electrode is used, one must consider a spherical diffusion field, the Ficks second law becomes,The initial and boundary conditions are same as that in planar electrode systems except that the spatial variable x has to be replaced by r - the radial distance from the center of the spherical electrode.,The solution for a Nernst electrode system gives,r0 - is the electrode radius,The current expression contains two parts:,As cOs 0