Stability of Electrochemical Systems
General mathematical stability conditions described in chapter “Basic Principles of Nonlinear Dynamics” are applied to electrochemical systems. The stability analysis of such systems refers to the characteristics of the entire electric circuit, and not on
- PDF / 529,282 Bytes
- 35 Pages / 439.37 x 666.142 pts Page_size
- 79 Downloads / 207 Views
Stability of Electrochemical Systems
2.1
2.1.1
The Role of Negative Differential Resistance in the Stability of Electrochemical Systems The Load Line and the Simplest Electrochemical Circuit
The subject of the present analysis is the stability of the entire electric circuit in which the electrochemical cell is only one of the components. We shall look for such characteristics (I–E dependence) of the electrode process that gives rise to instability of the whole circuit which, in general, consists of the power source and of a load. This way of analysis was described already in 1958 by Gerischer [1], who also invoked the ideas of Franck. We shall consider first a simple electrochemical cell consisting of two electrodes: the polarizable working electrode and an ideally non-polarizable reference electrode. All the resistances exhibited by this system will be summarized to a single value of an equivalent resistance Rs, connected in series with the cell. We apply sufficiently high external voltage which will compensate the own electromotive force of the cell and polarize the working electrode to the value at which the faradaic current flows at the working electrode and, in consequence, electric current flows through the entire circuit. In order to simplify thinking, we can represent this situation in terms of the equivalent circuit shown in Fig. 2.1, which consists of resistor Rs (linear element) and the electrolytic cell (nonlinear element), symbolized by a box with cross. The nonlinear current–potential dependence of the electrode process in this cell is denoted further as with I2(E). It is obvious that in the steady-state both currents are equal: I1 ¼ I2, so there is no increasing accumulation of the electric charge at the working electrode–solution interface, i.e., dE/dt ¼ 0. Beyond the steady-state, the electrode potential E changes according to the dependence:
M. Orlik, Self-Organization in Electrochemical Systems I, Monographs in Electrochemistry, DOI 10.1007/978-3-642-27673-6_2, # Springer-Verlag Berlin Heidelberg 2012
75
76
2 Stability of Electrochemical Systems
Fig. 2.1 Simplified equivalent circuit of the electrochemical system consisting of electrolytic cell and power source, with all resistances summarized into an equivalent ohmic resistance Rs
dE / ðI1 I2 Þ dt
(2.1)
Irrespective of that, whether the system is actually in steady-state or not, current I1 is given by: I1 ¼
UE U E ¼ Rs Rs Rs
(2.2)
where E means the potential drop at the working electrode/solution interface (interfacial potential drop). The dependence [Eq. (2.2)] is known as the equation of the load line, representing the response of a linear circuit connected to the nonlinear device. It is thus a straight line in the I–E coordinates, with the intercept U/Rs and the slope 1/Rs. In terms of such representation it is clear that the steadystate(s) of the circuit from Fig. 2.1 (Ess, Iss) is (are) determined by the intersection(s) of a load line with the I2(E) characteristics of the electrode process: i.e., when I1 (Ess) ¼ I2(Ess
Data Loading...
