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General relationship between complex impedance and linear stability in electrochemical systems

1999; American Institute of Physics; Volume: 111; Issue: 22 Linguagem: Inglês

10.1063/1.480345

1520-9032

M. Naito, Naoki Tanaka, Hiroshi Okamoto,

Iterative Learning Control Systems

The impedance of the electrochemical system is derived in an explicit analytical form in relation to the stability of the system under various driving conditions. It is shown that the complex impedance is represented as the ratio of characteristic polynomials of the Jacobian matrices of linearized system under potentiostatic control and under galvanostatic control. Thus it is definitely shown that the zeros of the impedance are the eigenvalues of the Jacobian of the system under potentiostatic control, and that the poles are the eigenvalues of the Jacobian under galvanostatic control. The obtained impedance formulas are used to derive or prove several electrochemical characteristics. A direct analytical relationship between the hidden negative impedance and the galvanostatic Hopf bifurcation is also derived.