The theory of electrochemical noise in equilibrium state within the Einstein concept

Abstract

• Autocorrelation analysis of electrochemical noise Brownian coordinate. • Fluctuation-dissipation relations for autocorrelations of Brownian coordinate. • Fluctuation-dissipation relations for structure function of Brownian coordinate. • Autocorrelations of Brownian coordinate of Voigt circuit noise. The theory of electrochemical noise is considered within the Einstein concept. Discrete fluctuation–dissipation relations for the Brownian coordinate of electrochemical potential noise are determined. It is shown that, in the equilibrium state, there is a linear relationship between the discrete autocorrelation function of the Brownian coordinate of electrochemical potential noise and the second order difference of macroscopic linear response of the electrochemical Brownian coordinate to the external action in the form of a single step of constant electric current. Using the discrete fluctuation–dissipation relations, the discrete autocorrelation function of the Brownian coordinate of equilibrium potential noise is calculated for the Voight electrochemical circuit, which contains the electric double layer capacitance and the electrochemical discharge resistance. In the direct experiment, it is shown that the intrinsic noise of the measuring instrument (based on the AD7176 evaluation board) does not hamper the measurement of the structure function of the Brownian coordinate of corrosion noise. The electrochemical noise diagnostics based on the Einstein concept is a promising supplement to the electrochemical noise diagnostics based on the Nyquist concept.