On Electro-chemical Phenomena Driven By Internal Fluctuations And External Noise In Both Dropping Mercury Electrode System And Rotating Disc Electrode System--A Reduced Stochastic Thermodynamics Of Non-Steady State Irreversible Electrode Processes

As the recent achievement of the stochastic thermodynamics of the finite chemical reaction system, a stochastic measure of the thermodynamic effects of both the internal fluctuations and the external noise on the finite chemical reaction system has been established, and then we can study the effects of fluctuations on the irreversible electrode processes quantitatively. The previous results about irreversible electrode processes show that polarization come from dissipations, and then a unite formalism of stochastic thermodynamics of both concentration polarization and activation polarization was established, meanwhile the polarization induced by external noise in the irreversible electrode processes has been exposed. But all the irreversible electrode processes concerning with above results take place on the fixed electrode surface.In the first chapter of this thesis, we review the development of the stochastic thermodynamics of the irreversible electrode processes concisely. Some methodologies, such as the Master equation for the time evolution of the probability, linear Fokker-Planck equation under the central limit theoremand Langevin equation complied by the time evolution of the fluctuations, useful to study the electrochemical phenomena driven by internal and external noise in the finite electro-chemical reaction system are emphasized.In the second chapter, the central part of this thesis, we devote ourselves to analyzing the dissipation of the potentiostatic irreversible dropping mercury electrode process whose surface is renewed periodically. We start with considering the time-dependent electrochemical characters of the potentiostatic D.M.E process based on the mechanism advanced by Heyrovsky, and a simplified stochastic model to describe the behavior of this kind of electrode reaction systems is proposed. We concentrate on the deduction of the general formalism of stochastic thermodynamics of dropping mercury electrode reaction systems by means of the formula of fluctuation-dissipation. Furthermore, its two special forms for this kind of electrode processes respectively with very hesitative electrochemical steps and very hesitative diffusion steps are presented. In the limit case of slow growth of the drop a simplified formalism is established to describe the instantaneous relation between potential and current in a period of the drop under quasi-steady state approximation, and a typical illustration is also given to show how to calculate the contribution of the fluctuations to the half-wave potential of the D.M.E. process. At the last part of the chapter, we take account of the stochasticity of externally controlled parameters for the very slow growth of D.M.E., and a series of explicit expressions about the current and potential induced by both Gauss white noise and internal fluctuations is also derived.As another important aspect to extend the stochastic thermodynamics of irreversible electrode processes, we discuss the rotating disc electrode systems in chapter III. At meso-statical level, based on both the dominating feature of the R.D.E. that the flow towards the electrode is the same in any plane that is parallel to the electrode and the condition that the rotation speedis lower so that the convection is kept the form of laminar flow, we can simulate the transport to an R.D.E. as diffusion loading on the convection, and then the effect of rotating on the electrode processes is reduced to both the boundary concentrations of electrochemical species and the effective thickness of diffusion layer influenced by the convection. Thus a simplified stochastic model to describe the behavior of this kind of electrode reaction system is proposed. A general mesoscopic statistical formalism about the polarization in the spinning irreversible electrode processes influenced by internal fluctuations and additive Gauss noise has been established respectively. Furthermore, a series of quantitative expressions about the polarization induced by fluctuations has been derived, valid for both the concentr...