Nonequilibrium electrochemical cell

When a d.c. voltage is applied across an electrochemical cell, the response of its electrodes can be considered in terms of two possible modes of idealized behavior. These are illustrated in Fig. 1. The left-side electrode is composed of the parent metal M(s) of an electrolyte for the conduction of a cation species MT ". Because of the presence of M(s) and at the electrode interface, an equilibrium M(s)= M + e is assumed to obtain. If establishment and maintenance of the equilibrium is ideally rapid, then the response of the interface to a nonequilibrium field is to drive the equilibrium predominantly in one of its component directions and result in a basically nonresistive transfer of charge across the interface. This is the well-known behavior of the ideally reversible electrode. 

Franco has designed this model to coimect within a nonequilibrium thermodynamics framework atomistic phenomena (elementary kinetic processes) with macroscopic electrochemical observables (e.g., I-V curves, EIS, Uceii(t)) with reasonable computational efforts. The model is a transient, multiscale, and multiphysics single electrochemical cell model accounting for the coupling between physical mechanistic descriptions of the phenomena taking place in the different component and material scales. For the case of PEMFCs, the modeling approach can account for detailed descriptions of the electrochemical and transport mechanisms in the electrodes, the membrane, the gas diffusion layers and the channels H2, O2, N2, and vapor... 

So far we have considered only standard cell potentials, that is, the electric potential difference developed by a chemical reaction that is at equilibrium in an electrochemical cell at normal atmospheric pressure and a temperature of 25 C, and when the chemical species are present in standard concentrations. We can derive an expression for the electric potential difference generated under nonequilibrium and nonstandard conditions (Fcdi) follows. If we write Eq. (2.41) in terms of concentrations and remove the requirement of molar concentrations, we get... 

Nonequilibrium electrochemical cells can be studied by methods that we have introduced in previous chapters. 

Consider the standard Zn/H2 electrochemical cell shown in Figure 17.5, which has been short-circuited such that oxidation of zinc and reduction of hydrogen occurs at their respective electrode surfaces. The potentials of the two electrodes are not at the values determined from Table 17.1 because the system is now a nonequilibrium one. The dis-polarization placement of each electrode potential from its equilibrium value is termed polarization,... 

This formulation is useful since, in equilibriiun or in the case of linear nonequilibrium effects, we have information concerning the behaviour of the electrochemical potential. All differences in within a phase and from phase to phase, disappear in the absence of a current, if the electrons concerned are mobile enough (see Eq. (7.1)). However, gradients in can certainly occur in electrochemical cells... 

An electrochemical reaction is said to be polarized or retarded when it is limited by various physical and chemical factors. In other words, the reduction in potential difference in volts due to net current flow between the two electrodes of the corrosion cell is termed polarization. Thus, the corrosion cell is in a state of nonequilibrium due to this polarization. Figure 4-415 is a schematic illustration of a Daniel cell. The potential difference (emf) between zinc and copper electrodes is about one volt. Upon allowing current to flow through the external resistance, the potential difference falls below one volt. As the current is increased, the voltage continues to drop and upon completely short circuiting (R = 0, therefore maximum flow of current) the potential difference falls toward about zero. This phenomenon can be plotted as a polarization diagram shown in Figure 4-416. 

In electrochemical systems, a steady state during current flow implies that a time-invariant distribution of the concentrations of ions and neutral species, of potential, and of other parameters is maintained in any section of the cell. The distribution may be nonequilibrium, and it may be a function of current, but at a given current it is time invariant. 

Traditionally, the electrochemical analysis of thin layers of electrodeposited nonequilibrium alloys has simply involved either galvanostatic or potentiostatic dissolution of the electrodeposit under conditions where passivation and/or replacement reactions can be avoided [194, 195]. A technique based on ALSY at a RDE has also become popular [196], To apply this technique, a thin layer (a 10 pm) of the alloy of interest is deposited on a suitable electrode in a solution containing the reducible ions of the alloy components. The plated electrode is then removed to a cell containing an electrolyte solution that is devoid of ions that can be reduced at the initial potential of the experiment, and the complete electrodeposit is anodically dissolved from the electrode surface using slow scan ALSV while the electrode is rotated. 

In the classical description of nonequilibrium systems, fluxes are driven by forces [73,76,77]. Equation (8) shows that the flux of electrons (7 ) is related to the (photo)electrochemical force (VEFn) by a proportionality factor (np ). Equation (8) and the related equation for holes can be employed as a simple and powerful description of solar photoconversion systems. However, it is useful to go beyond this analysis and break V > into its component quasithermodynamic constituents, V(7 an Vp, because this helps reveal the fundamental differences between the photoconversion mechanisms of the various types of solar cells. Equation (6) can be separated into two independent electron fluxes, each driven by one of the two generalized forces, Vf7 and Vp. Equations (9a) and (9b) are expressed in the form Flux = Proportionality factor X Force ... 

Potassium leaves the cell, while the net flow of sodium is inward. A nonequilibrium stationary state for the cell at rest is maintained by the sodium and potassium pumps, which pump out the entering sodium ions and pump the leaking potassium ions back into the cell interior, using a certain metabolic output. The sodium transfer is coupled with the chemical reaction. The electrochemical potential difference for sodium ions is expressed as... 

The nonequilibrium potentials measured in solid-electrolyte cells are established by electrochemical reactions, just as for equilibrium-based sensors. For example, in an environment containing CO and O2, the CO could be oxidized chemically according to the following reaction ... 

The subscript rev indicates that (p — cp" now has a value corresponding to this reversible behavior which will be exactly exhibited by the cell when 1 = 0. Each of the two electrodes is then in a state of electrochemical equilibrium. There can be nonequilibrium states of electrodes with / = 0, but we shall not discuss such cases here. 

The corresponding atomistic kinetics is then implemented into the nonequilibrium nanoscale MEMEPhys models collecting all the elementary events, catalytic and no-catalytic, to simulate the electrochemical observables. The nanoscale models introduce the electric field effect correction without empirical parameters and open interesting perspectives to scale up atomistic data into macroscopic models in a robust way. The impact of the catalyst chemistry and nanostructure on the electrodes and cell potentials can be then captured. 

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