Relaxation electrode/solution interface

Now, it has already been seen in Chapter 7 that one may write an equivalent circuit for a simple electrode/solution interface as given in Fig. 7.52, where Rsoln is the resistance of the solution RF is the Faradaic resistance and DL the double-layer capacitance then the relaxation time6 is given by ... 

The rapid temperature change of the electrode perturbs the equilibrium at the electrode-solution interface and causes a change in the potential of the electrode measured with respect to a reference electrode. The change in the open-circuit potential, A t, and its relaxation with time are used to obtain kinetic information about the electrode reaction. A number of different phenomena come into play to cause the potential shift with temperature (e.g., temperature dependence of the double-layer capacitance and the Soret potential arising from the temperature gradient between the electrode and the bulk electrolyte), but the response can be treated by a general master equation (40) ... 

Also, the potential dependence of ultrafast relaxation at electrochemical interfaces of 1-dodecanethiol- and 1-HT-modified Au(lll) electrodes has been investigated in HCIO4 and H2SO4 solutions, applying transient reflectivity measurements ]143]. 

Let us now consider the formation of the semiconductor/solution interface. The Fermi level in the solution phase, can be identified as Ji by (18.2.4) and is calculated in terms of values by the procedures described in Section 2.2. For most electrochemical purposes, it is convenient to refer values to the NHE (or other reference electrodes), but in this case it is more instructive to estimate them with respect to the vacuum level. This can be accomplished, as discussed in Section 2.2.5, by theoretical and experimental means with relaxation of thermodynamic rigor, so that one obtains an energy level value for the NHE at about —4.5 0.1 eV on the absolute scale (45) (Figure 18.2.5a). Consider the formation of the junction between an n-type semiconductor and a solution containing a redox couple 0/R, as shown in Figure 18.2.5. When the semiconductor and the solution are brought into contact, if electrostatic equilibrium is attained, in both phases must become equal (or equivalently the Fermi levels must become equal), and this can occur by... 

Other experimental method at a eomparable level of detail, although in some eases the conclusions reached support previous work by XANES using synchrotron radiation. Our results clearly demonstrate that due to a quantum mechanical electron density spillover from platinum, the interface is metallized, as evidenced by Korringa relaxation and Knight shift behavior. Thus, the adsorbate on a platinum electrode belongs to the metal part of the platinum-solution interface, and most likely other d-metal interfaces, and should be considered as such in any realistic models of the structure of the electrical double layer of interest to electrocatalysis. 

All voltammetric equations obtained at the moment by solving simple problems of linear semi-infinite diffusion (in particular, the well-known Randles-Sevcik equation) do not take into account the specific characteristics of anodic selective dissolution of a homogeneous alloy solid phase segregation of an alloy components, initial roughness of an electrode, coupled solid-liquid phase transport, displacement of an alloy/solution interface, concentration dependence of the interdiffusion coefficient, presence of the vacancy sinks and relaxation of the non-equilibrium vacancy subsystem. 

The theory and practical aspect of potentio- and galvanostatic measurements of selective dissolution of homogeneous alloys are developed quite good [24-27], but not all the possibilities of chronovoltammetry are utilized. This is primarily determined by the fact that a solution of even a simplest diffusion problem for a perfectly smooth electrode at the linear potential trace is given by an integral equation [28, 29]. Obviously, accounting such complex nonlinear effects of non-equilibrium vacancy subsystem relaxation and alloy / solution interface displacement is hardly possible without the use of labor-intensive numerical calculations. At the same time the surface roughness of an electrode, equilibrium solid-phase adsorption accumulation of alloy components before selective dissolution, and ability of the mixed kinetic control can be taken into account in the analytieal solution of the voltammetric problem. 

The structure of the double layer can be altered if there is interaction of concentration gradients, due to chemical reactions or diffusion processes, and the diffuse ionic double layer. These effects may be important in very fast reactions where relaxation techniques are used and high current densities flow through the interface. From the work of Levich, only in very dilute solutions and at electrode potentials far from the pzc are superposition of concentration gradients due to diffuse double layer and diffusion expected [25]. It has been found that, even at high current densities, no difficulties arise in the use of the equilibrium double layer conditions in the analysis of electrode kinetics, as will be discussed in Sect. 3.5. 

The distinction between Langmuir and Gibbs monolayers resembles that between an ideally polarizable and an ideally relaxed electrified interface (sec. 1.5.5b). An interface is polarizable when no charges (ions or electrons) can cross it it is reversible when such transport takes place until equilibrium between electrode and solution has been attained. In the former case the potential across the interface has to be applied from an external source so that it is an independent variable. For a relaxed interface this is not the case the potential is spontaneously established by preferential adsorption or desorption of ionic species. 

Dynamic properties of i.s.e.s. differ greatly for various electrode types and constructions. When the capacitance of analyte/active surface interface is the only cause of response delay, then relaxation time (or time constant of first-order step-response characteristic) is in the order of milliseconds. When the transport of ions across the dynamic Prandtl layer to the surface of the i.s.e. is the main factor (i.e., this transport is the slowest process of equilibrium reinstallation), for a mixing velocity of about lOcm/s a relaxation time of several seconds occurs. This is typical of solid-membrane electrodes with the exception of glass ones. On the other hand, the limited rate of the exchange process in the liquid membrane, the small diffusion flux of the tested ions into the membrane, the slow dynamics for the creation of diffusion potential and the solubility of the active component of the membrane in the testing solution are the main reasons for the slow response of liquid ion-exchanger electrodes (time constants 10-30 s or even more). 

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