Time constant, electrochemical electrode

Consideration of the equivalent circuit diagram of an electrochemical cell, such as that given in Figure 5.1, reveals the major limitation on the rate at which the potential of an electrode can be varied, namely, the time constant of the electrochemical cell, RuCd. When a potential sweep is applied across the cell, the nonfaradaic charging current that flows is described by [24]... 

When the electrochemical properties of some materials are analyzed, the timescale of the phenomena involved requires the use of ultrafast voltammetry. Microelectrodes play an essential role for recording voltammograms at scan rates of megavolts-per-seconds, reaching nanoseconds timescales for which the perturbation is short enough, so it propagates only over a very small zone close to the electrode and the diffusion field can be considered almost planar. In these conditions, the current and the interfacial capacitance are proportional to the electrode area, whereas the ohmic drop and the cell time constant decrease linearly with the electrode characteristic dimension. For Cyclic Voltammetry, these can be written in terms of the dimensionless parameters yu and 6 given by... 

Figure 17. Plots of the reduced current density against the applied potential obtained from the as-activated carbon (dotted line) and as-reactivated carbon (dashed line) electrode specimens. Solid line represents the ideal double layer capacitor where the time constant is zero. Reprinted from C.-H. Kim, S.-I. Pyun, and H.-C. Shin, J. Electrochem. Soc. 149 (2002) A93. Copyright 2001, with permission from The Electrochemical Society.

The greatly reduced double-layer capacitance of microelectrodes, associated with their small area, results in electrochemical cells with small RC time constants. For example, for a microdisk the RC time constant is proportional to the radius of the electrode. The small RC constants allow high-speed voltammetric experiments to be performed at the microsecond timescale (scan rates higher than 106V/s) and hence to probe the kinetics of very fast electron transfer and coupling chemical reactions (114) or the dynamic of processes such as exocytosis (e.g., Fig. 4.25). Such high-speed experiments are discussed further in Section 2.1. 

To be more specific, we now refer to Equations 8.86 and 8.88, which represent the impedance of the equivalent circuit corresponding to the electrochemical reaction at the electrode-electrolyte interface. If in Equation 8.86 we calculate the limit for co —> 0, then the intercept of the plot in the real axis is Zr = Rs + Rp on the other hand, if the limit for co —> is calculated, then Zr = Rs. Besides, at the frequency where a maximum of X, (co) is detected, we have Rp Cdl = l/comax = x, where the time constant, x, indicates how fast the electrochemical reaction is. Finally knowing Rp Cdl = l/comax, it is possible to calculate Cdi [129,130],... 

Figure 18 Various models proposed for the surface films that cover Li electrodes in nonaqueous solutions. The relevant equivalent circuit analog and the expected (theoretical) impedance spectrum (presented as a Nyquist plot) are also shown [77]. (a) A simple, single layer, solid electrolyte interphase (SEI) (b) solid polymer interphase (SPI). Different types of insoluble Li salt products of solution reduction processes are embedded in a polymeric matrix (c) polymeric electrolyte interphase (PEI). The polymer matrix is porous and also contains solution. Note that the PEI and the SPI may be described by a similar equivalent analog. However, the time constants related to SPI film are expected to be poorly separated (compared with a film that behaves like a PEI) [77]. (With copyrights from The Electrochemical Society Inc., 1998.)...

Reversibility — This concept is used in several ways. We may speak of chemical reversibility when the same reaction (e.g., -> cell reaction) can take place in both directions. Thermodynamic reversibility means that an infinitesimal reversal of a driving force causes the process to reverse its direction. The reaction proceeds through a series of equilibrium states, however, such a path would require an infinite length of time. The electrochemical reversibility is a practical concept. In short, it means that the -> Nernst equation can be applied also when the actual electrode potential (E) is higher (anodic reaction) or lower (cathodic reaction) than the - equilibrium potential (Ee), E > Ee. Therefore, such a process is called a reversible or nernstian reaction (reversible or nerns-tian system, behavior). It is the case when the - activation energy is small, consequently the -> standard rate constants (ks) and the -> exchange current density (jo) are high. 

There were significant difficulties associated with fitting models to impedance data. The electrochemical systems frequently did not conform to the assumptions made in the models, especially those associated with electrode uniformity. Constant-phase elements (CPEs), described in Chapter 13, were introduced as a convenient general circuit element that was said to account for distributions of time constants. The meaning of the CPE for specific systems was often disputed. 

How can such ordering processes be influenced and steered into a particular direction Electrochemistry is particularly useful in this respect, since the free energy of the surface system is directly correlated with the electrochemical potential. A simple variation of the electrochemical potential changes the state of the system and may eventually drive a transition into a different surface phase. The electrochemical potential can in general be varied very rapidly, just limited by the time constant of the electrochemical cell, which is given by the capacity of the electrodes electrochemical double layer and the electrolyte resistance [10]. 

Reducing the distance between the electrodes into the micro-to nanometer range, e.g., by employing the tip of an electrochemical STM as a local counter electrode, decreases the time constant of the electrochemical cell well into the... 

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