Concentration of electroactive species

In potentiometry the potential of an electrochemical cell is measured under static conditions. Because no current, or only a negligible current, flows while measuring a solution s potential, its composition remains unchanged. For this reason, potentiometry is a useful quantitative method. The first quantitative potentiometric applications appeared soon after the formulation, in 1889, of the Nernst equation relating an electrochemical cell s potential to the concentration of electroactive species in the cell. ... 

Smaller values of necessitate the appHcation of voltages greater than those calculated from the Nemst equation to obtain a corresponding set of surface concentrations of electroactive species. These voltages are called overpotentials and iadicate chemically related difficulties with the electrolysis. In other words, electron exchange between the electrode and the electroactive species is impeded by the chemistry of the process itself. 

Thus, for R - 1 pm and D - 10 cm sec, a 1 nA limiting current is obtained for concentrations of electroactive species, CQX re(j — 1.6 /jM. These calculations suggest that in the presence of a reversible redox couple at micro-molar concentrations, even STM tip-sample biases of AEt < 10 mV will drive a faradaic current that is comparable to that of the tip-sample tunneling current. STM imaging under such circumstances is likely to be experimentally demanding using conventional feedback methodology. 

The transition time in the galvanostatic mode is listed in Table El. The concentration of electroactive species is 0.1 M and the diffusion coefficient is 10-5 cm2/s. Find the number of electrons transferred and draw a current-time response in a potentiostatic mode. 

Here, A is the electrode area, C and D are the concentration and the diffusion coefficient of the electroactive species, AE and co(=2nfj are the amplitude and the angular frequency of the AC applied voltage, t is the time, and j=nF (Edc-Ei/2) / RT. For reversible processes, the AC polarographic wave has a symmetrical bell shape and corresponds to the derivative curve of the DC polarographic wave (Fig. 5.14(b)). The peak current ip, expressed by Eq. (5.24), is proportional to the concentration of electroactive species and the peak potential is almost equal to the half-wave potential in DC polarography ... 

Concentration polarization occurs when the concentration of electroactive species near an electrode is not the same as its concentration in bulk solution. Concentration polarization is embedded in the terms C(cathode) and E(anode). 

In the case of mass transport by pure diffusion, the concentrations of electroactive species at an electrode surface can often be calculated for simple systems by solving Fick s equations with appropriate boundary conditions. A well known example is for the overvoltage at a planar electrode under an imposed constant current and conditions of semi-infinite linear diffusion. The relationships between concentration, distance from the electrode surface, x, and time, f, are determined by solution of Fick s second law, so that expressions can be written for [Ox]Q and [Red]0 as functions of time. Thus, for... 

The product ix1/2 is a significant diagnostic parameter in chrono-potentiometry. It is apparent from the Sand equation that the quantity ixI/2 is a constant for a given concentration of electroactive species. The application of... 

In the case of semi-infinite linear diffusion, the concentration of electroactive species A will be maintained at zero at the electrode surface if the diffu-... 

Thus (L / Dma)1/2 is the appropriate factor used to convert an ambiguous material flux to a meaningful current term. In the simulations reported next, the dimensionless current parameter is given by Z(K). If diffusion-limited conditions are obtained, the relative concentration of electroactive species in the first element is zero. Thus the form most frequently used is... 

Potentiometric measurements are based on the Nernst equation, which was developed from thermodynamic relationships and is therefore valid only under equilibrium (read thermodynamic) conditions. As mentioned above, the Nernst equation relates potential to the concentration of electroactive species. For electroanalytical purposes, it is most appropriate to consider the redox process that occurs at a single electrode, although two electrodes are always essential for an electrochemical cell. However, by considering each electrode individually, the two-electrode processes are easily combined to obtain the entire cell process. Half reactions of electrode processes should be written in a consistent manner. Here, they are always written as reduction processes, with the oxidised species, O, reduced by n electrons to give a reduced species, R ... 

Electrochemical measurements are useful for determining concentrations of electroactive species in solution. Playing the role of solvent, the monomer studied in this chapter is styrene. One of its most remarkable characteristics is the low dielectric constant (e=2.43 at 298.0K) compared with that of water (e=78 at 298.0K). A solvent with a low dielectric constant is a highly resistive medium, in which voltammetric measurements are not evident. Voltammetric measurements in styrene as solvent have not been described before. Papers describing an electrochemical method for the determination of styrene in more polar organic solvents can be found in the literature13-17. 

Then appears linear sweep rate voltammetry in which the electrode potential is a linear function of time. The current-potential curve shows a peak whose intensity is directly proportional to the concentration of electroactive species. If the potential sweep takes place in two directions, the method is named cyclic voltammetry. This method is one of the most frequently used electrochemical methods for more than three decades. The reason is its relative simplicity and its high information content. It is very useful in elucidating the mechanisms of electrochemical reactions in the case where electron transfer is coupled... 

An electrochemical reaction is called reversible or nemstian when the Nemst s equation can be applied to the surface concentrations of electroactive species for any value of the applied potential (see Sect. 1.7). 

To date, there has been no explicit solution for this problem for p > 3, since the surface concentrations of electroactive species O and R are time dependent and therefore the Superposition Principle cannot be applied (see also Sect. 4.3) [1,5]. In these conditions, a non-explicit integral solution has been deduced using the Laplace transform method (see Appendix H). 

We can ask how effects of the double layer on electrode kinetics can be minimized and if the necessity of correcting values of a and of rate constants can be avoided In order for this to be possible, we have to arrange for s, that is all the potential drop between electrode surface and bulk solution is confined to within the compact layer, for any value of applied potential. This can be achieved by addition of a large quantity of inert electrolyte (—1.0 m), the concentration of electroactive species being much lower (<5mM). As stated elsewhere, other advantages of inert electrolyte addition are reduction of solution resistance and minimization of migration effects given that the inert electrolyte conducts almost all the current. In the case of microelectrodes (Section 5.6) the addition of inert electrolyte is not necessary for many types of experiment as the currents are so small. 

Normally electrode reactions take place in solutions, or sometimes in molten salts (e.g. aluminium extraction). In order to minimize the phenomenon of migration of the electroactive ions caused by the electric field (Chapter 2) and to confine the interfacial potential difference to the distance of closest approach of solvated ions to the electrode (Chapter 3), the addition of a solution containing a high concentration of inert electrolyte, called supporting electrolyte, is necessary. This has a concentration at least 100 times that of the electroactive species and is the principal source of electrically conducting ionic species. The concentration of supporting electrolyte varies normally between 0.01m and 1.0 m, the concentration of electroactive species being 5 mM or less. The... 

When a reaction is reversible, i ct—>0 and Zf = Zw = oco 1/2( 1-i). The observed phase angle is jt/4, and the impedance is the least possible for that value of co (o depends not only on the transport but also on the reciprocal of the concentration of electroactive species see (11.19)). If Rct > 0, Zf increases from its minimum value and there will be a lower phase angle. It is this phase-angle variation according to the rate of the electrode reaction that is used in the technique of a.c. voltammetry. 

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