Potential Transients

According to the material presented in Chapter 3, the value of convolution integral (see Eq. (3.10)) determines surface concentrations. Its analysis allows certain analogies between steady-state and non-steady-state processes to be found. Having inserted the condition x = 0 in the expressions of functions F i,x,t) (Table 3.2) and having compared them with Eq. (3.37), the criteria of similarity can be formulated, which allow transforming the above-discussed voitammograms into other non-steady-state characteristics. 

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Figure 7.10 Potential of maximum entropy (PME) of a Pt(lll) electrode modified by Bi, Pb, Se, and S deposition in 1 mM HCIO4 + 0.1 M KCIO4 solution, as a function of adatom coverage. The dashed, zero-slope line corresponds to the averaged reference PME value of unmodified Pt(lll). The cartoons show the schematic interpretation for the effect of the adatoms at high coverage on the potential transients. (Reprinted with permission from Garcia-Araez et al. [2008].)...

Climent V, Coles BA, Compton RG. 2002b. Coulostatic potential transients induced by laser heating of a Pt(lll) single-crystal electrode in aqueous acid solutions. Rate of hydrogen adsorption and potential of maximum entropy. J Phys Chem B 106 5988-5996. 

Gonczy This is very difficult to quantitate. As you have seen from the immunofluorescence images, there are many microtubules on either side in wild-type moreover, anaphase B takes places within a couple of minutes. Therefore, it will be difficult to uncover potential transient changes in microtubule numbers using fixed specimens. However, we have generated a green fluorescent protein... 

These equations cannot be used at higher overpotentials 77 > kT/e0. If the reaction is not too fast, a simple extrapolation by eye can be used. The potential transient then shows a steeply rising portion dominated by double-layer charging followed by a linear region where practically all the current is due to the reaction (see Fig. 13.2). Extrapolation of the linear part to t = 0 gives a good estimate for the corresponding overpotential. 

Forced convection can be used to achieve fast transport of reacting species toward and away from the electrode. If the geometry of the system is sufficiently simple, the rate of transport, and hence the surface concentrations cs of reacting species, can be calculated. Typically one works under steady-state conditions so that there is no need to record current or potential transients it suffices to apply a constant potential and measure a stationary current. If the reaction is simple, the rate constant and its dependence on the potential can be calculated directly from the experimental data. 

For capacity measurements, several techniques are applicable. Impedance spectroscopy, lock-in technique or pulse measurements can be used, and the advantages and disadvantages of the various techniques are the same as for room temperature measurements. An important factor is the temperature dependent time constant of the system which shifts e.g. the capacitive branch in an impedance-frequency diagram with decreasing temperature to lower frequencies. Comparable changes with temperature are also observed in the potential transients due to galvanostatic pulses. 

For the investigation of charge tranfer processes, one has the whole arsenal of techniques commonly used at one s disposal. As long as transport limitations do not play a role, cyclic voltammetry or potentiodynamic sweeps can be used. Otherwise, impedance techniques or pulse measurements can be employed. For a mass transport limitation of the reacting species from the electrolyte, the diffusion is usually not uniform and does not follow the common assumptions made in the analysis of current or potential transients. Experimental results referring to charge distribution and charge transfer reactions at the electrode-electrolyte interface will be discussed later. 

Metal deposition or stripping and capacitance under constant current, (a) What is the potential transient in the case of metal deposition under constant current (/ = 10 mA/cm ) Derive its transition time x. Consider silver deposition on a silver substrate as an example ( Ag = 0.799 V, DAg - 1.65 x 10-5 cm2/s at room temperature), (b) If this process is reversed (i.e., silver is stripped from the silver substrate electrode), what should the expression be Suppose the initial solution does not contain silver salt, (c) What will the potential be at t = 0 ... 

Diffusion control constant flux mode. Table P.3 contains the potential transient data obtained on a platinum working electrode (against SHE) immersed in an aqueous solution of 0.1 M ferric perchlorate and 1.0 M ammonium perchlorate. The experiment was carried out at a constant current of 10 mA/cm2, and the diffusion coefficient of both reactant and product is assumed to be 10 5 cm2/s. 

In a coupled nuclear hydrogen production system, a transient is initiated on either the nuclear reactor side or the chemical side of the plant. There are many potential transients that occur in a nuclear reactor system. Some examples are (Reitsma 2004) ... 

Fig. 14.14. Unit for potential transient measurement during excitation of a squid axon by current pulses from electrodes 1 and 1 2 and 2 are micropipettes. (Reprinted from A. L. Hodgkin and A. F. Huxley, J. Physiol. 116 497, 1952. Reprinted from J. Koryta, Ions, Electrodes and Membranes, Fig. 93. Copyright J. Wiley Sons, Ltd. 1991. Reproduced with permission of J. Wiley Sons, Ltd.)...

Drug potentiation Transient potentiation of the hypoglycemic effect of tolbutamide (see p. 260) or the anticoagulant effect of warfarin or of bishydroxycoumarin (see p. 199) results from their displacement from binding sites on serum albumin. Free methotrexate (see p. 378) levels may also rise through displacement. 

Jones and Greene (38) proposed that a current step method was attractive because of measurement speed and ability to contend with OCP drift during the time taken to conduct the measurement. For negligible Rs, it has been shown that the potential transient during a current step is given by... 

The temporary hyperpolarization caused by the sodium current is illustrated in Figure 7.8, which illustrates the predicted membrane potential transients for... 

Action potential—transient change in the electrical potential across a membrane which results in the generation of a nerve impulse. 

Equations (54) and (56) form a set of simultaneous differential equations which determine the time evolution of V and 6 during the decay of potential. In the paragraphs which follow, we show the results of solving these equations numerically to find V(t) and 6 t), given the (0, t) dependence of Vi, 2, and represented in Eqs. (50)-(52). The potential transients, V(t), thus obtained, may be compared directly with the appropriate experimental transient, and the rate constants which represent the behavior can be derived by seeking the... 

Schultze and Dickertmann [3.117-3.120] measured current and potential transients under potentiostatic and galvanostatic conditions, respectively, for the adsorption and desorption processes of Bi UPD on Au(lll). All transients were non-monotonous. A typical example is given in Fig. 3.47. The results are interpreted in terms of nucleative 2D Meads phase formation and dissolution processes. 

Easy TCA applied to pinpoint or cloudy white frosting causes virtually no infections, apart from a few potential transient infections of scratch lesions (the frequency is around 1 in a 1000). 

FIGURE 12.4 Open circuit potential transients for smooth polycrystalline platinum in 0.5 M sulfuric acid solution after applying 100 triangular cycles between 1.50 and 1.90 V at 0.2 V s-1. 

Most commonly situations of this kind are attacked by variants of the method of finite differences. A numerical model of the electrochemical system is set up within a computer, and the model is allowed to evolve by a set of algebraic laws derived from the differential equations. In effect, one carries out a simulation of the experiment, and one can extract from it numeric representations of current functions, concentration profiles, potential transients, and so on. 

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