Double pulse technique

The general features of the potential waveform applied and of the output currents of these double pulse techniques are shown. 

Among double pulse techniques, the simplest case is recording the current-time curves obtained when the two successive potential pulses are applied. Usually, the first is set at values corresponding to limiting current conditions for the reactant,... 

This double pulse technique is a modification of the DDPV one based on obtaining two differential signals corresponding to the same first potential, Ej (see Scheme 4.4) [3],... 

In this section only very fast charge transfer reactions will be considered in order to analyze their response in the different double pulse techniques considered in Sect. 4.1. 

In the differential double pulse techniques, the current response is the difference A/g = 12 - if obtained when two consecutive potentials E and 2 are applied... 

The charge current is minimized to a large extent with respect to other double pulse techniques including DDPV, a feature which gives it great analytical usefulness. 

Among the double pulse techniques, DDPV is very attractive for the characterization of multi-electron transfer processes. Besides the reduction of undesirable effects, this technique gives well-resolved peak-shaped signals which are much more advantageous for the elucidation of these processes than the sigmoidal voltammograms obtained in Normal Pulse Voltammetry and discussed in Sect. 3.3. 

Among double pulse techniques, RPV is the most powerful from the kinetic point of view, due to the information it provides on the degree of reversibility of the electrode process. This information is similar to that which can be obtained from... 

Since in this technique the duration of the pulse (tp) is much shorter than the period between pulses (t1 see Scheme 7.2), the response of reversible processes in DMPV is totally coincident with that obtained in the double pulse technique DDPV [9],... 

The electrode size is another important factor to be considered since it affects the magnitude of the diffusive transport, as shown in Fig. 7.14 for totally irreversible processes. At planar and spherical electrodes significant differences are found between double pulse and multipulse modes, with the discrepancy diminishing when the electrode radius decreases, since the system loses the memory of the previous pulses while approaching the stationary response. Thus, the relative difference in the peak current of a given double pulse technique and the corresponding multipulse variant is always smaller than 2 % when... 

The currents obtained with the multipulse technique SWV in the steady-state situation, which are shown in the box of Fig. 7.30c, are identical to those obtained with double pulse technique DDPV, whenever A DDPV = 27isw (i.e., when E (DDPV) = f(SW) and 2(DDPV) = fq(SW)) [46, 49], so the currents obtained with SWV in microelectrodes have the same characteristic as those shown for this double pulse technique. 

The Dimensionless Parameter is a mathematical method to solve linear differential equations. It has been used in Electrochemistry in the resolution of Fick s second law differential equation. This method is based on the use of functional series in dimensionless variables—which are related both to the form of the differential equation and to its boundary conditions—to transform a partial differential equation into a series of total differential equations in terms of only one independent dimensionless variable. This method was extensively used by Koutecky and later by other authors [1-9], and has proven to be the most powerful to obtain explicit analytical solutions. In this appendix, this method will be applied to the study of a charge transfer reaction at spherical electrodes when the diffusion coefficients of both species are not equal. In this situation, the use of this procedure will lead us to a series of homogeneous total differential equations depending on the variable, v given in Eq. (A.l). In other more complex cases, this method leads to nonhomogeneous total differential equations (for example, the case of a reversible process in Normal Pulse Polarography at the DME or the solutions of several electrochemical processes in double pulse techniques). In these last situations, explicit analytical solutions have also been obtained, although they will not be treated here for the sake of simplicity. 

Controlled electrodeposition of silver and gold nanoparticles by the electrochemical double-pulse technique delivers samples with varying particle size from 10 to 500 nm and varying particle density. 

SERS active structures can be prepared by a variety of chemical physical and electrochemical methods described in Sect. 4.1. The chemical preparation of colloidal nanoparticles is frequently used (Sect. 4.1.1). An interesting electrochemical preparation procedure is the so-called double-pulse technique. This method is an electrochemical tool for controlling the metal deposition with respect to particle size and particle density (Sect. 4.1.2). 

Double-Pulse Technique as an Electrochemical Tool for Controlling Particle Structure... 

The ideal method for transforming both principles, which favor monodispersity into an experimental procedure, can best be attained by applying the potentiostatic double-pulse technique. This method, introduced by Scheludko, Todorova, Kaischev, and Milchev [27, 28], is based on an extremely short nucleation pulse of high cathodic polarization, followed by a much longer growth pulse at... 

Based on a model on the features of the double-pulse technique, various structures of silver nanoparticles grown onto a thin ITO film covered glass plate were generated and characterized [30]. With this method, the conflict between both optimal conditions for nucleation and growth is partially defused. This is due to the amount of small seed additionally nucleated at the higher polarization and resolved as soon as the potential is switched over to the lower polarization of the growth pulse. The interaction of the pulse parameters was modeled, thus forming the basis for how the electrodeposition process of noble metal clusters can be variably controlled. 

Control of the Nanoparticle Preparation by Means of the Double-Pulse Technique... 

Fig. 8.6 Features of the double-pulse technique Model on the influence of the transition moment between nucleation pulse and growth pulse in the course of the double-pulse deposition on the Gaussian particle distribution formed after the nucleation pulse [29] (a) Gaussian particle distribution of N nuclei with radii r > tcr (T)i) for different over potentials of the first pulse ( t ib << t iAl)- The hatched area of the Gaussian distribution corresponds to the number of stable particles with radii r > rcr (tje). whereas the white area of particles of under critical size is amputated as these particles dissolve, (b) Representation of the result of the particle cut off, small (dark) particles dissolve but larger particles (white) survive under the lower overvoltage of the growth pulse.(c) If a small particle lies in the diffusion zone of a larger particle the under saturation can favor the dissolution of the smaller ones...

Ueda M, Dietz H, Anders A, Kneppe H, Meixner A, Plieth W (2002) Double-pulse technique as an electrochemical tool for controlling the preparation of metallic nanoparticles. 

The most straightforward test of the nucleation rate equation is to make a plot of the number of nuclei per unit area as a function of time at different overvoltages. The double-pulse technique developed by Scheludko and Todorova [4.32] has been successfully used in a wide range of experiments [4.33-4.36]. 

Figure 5.6 Schematic representation of the potentiostatic double pulse technique for investigations of the nucleation rate-overvoltage dependence. nuc and T/growth denote the overvolt es of 2D nucleation and growth, respectively.

There are several aspects of the nucleation and growth kinetics that can be investigated in detail with the potentiostatic double pulse technique as summarized in Table 5.1. 

Table 5.1 Potentiostatic double pulse technique applications.

Most probable values of the specific edge energy and the pre-exponential factor obtained by the potentiostatic double pulse technique on quasi-perfect cubic and octahedral faces of silver in the standard system Ag (M/)/AgN03 are listed in Table 5.3. 

Based on this phenomenon, a double-pulse technique, originally developed for the study of the electrolytic phase formation by Scheludko and... 

Bakker et al. reported this method improving the limit of detection during a thin-layer coulometric analysis [12-14]. An ionophore was doped enhancing the ion-selective ability of a thin-layer membrane. Using a thin-layer coulometry coupling with double-pulse technique, the analysis of nitrate (NOsOi potassium (K" ), Calcium (Ca" ) were successfully undertaken in the scale of micromolar (pM). Furthermore, the advanced compensation of non-faradic charging... 

Grygolowicz-PawlakE,NumnuamA,ThavatnnglajlP, Kanatharana P, Bakker E (2012) Interference ctnn-pensation for thin layta coulometric ion-selective membrane electrodes by the double pulse technique. Anal Chem 84(3) 1327-1335... 

---