**1. Introduction**

The aim of this Chapter is several folds (1) to provide a brief background on the derivative approach in measurements and its various applications in science and

engineering fields, (2) to review some of our research work on advances on derivatives voltammetry (DV) which have been scattered among dozens of different journls and conference presentations/proceedings in the past, together with additional new findings and development which have not been published yet, (3) to analyze and compare those characteristic results from each of different electrochemical reaction mechanisms, and to construct a master table of diagnostic criteria for differentiating various types of the electrode mechanisms. Namely, as the subtitle indicates, the primary goal of the project is, utilizing derivative voltammetry, to invent a general criteria for differentiating various types of electrode processes, in order to complement other methods such as cyclic voltammetry(CV), which is the most popular one, or Cyclic Square-Wave Voltammetry (CSWV).

important in developing electroanalytical methods for determining an analyte in a system but also devising effective electrochemical energy storage cells and other

*Advances in Derivative Voltammetry - A Search for Diagnostic Criteria of Several…*

As far as method of studying electrode reaction mechanisms concerned [1, 38], the cyclic voltammetry (CV) has been dominant in the field [39–41]. However, we have developed this new derivative approach to investigate electrode kinetics [11–15] in order to help in elucidating electrochemical reaction mechanisms: this is because CV has drawbacks of complications arising from the interference of the capacitive current to charge the electrical double layer at the interface; as results those peaks from CV are not purely Faradaic, and giving problems associated with defining/evaluating peak currents (ip), and peak potentials (Ep) and peak widths (Wp). In present work, currents are taken in normal pulse voltammetric (NPP) mode by sampling the current near the end of a pulse in order to minimize the non-Faradaic currents: then, first-, second-, and third- derivatives are taken from the

The electrochemical systems under present investigation includes the simple electron transfer process; the reversible electron transfer reaction (**Er** type of mechanism), and quasi-reversible (**Equasirev** type) and irreversible (**Eirr** type) electron transfer [11, 15], and chemically coupled e transfer processes with a prior chemical equilibrium (**CEr** type) [12, 13, 42] as well as those with a post-kinetic process (**ErC** type) [14] all on a planar electrode. The observed currents may be influenced by the heterogeneous kinetic constants for an electron transfer reactions

Equasirev type of processes [15], as well as the homogeneous rate constant (k) and equilibrium constant (Keq) for ErC or CEr type of processes [13, 14]. In this study, the effects of these various kinetic variables on the current and it's derivatives are

The theoretical voltammogram (zeroth-order derivative) is basically to emulate a normal pulse voltammogram (NPV) obtained with a normal pulse mode from an electrochemical analyzer with a DME or HMDE or SMDE (static mercury drop electrode) [11]; typically, with a pulse period of 1.000 s, pulse width of 50 ms, current sampling time of 33 ms, and scan rate of 1 mV/sec or 2 mV/s with a commercial electrochemical analyzer such an instrument as BAS-100 and Tacussel PRG-5 Pulse Polarograph. In calculation of theoretical currents, the original currents are normalized by dividing them with the diffusion controlled current (id) to

**1.3 Basic scheme with symmetry in the peaks associated with derivative voltammetry and definitions of various parameters from the plots of**

Please refer to the **Figure 1** for the definitions of all the dependent variables associated with the current-potential curve (zeroth order derivative) and it's first, second and third derivatives. All measured variable and derived variables associated

) for Eirr and

(*i.e*., the transfer coefficient, α, and heterogeneous rate constant, k<sup>o</sup>

applied fields of engineering.

NPP data.

also investigated.

**3**

*1.2.1 Drawbacks of cyclic voltammetry*

*DOI: http://dx.doi.org/10.5772/intechopen.96409*

*1.2.2 Several common types of electrochemical systems*

*1.2.3 Experimental measurements of derivatives*

obtain a dimensionless currents.

**currents and it's derivatives**

#### **1.1 Backgrounds**

Derivatives approaches in analyzing data signals, have attracted much interests producing numerous research articles in the past [1–32]. Although earlier pioneering reports on the derivative approach in electrochemistry are found in the reference sections in our previous reports in electronalyticalchemistry [11–15], the approach with derivatives is not only limited to electrochemical methods but also have extended to other various fields of science and engineering [23–27, 33]. These reviews and earlier articles introduces basics of the method and techniques of signal processing [2–4, 28, 34], as applied to spectroscopic and spectrophotometric data [2–9, 34], electrochemical data [10–21], and other signals from seismic data [23] and data from biomechanics measurements [24–27, 33]. Several group [3, 6] extended the derivatives to as high as fourth order for enhanced peak resolutions. For example, a single broad peak of UV absorption spectrum from a ternary mixture of amino acids (phenylalanine, tyrosine and tryptophan), were separated and resolved in its second and fourth derivatives [3]; the physiological states of certain algae have been assessed from an analysis of 4th derivative of absorption spectra of chlorophyll a and b [6]; a second order derivatives of an IR spectra of a DNA in malignant tissues exhibits some differences from those of a normal one [7]. The ever increasing interests in the derivative approaches in analysis of signals stem from (a) the information hidden behind in the raw data can be easily exposed from analysis of finer features emerged in the shapes of derivatives, the higher order the more the revelation, and (b) the technical advances in digital signal enhancing methods [2, 14, 15, 23–29, 34] that improve the S/N ratio which was not possible from analog instruments. A review of signal processing in electrochemistry with an introduction of software packages and extensive references therein by Jakubowska [29] may provide further assistance for interested readers.

In the field of electrochemical analysis, the derivative approach has been applied to potentiometric [10, 16] as well as to voltammetric measurements [10–22] with the enhanced resolution and better signal-to-noise (S/N) ratios.

More recent applications for derivative techniques have also been reported for analysis of oxidation of methanol [21], for improved quantification of ill-defined peaks in determining Pt in water and sediments [35], for analysis of alloxan [36], and for quantitation of naringin, an antioxidant [37].

#### **1.2 Application to study of electrochemical reaction mechanisms**

Most reports of derivative approach on electrochemical system has been for its application in chemical analysis [10, 19, 20] while only few groups have attempted to apply the approach to the study of kinetics of electrode reactions [11–18, 21, 22]. Elucidation of electrochemical reaction mechanisms on electrode surface is not only important in developing electroanalytical methods for determining an analyte in a system but also devising effective electrochemical energy storage cells and other applied fields of engineering.
