**4. Conclusions**

A quantitative measure of symmetry *in the original current are not readily available*, can be found indirectly from a ratio of difference in several potentials defined from a voltammogram: namely, a quarter-wave potentials (E1/4), half-wave potentials (E1/2) and a three-quarter-wave potentials); then a ratio of an anodic to cathodic quarter-wave potential differences (i.e., **ΔEq a /ΔEq <sup>c</sup>** = (E1/2-E1/4)/(E1/2-E3/4) is very limited. Nevertheless, the ratio is unity for a symmetrical curve (for a reversible case), but it deviates from one if the curve becomes asymmetrical, yielding 1.14 for Eirr (**Table 2**). On the other hand, asymmetry *in first derivatives is more readily found* in terms of a ratio of anodic-to-cathodic quarter-peak ratio (**Wq a /Wq c** ): this

ratio increases from 1.00 (for Erev) to 1.27 for Eirr. The anodic and cathodic parts of the peak-width (Wq and Wq c ) in the first derivative can be more conveniently measured than three potentials (i.e., E1/4, E1/2 and E3/4) in the zeroth derivative; in addition, the change of the ratio in the first derivative is more sensitive than the ratio in the zeroth derivatives (namely, 27% vs. 14%).

Meeting of American Chemical Society (ACS, San Diego, 2001), and the 65th South East Regional Meeting (SERM of ACS, Atlanta, GA 2013). This work was partially supported by Academic Computing Services of Old Dominion University, and with

Computer Services through Cornell National Super Computer Center (NSF supported), and by Faculty Fellowship Awards (2008-2009) from the Writers Institute of Georgia Perimeter College (GPC). The author acknowledges the work of all collaborators, Prof. Tae-Kee Hong (Haseo University, Korea) in particular. GPC has been consolidated to Georgia State University (GSU) as Perimeter College in

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

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

Department of Physical Sciences, Perimeter College, Georgia State University,

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: mkim124@gsu.edu

provided the original work is properly cited.

2016.

**Author details**

Myung-Hoon Kim

Dunwoody, USA

**27**

*In the second and third derivatives*, compared to first derivatives, *asymmetry in the peak shape is more pronounced*, and more than one symmetry parameters are readily obtained, which are given in terms of ratios of different peak-heights, and peakwidths, and peak-potentials; these parameters are based on peak heights (ip <sup>a</sup> and ip c ) as well as peak widths (W½ <sup>a</sup> and W½ c ) and peak potentials (Ep and Ep). Thus, symmetry ratios of **ip 2a/ip 2c**, **W1/2 2a/W1/2 2c** and **ΔEp 2a/ΔEp 2c** are introduced for second derivatives, and **ip 3a/ip 3c**, **W½ 3a/W½ 3c**, and **ΔEp 3a/ΔEp 3c** for third derivative (in **Tables 2** and **4**). All of these values become unity (1.00) for the reversible processes, indicating the symmetry in the curves; but they become no longer unity for quasi-reversible/irreversible electron transfer or chemically coupled processes as the shapes become asymmetrical. The results are summarized in **Tables 2** and **4** with all types of types of processes included. Basically, all of the symmetry parameters for the 0th derivative (ΔE<sup>a</sup> q/ΔEc q), for the 1st derivative (Wq 1a/Wq 1c), and for 2nd derivative (ip 2a/ip 2c, W1/2 2a/W1/2 2c, & ΔEp 2a/ΔEp 2c) and for third derivative (ip 3a/ip 3c, W½ 3a/W½ 3c, ΔEp 3a/ΔEp 3c) are unity for Erev, they become no longer unity for Eirr, Equasi-rev and two chemically coupled processes of CErev and ErevC. With the third derivatives, there are also minor symmetry parameters associated with the middle peak with values of 0.32 for the two peak-height ratios (ip 3a/ip 3m and ip 3c/ip 3m) and 1.32 for the two peak-width ratios (W1/2 3a/ W1/2 2m, and W1/2 3c/W1/2 3m) for reversible but these ratios are not as simple as the major ones, but changes to 0.22, 0.52, and 1.62 and 0.98 respectively for the irreversible case.

#### **5. Summary**

From careful analysis of derivatives of voltammetric current-potential curves, it is possible to extract various parameter which are associated with asymmetry of the derivatives associated with various types of electrode mehanisms. Among those parameters, some of them are strongly influenced by electron transfer kinetics and electrode reaction mechanisms associated with a system, and these parameters are particularly useful in elucidating the reaction mechaisms. In particular, the ratios of the anodic to cathodic peak-currents (*ip a /ip c* ), and the ratios of the anodic to cathodic peak-widths (*W½ a /W½ c* ) and the ratio of the difference in the anodic and cathodic peak potentials (*ΔEa /ΔE<sup>c</sup>* **)** or the anodic and cathodic peak potential difference (*ΔEa -ΔE<sup>c</sup>* **)** are most sensitive and useful when a simple reversible electron system is disturbed by other kinetics, breaking the symmetry in the derivatives. The parameters of each particular systems respond differently to each type of electrode process; thus analysis of symmetry parameters can provide much insight to the mechanistic nature of electrochemical systems. A useful master table for such a diagnostic criteria for differentiating several common types of electrode mechanisms is devised and presented.

#### **Acknowledgements**

Several parts of the work have been presented at various conferences including the 3rd Chemical Congress of North America (Toronto, Canada, 1988), the 57th Georgia Academy of Science Meeting (Lawrenceville, GA 1999), the 221st National *Advances in Derivative Voltammetry - A Search for Diagnostic Criteria of Several… DOI: http://dx.doi.org/10.5772/intechopen.96409*

Meeting of American Chemical Society (ACS, San Diego, 2001), and the 65th South East Regional Meeting (SERM of ACS, Atlanta, GA 2013). This work was partially supported by Academic Computing Services of Old Dominion University, and with Computer Services through Cornell National Super Computer Center (NSF supported), and by Faculty Fellowship Awards (2008-2009) from the Writers Institute of Georgia Perimeter College (GPC). The author acknowledges the work of all collaborators, Prof. Tae-Kee Hong (Haseo University, Korea) in particular. GPC has been consolidated to Georgia State University (GSU) as Perimeter College in 2016.
