Introduction to Molecular Chemistry for Energy

## **Chapter 1**

## Introductory Chapter: Molecules and Materials Associated with Redox Reactions

*Olivier Fontaine*

## **1. Introduction**

1992 was the year chosen by the Nobel Committee to name Professor Rudolph Marcus as the winner of this prestigious prize in chemistry [1] in recognition of his passionate investment in the atomic and electron transfer field. The consequences of the discovered formalism affect the area of redox reactions in the broadest sense: from the molecule to devices that convert or store electrical energy by the redox chemistry pathway. In modern times, redox reactions continue to be of undeniable significance for the technology that deals with the storage or conversion of energy [2].

## **2. Basic consideration of the electron transfer**

In its simplest form, the redox reaction involves an electron donor and an electron acceptor; a molecular disruption occurs when that electron jumps from the donor to the acceptor. This disruption is formalized as a solvent reorganization in a liquid phase. The probability of a redox reaction also results from the electronic coupling strength between the electron donor and acceptor. Quickly, the electron transfer is governed by the probability that the electron can move from the donor to the acceptor. This transfer probability is modulated by the energy required to reorganize the disruption associated with the displacement of an elementary charge. The equations from (1) to (3) put these two critical parameters into formalism with *Hab* for the coupling parameter and *λ* for the reorganization energy [3–5].

$$k\_{ET} = \kappa\_{el}(H\_{ab}) \bullet \mathfrak{u}\_n \bullet e^{-\frac{\left(\Delta G^0 + \mathfrak{l}\right)^2}{4\omega \cdot \mathfrak{l} \cdot R \cdot T}} \tag{1}$$

where *kET* is electron transfer rate constant (unit in s�<sup>1</sup> ), κ*el* is electronic transmission coefficient (dimensionless), υ*<sup>n</sup>* is nuclear vibration frequency (unit in s�<sup>1</sup> ), Δ*G*<sup>0</sup> is Gibbs-free energy (unit in eV or J), *λ* is reorganization energy (unit in eV or J), R is gas constant (8.314 J�K�<sup>1</sup> �mol�<sup>1</sup> ), and T is Kelvin temperature (unit in K).

$$m\_{el}(H\_{ab}) = \frac{4 \bullet \pi^2 \bullet H\_{ab}{}^2}{h\sqrt{4 \bullet \pi \bullet \lambda \bullet k\_B \bullet T}} = \frac{H\_{ab}{}^2}{\hbar} \bullet \sqrt{\frac{\pi}{\lambda \bullet k\_B \bullet T}}\tag{2}$$

In Eq. (2), *<sup>h</sup>* is Planck constant (6.626 � <sup>10</sup>�<sup>34</sup> <sup>J</sup>∙s or 4.14 � <sup>10</sup>�<sup>15</sup> eV∙s), <sup>ℏ</sup> is the reduced Planck constant (ℏ = h/2π), *λ* is reorganization energy, *kB* is Boltzmann constant (1.38 � <sup>10</sup>�<sup>23</sup> <sup>J</sup>�K�<sup>1</sup> ), T is Kelvin temperature, and *Hab* is the coupling term [6].

$$
\lambda = \frac{\varepsilon\_0^2}{8 \cdot \pi \cdot \varepsilon\_0} \cdot \left(\frac{1}{a\_0} - \frac{1}{2 \bullet d}\right) \cdot \left(\frac{1}{\varepsilon\_{op}} - \frac{1}{\varepsilon\_t}\right) \tag{3}
$$

For the third one, *a0* is the effective reactant radius (Stokes-Einstein radius, unit in m or Å), *d* is the distance from the center of the reactant to the surface of the electrode (unit in m or Å), *e0* is electron charge (constant, 1.6 � <sup>10</sup>�<sup>19</sup> C = 1.6 � <sup>10</sup>�<sup>19</sup> <sup>A</sup>�s), *<sup>ε</sup><sup>0</sup>* is vacuum permittivity (constant, 8.854 � <sup>10</sup>�<sup>12</sup> <sup>F</sup>�m�<sup>1</sup> = 8.854 � <sup>10</sup>�<sup>12</sup> <sup>s</sup> <sup>4</sup> � A2 �m�<sup>3</sup> � kg�<sup>1</sup> ), *εop* is solvent optical permittivity (square of the refractive index, dimensionless value), *ε<sup>S</sup>* is solvent static permittivity (dimensionless value), *λ* is reorganization energy (unit in J = kg �m<sup>2</sup> �<sup>s</sup> �2 , or eV) [7].

The formalism remains the same in its general idea in more complex forms, solid phases, or involving more complex structures than organic molecules. Solid-state physics is an example of this similarity through the small polaron theory. Eq. (4) shows the work involved in moving a small polaron. The polaron reflects the electron plus its surroundings moving in a crystal structure.

$$\lambda = -\frac{e\_0}{8 \cdot \pi \cdot \varepsilon\_0} \cdot \left(\frac{1}{r\_p}\right) \cdot \left(\frac{1}{\varepsilon\_{op}} - \frac{1}{\varepsilon\_s}\right) \tag{4}$$

where *rp* is radius of polaron (unit in m or Å), *e0* is electron charge (constant, 1.6 � <sup>10</sup>�<sup>19</sup> C = 1.6 � <sup>10</sup>�<sup>19</sup> <sup>A</sup>�s), *<sup>ε</sup><sup>0</sup>* is vacuum permittivity (constant, 8.854 � <sup>10</sup>�<sup>12</sup> <sup>F</sup>�m�<sup>1</sup> = 8.854 � <sup>10</sup>�<sup>12</sup> <sup>s</sup> <sup>4</sup> � A2 �m�<sup>3</sup> � kg�<sup>1</sup> ), *εop* is solvent optical permittivity (square of the refractive index, dimensionless value), *ε<sup>S</sup>* is solvent static permittivity (dimensionless value), and *<sup>λ</sup>* is reorganization energy (unit in J = kg �m<sup>2</sup> �s �2 , or eV). In these parameters and the relations that link these parameters, the equation resembles that of the reorganization energy.

## **3. Diversity of the redox reaction**

Therefore, it is natural that it appeared to be of common interest to gather a set of chapters regrouping the diversities of the redox reaction in this book. All the authors have presented a broad view of redox reactions in various fields. Fundamental aspects include the influence of the nature of the electrolyte on the redox potentials, the material of pseudocapacitors, the redox-active electrolytes of supercapacitors, and the redox flow battery technology. Here, we detail the unity that links these chapters.

In Chapter 1, the authors address the phenomena of redox molecules confined inside porous carbon through the concept of Redox Mediated Electrolytes in electrochemical capacitors. Redox processes are intimately connected to the field of electrochemistry. The chapter explains the fundamentals of electrochemical capacitors and offers a complete look at this technology. A particular emphasis is placed on hybrid systems, which uses the electrolytic solution's redox activity. Electrical current creation is accomplished by using charge transfer mechanisms in all electrochemical cells. Redox reactions are utilized in several processes, including charging and discharging battery packs. In addition, similar reactions may be used to enhance the operational characteristics of other energy storage devices, such as electrochemical capacitors.

## *Introductory Chapter: Molecules and Materials Associated with Redox Reactions DOI: http://dx.doi.org/10.5772/intechopen.106755*

Although, in theory, the energy in electrochemical capacitors is stored electrostatically (by the formation of electrical double layers), the redox reactions introduce an additional charge and improve the energy of these systems. This is because the redox reactions enhance the energy of these systems.

The alternative way between the battery and EDLC is pseudocapacitance. The reactivity of this class of materials is not apparent, and deep electrochemical investigation is necessary, as explained in Chapter 2. Pseudocapacitance is a charge storage phenomenon that occurs at the electrode/electrolyte interface and is characterized by redox transitions. The oxidation states of one or more components of an electrode and electrolyte can shift as a direct result of modulating electrode potential. The redox reaction may be restricted to the interface, or it may propagate into the bulk of the electrode material, which will significantly increase the charge capacitance of the material. The effectiveness of charge storage owing to pseudocapacitance events is primarily determined by several fundamental criteria, including the pace of the interfacial redox reaction and its ability to be reversed. In Chapter two, the authors look at how the properties of the interfacial redox reaction can affect how well the charge can be stored in pseudocapacitive materials. In particular, discussions center on the parallels and divergences that can be drawn between the methods of charge storage utilized by batteries and pseudocapacitors. The use of impedance spectroscopy to examine the pseudocapacitive behavior of electrode material is demonstrated.

Understanding the energetics of photochemical solar energy storage, organic photovoltaics, light-emitting diodes, and even photosynthesis requires understanding redox potentials, mainly as determined by cyclic voltammetry and other similar electrochemical methods. Even though none of the energy systems that were just discussed contain substantial quantities (usually 100 mM) of the supporting electrolyte necessary for electrochemical techniques to function, these prevalent methods continue to be the most prevalent ones. At the same time, the additional electrolytes frequently have considerable impacts on the energetics that are being researched, but these effects are not recognized. Despite significant attempts to utilize microelectrodes, it has not been able to use electrochemical methods to detect redox potentials without electrolytes. This is because electrolytes are necessary for the measurement. Chapter 4 will explain novel approaches that employ the process of pulse radiolysis to partially answer the question, "What is the influence of electrolytes on redox potentials?"

Chapter 4 will aboard another type of molecular chemistry used in energy storage with the case of the redox flow battery. The development of highly soluble charge carriers capable of storing several electrons during each charge cycle is required to increase the volumetric energy density of redox flow batteries beyond that of the prototypical all-vanadium system. In Chapter 4, the authors cover the design and performance of a variety of novel charge carriers for flow batteries, emphasizing those with multi-electron redox characteristics. Specifically, they will focus on those who can accept and release multiple electrons. Polyoxometalates, fullerene derivatives, metal coordination complexes, and multifunctional organic systems are some of these compounds.

These chapters show the redox reaction's impact on the energy storage field and the answers we still need to provide.

## **Author details**

Olivier Fontaine1,2

1 Molecular Electrochemistry for Energy, Vistec, Thailand

2 Institut Universitaire de France, Paris, France

\*Address all correspondence to: olivier.fontaine@vistec.ac.th

© 2022 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, provided the original work is properly cited.

*Introductory Chapter: Molecules and Materials Associated with Redox Reactions DOI: http://dx.doi.org/10.5772/intechopen.106755*

## **References**

[1] Marcus RA. Electron transfer reactions in chemistry. Theory and experiment. Reviews of Modern Physics. 1993;**65**(3):599-610. DOI: 10.1103/ RevModPhys.65.599

[2] Hadjipaschalis I, Poullikkas A, Efthimiou V. Overview of current and future energy storage technologies for electric power applications. Renewable and Sustainable Energy Reviews. 2009; **13**(6):1513-1522. DOI: 10.1016/j. rser.2008.09.028

[3] Lawrence JE, Fletcher T, Lindoy LP, Manolopoulos DE. On the calculation of quantum mechanical electron transfer rates. The Journal of Chemical Physics. 2019;**151**(11):114119. DOI: 10.1063/ 1.5116800 [Acccessed: May 26, 2022]

[4] Marcus RA. Generalization of the activated complex theory of reaction rates. I. Quantum mechanical treatment. The Journal of Chemical Physics. 1964; **41**(9):2614-2623. DOI: 10.1063/ 1.1726329 [Acccessed: May 26, 2022]

[5] Marcus RA. Generalization of the activated complex theory of reaction rates. II. Classical mechanical treatment. The Journal of Chemical Physics. 1964; **41**(9):2624-2633. DOI: 10.1063/ 1.1726330 [Acccessed: May 26, 2022]

[6] Savéant J-M. Effect of the electrode continuum of states in adiabatic and nonadiabatic outer-sphere and dissociative electron transfers. Use of cyclic voltammetry for investigating nonlinear activation-driving force laws. The Journal of Physical Chemistry B. 2002;**106**(36):9387-9395. DOI: 10.1021/ jp0258006

[7] Saveant J-M. Elements of Molecular and Biomolecular Electrochemistry. Wiley-Interscience; 2019

Section 2
