**Reactivity Indexes and Structure of Fullerenes**

**Reactivity Indexes and Structure of Fullerenes**

DOI: 10.5772/intechopen.70642

Ernestina Mora Jiménez, Francisco J. Tenorio, David Alejandro Hernández-Velázquez, Jaime Gustavo Rodríguez-Zavala and Gregorio Guzmán-Ramírez David Alejandro Hernández-Velázquez, Jaime Gustavo Rodríguez-Zavala and Gregorio Guzmán-Ramírez Additional information is available at the end of the chapter

Ernestina Mora Jiménez, Francisco J. Tenorio,

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70642

#### **Abstract**

The discovery of fullerenes and their production in measurable quantities launched many studies about their reactivity and possible applications. Their peculiar structure opened possibilities for their study, initially replacing carbon atoms with alternative atoms. The surface also offers the possibility of attaching several species and the interior of their hollow structure represents a challenge because of the possibility of confining elements or molecules that may become less stable when attached to the exterior of the cage. These modifications may considerably affect both chemical and physical properties. In this chapter, we propose the encapsulation of 3–10 nitrogen atoms as aggregates inside the C70 cage. We also study the structures and reactivity indexes and the stabilization conferred as a result of being part of the fullerene. These aggregates are mainly of interest because of their possible application as energetic materials.

**Keywords:** polynitrogen, endohedral fullerenes, Density Functional Theory, reactivity indexes, C70, energetic materials

#### **1. Introduction**

Over the course of time, carbon materials have become important components not only everyday aspects of life, but also vanguard research. The enormous diversity concerning their uses and applications is constantly increasing, representing an area of constant development. Whether as part of a compound or in pure form, carbon has always attracted attention. At least in its purest forms, its structural diversity is extremely attractive (**Figure 1**).

Research on the formation and arrangement of carbon compounds that included long chains of this element in interstellar space lead to the discovery of fullerenes in 1985. Subsequently,

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. © 2018 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.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

**Figure 1.** Allotropic forms of carbon. From left to right and up to down, diamond, graphite, nanotube and fullerene.

been as -BN- pairs, thus ensuring that isoelectronic species are obtained, although this has not necessarily been the only purpose; in the case of silicon, the main motive has been to search for useful applications in electronics [9–21]. Last but not least, endohedral fullerenes exist because of the fact that they are hollow; so they have the potential application of confining or protecting molecules, thus acting as carriers or stabilizers. Particularly, those with metallic atoms inside them—endohedral metallofullerenes—have been attractive for chemistry, physics and interdis-

Considerable interest in nitrogen compounds has emerged, especially those with a high content of this element, because of their particular properties and forms. Apart from the previously

sented a challenge or turned out to be surprisingly simple [27–30]. In spite of this, until now, the species with the highest content of nitrogen produced in measurable quantities has contained 5 nitrogen atoms, meaning that in particular the cyclopentazole anion could be considered as a motivator for theoretical studies on its formation, as well as representing a building block towards more complex structures [31–35]. As species with higher nitrogen content have

numbered experimental ones. Of these, it has been determined that the preferred forms of N<sup>4</sup>

must be formed from an azide-pentazole (N<sup>3</sup>

), little was known of species with higher nitrogen content, until

have been discovered or posited, whose synthesis has either repre-

) [26]. However, over time, new polynitrogenated species

–N5

, theoretical studies have out-

Reactivity Indexes and Structure of Fullerenes http://dx.doi.org/10.5772/intechopen.70642 31

) and that more complex

ciplinary areas, such as materials and biological sciences [22–25].

**Figure 2.** Comparison of C60 fullerene with a soccer ball and C70 with a rugby ball.

−

proved to be very unstable with respect to decomposition to N2

**1.2. Polynitrogenated materials**

known molecular nitrogen (N<sup>2</sup>

, N4 , N5 − and N5 +

are acyclic, N8

such as N3

and N6

the synthesis of the azide anion (N<sup>3</sup>

they were produced in measurable quantities for use in experiments [1–3]. Even though their study may have evolved accidentally, insufficient effort has been dedicated to understanding their structure, properties and applications. The best known examples of fullerenes are C60 and C70, both of which consist of 12 pentagons, and only differ concerning the number of hexagons in their structure: 20 in the case of the first and 25 in the second. These differences result in the C60 structure, which is more like a soccer ball and C70, which is more like a rugby ball (**Figure 2**). While C60 is more often known as a buckyball, the rest of the hollow structures are inscribed to the general fullerene group.

#### **1.1. Types of fullerenes**

Research into fullerenes has been extremely diverse, but can be categorized according to the structural aspect to be studied. Correspondingly, we have the following: exohedral fullerenes (with external ligands or molecules), endohedrals (with internal atoms or molecules) and heterofullerenes (with one or more carbon atoms in the cage replaced by heteroatoms).

Exohedral fullerenes have essentially resulted from efforts to "decorate" the surface of the fullerenes; mainly achieved by means of chemical functionalization. These types of fullerenes have proved to be extremely interesting, both for medical applications and for their possible applications in material sciences [4–8]. With respect to heterofullerenes, the substitution of carbon atoms by boron, nitrogen and silicon has been proposed; in the case of the first two, these have regularly

**Figure 2.** Comparison of C60 fullerene with a soccer ball and C70 with a rugby ball.

been as -BN- pairs, thus ensuring that isoelectronic species are obtained, although this has not necessarily been the only purpose; in the case of silicon, the main motive has been to search for useful applications in electronics [9–21]. Last but not least, endohedral fullerenes exist because of the fact that they are hollow; so they have the potential application of confining or protecting molecules, thus acting as carriers or stabilizers. Particularly, those with metallic atoms inside them—endohedral metallofullerenes—have been attractive for chemistry, physics and interdisciplinary areas, such as materials and biological sciences [22–25].

### **1.2. Polynitrogenated materials**

they were produced in measurable quantities for use in experiments [1–3]. Even though their study may have evolved accidentally, insufficient effort has been dedicated to understanding their structure, properties and applications. The best known examples of fullerenes are C60 and C70, both of which consist of 12 pentagons, and only differ concerning the number of hexagons in their structure: 20 in the case of the first and 25 in the second. These differences result in the C60 structure, which is more like a soccer ball and C70, which is more like a rugby ball (**Figure 2**). While C60 is more often known as a buckyball, the rest of the hollow structures

**Figure 1.** Allotropic forms of carbon. From left to right and up to down, diamond, graphite, nanotube and fullerene.

Research into fullerenes has been extremely diverse, but can be categorized according to the structural aspect to be studied. Correspondingly, we have the following: exohedral fullerenes (with external ligands or molecules), endohedrals (with internal atoms or molecules) and het-

Exohedral fullerenes have essentially resulted from efforts to "decorate" the surface of the fullerenes; mainly achieved by means of chemical functionalization. These types of fullerenes have proved to be extremely interesting, both for medical applications and for their possible applications in material sciences [4–8]. With respect to heterofullerenes, the substitution of carbon atoms by boron, nitrogen and silicon has been proposed; in the case of the first two, these have regularly

erofullerenes (with one or more carbon atoms in the cage replaced by heteroatoms).

are inscribed to the general fullerene group.

30 Fullerenes and Relative Materials - Properties and Applications

**1.1. Types of fullerenes**

Considerable interest in nitrogen compounds has emerged, especially those with a high content of this element, because of their particular properties and forms. Apart from the previously known molecular nitrogen (N<sup>2</sup> ), little was known of species with higher nitrogen content, until the synthesis of the azide anion (N<sup>3</sup> − ) [26]. However, over time, new polynitrogenated species such as N3 , N4 , N5 − and N5 + have been discovered or posited, whose synthesis has either represented a challenge or turned out to be surprisingly simple [27–30]. In spite of this, until now, the species with the highest content of nitrogen produced in measurable quantities has contained 5 nitrogen atoms, meaning that in particular the cyclopentazole anion could be considered as a motivator for theoretical studies on its formation, as well as representing a building block towards more complex structures [31–35]. As species with higher nitrogen content have proved to be very unstable with respect to decomposition to N2 , theoretical studies have outnumbered experimental ones. Of these, it has been determined that the preferred forms of N<sup>4</sup> and N6 are acyclic, N8 must be formed from an azide-pentazole (N<sup>3</sup> –N5 ) and that more complex polynitrogens may exist such as N<sup>7</sup> , N12, N18, N20 and a great etcetera [36–42]. Considering larger structures, there is no doubt that polyhedral or fullerene-type structures have provided inspiration, as they are considered as alternative polynitrogenous arrangements with a greater number of nitrogen atoms [18, 19, 21, 41, 43–47]. In this sense, a hollow structure could in principle be useful for storing internal molecules, which is why it is common to find hollow carbon structures as candidates for confining polynitrogenous species. Currently, the most notable examples have been studies of N@C60, N@C70 or even N2 @C60 [48–52], which have extended the use of the C60 cage as a way of confining up to 16 nitrogen atoms [53, 54]. Also recently, the encapsulation of a polymer nitrogen chain in a carbon nanotube was conceived, as in principle this could be stable up to room temperature [55]. This contrasts with other proposed polynitrogenated phases of nitrogen that have been inspired by the analogy to phosphorus and arsenic, all superior in energy to the "cubic gauche" (CG). These have been proposed for extreme conditions and some experimental evidence has even been found for them [56–61]. Therefore, confinement represents an alternative for the stabilization of polynitrogenated species that are not necessarily related to high temperatures and pressure.

Chemical potential was computed by conceptual Density Functional Theory approximation. For an N electron system with an external potential v(r) and total energy E, electronegativity is defined as the partial energy derivative to the number of electrons at constant potential and then by the definition of Mulliken as the mean of IE and EA and the negative of electronega-

> \_\_\_ ∂E <sup>∂</sup>N)ν(r)

chemical potential to the number of electrons, also at constant energy potential:

) or detected in experiments (N<sup>3</sup>

∂<sup>2</sup> \_\_\_\_E <sup>∂</sup>N2)ν(r)

Chemical hardness was calculated as defined by Parr and Pearson [71], differentiating the

Energies were also obtained for the stabilization reactions for polymer species within the C70 structure, applying the formula: ∆E = ΣE(products) − ΣE(reagents) for two possible schemes. In the first, the stabilization of isolated nitrogen atoms could be analyzed through the reaction *n*N + C70 Nn@C70. In the second scheme, the reagents are substituted with nitrogen as found

It was previously reported that the methodology consisted of an optimization at the PM6 level. As the refinement and electronic structure were performed at the B3LYP/6-311G level,

For the majority of the structures obtained, neutral and charged species correspond to the same arrangement. In cases where it is not observed, it will be mentioned in due course.

the same structure in charged and neutral systems, see **Figure 3**. There is also found a second

"isolated" nitrogen atom. The difference in the relative energies exceeds 40 kcal/mol, leading us to assume that the linear isomer encapsulated in C70 would predominate, if it was ever produced. Distances between nitrogen atoms (1.20 Å) suggest a weaker bond than that observed

Reaction energies were calculated based on various assumptions. First, it is considering only the stabilization due to the encapsulation of nitrogen atoms as reagents. Second, considering

(or not) of 3 isolated nitrogen atoms, compared to placing them within the cage in polymer

@C70 reaction was used to evaluate the role of the C70 box for the stabilization

. The minimum energy structure corresponds to a linear and centered N3

structures that can be found at room temperature as starting materials (**Table 1**).

stable structure that may closely resemble the association between the N2

≈ −\_\_\_\_\_\_ IE <sup>+</sup> EA

≈ \_\_\_\_\_\_ IE <sup>−</sup> EA

− , N5 − , etc).

<sup>2</sup> (1)

Reactivity Indexes and Structure of Fullerenes http://dx.doi.org/10.5772/intechopen.70642 33

<sup>2</sup> (2)

, which shows

molecule and an

tivity is the molecular chemical potential, μ:

μ = −χ = (

η = (

they are presented exclusively in the following.

**3.1. N***n***@C70 structures and reaction energies**

in standard state (N<sup>2</sup>

**3. Results**

**N3**

for N2

(1.11 Å).

The 3N + C70 → N3

As our work group has studied fullerenes and their reactivity [7, 16, 62–65] and it has been proposed that C60 might be an ideal candidate for trapping nitrogen by a polymer [53, 54], the intention now is to show that C70 might also be an alternative way of storing polynitrogenous species, contributing to the development of new materials in the future.
