**Abstract**

It has been demonstrated that matter at low dimensionality exhibits novel properties, which could be used in promising applications. An effort to understand their behavior is being through the application of computational methods providing strategies to study structures, which present greater experimental challenges. It is proven that thin and narrow carbon-based nanostructures, such as, nanoribbons show promising tunable electronic properties, particularly when they are substitutionally functionalized. This chapter is proposed as a guidance to help the readers to apply conceptual density functional theory to calculate helpful intrinsic properties, e. g., energetic, electronic and reactivity of one-dimension nanomaterial's, such as, carbon nanoribbons. As a case of study, it is discussed the effect of boron atoms on the properties of pristine carbon nanoribbons concerning the main aspect and considerations must take into account in their computational calculations.

**Keywords:** DFT, band structure, DOS, MEP

### **1. Introduction**

Carbon nanoribbons (CNRs) are strips of graphene whose edges symmetry, width and cut orientation give them specific electronic properties. These carbon nanostructures have attracted the attention in both experimental and theoretical fields because of their peculiar properties, which have been studied widely in the last decade as a function of topology, width, as well as doping. [1–5] Depending the chain-type along the periodic direction, carbon nanoribbons are commonly classified either armchair carbon nanoribbons (ACNR) when these grow through dimer chains, or zigzag carbon nanoribbons (ZCNR) if those have zigzag type chains along the periodic direction. **Figure 1** shows a pristine ACNR and ZCNR respectively, their distances between their C – C edged lengths are 13.44 and 24.19 Å respectively, although there could be named referring their length and width (*M*x*N*), in such case, both CNRs shown in **Figure 1** are 12x2 size.

Through different experimental techniques, it is possible to obtain carbon nanoribbons. [6–8] However, these techniques have not succeeded in controlling the edges shape of carbon nanoribbons. For example, Cai et al. [9] have proposed a chemical technique which is able to synthesize narrow nanoribbons having symmetric edges, so that, it is possible to obtain experimentally carbon nanoribbons with perfect edges

**Figure 1.** *Optimized structure of bare (a) ACNR and (b) ZCNR of size 12x2.*

and specific topology. To date, succeeding methods to obtain CNRs come from two different strategies, namely, top-down, which refers to break down large performed carbon-base structures, i. e., CNTs and multiwall CNTs (MWCNTs) and bottom-up, i. e., using several chemical reactions to tailor building-blocks into a complex structure. **Table 1** shows a comparative chart representing synthetic strategies to obtain CNRs, employed characterization techniques, advantages and disadvantages.

Because of their finite dimension, at nanoscale, CNRs have peculiar properties associated to their electronic states close the edges, playing an important role on the reactivity. [17–22] Several theoretical models, e. g., tight binding, all electron techniques, density functional theory (DFT), etc., have been applied to explore the electronic properties, magnetic states or band structure of carbon nanoribbons. [1, 5, 23] Some of them, have focused on the zigzag topology because they intrinsically have dangling bonds at the edges. This behavior provides active sites for chemical reactions. Moreover, ZCNRs have peculiar properties, e.g., theoretical calculations have shown that ZCNRs have localized electrons largely on the edge C atoms close to the Fermi level. [4, 22] This large contribution of electronic states forms two-fold degenerate flat band at Fermi level, such that, the ground state has spin coupling of each edge ferromagnetic whereas between edges antiferromagnetic. Despite zigzag edges of synthesized carbon nanoribbons have been observed, [8] there is not direct experimental evidence about the magnetic states of ZCNRs. It was theoretically suggested that magnetism of ZCNR could be destroyed substituting defects or vacancies directly on carbon edges. [24]

On the other hand, all hydrogen-passivated ACNRs are semiconducting [22]. However, ACNRs are expected to reach the graphene limit of zero band gap for sufficiently large widths. [25]

Concerning these fascinating properties, CNRs may fit for promising technological applications, mainly if the presence of donor or acceptor impurities bring

**307**

**Table 1.**

*Calculation of the Electronic Properties and Reactivity of Nanoribbons*

**Strategies Method Characteristics Advantages Disadvantages**

The production of 100 nm wide nanoribbons

It is possible to narrow the ribbons down to <10 nm using gas phase etching chemistry

This procedure gives highly conducting CNRs with over 80% yield at low cost fabrication.

Graphene flakes attractive for many applications

Produce micrometer length involving non complicated procedures

Because CNTs impose spatial limitations on the structure of the product, may obtain narrow CNRs

Defined edge type and narrow widths, potential techniques for scale-up

Complicated procedures, CNRs with edges abnormalities

Structures with large number of non-symmetric edge atoms

Resulting graphene oxide

Complicated procedures poorly defined edges

Depends on the precursor's nature, which defines the ribbon's dimension

Using potassium permanganate and sulfuric acid

Longitudinal splitting of MWCNTs using hydrothermal approach

Intercalating lithium and ammonia into MWCNTs followed by thermal expansion

Mechanical exfoliation of highly oriented pyrolyzed

Chemical oxidation/ exfoliation of graphite followed by reduction of the resulting nanomaterial

Cross coupling building blocks followed by dehydrogenation

Conversion of precursors

inside CNTs

Surface assisted polymerization followed by dehydrogenation in an ultra-high vacuum environment

graphite

[13]

specific reactive properties. [26, 27] So that, this chapter is proposed as a guidance to help the readers to apply conceptual density functional theory to calculate helpful intrinsic properties, e. g., energetic, electronic and reactivity of one-dimension nanomaterial's, such as, carbon nanoribbons in order to predict or tune their

*Comparative chart of synthetic methods to obtain nanoribbons and their advantages or disadvantages.*

properties; particularly when they are substitutional doped.

*DOI: http://dx.doi.org/10.5772/intechopen.94541*

CNTs by chemical oxidation [7]

Etching of graphene [10]

Treating multiwalled CNTs [11, 12]

Chemical Procedure Organic synthesis

Bottom-up Organic

synthesis [14–16]

Top-down Unzipping


#### *Calculation of the Electronic Properties and Reactivity of Nanoribbons DOI: http://dx.doi.org/10.5772/intechopen.94541*

#### **Table 1.**

*Nanofibers - Synthesis, Properties and Applications*

and specific topology. To date, succeeding methods to obtain CNRs come from two different strategies, namely, top-down, which refers to break down large performed carbon-base structures, i. e., CNTs and multiwall CNTs (MWCNTs) and bottom-up, i. e., using several chemical reactions to tailor building-blocks into a complex structure. **Table 1** shows a comparative chart representing synthetic strategies to obtain CNRs,

Because of their finite dimension, at nanoscale, CNRs have peculiar properties associated to their electronic states close the edges, playing an important role on the reactivity. [17–22] Several theoretical models, e. g., tight binding, all electron techniques, density functional theory (DFT), etc., have been applied to explore the electronic properties, magnetic states or band structure of carbon nanoribbons. [1, 5, 23] Some of them, have focused on the zigzag topology because they intrinsically have dangling bonds at the edges. This behavior provides active sites for chemical reactions. Moreover, ZCNRs have peculiar properties, e.g., theoretical calculations have shown that ZCNRs have localized electrons largely on the edge C atoms close to the Fermi level. [4, 22] This large contribution of electronic states forms two-fold degenerate flat band at Fermi level, such that, the ground state has spin coupling of each edge ferromagnetic whereas between edges antiferromagnetic. Despite zigzag edges of synthesized carbon nanoribbons have been observed, [8] there is not direct experimental evidence about the magnetic states of ZCNRs. It was theoretically suggested that magnetism of ZCNR could be destroyed

On the other hand, all hydrogen-passivated ACNRs are semiconducting [22]. However, ACNRs are expected to reach the graphene limit of zero band gap for

Concerning these fascinating properties, CNRs may fit for promising technological applications, mainly if the presence of donor or acceptor impurities bring

employed characterization techniques, advantages and disadvantages.

*Optimized structure of bare (a) ACNR and (b) ZCNR of size 12x2.*

substituting defects or vacancies directly on carbon edges. [24]

**306**

**Figure 1.**

sufficiently large widths. [25]

*Comparative chart of synthetic methods to obtain nanoribbons and their advantages or disadvantages.*

specific reactive properties. [26, 27] So that, this chapter is proposed as a guidance to help the readers to apply conceptual density functional theory to calculate helpful intrinsic properties, e. g., energetic, electronic and reactivity of one-dimension nanomaterial's, such as, carbon nanoribbons in order to predict or tune their properties; particularly when they are substitutional doped.
