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With the bond- order-length- strength (BOLS) estimation, applying the ab coupled calculating method, the electronic arrangement and properties are studied for the graphene nanoribbons (GYNRs) through the zigzag (ZGYNRs), together with the armchair (AGYNRs) edges. The results point out that both armchair-edge and the graphene nanoribbons are essential semiconductor, with appropriate energy gaps. In addition, their energy gad expands, while at the same time the width of the nanoribbons reduces. On the contrary, zigzag-edged displays features of a nil energy gap material. The investigation results show that, (I) there is stiffing and shortening of C-C bond by the atomic undercoordination, which is the main factor leading to Hamiltonian, and as a result, the energy gap (band gad) widens up naturally, (ii) absence of energy gad gap on the zigzag edge caused by lack of power, on the side of the undercoordination atoms, that lack the energy too of opening the graphene gap. (iii) Undercoordination edge of the particles takes place during the process of the charge entrapment.











Band Gap Modulation in Graphene Nanoribbnne


Carbon is one of the most crucial elements for life, and it plays a critical role in plant photosynthesis. Is one of the elements that has been suggested a potential candidate for the upcoming electronics. In specific, graphene is described as a carbon-form solid electronic that is very encouraging in the electronics part, and as a result led to a remarkable scientist research attention .Graphene material has an striking electronic configuration with Dirac cones features, at which the electrons together with the hole spec tract converge, at a single straight line point in the momentum space, which is known as the Dirac point. At that point, the charge transmitters acts as massless fermion, which tend to move with speed of 10/6 ms -1. Furthermore, there is an increase in the temperature and a rise in the effect of the quantum, which as a result, causes conductivity in the material, because of the existence of the Dirac cones. Elements linked with Dirac cones and Dirac itself carry properties related to graphene. However, in the recent research conducted they are considered to have the same unique characteristic of the graphene material which relates to the regular hexagonal shape of the Dirac cone.

Because of that, graphene been found to be one of the allotrope of group of carbon which comprise of the sp2 carbon hybridized, and this has made it to be a topic of little concern yet remaining to have a lot of interests between the structural, academic and the artificial scientist because of its electric optical, related mechanical properties, and also the suggested strategic practical’s ways of synthesizing the material. For, example, it has been discovered that a-graphene is a group of elements that are semiconductor, with a narrow energy gap or the bandgap. However, (Liu, Sun, and Huang, 2018), found that B-graphyne and some other graphyne materials can act as gables semiconductors like those members of graphyne. Hence resulting to an extension of the application of the range of the graphyne in materials that are Nano semiconductor and photoelectric technology. Furthermore, they also made an excellent film area of graphyne successfully, which is a member of the graphyne family. Additionally, many researchers have carried out a good number of study research on graphyne, and it’s the family associates, to find out the conductivity abilities and electronic properties. Due to this numerous experimental developments and progress, hope is created of much research on the graphyne properties, comprising of the energy gap, lithium storage ability, and also on the material charge ability and the structural features. Graphene nanoribbons can easily be found by cutting a piece of graphene ribbon. Monolayer graphyne contains different electronic and optical properties from those of the graphene nanoribbon. Hence, discovering, the possible features of GYNRs would be a topic of mysterious nature to the scientists.

In this research, I used ab initio process of calculation together with the bond-order-length-strength (BOLS) replication to explain the electronic and different optical operationally of armchair and zigzag. It also try to achieve real comprehension knowledge into the bonding characters, such as the length and the energy. Besides the conventional method, it approves that the degree of  GYNRs energy gap varies with the tunable portion of the undercoordunation edge, of particles in the edge which goes up to around three atomic levels in depth. Furthermore, the result from the analysis also produced quantifiable information approximately to the length of the bond. More so, the bond length, strength, and the feature pointed, and even their depending nature to each other. This extent, therefore, proves the scientific theoretical expectations and also offers guidelines of nanoscale tools and for different device designs.



Materials and Methods

The arrangement and electronic properties of the graphene nanoribbons (GYNRs)with armchair-edge (AGYNRs) together with zigzag (ZGYNRs)edge, was determined using the ab initio which involves coupled with bond -order -length -strength (BOLS) approximation (Liu, Sun, and Huang, 2018).

 The simulation described the electronic and optical functionality of armchair, zigzag, and the ((α, β). Additionally, it also gave the length and the strength in the bonding development.   

The size-effect energy gap or the band gap extension of GYNRs was discovered using the BOLS estimation and showed that the size trend is organized by an inadequate number of the edge atoms, while on the other hand, the bonds in the core keep their feature.

The formulation was formed in deliberation of the bond among the molecules and the three outer layer of the atom following the close association of the crystal budding and the energy gad relationship of the particles of the Nanosolid, which comprised of all of the edge atoms undergoing perturbation.

The following formula was expressed for the determination of the crystal potential and band energy gap.


The calculation method was employed for overall gradient estimation and was expressed by the Perdew Bark-Emzerh practical, and involved within the Vienna initio stimulus sets.

Armchair and zigzag-edged nanoribbons were obtained by cutting a fine graphyne alongside two significant directions.

An ab initio calculation of the geometric arrangement was used to help to understand the charges that were introduced on the entrapment of the uncordationated atoms of the GYNRs.

The energy gap of the size dependence gap of the GYNRs was achieved through using the following equation (Deng, Zhang, Sun, and Wu, 2017).

Eg=Eg0+Eg0Nj3Cj (C−MJ−1)




















Results and Discussion

For the verification of the BOLS expectation showing that the edge-undercoordinated particles prompted the dependency size in the energy gap of the GYNRS, the inadequate energy gap strength of the numerous GYNRs that comprise of  diverse sizes over the ab initio computation Was obtained. The computation method, together with the universal gradient estimation method, was used to determine the Perdew-Barke-Enzerh aspect of function (Kang, Wang, Xia, and, 2017). This was mainly involved in the Vienna Ab that contain the initio simulation and the packet. The emerged converged was 1.0 × 10−6 eV/atom, because the particle was entirely in a relaxed state. Thus making the pulls from each atom combine in lesser 0.02 eV/Å, vectors and the atomic position were optimized with 1 × 9 × 1 Monkhorst-Pack k-me and the energy was reduced of 450 eV produced lattice persistent of 6.92 Å and 6.97 Å for (α, β)-graphyne, hence creating void layer, to evade the intermingling of the z-direction that helped to prevent the layers in the line to interact.

In order to attain the nanoribbon layers, the two dimensional arrangement structure of the (α, β)-graphyne were adjusted on by picking lattice constant ranging from6.92 and 6.97 A, in the same direction. Infinite pieces of the graphyne were cut in into two pieces, which was indicated as vertical and the horizontal, both the armchair and the zigzag graphyne were achieved. Two major structure arrangement was taken into consideration that was, GYNRs and the armchair edged of the graphene nanoribbons that contained an armchair edged shape. Below are the figures illustrating the above application of the GYNs and the armchair? The figure displays both the zigzag edged graphyne and contain the edges in the zigzag shape. The hydrogen atoms hold the bond together at the edges. The arrangement of the structures and the quenching edge positions frequently are located on the with the energy gap.

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The figure of the structure of structures of GYNRs

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Figure 1

The figure 1 above, (Liu, Sun, and Huang, 2018), shows the structure of structures zigzag-edged graphyne

The comfy chair and the zigzag edged nanoribbons were acquired through cutting across the graphene sheet along two main directions, that was upright and in the parallel direction. In figure (ac) the armchair nanoribbons are displayed with the width N=1 and 6 in the same order, in which N represents the quantity of the chains of the carbon rings. In figure (b, d), the zigzag nanoribbons edged graphyne are exposed with width in the central of N =1, and 6.and carbon and hydrogen atoms hold the atom together.



Banda structure of (α, β) Graphyne

The calculated electronic-band structures of the monolayer (α, β)-graphyne displayed in the figure below. An external file that holds a picture, illustration, etc.  Object name is nanomaterials-08-00092-g003.jpg

Figure 2

The figure (a) the α-graphyne and (b) β-graphyne displays (Liu, Sun, and Huang, 2018),

 The PBE operational, functional method, α-graphyne is considered to a semiconductor with a small direct energy gap of 0.51 eV as displayed in figure (a). The lower conduction band and the highest variance conduction of the α-graphyne are based at the M point.  The similar band structure was obtained in the experimental research results. The energy gap is recognized to be e 0.52 eV, which indicate regularity with the GGA-PBA scheming (Liu, Sun, and Huang, 2018). Also, the same calculation is carried out on the β-graphyne, as shown in table (b) above. The valence and the transmission together with the band converge at the Dirac location .which are situated at the N location point in the Brillouin zone (Costa, Teeter, Enders, and Sinitskii, 2018). Therefore, the β-graphyne holds various electronic features in comparison to the α-graphyne sheet that contains a direct energy gap of 0.51 eV. Furthermore, the (α, β)-graphyne electric density match the wrong energy structure in a perfect manner. More so, the grounding of the GYNRs is facilitated by the good foundation of the graphyne structure


Band Structures of (α, β)-GYNRs

For successful use of the GYNRs to the devices, that produce photovoltaic features. The energy gap is a significant critical element which straight, defines the light-absorption and productivity and the success of the power conversion (Jarolimek at el, 2018). The marcher and zigzag electronic arrangement structures are displayed in the figures below.

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 Figure 3

Band structure of armchair-edged α-graphyne nanoribbons (Liu, Sun, and Huang, 2018), with (a) N = 3 to 6, and zigzag-edged α-graphyne nanoribbons with (b) N = 3 to 6. F=0


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Figure 4

Band structure of armchair-edged β-graphyne nanoribbons with (a) N = 3 to 6, and zigzag-edged β-graphyne nanoribbons with (b) N = 3 to 5      (Liu, Sun, and Huang, 2018) The F=0

In figure 4 and 5 correspondingly above, the marcher and zigzag electronic arrangement structures are displayed as they have given out by the ab initio computed .The layers of the band of the graphyne ribbons name N=3 to 5, where N represents the number of the carbon chains in the circle, this was used to display the research computed outcomes. Additionally, the band energy significantly rises because of the undercoodirnated edged atom (Ai, at el, 2018). In the computation, once N=3, the lousy energy gap of the armchair and cross-section edged α-GYNRs becomes 1.01 and 1.24 e eV correspondingly, the band energy gap, of the β-GYNRs armchair ((N = 3) is 0.44 eV correspondingly. Nevertheless, the zigzag edged β-GYNRs rest at zero, because of the under coordination atom dearth enough vigor to force β-graphyne to widen the gap up (Marangoni, at el, 2015). Band gap is located on all form of the (α, β)-GYNRs, which are more significant in contraction of the monolayer of the (α, β)-graphyne which contain a low figure of 0.51 and 0.00 eV in the same order correspondingly, because the edged uncoordinated particles have a shorten and well stiffen and reliable bonds in chemical form of (α, β)-GYNRs.

Additionally the movement of the carrier of the graphyne materials which are nanoribbons state was computed .while the internal movement of the α-graphyne carrier at usual house hotness was at 5.41 × 105 and 4.29 × 105 cm2·V−1·sthe holes and the electronic particles ,(Zheng, Huang, and Wang, 2017), showed that, electronics movement of α-graphyne at average house temperature can go up the order of 2.08 × 104 cm2·V−1·s−1, and  also confirmed that the armchair and the graphyne edged ribbons that are in Nano state and are more satisfactory equated to the zigzag-edged ones for the transportation of the electronics atoms. For instance, graphyne and graphdiyne contain the equal structures, because all of them are members of the same family, which is graphyne family. Therefore, an assumption was made that, AαGYNRs is also more suitable matched to the ZαGYNRs for electron transportation purposes (Yun, Lee, and Kim, 2016). Finally, noted that the energy gap emergence of the zigzag-edged β-GYNR as an energy gap ascertained that edge undercoordinated particles open the energy gap (α, β)-GYNRs.

Edge atomic charge entrapment

To be able to appreciative the prompted charge entrapment of the abnormal occurrence, but on the other hand the BOLS projected and the ab initio computed under coordinated particles of the mutual GYNRs, ab initio was more desired for computation of the geometrical layers and attain the outline of the Mulliken charge, alongside with the (α, β)-GYNRs macro ribbons width direction. As illustrated in figure 5 below (Liu, Sun, and Huang, 2018) suggested that, the entrapment of the uncoordinated atoms of the GYNRs, ab are more favorable compared to geometrical structure of the mulliken charge.

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Figure 6

The charge entrapment of graphyne nanoribbons (GYNRs) with (a) armchair- and zigzag-edged α-GYNRs; (b) armchair and zigzag-edged β-GYNRs.

In the research, the position of carbon molecule was well-defined alongside the GYNRs, the outer layer of the carbon molecule denoted C1. Therefore, the Mulliken charge is transmitted in a symmetric on each other center alongside the width way. Additionally, the Mulliken charge scattering at diverse atomic regions in the GYNRs is the like to those of the prompted normal strain at the edge of the dismissing up to exactly three nuclear strata. This occurrence confirms that, mulliken –charge dispersion of the atomic edge results to entrapment situation .The edged-undercoordinated atom results to change in the entrapment, which is forecast by the steadiness amongst BOLS predicted curves and the ab ambition computed data.

Size dependence of the band gad

The size reliance of the energy gap of the GYNRs was computed by the equation below (Liu, Sun, and Huang, 2018).

Eg=Eg0+Eg0Nj3Cj (C−MJ−1)

The equation above illustrations that the bad energy gap is a primary function of the series of the graphyne circles (N).Though, in the equation above, the bond feature shows m is not easily adjustable for an exact structure to join with the bond length and the strong strength. Also, the bond appearance shows (α, β)-GYNRs are computed as mα = 5.66 and the other mβ = 7.33. Centered on these adjusted m value, then a curve of BOLS is plotted and compeered with that of the ab initio based energy gap (Li, at el. 2018). Suitable parameters were obtained of bandgap energy(Eg0) and the achieved (Eg0 ) number values for both armchair and zigzag edged were combine to produce  0.31, 0.31, and 0.04 these numbers were near to the close band emery gap (α, β) of the graphyne. More so the refinement of both Eg0    and m was obtained by corresponding the ab initio and computed to the whole GYNRswith a series

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     Figure 6     

Comparison of the computed size effect in GYNRs between ab initio and BOLS with (a) armchair- and (b) zigzag-edged α-GYNRs, as well as (c) armchair-edged β-GYNRs (Liu, Sun, and Huang, 2018).

The figure (6) above shows the comparison between the ab initio computed and the method of the BOLS forecast outcome for the size and the dependency of the lousy energy gap (Seni and Karamitaheri, 2019). When both the α-GYNRs and the β-GYNR establish a similar number of C-C circle, the band energy gap of the α-GYNRs become primarily massive compared to the β-GYNRs as displayed in table six above.



Li, L., Bai, H., Li, Y. and Huang, Y., 2019. The electronic properties and magnetic states of edge-modified γ-graphdiyne nanoribbons. Computational Materials Science, 163, pp.82-90.

Deng, X.Q., Zhang, Z.H., Sun, L. and Wu, L.J., 2017. Modulation of the magnetic properties in zigzag-edge graphene nanoribbons by connection sites. Organic Electronics, 41, pp.376-383.

Kang, D., Wang, B., Xia, C. and Li, H., 2017. Perfect Spin Filter in a Tailored Zigzag Graphene Nanoribbon. Nanoscale research letters, 12(1), p.357.

Costa, P.S., Teeter, J.D., Enders, A. and Sinitskii, A., 2018. Chevron-based graphene nanoribbon heterojunctions: Localized effects of lateral extension and structural defects on electronic properties. Carbon, 134, pp.310-315.

Cloke, R.R., Marangoni, T., Nguyen, G.D., Joshi, T., Rizzo, D.J., Bronner, C., Cao, T., Louie, S.G., Crommie, M.F. and Fischer, F.R., 2015. Site-specific substitutional boron doping of semiconducting armchair graphene nanoribbons. Journal of the American Chemical Society, 137(28), pp.8872-8875.

Zheng, M., Huang, C. and Wang, G., 2017. Edge magnetism modulation of graphene nanoribbons via planar tetrahedral coordinated atoms embedding. Journal of Materials Science, 52(20), pp.12307-12313.

Yun, J., Lee, G. and Kim, K.S., 2016. Electron transport in graphene nanoribbon field-effect transistor under bias and gate voltages: isocheimal potential approach. The journal of physical chemistry letters, 7(13), pp.2478-2482.

Ai, Q., Jarolimek, K., Mazza, S., Anthony, J.E. and Risko, C., 2018. Delimited polyacenes: edge topology as a tool to modulate carbon nanoribbon structure, conjugation, and mobility. Chemistry of Materials, 30(3), pp.947-957.

Li, J.H., Guo, Y.D., Yan, X.H., Zeng, H.L., Song, X.C. and Mou, X.Y., 2018. Geometric symmetry modulated spin polarization of electron transport in graphene-like zigzag FeB 2 nanoribbons. The European Physical Journal B, 91(7), p.154.

Seni, H. and Karamitaheri, H., 2019. Thermal Conductance Engineering by Structural Modification of Width Modulated Graphene Nanoribbons. Journal of Nanoelectronics and Optoelectronics, 14(2), pp.204-210.