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C: Physical Processes in Nanomaterials and Nanostructures

The Role of Chemical Doping on Large Deformation Behavior of Spiral Carbon-Based Nanostructures: Unraveling Geometry-Dependent Chemical Doping Effects Ali Sharifian, Vahid Fadaei Naeini, Majid Baniassadi, Jianyang Wu, and Mostafa Baghani J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b04894 • Publication Date (Web): 17 Jul 2019 Downloaded from pubs.acs.org on July 17, 2019

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The Journal of Physical Chemistry

The Role of Chemical Doping on Large Deformation Behavior of Spiral Carbon-Based Nanostructures: Unraveling Geometry-Dependent Chemical Doping Effects Ali Sharifian,1 Vahid Fadaei Naeini,1 Majid Baniassadi,1,2 Jianyang Wu,3,4 and Mostafa Baghani, 1,* 1 School

of Mechanical Engineering College of Engineering University of Tehran, P.O. Box 11155-4563, Tehran, Iran 2 University

3

of Strasbourg ICube/CNRS, 2 Rue Boussingault, 6700 Strasbourg France

Department of Physics, Jiujiang Research Institute and Research Institute for Biomimetics and Soft

Matter, Fujian Provincial Key Laboratory for Soft Functional Materials Research, Xiamen University, Xiamen 361005, P. R. China 4

NTNU Nanomechanical Lab, Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), Trondheim 7491, Norway

Abstract The ever-increasing need for miniaturization of electromechanical devices has led us to exploit the properties of nanomaterials as well as controlling them. Chemical doping is one of the most commonly used techniques for controlling the properties of nanomaterials. Spiral carbon-based nanostructures possess fantastic electrical properties, which are highly improved with chemical doping; however, the effect of chemical doping on their mechanical properties is still unknown. In this study, molecular dynamics simulation is conducted to study the effect of randomly/patterned boron and nitrogen doping in different percentages on the mechanical properties of spiral carbon-based nanostructures. The results show a significant impact of the geometry on the mechanical response of doped spiral nanostructures. Furthermore, increasing the percentage of the chemical doping influences the mechanical behavior of these nanoparticles so that can reduce their extensive stretchability even up to 50%. Chemical doping at the position of the pentagon/heptagon defects of nanostructures -in addition to electrical properties- has led to interesting mechanical behavior. Thus, using the combination of a couple of effects such as chemical doping and changing the *

Corresponding author at: Mech, Eng. Dept. College of Engineering, University of Tehran, Iran. Tel: +98 21 8802 4035; fax: +98 21 8801 3029. Email: [email protected]

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geometry of the spiral carbon-based nanostructures, opens a new avenue to control the properties of these nanostructures in proportion to their electromechanical applications.

1. Introduction Currently, a remarkable number of research studies are carried out in the field of nanotechnology, especially nanomaterials, in order to understand their properties and functions. Consequently, carbon nanomaterials such as graphene1 and carbon nanotubes (CNT)2 with regard to their electrical3-5, chemical6, thermal7, and mechanical8 properties have attracted great deal attention in researchers. Applications of these features have been revealed in various technical fields, including electromechanical fields9-11, nano-resonators12, diagnosis devices13 and spintronic devices14. It is worthwhile to mention that these nanomaterials, with promising properties, e.g., remarkable thermal conductivity and tensile strength as well as high spring constant, are classified as the efficient elements of micronano-electrochemical devices15, nanomotors16-17 , artificial muscles18 and etc.. Moreover, as a common application, they play a pivotal role as reinforcing agents in nanocomposites to improve thermal and mechanical properties19-20 as well as hydrogen storage21. Based on the desired features of carbon nanomaterials, novel spiral structures were produced gradually in an inspired fashion by nature, such as coiled carbon nanotubes (CCNT) and graphene helicoids (GH). These nanostructures are investigated both experimentally22 and theoretically. In one of the first studies, the spiral carbon-based structures were proposed theoretically by Ihara et al.23. Furthermore, theoretical studies have been performed to measure mechanical and thermal24-33 as well as electrical properties34-35. Liu et al.36 comprehensively studied the mechanical properties of CCNTs by quantum approaches. They obtained Young's modulus for the various diameters of CCNTs in the range of 3 to 6 GPa. Wu et al.29-31 examined the stretchability of CCNTs with different diameters and lengths using molecular dynamics simulation and illustrated that the applied strain for some of the structures can be raised up to 10 times of their original length. They also investigated the mechanical behavior of CCNTs at different temperatures and elucidated that mechanical properties are affected by temperature. In another study carried out by Sharifian et al.28, 33, the dependency of mechanical properties and distinct stages of tensile test on the geometry of CCNTs was studied. They found that different geometry characteristics led to different tensile behaviour. Zhan et al.26 studied the mechanical properties of GHs through molecular dynamics simulation and clarified that these nanomaterials have a high elastic modulus, as well as distinctive stretchability (even more than 20 times their initial length), which is due to 2 ACS Paragon Plus Environment

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van der Waals (vdW) interaction between the layers. In another study25, they have also addressed the nonlinear behavior of these nanomaterials. In order to control mechanical, chemical, and electrical properties, special methods such as geometrical alteration, functionalization of nanostructures, and chemical doping are employed. Chemical doping means insertion of different atoms into material structure, which is one of the most effective approaches to manipulate the physical properties of the material37. For carbon-based nanomaterials, the doping procedure is usually performed by boron and nitrogen atoms, because of their similar atomic properties with carbon atoms such as strong valence bonds and atomic size38. In recent years, chemical doping of graphene and CNT has been carried out by experimental approaches39 in order to achieve various applications such as fuel cells40, energy storage systems41, and biosensors42. Considering some of the complicated aspects of experimental studies, atomic and quantum simulations have been employed to evaluate and characterize the physical properties of nanostructures4344.

Chemical doping of toroidal carbon nanotubes (TCNTs) has led to creating novel electrical45 and magnetic46 features. Recently, chemical doping of nitrogen and boron for CCNTs has been performed by experimental methods47-49. As a result of the considerable electrical properties of pristine CCNTs and constructive effects of chemical doping on it, the atomicscale studies in this research field have made significant progress36. Like the other common applications of chemical doping in spiral structures, one may mention the applications in fuel cells50-51, superconductors, photoluminescence49,

52-53

and photocatalyst as well as

nanocomposites54. Despite the various applications of chemical doping and significant studies in manipulating electrical, chemical and magnetic properties of doped spiral carbon-based nanomaterials, to the best knowledge of the authors, there is no study available in the literature to identify their mechanical properties. In this study, mechanical properties such as tensile strength, ultimate failure strain, different stages during the tensile test as well as toughness for various ranges of geometries and chemical doping percentage for spiral carbon-based nanostructures have been identified using molecular dynamics simulation.



2. Atomistic Modelling and Simulation Methods The spiral carbon-based nanostructures in this study are based on the modelling scheme suggested by Chuang et al55-57. According to this framework, a TCNT is firstly created by cutting a graphene plate, and then twisting and rotating it. In this research, all structures are constructed based on the Chuang model and have the pentagon and heptagon defects due to the cutting and folding conditions, and finally, a TCNT with hexagonal structure is constructed. The structure of TCNT has four main parameters (s, n75, n77, n55), in which “s” and “n75” represent the number of strips between the heptagon, and heptagon-pentagon defects, respectively. As illustrated in Figure 1, “n77”, and “n55” indicate half of the number of strips between the heptagon defects, and pentagon defects, respectively. Afterward, the distorted TCNT is cut in a particular direction to create a spiral shape (see Supporting information S12 for more details).

Figure 1. (2,1,2,1) TCNT which the produce structure of the corresponded (2,1,2,1) CCNT.

All simulations have been carried out by LAMMPS molecular dynamics package (Released of 16 May 2018), and visualization procedure was performed using VMD software58. In order to determine the interactions between carbon atoms, the adaptive intermolecular reactive empirical bond order (AIREBO) potential has been employed59, which is capable of determining the process of forming and breaking of the C-C bonds. In this study, the cut-off distance for the REBO potential is set to be 2 Å60, and in order to calculate the non-bonded interactions, the Lenard-Jones part of AIREBO potential with 10.2 Å cut-off radius is applied28-30. Moreover, the TERSOFF potential is utilized to compute the interaction between nitrogen and boron atoms, as well as their interactions with carbon atoms, which is able to predict the mechanical and thermal properties of carbon, nitrogen and boron nanostructure6162.

All structures are composed of four coils28-31 and in order to avoid the edge effects,

periodic boundary condition is assumed along the helix axis. Furthermore, to prevent the thermal effects, simulations have been carried out at temperature of 1 K26, 28-31. At the first 4 ACS Paragon Plus Environment

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stage, the energy of structures is minimized by the conjugate gradient method. Afterward, each CCNT structure is relaxed for 200 to 600 ps, depending on the structure, under the isothermal-isobaric (NPT) ensemble by Nosé–Hoover thermostat and barostat. Throughout the tensile process with the appropriate strain rate28-32 of 108 s-1, the NVT ensemble is employed with the Nosé–Hoover thermostat and the time step was set to 1 fs. To calculate the force-displacement diagram, the instantaneous force level is measured based on virial expression from the relation proposed by Thompson63. Time integration of equations of motion is undertaken using the velocity Verlet algorithm. More information is available on supporting information S10.

3. Results and Discussion In this section, the tensile behavior of spiral carbon-based nanostructures in different geometric structures has been investigated considering the chemical doping of boron and nitrogen. Accordingly, eight models of spiral structures with completely separate geometrical features have been prepared and categorized according to Table 1. The mentioned structures have been specified so that disparate types of spiral structures, such as circular and oval cross-section structures in different sizes of semi-major and semi-minor, GH, and doublewalled CCNT as well as double-helix CCNT to provide a comprehensive physical insight of the chemical doping procedure. These distinct geometrical characteristics have resulted in the different function of the pristine and chemically-doped spiral structures. Figure 2 demonstrates the atomic models of the structures listed in Table 1 with 1% B-doped, in which the colors indicate the potential energy. As illustrated in Figure 2, in addition to the fact that the pentagon and heptagon defects make alterations in potential energy, the doping of boron plays the same role. For instance, in the case of (2,1,7,1) CCNT, which is shown in Figure 2, the randomly doping of boron is located in the outer pentagon defect of the second coil and has changed the potential energy level remarkably. In addition, the doping procedure in (4,4,1,4) CCNT structure has also caused defects in the structure. At this stage, the investigation of chemical doping behavior in spiral structures has been carried out by two approaches. Firstly, the chemical doping was performed randomly for all samples at 1% to 6%. In order to further investigations, the doping percentage has increased by up to 20% for some models. In the second approach, the chemical doping is carried out in the specific sections within the pentagon/heptagon defects.



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Table 1. Geometrical properties of the investigated structures

Structural Parameters (s,n77,n75,n55)

(2,1,2,1) (3,2,3,2) (5,3,4,3) (2,1,7,1) (4,4,1,4) (6,1,2,1)-(5,3,4,3) double-walled CCNT (2,0,4,0) GH (2,1,2,1)-(2,1,2,1) double helix (4,1,2,1)

Number of Atoms

Pitch (Å)

Semimajor (Å)

Semiminor (Å)

Effective radius (Å)

Inner diameter (Å)

Outer diameter (Å)

initial length (Å)

1152 3024 6720 4752 3888

8.8 12.2 15.6 7.6 20.52

2.75 6 5.05 9.185 1.85

2.65 5.05 6.7 2.85 8.35

7.1875 10.6041 16.1867 14.3686 9.88625

9.8 13.4 18.9 8.9 15.8

19.7 28.8 43.4 43.4 22.6

34.97669 51.7157 70.53959 37.08874 83.20023

7056

17.1

5.9

6.43

16.2118

19.96

37.42

53.80339

1536

3.5

3.185

0

9.5611

10.1

26.8

27.91558

2304

17.3

2.75

2.65

11.4841

18.1

32.2

64.6535

1920

13.1

2.65

2.8

11.5335

17.57

28.34

35.14853

Figure 2. The side and top view of the spiral structures with randomly 1% B-doped. Color of atoms indicate the potential energy.

3.1. Spiral Structures with Random Chemical Doping As already stated, in order to explore the influence of chemical doping on tensile behavior of spiral structures, chemical doping of boron and nitrogen atoms was investigated in 1% and 6% of doping percent. Figure 3 shows the force-displacement profiles for the mentioned structures. Also, the effect of randomly doping distribution has been investigated. In general, it can be concluded that changing the chemical doping distribution of nanostructures does not affect their overall behavior in 1% randomly chemical doping percentage. However, for nanostructures with smaller internal radii, the chemical doping distribution can be slightly effective in the fracture strain of the final stage. More information is available on supporting 6 ACS Paragon Plus Environment

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information S11. In order to give the desirable insight of the displacement, this parameter is divided by the initial length (strain) to obtain a dimensionless criterion, and in accordance with Table 1, the original displacement can be achieved directly. Regarding the analysis of the diagrams, it can be inferred that not only the geometrical features of different structures cause completely distinct behaviors, but also chemical doping in each structure has led to different mechanical responses. Correspondingly, the chemical doping of nitrogen and boron result in a distinctive performance in structures. First and foremost, the effects of chemical doping of boron and nitrogen on the overall behavior of the first three samples with circular cross-sections are studied. In case of (2,1,2,1), (3,2,3,2), and (5,3,4,3) CCNTs the diameter of the circular cross-section increases respectively, in which the inner radius of (3,2,3,2) CCNT does not change significantly compared to the first one, but in the (5,3,4,3) CCNT the inner radius is much larger than the first one. Mechanical behavior of the models consists of four stages. In the first stage, vdW interactions are the main determinant of the structural deformations of the models, which occur for the models in strain levels less than 0.1. Afterward, the structures undergo buckling procedure, which lasts for up to 1.32 of strain level for (2,1,2,1) CCNT. However, in the case of (3,2,3,2) CCNT, the mentioned procedure continues up to 0.5 of strain level and then the next level of deformation starts. Increasing the diameter of the CCNT can be assigned as the main reason for strain reduction during this stage, in which the circular cross-section of the CCNT changes to oval to accommodate with the higher levels of strain throughout the stretching procedure. Besides, in this structure, the internal force is still very high due to the fact that the internal radius has not changed remarkably. Collectively, these factors led to a reduction in strain range in this stage. For (5,3,4,3) CCNT, the strain range of this stage was observed to be about 1. Similar to the reasons mentioned for (3,2,3,2) CCNT, the simultaneous effect of the distinct rise in the internal radius along with the increase in diameter led to lower strain range for this stage than the first model and a greater than the second one. In the third stage, twisting and kinking mechanism in the structure was observed. Considering the mentioned reasons given in the previous section, the strain range in this stage is justified, which remains for the analyzed models up to 3.1, 1.3, and 2.4 of strain respectively. In the last stage, bonds are severely broken and according to the structural features, the structures are distorted to the extent that they can be flattened and eventually torn. For instance, the stretching process in (2,1,2,1) CCNT extends to the strain of 4.5 and the structure is substantially flattened. Despite the increase in diameter, which results from 7 ACS Paragon Plus Environment


the deformation of the circular cross-section to the oval during tensile test in case of (3,2,3,2) CCNT, tensile procedure continues to up to a lower strain level (approximately 4.1) due to some of the mentioned mechanisms, including the buckling, the nanostructure has been damaged and more quickly torn. The same process was observed for (5,3,4,3) CCNT, and as demonstrated in Figure S1, the structure, which is less flattened than the two previous models, is ruptured at 3.8 of strain. To gain more comprehensive physical perception, structural conformations of the referred models are illustrated in Figure S2. By scrutinizing the models in order of increasing their diameter, the ultimate tensile strength for the structures is evaluated as 12.5, 13, and 17 nN, respectively. It was perceived that in the case of 1% B-doped (2,1,2,1) CCNT there is a first two-stage as pristine structure. In the third stage, at the same time as the twisting and buckling, the severe breaking of bonds has been observed; indicating the effects of chemical doping, and then the process continues to rupture. Furthermore, placement of several boron atoms by chemical doping in the pentagon/heptagon defect (mainly the heptagon defects) results in the regular structure of the pristine model no longer exist, and some of the covalent bonds do not form. However, it is worth mentioning that the ultimate strain has risen slightly. In addition to some of the geometrical characteristics provoking stress concentration in different domains of the nanostructure, chemical doping also make the bonds break in a faster manner. Relying on the combined effects of geometrical properties and the percentage of chemical doping, distinct behaviors can be identified. With respect to Figure 4, it is deduced that the faster breaking of the covalent bonds in different domains of the nanostructure, rather than the breaking bonds only at zones with stress concentration, resulting in the further opening of the CCNT rings. This ultimately leads to a flattened structure and an increase in the final strain. In case of 6% B-doped (2,1,2,1) CCNT, it was identified that the first stage occurs the same as in previous cases, but breakage of the covalent bonds along with buckling and twisting occurs in the middle of the second stage and is observed until the ultimate point. Unlike in the previous stage, as a consequence of an increase in the chemical doping, breaking the covalent bonds occur in a swift fashion resulting in the severely tearing of the damaged sections and the final failure of the nanostructure. As a result, the ultimate strain decreases. It is easily perceived that after a threshold of chemical doping, the structure will fail in the lower strain levels than the original structure. Moreover, this threshold depends on the geometrical properties of the nanostructure to reduce the final strain. The same behavior can be observed by examining nitrogen doping for (2,1,2,1) CCNT structure. 8 ACS Paragon Plus Environment

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Figure 3. Force-displacement profiles for spiral structures in Table 1: a) Force-displacement profiles for Bdoped structures, b) Force-displacement profiles for N-doped structures. “Dimensionless displacement” represents that displacement is divided by the initial length of each CCNT.



Figure 4. Atomistic configurations during the tensile procedure according to the mentioned stages for: a)(2,1,2,1), b)(3,2,3,2), and c)(2,1,7,1) B-doped spiral structures of 1% and 6%. Color of atoms indicate the stress in the tensile direction.

For this nanostructure with a small inner radius, the ultimate tensile strength was evaluated to be 11.5 and 9 nN for 1% and 6% B-doped respectively. The ultimate strength for 1% and 6% 10 ACS Paragon Plus Environment

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N-doped nanostructures was indicated as 10.5 and 10.3 nN. A distinct behavior was identified by examining the effects of chemical doping in (3,2,3,2) CCNT. As illustrated in Figure 4, a four-stage tensile behavior can be detected at 1% Bdoped case. Only the fourth stage, which is associated with the breaking of the bonds, began in a bit less strain level, and the model was failed in a lower strain. In pristine nanostructures with a circular cross-section, a significant increase in the diameter of the CCNT accompanied by a relatively low elevation in the inner radius triggered quick breaking of the bonds in the models and this process is accelerated due to the chemical doping. In 6% B-doped, a quicker breakage of the bonds was identified affecting on the other stages. In this case the first stage still takes place same as the other cases. Buckling happens by staring the second stage. In the third stage, rapid breakage of the bonds together with bending and torsion of the nanostructure was detected which continues until the ultimate point. Moreover, as a result of the rapid breakage of the bonds in the stress concentration domains, the nanostructure possesses some folded coils even the ultimate failure comes about. As (2,1,2,1) CCNT, in spite of distinctness in mechanical properties, the nitrogen doping of (3,2,3,2) CCNT exhibits similar overall behavior. The ultimate tensile strength was distinguished to be 15 and 14 nN for 1% and 6% B-doped respectively. The ultimate strength for 1% and 6% N-doped nanostructures was indicated as 13 and 13 nN. By increasing the diameter and the inner radius in (5,3,4,3) CCNT, it can be deduced that similar the two previous models with nitrogen or boron doping, the bond breakage occurs in earlier stages especially in the third stage. In addition, with a 1% boron or nitrogen doping, as described for the first model, the ultimate failure strain increases. In 6% of boron or nitrogen doping, the effectiveness of the doping procedure was discovered, resulting in a reduction of the ultimate strain compared to 1%, but still due to the geometrical features of the nanostructure, the ultimate strain is larger than the one in pristine structure. Eventually, at 10% of the doping procedure, the failure strain was less than the pristine sample. Moreover, by increasing the doping percentage in 1, 6, and 10% B-doped, the ultimate strength was calculated 17, 18, and 20 nN, respectively. While the ultimate strength for N-doped structures at 1 and 6% was evaluated to be 14.5 and 16.5 nN, which is slightly lower than the boron doping. In the other model, the effects of doping procedure on (2,1,7,1) CCNT, which has a higher ratio of semi-major to semi-minor, has been studied. According to Figure 3 and 4, the overall 11 ACS Paragon Plus Environment


behavior of the nanostructure can be classified into 3 stags. The first stage, like previous models, containing domination of the vdW interactions in which, due to the large size of the semi-major, a sharp increase in the force is indicated in the primary stage. In higher strain levels and the beginning of the second stage, a CCNT coil is separated from the other coils and the delamination process begins. In the final stage, the breaking of the covalent bonds occurs as a result of an increase in normal and shear stress along with the delamination procedure. The mentioned procedures continue until completion of delamination and then are terminated by the breakage of the covalent bonds in stress concentration domains resulting in ultimate fracture. For 1% B-doped (2,1,7,1) CCNT, the same stages are observed exactly. The notable distinction corresponds to the third stage in which during the delamination process, the breaking of the bonds, instead of happening at some initial points, continues to occur more uniformly at different points in the nanostructure resulting in a 30% increase in fracture strain. However, a totally different behavior was recognized for 6% B-doped. In this case, a sharp rise in tensile force is observed same as the pristine model, but the breakage of the bonds initiates and spreads rapidly at the beginning of delamination and even before it, and CCNT is torn quickly. In 1% and 6% N-doped nanostructures, an almost identical behavior is recognized. At 6% Ndoped structure, the ultimate strain is slightly higher than the one in B-doped case. In accordance with Figure 4 and S3, it is concluded that for N-doped structures the bonds break down more easily, which results in the rapid progression of tearing not only at one point but also in other domains. This has led to an increase in the final strain of the N-doped model. In this case, the ultimate tensile strength for the pristine structure was calculated to be 21 nN, while the ultimate strength for B-doped structures at 1 and 6% was evaluated to be 14 and 13 nN respectively. For N-doped nanostructures at 1 and 6%, the strength was evaluated to be 13.5 and 17 nN respectively. In order to determine the chemical doping influence on features of the nanoparticles with a high semi-minor to semi-major ratio, which so-called helical arrays, (4,4,1,4) CCNT has been investigated. With regard to Figure 4 and S4, it can be inferred that there are three general stages for the tensile behavior of this nanostructure. At first, an initial rise was discerned in tensile force, resulting from releasing a coil from attractive interaction with the other layer. Afterward, the structure began to be delaminated. Nevertheless, due to the structural features, 12 ACS Paragon Plus Environment

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torsion plays a pivotal role in the tensile behavior of the CCNT. In this stage, even breaking of the covalent bonds is occurred, and as it approaches the ultimate point the CCNT is almost flattened. In fact, the CCNT experiences approximately the same initial shape in a smaller inner radius, consequently, the breakage of the bonds becomes more severe. It was perceived that the same stages are repeated exactly in case of boron or nitrogen doping in 1% and 6%wt. Although as previously mentioned, more complicated aspects of tensile behavior can be identified caused by some defects in the structure. On the one hand, the defects cause the nanostructure to reach the fracture point swiftly, and on the other hand, sometimes there are bonds between the defective domains with the upper layer. But it is collectively concluded that, as in the previous examples, the CCNT breaks more quickly in higher doping percentages. The ultimate tensile strength for the pristine structure is about 23 nN, while the ultimate strength for B-doped structures at 1 and 6% was indicated to be 15 and 12 nN respectively. In the case of N-doped nanostructures at 1 and 6% the ultimate strength was obtained 17 and 17 nN respectively. The tensile procedure in double-walled CCNTs consists of three main stages. In the first stage a sharp rise in tensile force, due to the vdW forces, is detected, and in the second stage the structure buckles. Finally, in the last stage, the covalent bonds start breaking. The same stages are also observed in B-doped models as illustrated in Figure 3 and 5. It is noteworthy that chemical doping up to 10% results in an increase in ultimate strain by tearing the different sections of the nanostructure. Nonetheless, in case of 20% doping, a limited reduction of the second stage strain (up to about half) is detected and the final stage starts in a rapid manner, in which finally the doping rate lead to quick fracture of the model. The ultimate tensile strength for the pristine structure is indicated as 15 nN, while the ultimate strength for B-doped structures at 1, 6, 10, and 20% was calculated to be 21, 21, 22, and 28.5 nN respectively. For N-doped nanostructures at 1 and 6%, the strength was evaluated to be 17 and 20 nN respectively. Atomic configuration of the models during tensile stages along with the ultimate strain for each stage is presented in Figure 5 and S5. The influence of chemical doping on another spiral structure obtained by adjusting the semiminor parameter to zero due to form so-called GH is also investigated. The tensile behavior of the main structure comprises four main stages and the first stage is definitely similar to double-walled CCNT. Subsequently, by increasing tensile strain and release a layer, delamination comes about, and due to the delamination procedure, a sharp reduction in tensile force is expected. In the next stage and by unfolding procedure, the structure begins to 13 ACS Paragon Plus Environment


be flattened out and the tensile forces increase intensely, especially in the domains adjacent to the center. In the final stage, the structure is stretched up to the ultimate limit and the bonds begin breaking. As depicted in Figure 5, several carbon monatomic chain are identified in the final conformation.

Figure 5. Atomistic configurations during the tensile procedure according to the mentioned stages for: a) double-walled CCNT, b) (2,0,4,0) CCNT, c) (2,1,2,1) double helix. The left and right panels represent the


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pristine and 1% B-doped structures respectively. (In panel a, red and blue represent the inner and outer CCNT atoms respectively. In b and c, color of atoms indicate the stress in the tensile direction).

By nitrogen or boron doping at higher percentages, it was identified that some covalent bonds were formed between atoms in adjacent layers which leads to a faster finish of the delamination process. Besides, the third stage begins at lower strain levels. Before forming much more carbon monatomic chains, the ultimate fracture happens as a consequence of chemical doping. The ultimate tensile strength for N-doped structures at 1% is obtained about 6.5 nN, while the strength for other percentage of chemical doping is indicated to be 8 nN. In the last structure investigated, the tensile behavior of (2,1,2,1) double helix is explored. Having regard to Figure 3 and 5, there are three major stages for tensile behavior of the pristine structure. After completion of the first stage, which is affected by the vdW interactions, the layers are bifurcated. After the separation, the tension in the inner portion is greatly increased. In the next stage, the structure begins to be flattened, and in order to adapt to higher strain levels, some bonds are broken as well. In addition, after tearing a helix, the strain continues as long as the next helix is torn. With chemical doping of boron and nitrogen, it is observed that the stages are repeated without changes, and only the final strain decreases. Since the organic structure was almost completely flat, it could be concluded that the chemical strain decreases the final strain. Also, the observed carbon monatomic chain in the structure are either not formed or ruptured more quickly. 3.2. Spiral Structures with Chemical Doping in Specified Domains In accordance with previous studies, mechanical features of nanostructures can be controlled by chemical doping in particular regions. In addition, it was demonstrated that the insertion of boron in heptagon and nitrogen in pentagon defects can improve the electrical properties of these nanostructures45. In this section, we examine mechanical properties of (4,1,2,1) CCNT resulting from insertion of a boron atom and a nitrogen atom in heptagon and pentagon defects, respectively, compared with pristine and 1% randomly doped structures, as shown in Figure S6. Therefore, the mechanical behavior of the patterned doped nanoparticles is studied in such a way that: 1) a boron atom is placed in each of the heptagonal defects, 2) a nitrogen atom is placed in each of the pentagonal defects; and 3) simultaneously a boron atom and a nitrogen atom are placed in heptagonal and pentagonal defects. It should also be noted that in the patterned chemical 15 ACS Paragon Plus Environment


doping, the number of doped atoms is the same for all structures, equal to the number of defects. Therefore, there is no dependence on the total number of atoms. According to Figure 6, doping of boron or nitrogen in the heptagon and pentagon defects caused a notably high change in potential energy, so that even the presence of nitrogen in the pentagon defects has an intense efficacy on potential energy making the unfavorable state of

energy (due to pentagonal defect) become favorable. There are quadruple stages for tensile behavior of the pristine structure of (4,1,2,1) CCNT with circular cross-sections during Figure 6. Effects of Boron and Nitrogen doping on heptagon and pentagon defects. a) The effect of the doped atoms on the potential energy of the spiral structure. b) Force-displacement diagram of pristine structures, 1% of boron/nitrogen doping and the specific position of boron and nitrogen in defects. “Dimensionless displacement” represents that displacement is divided by the initial length of each CCNT. Color of atoms indicate the potential energy.

stretching deformation, so that in the first stage, as a result of an increase in vdW interactions, the buckling and twisting mechanisms begin. In the next stage, the several domains of the nanostructure are torn to be adapted to the higher strain levels. In the final stage, the covalent bonds are broken strictly and the structure is flattened as much as possible and ultimately breaks. In 1% randomly B/N-doped structure, the final stage, which is affected by chemical doping, comes about by breaking the covalent bonds in diverse sections. Thus, this leads to increase the ultimate strain. At the same time, the other stages take place similar to the pristine CCNT. By doping boron atoms in heptagon defects, these stages are accompanied by some details. As an instance in the second stage, the coils can easily be separated from each other and the structure is not buckled as in the pristine structure or 1% randomly B-doped, which is revealed in Figure 6 by diminishing the tensile force compared to the previous ones. In the 16 ACS Paragon Plus Environment

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next stage, subsequent to complete separation of the coils, the buckling and twisting mechanisms occur the same as previous cases. In the third and fourth stages, doping of the boron atoms in the inner domains, in which the stress concentration effect is evident, has led to a quicker and more uniformed fracture in several domains. Consequently, the ultimate strain of the structure is nearly equal to the ultimate level in 1% randomly B-doped one. The different stages of stretching deformation for the mentioned structures are depicted in multiple panels in Figure S7 and S8. When nitrogen atoms are doped in pentagon defects, despite the remarkable effects on potential energy, the tensile behavior has not been significantly affected. As shown in Figure 6, specifically in defect points, the pristine and patterned N-doped structures are roughly coincided and behave quite similarly. Therefore, doping by nitrogen, despite considerable changes in predicted electrical properties which are mentioned in previous studies; does not alter the mechanical properties expressively. Stretching deformation trajectories illustrated in Figure S7 and S8 also indicates comparable tensile behavior for two mentioned models. By simultaneous patterned doping of boron and nitrogen in the nanostructure, the tensile stages are obtained as pristine structure. Doping by nitrogen and boron atoms did not have a desirable effect on ultimate strain as well. In the second stage, doping by nitrogen and boron atoms makes the separation of the coils easier, which is also elucidated in terms of reduction in the tensile force. The chemical doping further expands the structure and increases the ultimate strain eventually. 3.3. Correlation between Chemical Doping and Toughness The toughness parameter evaluates the absorbed energy so that it deals with the relationship between the force and displacement, taking into account elastic and plastic deformation. Given the valuable information that toughness represents, it can provide an insight into the specific applications of these nanostructures. The toughness is calculated according to:

 Fxdx

(1) m where F, x, and m represent the force, displacement, and mass of the nanostructure ET 

respectively. In Table 2, some typical values of toughness calculated for the models are represented. Taking into account the obtained values, toughness is varied from the lowest value which belongs to 20% N-doped up to the maximum one for the pristine structure of the graphene helicoid. There are also distinctions in toughness values for N-doped and B-doped 17 ACS Paragon Plus Environment


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structures in the same doping percentages. This variety of toughness can lead to the development in the applications of these structures. Table 2. Toughness of the investigated structures

Structural Parameters (2,1,2,1)

(3,2,3,2)

(5,3,4,3)

(2,1,7,1)

(4,4,1,4)

(6,1,2,1)-(5,3,4,3) double-walled CCNT

(2,0,4,0) GH (2,1,2,1)-(2,1,2,1) double helix

(4,1,2,1)

Doping Percent (%)

B-doped Toughness (J/g)

N-doped Toughness (J/g)

0 1 6 0 1 6 0 1 6 10 0 1 6 0 1 6 0 1 6 10 20 0 1 6 0 1 6 0 1 B-doped N-doped Br-N doped

4841.709 5545.575 3115.725 3339.492 2976.353 1558.515 1508.066 2095.123 1892.719 1237.865 2123.556 2763.453 1369.98 2623.458 1994.664 1235.891 1720.456 2291.786 2615.044 2961.396 955.4134 8539.267 7874.187 5139.678 5780.597 5045.42 4949.166 3236.196 4080.124 3723.777 3192.564 3481.425

4841.709 4974.452 4319.688 3339.492 2510.64 2705.541 1508.066 1839.636 1956.354 2123.556 2870.214 1869.966 2623.458 1763.046 1818.736 1720.456 2319.723 2429.761 8539.267 5374.563 4078.415 5780.597 5425.066 4758.999 3236.196 3723.777 3192.564 3481.425


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4. Summary and Concluding Remarks In this research, the effect of boron/nitrogen doping on the spiral carbon-based nanostructures with a variety in geometry such as circular cross-sections (2,1,2,1), (3,2,3,2) and (5,3,4,3) CCNTs, (2,1,7,1) double layer GH, (4,4,1,4) helical arrays, (2,0,4,0) GH, (2,1,2,1) double-helix and (6,1,2,1)-(5,3,4,3) double-walled CCNTs were investigated. The effect of chemical doping on spiral structures was studied by two approaches. Firstly, the chemical doping was performed randomly at 1% to 6% for all samples and even up to 20% for some samples. Different stages of the mechanical response of pristine structures and their boron/nitrogen doped structure were contrasted in detail. Unlike the chemical doping effect on simple structures such as graphene and CNT, each spiral structure exhibited a unique behavior at different stages of mechanical response. Moreover, each nanostructure demonstrated special behavior at a higher percentage of chemical doping. However, the sharp rise in the percentage of chemical doping (above 20%) resulted in the rapid rupture for all samples. The behavior of boron and nitrogen doping for nanostructures was similar, although nitrogen doping had more destructive effect for a simpler spiral structure such as GH which is similar to previous researches on graphene and CNT. In the second approach, patterned chemical doping of spiral nanostructures was performed on pentagon-heptagon defective parts of (2,1,4,1) CCNT. The chemical doping of nitrogen in pentagon defects led to a significant change in potential energy but did not affect the tensile behavior of the nanostructure. While boron doping in heptagon defects led to the easier opening of coils without severe buckling and ultimately increased stretchability. At the synchronous dopes of nitrogen and boron in defective parts of nanostructures, the stages of mechanical response were observed as pristine structure except that the strain was increased for the last stage. Finally, the relationship between the chemical doping effect and toughness was investigated for all samples.

Due to the well-known extensive applications of randomly/patterned

chemical doping, this research can lead to a better understanding of the mechanical response of spiral carbon-based nanostructures and, consequently, their optimal performance in nanodevices.



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ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge in another document. Results, discussions, and additional figures for CCNT structures under tensile loading: Stress Distribution; Atomic configuration: Pristine structures; Atomic configuration: 6% N-doped (2,1,7,1) CCNT; Structural configuration of pristine and 1% B-doped CCNT; Atomic configuration of 10% B-doped double-walled CCNT; Location of the heptagon and pentagon defects in CCNT structures; Uniaxial tensile test: Atomistic conformation of pristine (2,1,2,1) CCNT

and

randomly

1%

B-doped;

Atomistic

conformation

of

B/N-doped

in

heptagon/pentagon defects of (2,1,4,1) CCNT; Tensile behavior of the doped structures: Effects of the Inner Radius; Tensile behavior of the doped structures; Effect of different doping distribution on tensile behavior of (2,1,2,1) CCNT and (4,1,2,1) CCNT; and Describing the parameters (s, n75, n77, n55) of CCNTs. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] NOTES The authors declare no competing financial interest.


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