Adamantane-Derived Carbon Nanothreads: High Structural Stability

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C: Physical Processes in Nanomaterials and Nanostructures

Adamantane-Derived Carbon Nanothreads: High Structural Stability and Mechanical Strength Srinivasan Marutheeswaran, and Eluvathingal D. Jemmis J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12603 • Publication Date (Web): 15 Mar 2018 Downloaded from http://pubs.acs.org on March 16, 2018

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The Journal of Physical Chemistry

Adamantane-Derived Carbon Nanothreads: High Structural Stability and Mechanical Strength S. Marutheeswaran and Eluvathingal D. Jemmis* Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012 We study the stability and mechanical properties of adamantane-derived nanothreads (ANTs) and compare with Benzene-derived nanothreads (BNTs) using density functional theory. The zigzag-catafused ANT has better thermodynamic stability, failure strain, and mechanical strength than that of the BNTs. The presence of six-member ring with chair conformation and the absence of non-bonded hydrogen interactions enhances the stability of zigzag-catafused ANT with desirable mechanical properties. The structural deformation of nanothreads under tensile strain are also studied, to understand its stiffness and stability.

Keywords: Nanothread, Diamondoids, DFT, structural deformation, Mechanical property.

1. Introduction

The sp2 hybridization and electron mobility in carbon nanotubes and graphene render them ideal for electronic devices. Whereas sp3 hybridization and localized bonding of carbon atom in carbon nanothreads are expected to make them stiff material with higher thermal conductivity.1-8 The onedimensional (1-D) carbon nanothreads (CNTs) has attracted immense experimental and theoretical

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interest in recent years.9-12 CNTs derived from benzene and adamantane units inspired the study of several structural possibilities,3,13-17 chemical functionalization,18 and nanofiber applications.19 These studies also led the search for nanothreads of other elements.20 The fusion of benzene molecules could lead to several possible benzene-derived nanothreads (BNTs) depending upon the connectivity patterns.8,16 Among these isomers, hydrogenated (3,0) nanotube (1a) and its Stone-Wales defected NT (1b); and polytwistane NT (1c) in Figure 1 is found to be the most stable ones. The BNTs (1a) and (1b) in Figure 1 have cyclohexane chair like connections between the six-member rings whereas BNT (1c) have twist boat connections. Computational studies predicted that the most stable BNT (1a) have Young’s moduli, strength and bending rigidity to around 850GPa-1160GPa, 26.4 x10-9N and 5.35×10−28Nm2 respectively.2,5,8 Various finite sized molecular rods, similar to BNTs, are synthesized from ethyne, twistane, [n]staffane and various bicyclo compounds.21 While BNTs have an iceane skeleton, it is interesting to probe nanothreads based on adamantane itself. Syntheses of polymantanes from diamondoid molecules are difficult due to the higher strength of σCH ~ 98.5 kcal mol-1 bond compared to σC-C ~ 83.2 kcal mol-1 bond. Recently, two new adamantane-derived nanothreads (ANTs) are successfully synthesized from diamantane-4,9-dicarboxylic acid and bridgehead-halogenated diamantane molecule based on nanotemplate reaction.11,12 Balaban et al. extensively studied diamondoids from adamantane-derived molecules based on connectivity patterns.13,

22-25

Adamantane has two types of carbon atoms; six secondary carbon atoms connected to each other by four tertiary carbon atoms. Thus, the possible connectivity patterns would lead to four major varieties: (i) C-C bond connected- (ii) atom shared- (iii) edge shared- and (iv) face fused- NTs.24,25 Here we have studied these varieties and compared with the reported stable BNTs using density functional theory. A selection is made among the many possibilities, by avoiding structures with


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obvious strong repulsive non-bonded interactions26 (Figure 1). The dependence of ring conformations such as chair, and boat, and ring sizes (5-, 6-, and 7- ) on the relative stability and mechanical properties of nanothreads are presented. In addition, mechanical properties of these ANTs are studied by applying axial strain on these nanothreads to see inherent structural defects.

2. Computational method First principles computations are done using DFT. The Vienna ab initio simulation package (VASP)27,28 is used for all studies. The generalized gradient approximation (GGA) with PBE functional29,30 is used to incorporate the electron exchange-correlation and the PAW pseudopotentials31 are used to treat the electron-ion interactions. Dispersion correction was included by the zero damping DFT-D3 methods of Grimme.32 The energy cutoff for the plane wave basis set is kept as 800eV and Monkhorst–Pack 1×1×11 k-point mesh33 is taken to the 1- D Brillouin zones of the NTs. A supercell size of 15 Å along the two non-periodic directions are provided during geometry optimization. The convergence threshold is set to 10-6 eV in energy and 10-5 eV/Å in force. Atom positions are fully relaxed during the geometry optimization. The strain energy of the all the nanothreads are calculated by a methodology previously described for fulleranes and diamondoids.34 The strain energy (ΔE) can be obtained according to eqn 1 ΔE = [E(NTs) - xE(C) - yE(CH) - zE(CH2)] /(x+y+z)

------ 1

where E(NTs) represents the unit cell energy of the optimized NTs, E(CH2) is the energy of the infinite polyethene chain per CH2 unit, E(CH) is the energy of graphane sheet per CH unit, E(C) is the energy of the bulk diamond per carbon atom and x, y, z represents the number of C, CH, CH2 units respectively present per unit cell of the corresponding NTs. As a first approximation, polyethylene chain, graphane sheet, and diamond are taken as strain-free standard systems. The Young’s moduli (Ys) of NTs is computed using eqn 2


3


1 ⅆ2 𝐸

𝑌𝑠 = 𝑉

0

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------2

ⅆ𝜀 2

Here, V0 corresponds to the effective volume of the NT, which is calculated by multiplying number of atom present in the unit cell with the effective volume of carbon atom in diamond (5.536Å3/atom), as reported earlier.1,8 E is the strain energy and ɛ is the axial strain applied to the thread. The elastic limit is calculated from the stress−strain curves under the tensile stretch (by gradually increasing the lattice parameters). The following eqn 3 is used to calculate the percentage (%) of strain applied: % 𝑠𝑡𝑟𝑎𝑖𝑛 =

𝑎−𝑎1 𝑎

∗ 100

------3

where a and a1 are the NT lengths before and after the strain. Tensile strain is applied along the uniaxial direction to evaluate the mechanical stability of NTs. Atomic positions are relaxed at each strain. The dimensions of the unit cell directions are kept constant during the tensile test. The force on each atom in each strain level is relaxed to less than 0.01 eV/Å. The stress for each strained state is rescaled by multiplying computed stress with So/St to get the equivalent stress, where So is the surface area of the unit cell and St is an effective surface area of the NTs. St is calculated by V0/L, where L is the nanothread length. Failure Strain(Fs) and Ideal Strength(Is) are extracted directly from the Stress-Strain curves.

3. Result and Discussion Structure

Among the number of possible ANTs reported earlier,22-25 we start with bond connected ANTs,

(2a) and (2b), obtained by formation of a C-C bond connection between the adamantane units. Sharing a single carbon atom between the adamantane units in a spiro-linkage gives NT (2c). ANTs (2d) and (2e) are obtained by sharing one and two C-C bonds respectively. The face fusion gives rise to the fourth type denoted as (2f) and (2g) in Figure 1. We introduce two other type of ANTs,


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(3a) and (3c) as shown in Figure 2. The ANT (3a) is obtained by connecting the adamantane units through three C-C bonds (connections are represented by pink lines). Unlike 1-bond connected ANT (2a in Figure 1), here the adamantane units are not connected uniformly throughout repeating unit. Two possibilities could arise depending upon the fusion of the adamantane units. Figure 2A shows a schematic representation for these possibilities. Starting from a single adamantane monomer, the second unit could fuse in only one fashion denoted as 3-bond connected dimer in Figure 2A. For the third adamantane unit, two different fusion modes are possible; shown with green and red bonds. The addition of third adamantane unit through red bonds on one side and green bonds on another side results in the helical-ANT (C80H80, 3a) with a periodicity of 22.86 Å. Extension along either the green or red bonds on both sides gives the closed ring form C50H50 (3b). Figure 1. Schematic diagram of Benzene-derived NTs such as (1a) hydrogenated (3,0) nanotube, (1b) Stone-Wales defected NT and (1c) polytwistane NT. Adamantane-derived NTs such as (2a) 1-bond ANT, (2b) 2-bond ANT, (2c) 1-atom shared ANT, (2d) 1-edge shared ANT, (2e) 2-edge shared ANT, (2f) helical face fused ANT and (2g) zigzag face fused ANT.

The ANT (3c) (Figure 2(B)) is obtained from ANT (2g) through 1-D Stone-Wales (SW) type rearrangement of the C-C bonds periodically. The anti-clockwise rotation of green C-C bonds in ANT (2g) breaks the C-C bonds denoted in blue, and the new C-C bonds (brown) are formed


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periodically along the thread direction. This rearrangement transforms the fused six-membered rings in ANT (2g) into the five and seven-membered rings. The connectivity patterns seen in most of these ANTs are part of several three-dimensional carbon allotropes reported earlier.35,36 For instance, the defected NTs (1b) and (3c) have similar bonding connectivity as present in H-carbon allotrope.35 The NTs (1a) and (3d) have bonding pattern resembling the CcoC8-carbon allotrope.36 Similarly, several nanothreads are possible from different carbon allotropes which are shown in Figure S1-S4 (supporting information).

Stability The calculated strain energy (ΔE) of all NTs using eqn 1 are shown in Table 1. Except for zigzag-catafused ANT 2(g), all other ANTs contain 1,3-diaxial or proximal H---H interactions due to their different connections between adamantane monomer as shown in Figure 2(D). Thus, ANT (2g) have lowest strain energy. The strain energy increases as the number of non-bonded H---H interactions increases. The shortest H---H non-bonded distances of around 1.30Å and 1.37Å in ANTs 2(b) and 2(e) respectively increases the strain energy to the highest (5.84 kcal mol-1 for 2(b) and 5.50 kcal mol-1 for 2(e)) as shown in Figure 2(D). However, in 3-bond connected ANT (3a), the presence of three boat conformations between adamantane unit brings in six fp-fp non-bonded hydrogen interactions per cyclohexane ring. This leads to enhancement of strain energy to 2.23 kcal mol-1. The boat conformations are also present in (2,2) hydrogenated nanotube (3d) and BNT (1a, 1b, and 1c). Nevertheless, fp-fp interactions are present only in BNT (1a). In (3d), the reduction of pyramidalization angle associated with tertiary CH groups from the normal value (31.5⁰ to 21.8⁰) induces an angular strain in the system. Whereas in (1b) and (1c), the induced strain appears due to the presence of five-membered rings and the twist-boat conformation of the hexagonal units.


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The seven- and five-membered rings in ANT (3c) reduces its stability significantly. Relative stability obtained per CH units of the nanothreads (except for (2a) to (2e)) denoted with molecular formula CnHn in Table 1, follow similar trend as the strain energy. The nanothread (2g) with least strain energy has the highest energy per CH. The values decrease as the strain energy increases. However, such a correlation is not possible for (2a) to (2e), since the number of C and H atoms are different Figure 2. (A) Schematic illustration of the connections between the adjacent adamantane units present in the helical (3a) and the ring (3b) three C-C bond connected NTs. The connections are colored differently for clarity. (B) Stone-Wales transformation from (2g) to (3c). (C) Defected NTs (3c) and (1b) from H-carbon allotrope; hydrogenated (3,0) nanotube (1a) and hydrogenated (2,2) nanotube (3d) are from CcoC8 -carbon allotrope. (D) The bond connectivity and the type of rings present in the ANTs. The pink lines denote the H atoms. The non-bonded H---H interactions between the adjacent monomer unit are shown in dotted black lines.


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Table 1. Strain Energy ΔE, ECH per CH and relative energy (R.E.) of the different NTs.


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Strain Energy ECH per

ECH R.E. Destabilizing CH (kcal (kcal monomer unit mol-1) mol-1)

factors

between

NTs

ΔE (kcal mol-1)

(1a) C12H12

3.24

-294.32

2.77

six fp-fp H---H interactions

(1b) C12H12

3.69

-293.86

3.23

5-member ring

(1c) C28H28

2.89

-294.67

2.42

twist boat conformation

(2f) C16H16

0.92

-296.53

0.55

two 1,3-diaxial H---H interactions

(2g) C8H8

0.35

-297.09

0.00

-

(3a) C80H80

2.23

-295.29

1.80

six fp-fp, two 1,3-diaxial and two proximal H---H interactions

(3c) C16H16

3.25

-294.18

2.91

5- and 7-member ring

(3d) C8H8

2.88

-294.69

2.40

pyramidalization angle of carbon

(2a) C20H28

1.12

four 1,3-diaxial H---H interactions

(2b) C20H24

5.84

shortest H---H interactions

(2c) C9H12

1.57

eight 1,3-diaxial H---H interactions

(2d) C16H20

1.29

eight 1,3-diaxial H---H interactions

(2e) C7H8

5.50

shortest H---H interactions

Structural deformation and mechanical properties The effective volume (V0), linear atom density (λ), Young’s moduli(Ys), failure strain(Fs) and ideal strength(Is) of the ANTs and BNTs are reported in Table 2. In order to compare the accuracy of our methods, the corresponding mechanical properties are calculated for (8,0) carbon nanotube


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using similar methods as reported in Table 2. The (8,0) Carbon nanotube exhibit Fs ~20% and Is ~114GPa, which is similar to the previous report.37 The stress-strain relationship curves for the eight NTs with molecular formula CnHn are shown in Figure 3 and changes observed in the NTs after application of uniaxial strain are shown in Figure 4. The deformed NTs are denoted with single and double bar in the superscript, such as deformation of (1c) gives (1c') and (2c) gives (2c') etc. Except for (1c), (2g), and (3d), all NTs have a sudden break at 14-20% denoting their brittle nature (Figure 3). The NTs (2g) and (3d) are broken when the length is increased to around 26% and 38% respectively from optimized length. This is due to the symmetric elongation of all the axial C-C bonds when an axial strain is applied (dotted line in Figure 4 (2g') and (3d')). The Is and Ys values are also higher for the two NTs (3d) and (2g) compared to other NTs (Table. 2). On the other hand, the NTs (1a), (1b) and (3a) are converted to the respective monomers such as benzene in (1a'), fused noradamantane in (1b'), and adamantane in (3a'), respectively after elongation. Hence, the inter-monomer C-C bonds are weakened, reducing the Ys and the Is values (Figure 3). One of the three helical C-C bonds in the NT 1(c), remains intact when an axial strain is applied as shown in (1c'), Figure 4. Thus, the Ys, Fs and Is values are greater than that of (1a), (1b) and (3a). However, NT 1(c) has slightly lower mechanical stability towards axial elongation compared to both (2g), and (3d). Table 2. Linear atom density (λ), Effective volume (V0), Young’s moduli(Ys), Failure strain(Fs) and Ideal strength(Is) of the stable NTs. NTs

(1a) C12H12

V0

Ys

λ

Failure

Ideal

Å3/atom

(GPa)

atoms/Å

Strain(Fs)

Strength(Is)

~ (%)

(GPa)

18

114

15.47

1176

2.79


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(1b) C12H12

13.37

1053

2.41

17

110

(1c) C28H28

13.54

1178

2.44

20

144

(2f) C16H16

19.95

979

3.60

16

96

(2g) C8H8

17.43

1181

3.14

26

168

(3a) C80H80

19.37

682

3.49

20

87

(3c) C16H16

18.23

1027

3.29

18

112

(3d) C8H8

17.48

1225

3.15

38

204

Upon further elongation in the axial direction, NT 1(c') forms helical polyacetylene chain 1(c'') as shown in Figure 4. When the NT (3c) and (2f) are elongated beyond its failure strain, structural transformations are observed (Figure 4, (3c'') and (2f'') respectively). The first one transforms into polycyclophane NT (3c''), which is 8.60 kcal mol-1 per CH less stable compared to NT (3c). It is composed of 4-cyclohexadiene rings bridged through the methylene groups linearly. Though the unit cell formula remains the same in NT (2f''), stability is reduced by around 3.15 kcal mol-1 than NT (2f). The connections present in both NT (2f'') and (3c'') resemble the hypothetical dense 3,4-carbon net as discussed by Hoffmann et. al.14 Figure 3. The Stress-Strain relationship of NTs. (1a), (1b) and (1c) are benzene-derived NTs. (2f), (2g), and (3a) are adamantane-derived NTs. (3c) and (3d) are defected NT and (2,2) hydrogenated nanotube respectively.


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Figure 4. Changes observed on the NTs under uniaxial tensile strain. NTs (1a), (1b), and (3a) are transformed to molecular type (1a'), (1b'), and (3a'); NTs (2g) and (3d) are transformed to (2g') and (3d'); NTs (1c), (2f), and (3c) give intermediate NTs such as (1c'), (2f'), and (3c') respectively, where few of the C-C bonds are broken. Further elongation of these intermediate NTs results in new NTs (1c''), (2f''), and (3c'').


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4. Conclusions The factors that control the relative stability and mechanical properties of different carbon nanothreads derived from adamantane and benzene motifs are studied. The presence of more number of non-bonded H---H interactions between the monomer units decreases the relative stability of the ANTs. Thus, the catafused and the three C-C bond connected ANTs are found to have the highest stability. The stability also depends on the ring size and their conformations. As expected, six-membered rings with chair conformation contribute towards greater stability in comparison to BNTs with boat or the twist-boat conformation or the five-membered rings as building blocks. The zigzag-catafused ANT and (2,2) NT are found to have greater mechanical strength in comparison to the benzene-derived ones. Application of axial strain forces some of the C-C bonds in ANTs to rearrange to newer types of NTs with reduced mechanical stability. In general, nanothreads from adamantane would be promising materials due to its greater stiffness in comparison to other 1-D carbon nanomaterials.

ASSOCIATED CONTENT Supporting Information The following files are available free of charge. Nanothreads from carbon allotropes in a PDF format and Crystallographic information file (.zip) AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] ORCID


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E.D. Jemmis 0000-0001-8235-3413 Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ‡These authors contributed equally. (match statement to author names with a symbol) Funding Sources D. S. Kothari Post-Doctoral Fellowship (SM) and SERB through J. C. Bose Fellowship (EDJ). ACKNOWLEDGMENT The authors acknowledge the financial support from University Grants Commission, Govt. of India through the D. S. Kothari Post-Doctoral Fellowship (SM) and from SERB-DST through J. C. Bose Fellowship (EDJ). The Supercomputer Education and Research Centre(SERC)-IISc provided computational facilities. REFERENCES 1.

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Graphical Abstracts


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Adamantane-Derived Carbon Nanothreads: High Structural Stability

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