Reactive Molecular Dynamics Simulations of Self- assembly of

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C: Physical Processes in Nanomaterials and Nanostructures

Reactive Molecular Dynamics Simulations of SelfAssembly of Polytwistanes and Its Application for Nanofiber Biswajit Saha, and Ayan Datta J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05066 • Publication Date (Web): 01 Aug 2018 Downloaded from http://pubs.acs.org on August 2, 2018

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The Journal of Physical Chemistry

Reactive Molecular Dynamics Simulations of Selfassembly of Polytwistane and its Application for Nanofiber Biswajit Saha*, Ayan Datta* Department of Spectroscopy, Indian Association for the Cultivation of Science 2A & 2B Raja S. C. Mullick Road, Jadavpur, Kolkata - 700032, West Bengal, India

Corresponding Authors B. Saha ([email protected]), A. Datta ([email protected]) Phone: +91-8670377264 (B. Saha), +91-9874295938 (A. Datta)

ABSTRACT: We investigated self-assembly and mechanical properties of polytwistane, particularly 7-strands polytwistane (PT) rope using reactive force field (ReaxFF) based molecular dynamics simulations at different temperatures. We show that upon self-assembly due to strong van der Walls interaction among PT units, PTs form twisted structure (rope-like) with twisting angle ~0.16 rad/nm at 300 K, which makes it mechanically stronger. The PT rope has high Young’s modulus (~0.45 TPa) at 300 K. Interestingly, the Young’s modulus increases with temperature for the 7-strands PT rope while it decreases with temperature for single strand PT. This is because in 1

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case of 7-strands PT twisting angle also contributes to the elastic property of the PT rope and twisting depends on temperature. We estimate a maximum load transfer of ~1.1 nN and ~3.3 nN to the central unit at 100 K and 300 K, respectively. Hence, the amount of load transfer critically depends on the twisting in the rope. The fracture behavior of single strand PT and seven strands PT rope are also investigated. We find two major mechanism of PT fracture: In the first case, an acetylene-like structure is attached with one of the twistane unit at the breaking region. In the other case, all the three sp3 C-C bonds of the participating twistane units break creating three sp2-C sites along the breaking region. In case of, PT rope the fracture in the individual strands occurs in a sequential manner. We predict that the self-assembled twisted PT rope is a promising candidate for carbon fiber application where mechanical properties are of interest.

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1. INTRODUCTION Diamond nanothread (DNT) consisting of sp3-carbon is a promising candidate for carbon nanofiber production in light of their recent experimental synthesis and extraordinary physical properties.

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Fitzgibbons et al derived, for the first time, nanothreads from benzene at high-

pressure (20 GPa at room temperature) and predicted that Stone-Wales (SW) defects are likely to be present in nanothread structures.2 Olbrich et al have recently synthesized oligomer of twistane for the first time.1,3 It has been reported that single strand polytwistane (PT) has a helical structure without any SW defect.6 In this context, it is worth mentioning that computational study has shown that sp3–hybridized bonded carbon could adapt the same topology as of sp2-hybridized carbon.7 The estimated the Young’s moduli of sp3-hybridized (3, 0) and (2, 2) carbon nanotubes are significantly higher than that of familiar sp2-hybridized carbon nanotubes. As a result, there has been a significant interest to computationally study the mechanical properties of 1D nanostructures consisting of sp3–hybridized carbons, such as nanothreads8,9, PT6, polytriangulane10 and poly[5]asterane11 as they also can be potential candidates to compete with sp2-hybridized carbon nanotubes and graphene when hardness and mechanical stability of the materials are of interest.9,12,13 Mechanical properties of DNT have been computed using density functional theory (DFT) and classical force fields like adaptive inter-molecular reactive empirical bond order (AIREBO) and reactive force field (ReaxFF) which show that classical force fields worked reasonably well for such systems.14 Very recently, Chen et al applied computational technique and proposed possible formation of saturated singly substituted 1D nanothreads of the (CH)5E and (CH)5CR type, where E is a heteroatom and R is a substituent by adopting symmetry-condition.15 Recently, Li and co-workers have shown the formation of a well-ordered sp3-carbon nitride nanothreads, from pyridine under pressure of 23 GPa.16 3



Carbon nanotube (CNT) fibers produced from highly packed and axially aligned CNTs have much higher modulus and strength compared to fibers produce from commercial carbon and polymers. Various experimental techniques like (i) spinning from CNT solution, (ii) spinning from vertically aligned CNTs, and (iii) twisting/rolling from a CNT film are used to produce CNT fibers.17-22 Carbon nanothread single crystals have been synthesized recently adopting a mechanochemical approach where it was shown that nanothread fibers could be prepared by mechanical exfoliation of nanothread crystals.4 Until now however, there is no report on the formation of naturally twisted rope-like structure of polytwistanes bundle. DNT with SW defects bundles have studied using AIREBO potential for its possible application to carbon nanofibers.23 They showed that nanothread bundles had excellent torsional deformation capability and interfacial load-transfer efficiency with a high torsional elastic limit of ~0.57 rad/nm. Nevertheless, the issue of natural twisting during bundle formation has not been addressed. Also, in the context of fabrication of high-performance DNT fibers, the alignment of the individual DNTs along the fiber axis and hence, twisting is expected to be crucial. The load transfer also estimated using experimental (~1.7 nN per CNT-CNT interaction) and computational (~1.5 nN per CNT-CNT interaction) techniques for double wall CNT bundle.24,25 Recently nuclear magnetic resonance (NMR) studies were performed both by experimental and computational (DFT) techniques and the presence of fully saturated “degree-6” carbon nanothreads in the nanothread crystal was confirmed.26,27 One cannot uniquely determine the atomic-scale structure of the DNT from the available diffraction data. However, based on the DFT calculations and diffraction data it was shown that polytwistane and/or tube (3,0) may be the possible DNT candidates that were synthesized.4 Moreover, DFT calculations shows that chiral polytwistane has the lowest energy (0.57 eV per (CH)6 unit relative to graphene) among the 4


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allotropes studied.9 Therefore, here, we will show that the PT can self-assemble to form a rope to result in a twisted structure naturally. The effects of temperature on the stability of the selfassembly and mechanical properties of the PT rope was investigated using reactive molecular dynamics simulations. We observe clear indication for the formation of a natural helical order in the self-assembled ropes. This makes them better candidates for fiber production with improved mechanical properties. Remarkably, while CNTs get compressed along the short axis during bundling which deteriorate the mechanical properties of fiber28,29, DNTs show no such deterioration.

2. COMPUTATIONAL DETAILS We performed molecular dynamics (MD) simulations using reactive force field (ReaxFF) available in Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS).30 ReaxFF potential, where a general relationship between bond-length and bond-order and between bond order and bond energy is explicitly considered, predicts reasonable dissociation of bonds. 31-33 Other valence terms (angle and torsion) are defined in terms of the same bond orders to ensure that they converge to zero as bonds break. ReaxFF applied intensively to study hydrocarbon systems and on carbon based nanostructures.11,14,34-39 Additionally, since ReaxFF includes van der Waals (vdW) interaction appropriately, it is suitable to study material aggregation. Hence, the ReaxFF potential performs reasonably well when the model system is under strain or even at around fracture region since beyond ‘harmonic conditions’ can be captured. The reactive MD force field parameters for carbon and hydrogen were taken from Singh et al.36 At first, self-assembly simulations were performed by considering randomly oriented 30 polytwistanes (~2.10 nm and consists of 5

5



building block unit, twistane (C10H10)) of same chirality in a periodic cubic box of dimension 58 Å as shown in Fig. 1a. Snapshot after self-assembly is presented in Fig. 1b. This initial structure was generated using Packmol.40 We also considered different densities by varying the box dimensions and these self-assembly simulations were performed at 300 K for 200 ps. Next, we performed simulations considering a single strand polytwistane (C260H266) of length ~10.8 nm and its mechanical properties were estimated. The polytwistane (PT) is consists of 26 building block unit, twistane (C10H10) as shown in Fig. 2a and it was optimized by using conjugate gradient method. View along long axis and building block, unit twistane (C10H10), are shown in Fig. 2c and Fig. 2d, respectively. We added six extra hydrogen to passivate the radical sights at the termini of the thread. No boundary conditions were applied in these simulations as well as in the following simulations. Literature reports show that better carbon fiber can be produced from axially aligned CNT with superior mechanical properties.17-‐22 Therefore, in the next step, we performed selfassembly simulations considering axially aligned PT of length ~10.8 nm and same chirality with 2-strands to 7-strands PT. For 2-strands to 6-strands PT, the simulations are performed at 300 K for 1.0 ns and self-assembly and twisting nature were studied. As a monoclinic (pseudohexagonal) nanothread crystal was reported from diffraction studies4,16, more detailed simulations were performed for axially aligned 7-strands PT to study their thermal and mechanical properties. The model systems were equilibrated at 100 K, 300 K and 500 K for 1.0 ns to 1.40 ns considering microcanonical ensemble. We used a time step of 0.25 fs in combination with Nosé-Hoover thermostat with damping constant of 25.0 fs for all these simulations.41,42 The equilibrated structures were used for studying mechanical properties.

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Figure 1. Snapshots sowing self-assembly of PT at 300 K. (a) initial randomly oriented PT and (b) self-assembled structure. A selected part of (b) is shown in the inset to visualize the axial orientation of PT.

A tensile force was applied by subjecting a constant velocity of 2×10%& Å/fs in one end while keeping other end fixed. Five sets of simulations were performed at each temperature by collecting equilibrated structure at every 100 ps from 1.0 ns of equilibration simulation onwards. Virial stress (𝑆 )* ) was calculated during the tensile simulation using the standard formulation as:

𝑆 )* =

1 − 𝑉

*

𝑚0 𝑣0) 𝑣0 + 0

1 2

*

𝑓04) 𝑟04 0

460

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Here, indices 𝛼 and 𝛽 represent the Cartesian components; 𝑉 is the volume of the system; 𝑚0 is *

*

the mass of atom 𝑖; 𝑣0) and 𝑣0 are velocity components of atom 𝑖; 𝑓04) and 𝑟04 force and distance between atoms 𝑖 and 𝑗.

Figure 2. (a) Single strand polytwistane (PT) of length 10.8 nm equilibrated at 300 K for 1.0 ns and (b) view along long axis. (c) The building block unit, twistane (C10H10). Blue color and silver color represent position of carbon and hydrogen atom, respectively.

Tensile strain was applied at different temperatures to illustrate the effect of temperature on the tensile properties. The visual molecular dynamics (VMD) software package was used to analyze the simulation data, to prepare the snapshots of the model systems and generating movie files.43

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3. RESULTS AND DISCUSSIONS 3.1. Single Strand Polytwistane. The molecular structure of single strand PT simulated at 300 K for 1.0 ns is shown in Fig. 2a, Fig. 2b and Fig. 2c. The C-C bond radial distribution function (RDF) at different temperatures after 1.0 ns of constant temperature simulations are shown in Fig. S1. The first peak at ~1.55 Å corresponds to C-C bond. As expected, at higher temperatures the C-C bonds elongated as evident from the distribution. Hence, the peak height decreases and broadens as temperature increases. Our estimation of C-C bond length value agree reasonably well with DFT estimated a value of ~1.54 to ~1.57 Å9 The stress-strain plots for single strand PT at different temperatures are shown in Fig. S2. Here, we would like to mention that the definition of the cross-section of 1D nanostructure is very critical. We defined the cross-sectional area of PT as that corresponding to an equivalent number of carbon atoms in a bulk diamond structure and assigned a volume (𝑉) of 5.536 Å3 per carbon atom to PT. This approach is systematized for the calculation of elastic modulus of nanoscale materials.7,9,44. The linear atom density (𝜌) used to calculate the volume of the PT is 2.41 atoms/Å. Hence, the cross-sectional area of PT is given by 𝜌𝑉. The Young’s moduli at different temperatures were calculated by linear fitting the liner part (between 1.5% to 10.0% strain) of the stress-strain curve. We omitted the initial part of the stressstrain curve as it shows fluctuation, which arises due to the bends in the PT structure that require straightening. The Young’s modulus, tensile strength and failure strain at different temperatures for single strand PT are reported in Table 1. Table 1. Tensile properties of single strand polytwistane (PT) at different temperatures. Temperature (K) Young’s modulus (TPa) Tensile strength (GPa) Failure strain (%) 100

0.95

173.7

9


22


a

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300

0.91

156.8

19

300

1.17a

117.0a

15a

500

0.89

137.1

16

Calculated using AIREBO potential.44

These values are averaged over five trajectories at each corresponding temperature. The Young’s moduli, calculated from the stress-strain curves, at each temperature are 0.95 TPa, 0.91 TPa and 0.89 TPa at 100 K, 300 K and 500 K, respectively. It is apparent that, the Young’s modulus decreases with increasing temperature albeit by only a small extent only (4% and 6% at 300 and 500 K, respectively) in this temperature range. Young’s modulus of single strand PT reported as 1.11 TPa using DFT9, and 1.17 TPa using AIREBO potential at 300 K.44 It is noteworthy to mention here that the previous literature reports for the nanothreads contain one or more SW defects except the work by Zhan et al44 and Feng et al 5 where pure DNTs were considered. Feng et al also studied the effect of temperature on the tensile properties of DNTs using ReaxFF MD simulations.5 They reported the tensile strength and failure strain for PT as ~100 GPa and 28% at 1 K. Tensile strength (at which fracture occurs) and failure strain also show concomitant reduction with increased temperature. This trend is in accord with the results reported for other DNTs by Feng et al.

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Deformation of the PT is elastic for small strain (< 10%) and higher strain creates

defects which result in fracture in PT. The defect eventually leads to fracture in the PT (Fig. S3a, Fig. S3b, Fig. S3c and Fig. S3d). The bonds parallel to the long axis get stretched while the bonds along transverse direction are shrunk, although it maintains an overall sp3 nature till a strain of ~10% which also depend on temperature. We estimated the axial deformation qualitatively by calculating the number of 6-membered rings in the PT throughout the strain simulations and 10


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presented in Fig. S4. The rings started breaking at ~12.8% and ~14.9% of strain at 100 and 300 K, respectively. At higher temperature, the C-C (sp3) bonds are elongated and hence PT can break easily. Once one C-C bond shared by hexagons breaks during starching, complete fracture occurred. Complete breaking of PT occurred at a failure strain of ~22.0%, ~19.0% and ~16.0% at 100 K, 300 K and 500 K, respectively. Stress concentration was not observed locally; instead, stress shared along the PT and bond cleavage occurs as the elongation increases (Fig. S3d). Beyond the failure limit, the rings are formed aging except the ring at the breaking region remains broken (Fig. S3d and Fig. S3e). We observed two major atomistic mechanisms for cleavage of PT structure irrespective of temperature as shown in Fig. S5. In the first case, an acetylene-like structure is attached with one of the twistane unit at the breaking region (Fig. S5a). In the other case, all the three sp3 C-C bonds of the participating twistane units break creating three sp2 C sites along the breaking region (Fig. S5b). In some cases, we also observed release of a C2H2 molecule during complete breaking. However, we did not observe any C-H bond breaking when the thread breaks under strain.

3.2 Polytwistane Self-assembly. Self-assembly of polytwistanes is shown from simulations considering an initially randomly oriented polytwistane system and snapshots are presented Fig. 1a. Interesting features, such as, alignment of the polytwistanes along long axis and formation of rope-like structures because of dispersion interactions are clearly observed from these simulations (Fig. 1b). A selected part of the assembled bundle is shown in the inset for clarity. It is clear from this figure that polytwistanes forms a monoclinic (pseudohexagonal) crystal in agreement with diffraction studies.4,16 Twisting of individual polytwistane is also observed upon bundle formation irrespective of their position in the bundle. The twisting is clearer from the 11



bundle formation of longer polytwistanes with 2-strands to 6-strands PT as shown in Fig. S6. In all these cases, we observed formation of twisted rope like structure. The twisting angle estimated in these cases as ~0.16 rad/nm. The interdigitation of the neighboring PTs is shown in Fig. S7 for 2-strands bundle. If we say there are ridges (the C-H bonds) and valleys (the region between the C-H bonds) on the surface of the thread, then it is clear from Fig. S7 that the C-H bonds (ridges) point to the valleys on the neighboring threads. Further detail study on the self-assembly and mechanical properties of PT bundle were performed by considering a model system consisting of axially aligned 7-strands PT as shown in Fig. 3a. In Fig. 3a, we presented initial model structure where the PTs are separated by ~9.0 Å. They come closer after bundle formation as shown in Fig. 3b, Fig. 3c and Fig. 3d. The representative snapshots of the model systems equilibrated at 100 K, 300 K and 500 K for 1.0 ns are shown in Fig. 3b, Fig. 3c and Fig. 3d, respectively. The selfassembly processes is fast due to the presence of strong vdW interaction among the PTs and they remains as a bundle during the rest of the simulation. It is apparent from the snapshots that upon self-assembly the PTs form rope (helical) structure. This is a very distinct feature in PT and arises due to strong vdW interaction between the individual helical PT structure and orientation of hydrogen on its surface. The effective length of individual PT’s in the bundle is shorter, although by small amount ~0.5 Å, than that of its initial length due winding

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Figure 3. Self-assembled 7-strands PT rope at different temperatures. Initial structure (a), final structures after 1 ns of simulation at 100 K (b), 300 K (c) and 500 K (d). Corresponding views along long axis are shown in the right panel. Atoms are colored according to the strand number in the rope.

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among themselves. We estimated the helical angle of the PT rope as schematically shown in Fig. S8a, Fig. S8b, Fig. S8c and Fig. S8d. We used the center of mass of each twistane unit for computing the helical angle and assumed the PT is along z-axis. zi correspond to the Z-coordinate of each center of mass. We took projection of each center of mass on the XY plane, orthogonal to the polytwistane rope long axis (Z-axis). Angle between subsequent twistane units were calculated from z1 and z1+i as shown in Fig. S8d. The helical angles are 0.05 rad/nm, 0.16 rad/nm and 0.16 rad/nm (averaged over five trajectories), at 100 K, 300 K and 500 K, respectively. Hence, the estimated helical angle at 300 K for all 2-strands to 7-strands bundles is same. It is apparent that at 300 K, the helical angle is significantly high compare to 100 K implying a stronger binding among the PTs. The helical angle does not alter much on going to 500 K from 300 K indicating the thermal stability of the bundle. Hence, PT remains quite stiff at lower temperature towards helix formation around each other while at higher temperature winding occurs much easily. Nonetheless, further increase in temperature makes binding weaker due to thermal fluctuation. The center of mass (COM) information of individual twistane unit was used to calculate the COM distance between adjacent PTs. The average COM separation between adjacent PT strands are ~5.9 Å, ~5.9 Å and ~6.0 Å at 100 K, 300 K and 500 K, respectively. It is apparent that there is no significant difference among COM distances at different temperatures. This is anticipated as at higher temperature the bundles get more twisted structure without significantly altering under thermal fluctuations. Based on the estimates of the COM values, we calculated the radius of the self-assembled 7-strands PT rope. The 7-strands PT rope forms a hexagonal (triangular) crystal with lattice constant 8.40 Å assuming the single strand PT radius as 2.50 Å and the average COM distance of self-assembled 7-strands PT as 5.9 Å. The COM distance estimated

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Figure 4. Stress-strain curve for 7-strands PT rope at different temperatures, (a) 100 K, (b) 300 K and (c) 500 K. 15



using AIREBO potential was ~6.25 Å for DNT (with SW defect) bundles.23 The stress-strain curve for 7-strands PT rope at different temperatures are shown in Fig. 4. It is observed that the fracture into individual strand occurs at ~20.2% strain at 100 K for the first occurrence. At 300 K and 500 K, one requires strain of ~18.5% and ~15.5%, respectively for the first occurrence. Hence, at lower temperature the bundle shows more brittle like behavior. The Young’s moduli for the PT ropes were again estimated from the linear fit of the linear part of the stress-strain curves and the corresponding values are reported in Table 2. The tensile strengths and failure strains at different temperatures also reported in Table 2. The Young’s modulus for the 7-strands PT rope obtained as 0.44 TPa, 0.45 TPa and 0.46 TPa which is indeed quite high and promising fiber application. It is apparent from Table 2 that the Young’s modulus increases marginally with temperature (an increment of ~2% and ~5% at 300 and 500 K, respectively). Upon application of a large strain (one requires strain of ~19.7%, ~17.8% and ~15.0% at 100 K, 300 K and 500 K, respectively) fracture is observed in the rope and permanent defects are formed. Comparing the tensile strengths and failure strains at different temperatures from Table 1 and Table 2, it appears that in the bundle the PT becomes stiffer than the isolated PT. On the other hand, the tensile strengths and failure strains reduce with increasing temperature. It is important to note that the Young’s modulus shows opposite trend for 7-strands PT rope with temperature vis-a-vis single strand PT. The snapshots of fracture behavior for the 7-strands PT rope is shown in Fig. 5 from a representative trajectory simulated at 300 K and at 100 K in Fig. S9.

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Table 2. Tensile properties of 7-strands PT rope at different temperatures. Temperature (K) Young’s modulus (TPa) Tensile strength (GPa) Failure strain (%) 100

0.44

77.6

19.7

300

0.45

72.5

17.8

500

0.46

62.8

15.0

We do not observe the fracture of all the 7-strands simultaneously. Rather we observe that one or two strand/strands fractured initially and subsequently fracture in the remaining strands occurred within a time of ~100 ps. Once a PT fractured, the strand/strands comes/come out of the fiber surface or disassemble for a while (~20 ps). They again assembled to form a bundle due to strong vdW interaction among PTs although permanent fracture remains in the rope structure.

3.3 Load Transfer in Polytwistane Rope. Load transfer is an important parameter in the context of fiber application. Therefore, we performed simulations where the surrounding six PTs were kept fixed at one end and free at the other end while the central PT was pulled out by applying a constant velocity of 2×10%& Å/fs. The central PT was pulled out by 10 Å. The transferred load as a function of displacement is shown in Fig. S10. It is clear from the figure that the transferred load is highly fluctuating in nature and does not diminish during this part of the pull-out simulation. In Fig. 6a, Fig 6b, Fig. 6c, Fig. 6d, Fig. 6e and Fig. 6f, we show the histogram of C-C bond length of the central PT unit before (blue) and after (red) the pull-out processes at different temperatures. The histogram

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Figure 5. Fracture behavior of 7-strands PT rope under strain at 300 K. Time reset to zero after equilibration of 1.2 ns at 300 K. Therefore, here the time corresponds to strained simulation part only. Atoms are colored according to the strand number in the rope.

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peak is at ~1.57 Å and has wider distribution at higher temperatures before the pull-out process. After the pull-out process the peak value remains at ~1.57 Å and but has more wider distribution on the higher side of the peak indicating elongation of many of the some C-C bonds. Contraction of few other C-C bonds also are observed which is in agreement with the negative Poisson ratio as reported in the literature.14 Therefore, it is clear from the histograms that a large number of C-C bonds elongated after pull-out, an indication of large load transfer to the central PT unit. At higher temperature, e.g. at 300 K, the C-C bonds get more elongated due to even larger load transfer compare to at 100 K case. This is due the fact that at higher temperatures, the PTs form more winding structure and thus large load transfer is observed. The maximum force acting on the central unit during the initial stage of pull-out process are estimated as ~1.1 nN and ~3.33 nN at 100 K and 300 K, respectively. Therefore, the amount of load transfer is more for the more twisted structure as also reported previously by Zhan et al for DNTs.23 For soft spiral DNT the maximum transferred load of ~5.28 nN was reported by Zhan et al during early stage of sliding.23 The twist angle was also evaluated during this pull-out process and that the twisting nature of PT rope remained intact. Hence, during the pull-out process the load transfer remains intact and makes the rope mechanically robust. It is worth mentioning here that the force is not that huge so that the any fracture may occur in the central unit. Once the external pull-out force was removed from the central PT, it again gets back inside the rope bundle due to strong vdW force. PT posses an ultrathin tetrahedral like structure and does not show radial breathing mode and aromatic surfaces as there is no π-π interactions. Rather, the PT bundle has an interface like that of hydrogenated diamondlike surfaces which have very low friction coefficient.45

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Figure 6. C-C bond length distribution before (blue histogram, left panel) and after (red histogram, right panel) the pull-out processes in 7-strands PT at different temperatures. At 100 K (a, b), 300 K (c, d)) and 500 K (e, f).

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This seems to counterintuitive in light of our estimate of large load transfer in 7-strands PT rope. This is rationalized on the basis of the fact that during the pull-out process, one may consider that the central polytwistane strand more or less like a straight cylindrical structure analogous to the CNT bundles. Hence, the work done by the transferred load equals to the surface energy of the newly created surfaces during the pull-out processes. Moreover, the transferred load is independent of the overlapped length of the central PT unit. We do not observe any stick-slip motion for the PT rope, unlike other DNT bundles with SW defect and CNT bundles23 although oscillation is observed in the force vs displacement curve. This is because of the unique twisted rope like nature of PT bundles which is absent for self-assembled CNT. Moreover, in case of CNTs and DNTs bundles there exist several different configurations like AA and AB stacking or due to SW defects. Therefore, one expects a unique uniform load transfer behavior throughout the pull-out processes.

4. CONCLUSIONS We report that polytwistane (PT) can self-assemble to form rope like structure due to the strong van der Waals interaction among the individual PT units and due to the unique helical structure of the PT unit itself. The Young’s modulus obtained for 7-strands PT rope is ~0.45 TPa which is significantly higher than the CNT bundle fiber. The Young’s modulus increases with temperature for PT rope whereas maximum stress and maximum strain decrease with temperature. However, in case of single strand PT, the Young’s modulus, tensile strength and failure strain all decrease with temperature. Upon application of a large strain (one requires strain of ~19.7%, ~17.8% and ~15.0% at 100 K, 300 K and 500 K, respectively) fracture is observed in the rope and permanent defects are formed. The pull-out simulations show that a large load transfer of ~1.1 nN and ~3.3

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nN at 100 K and 300 K, respectively to the central unit and it depends on the twisting angle in the rope. Moreover, the rope maintains structural integrity during the pull-out process. Our simulations therefore, strongly advocate polytwistane bundled as novel carbon materials for superior mechanical properties.

Supplementary Information Radial distribution function ( 𝑔== (𝑟)), stress-strain curve, structural change and fracture behavior of PT, rings evolution upon strain application, helical angle calculation for PT rope, fracture behavior of 7-strands PT rope at 100 K. Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS B.S. is thankful to Indian Association for the Cultivation of Science (IACS), Kolkata, India for the fellowship and facilities provided to him. A.D. thanks to Department of Science and Technology (DST), India, Board of Research in Nuclear Sciences (BRNS), India and TATA Steel, India for partial funding.

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Reactive Molecular Dynamics Simulations of Self- assembly of

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