Computational study of effect of radiation induced crosslinking on the properties of flattened carbon nanotubes

Flattened carbon nanotubes (flCNTs) are a primary component of many carbon nanotube (CNT) yarn and sheet materials, which are promising reinforcements for the next generation of ultra-strong composites for aerospace applications. Significant improvements in the performance of CNT materials can be realized with improvements in the load transfer between flCNTs, which are generally oriented at different angles with respect to each other. An intriguing approach to improving the load transfer is via irradiation-induced chemical crosslinking between adjacent flCNTs. The objective of this research is to use molecular dynamics (MD) simulations to predict the behavior of flCNT junctions with 0- and 90-degree orientations and varying levels of crosslinking. The results indicate that crosslinking improves the flCNT interfacial load transfer for both orientations, but degrades the flCNT tensile response. The primary toughening mechanism at the flCNT/flCNT interface is the formation of carbon chains that provide load transfer up to the point of total rupture. Based on these results, it is clear that irradiation-induced crosslinking is beneficial in CNT-based composite systems in which interfacial load transfer between flCNTs is of primary importance, even though individual flCNTs may lose some mechanical integrity with crosslinking.


bon chains th
t provide load transfer up to the point of total rupture.Based on these results, it is clear that irradiation-induced crosslinking is beneficial in CNT-based composite systems in which interfacial load transfer between flCNTs is of primary importance, even though individual flCNTs may lose some mechanical integrity with crosslinking.

Introduction

For future deep space manned missions to be affordable and efficient, there is a need to build ultra-high-strength lightweight composite materials for structural components of aerospace vehicles.Carbon nanotube (CNT) materials, because of their exceptional specic strength and stiffness, are promising reinforcement candidates for this purpose. 1,2In particular, attened CNTs (CNTs) exhibit self-alignment and efficient packing in stacked arrays and can be used with highperformance resins to make the next generation of composite materials. 3,4However, TEM-observed fracture surfaces of CNT materials hav

Introduction
For future deep space manned missions to be affordable and efficient, there is a need to build ultra-high-strength lightweight composite materials for structural components of aerospace vehicles.Carbon nanotube (CNT) materials, because of their exceptional specic strength and stiffness, are promising reinforcement candidates for this purpose. 1,2In particular, attened CNTs (CNTs) exhibit self-alignment and efficient packing in stacked arrays and can be used with highperformance resins to make the next generation of composite materials. 3,4However, TEM-observed fracture surfaces of CNT materials have revealed intra-stack sliding in addition to complete stack pull-out when subjected to external loads. 3Since the CNT yarns suffer from poor internal load transfer, 5 and CNTs are major constituent of CNT yarns, 3 a major challenge to utilize CNTs in structural composites is achieving sufficient levels of CNT/CNT interfacial load transfer.
revealed intra-stack sliding in addition to complete stack pull-out when subjected to external loads. 3Since the CNT yarns suffer from poor internal load transfer, 5 and CNTs are major constituent of CNT yarns, 3 a major challenge to utilize CNTs in structural composites is achieving sufficient levels of CNT/CNT interfacial load transfer.

7][8] Filleter et al. experimentally demonstrated up to 16-fold increases in the mechanical properties of double-walled CNTs following high-energy e-beam irradiation via TEM. 9Locascio et al. 10 observed that irradiation-induced crosslinking improved the strength of multi-walled CNTs by more than a factor of 10 with a small reduction in the strain to failure.Post irradiation, Miller et al. 11 observed a 48% increase in tensile strength of functionalized CNT sheets.Using the molecular dynamics (MD) approach, Pregler et al. 12 studied the effect of ion and e-beam irradiation crosslinking on the failure of MWCNT inner-tube sliding and observed a signicant increase in the force required for multiwalled CNT failure.Peng et al. 13 experimentally demonstrated that e-beam irradiation leads to multi-shell failure in multi walled CNTs, which drastically improves the sustainable loads by a factor of 2-11 as compared to the non-irradiated samples.Kis et al. 14 observed a 30-fold increase in the bending modulus of single walled CNTs exposed to e-beam treatment.Astrom et al. 15 observed an increase in stiffness and strength of CNT materials with irradiation induced crosslinks.Using MD, Cornwell and Welch 16 observed an increase in tensile strength of bers (aligned CNTs) up to 60 GPa due to interstitial crosslinks.Despite the previous computational and experimental studies on the effect irradiation-induced crosslinks on CNTs, there is 7][8] Filleter et al. experimentally demonstrated up to 16-fold increases in the mechanical properties of double-walled CNTs following high-energy e-beam irradiation via TEM. 9Locascio et al. 10 observed that irradiation-induced crosslinking improved the strength of multi-walled CNTs by more than a factor of 10 with a small reduction in the strain to failure.Post irradiation, Miller et al. 11 observed a 48% increase in tensile strength of functionalized CNT sheets.Using the molecular dynamics (MD) approach, Pregler et al. 12 studied the effect of ion and e-beam irradiation crosslinking on the failure of MWCNT inner-tube sliding and observed a signicant increase in the force required for multiwalled CNT failure.Peng et al. 13 experimentally demonstrated that e-beam irradiation leads to multi-shell failure in multi walled CNTs, which drastically improves the sustainable loads by a factor of 2-11 as compared to the non-irradiated samples.Kis et al. 14 observed a 30-fold increase in the bending modulus of single walled CNTs exposed to e-beam treatment.Astrom et al. 15 observed an increase in stiffness and strength of CNT materials with irradiation induced crosslinks.Using MD, Cornwell and Welch 16 observed an increase in tensile strength of bers (aligned CNTs) up to 60 GPa due to interstitial crosslinks.Despite the previous computational and experimental studies on the effect irradiation-induced crosslinks on CNTs, there is an insufficient understanding of how irradiation-induced crosslinks between CNTs affects mechanical performance of CNT arrays.
n insufficient understanding of how irradiation-induced crosslinks between CNTs affects mechanical performance of CNT arrays.

The objective of this research is to determine the effect of irradiation-induced crosslinking on the properties of CNT composites using MD simulation.As the CNTs within CNT yarns and bundles are entangled with each other at different orientations, 17 two extreme orientation cases of CNTs junctions were considered: 0 and 90 , which represent two aligned and perpendicular CNTs, respectively.In this study, crosslinking is dened as the ratio of the number of carbon atoms forming the bonds between the two CNT sheets to the total number of carbon atoms in the overlapped area.For each of the orientation cases, the amount of crosslinking was varied from 0% to 20%.For these models, the shear and transverse strengths were determined to identify the role of the CNT alignment and irradiation-induced crosslinks on junction performance.The 0 orientation model was used to study the effect of crosslinking (and the associated CNT wall damage) on the axial properties when the CNT sheets are pulled along the armchair (along the x-axis) and zigzag (along the y-axis) directions.It is important to note that similar to Patil et al., 18 Pisani et al., 19 Deshpande et al., 20 and Gaikwad et al., 21 experimental validation of the predicted mechanical response is not performed because the relevant experimental characterization met The objective of this research is to determine the effect of irradiation-induced crosslinking on the properties of CNT composites using MD simulation.As the CNTs within CNT yarns and bundles are entangled with each other at different orientations, 17 two extreme orientation cases of CNTs junctions were considered: 0 and 90 , which represent two aligned and perpendicular CNTs, respectively.In this study, crosslinking is dened as the ratio of the number of carbon atoms forming the bonds between the two CNT sheets to the total number of carbon atoms in the overlapped area.For each of the orientation cases, the amount of crosslinking was varied from 0% to 20%.For these models, the shear and transverse strengths were determined to identify the role of the CNT alignment and irradiation-induced crosslinks on junction performance.The 0 orientation model was used to study the effect of crosslinking (and the associated CNT wall damage) on the axial properties when the CNT sheets are pulled along the armchair (along the x-axis) and zigzag (along the y-axis) directions.It is important to note that similar to Patil et al., 18 Pisani et al., 19 Deshpande et al., 20 and Gaikwad et al., 21 experimental validation of the predicted mechanical response is not performed because the relevant experimental characterization methods for this material have not yet been developed and performed, mostly because of the very small length scales involved.

ds for this materia
have not yet been developed and performed, mostly because of the very small length scales involved.


Molecular modeling

The LAMMPS (Large scale Atomic/Molecular Massively Parallel Simulator) soware package 22 was used to perform the MD simulations in this study.The Reactive Force Field (ReaxFF) developed van Duin et al. 23 was used to describe the interatomic forces using the C/H/O/N parameterization of Kowalik et al. 24 ReaxFF is a bond-order force eld, which directly enables bond formation and scission during MD simulations.For ReaxFF, different parameter sets are developed for specic applications.Thus, the accuracy of ReaxFF simulations is highly dependent on the choice of an appropriate parameter set.The parameter set used in this study was originally developed to investigate the chemical reaction processes during carbonization of oxidized polyacrylonitrile and poly(p-phenylene-2,6-benzobisoxazole), and incorporates parameters developed by Srinivasan et al. 25 and Ashraf and van Duin. 26The performance and accuracy of this parameterization was demonstrated by Gaikwad et al. 21for systems containing CNTs

Molecular modeling
The LAMMPS (Large scale Atomic/Molecular Massively Parallel Simulator) soware package 22 was used to perform the MD simulations in this study.The Reactive Force Field (ReaxFF) developed van Duin et al. 23 was used to describe the interatomic forces using the C/H/O/N parameterization of Kowalik et al. 24 ReaxFF is a bond-order force eld, which directly enables bond formation and scission during MD simulations.For ReaxFF, different parameter sets are developed for specic applications.Thus, the accuracy of ReaxFF simulations is highly dependent on the choice of an appropriate parameter set.The parameter set used in this study was originally developed to investigate the chemical reaction processes during carbonization of oxidized polyacrylonitrile and poly(p-phenylene-2,6-benzobisoxazole), and incorporates parameters developed by Srinivasan et al. 25 and Ashraf and van Duin. 26The performance and accuracy of this parameterization was demonstrated by Gaikwad et al. 21for systems containing CNTs and amorphous carbon.The atomistic visualizations provided herein were created using the OVITO soware package. 27

d amorphous
arbon.The atomistic visualizations provided herein were created using the OVITO soware package. 27


CNT sheets

9][30][31] In this study, only the at region is modelled, similar to Patil et al., 18 Pisani et al., 19 Deshpande et al., 20 and Gaikwad et al. 213][34] In this study, each CNT is modelled as two sets of graphene sheets representing the at region of CNTs.The "lattice" command in LAMMPS was used to create the models of the graphene sheets.The lattice parameters for the planar structure of graphene were taken from Gray et al. 35 The xand y-dimensions of the graphene sheet were set to 100 Å and 50 Å, respectively.A total of two CNT sheets (four graphene layers) were modelled, accounting for a total of 7872 atoms.Fig. 1 shows the two models having 0 and 90 orientations between the two CNT sheets.


Crosslinking

The interlayer spacing between graphene sheets is about 3.44 Å, 36 while the length of a single C-C bond is 1.55 Å. 37 Therefore, it is not possible to form a single stable C-C bond between the

CNT sheets
9][30][31] In this study, only the at region is modelled, similar to Patil et al., 18 Pisani et al., 19 Deshpande et al., 20 and Gaikwad et al. 213][34] In this study, each CNT is modelled as two sets of graphene sheets representing the at region of CNTs.The "lattice" command in LAMMPS was used to create the models of the graphene sheets.The lattice parameters for the planar structure of graphene were taken from Gray et al. 35 The xand y-dimensions of the graphene sheet were set to 100 Å and 50 Å, respectively.A total of two CNT sheets (four graphene layers) were modelled, accounting for a total of 7872 atoms.Fig. 1 shows the two models having 0 and 90 orientations between the two CNT sheets.

Crosslinking
The interlayer spacing between graphene sheets is about 3.44 Å, 36 while the length of a single C-C bond is 1.55 Å. 37 Therefore, it is not possible to form a single stable C-C bond between the two graphene layers.Thus, an in-house python script was used to induce the crosslinking within and between the graphene sheets.The following procedure was followed (each step is shown graphically in Fig. 2):

wo graphene l
yers.Thus, an in-house python script was used to induce the crosslinking within and between the graphene sheets.The following procedure was followed (each step is shown graphically in Fig. 2):

Step 1: a carbon atom on the graphene sheet was randomly chosen.

Step 2: the selected carbon atom was displaced from its initial position towards the neighbouring sheet, which resulted in mono-valency or di-v Step 1: a carbon atom on the graphene sheet was randomly chosen.
Step 2: the selected carbon atom was displaced from its initial position towards the neighbouring sheet, which resulted in mono-valency or di-valency defects.This displaced atom is henceforth referred to as the crosslinked atom (C crosslinked ).
lency defects.This displaced atom is henceforth referred to as th crosslinked atom (C crosslinked ).

Step 3: the carbon atom (C top ) above and attached to C crosslinked was displaced in the downward direction by 0.5 Å, and the carbon atom (C bottom ) below and attached to C crosslinked was displaced upwards b Step 3: the carbon atom (C top ) above and attached to C crosslinked was displaced in the downward direction by 0.5 Å, and the carbon atom (C bottom ) below and attached to C crosslinked was displaced upwards by 0.3 Å, which resulted in the formation of a covalent bond chain between the two graphene sheets.Step 4: this process was repeated for each model until the desired crosslink density was achieved.
0.3 Å, which resulted in the formation of a covalent bond chain between the two graphene sheets.Step 4: this process was repeated for each model until the desired crosslink density was achieved.

Aer the formation of crosslinks, the models were equilibrated at room temperature (300 K) at 1 atm pressure using the xed pressure and temperature (NPT) ensemble.The equilibration simulation was run for 500 Aer the formation of crosslinks, the models were equilibrated at room temperature (300 K) at 1 atm pressure using the xed pressure and temperature (NPT) ensemble.The equilibration simulation was run for 500 picoseconds (ps) with a timestep of 1 femtosecond (fs).For both orientation cases, ve crosslinked models having 0, 1, 3, 5, 10 and 20% were created.A total of ve independent models were created for each orientation case and crosslink density to account for statistical deviations in the predicted properties.Representative images of these models are included in the ESI (Fig. S1 and S2 †).The evolution of the chemical bonding of the CNTs with increasing crosslinking is shown in Fig. S3.† icoseconds (ps) with a timestep of 1 femtosecond (fs).For both orientation cases, ve crosslinked models having 0, 1, 3, 5, 10 and 20% were created.A total of ve independent models were created for each orientation case and crosslink density to account for statistical deviations in the predicted properties.Representative images of these models are included in the ESI (Fig. S1 and S2 †).The evolution of the chemical bonding of the CNTs with increasing crosslinking is shown in Fig. S3.†

In general, two different types of covalent bond formations occur during the crosslinking process.Bonds can form between crosslinking atoms and the CNTs (Fig. 3a), and between carbon atoms in a single CNT layer aer a local disruption of the aromatic structure with crosslinking (Fig. 3b).Fig. 4a and  b show the number of crosslinked and interlayer bonds formed in the 0 and 90 orientations, respectively.The data in the gures demonstrate that the bonding between crosslinked atoms was much higher than the interlayer bonding during the crosslinking simulations for both 0 and 90 orientations.


Shear simulation

[21][38][39][40] Pull-out simulations were performed herein on each replicate of the crosslinked models for each orientation case to investigate the interfacial shear strength between the two CNT In general, two different types of covalent bond formations occur during the crosslinking process.Bonds can form between crosslinking atoms and the CNTs (Fig. 3a), and between carbon atoms in a single CNT layer aer a local disruption of the aromatic structure with crosslinking (Fig. 3b).Fig. 4a and  b show the number of crosslinked and interlayer bonds formed in the 0 and 90 orientations, respectively.The data in the gures demonstrate that the bonding between crosslinked atoms was much higher than the interlayer bonding during the crosslinking simulations for both 0 and 90 orientations.

Shear simulation
[21][38][39][40] Pull-out simulations were performed herein on each replicate of the crosslinked models for each orientation case to investigate the interfacial shear strength between the two CNT sheets.The interfacial shear strength was predicted by applying a pulling force on each carbon atom on one CNT sheet (using the "x addforce" LAMMPS command), while the movement of the other CNT sheet was restrained using a spring of stiffness 100 kcal mol −1 Å−2 / Å (using the "x spring" LAMMPS command).The pulling force was incrementally increased every 0.1 fs by 2 Â 10 −6 kcal mol −1 Å−1 .The pull-out simulations were carried out at 300 K and 1 atm using the NPT ensemble for 1 nanosecond (ns).

eets.The interfac
al shear strength was predicted by applying a pulling force on each carbon atom on one CNT sheet (using the "x addforce" LAMMPS command), while the movement of the other CNT sheet was restrained using a spring of stiffness 100 kcal mol −1 Å−2 / Å (using the "x spring" LAMMPS command).The pulling force was incrementally increased every 0.1 fs by 2 Â 10 −6 kcal mol −1 Å−1 .The pull-out simulations were carried out at 300 K and 1 atm using the NPT ensemble for 1 nanosecond (ns).


Transverse tension

To predict the transverse strength between the two CNT sheets, the simulation box was uniaxially deformed in tension along the z-direction, which is the direction transverse to CNT surface.9][20] These simulations were performed on each replicate of the crosslinked models for both orientation ca

Transverse tension
To predict the transverse strength between the two CNT sheets, the simulation box was uniaxially deformed in tension along the z-direction, which is the direction transverse to CNT surface.9][20] These simulations were performed on each replicate of the crosslinked models for both orientation cases at room temperature (300 K) and 1 atm pressure using the NPT ensemble.The simulation box was deformed at a rate of 2 Â 10 8 s −1 and a 200% total strain was applied to capture the complete failure of the interface.The stress-strain response along the zdirection was recorded over the entire strain range.Three metrics were determined from the stress-strain curve.First, the stiffness was determined from the slope of stress/strain response in the initial linear region.Second, the ultimate strength was determined from the maximum stress value achieved during the simulation.Third, the toughness was calculated from the total area under the stress-strain curve.

s at room temperatu
e (300 K) and 1 atm pressure using the NPT ensemble.The simulation box was deformed at a rate of 2 Â 10 8 s −1 and a 200% total strain was applied to capture the complete failure of the interface.The stress-strain response along the zdirection was recorded over the entire strain range.Three metrics were determined from the stress-strain c rve.First, the stiffness was determined from the slope of stress/strain response in the initial linear region.Second, the ultimate strength was determined from the maximum stress value achieved during the simulation.Third, the toughness was calculated from the total area under the stress-strain curve.


Pulling along armchair and zigzag direction

To predict the effect of the crosslinking on the axial properties of CNTs, the simulation boxes were uniaxially deformed in the armchair and zigzag directions of the graphene sheets (Fig. S5 †).These simulations were performed at room temperature (300 K) and pressure (1 atm) using the NPT ensemble.The simulation boxes were deformed at a rate of 2 Â 10 8 s −1 with a total applied strain of 100% to fully capture the failure of each model.These simulations were performed on each replicate of the crosslinked models for the 0 orientation case.For each simulation, the stiffness, ultimate strength, and toughness were determined.


Results

The results of the interfacial shear strength, transverse tension, and axial tension simulations

Pulling along armchair and zigzag direction
To predict the effect of the crosslinking on the axial properties of CNTs, the simulation boxes were uniaxially deformed in the armchair and zigzag directions of the graphene sheets (Fig. S5 †).These simulations were performed at room temperature (300 K) and pressure (1 atm) using the NPT ensemble.The simulation boxes were deformed at a rate of 2 Â 10 8 s −1 with a total applied strain of 100% to fully capture the failure of each model.These simulations were performed on each replicate of the crosslinked models for the 0 orientation case.For each simulation, the stiffness, ultimate strength, and toughness were determined.

Results
The results of the interfacial shear strength, transverse tension, and axial tension simulations are discussed in this section.CNT.Snapshots of a representative 0 orientation system having 1% crosslinks undergoing pull-out is included in the ESI (Fig. S4 †).Fig. 5b shows a representative CNT displacement vs. pull-out force plot for the 90 orientation for each level of crosslinking.A similar behavior is observed in these systems as with the 0 systems, except the force corresponding to the slipping onset is much lower because the overlapping surface area in the 90 orientation is lower than that in the 0 orientation, which results in a lower number of crosslinks between the two CNT sheets.

re discussed in this section.CNT.Snapshots
f a representative 0 orientation system having 1% crosslinks undergoing pull-out is included in the ESI (Fig. S4 †).Fig. 5b shows a representative CNT displacement vs. pull-out force plot for the 90 orientation for each level of crosslinking.A similar behavior is observed in these systems as with the 0 systems, except the force corresponding to the slipping onset is much lower because the overlapping surface area in the 90 orientation is lower than that in the 0 orientation, which results in a lower number of crosslinks between the two CNT sheets.


Interfacial shear strength


Transverse tension

Fig. 6a and b show represent

Transverse tension
Fig. 6a and b show representative stress-strain curves for transverse tension for the 0 and 90 orientation models, respectively.A signicant increase in the toughness of the interfacial regions is observed for increasing levels of crosslinking.Snapshots of a representative 0 orientation model having 0% crosslinks between and within the CNT sheets are shown in Fig. 7a.Fig. 7a shows that as the model is strained in the transverse direction, failure is observed in the region between the two CNT sheets which is dominated by van der Waals interactions.Snapshots of representative 0 orientation models having 1%, 5%, 20% crosslinks between and within the CNT sheets are shown in Fig. 7b-d, respectively.As the crosslinked models are strained in the transverse direction, the formation of sp-hybridized carbon atom chains (Fig. 8) is observed, and the concentration of carbyne chains increases with increases in the number of crosslinks.Carbyne chains are relatively reactive and unstable, 41,42 but can exist on the short time scales of MD simulations. 43ig. 9a shows the stiffness as a function of crosslinking for the 0 orientation.The addition of crosslinks increases the defects in the aromatic structure, which initially disrupts the integrity of the CNT sheets, resulting in a decrease in stiffness up to 5% crosslinking.However, aer 5% crosslinking, a sharp increase in stiffness is observed, which is attributed to the increasing number of covalent bonds between the CNT sheets with increasing crosslinking.

ive stre
s-strain curves for transverse tension for the 0 and 90 orientation models, respectively.A signicant increase in the toughness of the interfacial regions is observed for increasing levels of crosslinking.Snapshots of a representative 0 orientation model having 0% crosslinks between and within the CNT sheets are shown in Fig. 7a.Fig. 7a shows that as the model is strained in the transverse direction, failure is observed in the region between the two CNT sheets which is dominated by van der Waals interactions.Snapshots of representative 0 orientation models having 1%, 5%, 20% crosslinks between and within the CNT sheets are shown in Fig. 7b-d, respectively.As the crosslinked models are strained in the transverse direction, the formation of sp-hybridized carbon atom chains (Fig. 8) is observed, and the concentration of carbyne chains increases with increases in the number of crosslinks.Carbyne chains are relatively reactive and unstable, 41,42 but can exist on the short time scales of MD simulations. 43ig. 9a shows the stiffness as a function of crosslinking for the 0 orientation.The addition of crosslinks increases the defects in the aromatic structure, which initially disrupts the integrity of the CNT sheets, resulting in a decrease in stiffness up to 5% crosslinking.However, aer 5% crosslinking, a sharp increase in stiffness is observed, which is attributed to the increasing number of covalent bonds between the CNT sheets with increasing crosslinking.

For the ultimate strength (Fig. 9b) and toughness (Fig. 9c) of the 0 orientation, an increase is observed immediately aer the addition of crosslinks between and within the two CNT sheets.This increase is attributed to the increasing levels of interfacial load transfer with the addition of chemical crosslinks.

Fig. 10a shows the stiffness as a function of crosslinks for the 90 orientation.The stiffness values remain nearly constant up to 10% crosslinking, followed by an increase at 20% crosslinking.For ultimate strength (Fig. 10b), a near constant trend is observed up to 5% crosslinking, where a signicant increase is observed for increasing crosslinking levels.Fig. 10c shows a linear increase in the toughness as a function of crosslinking, w For the ultimate strength (Fig. 9b) and toughness (Fig. 9c) of the 0 orientation, an increase is observed immediately aer the addition of crosslinks between and within the two CNT sheets.This increase is attributed to the increasing levels of interfacial load transfer with the addition of chemical crosslinks.
Fig. 10a shows the stiffness as a function of crosslinks for the 90 orientation.The stiffness values remain nearly constant up to 10% crosslinking, followed by an increase at 20% crosslinking.For ultimate strength (Fig. 10b), a near constant trend is observed up to 5% crosslinking, where a signicant increase is observed for increasing crosslinking levels.Fig. 10c shows a linear increase in the toughness as a function of crosslinking, which is due to the formation of carbon chains (Fig. 8) formed during transverse tension, which allows a load-bearing feature that persists until failure, resulting in higher energy absorption.respectively.Unlike the transverse tension behavior, decreases in the mechanical performance with increases in crosslinking are observed when the CNT sheets were pulled along both armchair and zigzag directions.Snapshots of the 3% crosslinked model strained along the armchair and zigzag directions are shown in Fig. 12a and b, respectively.As the simulation box   is pulled along the armchair and zigzag directions, the formation of carbon atom chains is observed.The carbon chains are formed between segments of the same sheet and different sheets.

carbon chains (Fig
8) formed during transverse tension, which allows a load-bearing feature that persists until failure, resulting in higher energy absorption.respectively.Unlike the transverse tension behavior, decreases in the mechanical performance with increases in crosslinking are observed when the CNT sheets were pulled along both armchair and zigzag directions.Snapshots of the 3% crosslinked model strained along the armchair and zigzag directions are shown in Fig. 12a and b, respectively.As the simulation box   is pulled along the armchair and zigzag directions, the formation of carbon atom chains is observed.The carbon chains are formed between segments of the same sheet and different sheets.


Tension along armchair and zigzag directions

Fig. 13a-c show the stiffness, ultimate strength, and toughness, respectively, as a function of crosslinking for CNT sheets subjected to tensile loading along the armchair and zigzag directions.A decrease in all three properties is observed for increasing crosslinking.As the amount of crosslinking increases, the damage within the CNT sheets also increases.Because the initiation point of failure is located at a crosslinking site (Fig. S6 †), the failure of the structure occurs at a much lower strain value relative to the model having 0% crosslinking.From Fig. 13c it is evident that higher values of toughness are observed when the sheets are pulled along the zigzag direction.This is because of the higher number of carbon chains formed during extended tensile deformation along the zigzag direction (Fig. 12), which requires more applied strain energy for failure.


Conclusions

The results of this study clearly show that irradiation-induced crosslinking has a signicant impact on the mechanical performance of CNT junctions in CNT yarn materials.For both 0 and 90 CNT orientations subjected to transverse tension, increasing levels of crosslinking result in increasing amounts of CNT interfacial toughness, stiffness, and strength.The formation of covalent bonds between CNTs during the irradiation process provides for effective interfacial load transfer.Once interfacial failure initiates, the primary toughening mechanisms for the crosslinked systems is the formation of sphybridized carbon chains that continue to carry load until nal interfacial rupture.

For tension applied along armchair and zigzag directions of CNTs, inc

Tension along armchair and zigzag directions
Fig. 13a-c show the stiffness, ultimate strength, and toughness, respectively, as a function of crosslinking for CNT sheets subjected to tensile loading along the armchair and zigzag directions.A decrease in all three properties is observed for increasing crosslinking.As the amount of crosslinking increases, the damage within the CNT sheets also increases.Because the initiation point of failure is located at a crosslinking site (Fig. S6 †), the failure of the structure occurs at a much lower strain value relative to the model having 0% crosslinking.From Fig. 13c it is evident that higher values of toughness are observed when the sheets are pulled along the zigzag direction.This is because of the higher number of carbon chains formed during extended tensile deformation along the zigzag direction (Fig. 12), which requires more applied strain energy for failure.

Conclusions
The results of this study clearly show that irradiation-induced crosslinking has a signicant impact on the mechanical performance of CNT junctions in CNT yarn materials.For both 0 and 90 CNT orientations subjected to transverse tension, increasing levels of crosslinking result in increasing amounts of CNT interfacial toughness, stiffness, and strength.The formation of covalent bonds between CNTs during the irradiation process provides for effective interfacial load transfer.Once interfacial failure initiates, the primary toughening mechanisms for the crosslinked systems is the formation of sphybridized carbon chains that continue to carry load until nal interfacial rupture.
For tension applied along armchair and zigzag directions of CNTs, increasing levels of crosslinking result in decreasing values of modulus, strength, and toughness.These decreases are a result of the damage that is induced in the aromatic structure of the CNTs when crosslinked.Similar to the behavior in transverse tension, the primary mechanisms that provides toughness is the formation of carbon chains along the direction of applied tension, especially along the zigzag direction.

ng values of
modulus, strength, and toughness.These decreases are a result of the damage that is induced in the aromatic structure of the CNTs when crosslinked.Similar to the behavior in transverse tension, the primary mechanisms that provides toughness is the formation of carbon chains along the direction of applied tension, especially along the zigzag direction.

Based on these results, it is clear that irradiation-induced crosslinking is benecial in composite systems in which interfacial load transfer between CNTs is of primary importance.This is especially relevant for CNT yarns, which contain substantial levels of CNTs which can easily slide past each other with localized shear forces.If Based on these results, it is clear that irradiation-induced crosslinking is benecial in composite systems in which interfacial load transfer between CNTs is of primary importance.This is especially relevant for CNT yarns, which contain substantial levels of CNTs which can easily slide past each other with localized shear forces.If increased levels of shearing resistance between CNTs can be induced, then improved load transfer is expected, which can improve the overall performance of CNT yarns, even though the individual CNTs may lose some mechanical integrity with crosslinking.It is expected that these conclusions could also apply to other types of CNT-based and graphene-based composites, as the chemical structure of the carbon is similar in these aromatic systems.
increased levels of shearing resistance between CNTs can be induced, then improved load transfer is expected, which can improve the overall performance of CNT yarns, even though the individual CNTs may lose some mechanical integrity with crosslinking.It is expected that these conclusions could also apply to other types of CNT-based and graphene-based composites, as the chemical structure of the carbon is similar in these aromatic systems.

Fig. 1
1
Fig. 1 (a) 0 orientation model of

Fig. 1
Fig. 1 (a) 0 orientation model of two flCNTs and (b) 90 orientation model.The dark and light grey colors distinguish the two flCNT sheets.
wo flCNTs and (b) 90 orientation model.The dark and light grey colors distinguish the two flCNT sheets.


Fig. 2
2
Fig. 2 Steps for building crosslinked models: Step 1random selection of carbon atoms (blue color), Step 2displacement of selected atoms from their initial position resulting in di-vacancy (blue color) and mono vacancy formation (red color), Step 3the displaced carbon atom forms a crosslink between the two graphene sheets (blue color).


Fig. 3
3
Fig. 3 Bonds between (a) crosslinked atoms and (b) interlayer atoms.The blue-colored atoms are the crosslink atoms, while the grey-and black-colored atoms are the flCNT atoms.


Fig. 5a shows

Fig.5ashows a representative CNT shear displacement vs. pull-out force plot for the 0 orientation for each level of crosslinking

Fig. 2
Fig. 2 Steps for building crosslinked models: Step 1random selection of carbon atoms (blue color), Step 2displacement of selected atoms from their initial position resulting in di-vacancy (blue color) and mono vacancy formation (red color), Step 3the displaced carbon atom forms a crosslink between the two graphene sheets (blue color).

Fig. 3
Fig. 3 Bonds between (a) crosslinked atoms and (b) interlayer atoms.The blue-colored atoms are the crosslink atoms, while the grey-and black-colored atoms are the flCNT atoms.

Fig. 5a shows
Fig.5ashows a representative CNT shear displacement vs. pull-out force plot for the 0 orientation for each level of crosslinking.Three distinct regions are observed in the displacement prole: initial sticking, slipping onset, and smooth sliding.The sticking region corresponds to the resistance to shearing caused by long-range van der Waals forces and CNT crosslinks.The onset of slipping corresponds to the scission of the crosslinks, each of which occurs in quick succession aer the failure of the rst crosslink.In the smooth sliding region, only the van der Waals forces of adjacent CNTs act on the atoms, thus there is little resistance to pull-out of the

hree distinct regions
are observed in the displacement prole: initial sticking, slipping onset, and smooth sliding.The sticking region corresponds to the resistance to shearing caused by long-range van der Waals forces and CNT crosslinks.The onset of slipping corresponds to the scission of the crosslinks, each of which occurs in quick succession aer the failure of the rst crosslink

n the smooth sliding r
gion, only the van der Waals forces

Fig. 4
Fig. 4 Number of bonds as a function of crosslinks for (a) 0 orientation, (b) 90 orientation.The uncertainty represents the standard deviation between the independently-built replicate models.

Fig. 11a and
Fig. 11a and b show representative stress-strain curves for tension loading along the armchair and zigzag directions,

Fig. 8
Fig. 8 Snapshot of carbon chain formation while undergoing transverse tension.

Fig. 9
Fig. 9 Mechanical properties as a function of crosslinks for the 0 orientation in terms of (a) stiffness, (b) ultimate strength, (c) toughness.Each data point represents the average of five MD replicates and the vertical error bars represent the standard deviation.

Fig. 10
Fig. 10 Mechanical properties as a function of crosslinks for the 90 orientation in terms of (a) stiffness, (b) ultimate strength, (c) toughness.Each data point represents the average of five MD replicates and the vertical error bars represent the standard deviation.

Fig. 11
Fig. 11 Representative stress-strain plots during tension loading along the (a) armchair and (b) zigzag directions.

Fig. 12
Fig. 12 Snapshots of the 3% crosslinked model undergoing tension along the (a) armchair and (b) zigzag directions.

Fig. 13
Fig. 13 Mechanical properties as a function of crosslinking for tensile deformation in armchair and zigzag directions for (a) stiffness, (b) ultimate strength, (c) toughness.Each data point represents the average of five MD replicates and the vertical error bars represent standard deviation.