Mesoscopic friction and network morphology control the mechanics and processing of carbon nanotube yarns

Accepted Manuscript Mesoscopic friction and network morphology control the mechanics and processing of carbon nanotube yarns Yuezhou Wang, Hao Xu, Grigorii Drozdov, Traian Dumitrică PII:

S0008-6223(18)30605-5

DOI:

10.1016/j.carbon.2018.06.043

Reference:

CARBON 13248

To appear in:

Carbon

Received Date: 10 May 2018 Revised Date:

14 June 2018

Accepted Date: 17 June 2018

Please cite this article as: Y. Wang, H. Xu, G. Drozdov, T. Dumitrică, Mesoscopic friction and network morphology control the mechanics and processing of carbon nanotube yarns, Carbon (2018), doi: 10.1016/j.carbon.2018.06.043. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Mesoscopic friction and network morphology control the mechanics and processing of carbon nanotube yarns

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Department of Mechanical Engineering, University of Minnesota, Twin Cities, MN 5545 Integrated Engineering, Minnesota State University, Mankato, MN 56001

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Department of Aerospace Engineering and Mechanics, University of Minnesota, Twin Cities, MN 55455

Scientific Computing Program, University of Minnesota, Twin Cities, MN 55455,

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Corresponding Author

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*E-mail: [email protected].

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Yuezhou Wang,1,2 Hao Xu,3 Grigorii Drozdov,4 and Traian Dumitrică1,3,4,*

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Carbon nanotube (CNT) yarns are nanomaterials of interest for diverse applications. To bring fundamental understanding into the yarn formation process, we perform mesoscopic scale distinct element method (mDEM) simulations for the stretching of CNT networks. The

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parameters used by mDEM, including the mesoscale friction, are based on full atomistic results. By bridging across the atomistic and mesoscopic length scales, our model predicts accurately the mechanical response of the network over a large deformation range. At small and moderate

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deformations, the microstructural evolution is dominated by zipping relaxations directed along the applied strain direction. At larger deformations, the occurrence of an energetic elasticity

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regime promotes yarn densification, by lowering CNT waviness and elimination of squashed pores. Next, by varying the mesoscopic dissipation as well as the network structure, we reveal that the mesoscale friction and film morphology are key factors for the yarn formation: While lack of friction compromises the strain-induced alignment process, phononic and polymeric

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friction promote CNT alignment by enabling load transfer and directed zipping relaxations,

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especially in networks containing long and entangled individual CNTs. Yarns drawn from

friction.

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1. Introduction

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cellular networks are shown instead to maintain high porosity, even with enhanced polymeric

Carbon nanotubes (CNTs) [1] have outstanding physical properties including very high elastic modulus and tensile strength [2], and high electrical and thermal conductivities [3-5]. Commercial methods produce a buckypaper sooth-like CNT material containing also impurities in the form of catalyst nanoparticles [6]. A critical problem hindering applications [7, 8] is the processing of the as produced material into yarns and sheets comprising highly aligned CNTs so that the outstanding properties of individual CNTs can be more effectively utilized.

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Here we focus on pristine (no impurities) CNT networks, which present a porous structure with CNTs aggregated by intertube van der Waals (vdW) attractions.

It is known that both

entanglement and adhesion-driven bundling mechanisms play important roles in forming

, which describes the importance of CNT bending stiffness

. On one hand, when

< 40 nm, the dominant adhesion leads to

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vdW adhesion energy (

) relative to the

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is set by

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these network structure [9, 10]. Across CNT types (diameter, chirality), a relevant length scale

a well entangled network. On the other hand, when

> 40 nm the dominating bending strain

energy favors a network structure comprising bundled CNTs. For the (10,10) CNTs considered

here,

=41.5 nm, which is just above the critical 40 nm length. This suggests that the low-

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energy film structure should exhibit a trend for CNT bundling over ring/racket-like

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entanglement [9-12]. For a given CNT type, such as (10,10) CNTs, the length of individual

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CNTs also influences the network microstructure. When (10,10) CNTs are less than 120 nm, the contact length between different CNTs is limited and vdW energy cannot compensate the

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bending energy penalty [10]. As a result, the network disintegrates into separate bundles. When (10,10) CNTs are above 120 nm in length, the bending energy can be overcome by inter-tube adhesion to form low-energy entangled cellular networks. Nevertheless, the (10,10) CNT of the cellular network are still sliding toward a disintegrated network comprising randomly-oriented bundles [10]. Thus, dynamic friction effects are important for “delaying” the cellular network disintegration.

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Continuous yarns, composed of aligned CNTs stacked together, can be drawn out from CNT forests (a system with low degree of entanglement) [13, 14], or can be formed by stretching CNT ribbons cut from buckypaper formed by sticky CNTs thinly coated with polymeric compounds

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[15]. Twist-based spinning processes were also developed to increase the density of the CNT yarns and improve their mechanical properties [14-18]. Significant insights into the straininduced alignment of stretched networks comprising multi-walled CNTs have been obtained

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from in situ X-ray [19] and scanning electron microscopy [20] characterizations. These studies identified important load-induced changes at the microstructural-level, including elongation to

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reduce CNT waviness, de-bundling, self-assembly into large bundles, and sliding friction, and have revealed the importance of the polymeric layers in promoting the strain-induced alignment. Nevertheless, the mesoscale features that most decisively impact the transition from the rather stochastic network structure to the bundled structure comprising highly aligned CNTs are not

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well understood. In order to gain a better understanding of this process, we simulate the stretching of

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a collection of various networks consisting of several hundred CNTs with the coarse grained (CG) mesoscopic distinct element method (mDEM) [21, 22].

In the pursuit of engineering high quality

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yarns comprising highly aligned CNTs and reduced porosity, we explore by mesoscale simulations the impact of CNT length, friction, entanglement and bundling, and identify the significant

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contributing factors to the yarn formation. 2. Models and Methods

A major challenge for modeling is to bridge the gap between the mechanical properties of the individual CNT and the collective response of a network of such CNTs. In the area of semiflexible polymers, athermal mesoscale models have been developed in order to address this challenge [23, 24]. Although CNTs are often idealized as cylindrical beams [25], and the experimental mechanics of

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buckypaper suggests temperature invariant behavior [26], athermal modeling of CNT networks is scarce.

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mDEM is an athermal model in which the CNT buckypaper is modeled by as a network of elastic filaments interacting by long ranged van der Waals (vdW) interactions. Recently, we have informed from full atomistic scale calculations our mDEM contact models to reproduce the elasticity of individual CNTs and the vdW interactions acting between CNTs. In order to regain the main

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deformation stages of the CNT buckypapers observed in experiment, we finalize the bridging of the

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two length scales by incorporating into mDEM the dissipation processes associated with the damping of the relative motion of aligned (i.e., nanofriction) and crossed CNTs, as obtained from atomistic scale simulations.

CG molecular dynamics models, such as the simple bead-and-spring models appropriated from

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polymer physics, are widely used for studying the mechanical properties of CNT systems, and these

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models have been recently used for studying the stability and mechanical behavior of buckypaper films [9, 27, 28]. While these CG models as well as the more advanced ones, like shape-based

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mesoscopic dynamics [10], recognized that sliding friction and zipping are important microstructural processes involving individual CNTs, training these key dissipative processes to

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the underlying atomistic representation has not been yet attempted. In fact, the simple bead-and spring representation of CNTs virtually removes the dynamical sliding friction of CNTs (see SI – Figure S1). Here we show that changes in mesoscopic dissipation can lead to significant differences in the film microstructure and its mechanical behavior under large stretching. Thus, our results point out to the need of fully training the mesoscopic models beyond elasticity and vdW interactions in order to perform multiscale predictions of the mechanical response.

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2.1. The Mesoscopic Distinct Element Method (mDEM) Ideally, one would like to investigate the CNT network mechanics with all-atom simulations [29, 30]. Since such tretament is computationally prohibitive for the systems at hand, we are required

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to explore the yarn formation with mesoscale-level simulations [31-33], where the atomistic degrees of freedom are completely eliminated. In order to transfer the essential nanomechanics to the mesoscale, our CG model is informed by accurate atomistic-level input. Simulations are

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performed with the recently proposed mDEM [21, 22] for CNTs, where the CNT network is represented by a collection of cylindrical elements interacting via bonded, non-bonded, and

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dissipative contacts.

mDEM is a CG representation of the system in question as each element generally represents a segment of the detailed CNT containing many carbon atoms. Specifically, we have discretized a (10,10) single-walled CNT such that each cylindrical element with length 1.36 nm and radius

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0.68 nm, and thickness 0.335 nm represents 220 carbon atoms. These mesoscopic elements are

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tracked in the Lagrangian frame. In the PFC3D implementation [34], they are evolved

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deterministically in time as rigid bodies with a damped scheme based on a velocity Verlet algorithm for translations and a fourth-order Runge–Kutta for rotations. The time step used here

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is 30 fs.

Parallel-bond contacts were trained [21] to capture the intra-tube covalent interactions responsible for the local linear elasticity of individual CNTs. The cylindrical distinct elements are coupled by parallel-bond contact, which introduce normal and shear forces (Fn and Fs) and moments (Mn and Ms) to resist relative displacements and rotations. The chain of calibrated parallel-bonded elements describes the individual CNT as a Euler–Bernoulli beam. Mesoscopic elements located on two different CNTs may interact via vdW and viscous contacts. The vdW

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contact has been developed by us via a procedure that involves the integration of the atomistic vdW interactions between two CNTs [21]. Our vdW contacts capture the general case when two finite size CNTs are misaligned and crossed. Unlike isotropic potentials [9, 16, 27], our

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anisotropic vdW potential is free of “corrugated” spurious effects [32], which could cause artificial load transfer between CNTs. Thus, in mDEM, misaligned (shifted) parallel CNTs will undergo smooth sliding under the action of mesoscopic vdW forces. Similarly, crossed CNTs

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will be zipping under the action of the long-ranged vdW forces and aligning moments. Reference

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[21] gives the explicit form for the mesoscopic vdW forces and moments used here.

2.2 Bridging across length scales to capture dissipation effects

The athermal model overviewed above is augmented here to capture the dissipative atomistic scale processes associated with relaxation of crossed and misaligned CNT. mDEM presents two

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channels for energy dissipation: a viscous damping and a local damping [21, 22]. The effective

the constitutive equation

(M),

is the friction force,

the relative velocity of the distinct elements in vdW

is the linear viscous coefficient. Local damping adds forces (F) and moments

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contact, and

. The viscous contacts act simultaneously with the vdW

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contacts. Here

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dissipative force acting between two aligned CNTs is captured by dashpot viscous contacts with

and

, where 𝑭 and 𝑴 are the unbalanced

force and moment, respectively, while 𝒗 and 𝝎 are the translational and rotational velocities of an element, respectively.  is the local damping parameter, which is introduced in DEM [34] with the sole goal of stabilizing the numerical time integration. We discuss next classical molecular dynamics (MD) simulations performed with the goal of informing these two dissipative channels.

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2.2.1 Molecular dynamics simulations

MD simulations were performed with LAMMPS [35] and rely on the Kolmogorov–Crespi vdW

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potentials [36] among inter-tube CNT atoms and standard AIREBO potentials [37] among intratube CNT atoms. The use of the KC potential is particularly important for characterizing the sliding friction since this potential captures the registry-dependent corrugation between armchair

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cylindrical CNTs [38].

Figure 1. (a) MD setup used to compute dynamical friction between two aligned (10,10) CNTs.

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The desired sliding velocity is imposed to the one unit cell “ring” and one distinct element (red) belonging to the upper CNT. One unit cell “ring” and one distinct element (blue) belonging to (per unit length) vs.

. MD data (black circles) shows smooth

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the lower CNT is at rest. (b)

sliding. (c) mDEM setup used to calibrate mesoscale friction. The purple lines indicate the vdW

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contacts between distinct elements located on the two CNTs. First, we focus on characterizing the nanofriction developed between two (10,10) CNTs in vdW contact. The MD setup consists of two aligned (10,10) CNTs each 13.6 nm in length placed under periodic boundary conditions (PBC), Figure 1(a). Because the periodicity is kept large in the transversal directions, the two (10,10) CNTs have only one surface in vdW contact.

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After carrying out initial relaxations, a one-unit ring belonging to bottom CNT is kept fixed to Velocity

controlled sliding is realized by

imposing a desired

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prevent the motion of its center of mass.

along the CNT axis to a one-unit ring belonging to top CNT. Note that

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because of the imposed PBC, no new vdW surfaces are created during sliding. All unconstrained atoms are evolved in time in the microcanonical ensemble corresponding to an average temperature of 300 K. The friction force

measurements are carefully done after 100

ps time, in order to allow for equilibration after the initial acceleration period. The measured

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is the net vdW force exerted onto the upper CNT projected onto its axis, averaged over the

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subsequent 500 to 3,000 ps. During averaging, the instantaneous temperature in increases only up to 350 K. We considered

as low as 10 m/s in order to approach the regime of the

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conventional pulling velocity exerted on materials.

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Figure 2. (a) MD setup used to compute the relaxation time of two crossed (10,10) CNTs each 30 nm in length. (b) mDEM setup used to calibrate the crossing relaxation at the mesoscale. The purple lines indicate the vdW contacts between distinct elements. Our simulations summarized in Fig. 1b uncover a

dependent nanofriction, which differs from

the velocity-independent friction of the macroscopic scale. We expect that the MD-computed room-temperature

will decrease with increasing temperature [40]. Nanofriction also depends

on the contact interface area [39, 40]. In this respect, we find that

between cylindrical (10,10)

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CNTs (for example than

nN/nm at

=10 m/s) is an order of magnitude smaller

computed for collapsed (35,35) CNTs (for example

nN/nm at

m/s) [40], which present a much larger contact area. We also note that the

=10

computed here is

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two orders of magnitude larger than the room temperature dynamical friction generated by beadand-spring CG representation of (10,10) CNTs, Figure S1. We expect that the MD-computed will decrease with increasing temperature [40].

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room-temperature

Second, we focus on MD simulations aimed at determining the relaxation timescales for the Since in the network environment, an individual CNT crosses

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spontaneous zipping process.

with a number of other CNTs, the zipping relaxation occurs rather locally, over small CNT portions. Thus, our simulations focused on zipping of short CNTs. Figure 2a shows the MD setup in which two (10,10) CNTs, first equilibrated at room temperature, are placed in a crossed

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configuration. At the crossing point, the minimal wall-to-wall distance is 0.5 nm [21]. Due to the

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long-range vdW inter-tube forces, the two CNT align spontaneously with a coherent motion under velocity Verlet dynamics, forming the bundle shown at the bottom. The measured

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zipping relaxation times function of the initial crossing angle are recorded in Table 1.

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Crossing Angle

MD

Zipping time (ps) mDEM

=0.12 (pN s/m)

mDEM

30o

50

55

40

45o

140

144

118

60o

220

216

180

=0

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Table 1. Computed zipping relaxation time of two crossed (10,10) CNTs each 30 nm in length.

.

In the mDEM simulation results of the last two columns, we selected 2.2.2 MDEM calibration

and  parameters of the mDEM is based on the atomistic level behavior

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Calibration of

obtained above. Since local damping produces a negligible dynamic nanofriction [21], we first to the MD data and next adjust  to reproduce the zipping relaxation times of crossed

train

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CNTs.

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Figure 1c shows the parallel mDEM realization of the sliding simulation setup, which comprises two CNTs each represented by 10 mesoscopic elements. The system is placed under PBC, and velocity-controlled sliding is imposed in the same manner as in MD. mDEM simulations were performed under different

values. As it can be seen in Figure 1c, the

=0.12 pN s/m. Figure 1c also confirms that the mesoscale friction force is practically

vanishing when

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with

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dependent room temperature phononic friction revealed by MD is best matched in mDEM

. This result insures that the numerical damping plays a negligible role in

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the mesoscopic friction. At the same time, this result demonstrates that accounting for vdW

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adhesion alone is not sufficient to capture the dynamical friction at the mesoscale.

In Table 1, we see that the numerical damping parameter relaxation times with a undamped (

matches the MD zipping

ps precision. Due to significantly reduced degrees of freedom, the

) simulations leads to relaxation times shorter than in MD, Table 1 last

column.

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3. Results and discussion 3.1 Mechanical behavior under tension leading to yarn formation 3.1.1 MDEM simulations of spontaneous film formation

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Figure 3a displays the characteristics of a mDEM network which was directly relaxed under the influence of the mesoscopic contact interactions. The shown film was constructed from 500 (10,10) CNTs, each 950 nm in length. The network has a density of 0.14 g/cm3 and a porosity of

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83.5 %. To arrive at this structure, we computer generated a random network of straight (strain free) CNTs, which was evolved freely for 6 ns. The first nanoseconds are dominated by the

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zipping relaxation of CNT portions, which act to increase the vdW cohesive energy of the network at the expense of increasing the bending energy, Figure 3b. After 2 ns, we find that the energy variations slow down significantly, and that the network structure is practically equilibrated at around 6 ns. We note that the zipping relaxation leads to formation of local

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aggregates of several CNTs, which are separated by pores. The relaxed network can be viewed

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as a collection of wavy CNTs, which present larger curvatures around the network pores. We note that the pore dimensions of the relaxed network, shown in Fig. 3c, are in good agreement

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with those of the ultrathin films prepared through the vacuum filtration of aqueous CNT solutions [41]. Stabilizing the structure by inserting nanoparticles in order to inhibit zipping has

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been recently proposed [42-44].

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Figure 3. (a) mDEM-simulated CNT network, measuring 1000 nm x 1000 nm x 11 nm in size, after 6 ns relaxation. (b) Bending and vdW energy during the network relaxation process. (c) Pore size distribution after 6 ns relaxation. The units for

are pN s/m.

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To illustrate the importance of dissipation, Figures 3b and b also display a comparison with the

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characteristics of same network relaxed under

=0. As expected, in the purely athermal model

the zipping relaxation is accelerated, leading to a larger cohesion, increased bending, and larger

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pore sizes. This means that the network evolves faster toward a cellular network state, which is

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further susceptible to disintegrate into randomly-oriented bundles. 3.1.2 Pre-equilibrated network with 950 nm long CNTs subjected to uniaxial tensile load We have further conducted simulations of the mDEM-represented networks to uniaxial tensile loadings. As in our previous simulations [42-44], two thin layers of distinct elements at the left and right edges of a film were designated as grips. Displacement-controlled loading was enabled by prescribing both grips to accelerate from 0 to the given horizontal velocity during 0.6 ns. This acceleration period is used to reduce the undesired dynamic response, which is significant in the

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case of instantaneous acceleration of the grips. The grip elements are allowed to evolve in the transversal direction. In a series of simulations, the network sample was elongated at the over the 0%-to-150% strain (

range.

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constant strain rate of

The stretched network undergoes significant restructuring, with the formation of a central yarn comprising aligned CNTs, Figure 4. To understand this remarkable process, Figure 5 shows the

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calculated stress-strain curve as well as the evolution of the network energy composition, and number of aligned distinct element pairs during stretching. In Figure 5a, the flow stress was

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derived from the unbalanced force on the grip elements. Note that this quantity doesn’t account for the transverse shrinking effect in the cross-sectional area. In computing the number of aligned distinct element pairs shown in Figure 5c two elements in close vdW contact (within a 1.7 nm center-to-center distance) were considered aligned when their crossing angle is less than 10 deg. The evolution of this number will serve as an indicator for the bundling process as well

networks [45-47].

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as a proxi for the evolution of the mechanical, thermal, and electrical properties of CNT

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The evolution of the sample shape and regimes revealed by our simulations are in good qualitative agreement with the experimental tensile tests on neat buckypapers [20]. Specifically,

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our stress-strain and strain energy curves exhibit distinct variations, which indicate four contiguous regimes: (i) elastic, for 30%

< 3%, (ii) softening, for 3%

< 60%, and (iv) softening and failure, for

< 30%, (iii) stiffening, for

> 60%. We discuss next the underlying

distinct microstructural changes occurring in these regimes. As a common feature of these regimes, we note that the vdW energy gain and degree of bundling are increasing. Additionally,

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the parallel contact bonds are permanently stretched, Figure 5b, suggesting a good load transfer throughout deformation. The linear elastic stretching (regime i), visible in Figure 5a and analyzed in detail in our previous

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work [42], presents a Young’s modulus of 8.6 GPa. The lowering of the vdW energy of Figure 5b and the increase in number of aligned pairs of Figure 5c, indicate that the initial elastic ~3%.

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deformation is limited by the activation of the zipping relaxation, which starts just above

As stretching progresses (regime ii), the network softens significantly. The behavior can be seen

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in the slope changes presented by the stress-strain and stretching energy curves of Figure 5a and 5b, respectively. At the microstructure level, the local bundling and the pore sizes are increasing. Pores undergo squashing, especially in the central region of the network, under the transverse contraction caused by the Poisson’s effect and the zipping relaxation directed by the strain direction. In Figure 4a, the right callout indicates that the largest bending energy is stored into

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the parallel bonds located at the non-flattened side of the pores. Thus, we conjuncture that a large

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part of the bending energy increase of Figure 5b can be attributed to pore squashing. We note

[20].

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that the “neck” developed in the central region of the film is in agreement with experimentation

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The occurrence of network hardening [20] (regime iii) is intriguing, considering the mDEM linear elastic representation of CNTs. The underlying mechanism is the energetic elasticity of wavy CNTs, an effect visible in the evolution of the stretching energy, Figure 5b. Energetic elasticity is enabled by the increase in entanglement under pore squashing. We also note that regime iii is important for yarn formation as the number of aligned pairs increases significantly, Figure 5c. This increase is the result of straightening up selected portions of wavy CNTs, an effect that promotes bundling and small pore elimination. Note that the torsional deformation

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modes of individual CNTs, which are neglected in the standard bead and spring CG representations of CNTs, are captured by the parallel-bond contacts [17]. This is important for insuring the robustness of our result because torsion and shear deformation were previously

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reported to lead to significantly more complaint CNT networks with significant waviness [48-

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a.

Figure 4. The CNT network of Figure 3 under (a)

=30%, (b)

=75%, and (c)

=150%. Color

gives the magnitude of the bending moments stored by the parallel bonds. The callouts detail the structure around selected pores (a and b) and yarn packing (c).

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Figure 5. (a) Engineering stress, (b) energy, and (c) number of aligned distinct element pairs, vs.

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. The shadings mark the four regimes (i-iv) occurring during stretching the network of Figure

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3.

Figure 6. Two CNTs during horizontal network stretching, showing the removal of waviness. values are indicated above each CNT. Color code shows the bending moment magnitude, with

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the scale of Figure 4. The high curvature portions are coupled with the squashed pores of the network. Above

=60% (regime iv), the locking of the CNTs provided by the entanglement can no longer

sustain the load transfer. The network begins its final softening and failure. At this deformation stage, the stretched CNTs begin to straighten their severely bent portions located around larger pores, Figure 6. The signature of disentanglement is visible in the bending energy drop, Figure 5b.

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The

=75% network depicted in Figure 4b, where the ultimate stress of 0.68 GPa is reached,

conveys the remarkable microstructural changes that occurred up to this point. To arrive here, the earlier “neck” develops into a central yarn 150 nm in width, comprising highly aligned bundles

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with 10 to 20 CNTs each, separated by pores of nm widths. The CNT bundling and the yarn density have increased significantly in the middle part of the network. This is because many of the smaller pores closed when bent portions of CNTs were eliminated in regime iii. The

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remaining pore defects come from the larger pores of the original network, like the pores III and IV, which underwent significant squeezing to nm widths. We note that only the large pores

Figure 5c shows that the

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located in the vicinity of the grip elements, such as I and II, are preserving their shape. Overall, =75% network stores significant bending, about 50% more than the

initial network.

=75%, the dominance of elastic deformation is substituted by inter-tube CNT sliding. It

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further leads to the thinning of the bundle, Figure 4c, and increase in packing density. The disentanglement process continues, and more pores, like III and IV, are eliminated. To give a

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sense for this process, Figure 6 shows the evolution of two CNTs extracted from the network structure (away from the edges) showing high curvature elimination. In the network, this effect

of the

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lead to disentanglement and pore closing. During further film stretching, the central cross section =150% network (Figure 4c) shows organization into three main aligned bundles, each

containing about 30 CNTs, separated by nm-size pores. As deformation continues, the network will eventually fail by smooth sliding, i.e., when aligned CNTs lose their inter-tube binding [22, 42]. The tensile strength of such yarn could be enhanced for example by CNT crosslinking [44].

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3.2 Parametric study of the yarn formation Having identified the evolution of the stochastic network subjected to large uniaxial deformations, we now explore the parameter design space, which consists of the magnitude of

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the mesoscale friction, sample shape, CNT length, entanglement, and high degree of CNT bundling. After first confirming the robustness of the yarn formation process by stretching of a ribbon network, we are required to consider a smaller size network to gain a reasonable

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computational efficiency.

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3.2.1 Pre-equilibrated ribbon network of 814 nm CNTs under uniaxial tensile load We have next probed the stretching response of a ribbon network with 2000 nm x 500 nm x 11 nm dimensions. The ribbon contains 800 (10,10) CNTs, and was cut out of a buckypaper containing CNTs 814 nm in length. The density is 0.19 g/cm3. The ribbon structure after 6 ps relaxation is shown in Figure 7a. Two sets of mechanical simulations consider on one hand a =0) and, on the other hand, a model with enhanced,

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purely athermal model (i.e.,

=0.36 pN

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s/m, friction. For the latter case, the three times larger than the phononic friction was selected to

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explore the trend when dissipation is enhanced by the presence of polymeric layers between CNTs [15, 20]. Figure 7. (a) mDEM relaxed CNT ribbon, measuring 2000 nm x 500 nm x 11 nm in size. (b) =30 % ribbon. The double arrow indicates the

(i.e.,

=0). (c)

=30 % (top) and

direction. Friction was not accounted for

=90% (bottom) ribbon. Here,

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The

=0.36 pN s/m. Color reflects

the magnitude of the normal force stored by the parallel bonds. The callouts detail the yarn

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packing.

The differences in the ribbon network morphologies shown in Figure 7a and b, and the stress-

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strain curves of Figure 8a highlight the key role of mesoscopic friction. Both networks can sustain the short-lasting elastic deformation, where the Young’s modulus measures 6.6 GPa. However, the friction-free network fails shortly afterwards by pulling out of the network the gripped CNTs. The magnitude of the stretching force at each contact bond displayed in Figure =30%. The load “penetration” distance of about 500 nm on

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7b indicates poor load transfer at

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each side leaves intact the central section, which lacks the characteristic necking observed in experiment [20]. It follows that accounting for mesoscale friction (of phononic or polymer

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origin) is critical for establishing the load transfer through ribbon, which in turn triggers the

deformation regime ii.

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Figure 8. (a) Engineering stress, (b) energy, and (c) number of aligned distinct element pairs, vs.

. The shadings mark the four contiguous regimes (i-iv) occurring during the stretching of

the pre-equilibrated CNT ribbon of Figure 7a. The units for

are pN s/m.

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As it can be inferred from Figures 7c and 8, the deformation of the ribbon with enhanced friction follows the deformation regimes identified in Section 3.1. The formation of the yarn is significantly accelerated by the faster zipping relaxation of the nearly-transversal oriented CNTs,

At the end of the first softening regime, the

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which by construction are expected to be shorter than the 814 nm in length nearly-axial CNTs. =30 % ribbon presents an extended neck. As it can

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be seen in the shown cross-section, the yarn contains many bundles, each containing only a few CNTs.

The strain hardening regime follows. Reflecting the increase in nanofriction, the stiffening presents a modulus of 1.2 GPa, which is slightly larger than the 0.9 GPa measured in Figure 5a.

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As it can be seen in the side and cross sectional views at

=90%, the packing and density of the

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yarn are significantly enhanced with respect to the isotropic network, Figure 4c.

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3.2.2 Pre-equilibrated network of 475 nm CNTs under uniaxial tensile load Experimentation observations [20] suggest that hooked CNTs are playing a benefic role in the

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CNT alignment process. To investigate this aspect, we have designed controlled simulations involving a 500 nm x 500 nm x 11 nn film constructed from 350 (10, 10) CNTs, each 475 nm in length. Prior initial relaxation, we have added 9 pairs of hooked self-folded CNT rackets with their handle part aligned. The structure of the hooked rackets after 6 ns relaxation is shown in Figure S2, while the relaxation process and film characteristics are described in Figure S3

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The entanglement provided by the hooked rackets is expected to enhance the load transfer along the handle direction [12]. Indeed, exploratory stretching simulations considering the 90o rotated hooked rackets in the network demonstrated that the neck development is significantly inhibited,

transfer enhancement by entanglement.

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Figure S5a and b. It is important to realize the critical role of nanofriction in realizing the load In spite of the added hooked rackets, our simulations

show a highly nonaffine deformation when

=0 pN s/m. Note that during our tensile tests, the

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“handles” of the rackets are not directly gripped, and their evolution is entirely governed by their interaction with the network. Figure 9a shows that instead of promoting CNT alignment, the

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applied uniaxial strain accelerates the film evolution toward a cellular network, characterized by

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disparate bundles and large pores. For example, at

=100% we measured pores 25 nm wide and

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168 nm long. Although the inserted rackets remained hooked, they are not carrying load. For this

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84 nm

10a.

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reason, the stress-strain curves with and without hooked rackets are indistinguishable, Figure

Figure 9. The 500 nm x 500 nm x 11 nm CNT network with added hooked rackets, under =30% (left) and

=100% (right) with (a)

=0 pN s/m and (b)

=0.36 pN s/m. Color gives the

magnitude of the normal force stored by the parallel bonds. The added entangles rackets are shown under each network. The callout details the yarn packing at the indicated central location.

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When friction is accounted for, especially the enhanced polymeric-like

=0.36 pN s/m friction,

the hooked rackets acquire significant tension, Figure 9b. Due to the effective repulsive-volume interactions, which are included in our model [21], the hooked racket “heads” are able to carry ~4%, is enhanced from 0.28

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load. The ultimate tensile strength of the network, occurring at

GPa to 0.32 GPa, Figure 10a. As it can be seen in Figure 9b(right), rackets remain hooked throughout the network evolution, and became part of the central yarn. Their presence promotes

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accumulation of tensile strain in the network, Figure 10b, which is beneficial for directing the zipping-relaxation of CNTs into a single bundle, Figure 10c. Even with enhanced friction, they

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appear to play no additional role in the network disentanglement process.

The energy components of Figure 10b reveal the important role played by the CNT length in the strain-alignment process. Unlike the previously simulated networks composed of longer CNTs,

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here we find no bending-stretching energy crossover. The stretching energy component is always smaller than the bending one. Furthermore, the bending energy never decreases throughout the

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deformation. As a result, the stress-strain curves of Figure 10a for 𝛾=0.36 pN s/m lack the

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strengthening regime iii. Because of the poorer load transfer and because the skipping pf the

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disentanglement stage, the central yarn maintains larger pore defects, Figure 9b(right), which

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Figure 10. (a) Engineering stress, (b) strain energy, and (c) number of aligned pairs, vs. are pN s/m. The down arrows indicate the network with added hooked rackets.

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units for

. The

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3.2.3 Preconditioned network of 475 nm CNTs under uniaxial tensile load

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On a long time scale, a (10,10) CNT network is slowly evolving toward a cellular network with large pores. An efficient way to remove the kinetic barriers encountered during this evolution, and accelerate the dynamics is to apply cycling strain loading [27]. Following this approach, we

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have subjected our network to six 60% compression-recovery cycles. The resulting cellular network lowered its energy by nearly 100%, Figure S4, due to the significance increase in vdW energy. Interestingly, the subsequently applied 6 ns relaxation protocol gave a decreasing trend

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for the bending energy component, which is opposite to the bending energy increase presented

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by the initially prepared network, Figure S3. This behavior suggests that the evolution of the

preconditioned film starts to be dominated by the individual CNT sliding relaxation, which eventually disintegrates the network into disconnected bundles [10].

Figure 11. The preconditioned 500 nm x 500 nm x 11 nm network at (a) (c)

=30%, and (d)

=0%, (b)

=10%,

=75%. Color gives the magnitude of the normal force in parallel bonds

(scale bar of Figure 9). The upper callouts detail un-zipping (yellow arrow) followed by zipping.

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The lower callouts exemplify bundle zipping (yellow arrows). Yarn packing at

=75% is also

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shown.

Figure 12. (a) Engineering stress, (b) strain and vdW energy components, and (c) number of . Here

=0.36 pN s/m.

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aligned pairs, vs.

Representative snapshots of the network evolution during stretching are shown in Figure 11, while the engineering flow stress, network energy decomposition, and number of aligned pairs, vs. 𝜀 are shown in Figure 12. As in Figure 10b, bending modes are still dominating the

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deformation of the preconditioned network, in spite of its significantly thicker bundles. To

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understand this similarity, it is important to recall that, because the of the CNT smooth sliding, CNT bundles are still softer in bending [11]. Nevertheless, the deformation of the preconditioned

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network reveals also some new distinctive features. In the initial stages of the deformation, the applied tensile load is carried by the CNTs which are most aligned to the applied strain direction.

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At the microstructure level, the stretching of these CNTs can lead to un-zipping (or de-bundling), Figure 11a-b, a new effect that gives an initial increase in the vdW energy of the network until 𝜀=10%, Figure 12b, and the drop in the number of aligned pairs measure, Figure 12c. After the network yields, at 0.32 GPa, there is a continuous drop in stretching energy. Although the vdW energy component is lowered and number of aligned pairs increases significantly, the load transfer is not sufficiently potent to insure a massive bundle-to-bundle zipping relaxation directed along the applied strain direction. (The callouts of Figure 11 exemplify two strain-

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directed bundle-level zipping relaxations.) As a result, the yarn presents many disparate bundles separated by large pores evolved from the original structure, Figure 11d. Further stretching does

failure occurring gradually in each bundle, Figure S6.

4. Summary

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not lead to significant yarn densification. Instead, the network fractures, with smooth sliding

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In this paper we have developed a framework to introduce the MD computed phononic friction into our athermal mDEM method. The resulted model was used to simulate the CNT yarn formed

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by stretching (10,10) CNT networks, which are stabilized by room-temperature nanofriction. The deformation stages obtained in the simulations, including a strain hardening one, are in good agreement with experimental observations on stretching the buckypaper formed from multi-walled CNTs. The model facilitates fundamental understanding and exploration of the parameter design space for the development of yarn processing strategies. Our simulations indicated that achieving

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a good load transfer through the stretched network is key for directing the zipping relaxations in order

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to process a yarn with well-aligned CNTs and nano-scale porosity. This type of response cannot be

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achieved with the purely athermal model, i.e., without accounting for the CNT “stickiness” provided by nanofriction. Further enhancing nanofriction by polymer coatings is beneficial, especially in

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networks containing long and hooked individual CNTs, while reducing the room-temperature phononic nanofriction for example by increasing the temperature, compromises the strain-induced alignment process. Without being directed by the applied strain, the zipping relaxation evolves the CNT film into a highly bundled, cellular network structure. Yarns formed by stretching these cellular networks are shown to maintain a higher porosity. Our exploratory results considering increased nanofriction (for

=0.36 pN s/m) anticipate that the bridging of the scales approach pursued here for

neat CNTs can be extended to include the enhancement in dissipation caused by the presence of

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specific polymeric layers, and to simulate the different regimes of deformation from polymerspecific impregnated CNT networks. Coating the CNT surface with aromatic rings of the polymer chain is particularly attractive as the π‐stacking enhances mesoscale friction, which in

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turns improves the load transfer [52].

While focused on stochastic CNT networks, our study presents implications for the processing CNT forest materials. The fundamental dynamical friction might be similarly important for the

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dry-drawing of yarns from CNT forests process [13,14]. During drawing, the effect will likely

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facilitate the load transfer between the large bundles and the important CNT bundle interconnectors (individual CNTs and small CNT bundles) [53,54]. Previous studies have explored alternative densification pathways of CNT forests by application of mechanical and capillary driven lateral compression [55-57]. It is already recognized that friction at the CNT junction plays an important role in the strain hardening and waviness removal [55]. Our

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simulations showing continuous increase in the number of aligned pairs and densifications at

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large strains suggests that the axial stretching CNT forests could be an alternative processing

Acknowledgments

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pathway for material densification.

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This work was supported by NASA's Space Technology Research, Grant NNX16AE03G and by the Institute for Ultra-Strong Composites by Computational Design, Grant NNX17AJ32G. Resources supporting this work were provided by the NASA High End Computing Program through the NASA Advanced Supercomputing Division at Ames Research Center. We thank the Itasca Consulting Group for the PFC3D software support.

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