Nano Futures 3 (2019) 011003 https://doi.org/10.1088/2399-1984/aafe16

LETTER

Morphology control of aligned carbon nanotube pins formed viapatterned capillary densification

Ashley LKaiser1 , Itai Y Stein2 , KehangCui3 andBrian LWardle2,4

1 Department ofMaterials Science and Engineering,Massachusetts Institute of Technology, Cambridge,MA 02139,United States ofAmerica

2 Department of Aeronautics andAstronautics,Massachusetts Institute of Technology, Cambridge,MA02139,United States of America3 Department ofMechanical Engineering,Massachusetts Institute of Technology, Cambridge,MA 02139,United States of America4 Author towhomany correspondence should be addressed.

E-mail: kaisera@mit.edu andwardle@mit.edu

Keywords:nanofibers, capillary densification, patterning, self-assembly, confinement, scaling relations, carbon nanotubes

Supplementarymaterial for this article is available online

AbstractThe exceptional intrinsic properties of alignednanofibers, such as carbonnanotubes (CNTs), and theirability to be easily densified by capillary forcesmotivates their use as shape-engineerablematerials.Whilea variety of self-assembledCNTstructures, such as cell networks,micropillars, andpins havepreviouslybeen fabricated via the capillary-mediated densificationof patternedCNTarrays, predicting the criticalpattern size (scr) that separates cell versus pin formation and the corresponding process-morphologyscaling relationswithin themicrometer range are outstanding.Here, facile and scalablemechanicalpatterning and capillary densification techniques are used to establish scr by elucidating how the effectiveelasticmodulus of alignedCNTarrays during densification governs the resulting pin geometries.Experiments andmodeling show that this effectivemodulus scaleswithCNTheight and is about anorderofmagnitude smaller for pins as compared to cell networks formed frombulk-scale (i.e. non-patterned)CNTarrays. Patterning therefore results in pinswith a lower packing density (commensuratewith doublethewall thickness) and a larger characteristic length scale thanbulk cell networks (i.e. scr∼ 5× cellwidth). CNTarrayswith the initial randomly-oriented carbon ‘crust’ removed via oxygenplasma etchingyield ahigher degree of structural uniformity andbetter agreementwith theproposed elasto-capillarymodel,which enables the use of capillary densification topredictively designhierarchical and shape-tunablematerials for advanced thermal, electronic, andbiomedical devices.

1. Introduction

Recent advances in the synthesis and densification of low-dimensional nanostructures, including alignednanofibers (NFs), nanotubes, and nanoribbons, provide new opportunities for large-scalemanufacturing ofhigh-value nanomaterials [1–6]. In particular, scalable capillary-mediated densification techniques, whichoperate on the principles of evaporative self-assembly [7–11], are promisingmethods to create hierarchicaland functional material structures without the need for cost-prohibitive cleanroom techniques [12, 13]. Forexample, solid pins and long-range cell networks can be formed by densifying alignedNF arrays within smalland large pattern sizes (s), respectively [14–17], with the critical pattern size (scr) separating these twomorphologies for a givenNF height (h) [18] (see figure 1). However, to fully realize the potential of capillaryself-assembly formultiscalematerial design, enhanced process-structure control is necessary to predict NFdensification withinmicron-scale scr values [18–20] by incorporating pattern-induced confinement andinterfacial effects into existingmodels for bulk-scale densification [19–25]. In this work, we present process-morphology scaling relations to describe solid pin formation from the capillary densification of patternedalignedNF arrays of h< 60 μmwith scr< 200 μm, andwe demonstrate a predictive capability including the

RECEIVED

4 January 2019

ACCEPTED FOR PUBLICATION

14 January 2019

PUBLISHED

31 January 2019

© 2019 IOPPublishing Ltd

finding that the effective elasticmodulus scaling of the pin wall with h governs the pin wall thickness,densification factor, and corresponding scr values.

Capillary densification has been used in recent years to leverage the excellent thermal, electrical, andmechanical properties of aligned carbon nanotube (CNT) arrays [34–37] by forming them into dense three-dimensional structures [8, 9, 38], which have applications as electrical interconnects [39–41], sensors andactuators [42–46],field emitters [47, 48], and z-direction composite reinforcement [49, 50].While thesegeometrically complexmicrostructures can be formed by growing and then densifying patternedCNT arrays[8, 16] (see figure 1), it is currently challenging to control the densifiedCNTmorphology as a function of h and s,especially without incurring the cost and process hurdles of cleanroom techniques. Spatially selective CNT array

Figure 1.Capillary-mediated densification of patterned aligned carbon nanotube (CNT) arrays forming cell networks or pinstructures based on the pattern size, s. (a) Illustrations and scanning electronmicroscopy (SEM) images show selective CNT arraygrowth on scribed substrates, including the synthesis-induced carbon ‘crust’ on top of the array. (b) Illustrations and SEM imagesshowhow the critical pattern size (scr) separates CNT cell formation (s> scr) frompin formation (sscr) at a givenCNTheight (h).Here, h and s govern the cell width (w), cell wall thickness (tc), and pinwall thickness (tp), shownhere forCNTswith the carbon crustremoved viaO2 plasma treatment. (c)Previously reportedw of cellsmade fromCNT arrays of s 1000 μm () via bulk-scaledensification [8, 14, 15, 17, 26, 27–33] alongside the linearw versus h scaling relation proposed in [27]. Also shown are previouslyreported scr of pins ( ) formed by densifying patternedCNT arrays [18] and scr of pins reported in this work ( ) alongside the scalingrelation proposed in [14], which is shifted upwards for pin formation, as wefind scr∼ 5 × w for theCNT arrays studied here.

2

Nano Futures 3 (2019) 011003

growth has previously been achieved by patterning catalyst layers via photo- and electron-beam-lithography[51, 52] and by usingmetallic layers as catalyst deactivators [53–55], but these processes are time-consuming andcost-prohibitive at large scales. Additionally, they often produce fragile CNT arrays with synthesis-inducedstructural variations [56–58] and a low density per unit area [59, 60], which collectively yield properties that canbe orders ofmagnitude below theoretical values [61–63]. To overcome these limitations, scalable processingtechniques, such as simple catalyst patterning viamechanical scribing [26, 64, 65] (figure 1(a)), post-CNT-growthO2 plasma treatment to increase structural uniformity [18], and capillary densification (figure 1(b)) areattractivemethods to create high-density,morphology-controlled bulk nanostructuredmaterials provided thatmodels can guide the processing towards these desired structures.

Previousmodel development has focused on the self-assembly offiber arrays undergoing bulk-scale (i.e.non-patterned and cell-forming) capillary densification [9, 21–25], including thewell-characterized formationof cell networks frombulk-scale alignedCNT arrays [14, 26, 27–33].While cells are desirable for long-rangeopen structures, patternedCNTarray densification offers new capabilities to create relatively dense pinsneeded for nano- andmicron-scale device-specific geometries [66–68]. Accurately predicting densifiedCNTmorphologies in this regime is not yet possible, particularly for dense pin geometries with scr< 200 μm [8, 18](see figure 1(c)). Experimentally-validatedmodels are needed to explain the confinement and interfacial effectsgoverning patterned densification. Through extensive quantification of alignedCNTpins forming at scr as afunction of h andO2 plasma treatment, wemodel themechanical behavior of CNT array densification and showthat previous theories for the elasto-capillary self-assembly of bulk-scale CNTs [9, 14] can also be applied to thedensification of patternedCNTs, when appropriate (but counter to prior work) pinwallmoduli and volumefractions are incorporated.We show that the effective elasticmodulus scaling of the pinwall with h governs CNTpin formation and is about an order ofmagnitude smaller compared to bulk-scale cell formation, a direct resultof dominating interfacial effects in patternedCNTdensification to pins.

2.Methods

We synthesized and densified patterned alignedCNT arrays to study samples of varying heights and plasmatreatments. Capillary-densifiedCNT geometries weremeasured via scanning electronmicroscopy (SEM), andan elasto-capillarymodel was used to develop the scaling relations for CNTpinmorphology at the critical patternsize (scr, i.e. pin not cell formation) as a function of CNTheight.

2.1. Substrate patterning andCNT synthesisTo create patternedCNTarrays as pin precursors, SiO2/Si wafers were first coatedwith a 10 nmAl2O3 and a1 nmFe layer deposited via electron beamphysical vapor deposition [69, 70]. These substrates were cut into1 cm×1 cm squares andmechanically scribed by hand to remove the Fe/Al2O3 catalyst layers in outlined gridpatterns of rectangular dimensions s×l, as shown infigure 1(a). Due to the selective removal of catalyst in the∼40 μmwide grid lines, CNT arrays only grow inside the rectangular patternwhere the catalyst remains.Here,l? s so that the densifiedCNTpinwall thickness (tp) at the critical pattern size (scr) can bemeasured laterallyacross the center of the pin, representing one-dimensional densification of theCNT array away from the patternedges (seefigure 2 and section S1 of the supplementarymaterial available online at stacks.iop.org/NANOF/3/011003/mmedia). Corner effects resulting frombiaxial densification at the pin ends are not considered here, astheywould dominate the formation of complex pillar shapeswhen l approaches s, as shown by SEM images infigure 1(b).

Following substrate patterning, vertically-aligned CNTarrays were grown by a base-growthmechanism in a22 mm internal diameter quartz tube furnace at atmospheric pressure via a previously-described thermalcatalytic chemical vapor deposition process, which uses ethylene as the carbon source and 600 ppmofwatervapor added to the inert gas, allowing cm-scale CNT arrays to be grown [71–73]. In each pattern, the growingCNTs self-assemble into aligned arrays of height (h)∼ 10−50 μm, controlled by growth time andmeasured viaopticalmicroscopy. The arrays are comprised ofmultiwalled CNTswith an average outer diameter of∼8 nm(3–7walls with∼5–6 nm inner diameter and intrinsic CNTdensity of≈1.6 g cm−3) [73–75], inter-CNT spacingof∼60–80 nm [76, 77], and volume fraction of∼1%CNTs [73].

2.2. Capillary densificationAfter growth, a subset of the patterned CNT array samples were exposed to a previously-developed recipe forO2 plasma treatment to remove the tangled CNT crust layer [18], which forms on top of the CNT array as aresult of the growth process [56, 57] (see figure 1(a)). This leads to non-O2-treated CNTs (nO-CNTs) andO2-treated CNTs (O-CNTs) to investigate the effect of the carbon crust constraint on densification as asecondary objective. All CNT arrays were then densified via a previously reported paper-soaking technique

3

Nano Futures 3 (2019) 011003

[78] using acetone, as this process enablesmore controlled wetting (via the hydrodynamics of acetone leavingthe paper) to avoid CNTdelamination from the substrate, compared to direct immersion procedures [8].After capillary densification, scr values of the CNTpins weremeasured via SEM (ZeissMerlin, 5 mmworkingdistance, 5 kV accelerating voltage) andwere defined as the pattern size yielding solid pins at the transitionbetween pin and cell formation, where any larger swould initiate cell formation inside the pin structure (seefigure 1(b)). Since a variety of pattern sizes were scribed in the substrate, many pins at scr, cell networks abovescr, and pins below scr could be located on one sample, and only the pins at scr were considered in this work.Then, pin wall thickness (tp) at scr as a function of hwasmeasured via SEM, and the h dependence of tp and scrwas investigated by averaging these values from 3–4 samples. This is presented in figure 2 for comparisonbetween bulk-scale CNT cell networks andO-CNT pins, figure 3 for comparison between nO- andO-CNTpins, and table S1 in section S3 of the supplementarymaterial.

Figure 2.Morphological evolution of aligned carbon nanotube (CNT) cells (a) and pins (b) formed from the bulk-scale [14] andpatterned densification ofO2-plasma-treated CNTarrays, respectively. Schematics illustrate the structural parameters, includingwallthicknesses (t), cell width and critical pattern size (w and scr), CNTdensification factors (Ξ), effective axial wall elasticmoduli (E), andCNTheight (h) for cells (tc,w,Ξc,Ec) and pins (tp, scr,Ξp,Ep). Plots of t versus h show that tp∼2×tc, and exemplary SEM imagesshow 10 μm-tall CNT cell and pinwall thicknesses (see insets). Plots of E versus h show that Ec∼10×Ep, and inset SEM imagesillustrate 30 μm-tall cells and pins. Finally, plots ofΞ versus h show thatΞc∼1.3×Ξp, and inset SEM images illustrate 50 μm-tallcells and pins.

4

Nano Futures 3 (2019) 011003

2.3.Modeling of capillary-densifiedCNTpinsThe capillary-mediated self-organization of patternedCNTarrays into pin structures at scr ismodeled via a one-dimensionalmechanism following previouswork describing the densification of bulk-scale CNT arrays into cellnetworks, which used the same paper-soaking densification procedure [14]. Here, tp is estimated from themaximumelasto-capillary bundle size [9, 25, 79] by considering the patternedCNT arraymorphology[58, 75, 76], yielding the following relation:

tE

h

D

4, 1p f

p

2 38 3

cnt2

i4 3

1 3g

» GG

⎛⎝⎜⎜⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎞⎠⎟⎟ ( )

where γ is the surface tension of the solvent (25 10 3´ - Nm–1 for acetone),Ep is the effective axial elasticmodulus of the pinwall (calculated via equation (1)) that corresponds to the collective elastic response of thewavyCNT array,Γi andΓf are the initial (i.e. as-grown) andfinal (i.e. densified) inter-CNT spacings,Dcnt is theCNTouter diameter, and h is themeasuredCNTheight. As discussed in section S1 of the supplementarymaterial, a one-dimensional unit cell of size scr is defined so that scr can be estimated from tp as follows, assumingthorough solvent wetting [80] and that all CNTswithin scr comprise the pinwall after densification:

s t , 2cr p p» X ( )

whereΞp is the one-dimensional densification factor.Ξp describes the increase inCNT array packing density as aresult of the elasto-capillary self-assembly process and is discussed further in section S1 of the supplementarymaterial, alongwith the estimations ofΓi andΓf. Using equations (1) and (2), the experimentally-quantified tpvalues and calculated Ep andΞp values infigures 2 and 3 forO-CNTs (i.e.EO andΞO) can be analyzed. Thisframework is also applied to analyze the tp, scr,EnO, andΞnO scaling of pins presented infigure 3 as a comparisonbetween nO- andO-CNTs.

Figure 3.Effect ofO2 plasma treatment (i.e. post-growth carbon crust removal from aligned carbon nanotube (CNT) arrays): (a)noO2 treatment (nO-CNTs) and (b)O2 treatment (O-CNTs) onCNTpinmorphology resulting from capillary densification at thecritical pattern size (scr) as a function of CNTheight (h). SEM images show that scr for exemplary 20 μm-tall CNT arrays is larger fornO-CNTs. Plots show thatO2 treatment yields improved scaling relations as derived via the proposed elasto-capillarymodel for bothpinwall thickness (tp) and scr due to reduced structural variability inO-CNT arrays.

5

Nano Futures 3 (2019) 011003

3. Results and discussion

Wecompared themorphological evolution of capillary-densified cell networks that formed frombulk-scaleO-CNT arrays with pins that formed at scr frompatternedO-CNT arrays, including thewall thicknesses,effective elastic wallmoduli, and densification factors (i.e. CNTpacking density within the cell and pinwalls).We then used the elasto-capillarymodel to compare these parameters, including the scaling of tp and scr with h,for pins that formed frompatterned nO- andO-CNT arrays.

3.1. Comparison ofO2-treatedCNT cells and pinsAsfigure 2 illustrates, similar schematics describe the geometries of cell [14] and pin structures resulting fromthe capillary densification of alignedCNTarrays. These structures are differentiated by the one-dimensionallength across which densification occurs, as bulk-scale cells exhibit a characteristic length approximately equalto the cell width (w), while pins forming at their critical pattern size are confined to densify within the scribedlength of scr.While the cell and pinwall thicknesses (tc and tp) scale almost linearly with h (as shown infigure 3and in previouswork [14]), average t values can be used to compare the relativemagnitude of tc and tp. Here,figure 2 shows that tp∼ 2× tc as s approaches scr, which can be understood as an imaginary ‘cell’ inside of theCNT array collapsing during densification to form the solid pin structure.

For both cell and pinmorphologies, previous work showed that a higher degree of densification at a given h islinked to a higherwallmodulus and lowerwall thickness, as a correspondingly thinner, stiffer, and denser wallcan better support the load from capillary forces [8, 14, 81]. However, the overallmagnitude and scaling ofthese parameters with h and swill depend upon the ability of CNTs to self-organize in themost energeticallypreferentialmanner, whichwould result in the highest packing densities [8, 76, 82], but such ideal packingmaynot be allowed if the CNTs are forced to densify along a specific direction due to their confinementwithin apattern. To investigate this scenario, which applies to the pins formed here, one can describe a patternedCNTarray as having amore ‘unconstrained’ perimeter (i.e. fewer CNT–CNT sidewall interactions) compared to thesameCNTswithin a bulk-scale array, where the surroundingCNTs increase the extent of such interactions.Relative to its size, a patterned array also has enlarged solvent-air interfaces along its perimeter during solventevaporation, which influences the spatial trajectory of densifyingCNTs owing to the greater difference inhydrostatic dilation stress created across these interfaces [29, 81]. Therefore, as previous studies on patternedCNTdensification have shown [26, 29, 81], CNT translation is directed laterally towards the center of the patterndue to the solvent-air interfaces receding from the array and a thin solvent layer remaining pinned to the outerCNTs via surface tension, which act to push theCNT array inwards. This process is also aided by fewerCNT–CNT sidewall interactions present along the perimeter that could forceCNT translation in otherdirections (which occurs in bulk-scale cell network formation). These interfacial effects are consistent with priorobservations of wettedCNTarrays densifying from low-density to high-density regions under capillary forces[26, 29, 81].

The consequences of such effects can be observed in the patternedCNT arrays used here by comparing thedifferentmorphological evolution ofO-CNT cells and pins. These differences are revealed by the scaling ofE andΞwith h (figure 2), which shows thatEp andΞp evolve similarly but are generally smaller than Ec andΞc [14].Here,Ec andEp both scale as h

8/3, which can be estimated asE∝ α(h)ψ, where 0.030 0.006 10c pa a» µ ´and 8 3c py y= » . Because they are longer, taller CNTs inherently havemore connections between them toreinforce the array, and henceEhas been observed to scale with h [14, 61]. Similarly,Ξc andΞp both scale as h

0.5,which is estimated here asΞ∝ β(h)ω, where 3.7 1 1.3c pb b» µ ´ and 0.5c pw w= » . This scaling leadsto t tc p< at a given h and is consistent with patterned densification reducing the effective pinwall stiffness andvolume fraction. Therefore, the effective axial arraymodulus of the pinwall, and not the orders-of-magnitudehigher isolatedCNT axialmodulus [83] governs the one-dimensional densification of patternedCNT arrays,similar to bulk-scale arrays.

Finally, since these CNTs are forced to densify towards the center of their pattern and thus do not pack astightly as bulk-scale arrays, larger densification lengths (i.e. scr>w) and lowerCNTwall volume fractions andstiffnesses are observed for pins versus cells, especially for small h (i.e. lower overall surface areas), where theelasto-capillary pairing efficacy of neighboringCNTs is reduced [8, 9, 18]. The directive interfacial factorsincreasing this characteristic length are consistent with prior observations of increasedCNT-substrate adhesionhindering CNTmobility, as this also resulted in larger cell widthswith thicker cell walls and a lower stiffness [14].Taken together, these interfacial effects could provide versatilemethods to direct the densification process in thefuture and control the resulting CNTgeometries.

3.2. Comparison ofO2-treated andnon-treated pinsNext, to establish scaling relations for scr and tp as a function of h via the elasto-capillarymodel, and to investigatethe effect of the synthesis-induced carbon crust [12, 18, 56] (figure 1(a)) onCNT array densification, pin

6

Nano Futures 3 (2019) 011003

geometries resulting from the densification of patterned nO- andO-CNT arrays are compared. Figure 3illustrates that scr is larger on average for nO-CNTs, as the crust is presumed to partially restrict elasto-capillarypairing and overall CNTmobility by preventing nO-CNTs fromproperly reinforcing one another via freetranslation across the substrate [18]. Therefore, since nO-CNTdensification is slightly hindered compared toO-CNTs, nO-CNTs often need to form thicker pinwalls to support the capillary forces and exhibitmorevariableEnO andΞnO scalingwith h, as discussed further in section S2 of the supplementarymaterial. Thismechanism is consistent with previous results for the densification of bulk-scale CNT arrays with increasedsubstrate adhesion (achieved via thermal post-processing), as those resulting cells also exhibited a larger averagewall thickness, cell width, and smaller effective wall stiffness due to reducedCNTmobility [14].

Asfigure 3 shows, the scaling of tp and scr with h (equations (1) and (2), respectively) for both nO- andO-CNTs can be accurately represented by the governing elasto-capillarymechanics via the one-dimensionalmodel. Owing to the structural irregularities caused by the crust, less variable scalingwith h is seen forO-CNTpins, which is similar to previous work showing enhanced densification and lower structural variationwithindensifiedO-CNTmicropillars [8, 18]. Removing the crust constraint allows for easier andmore energeticallypreferential densification due to enhancedCNTmobility, yielding better agreementwith the proposeddensificationmodel [9, 25, 79] as ameans to enable the tunable fabrication of highly precise and uniformCNTmicrostructures.

The results presented here for CNT arrays of h< 60 μmwith scr< 200 μmalso provide insight into thediscrepancies between past experimental results and analyticalmodels for capillary densification, which cansignificantly overestimate the h values required to formdensified cell and pin structures within pattern sizesbelow 150 μm [18–20]. Thesemodels commonly set E equal to the individual CNT axial elasticmodulus of1 TPa [83], but the effective elasticmodulus of densifying CNTbundles is often orders ofmagnitude lower(∼1MPa−1 GPa) [14, 61, 84] due to the stochastic nature of CNTpacking and inherent waviness [61–63, 84].For a given scr, thesemodels can therefore over-predict the effective stiffness required for CNT arrays to form apin at a given h, and experimental results (including those presented here) often show that CNT arrays exhibit alower effective stiffness to densify at a lower h to formpin structures [14, 81]. Therefore, while the 1 TPa intrinsicCNT elastic axialmodulusmay be appropriate for large s and h, when the elasto-capillary pairing efficacy ofCNTs is relatively strong and can overcome structural variability within the array [8, 9, 18], this assumptionbecomes less accurate as s and h are reduced to themicro- and nano-meter regime, wheremore appropriatescaling and smallerE values are required to describe capillary densification.

4. Conclusion

In summary, the effects of alignedCNTheight andO2 plasma treatment on the capillary densification ofpatternedCNTarrays into pins was quantified andmodeled based on the underlying elasto-capillary physics. Bydeveloping process-morphology scaling relations for pin evolutionwithCNT array height (h), this work reportsexperimentally-validatedmodels that enable accuratemorphology control of densified pin geometries created atthe critical pattern size (scr) separating cell versus pin formation, which are applicable above and below scr withappropriate wallmodulus scaling. Experimental andmodeling results indicate that the pinwall effective axialelasticmodulus (Ep) and densification factor (Ξp) scalewith h and are smaller compared to corresponding valuesfor cell networks formed via bulk-scale densification. This is primarily attributed to pattern-induced solvent-airinterfacial effects andmechanistic CNT–CNT sidewall interactions, which also yield a larger scr and pinwallthickness compared to the cell width and cell wall thickness. Finally, applying a post-growthO2 plasmatreatment yields improved agreement with scaling relations that could enable preciseNF patterning in the futurefor applications requiringmicrostructural control.

Additionally, it should be noted that CNTpins formedwithin isotropic patterns, as opposed to the non-isotropic patterns used here, are likely to experience two-dimensional (2D) effects during densification.Modeling 2Dpatterned densificationwould require quantification of topological inhomogeneities andsimulation of physical CNT–CNT interactions, including the inherent waviness in alignedCNT arrays[58, 61, 76].Moreover, since an increasedCNT-substrate adhesion force (Fa) [85] has recently been shown toreduceCNTmobility and enable the capillary densification of taller, bulk-scale CNT arrays intowider cells withthicker walls [14], it is postulated that CNTpin geometries will scale similarly with Fa. This could provideadditional tunability over densifiedCNT architectures by using Fa as a design parameter, potentially enabling thedensification of alignedCNTarrays intomm- to cm-scale structures at large Fa. Further work is required in thisarea, since characterization andmodeling of the physiochemicalmechanisms governing Fa scalingwithprocessing and the corresponding Fa effects onCNT elasto-capillarymechanics are not currently available. Onceexperimentally-validatedmodels are developed to accurately predict 2D densification and Fa effects, capillarydensificationmay be used as a versatilemethod to creatematerials with controlled shapes, densities, and

7

Nano Futures 3 (2019) 011003

functionalities for next-generation composite reinforcement, flexible electronics, optoelectronics, and otheremerging nanoscale applications.

Acknowledgments

Thisworkwas partially supported byAirbus, ANSYS, Embraer, LockheedMartin, SaabAB, Saertex, andTeijinCarbonAmerica throughMIT’sNano-EngineeredComposite aerospace STructures (NECST)Consortium, andpartially supported by theNational Aeronautics and Space Administration (NASA) Space Technology ResearchInstitute (STRI) forUltra-StrongComposites byComputational Design (US-COMP), grant numberNNX17AJ32G. ALKwas supported by theDepartment ofDefense (DoD) through theNational Defense Scienceand EngineeringGraduate Fellowship (NDSEG)Program. AtMIT, the authors thankDr SKim and Professor AJHart for helpwithO2 plasma treatment, themembers of necstlab for technical support and advice, andProfessor CVThompson and ProfessorM JCima for helpful discussions. This workmade use of theMITMaterials Research Laboratory (MRL) Shared Experimental Facilities, supported in part by theMRSECProgramof theNational Science Foundation under award numberDMR-1419807, andwas carried out in part throughthe use ofMIT’sMicrosystems Technology Laboratories.

ORCID iDs

Ashley LKaiser https://orcid.org/0000-0002-6304-6992Itai Y Stein https://orcid.org/0000-0003-3229-7315KehangCui https://orcid.org/0000-0002-1768-0845Brian LWardle https://orcid.org/0000-0003-3530-5819

References

[1] ZhangY, Zhang F, YanZ,MaQ, Li X,HuangY andRogers J A 2017Nat. Rev.Mater. 2 17019[2] KenryK and LimCT2017Prog. Polym. Sci. 70 1–17[3] ZhangR, Zhang Y andWei F 2017Chem. Soc. Rev. 46 3661–715[4] Chen L F, Feng Y, LiangHW,WuZY andYu SH2017Adv. EnergyMater. 7 1700826[5] Bai Y et al 2018Nat. Nanotechnol. 13 589–95[6] McLeanB, Eveleens CA,Mitchell I,WebberGB and Page A J 2017Phys. Chem. Chem. Phys. 19 26466–94[7] Bico J, Reyssat E andRomanB 2018Annu. Rev. FluidMech. 50 629–59[8] DeVolderM andHart A J 2013Angew. Chem. Int. Ed. 52 2412–25[9] Tawfick SH, Bico J and Barcelo S 2016MRSBull. 41 108–14[10] TanATL, Beroz J, KolleM andHart A J 2018Adv.Mater. 30 1803620[11] Pokroy B, Kang SH,Mahadevan L andAizenberg J 2009 Science 323 237–40[12] DeVolderM, Tawfick SH, Park S J, CopicD, ZhaoZ, LuWandHart A J 2010Adv.Mater. 22 4384–9[13] Tawfick S, ZhaoZ,MaschmannM, Brieland-Shoultz A, DeVolderM, Baur JW, LuWandHart A J 2013 Langmuir 29 5190–8[14] Kaiser A L, Stein I Y, Cui K andWardle B L 2018Phys. Chem. Chem. Phys. 20 3876–81[15] ZhangK, Li T, Ling L, LuH, Tang L, Li C,Wang L andYaoY 2017Carbon 114 435–40[16] DeVolderMFL, Tawfick S, Park S J andHart A J 2011ACSNano 5 7310–7[17] QiuA andBahrDF 2013Carbon 55 335–42[18] DeVolderM, Park S J, Tawfick SH, VidaudDOandHart A J 2011 J.Micromech.Microeng. 21 045033[19] Journet C,Moulinet S, Ybert C, Purcell S T andBocquet L 2005Europhys. Lett. 71 104[20] ZhaoYP and Fan JG 2006Appl. Phys. Lett. 88 103123[21] SengabA and PicuRC 2018Phys. Rev.E 97 032506[22] PicuRC and SengabA 2018 SoftMatter 14 2254–66[23] ZhouM,Tian Y, ZengH, PesikaN and Israelachvili J 2015Adv.Mater. Interfaces 2 1400466[24] ZhouM,ChenK, Li X, Liu L,MoY, Jin L, Li L andTianY 2018 Langmuir 34 11629–36[25] Chiodi F, RomanB andBico J 2010Europhys. Lett. 90 44006[26] LiuH, Li S, Zhai J, LiH, ZhengQ, Jiang L andZhuD2004Angew. Chem. Int. Ed. 43 1146–9[27] ChakrapaniN,Wei B, Carrillo A, Ajayan PMandKane R S 2004Proc. Natl Acad. Sci. USA 101 4009–12[28] Kaur S, Sahoo S, Ajayan P andKaneR 2007Adv.Mater. 19 2984–7[29] LiQ,DePaula R, ZhangX, Zheng L, Arendt PN,Mueller FM, ZhuYT andTuY 2006Nanotechnology 17 4533[30] Correa-DuarteMA,WagnerN, Rojas-Chapana J,Morsczeck C, ThieM andGiersigM2004Nano Lett. 4 2233–6[31] Dumee L F, Sears K, Schutz J A, FinnN,DukeM,Mudie S, KirbyN andGray S 2013 J. Colloid Interface Sci. 407 556–60[32] Qu J, Zhao Z,WangX andQiu J 2011 J.Mater. Chem. 21 5967–71[33] FutabaDN,HataK, Yamada T,Hiraoka T,Hayamizu Y, Kakudate Y, TanaikeO,HatoriH, YumuraMand Iijima S 2006Nat.Mater.

5 987–94[34] DeVolderMFL, Tawfick SH, BaughmanRHandHart A J 2013 Science 339 535–9[35] Di J,WangX, Xing Y, ZhangY, ZhangX, LuW, LiQ andZhuYT 2014 Small 10 4606–25[36] Zhang L, ZhangG, LiuC and Fan S 2012Nano Lett. 12 4848–52[37] Wang F,Drzal L T,QinY andHuangZ 2015 J.Mater. Sci. 50 1082–93[38] LiuQ, LiM,GuY, Zhang Y,Wang S, LiQ andZhang Z 2014Nanoscale 6 4338–44[39] XiangD,WangX, Jia C, Lee T andGuoX2016Chem. Rev. 116 4318–440

8

Nano Futures 3 (2019) 011003

[40] CuiK, Chiba T,Omiya S, Thurakitseree T, Zhao P, Fujii S, KatauraH, Einarsson E, Chiashi S andMaruyama S 2013 J. Phys. Chem. Lett.4 2571–6

[41] WuW2017Nanoscale 9 7342–72[42] Zhang J, LiuX,Neri G and PinnaN2016Adv.Mater. 28 795–831[43] Fennell J F, Liu S F, Azzarelli JM,Weis J G, Rochat S,Mirica KA, Ravnsbaek J B and Swager TM2016Angew. Chem. Int. Ed. 55 1266–81[44] StoychevGV and Ionov L 2016ACSAppl.Mater. Interfaces 8 24281–94[45] Kong L andChenW2014Adv.Mater. 26 1025–43[46] Liang Y, SiasD, Chen P J andTawfick S 2017Adv. Eng.Mater. 19 1600845[47] ShinDH, YunKN, Jeon SG,Kim J I, Saito Y,MilneW I and LeeC J 2015Carbon 89 404–10[48] ZhangQ,WangX j,Meng P, YueH x, ZhengR t,WuXL andChengGA2018Appl. Phys. Lett. 112 013101[49] Garcia E J,Wardle B L and JohnHart A 2008CompositesA 39 1065–70[50] Kalfon-Cohen E et al 2018Compos. Sci. Technol. 166 160–8[51] Fan S, chlineMG, FranklinNR, Tombler TW,Cassell AMandDaiH 1999 Science 283 512–4[52] DeVolderMFL, Vansweevelt R,Wagner P, Reynaerts D, VanHoof C andHart A J 2011ACSNano 5 6593–600[53] Yemini R,MuallemM, Sharabani T, TeblumE,Gofer Y andNessimGD2016 J. Phys. Chem.C 120 12242–8[54] Yemini R, ItzhakA, Gofer Y, Sharabani T,DrelaM andNessimGD2017 J. Phys. Chem.C 121 11765–72[55] AvrahamES,Westover A S, ItzhakA, Shani L,MorV,Girshevitz O, Pint C L andNessimGD2018Carbon 130 273–80[56] AhnHS, SinhaN, ZhangM,BanerjeeD, Fang S andBaughmanRH2006 J. Heat Transfer 128 1335–42[57] BedewyM,Meshot ER, GuoH,Verploegen EA, LuWandHart A J 2009 J. Phys. Chem.C 113 20576–82[58] Stein I Y andWardle B L 2016Phys. Chem. Chem. Phys. 18 694[59] Liu L,MaWandZhang Z 2011 Small 7 1504–20[60] LimYD,GrapovD,HuL, KongQ, Tay BK, LabunovV,Miao J, Coquet P andAditya S 2018Nanotechnology 29 075205[61] Stein I Y, LewisD J andWardle B L 2015Nanoscale 7 19426–31[62] Stein I Y andWardle B L 2016Nanotechnology 27 035701[63] Natarajan B, LachmanN, LamT, JacobsD, LongC, ZhaoM,Wardle B L, SharmaR and Liddle J A 2015ACSNano 9 6050–8[64] HuangT, JiangK, Li L, Chen S, Li R, ShenG andChenD2018ChemElectroChem 5 1652–7[65] YangM,KimDH,Klein TR, Li Z, ReeseMO,Tremolet deVillers B J, Berry J J, vanHestMFAMandZhuK2018ACS Energy Lett.

3 322–8[66] ShinD andTawfick S 2018 Langmuir 34 6231–6[67] Tawfick S,Hart A J andDeVolderM2012Nanoscale 4 3852–6[68] Grinthal A, Kang S, Epstein A, AizenbergM,KhanMandAizenberg J 2012Nano Today 7 35–52[69] Hart A J and SlocumAH2006 J. Phys. Chem.B 110 8250–7[70] Stein I Y andWardle B L 2014Carbon 68 807–13[71] Lee J, Stein I Y, Kessler S S andWardle B L 2015ACSAppl.Mater. Interfaces 7 8900–5[72] Stein I Y, Kaiser A L, Constable A J, Acauan L andWardle B L 2017 J.Mater. Sci. 52 13799–811[73] Lee J, Stein I Y,DevoeME, LewisD J, LachmanN, Kessler S S, Buschhorn ST andWardle B L 2015Appl. Phys. Lett. 106 053110[74] LachmanN, Stein I Y, UgurA, LidstonDL, GleasonKK andWardle B L 2017Nanotechnology 28 24LT01[75] Stein I Y, LachmanN,DevoeME andWardle B L 2014ACSNano 8 4591–9[76] Stein I Y andWardle B L 2013Phys. Chem. Chem. Phys. 15 4033–40[77] MuthaHK, Lu Y, Stein I Y, ChoH J, SussME, Laoui T, ThompsonCV,Wardle B L andWang EN2017Nanotechnology 28 05LT01[78] JiangD,WangT, Chen S, Ye L and Liu J 2013Microelectron. Eng. 103 177–80[79] PyC, Bastien R, Bico J, RomanB andBoudaoudA 2007Europhys. Lett. 77 44005[80] Qiu J, Terrones J, Vilatela J J, VickersME, Elliott J A andWindle AH2013ACSNano 7 8412–22[81] LimX, FooHWG,Chia GH and SowCH2010ACSNano 4 1067–75[82] Liu L, YuanY,DengWand Li S 2018 J. Chem. Phys. 149 104503[83] Salvetat J P, Bonard JM, ThomsonN,Kulik A, Forro L, BenoitWandZuppiroli L 1999Appl. Phys.A 69 255–60[84] CebeciH, Stein I Y andWardle B L 2014Appl. Phys. Lett. 104 023117[85] LidstonDL 2017 Synthesis, characterization, andmode I fracture toughness of aligned carbon nanotube polymermatrix

nanocompositesMaster’s ThesisMassachusetts Institute of Technology hdl.handle.net/1721.1/112473

9

Nano Futures 3 (2019) 011003

Supplementary Material: Morphology control of

aligned carbon nanotube pins formed via

patterned capillary densification

Ashley L. Kaiser,∗,† Itai Y. Stein,‡ Kehang Cui,¶ and Brian L. Wardle∗,‡

†Department of Materials Science and Engineering, Massachusetts Institute of Technology,

Cambridge, Massachusetts 02139, USA.

‡Department of Aeronautics and Astronautics, Massachusetts Institute of Technology,

Cambridge, Massachusetts 02139, USA.

¶Department of Mechanical Engineering, Massachusetts Institute of Technology,

Cambridge, Massachusetts 02139, USA.

E-mail: kaisera@mit.edu; wardle@mit.edu

S1

S1 Pin Geometry Modeling

The capillary-mediated self-organization of patterned, vertically-aligned carbon nanotube

(CNT) arrays into solid pins is modeled based on previous work detailing the one-dimensional

(1D) capillary densification of bulk-scale CNT arrays into cellular networks.1 In this frame-

work, only geometric distinctions related to the pattern size differentiate model development

for pin and cellular networks. Since pin formation is defined as occurring within the 1D

critical pattern size (scr) to yield solid CNT structures (see figure S1a), pin formation is

subject to a different side-wall boundary condition compared to bulk-scale densification. In

this work, pin walls are formed in long, non-isotropic patterns (see figure S1b) as opposed

to square or cylindrical patterns, which would involve CNT densification in two dimensions.

Therefore, pin formation is modeled via the same 1D densification mechanism as bulk-scale

cell networks owing to similar underlying physics. As discussed in the main text, the mor-

phological differences between CNT pins and bulk-scale cells is attributed to smaller effective

elastic pin wall moduli and densification factors due to the geometric constraint of scr.

With this framework established, the model describing the capillary densification of pat-

terned CNT arrays begins akin to cell formation1 by considering the maximum fiber bundle

size (Nmax), which was previously derived for the self-assembly of thoroughly-wetted fibers

subject to capillary forces:2–4

Nmax =( γE

)2/3( 4h8/3

D2cntΓ

4/3i

)(S1)

Here, γ is the surface tension of the solvent, E is the effective axial elastic modulus of the

densified fiber wall (here aligned CNTs), h is the CNT height, Dcnt is the CNT outer diameter

(∼ 8 nm),5 and Γi is the as-grown inter-CNT spacing (∼ 60−80 nm).5–7 The effective elastic

modulus of aligned CNT arrays is a function of the CNT volume fraction (Vf), waviness ratio,

and interactions due to CNT-CNT junctions,8,9 which leads to non-negligible CNT-CNT

frictional effects during densification.9 Since inter-fiber adhesion affects the self-organization

S2

(b)

(a)

Side View Top View

t

h

Pin Unit Cell

Solvent in

scrscr

t

Pin Geometry

CNT PinEvaporation

Si2O3

SiO2

Fe

CNT

CNT ArrayDensified

Al

EtchedCatalyst

l

scr

p p

Layers

EtchedCatalystLayers

Figure S1: Overview of carbon nanotube (CNT) pin densification and modeling geometry.(a) One-dimensional (1D) illustration showing an aligned CNT array on a patterned substrateundergoing CNT self-assembly as the solvent evaporates, shown here for CNTs with thetangled upper carbon crust removed via O2 plasma treatment. (b) Side view illustrationshowing the CNT pin height (h), critical pattern size (scr), and pin wall thickness (tp), andtop view illustration showing tp resulting from 1D densification and the pin unit cell of sizescr x l used in equation S3, where l scr to consider only 1D effects.

of nanofibers into cellular networks and bundles,10–13 the bending stiffness scaling for CNT

pin walls (as in cell walls)1 is expected to scale as N3 for this 1D geometry, while scaling

as N is expected when frictional effects are ignored.4 Therefore, equation S1 corresponds to

N3max, and the CNT pin wall thickness (tp) can be estimated as follows:1

tp = NmaxΓf (S2a)

→ tp = Γf

((γ

Ep

)2/3(

4h8/3

D2cntΓ

4/3i

))1/3

(S2b)

where Γf is the final inter-CNT spacing within the CNT pin wall, reflecting the degree of

CNT densification, and Ep is the effective axial elastic modulus of the pin wall. Assuming

S3

that all of the CNTs in the original pattern of size scr densify into the final pin structure,

the densification factor (Ξp) and scr can be defined as follows:

Ξp =scrtp

(S3a)

scr = tpΞp (S3b)

Here, Ξp describes the increase of CNT array packing density as a result of elasto-capillary

self-organization and is equal to the final CNT volume fraction within the pin wall. Finally,

to enable the full use of equation S2, Γf can be approximated as shown below by incorporating

Ξp and the as-grown CNT volume fraction (Vf ∼ 1%)5,6 into the previously-derived functional

form of the inter-CNT spacing scaling as a function of the CNT waviness:6–8

Γf = ΩDcnt

(11.77(3.2(ΞVf)0.6 + 4.1)−3.042 + 0.9496)

√√3π

6ΞVf− 1

(S4a)

Ω = −0.002ΞVf + 1.072 (S4b)

where Ω is the waviness correction factor developed from a three-dimensional stochastic sim-

ulation of the packing morphology of wavy CNTs.7 Equations S2b and S3b are reproduced

in the main text for comparison with experimental values.

S4

S2 Effective Elastic Modulus and Densification Factor

Scaling for Non-O2-Plasma-Treated CNT Pins

Figure S2 shows the scaling of EnO (estimated from equation S2b) and ΞnO (estimated from

equation S3a) with h for CNT pins that were not treated O2 plasma prior to densification

(i.e. nO-CNTs). EnO scaling can be estimated as EnO ∝ α(h)ψ with α ≈ 3.0 ± 2 × 10−3

and ψ ≈ 8/3, and ΞnO scaling can be estimated as ΞnO ∝ β(h)ω with β ≈ 3.0 ± 2 and

ω ≈ 0.5. Here, nO-CNTs experience an additional constraint compared to O2-treated CNTs

(O-CNTs) during pin formation due to the presence of the upper carbon crust arising from

the growth process, which causes greater variability in EnO and ΞnO. This constraint limits

the overall CNT mobility and packing efficacy, yielding larger tp and smaller EnO, as discussed

in the main text. This effect can be reduced at larger h due to the enhanced ability of longer

CNTs to densify via elasto-capillary pairing due to increases in CNT surface area.2,14

(b)(a)

101 102

100

101

102

103

Mod

ulus

, EnO

[M

Pa]

CNT Height, h [µm]

ExpE ~ h 8/3

nO ± δ

101

ExpΞ ~ hnO ± δ

Den

sific

atio

n F

acto

r, Ξ

nO [-

]

101 102

CNT Height, h [µm]

1/2

Figure S2: Parameters describing pin formation from non-O2-plasma-treated CNTs (nO-CNTs). Plots show the evolution with CNT height (h) of (a) the effective pin wall axialelastic modulus (EnO) and (b) the densification factor (ΞnO). Higher variability is attributedto the carbon crust, which causes structural inhomogeneities within the CNT array.

S5

S3 Pin Geometry as a Function of Carbon Nanotube

Array Height

Table S1 presents the raw data that were evaluated experimentally (i.e. ‘Measured’), and

the values that result from equations S1 - S4 in section S1 (i.e. ‘Calculated’). These data

are also presented in figure S2 and figures 2 and 3 in the main text.

Table S1: Experimentally-determined carbon nanotube (CNT) pin height (h), pin wall thick-ness (tp), and critical pattern size (scr) in addition to the calculated pin wall effective axialelastic modulus (Ep, estimated from equation S2b), and densification factor (Ξp, estimatedfrom equation S3a) for non-O2-plasma-treated CNTs (nO-CNTs, ‘No O2’) and O2-plasma-treated CNTs (O-CNTs, ‘O2’), along with standard error. These data originate from CNTarray densification with acetone-soaked paper, as discussed further in the main text.

Measured Calculatedh tp scr Ep Ξp

[µm] [µm] [µm] [MPa] [-]

NoO

2 11± 2 6.1± 2 62± 30 0.83± 0.08 10.1± 1.220± 4 11± 3 105± 10 0.79± 0.08 9.55± 1.025± 5 14± 3 110± 10 0.78± 0.08 7.86± 1.040± 8 11± 8 140± 20 1700± 700 24.4± 17

O2

13± 2 5.8± 0.1 50± 5 2.6± 0.6 8.6± 0.620± 4 7.3± 0.7 90± 10 4.9± 0.5 12.3± 1.325± 5 6.4± 0.6 110± 10 22± 2 16.4± 1.643± 7 7.2± 2 150± 50 130± 30 22.0± 2.3

S6

References

(1) Kaiser, A. L.; Stein, I. Y.; Cui, K.; Wardle, B. L. Process-morphology scaling relations

quantify self-organization in capillary densified nanofiber arrays. Phys. Chem. Chem.

Phys. 2018, 20, 3876–3881.

(2) Tawfick, S. H.; Bico, J.; Barcelo, S. Three-dimensional lithography by elasto-capillary

engineering of filamentary materials. MRS Bull. 2016, 41, 108–114.

(3) Chiodi, F.; Roman, B.; Bico, J. Piercing an interface with a brush: Collaborative

stiffening. Europhys. Lett. 2010, 90, 44006.

(4) Py, C.; Bastien, R.; Bico, J.; Roman, B.; Boudaoud, A. 3D aggregation of wet fibers.

Europhys. Lett. 2007, 77, 44005.

(5) Lee, J.; Stein, I. Y.; Devoe, M. E.; Lewis, D. J.; Lachman, N.; Kessler, S. S.;

Buschhorn, S. T.; Wardle, B. L. Impact of carbon nanotube length on electron transport

in aligned carbon nanotube networks. Appl. Phys. Lett. 2015, 106, 053110.

(6) Stein, I. Y.; Wardle, B. L. Coordination Number Model to Quantify Packing Morphol-

ogy of Aligned Nanowire Arrays. Phys. Chem. Chem. Phys. 2013, 15, 4033–4040.

(7) Stein, I. Y.; Wardle, B. L. Packing morphology of wavy nanofiber arrays. Phys. Chem.

Chem. Phys. 2016, 18, 694.

(8) Stein, I. Y.; Lewis, D. J.; Wardle, B. L. Aligned Carbon Nanotube Array Stiffness from

Stochastic Three-dimensional Morphology. Nanoscale 2015, 7, 19426–19431.

(9) Cebeci, H.; Stein, I. Y.; Wardle, B. L. Effect of Nanofiber Proximity on the Mechanical

Behavior of High Volume Fraction Aligned Carbon Nanotube Arrays. Appl. Phys. Lett.

2014, 104, 023117.

(10) Picu, R. C.; Sengab, A. Structural evolution and stability of non-crosslinked fiber net-

works with inter-fiber adhesion. Soft Matter 2018, 14, 2254–2266.

S7

(11) Zhou, M.; Chen, K.; Li, X.; Liu, L.; Mo, Y.; Jin, L.; Li, L.; Tian, Y. Clumping Stability

of Vertical Nanofibers on Surfaces. Langmuir 2018, Article ASAP .

(12) Pokroy, B.; Kang, S. H.; Mahadevan, L.; Aizenberg, J. Self-Organization of a Mesoscale

Bristle into Ordered, Hierarchical Helical Assemblies. Science 2009, 323, 237–240.

(13) Shin, D.; Tawfick, S. Polymorphic Elastocapillarity: Kinetically Reconfigurable Self-

Assembly of Hair Bundles by Varying the Drain Rate. Langmuir 2018, 34, 6231–6236.

(14) De Volder, M.; Park, S. J.; Tawfick, S. H.; Vidaud, D. O.; Hart, A. J. Fabrication and

electrical integration of robust carbon nanotube micropillars by self-directed elastocap-

illary densification. J. Micromech. Microeng. 2011, 21, 045033.

S8