Extreme Energy Dissipation via Material Evolution in Carbon Nanotube Mats

Abstract Thin layered mats comprised of an interconnected meandering network of multiwall carbon nanotubes (MWCNT) are subjected to a hypersonic micro‐projectile impact test. The mat morphology is highly compliant and while this leads to rather modest quasi‐static mechanical properties, at the extreme strain rates and large strains resulting from ballistic impact, the MWCNT structure has the ability to reconfigure resulting in extraordinary kinetic energy (KE) absorption. The KE of the projectile is dissipated via frictional interactions, adiabatic heating, tube stretching, and ultimately fracture of taut tubes and the newly formed fibrils. The energy absorbed per unit mass of the film can range from 7–12 MJ kg−1, much greater than any other material.


Extreme Energy Dissipation via Material Evolution in Carbon Nanotube Mats
Jinho Hyon, Olawale Lawal, Ramathasan Thevamaran, Ye Eun Song and Edwin L. Thomas*

Launch Pad Preparation
The projectile launch pad was made following the procedure of Lee et al. [1] using a 22×22 mm 2 microscope cover slip (Fisherbrand 12-541-B) with 10 nm of gold coated onto the cover glass using a sputter coater (Denton Desk V Sputter System). The PDMS pad was prepared using a PDMS kit (Sylgard 184, Dow Chemical), consisting of a DMS monomer and a hardener with a 10 to 1 ratio of DMS monomer to hardener. To make a 20 μm thick PDMS top layer, the liquid was spin coated at 3000-4000 rpm using a Laurell WS-400BZ-6NPP/LITE. Residual air pockets were removed by placing the cover slips in a vacuum (Lab-Line 3628-1 Squaroid Duo-Vac Vacuum Oven) for 30 minutes. The PDMS was further cured by post baking just under 60 °C for 24 h. Silica projectiles (microParticles GmbH, 3.72 μm diameter-silica density of 1,900 kg/m 3 ) were suspended and diluted in ethanol solution (0.015 wt%). A 10 μL pipet was used to place about 6 drops onto the PDMS launch pad and the silica particles were spread across the surface using a lab wipe sheet (Kimberly-Clark Kimwipe).

Electron Microscopy and Electron Diffraction
From examination of the micrographs of the tubes surrounding and adhering to the projectile, we are able to draw conclusions concerning the evolution of the shapes and positions of the tubes as influenced by the penetrating sphere. Transmission electron microscopy was performed on a FEI Titan Themis TEM operated at 80 keV. Bright field images at low beam flux and dose were taken to avoid specimen damage. Such images allow measurement of the MWCNT tube and bundle widths and the detailed network morphology of the tubes and bundles in a single sock layer and in the impacted regions of various thickness films for various incident velocities. Electron diffraction patterns of the pristine mats were obtained using a 20 micron diameter selected area diffraction aperture. SEM imaging of the uncoated MWCNT film, cross sections, deformation and perforation features was done using the FEI Helios NanoLab 660 SEM operated at 1 keV. Front and exit surface images were taken at tilts ranging from 0˚ to 52˚.

Mat Thickness Measurements
The thicknesses of the peeled MWCNT mat specimen targets were estimated from crosssectional SEM images. Before milling, a protective layer of ~200 nm of Pt was deposited onto the mat to minimize ion beam damage. The cross section was made with a Helios 660 instrument using the focused gallium ion beam (30 keV, 7.7 pA). Two to three thickness measurements were conducted at the sides of each perforation to obtain the average local mat thickness.

Normalization of Energy Absorption
In macroscopic ballistic testing, good ballistic materials dissipate the impact energy far beyond the region defined by the projectile strike face area. But because the actual amount of target material involved in the deformation is difficult to determine (there is often a strong radial gradient of the deformation and associated energy dissipated), it is common to use the mass of the material below the strike face area for normalization/comparison for all materials investigated (Table S2).

Fracture of MWCNTs
The published experimental quasi-static uniaxial work to fracture (toughness) of MWCNT fibers [2] (made in a process similar to Tortech) is 0.12 MJ/kg, about 100× smaller than our high rate value. Macroscopic, well aligned MWCNT fibers load elastically until failure when shear stresses cause the tubes to slide apart due to the very low inter-graphene shear strength with little to no actual tensile fracture of tubes. [3] On the contrary, the meandering collapsed tube network in the MWCNT mats dissipates energy due to many different deformation mechanisms and because of the loading geometry, importantly the specific work to fracture includes tensile fracture of principal tubes ( Figures S1 and S5).

Projectile Spin
The spherical projectiles are sometimes found after perforation with with tubes wrapped latitudinal directions ( Figure S4). This could arise from either having variable local mat properties such that the sphere penetrates more readily on one side or from projectile spin.
For example, in the left region of Figure S4a, the projectile has deflected part of the mat forward into a dome-like shape, but at the right side, the combination of the forward and rotational motions of the sphere have thinned the mat and extended and aligned the tubes into a parallel array with the direction of tube alignment normal to the axis of rotation. Previous LIPIT testing [1,[4][5][6] did not address projectile spin but here the occasional distinct latitudinal wrapping by the tubes clearly implies that friction strongly couples the tubes to the silica surface and that projectiles can sometimes carry rotational KE. We crudely estimate the (initial) surface rotational velocity and hence incident rotational kinetic energy of ⁄ , where I is moment of inertia of the projectile, by using the time it takes for the sphere to be

Strain Rate
The strain rate ⁄ varies greatly due to the complex microstructure of the MWCNT mat containing meandering and branched tubes resulting in differences of the loading of tubes in the impact area as well as significant densification and inwards flow of material into the deforming region. If we only consider the film to undergo 1D elastic deformation as done in previously, [1,5] the average ⁄ can be approximated as ~10 7 s -1 . Computational modeling of a shock impact into a thin film for velocities in the 300-900 m/s range shows that the local strain rates at the impact site are much larger due to the size effect and thermodynamic equilibration rate behind a shock front.

Air Drag Corrections
The influence of projectile-air drag and air resistance to the movement of the target film were considered on the translational KE loss of the projectile during target perforation as previously addressed. [5] In order to correct the initially measured velocity to the velocity just before impact and the measured residual velocity to that immediately after perforation of the film, we use our previous determination of the projectile drag coefficient C D , for different velocities (100-1000 m/s) measured using a multiframe video camera. The impact velocity is calculated from a double-exposure image of the projectile (with no target present) and the residual velocity is calculated in a separate measurement by a second double-exposure of the projectile after target perforation. We then recheck the v i without a target and find consistent values (e.g. 611±6 m/s). The small drag correction is applied to incident and exit velocities to give the instantaneous speeds at the target film location. Due to the high porosity of the thin MWCNT film and the relatively steep film shape during penetration/perforation, the target-air dissipation will be small and we estimate <0.06 nJ.

Figure S8. V50 ballistic limit
The V50 ballistic limit is an important standard for protective materials and was determined for the h 205 mats. The probability of perforation vs. impact velocity data was fit to logistic and probit curves [13] with 95% confidence level (CL) and both fits yield a nanoscale V50 as ~540 m/s (n = 51 shots). The close values of the probit and logistic 95% CLs indicates that the MWCNT material displays consistent ballistic performance over many impacts. [14]