Liquid-induced collapse ('zipping') of vertically aligned single-walled carbon nanotube (SWNT) forests yields single-body solids with near-graphitic inter-tube packing, high orientational order (X-ray order parameters 0.62-0.72, polarized Raman G-band anisotropy ratio 6.8), and strongly anisotropic ion transport (tortuosity 1.3 along the tube alignment versus 16 across it). Yet the electronic transport of these same solids is nearly isotropic: sheet resistance and DC conductivity differ by only a factor of about 1.5 between the directions parallel and perpendicular to the nanotube alignment. The unresolved problem is to determine the microscopic origin of this discrepancy between structural and electronic anisotropy - attributing and quantifying the role of each candidate mechanism, inter-tube electronic coupling and contact resistance, phonon-assisted inter-tube tunnelling, tube waviness and percolation-path geometry, and chirality/disorder effects - and to establish a quantitative, predictive relation between alignment, packing, and electronic anisotropy in dense SWNT solids, and whether and by which microstructural modifications that anisotropy can be substantially increased while retaining the high density and aligned ion-transport pathways.

Background

A single-walled carbon nanotube (SWNT) is a rolled-up graphene sheet with a nanometre-scale diameter; millimetre-tall vertically aligned SWNT 'forests' can be grown by water-assisted chemical vapour deposition, but as-grown forests are about 97% void, so their volumetric loading of active material is far too low for compact devices. Futaba, Hata and co-workers (Nature Materials 5, 987-994, 2006) showed that immersing an intact forest in a liquid and letting the liquid evaporate draws neighbouring tubes together by capillary forces, and van der Waals attraction then 'zips' them into a single-body, densely packed, still-aligned SWNT solid: the mass density rises from about 0.0290.029 to about 0.57 g cm−30.57\ \mathrm{g\,cm^{-3}}, the Brunauer-Emmett-Teller (BET) gas-adsorption surface area stays near 1000 m2 g−11000\ \mathrm{m^2\,g^{-1}}, and Raman spectra are unchanged. Because such solids combine high accessible surface area, high active-material fraction per volume, binder-free electrical continuity and engineerable shape, they were proposed and demonstrated as electrodes for electric double-layer capacitors (EDLCs, also called supercapacitors), which store charge by ionic separation at the electrode-electrolyte interface.

The 2006 paper noted several issues for future work, among them a striking transport puzzle. Structurally, the solid is well aligned: polarized Raman spectroscopy gives an anisotropy ratio of 6.8 for the G band (the graphitic vibrational mode of the nanotube walls, whose intensity depends on the angle between the laser polarization and the tube axis), and two-dimensional X-ray diffraction yields orientational order parameters f(002)=0.72f_{(002)}=0.72 and fCP=0.62f_{\mathrm{CP}}=0.62 (equal to 1 for perfect alignment of the tube axes). Electronically, however, four-point-probe sheet resistance (the lateral resistance of a square sheet of material, quoted in ohms per square) of a 50 μm50\ \mu\mathrm{m}-thick solid sheet was 1.74 Ω1.74\ \Omega per square along the alignment versus 2.61 Ω2.61\ \Omega per square across it - an anisotropy of only about 1.5. Later measurements by the same group (JACS 2010) of the DC conductivity of a 1 mm31\ \mathrm{mm^3} densified aligned solid cube gave 24 S cm−124\ \mathrm{S\,cm^{-1}} (parallel) versus 16 S cm−116\ \mathrm{S\,cm^{-1}} (perpendicular), confirming the weak electronic anisotropy, while ion diffusion in the same solid was strongly anisotropic: the effective diffusion coefficient of an electrolyte along the tube alignment, D∥=1×10−5 cm2 s−1D_{\parallel}=1\times10^{-5}\ \mathrm{cm^2\,s^{-1}}, corresponds to a tortuosity (ratio of effective path length to straight path length) of 1.3, near the theoretical optimum, whereas across the alignment D⊥=8×10−7 cm2 s−1D_{\perp}=8\times10^{-7}\ \mathrm{cm^2\,s^{-1}} gives tortuosity 16.

This makes the solid an anomalous case within the broader literature on aligned nanotube assemblies. In highly aligned ultralong SWNT films, Pint et al. (APL 2009) measured a conductivity anisotropy ratio of about 175, with parallel transport following one-dimensional and perpendicular transport three-dimensional Mott variable-range hopping (a thermally activated hopping mechanism between localized states whose exponent reveals the effective dimensionality of the hopping network) - so large electronic anisotropy is attainable in aligned SWNT assemblies. Zamora-Ledezma et al. (Phys. Rev. E 2011) modelled the conductivity anisotropy of oriented nanotube films as a geometric percolation effect: the number and length of conducting paths, and hence inter-tube contacts, along each direction are set by the orientation distribution, giving ratios of order 8 for orientational order parameter near 0.6. For phonons the picture is starker still: Yamaguchi et al. (APL 2019) found a thermal-conductivity anisotropy ratio of about 500 in densely aligned SWNT films, controlled by the weak inter-tube contact conductance. On the microscopic side, Adinehloo et al. (PRL 2023) computed the inter-tube electronic conductance of nanotube junctions, including phonon-assisted tunnelling and contact relaxation, and showed it can account for macroscopic film conductance. None of these works, however, explains why the liquid-collapsed dense SWNT solid - with order parameters 0.62-0.72 - shows an electronic anisotropy of only about 1.5, far below both its own optical/ion-transport anisotropy and the values achieved in other aligned SWNT films. The original paper attributed the matter to unexplored inter-tube electronic coupling and contact resistance within the solid, and this attribution has not been converted into a quantitative account.

Problem Statement

For densely packed, aligned SWNT solids produced by liquid-induced collapse of vertically aligned forests, determine the microscopic origin of the discrepancy between structural and electronic anisotropy: the solids exhibit high orientational order (X-ray order parameters 0.62-0.72, where 1 means perfect alignment of the tube axes, and a polarized-Raman G-band anisotropy ratio of 6.8) and strongly anisotropic ion transport (tortuosity, the ratio of the effective ion path length to the straight path length, of 1.3 along versus 16 across the alignment), yet their electronic conductivity is nearly isotropic (about 2424 versus 16 S cm−116\ \mathrm{S\,cm^{-1}}; sheet resistance 1.741.74 versus 2.61 Ω2.61\ \Omega per square). The question has three parts: (i) Attribute and quantify the role of each of the candidate mechanisms - inter-tube electronic coupling and junction (contact) resistance, phonon-assisted inter-tube tunnelling, tube waviness and the geometry of percolating conduction paths, and the chirality/defect distribution of the tubes - in setting the observed electronic anisotropy, including any candidate mechanism whose role proves negligible. (ii) Establish a predictive quantitative relation between the orientation distribution, packing density and inter-tube contact network of such solids and their directional electronic conductivity, consistent with the measured values above and with the much larger anisotropy ratios (up to about 175) reported for other highly aligned SWNT films. (iii) Establish whether and by which microstructural modifications (for example improved alignment or straightness, controlled junction density, or chirality sorting) the electronic anisotropy of these dense solids can be substantially increased while retaining the high density, aligned ion-transport pathways and binder-free integrity that make them attractive as compact supercapacitor electrodes.

References

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