THE MECHANICAL AND ELECTRICAL PROPERTIES OF DIRECT-SPUN CARBON NANOTUBE MATS

The mechanical and electrical properties of a direct-spun carbon nanotube mat are measured. The mat comprises an interlinked random network of nanotube bundles, with approximately 40 nanotubes in a bundle. A small degree of in-plane anisotropy is observed. The bundles occasionally branch, and the mesh topology resembles a 2D lattice of nodal connectivity slightly below 4. The macroscopic in-plane tensile response is elasto-plastic in nature, with significant orientation hardening. In-situ microscopy reveals that the nanotube bundles do not slide past each other at their junctions under macroscopic strain. A micromechanical model is developed to relate the macroscopic modulus and flow strength to the longitudinal shear response of the nanotube bundles. The mechanical and electrical properties of the mat are compared with those of other nanotube arrangements over a wide range of density.


Introduction
Individual carbon nanotubes (CNTs) possess exceptional mechanical and electrical properties [1]. The walls of CNTs have a Young's modulus of 1 TPa and a tensile strength of approximately 100 GPa [2], whilst isolated CNTs possess electrical conductivities of 2 x 10 7 s/m [3], ampacity of 10 13 A/m 2 [4], and thermal conductivity of 3500 W/mK [5]. These properties are sufficiently impressive that significant research and industrial interest has arisen in the development of materials with CNTs as their primary constituents, and suitable for manufacture in industrial quantities. The 'Windle Process' involves spinning a CNT aerogel from a gas phase, and has received much attention since the method was introduced by Li et al. [6] in 2004.
Methods for producing CNT materials may be divided into three families, together resulting in eight different types of CNT material. Figure 1 illustrates the three families, the methods which comprise them, and their morphologies. The first family involves processing vertically aligned CNTs grown from substrates by chemical vapour deposition; these CNT 'forests' may be (i) densified into pillars, (ii) spun into 1-dimensional fibres, or (iii) drawn into aligned 2-dimensional mats. The second family utilises liquids to create suspensions or solutions of short, mass-produced CNTs. CNT-solvent solutions can be filtered to create (iv) random planar 'buckypaper' mats, or spun into coagulating fluids to produce (v) single fibres. Porous CNT foams (vi) are often produced from aqueous gel precursors by critical point drying, or freeze drying. The final family uses direct-spun carbon nanotube aerogels, produced via the 'Windle process'. Direct-spun fibres (vii) are produced by on-line solvent-condensation of the aerogels; alternatively, the spinning of aerogel layers onto a rotating mandrel, with or without solvent condensation, produces direct-spun mats, labelled (viii).
Charts that summarise the elastic moduli, strength, and electrical and thermal conductivity as a function of density for these CNT-based materials are presented in Figure 2. Note that the bulk density of CNT materials ranges from a few kg/m 3 for CNT foams to over 1000 kg/m 3 for CNT fibres, whilst their moduli range from tens of kPa to hundreds of GPa. Large differences in strength and conductivity are also observed. Wide property variations occur between classes and also within individual material classes. For example, directspun materials exhibit a large variation in mechanical properties due to their range of material alignment and density [7].
The macroscopic modulus of CNT materials is much below the Voigt upper bound, based on the in-plane modulus of a CNT wall (i.e. graphene). A similar observation can be made for strength as follows. If the ultimate tensile strength of CNT walls is assumed to be 100 GPa, all CNT morphologies lie more than an order of magnitude below the Voigt bound for ultimate tensile strength, as illustrated in Figure 2(b). In broad terms, the moduli and compressive yield strength of CNT foams and CNT forest based materials appear to scale with density according to ~3 and ~2 respectively. This scaling law is representative of cellular solids of low nodal connectivity [8].
The modulus and ultimate tensile strength of aligned CNT materials, such as fibres spun from solution and mats drawn from CNT arrays, vary by up to two orders of magnitude for a given density. Electrical conductivity also exhibits considerable variation between categories and also within individual categories. In the case of fibres spun from solution, a high electrical conductivity close to the Voigt bound is possible due to doping by acids, or by treatment with iodine [9]. The specific electrical conductivities of these materials are close to those of metallic alloys. Now consider the chart of thermal conductivity versus density, see Figure 2(d). Aside from CNT foams, all categories of CNT materials have exceptionally high thermal conductivity compared to most other engineering solids. A line of specific thermal conductivity ⁄ = 0.0449 m 4 /Ks 3 , equal to that of pure copper, has been added to Figure 2(d). This line lies well below that of many CNT materials. Figure 3 presents a schematic of the continuous manufacturing method for direct-spun CNT materials as used in the present study, and the typical microstructure of CNT mat. A carbon source, often methane, is mixed with iron and sulphur catalysts and a carrier gas, typically hydrogen, in a furnace at 1570 K [10]. The catalysts initially vaporise but later, as the mixture cools, iron nanoparticles re-condense out of the gas phase.
The iron particles grow, and develop a sulphur coating [11]. Fullerene caps form on the surface of the nanoparticles, and the nanoparticles then evolve into individual CNTs [12], and these in turn bind together into a network of CNT bundles by van-der-Waals attraction [11]. This network forms a cylindrical aerogel 'sock', and the sock is drawn from the reactor by winding it onto a mandrel. The degree of anisotropy in directspun CNT materials is sensitive to the ratio of draw speed to velocity of gas flow [7]. Many layers of drawn   CNT aerogel stack to form a carbon nanotube mat. Immersion in a solvent, typically acetone, followed by evaporation, results in capillary condensation and a thinner, denser sheet [13].
Direct-spun mats exhibit three distinct hierarchies of microstructure, as illustrated in Figure 4: the carbon nanotube, nanotube bundle, and the interlinked bundle network [14]. Although CNT bundles possess high tensile strength and stiffness in the axial direction [15], the weak van-der-Waals bonds between adjacent CNTs endow the bundles with a low longitudinal shear modulus and strength [16][17][18] [19,20], and the additional presence of a polymer coating inherent to the chemical vapour deposition process can raise the inter-bundle shear-strength to 400 MPa [21,22].
While microscopy studies of CNT mats during interrupted tensile tests [22][23][24][25] have shed light on microstructural changes in CNT mats due to strain, they do not inform us about the deformation mechanisms.
To do so, in-situ observation is needed of microstructure evolution during tensile testing. In this study, we measure the nonlinear stress-strain response, piezoresistive behaviour [26] and electrical, physical and chemical properties of a commercially available direct-spun CNT mat. In-situ tensile tests reveal that the bundles undergo bending (and longitudinal shear) without slippage at junctions. A micromechanical model is then developed to relate the mechanical properties of the bundle network to those of individual bundles.

Materials and Methods
Direct-spun CNT mat was provided by Tortech Nano Fibers Ltd ‡ . 1 Before characterisation, the mat was Uniaxial tensile tests were performed using a screw-driven test machine, with the loading direction inclined at 0°, 45° and 90° to the draw direction of the CNT mat onto the mandrel. The test set-up is shown in Figure   5(a). The in-plane strain state was measured in the central portion of the sample by tracking the movement of dots of white paint applied prior to testing, using a digital camera and image processing software. Rollergrips enabled high tensile strains to be reached, with failure occurring at a strain level of 20% to 30%. In-situ tensile tests were conducted with a micro-test stage equipped with a 2N load cell, inside a scanning electron microscope (SEM).
The in-plane toughness was measured by a trouser-tear test [27], illustrated in Figure 5(b). This toughness is determined from the steady state load for tearing, , and the sample thickness, , according to = 2 ⁄ [28]. Trouser-tear tests were attempted in two directions, with the tear direction aligned with the draw direction, and in the transverse in-plane direction. Additionally, the out-of-plane delamination toughness, , was quantified by a peel test [29], as illustrated in Figure 5(c Now consider the measurement of electrical properties. The in-plane and through-thickness electrical conductivity were measured using a 4-point probe method, as illustrated in Figure 6. A 4-point probe was also used to measure the in-plane electrical resistance during tensile testing, at a strain rate of ̇ = 10 -4 s -1 . The tensile strain and in-plane resistance were measured with full, partial and cyclic unloading of stress, and a limited number of creep tests at constant stress were also performed.  The nominal stress-strain response, as illustrated in Figure 7(a), exhibited an initial linear behaviour, followed by a strain-hardening plastic response at approximately 4% strain. Above 15% strain, the hardening rate increases. The response has a moderate degree of anisotropy. The in-plane transverse strain is plotted as a function of tensile strain in Figure 7(b). The apparent Poisson's ratio, 12 , initially equals 0.6, but increases to between 2.7 and 3.5 at higher strains. An explanation for these high values of 12 is evident from images taken during in-situ tensile testing, see Figure 7(c), which illustrates the appearance of out-of-plane wrinkles at the micron level. This wrinkling appears to contribute to the compressive transverse strain. No noticeable rate dependency was observed for strain rates between 10 -4 s -1 and 10 -2 s -1 , as illustrated in Figure 7    The stress-strain and resistance-strain response with periodic partial unloading of samples at 0˚, 45˚ and 90˚ to the draw direction are illustrated in Figure 8  A stable response to cyclic stress is of importance in many sensing and structural applications. An initial exploration into the response under cyclic uniaxial loading was conducted by applying four loading packets of ten unloading cycles, with results as illustrated in Figure 8 This loading packet gave rise to an elastic response.
The creep behaviour of the CNT mat was investigated by holding a sample at a constant tensile stress of 8.3 MPa, 17 MPa, and then at 25 MPa, each time for 1500 seconds, before unloading the sample to 17 MPa for a further 1500 seconds. The strain, 11 , recorded at each of these constant stresses is plotted against time in Figure 8

A Model for in-plane Mechanical Properties
There is a major deficit in stiffness and strength when one compares individual CNTs with bulk CNT materials.
In the case of direct-spun mats, why does a random, interconnected network of CNT bundles possess inferior tensile properties to those of individual CNTs? This question is addressed via the model below.
At the microstructural level, the junctions between CNT bundles are of low nodal connectivity, of between 3 and 4. Consequently, the mechanical properties are governed by the bending and shear response of CNT bundles, rather than by axial stretch [30]. For an approximate prediction of stiffness and strength, this justifies the use of a periodic 2D honeycomb unit cell, as illustrated in Figure 10(a), with struts of thickness and length that deform by bending and shearing [8,30]. CNT bundles form the struts of this unit cell, and are connected to one another at nodes by the exchange of nanotubes from one bundle to the next. We write the relative density of the network ̅ = ⁄ as [8]: where is the angle of the inclined strut to the horizontal, see Figure 10 symmetry boundary conditions, as illustrated in Figure 10(b). The beam of length 2 ⁄ is built-in at its lefthand end, labelled 1, and is subjected to an end load 2 ⁄ at its point of inflection ( = 0), at location 2.
The co-ordinate along the beam mid-surface is . The bending moment along the beam ( ) and shear force ( ) are given by: where is the second moment of area, the cross-sectional area, and the shear coefficient equals = 8 9 ⁄ [31]. We substitute equation (4) into (2) and integrate to obtain Substitution of equation (6) and (3) into (5), followed by rearrangement and integration, yields It remains to estimate the shear modulus and axial modulus for a bundle. Whilst the axial bundle modulus derives from covalent bonding within the CNT wall, the shear modulus is dictated by the much more compliant van-der-Waals bonding between adjacent CNTs. We follow the approach of [18] in estimating the axial bundle modulus as = ( ⁄ ) where = 2200 kg/m 3 (i.e. that of graphene at an interlayer spacing of 0.34 nm). For = 1 TPa, it follows that = 680 GPa. Values for in literature have been deduced from in-situ 3-point bending tests [16,17], and from thermal vibration [32], varying from 0.7 to 6.5 GPa ± 50%. Our measured mat modulus of 3.3 GPa from unloading tests and assumed value for implies = 9.5 GPa via equation (10), which is within the range of experimental measurements [16]. Inspection of equation (10)  Now consider the tensile yield strength of the hexagonal lattice. The tensile stress on the outermost fibre of the inclined strut, due to the bending moment ( ) and axial tension, is given by whereas the average shear stress on the cross section due to the shear force ( ) is given by = ( )⁄ .
As the bending moment is greatest at the location labelled 1 on the inclined strut illustrated in Figure 10 The ratio between bundle tensile stress and average shear stress is given by = 9 2 cos (1 + sin ) ̅ + sin cos .
Now, for a relative density ̅ = 0.25 and = 6 ⁄ , it follows that ⁄ = 14.4. If the ratio of bundle tensile strength to bundle shear strength is greater than ⁄ , macroscopic yield will be limited by the bundle shear strength, rather than by the fracture of CNT walls. We argue that this is the case, on the basis that that the ratio ⁄ is more than four times greater than ⁄ , with the following justification.
Tensile tests conducted on individual CNT bundles grown by the chemical vapour deposition process suggest that the wall fracture strength of individual CNTs lies between 5.5 GPa and 25 GPa [22]. Assume that the bundle strength scales with the CNT wall strength according to = ( ⁄ ) , and take = 5.5 GPa. Then, the bundle fracture strength equals = 3.7 GPa.
Now consider the CNT bundle shear strength . Values for the bond shear strength between CVD-grown tubes, as measured in the literature, vary from 0.04 MPa to 70 MPa [19,20], with values sensitive to the concentration of graphitic defects [20,33]. For adjacent pristine CNT surfaces with long overlap lengths, the bond shear strength lies between 30 MPa and 60 MPa [34]. Here, we shall assume the value = 60 MPa, as this implies a macroscopic yield stress of 17 MPa from equation (12)   Appendix A: Composition of the Direct-Spun Mat The chemical composition of the mat was determined by thermogravimetric analysis, conducted using a PerkinElmer TGA 4000. The temperature was held at 100 °C to remove adsorbed moisture, then increased at a scan rate of 5 °C/min. The results revealed an Fe content of 6 wt. %, remainder CNT; the relationship between sample mass and temperature, and the rate of mass change with respect to temperature are plotted in Figure A.1(a).
The Raman spectrum of the CNT mat was obtained with an EZRAMAN-N instrument, using a laser power of 50 mW, and 3 scans at 30 seconds integration time. A Raman spectrum of the CNT mat is illustrated in Figure   A.1(b). The high intensity G-band at 158 mm -1 corresponds to vibration of sp 2 bonds. Dividing the G-band intensity by that of the D-band at 134 mm -1 gives a G/D ratio of 4.5. The D-band results from the breathing mode of a six-fold aromatic ring, and cannot occur unless disorder is present, either in the crystalline structure of the CNT walls, or in the form of additional amorphous carbon materials [35,36]. The relatively high G/D ratio observed here indicates that neither of those defects are particularly prevalent. The absence of radial breathing modes at low frequency (<50 mm -1 ) indicates that small diameter single-or double-walled CNTs are not present within the mat [35].
Bundle density was determined with helium pycnometry (performed by Quantachrome UK Ltd). This involves placing a CNT mat sample in a chamber of known volume, which is then purged of air and pressurised with helium gas. After the pressure of this chamber is measured, a valve is opened to link it with another chamber of known volume, initially at vacuum. After the pressure has stabilised, it is recorded; the perfect gas law is then used to calculate the sample volume from the measured gas pressures and known chamber volumes.