Figure 19. AFM (left) and UFM (right) image data of a carbon MWNT deposited via chemical vapor deposition (1 /m x 1 /m scan). The nominal diameter of the uniform section is 63 nm (image not corrected for tip convolution). The tube consists of a central uniform region and two defected regions near the edges of the scan. The defected regions are characterized by axial variations of the tube radius (so-called volume defects ). Significant modulus variations (apparent in the UFM scan) accompany these defects.
the unique electrical and thermal conduction properties of NTs provide other avenues for nanocomposite material design. From a purely mechanics point of view, the critical parameter for composite performance is the interfacial stress transfer ability (sustainable load transfer) between the matrix and the reinforcing component (typically fibrous) . This elevates materials processing issues, including NT alignment, NT dispersion, and NT/matrix interfacial adhesion to a level equal to that of NT materials properties. Early studies noted poor adhesion between NTs and an epoxy matrix [84, 136] following cutting of a crude composite with a microtome. The NTs were essentially pulled from the composite during the process, and effectively aligned. While highlighting the strength of carbon NTs, this early observation underscored material challenges in NT-based nanocom-posite engineering.
Wagner et al. investigated the nanotube-matrix stress transfer efficiency of composites consisting of arc-deposited MWNTs dispersed in a urethane/diacrylate oligomer prior to curing . Their results indicated an increase in this stress transfer efficiency by over an order of magnitude compared to conventional carbon fiber-based composites. This increase is attributed to a possible "2 + 2" cycloaddition reaction occurring at the polymer/NT interface. Fragmentation of nanotubes within the composite during stress testing lends credence to the high interfacial adhesion in this system. Characterization of the load-transfer ability of carbon nanotubes was also investigated by Schadler and coworkers . The optimization of load transfer requires a high interfacial shear modulus to effectively transfer the applied load to the fiber. Important factors in optimizing this modulus are micromechanical interlocking between fiber and matrix, and bonding (either covalent or van der Waals) between the two. For NTs (5% by weight) dispersed in a Shell Epon 828 epoxy resin, Schadler noted an increase in the tensile modulus ET from 3.1 GPa for the epoxy alone to 3.78 GPa for the composite. The compression modulus exhibited a larger increase from EC = 3.63 to 4.5 GPa. The hysteretic nature of the stress-strain curves in the composite is attributed to either poor bonding between the matrix and the outer surface of the nanotube, or slipping within individual MWNTs, resulting in load transfer to only the outermost layer. Compared to the earlier work of Wagner et al. , the latter was presumed responsible.
For composites requiring high uniaxial strength, NT alignment and dispersion are critical parameters. Anisotropic mechanical stress was shown to align NTs in a thermoplastic polymer. Zhou and co-workers dispersed MWNTs produced via the arc-discharge method into a chloroform/polyhydr-oxyaminoether (PHAE) mixture . Anisotropic stress was applied to the postdried composite mixture (50% NT by weight) at 373 K. After cooling and release, the NT orientation distribution was characterized via X-ray diffraction and transmission electron microscopy. The former revealed an NT mosaic of approximately ±23° roughly parallel to the composite stretching direction. Internal fractures in the composite displayed NT pull out similar to previous work, highlighting the need for optimization of NT/composite adhesion in the PHAE/NT system.
Composite films consisting of polyvinyl-alchohol (PVA) and MWNTs were studied by Shaffer and Windler .
Using short-fiber composite theory, they inferred an elastic modulus of the MWNTs of 150 MPa, approximately three orders of magnitude lower than direct measurements. This implies poor stress transfer properties of the matrix/NT interface, most likely driven by the polymer system considered. In contrast, Qian et al.  examined a polystyrene composite containing 1% by weight carbon MWNTs. The elastic stiffness and tensile strength of the NT composite increased 39 and 25%, respectively. Similar to other studies of NT composites, fracture in the NT/polystyrene system revealed NT pull out from the matrix. Increases in composite performance were also observed by Andrews et al. for 5% (by weight) SWNTs dispersed in pitch precursors (Ashland A500 petroleum pitch) . Increases in the tensile strength from 500 MPa (pure pitch) to 850 MPa (pitch + SWNTs) were observed. The measured modulus values were 35 and 80 GPa without and with SWNTs, respectively.
As noted, stress transfer is the key figure of merit for the exploitation of nanotube mechanical properties in composites. Hence, the optimization of matrix/nanotube adhesion is critical. Liao and Li carried out theoretical investigations of a double-wall nanotube/polystyrene system using classical elasticity theory and molecular mechanics simulations to investigate this . In their study, no covalent bonding was specifically considered. Rather, the simulations implied that electrostatic and van der Waals interactions between the polystyrene molecules and the nanotube surface dominated the adhesion energy. These authors also noted that mechanical deformation of the nanotube in the matrix will contribute to the adhesion. Their work pointed to mismatches in the coefficient of thermal expansion (CTE) as an important source of such deformation. Simulations of composite "cooling" from the melt implied that CTE mismatches were the primary cause for stress-induced nanotube deformations that resulted in corresponding adhesion improvements. A possible experimental route to optimize electrostatic pathways to increase NT/matrix adhesion was taken by Gong et al. . That group utilized nonionic surfactants to improve the processing of NTs in an epoxy matrix with respect to dispersion and interfacial adhesion. An increase in the elastic modulus of 30% was seen; however, no comparative conclusions could be drawn regarding the modification of interfacial adhesion.
One aspect not already discussed is the effect of the multiwall nature of the tube during deformation in a nanocom-posite matrix. Simplistic models assume a uniform "nonslip" bending of MWNTs in elastic composites. However, intershell slipping may significantly alter the mechanical response of the composite. This issue was considered in detail by Ru . Using a multiple-shell model to study the compressed buckling of MWNTs, Ru incorporated a direct van der Waals coupling between the interior NT walls. Compared to an equivalent "single-wall" shell, the axial buckling strain for the multiple-shell model exhibited significant degradation (proportional to 1/N, where N is the wall number). This degradation was attributed to interwall slips during bending. Although such an effect has not been demonstrated experimentally, it is an extremely important result in mapping the potential performance of MWNTs in composite applications.
Nanocomposites have also been exploited for other aspects of nanomechanical research. Li et al. used a nanocomposite to infer the elastic modulus of SWNT ropes . Such ropes were dispersed in a polyvinyl chloride resin, and subjected to standard mechanical testing. Similar to other studies, nanotube pull out was a common feature of the fracture surface, and it was noted that the stress transfer from the SWNT bundles to the matrix resin was poor. From these experiments, average tensile strengths of the composites, the SWNT ropes, and the individual SWNTs were measured at 3.6, 7.5, and 11.5 GPa, respectively, on the basis of the rule of mixtures. The anomalously low value of the latter quantity is more indicative of the poor adhesion at the resin/NT interface rather than the true mechanical property of the SWNT itself.
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