Flexural deflection as a measure of van der Waals interaction forces in the CNT array

The flexural stiffness of the hexagonal carbon nanotube (CNT) array is shown to directly correlate with the magnitude of the shearing traction between the individual CNT and thereby provide a convenient measurement of van der Waals forces in the CNT hexagonal array. Relationships for flexural stiffness and shearing traction are developed systematically and illustrated for the 7, 61 and127-element arrays. Shearing traction is calculated for a lateral load sufficient to produce lateral deflection of the array equal to 10% of the span length. Both fixed–fixed and simple–simple beam end conditions are examined. Model predictions are combined with the experimental results of Salvetat et al. [Salvetat J-P, Briggs GAD, Bonard J-M, Bacsa RR, Kulik AJ, Stockli T, Burnham NA, Forro Laszlo. Elastic and shear moduli of single-walled carbon nanotube ropes, Phys Rev Lett 1999;82(5):944–7.] to determine the magnitude of the maximum shearing traction due to van der Waals forces in each of the arrays. Shearing tractions are shown to vary from 140 to 260 MPa over the range in number of array elements from 7 to 127 and array heights from 4.7 to 19.7 nm. These new results suggest that the van der Waals interactions will likely provide array coherence and cohesiveness sufficient for the CNT arrays of 7, 61 and 127 elements to serve as effective reinforcements in high performance materials.