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Computational Description of the Geometry of Aligned Carbon Nanotubes in Polymer Nanocomposites



The paper considers nanocomposites, reinforced with aligned carbon nanotubes (A- CNTs). Nominally aligned, the CNTs in the forest are wavy, which has important consequences in downgraded mechanical properties, and influences electric and thermal performance. The most detailed geometrical model of A-CNTs was proposed by Stein and Wardle (Nanotechnology, 27:035701, 2015). It creates a centerline trajectory of a CNT in steps, each step defining a section of the CNT, growing in the alignment direction with certain deviations. The paper, starting from this framework, formulates a model of the CNT geometry, which is based on the concept of correlation length of the CNT waviness and maximum admissible CNT curvature and torsion. The value of the maximum curvature can be linked to the buckling criteria for CNTs, or derived from ab initio and finite element modelling. It is used as a limiting factor for the growth, defining the waviness and tortuosity of the CNTs. The CNTs in the forest are placed in a random non-regular way, using Voronoi tessellation. The full paper includes investigation of the proposed algorithm for several values of the CNT volume fraction (in the range 0.5%…8%), the dependency of the modelled geometry on the curvature, and the apparent twist of the CNT centerlines. The modelling results are compared with experimental observations in 3D TEM imaging.


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Natarajan, B., I.Y. Stein, N. Lachman, N. Yamamoto, D. Jacobs, R. Sharma, J.A. Liddle, and B. Wardle, Aligned Carbon Nanotube Morphogenesis Predicts Physical Properties of their Polymer Nanocomposites. Nanoscale, 2019. 11: p. 16327.

Stein, I.Y., D.J. Lewis, and B.L. Wardle, Aligned carbon nanotube array stiffness from stochastic three-dimensional morphology. Nanoscale, 2015. 7(46): p. 19426-19431.

Stein, I.Y. and B.L. Wardle, Mechanics of aligned carbon nanotube polymer matrix nanocomposites simulated via stochastic three-dimensional morphology. Nanotechnology, 2016. 27(3): p. 035701.

Stein, I.Y. and B.L. Wardle, Packing morphology of wavy nanofiber arrays. Physical Chemistry Chemical Physics, 2016. 18(2): p. 694-699.

Blacklock, M., H. Bale, M. Begley, and B. Cox, Generating virtual textile composite specimens using statistical data from micro-computed tomography: 1D tow representations for the Binary Model. Journal of the Mechanics and Physics of Solids, 2012. 60(3): p. 451-470.

Vanaerschot, A., B.N. Cox, M. Blacklock, G. Kerckhofs, M. Wevers, S.V. Lomov, and D. Vandepitte, Stochastic framework for quantifying the geometrical variability of laminated textile composites using micro-computed tomography. Composites Part A, 2013. 44: p. 122-131.

Vanaerschot, A., B.N. Cox, S.V. Lomov, and D. Vandepitte, Simulation of the cross-correlated positions of in-plane tow centroids in textile composites based on experimental data. Composite Structures, 2014. 116: p. 75-83.

Vanaerschot, A., B.N. Cox, S.V. Lomov, and D. Vandepitte, Experimentally validated stochastic geometry description for textile composite reinforcements. Composites Science and Technology, 2016. 122: p. 122-129.

Vanaerschot, A., B.N. Cox, S.V. Lomov, and D. Vandepitte, Multi-scale modelling strategy for textile composites based on stochastic reinforcement geometry. Computer Methods in Applied Mechanics and Engineering, 2016. 310: p. 906-934.

Fast, T., A.E. Scott, H.A. Bale, and B.N. Cox, Topological and Euclidean metrics reveal spatially nonuniform structure in the entanglement of stochastic fiber bundles. Journal of Materials Science, 2015. 50: p. 2370-2396.

Romanov, V., S.V. Lomov, I. Verpoest, and L. Gorbatikh, Modelling evidence of stress concentration mitigation at the micro-scale in polymer composites by the addition of carbon nanotubes. Carbon, 2015. 82: p. 184-194.

Yao, X.H., Q. Han, and H. Xin, Bending buckling behaviors of single- and multi-walled carbon nanotubes. Computational Materials Science, 2008. 43(4): p. 579-590.

Cao, G.X. and X. Chen, Buckling behavior of single-walled carbon nanotubes and a targeted molecular mechanics approach. Physical Review B, 2006. 74(16).

Silvestre, N., On the accuracy of shell models for torsional buckling of carbon nanotubes. European Journal of Mechanics A/Solids, 2011. 32: p. 103-108.

Deserno, M., How to generate exponentially correlated Gaussian random numbers. 2002, Department of Chemistry and Biochemistry, UCLA, USA.

Chen, J.-T., Using the sum-of-uniforms method to generate correlated random variates with certain marginal distribution. European Journal of Operational Research, 2005. 167(1): p. 226-242.

Natarajan, B., N. Lachman, T. Lam, D. Jacobs, C. Long, M. Zhao, B.L. Wardle, R. Sharma, and J.A. Liddle, The evolution of carbon nanotube network structure in unidirectional nanocomposites resolved by quantitative electron tomography. ASC Nano, 2015. 9: p. 6050-6058.

Liddle, J.A., Transmission electron microscope tomographic data of aligned carbon nanotubes in epoxy at volume fractions of 0.44%, 2.6%, 4%, and 6.9%, National Institute of Standards and Technology. 2020.

Straumit, I., S.V. Lomov, and M. Wevers, Quantification of the internal structure and automatic generation of voxel models of textile composites from X-ray computed tomography data. Composites Part A, 2015. 69: p. 150-158.

Advani, S.G. and C.L.I. Tucker, The use of tensors to describe and predict fibre orientation in short fibre composites. Journal of Reology, 1987. 31(8): p. 751-784.


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