A stochastic algorithm for modeling heat welded random carbon nanotube network M. Kirca a , X. Yang b , A.C. To a,⇑ a Department of Mechanical Engineering and Materials Science, University of Pittsburgh, PA 15261, USA b Department of Power Engineering, North China Electric Power University, Baoding 071003, China article info Article history: Received 8 January 2012 Received in revised form 22 January 2013 Accepted 24 February 2013 Available online 13 March 2013 Keywords: Carbon nanotubes Network Foam Welding abstract Carbon nanotubes (CNTs) are one of the presents of nanotechnology being investigated due to their extraordinary mechanical, thermal and electrical properties. Carbon nanotube networks feed the idea that CNTs can be used as the building blocks of new advanced materials utilizing the superior character- istics of CNTs. In this way, nanoscale features of CNTs can be scaled up to even continuum proportions. In this study, 2-D and 3-D CNT network generation methods are introduced by which the geometrical parameters, such as CNT length, chirality, intersection angle and junctional density, can be controlled and a random CNT network is obtained. Then, molecular dynamics (MD) simulations are used to create covalent bonds between intersecting CNTs, which allow the investigation of the mechanical, thermal and electrical properties of random CNT networks. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction Carbon nanotubes (CNTs) are one of the extraordinary nanoma- terials that are promising candidates for thermal, electrical and structural applications due to their unique properties [1,2]. Since their discovery by Iijima (1991), thousands of studies, so far, have been adopted to their exceptional high strength and unusual elec- trical and thermal properties, displaying the desirable nature of their multifunctional capability. In the last years, the usefulness of CNTs has been enormously extended by their use as CNT net- works through which CNTs are self-intersected in two or three dimensional space [3–9]. Because of their strong electrical conduc- tivity with high light transmittance, CNT networks are attractive alternatives to silicon based macroelectronic devices [10]. Initial studies on 2-D CNT networks deposited onto flexible and polymeric substrates have focused on their electronic and sensor properties [11–14]. Several CNT network based thin films have been proposed to obtain lightweight, unbreakable displays and other flexible elec- tronic devices [15]. Bottom-up controlled production of such net- works can also enable them to be used in applications such as sensors, filters, composites and electromechanical actuators [1]. However, CNT networks also display the charming mechanical abil- ities of individual CNTs to macro-mechanical applications such as nanocomposites, similar to CNTs that are used as reinforcing units in nanocomposites, CNT networks can also be employed in nano- composites for both reinforcement and damage detection purposes [16–18]. In this study, a self-controlled algorithm for generating a 2- or 3-D CNT network consisting of randomly oriented and inter- sected CNTs has been introduced, and a heat welding method is ap- plied on sample networks to obtain covalently bonded networks by molecular dynamics (MD) simulations. Furthermore, a recently developed CNT aerogel [4] material that is nanostructured by self-intersecting CNTs forming a random net- work at the continuum scale is one of the important examples dis- playing an ultra-high stiffness-to-weight ratio material with conductive properties. Instead of having a reinforcement role in nanocomposites, this material enables the CNT network to consti- tute a bulk material on its own. Unquestionably, the electrical, thermal or mechanical proper- ties of CNT networks depend on the density of junctions between CNTs as well as junction properties and impurities throughout the network. It has been shown that electrical conductance and mechanical strength of the junctions may be enhanced by manip- ulating junction area, i.e. increasing the crossing area [19]. In this manner, the algorithm proposed in this study will provide com- plete control on the junction properties and all the other geomet- rical features (e.g. CNT length, diameter, CNT intersection angle), which will enable the exploration of CNT networks theoretically or numerically by using much more realistic models. Generally, CNT networks can be formed randomly by depositing CNTs locally on the catalyzed substrates by chemical vapor deposi- tion methods (CVD) or depositing from CNT embedded polymeric suspensions remotely by using spin coating, spray coating, or 0045-7825/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cma.2013.02.014 ⇑ Corresponding author. Address: Department of Mechanical Engineering and Materials Science, University of Pittsburgh, 508 Benedum Hall, Pittsburgh, PA 15261, USA. Tel.: +1 (412) 624 2052; fax: +1 (412) 624 4846. E-mail address: albertto@pitt.edu (A.C. To). Comput. Methods Appl. Mech. Engrg. 259 (2013) 1–9 Contents lists available at SciVerse ScienceDirect Comput. Methods Appl. Mech. Engrg. journal homepage: www.elsevier.com/locate/cma