Multiscale modelling of electron transport in carbon nanotube reinforced composites

Abstract

Development of functional composite materials by addition of inorganic inclusions to polymer matrix attracts growing attention in last decades and carbon nanotubes (CNT) attract particular interest as reinforcement material due to their unique properties tunable by doping and functionalization. However such material characteristics depend not only on the concentration and properties of nanoinclusions but also on their distribution inside embedding polymer, mutual orientation, interaction with surrounding matrix etc., which complicates prediction and optimization of composite properties and leads to large discrepancies in experimental data [1]. Different properties of carbon nanotubes were successfully studied in silico in numerous papers by atomistic calculations. However computational chemistry is limited to systems containing hundreds to several thousands of atoms so only fragments of polymer chains and nanotubes are accessible. Meanwhile optical microscopy analysis shows that industrial-scale CNT-polymer composites contain distribution irregularities and agglomerates of CNTs up to ~10 micron size [2]. Charge transport in such composites mostly explained by electron tunneling between conductive inclusions, probability of which depends on nanotube's electronic structure as well as on tunneling distance and local electric field in the contact region, affected by the presence of other conducting inclusions. To facilitate the investigation of CNT-polymer composites' electric properties a two-level modeling procedure is suggested: first, local density of states (LDOS) around CNT's Fermi level is evaluated from ab initial calculations including the effect of doping and functionalization, then a Monte Carlo simulation of charge transport between CNTs is carried out where the tunneling probability is estimated using previously calculated LDOS and simplified representation of electronic wave functions in the inter-CNT space as spherical or cylindrical waves. The suggested procedure, although very simplistic, allows charge transport studies on a length scales of ~100 um compared to the scale of CNTs' distribution irregularities in composites and direct comparison with experimental data. In this work we study the impact of nanotube agglomerates' size and volume fraction on the composite electrical conductivity by computer modeling. Model samples are created by home-developed tool to generate non-uniform filler particle distribution according to a predefined probability map avoiding unphysical intersection of inclusions. Variations of as generated samples due to change in filler content and agglomerates' amount and size distribution is then studied by three methods: finite difference solution of Kirchhoff's current equation using continuum percolation-like local conductivity dependence on CNT volume fraction, construction of equivalent resistor network and statistical simulation of electron tunneling using Monte Carlo approach. REFERENCES [1] Z. Spitalsky, D. Tasis, K. Papagelis, C. Galiotis, Prog. in Polymer Sci. 35, 357-401 (2010). [2] G. Olowojoba, S. Sathyanarayana, B. Caglar, B. Kiss-Pataki, I. Mikonsaari, C. Hübner, and P. Elsner. Polymer, 54(1), 188 – 198 (2013).