Multi-scale approach for prediction of electrical properties of carbon nanotube reinforced polymers
Final Report Abstract
Aim of this project was the investigation of simulation-based prediction of electrical conductivity in carbon nanotube reinforced polymers (CNRP) by combining atomistic and mesoscopic models. This multi-scale combination helps to understand the transport mechanism at atomistic scale on one hand and to estimate the effect of CNT distribution inside a polymer matrix on the electrical transport at mesoscopic scale on the other hand. CNTs are predestined for such multi-scale simulation approaches since they are both objects at atomistic scale with diameter of several nanometres underlying atomistic effects like electron tunneling as well as objects at mesoscopic scale with lengths of micrometres underlying macroscopic conditions like process-induced CNT distributions. Main problem for simulation models of CNRP is the huge computational effort. Neither mesoscopic simulation models with a precision of nanometres nor atomistic simulation models extended to micrometres have the possibility to obtain results on an acceptable time scale. Hence, both approaches adapt their models to the results of the other length scale. Atomistic models got their main leakage at system size of several nanometres and are limited concerning realistic CNT distributions within CNRP or different volume fractions. Furthermore, atomistic results are very sensitive to various conditions like system temperature, pressure, lattice details between two CNTs as CNT-CNT stacking or CNT structure (zig-zag, armchair or chiral). In the opposite direction, mesoscopic models neglect various impact parameters like temperature differences, orientation of polymer molecules or time-dependency of the system. Effects of atomistic details on electrical conductivity are averaged according to the solution of a nearly constant, rectangular potential barrier. Even the differentiation between multi-wall and single-wall CNTs is reduced to a constant factor. However, the project results demonstrate a possible parameter which links atomistic and mesoscopic simulation models. Increasing the distance between two adjacent CNT tips, polymer molecules start penetrating the space between those CNTs as recently as a certain distance is reached. Below this distance polymer molecules are excluded between the CNTs according to repulsive forces between carbon atoms of CNTs and polymer atoms. As polymer molecules fill the space between the CNTs, the transmission coefficient shows a significant sharp increase due to enhanced electrical conductivity. Above the distance the transmission coefficient decreases as well as common tunnel effects. Since the transmission coefficient is divided into two regions due to this result, the mesoscopic model assumes a polymer CutOff as the critical distance from which on polymer molecular are located between CNTs and contribute to an increase of the transmission coefficient. Moreover, atomistic simulations demonstrate a fluctuation of conductance for various angles between two CNTs in the range of one magnitude and mesoscopic simulations show a dependency of electrical conductivity on the curvature degree of CNTs and their alignment to current flow direction. From mesoscopic view there is an optimised arrangement for approximately isotropic electrical conductivity for slightly curved and slightly aligned CNTs in direction of current flow. The industrial relevant determination of the minimal amount of CNTs inside a CNRP to turn the composite into a conductor (percolation threshold) is estimated with a fitting function. The percolation threshold is one parameter of the fitting function for several conductivity values of different CNT volume fractions. The accuracy of the percolation threshold value differs since the setting of CNTs inside a CNRP is assumed to be random and may differ in realistic composite due to the manufacturing process. The most important outlook is the transferability of the multi-scale simulation model on another polymer matrix material. A calculation of the specific polymer CutOff with atomistic simulations and its possible influence on electrical conductivity at mesoscopic scale is going to clarify whether this linkage parameter between atomistic and mesoscopic simulation models has a significant impact and have to be regarded. Furthermore there are possible outlooks at both length scales like investigations of conductivity dependency on various CNT-CNT junction angles with distances larger than direct contact at atomistic scale or further development of mesoscopic simulations concerning bending of adjacent CNTs.
Publications
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“Atomistic Modeling of Charge Transport across a Carbon Nanotube-Polyethylene Junction”, Journal of Physical Chemistry C, pp. 8020-8027, 117, 2013
G. Penazzi, J. Carlsson, C. Diedrich, G. Olf and A. Pecchia
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“A Self Energy Model of Dephasing in Molecular Junctions”, Journal of Physical Chemistry C, pp. 16383-16392, 120 (30), 2016
G. Penazzi, A. Pecchia, V. Gupta and T. Frauenheim
