Electrical conductivity and percolation threshold of hybrid carbon/polymer composites Atieh Motaghi, 1 Andrew Hrymak, 1 Ghodratollah Hashemi Motlagh 2 1 Department of Chemical & Biochemical Engineering, Western University, London, Ontario N6A 5B9, Canada 2 Department of Chemical Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran 14395/1311 Correspondence to: A. Hrymak (E - mail: ahrymak@uwo.ca) ABSTRACT: The electrical conductivity and percolation threshold of single and hybrid carbon filled composites are experimentally investigated. Polystyrene, carbon fiber (CF) and carbon black (CB) at three CF/CB ratios of 1.67, 3.33, 6.67 were compounded in a twin screw extruder micro-compounder and compression molded into sheets. The through-plane and in-plane electrical conductivity of the composites are measured by 2 and 4 probe techniques. The percolation threshold of the single filler and hybrid composites are determined from the experimental results using a percolation model. The hybrid composites have a higher value of electrical conduc- tivity and lower percolation threshold than the single CF filler composite except for the CF/CB ratio of 6.67. The percolation thresh- old for the cases of single filler and hybrid composites are modeled. The hard core / soft shell model is used and it is assumed that the percolation in a particle filled system depends on the ratio of tunneling distance to particle diameter. This ratio is determined by modeling single filler composites using the experimental data and kept constant in the modeling of the hybrid system. Finite size scal- ing is used to determine the percolation threshold for the infinite size hybrid system containing (nanosize) particles and micron size fibers for three CF/CB ratios. The simulation results show that the percolations of hybrid composites have the same trends observed in the experimental results. VC 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 41744. KEYWORDS: conducting polymers; polystyrene; theory and modeling; thermoplastics Received 4 August 2014; accepted 7 November 2014 DOI: 10.1002/app.41744 INTRODUCTION Most polymers are inherently electrically insulating. The electri- cal conductivity of polymers can be increased by the addition of conductive fillers. 1 Electrically conductive particles usually ran- domly distribute within an insulating matrix, and thus the entire composite may be insulating or electrically conducting depending on the percolation threshold, where the critical amount of conducting particles for the onset of electrical con- duction is reached and the electrical properties of the material typically exhibit a non-linear behavior. 2 The resulting conductive composites can substitute metals in some application such as electromagnetic shielding, and are light weight, and corrosion resistant thus lending themselves for special applications. 3–5 The electrical conductivity of composite materials has been modeled by several approaches for low or high content conduc- tive fillers. However, most existing models are not able to pre- dict the sharp transition in electrical conductivity. 6–9 Many attempts have been made to reduce the amount of filler by varying matrix type and filler size, shape and conductivity. Recently, combination of two types of conductive fillers has promoted the formation of a conductive network for transfer- ring charge within the insulating matrix. 10–13 At present, it seems there is insufficient knowledge about the physics of electrically networks of fillers in the polymeric mate- rial. To address the question of how to control the percolating network, percolation formulations in two- and three- dimensional systems for several types of lattice and continuum models (including circles, squares, sticks, spheres, and hemi- spheres) were first explored by Pike and Seager 14 Moreover, Ber- han and Sastry 15 proposed a more realistic model by investigating the percolation threshold of systems of three- dimensional straight spherocylinders, which are randomly ori- ented within a unit cube using both hard-core and soft-core models. 15 The soft core spherocylinder model erroneously sup- poses the fibers can merge, which can be significant even for very high aspect ratio fibers. The hard core spherocylinder model supposes the hard impenetrable core in fibers. Based on the excluded volume concept, it was found the percolation threshold is strongly dependent on the ratio of hard core to the soft shell rather than on the aspect ratio of fibers themselves. VC 2014 Wiley Periodicals, Inc. WWW.MATERIALSVIEWS.COM J. APPL. POLYM. SCI. 2015, DOI: 10.1002/APP.41744 41744 (1 of 9)