Estimation of average contact number of carbon nanotubes (CNTs) in polymer nanocomposites to optimize the electrical con

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ORIGINAL ARTICLE

Estimation of average contact number of carbon nanotubes (CNTs) in polymer nanocomposites to optimize the electrical conductivity Yasser Zare1 · Kyong Yop Rhee2 Received: 8 June 2020 / Accepted: 18 August 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020

Abstract The present paper suggests an equation for the average contact number of carbon nanotubes (CNTs) in CNT-reinforced polymer nanocomposites (PCNT) by two developed equations for electrical conductivity. Several novel parameters in PCNT such as CNT size, CNT concentration, network fraction, interphase depth, tunneling effect, and CNT wettability by the polymer medium are considered to define the average contact number (m). “m” is calculated for some samples and the variation of “m” is explored over a range of parameters’ values. The results show that dense interphase, high fraction of networked CNTs, reedy and short CNTs, low CNT surface energy, high polymer surface energy, low tunneling distance, and small contact diameter increase the “m” improving the conductivity. Moreover, tunneling distance and CNT contact diameter have the greatest effects on the “m”. The optimized level for “m” is necessary to control the nanocomposite’s conductivity. Keywords  Carbon nanotubes (CNTs) · Polymer nanocomposites · Contact number · Tunneling effect

1 Introduction Carbon nanotubes (CNTs) are promising nanofiller for the preparation of advanced nanocomposites, due to their excellent mechanical and conductivity performances [1–16]. The extraordinary electrical conductivity of polymer nanocomposites reinforced by CNTs (PCNT) progresses some latent requests in electronic engineering, sensing, protecting and activating [17–19]. The PCNT conductivity meaningfully advances when nanoparticles establish the conductive networks at percolation threshold [20, 21]. However, the percolation threshold and conductivity of PCNT not only depend on the properties of polymer and CNTs, but also correlate to some special terms attributed to nanoscale such as tunneling effect and interphase regions [22–24]. The earlier

* Kyong Yop Rhee rheeky@khu.ac.kr 1



Biomaterials and Tissue Engineering Research Group, Department of Interdisciplinary Technologies, Breast Cancer Research Center, Motamed Cancer Institute, ACECR, Tehran, Iran



Department of Mechanical Engineering, College of Engineering, Kyung Hee University, 1 Seocheon, Giheung, Yongin, Gyeonggi 449‑701, Republic of Korea

2

researchers have commonly neglected the characters of these terms in the conductivity. The key instrument for PCNT conductivity is tunneling effect involving the electrons conveyance over contiguous CNTs [25, 26]. Therefore, the electron hopping via small tunnels can increase the conductivity of PCNT. This mechanism is meaningful for small distance between adjacent CNTs (< 10 nm [27]), but the mainly detached CNTs cannot provide the tunneling consequence. Generally, the nature of the conductive mechanisms in polymer nanocomposites is highly affected by temperature, electrical fiel