Tensile strength prediction of carbon nanotube reinforced composites by expansion of cross-orthogonal skeleton structure

Abstract

Kolarik suggested a cross-orthogonal skeleton model (COS) for tensile strength of polymer blends with co-continuous morphology assuming interfacial parameter and percolating effect. In the current study, this model is developed for polymer/carbon nanotubes (CNT) nanocomposites (PCNT) containing CNT network above percolation threshold. Kolarik model is joined with Pukanszky equation for tensile strength of polymer nanocomposites to express “A” interfacial parameter by CNT dimensions, interphase properties and the density and strength of network. The experimental data and the justification of trends between strength and all parameters show the predictability of the suggested model. The strength meaningfully changes at different dimensions of CNT and network density (N). A main improvement in the strength of PCNT (250%) is obtained by aspect ratio (length per diameter) of 1000 and network density of 2000.

Introduction

Polymer/carbon nanotubes (CNT) nanocomposites (PCNT) have involved much attention, due to their potential applications in electronic and photovoltaic devices, superconductors, electromechanical actuators and sensors [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]]. Moreover, CNT have been accepted as a good candidate for reinforcement and electrical conductivity of polymers, because they show outstanding physical and mechanical properties, large aspect ratio (length per diameter), high electrical conductivity and light weight [[13], [14], [15]]. The surface of CNT is commonly modified by functional groups such as COOH or OH in an oxidation process using acids to facilitate their dispersion in polymer matrices [16,17], because of strong van der Waals interactions between nanotubes which produce aggregates/agglomerates [18].

The electrical conductivity of PCNT is obtained above a critical filler concentration which is named as percolation threshold [19]. In other words, the formation of a conducting network in an insulating matrix at percolation point creates the conductivity. The large aspect ratio of CNT causes a low percolation threshold in PCNT which promotes the conductivity by only very low percentages of nanoparticles [20,21]. Percolation threshold was also detected in mechanical behavior of polymer nanocomposites as mechanical percolation [[22], [23], [24]]. Some researchers such as Favier et al. [22] and Chatterjee [23] have correlated the remarkable values of modulus in the reinforced composites and nanocomposites to percolation effect. However, this term has received less attention in previous studies on nanocomposites compared to electrical percolation.

The previous articles reported the formation of a third phase between polymer matrix and nanoparticles in polymer nanocomposites as interphase and investigated its reinforcing role [[25], [26], [27]]. It was explained that the significant surface area of nanoparticles and the robust interfacial interactions can form a different phase around nanoparticles as interphase [28,29]. However, the slight size and complex nature have limited the experimental characterization of interphase. As a result, some authors have attempted to measure the properties of interphase by modeling methods. The interphase regions can also improve the mechanical percolation in polymer nanocomposites by formation of a connected structure before the real networking of nanoparticles. Therefore, the percolating role of interphase regions in nanocomposites has increases the significance of interphase beside its reinforcing effect.

From a modeling point of view, the effective medium models studied the elastic properties of nanocomposites based on continuum elasticity theory [30]. Also, the micromechanical models estimated the deformation energy stored in elastic fibers to approximate the modulus [31,32]. The micromechanical models are effective above percolation threshold, but the effective medium theories are valid below it. Also, few power-law equations were suggested for tensile modulus of conventional composites similar to those for electrical conductivity. Ouali et al. [33] proposed a model for modulus of polymer composites by percolation threshold. Although this model was commonly applied for tensile modulus of polymer nanocomposites above percolation threshold, it cannot predict the suitable results, due to disregarding of some terms such as interphase [34,35].

Kolarik [36] suggested a cross-orthogonal skeleton model (COS) for yield/tensile strength of polymer blends with co-continuous morphology by an interfacial parameters (A). He also advised that the filler fraction increases by percolating effect. This model includes some complex and vague parameters such as “A”, which weaken the predictions. In addition, this model cannot assume the properties of interphase regions surrounding CNT. In this article, COS is developed for PCNT above percolation threshold assuming CNT network as a continuous structure in polymer matrix and interphase regions surrounding nanoparticles. This model is joined with Pukanszky equation for tensile strength of polymer nanocomposites to express the “A” parameter by material and interphase parameters. Moreover, the effect of filler network is also considered by “B_N” parameter as a function filler aspect ratio and network characteristics. The predictions of suggested model are evaluated by experimental results and justified roles of various parameters in the tensile strength of nanocomposites.