A Cohesive Law for Carbon Nanotube/Polymer Interface Accounting for Chemical Covalent Bonds

Abstract

The influence of chemical bonds formed between a single-walled carbon nanotube (CNT) and a polymer matrix upon the interface behavior has been studied through the development of an interfacial cohesive law. By using the interatomic potential directly, the tensile cohesive stress and cohesive energy for the interface with opening mode separation are expressed in terms of the area density of the carbon atoms of the CNT, the volume density of the polymer molecules, the material constants of the CNT and the polymer matrix, the parameters in the van der Waals potential, and the Brenner potential and the chemical bond density. This cohesive law avoids any phenomenological assumption between the normal traction and interface opening displacement. For a CNT in an infinite polymer, the shear cohesive stress vanishes, and the tensile cohesive stress depends only on the opening displacement. The cohesive properties, such as the total cohesive energy, have increased significantly, which results in a stronger interfacial bonding due to the creation of new chemical bonds at the interface. The developed cohesive law is useful to study the interaction between the CNT and the polymer, such as in CNT-reinforced composites.Key Words: Cohesive law, chemical bond, van der Waals force, carbon nanotube/polymer interface, nanocomposites INTRODUCTONSince the discovery of carbon nanotubes (CNTs) [1] and the establishment of new effective techniques to produce CNTs [2], the properties of these novel materials and their potential applications have stimulated considerable interests. For example, the superior mechanical properties of CNTs have made them ideal candidates to replace the traditional fibers in composites with lighter weight and higher strength [3][4][5][6][7][8][9]. To facilitate the full potential of CNTs as reinforcement in nanocomposites, it is essential to understanding the interfacial interactions between CNTs and a polymer matrix. Similar to the conventional fiber-reinforced composites, there are mainly three interaction mechanisms at the CNT/polymer interface, i.e., the covalent chemical bond, mechanical interlocking, and the van der Waals interaction [10,11]. The covalent bond is the strongest adhesion for the interface, which comes from the reaction of atoms between the CNT and the polymer matrix. It is expected that the covalent bond may significantly improve the load transfer efficiency at the interface. For example,

Advanced nanoindentation simulations for carbon nanotube reinforced nanocomposites

“…The idea was primarily developed by Jiang et al. (2006) where they developed the normal cohesive force between matrix and graphene sheet and they further developed the formulation for MWCNTs with polymer matrix [ 57 , 58 , 59 ].…”

“…This study uses the technique to simplify the computation by considering the number of atoms per unit surface area of CNT and number of molecules per unit volume of polymer rather considering individual atom or molecules interactions. The idea was primarily developed by Jiang et al (2006) where they developed the normal cohesive force between matrix and graphene sheet and they further developed the formulation for MWCNTs with polymer matrix [57,58,59]. For convenience, the derived formulas and terms are recalled here briefly.…”

A shear-lag model with a cohesive fibre–matrix interface for analysis of fibre pull-out

“…For examples, the van der Waals interfacial interaction between the polymer matrix and the CNT and the interfacial chemical bonding have been modelled with the Lennard-Jones potential, and the many-body bond-order potential, respectively, in analysis of the shear strength of carbon nanotube-polymer matrix interfaces (Chen et al, 2010;Frankland et al, 2002;. Nonlinear cohesive laws for CNT-polymer matrix interfaces have been established based on the van der Waals interfacial interaction (Jiang et al, 2006;Lu et al, 2008) and chemical bonding (Jiang, 2010), respectively. The classical shear-lag model has been adopted to predict the interfacial stress transfer in CNT-reinforced polymer composites (Gao and Li, 2005), to analyse the carbon nanotube pull-out from a polymer matrix , and to investigate fracture toughness enhancement with introducing a linear interface law to account for CNT-matrix interfacial bond breaking (Chen et al, 2010).…”

Toward local identification of cohesive zone models using digital image correlation

“…Some recent attempts have been proposed in the literature to derive cohesive laws from experimental measurements. At the nanoscale, these attempts often concern the identification of a potential from which the cohesive model derived (Jiang, 2010;Ngo et al, 2010). At higher scales, most studies have been based on the assumption of a general shape for the constitutive equations and a predefined crack path, and the material parameters have been derived from experimental strain data (see e.g.…”