Cohesive laws for van der Waals interactions of super carbon nanotube/polymer composites

• Cohesive laws for van der Waals interactions of SCNT/polymer composites are derived.
• Tensile cohesive strength and cohesive energy of SCNT/polymer composites are given.
• Interfacial stresses–displacement relations of SCNT/polymer composites are obtained.

Novel macrostructures built up by carbon nanotubes (CNTs), such as super-graphene (SG) similar to a single graphite layer and super carbon nanotube (SCNT) analogous to a single-walled CNT (SWCNT), have been developed to extend the superior mechanical properties of the CNTs. This paper describes cohesive laws for the interfacial interactions of SG/polymer and SCNT/polymer composites induced by the weak van der Waals force. By denoting the volume density function of the SG in terms of the length and area density of the CNT, the van der Waals force and the cohesive energy are obtained for infinite SG/graphene at first. Then the tensile cohesive strength and cohesive energy between the SCNT and the polymer matrix are given in terms of the volume density of the SCNT and volume density of the polymer. It is shown that for a SCNT embedded in finite polymer matrix, the tensile cohesive stress depends only on the opening displacement of the interface, while the shear stress depends on both opening displacement and sliding displacements of the interface.

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