Minimum energy structures of short (3,3) single wall carbon nanotube (SWCNT)–polyethylene (PE) structures, as well as the binding energy between the SWCNT and PE, were obtained from three commonly used molecular mechanics force fields and first principles methods. The molecular force fields were the Dreiding, Universal and Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) force fields and the first principles methods included the B3LYP density functional and MP2 post-Hartree Fock methods with, typically, 6-311G, 6-311G(d,p) and 6-311G(2d,2p) basis sets. These calculations show that the results obtained from all force fields are in qualitative agreement with the first principles results, and that PE prefers to be aligned with a non-zero angle along the SWCNT axis, where the angle depends on the force field or first principles method used. This indicates that longer PE chains may wrap around SWCNTs. This was studied using the COMPASS force field with longer (5,5) SWCNTs interacting with a PE chain and, in agreement with the minimum energy calculations, the PE wrapped around the SWCNT thereby increasing the radius of gyration of the PE. This force field was also used to assess the effect of (5,5) SWCNTs on the mechanical properties of PE nanocomposites. The calculated interfacial shear stress and interfacial bonding energy of SWCNT–PE structures was 141.09 MPa and 0.14 N/m. The simulations show that using short SWCNTs as reinforcement does not increase the Young’s modulus for the systems studied here, whereas longer, aligned SWCNTs increased the Young’s modulus in the SWCNT axial direction.
Density functional theory (DFT) and semiempirical tight-binding (TB) methods have been used to study the mechanism of graphene growth in the presence and absence of a catalytic surface. Both DFT and TB geometry optimized structures relevant to graphene growth show that the minimum energy growth mechanism is via the sequential addition of carbon hexagons at the edge of the graphene sheet. Monte Carlo (MC) simulations based on the TB model show that defect-free graphene sheets can be grown provided one has the proper combination of temperature, chemical potential, and addition rate. In this work, growth of perfect graphene structures has been simulated at the atomic level. Comparison of the growth mechanism in the absence and presence of a nickel catalyst surface shows that the catalyst (i) allows for adsorption of carbon atoms at surface and subsurface sites, (ii) enables formation of long, stable strings of carbon atoms, and (iii) stabilizes small flakes of graphene that can act as precursors to subsequent growth.
Semiempirical tight binding (TB) and density functional theory (DFT) methods have been used to study the mechanism of single walled carbon nanotube (SWNT) growth. The results are compared with similar calculations on graphene. Both TB and DFT geometry optimized structures of relevance to SWNT growth show that the minimum energy growth mechanism is via the formation of hexagons at the SWNT end. This is similar to the result for graphene where growth occurs via the formation of hexagons at the edge of the graphene flake. However, due to the SWNT curvature, defects such as pentagons are more stable in SWNTs than in graphene. Monte Carlo simulations based on the TB energies show that SWNTs close under conditions that are proper for growth of large defect-free graphene flakes, and that a particle such as a Ni cluster is required to maintain an open SWNT end under these conditions. The calculations also show that the proper combination of growth parameters such as temperature and chemical potential are required to prevent detachment of the SWNTs from the Ni cluster or encapsulation of the cluster by the feedstock carbon atoms.