On any size scale, it is important to know how strongly structural components are held together. The purpose of this work was to develop a means to estimate the collective binding energy holding together a bundle of aligned carbon nanotubes (CNTs). Carbon nanotubes in isolation and in bundles have unique and useful properties and applications within supramolecular structures and nanotechnology. Equations were derived to represent the total number of pairwise interactions between the CNTs found in various size and shape bundles. The shapes considered included diamond, hexagon, parallelogram, and rectangle. Parameters were used to characterize the size of a bundle for each defined shape. Force field molecular modeling was used to obtain the total bundle binding energies for a number of sample bundles. From the number of interactions per bundle, the binding energy per interaction was determined. This process was repeated for armchair CNTs having a range of length and circumference values. A simple equation described the interaction energy based on the length and circumference of the component armchair type nanotubes. When combined with the bundle shape and size parameters, the total bundle binding energy could be found. Comparison with whole bundle molecular mechanics calculations showed our formula-based approach to be effective.
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