Using a continuum model, expressions for the elastic energy, defect energy,structure entropy, and mixing entropy of carbon nanocones are proposedanalytically. The optimal conformation of carbon nanocones is studied byimposing minimization of free energy and analyzing the effects that thebuckling of a nanocone's walls have during formation. The model explains theexperimentally observed preference of 19.2 degrees for the cone angle of carbonnanocone. Furthermore, it predicts the optimal conformation of carbon nanoconesto result in a cone angle of 19.2 degrees, radius of 0.35 nm, and criticallength of 24 nm, all of which agree very well with experimental observations.
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