Figure 6.

Curvature definition and global unfolding. (a) Defining local radius of curvature, r(ŝ), in the carbyne loop (ŝ = 0 to L), averaged to calculate the global radius of curvature and κ. (b) Schematic of coordinates used for the numerical solution to Equation 2, where each point represents adjacent carbon atoms. (c) Averaging the local curvatures across the molecule (here, n = 72 and n = 144) and calculating the associated radius of curvature, stable loop configurations have little change in radius at low temperatures (dashed arrows), while unfolding induced by high temperature results in a global increase in radius with respect to time (solid arrows) as anticipated (by definition, the unfolded structure will have a lower curvature).

Cranford Nanoscale Research Letters 2013 8:490   doi:10.1186/1556-276X-8-490
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