Statistical mechanics of triangulated ribbons

Abstract

We use computer simulations and scaling arguments to investigate statistical and structural properties of a semiflexible ribbon composed of isosceles triangles. We study two different models, one where the bending energy is calculated from the angles between the normal vectors of adjacent triangles, the second where the edges are viewed as semiflexible polymers so that the bending energy is related to the angles between the tangent vectors of next-nearest-neighbor triangles. The first model can be solved exactly whereas the second is more involved. It was recently introduced by Liverpool and Golestanian, Phys. Rev. Lett. $80,$ 405 (1998); Phys. Rev. E $62,$ 5488 (2000) as a model for double-stranded biopolymers such as DNA. Comparing observables such as the autocorrelation functions of the tangent vectors and the bond-director field, the probability distribution functions of the end-to-end distance, and the mean-squared twist we confirm the existence of local twist correlation, but find no indications for other predicted features such as twist-stretch coupling, kinks, or oscillations in the autocorrelation function of the bond-director field.