On the deformation of spontaneously twisted fluctuating ribbons

摘要

A theoretical analysis of the effect of force and torque on spontaneouslytwisted, fluctuating elastic ribbons is presented. We find that when a filamentwith a straight center line and a spontaneously twisted noncircular crosssection is subjected to a sufficiently strong extensional force, its averageelongation exhibits an asymmetric response to large over and undertwist. Weconstruct the stability diagram that describes the buckling transition of suchribbons under the opposing action of force and torque and show that all thepredicted behaviors can be understood in terms of continuous transformationsbetween straight and spiral/helical states of the ribbon. The relation betweenour results and experimental observations on DNA is discussed and a newreentrant spiral to rod transition is predicted at intermediate values of twistrigidity and applied force.