Worm-Like Chain under External Forces: Some Analytic Results

Department of Physics, Tamkang University, Tamsui, Taiwan 251, R.O.C.(Received October 24, 2003)Exact results of the classical mechanical solution of the worm-like chain model under anexternal stretching force are derived. The locus of the chain under an arbitrary stretchingforce and grafting conditions is calculated explicitly in terms of elliptic functions. In the longchain limit, the chain locus can be expressed in terms of elementary functions. In addition,the solution of a worm-like rod chain under a small twisting torque is also calculated pertur-batively. The relative extension, writhe number, and the locus of the chain are computed toleading orders in the reduced torque.