Semiflexible Polymer Confined to a Spherical Surface

We develop a formalism for describing the kinematics of a wormlike chain confined to the surface of a sphere that simultaneously satisfies the spherical confinement and the inextensibility of the chain contour. We use this formalism to study the statistical behavior of the wormlike chain on a spherical surface. In particular, we provide an exact, closed-form expression for the mean square end-to-end distance that is valid for any value of chain length L, persistence length l_p, and sphere radius R. We predict two qualitatively different behaviors for a long polymer depending on the ratio R/l_p. For R/l_p>4, the mean square end-to-end distance increases monotonically with the chain length, whereas for R/l_p<4, a damped oscillatory behavior is predicted.