  The freely rotating chain is one of the classic discrete models of a polymer
in dilute solution. It consists of a broken line of N straight segments of
fixed length such that the angle between adjacent segments is constant and the
N-1 torsional angles are independent, identically distributed, uniform random
variables. We provide a rigorous proof of a folklore result in the chemical
physics literature stating that under an appropriate scaling, as N tends to
infinity, the freely rotating chain converges to a random curve defined by the
property that its derivative with respect to arclength is a brownian motion on
the unit sphere. This is the Kratky-Porod model of semi-flexible polymers. We
also investigate limits of the model when a stiffness parameter, called the
persistence length, tends to zero or infinity. The main idea is to introduce
orthogonal frames adapted to the polymer and to express conformational changes
in the polymer in terms of stochastic equations for the rotation of these
frames.
