Forces and extensions in semiflexible and rigid polymer chains and filaments

We present a revised theoretical study of statistical properties of semiflexible filaments. Using a single auxiliary field and mean-field theory, we succeed in obtaining the exact analytical results for force-extension relations for a chain with arbitrary stiffness, and compare it with earlier theories and experiment. At a small persistence-to-contour length ratio, l(p)/L << 1 the chain behaves classically, as an entropic spring. However, we find a critical value for L/l(p) approximate to 3.0 in 3D (or L/l(p) approximate to 5.4 in 2D) above which the restoring force of the chain becomes negative for the end-to-end distance R-3D/L <root 1-L/3l(p) (or R-2D/L < root 1-L/5.4p). That is, very stiff (or very short) chains and filaments resist an attempt to reduce their preferred end-to-end distance as much as to stretch it.