Worm-like chain

The worm-like chain (WLC) model in polymer physics is used to describe the behavior of polymers that are semi-flexible: fairly stiff with successive segments pointing in roughly the same direction, and with persistence length within a few orders of magnitude of the polymer length. The WLC model is the continuous version of the Kratky–Porod model. The worm-like chain (WLC) model in polymer physics is used to describe the behavior of polymers that are semi-flexible: fairly stiff with successive segments pointing in roughly the same direction, and with persistence length within a few orders of magnitude of the polymer length. The WLC model is the continuous version of the Kratky–Porod model. The WLC model envisions a continuously flexible isotropic rod. This is in contrast to the freely-jointed chain model, which is only flexible between discrete freely hinged segments. The model is particularly suited for describing stiffer polymers, with successive segments displaying a sort of cooperativity: nearby segments are roughly aligned. At room temperature, the polymer adopts a smoothly curved conformation; at T = 0 {displaystyle T=0} K, the polymer adopts a rigid rod conformation. For a polymer of maximum length L 0 {displaystyle L_{0}} , parametrize the path of the polymer as s ∈ ( 0 , L 0 ) {displaystyle sin (0,L_{0})} . Allow t ^ ( s ) {displaystyle {hat {t}}(s)} to be the unit tangent vector to the chain at point s {displaystyle s} , and r → ( s ) {displaystyle {vec {r}}(s)} to be the position vector along the chain, as shown to the right. Then: