Wormlike chain or tense string ? A question of resolution

It is shown that a wormlike chain, i.e., a filament with a fixed contour-length ¯ S and a bending elasticity κ, attached to a frame of length L, can be described—at low resolutions—by the same type of elastic free-energy as a tense string. The corresponding tension is calculated as a function of temperature, L, κ and ¯ S. Elastic free-energies are used to describe the distorted states and fluctuations of soft-1989). In this paper, we investigate how the elastic free-energy functional of a filament with a fixed contour-length and a bending rigidity (wormlike chain) depends on the spatial resolution at which it is described. We perform a finite renormalization group (RG) iteration in order to determine the free-energy associated with the length of the filament that is hidden at low-resolution. A similar study, focused on surfactant membranes, was recently published in a short paper (Fournier et al., 2001). The filaments considered here are known as wormlike chains a filament with a bending rigidity κ has a persistence length L p = κ/k B T (Landau and Lifshitz, 1971): for contour-lengths ¯ S ≪ L p it resembles a flexible rod, while for ¯ S ≫ L p it resembles a wandering polymer. There are various natural realizations of semi-flexible polymers: actin cy