Soluble Model for Fibrous Structures with Steric Constraints

Abstract

We consider a set of thin, long, flexible chains in two dimensions. The chains are in thermal equilibrium under a strong unidirectional stretching force. Configurations where different chains intersect each other are excluded. The chain configurations $y_n\mathrm{(x)}$ are interpreted as the trajectories of an assembly of quantum mechanical particles, x playing the role of the time. The model is thus brought into correspondence with a one‐dimensional gas of free fermions, and can be solved exactly. The system of chains has no long‐range order, but a remarkably strong short‐range order: the x‐ray form factor, for a wave vector q normal to the stretching direction, shows a sharp peak at ${\text{q\hspace{0.17em}=\hspace{0.17em}2k}}_F$ , where $k_F$ is the Fermi wave vector of the associated set of particles.