Soluble Model for Fibrous Structures with Steric Constraints

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 yn(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 q = 2kF, where kF is the Fermi wave vector of the associated set of particles.