Two-stage jamming in semiflexible polymers and fibers

We find that jamming in model freely rotating polymers with bond angle θ₀ occurs in two stages. The first, precursor stage occurs when the average number of unique interchain contacts Z_chain jumps discontinuously as chains “entangle” at a packing fraction φ_e(θ₀). Entanglement is a necessary but not a sufficient condition for mechanical rigidity; systems rigidify (i.e. jam) at φ_J(θ₀) > φ_e(θ₀), and Z_chain jumps discontinuously again at φ_J(θ₀). These discontinuities become sharper as polymers stiffen (as θ₀ decreases). We find that φ_e(θ₀) ~ .8φ_J(θ₀) despite the fact that both decrease by a factor of nearly two as polymers stiffen. Our results for small θ₀ may also describe jamming phenomena in fiber networks.