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Two-stage athermal solidification of semiflexible polymers and fibers

We study how solidification of model freely rotating polymers under athermal quasistatic compression varies with their bond angle $θ_0$. All systems undergo two discrete, first-order-like transitions: entanglement at $ϕ= ϕ_E(θ_0)$ followed by jamming at $ϕ= ϕ_J(θ_0) \simeq (4/3 \pm 1/10)ϕ_E(θ_0)$. For $ϕ< ϕ_E(θ_0)$, systems are in a "gas" phase wherein all chains remain free to translate and reorient. For $ϕ_E(θ_0) \leq ϕ\leq ϕ_J(θ_0)$, systems are in a liquid-like phase wherein chains are entangled. In this phase, chains' rigid-body-like motion is blocked, yet they can still locally relax via dihedral rotations, and hence energy and pressure remain extremely small. The ability of dihedral relaxation mechanisms to accommodate further compression becomes exhausted, and systems rigidify, at $ϕ_J(θ_0)$. At and slightly above $ϕ_J$, the bulk moduli increase linearly with the pressure $P$ rather than jumping discontinuously, indicating these systems solidify via rigidity percolation. The character of the energy and pressure increases above $ϕ_J(θ_0)$ can be characterized via chains' effective aspect ratio $α_{\rm eff}$. Large-$α_{\rm eff}$ (small-$θ_0$) systems' jamming is bending-dominated and is similar to that observed in systems composed of straight fibers. Small-$α_{\rm eff}$ (large-$θ_0$) systems' jamming is dominated by the degree to which individual chains' dihedrals can collapse into compact, tetrahedron-like structures. For intermediate $θ_0$, chains remain in highly disordered globule-like configurations throughout the compression process; jamming occurs when entangled globules can no longer even locally relax away from one another.