  We study how solidification of model freely rotating polymers under athermal
quasistatic compression varies with their bond angle $\theta_0$. All systems
undergo two discrete, first-order-like transitions: entanglement at $\phi =
\phi_E(\theta_0)$ followed by jamming at $\phi = \phi_J(\theta_0) \simeq (4/3
\pm 1/10)\phi_E(\theta_0)$. For $\phi < \phi_E(\theta_0)$, systems are in a
"gas" phase wherein all chains remain free to translate and reorient. For
$\phi_E(\theta_0) \leq \phi \leq \phi_J(\theta_0)$, 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 $\phi_J(\theta_0)$. At and slightly
above $\phi_J$, 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
$\phi_J(\theta_0)$ can be characterized via chains' effective aspect ratio
$\alpha_{\rm eff}$. Large-$\alpha_{\rm eff}$ (small-$\theta_0$) systems'
jamming is bending-dominated and is similar to that observed in systems
composed of straight fibers. Small-$\alpha_{\rm eff}$ (large-$\theta_0$)
systems' jamming is dominated by the degree to which individual chains'
dihedrals can collapse into compact, tetrahedron-like structures. For
intermediate $\theta_0$, 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.
