  Using molecular dynamics simulations of a tangent-soft-sphere bead-spring
polymer model, we examine the degree to which semiflexible polymer melts
solidify at isostaticity. Flexible and stiff chains crystallize when they are
isostatic as defined by appropriate degree-of-freedom-counting arguments.
Semiflexible chains also solidify when isostatic if a generalized isostaticity
criterion that accounts for the slow freezing out of configurational freedom as
chain stiffness increases is employed. The dependence of the average
coordination number at solidification $Z(T_s)$ on chains' characteristic ratio
$C_\infty$ has the same functional form [$Z \simeq a - b\ln(C_\infty)$] as the
dependence of the average coordination number at jamming $Z(\phi_J)$ on
$C_\infty$ in athermal systems, suggesting that jamming-related phenomena play
a significant role in thermal polymer solidification.
