Isostaticity and the solidification of semiflexible polymer melts

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.