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 configurational freedom associated with bond angles (θ) can be associated with the characteristic ratio C_∞ = (1 + 〈cos(θ)〉)/(1 - 〈cos(θ)〉). We find that the dependence of the average coordination number at solidification [Z(T_s)] on chains' characteristic ratio C_∞ has the same functional form [Z ≃ a - b ln(C_∞)] as the dependence of the average coordination number at jamming [Z(ϕ_J)] on C_∞ in athermal systems, suggesting that jamming-related phenomena play a significant role in thermal polymer solidification.