  In this paper, we report dynamic Monte Carlo simulations of melting and
crystallization in a single-chain system. Their free energy barriers are
calculated by the umbrella sampling method and can be described well by a
simple expression DeltaF = n Deltaf+sigma (N-n)^(2/3), where n is the amount of
molten bonds, Deltaf is the free energy change of each molten bond from a
crystalline state, N is the chain length, and sigma is the surface free energy
of crystallite. We found that, together with the expression Delta F = n Delta
f+ sigma (N-n)^(1/2) for molecular nucleation, the molecular-weight dependent
properties of the free-energy barriers for polymer primary and secondary
nucleation, in particular, the molecular segregation during crystal growth, can
be reproduced. Then for the mechanism of polymer crystallization, we suggested
a quantitative model of intramolecular nucleation, as a direct development from
the previous qualitative description of molecular nucleation model.
