Free energy barrier for single-chain melting and crystallization
  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. 
Wenbing Hu, Daan Frenkel, Vincent B. F. Mathot