Modeling of Polymer Melting

We have employed modified Potts model with anisotropic interaction to simulate melting of polymer crystals. Using this coarse-grained model with fixed lamellar thickness, we have successfully reproduced many experimental results. A broad melting transition is found and becomes broader with decreasing crystallization temperature $T_c$, increasing heating rate $\beta$ or crystallization time $t_c$. The melting temperature $T_m$ depends on $\beta, t_c$ and $T_c$ as follows: $T_m \propto \beta^{0.5}$; $T_m\propto\log t_c$ for intermediate $t_c$ values; $T_m$ is constant in low-$T_c$ region and gradually increases with $T_c$ in high-$T_c$ region, in contradiction with Hoffman- Weeks plot but consistent with experimental observations over a wide $T_c$ range. A new relation for $T_m$ is proposed: $T_m=T_m(\beta=0)+const \sqrt{\beta}\log R $, where $R$ is the average lamellar diameter following the law $R\propto t_c^{1/3}$.