  Based on classical nucleation theory, we propose a couple of theoretical
models for the nucleation of polymer crystallization, i.e. one for a single
chain system (Model S) and the other for a multi-chain system (Model M). In
these models, we assume that the nucleus is composed of tails, loops and a
cylindrical ordered region, and we evaluate the conformation entropy explicitly
by introducing a transfer matrix. Using these two models, we evaluate the
occurrence probability of critical nucleus as a function of the polymer chain
stiffness. We found that the critical nucleus in Model M is easier to occur
than in Model S because, for semi-flexible chains, the nucleus in Model M can
grow by adding a new polymer chain into the nucleus rather than to diminish the
loop and tail parts as in the case of Model S.
