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Kinetic analysis of quasi-one-dimensional growth of polymer lamellar crystals in dilute solutions.

Flexible polymers are featured with two-dimensional growth of metastable chain-folded lamellar crystals in quiescent dilute solutions. Recently, a massive cylindrical micelle with quasi-one-dimensional (quasi-1D) growth driven by confined crystallization of diblock copolymers in dilute solutions raised a new challenge. We performed dynamic Monte Carlo simulations to investigate the kinetics of quasi-1D growth of lamellar crystals in two typical cases of dilute but not very dilute polymer solutions. We found that in both cases the growth kinetics is dominated by the surface-nucleation-controlled mechanism. Moreover, in the first case corresponding to few and small crystals grown under almost constant polymer concentrations in the huge bulk of solutions, the driving-force term in the kinetic equation dominates a linear concentration dependence of crystal growth rates in the high-concentration region, and the nucleation-barrier term dominates their nonlinear deviation in the low-concentration region. In the second case corresponding to massive crystals grown under depleting polymer concentrations in a limited volume of solutions, the crystal growth rates decay with time, but at the early stage, they follow exactly with the linear-concentration-dependent growth rates of the first case. Therefore, the growth size at the early stage of the second case can be described as an exponential-decay function of time, which provides a theoretical model to the data analysis of corresponding experimental observations.