  Based upon kinetic Monte Carlo simulations of crystallization in a simple
polymer model we present a new picture of the mechanism by which the thickness
of lamellar polymer crystals is constrained to a value close to the minimum
thermodynamically stable thickness, l_{min}. The free energetic costs of the
polymer extending beyond the edges of the previous crystalline layer and of a
stem being shorter than l_{min} provide upper and lower constraints on the
length of stems in a new layer. Their combined effect is to cause the crystal
thickness to converge dynamically to a value close to l_{min} where growth with
constant thickness then occurs. This description contrasts with those given by
the two dominant theoretical approaches. However, at small supercoolings the
rounding of the crystal profile does inhibit growth as suggested in Sadler and
Gilmer's entropic barrier model.
