Crystal lamella equilibrium shape

The lamellar thickening proceeds through many metastable states, each metastable state corresponding to a particular number of folds per chain, as illustrated in Fig. 8. In the original simulations of [22], Kg was monitored. Rg is actually very close to the lamellar thickness due to the asymmetric shape of the lamella. The number of folds indicated in Fig. 8 were identified by inspection of the coordinates of the united atoms. This quantization of the number of folds has been observed in experiments [50], as already mentioned. The process by which a state with p folds changes into a state with p - 1 folds is highly cooperative. The precursor lives in a quiescent state for a substantial time and suddenly it converts into the next state. By a succession of such processes, crystals thicken. If the simulation is run for a reasonably long time, the lamella settles down to the equilibrium number of folds per chain. 

The above insight, gained soon after the discovery of polymer single crystals, and the subsequent discovery of chain folding (1-3), has mapped out the route taken by much of the research into polymer crystallization over the subsequent decades. It soon became clear that the thickness of polymer lamellae was controlled by the supercooling at which they were crystallized and defined by the kinetics of crystallization. The crystal thickness, or alternatively the thickness of each new crystalline layer in a growing crystal, is the one that grows the fastest (4,5) rather than the one that is at equilibrium (6). There is now a wealth of information available on the crystallization of many polymers, as well as several theories that aim to predict the crystallization rates, crystal shapes, and lamellar thickness. 

The melting of polymer crystals exhibits many instructive features of non-equilibrium behaviour. It has been known since the 1950s that the crystals of flexible-chain polymers, e.g. polyethylene (PE), are lamella-shaped with the chain axis almost parallel to the normal of the lamella. The lamellar thickness (LJ is of the order of 10 nm, corresponding to approximately 100 main chain atoms, which is considerably less than the total length of the typical polymer chain. This fact led to the postulate that the macroconformation of the chains must be folded. The... 

---