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The topological connectivity of polymer chains spontaneously imposes entropic frustrations in their ordering into crystalline states. With a combination of analytical arguments and molecular modeling, butressed with experimental facts, we have revisited the long-standing problem of polymer crystallization and evaluated the significant role played by conformational entropy of polymer chains. We will focus on (i) the onset of nucleation during the primordial stage of crystallization, (ii) spontaneous selection of finite lamellar thickness in equilibrium, (iii) lamellar growth kinetics, and (iv) spontaneous chiral symmetry breaking in spherulites. The basic concepts of polymer crystallization are applicable also to directional self-assemblies in biological systems, such as amyloids, bacterial walls, and viruses, and the anologies will be briefly mentioned.
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