Stability of the sectored morphology of polymer crystallites

When an entangled interpenetrating collection of long flexible polymer chains dispersed in a suitable solvent is cooled to low enough temperatures, thin lamellar crystals form. Remarkably, these lamellae are sectored, with several growth sectors that have differing melting temperatures and growth kinetics, eluding so far an understanding of their origins. We present a theoretical model to explain this six-decade-old challenge by addressing the elasticity of fold surfaces of finite-sized lamella in the presence of disclination-type topological defects arising from anisotropic line tension. Entrapment of a disclination defect in a lamella results in sectors separated by walls, which are soliton solutions of a two-dimensional elliptic sine-Gordon equation. For flat square morphologies, exact results show that sectored squares are more stable than plain squares if the dimensionless anisotropic line tension parameter α=γ_{an}/sqrt[h_{4}K_{ϕ}] (γ_{an} = anisotropic line tension, h_{4} = fold energy parameter, K_{ϕ} = elastic constant for two-dimensional orientational deformation) is above a critical value, which depends on the size of the square.