In general, when a crystal is molten, all molecules forget about their mutual correlations and long-range order is lost. Thus, a regrown crystal does not inherit any features from an initially present crystal. Such is true for materials exhibiting a well-defined melting point. However, polymer crystallites have a wide range of melting temperatures, enabling paradoxical phenomena such as the coexistence of melting and crystallization. Here, we report a self-seeding technique that enables the generation of arrays of orientation-correlated polymer crystals of uniform size and shape ('clones') with their orientation inherited from an initial single crystal. Moreover, the number density and locations of these cloned crystals can to some extent be predetermined through the thermal history of the starting crystal. We attribute this unique behaviour of polymers to the coexistence of variable fold lengths in metastable crystalline lamellae, typical for ordering of complex chain-like molecules.
A level-set method for the simulation of fluid interfaces with insoluble surfactant is presented in two-dimensions. The method can be straightforwardly extended to three-dimensions and to soluble surfactants. The method couples a semi-implicit discretization for solving the surfactant transport equation recently developed by Xu and Zhao [62] with the immersed interface method originally developed by LeVeque and Li and [31] for solving the fluid flow equations and the Laplace-Young boundary conditions across the interfaces. Novel techniques are developed to accurately conserve component mass and surfactant mass during the evolution. Convergence of the method is demonstrated numerically. The method is applied to study the effects of surfactant on single drops, dropdrop interactions and interactions among multiple drops in Stokes flow under a steady applied shear. Due to Marangoni forces and to nonuniform Capillary forces, the presence of surfactant results in larger drop deformations and more complex drop-drop interactions compared to the analogous cases for clean drops. The effects of surfactant are found to be most significant in flows with multiple drops. To our knowledge, this is the first time that the level-set method has been used to simulate fluid interfaces with surfactant.
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