Spatiotemporal growth of faceted and curved single crystals

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Abstract
The spatiotemporal growth of single crystals in a crystalline polymer has been investigated theoretically based on a nonconserved time dependent Ginzburg-Landau equation (known as TDGL model A). In the description of the total free energy, a double-well local free energy density signifying metastability of crystal ordering is combined with a nonlocal free energy term representing an interface gradient. The resulting nonlinear reaction diffusion equation after renormalization possesses a solitary wave property. Two-dimensional numerical calculations were performed to elucidate the faceted single crystal growth including square, rectangular, diamond-shaped, and curved single crystals. A three-dimensional simulation was also undertaken for the emergence of diamond-shaped single crystals in polyethylene. Of particular importance is that the model field parameters can be linked directly to the material parameters of polyethylene single crystals. Simulation with various elements of the interface gradient coefficient tensor captures various topologies of polymer single crystals.