Fang Alta, Haataja Mikko
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA.
Department of Mechanical and Aerospace Engineering, Princeton Institute for the Science and Technology of Materials (PRISM), the Andlinger Center for Energy and the Environment (ACEE), and Program in Applied and Computational Mathematics (PACM), Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042404. doi: 10.1103/PhysRevE.92.042404. Epub 2015 Oct 15.
Many polymer and organic small-molecule thin films crystallize with microstructures that twist or curve in a regular manner as crystal growth proceeds. Here we present a phase-field model that energetically favors twisting of the three-dimensional crystalline orientation about and along particular axes, allowing morphologies such as banded spherulites, curved dendrites, and "s"- or "c"-shaped needle crystals to be simulated. When twisting about the fast-growing crystalline axis is energetically favored and spherulitic growth conditions are imposed, crystallization occurs in the form of banded spherulites composed of radially oriented twisted crystalline fibers. Due to the lack of symmetry, twisting along the normal growth direction leads to heterochiral banded spherulites with opposite twist handedness in each half of the spherulite. When twisting is instead favored about the axis perpendicular to the plane of the substrate and along the normal growth direction under diffusion-limited single-crystalline growth conditions, crystallization occurs in the form of curved dendrites with uniformly rotating branches. We show that the rate at which the branches curve affects not only the morphology but also the overall kinetics of crystallization, as the total crystallized area at a given time is maximized for a finite turning rate.
许多聚合物和有机小分子薄膜在结晶时会形成微观结构,随着晶体生长的进行,这些微观结构会以规则的方式扭曲或弯曲。在此,我们提出了一个相场模型,该模型在能量上有利于三维晶体取向围绕特定轴并沿着特定轴发生扭曲,从而能够模拟诸如带状球晶、弯曲枝晶以及“s”形或“c”形针状晶体等形态。当围绕快速生长的晶轴发生扭曲在能量上更有利且施加球晶生长条件时,结晶会以由径向取向的扭曲晶体纤维组成的带状球晶形式发生。由于缺乏对称性,沿着法向生长方向的扭曲会导致在球晶的每一半中具有相反扭曲手性的异手性带状球晶。相反,在扩散限制的单晶生长条件下,当围绕垂直于基底平面的轴并沿着法向生长方向发生扭曲更有利时,结晶会以具有均匀旋转分支的弯曲枝晶形式发生。我们表明,分支弯曲的速率不仅会影响形态,还会影响结晶的整体动力学,因为在给定时间的总结晶面积对于有限的转向速率是最大化的。