Xu Haijun, Matkar Rushikesh, Kyu Thein
Department of Polymer Engineering, The University of Akron, Ohio 44325, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jul;72(1 Pt 1):011804. doi: 10.1103/PhysRevE.72.011804. Epub 2005 Jul 15.
Spatio-temporal growth of isotactic polystyrene single crystals during isothermal crystallization has been investigated theoretically based on the phase field model by solving temporal evolution of a nonconserved phase order parameter coupled with a heat conduction equation. In the description of the total free energy, an asymmetric double-well local free energy density has been adopted to represent the metastable melt and the stable solid crystal. Unlike the small molecule systems, polymer crystallization rarely reaches thermodynamic equilibrium; most polymer crystals are kinetically stabilized in some metastable states. To capture various metastable polymer crystals, the phase field crystal order parameter at the solidification potential has been treated to be supercooling dependent such that it can assume an intermediate value between zero (melt) and unity (perfect crystal), reflecting imperfect polycrystalline nature of polymer crystals. Two-dimensional simulations exhibit various single crystal morphologies of isotactic polystyrene crystals such as faceted hexagonal patterns transforming to nonfaceted snowflakes with increasing supercooling. Of particular interest is that heat liberation from the crystallizing front influences the curvature of the crystal-melt interface, leading to directional growth of lamellar tips and side branches. The landscape of these morphological textures has been established as a function of anisotropy of surface energy and supercooling. With increasing supercooling and decreasing anisotropy, the hexagonal single crystal transforms to the dense lamellar branching morphology in conformity with the experimental findings.
基于相场模型，通过求解与热传导方程耦合的非守恒相序参数的时间演化，从理论上研究了等规聚苯乙烯单晶在等温结晶过程中的时空生长。在总自由能的描述中，采用了不对称双阱局部自由能密度来表示亚稳熔体和稳定的固体晶体。与小分子体系不同，聚合物结晶很少达到热力学平衡；大多数聚合物晶体在某些亚稳状态下动力学稳定。为了捕获各种亚稳聚合物晶体，凝固势下的相场晶体序参量被处理为与过冷度有关，使其可以取介于零（熔体）和一（完美晶体）之间的中间值，反映了聚合物晶体不完美的多晶性质。二维模拟展示了等规聚苯乙烯晶体的各种单晶形态，例如随着过冷度增加，有面的六边形图案转变为无面的雪花状。特别有趣的是，结晶前沿的热释放影响了晶体 - 熔体界面的曲率，导致片晶尖端和侧枝的定向生长。这些形态纹理的格局已被确定为表面能各向异性和过冷度的函数。随着过冷度增加和各向异性减小，六边形单晶转变为致密的片层分支形态，这与实验结果一致。
