Phase-field modeling on morphological landscape of isotactic polystyrene single crystals

Abstract

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.

Computational approaches to substrate-based cell motility

“…Phase-field method The phase-field method 70,71 had been originally introduced to model solidification processes, but later on was applied to a diversity of systems including domain growth, microstructure evolution, and structural transformations in materials science, [72][73][74] the Saffman-Taylor fingering instability, 58,75 elastic surface instabilities 76 and fracture mechanics, 77,78 the fluidisation transition in granular media, 79 the crystallisation of polymers 80 and finally biological systems such as vesicles [81][82][83] (where it also goes under the name 'advected field approach') and growing actin gels. 84 This list clearly demonstrates the method's versatility, which meanwhile has developed into a standard tool in the vast field of multiphase/composite materials.…”

Discrepancy in determination of χ parameters by melting point depression versus small-angle neutron scattering in blends of deuterated polycarbonate and isotactic poly(methyl methacrylate)

“…A unified theoretical model (Matkar & Kyu, 2006b) has been developed in the framework of the phase field model of solidification involving the Landau-type double-well potential pertaining to the first order solid-liquid phase transition (Xu et al, 2005) coupled with the FH free energy for liquid-liquid demixing (Flory, 1953).…”

“…The coefficients of the Landau free energy expansion based on the crystal order parameter ( i ) of the constituents are treated as temperature dependent in polymer crystallization to account for the imperfect nature of polymer crystals. These crystal phase order parameters are defined as the ratio of the lamellar thickness (l i ) to the lamellar thickness of a perfect polymer crystal (l 0 i ), i.e., i ¼ l i =l 0 i , to represent the one-dimensional crystallinity (Xu et al, 2005). W i is a dimensionless coefficient representing the energy penalty, i represents the crystal order parameter at the peak position of the barrier, and i;0 represents the stable potential well for the system to equilibrate during solidification.…”

Phase-Field Simulation of Polymer Crystallization during Cooling Stage

“…From references [5], [12], [13], the model parameters can be calculated by n is the amount of substance of polymer monomers per unit volume.…”

“…Except the above mentioned approaches, the phase-field methods can also be used to model the crystallization morphologies of semi-crystalline polymers [5]- [9]. This kind of method has been successfully applied to simulate the polycrystalline growth of polymers and reveal the corresponding formation mechanisms under isothermal conditions.…”