Role of Gaussian curvature on local equilibrium and dynamics of smectic-isotropic interfaces
Role of Gaussian curvature on local equilibrium and dynamics of smectic-isotropic interfaces
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高斯曲率对近晶各向同性界面的局部平衡和动力学的作用
DOI：
10.1103/physreve.100.032805
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发表时间：
2019
影响因子：
2.4
通讯作者：
Viñals, Jorge
中科院分区：
文献类型：
--
作者：
Vitral, Eduardo;Leo, Perry H.;Viñals, Jorge
近年来对近晶膜界面不稳定性的研究显示出经典局部平衡热力学无法完全解释的意想不到的形态。对焦锥域进行退火处理，可以得到锥形锥体，改变高斯曲率的符号，并在界面处暴露出近晶层。为了探索高斯曲率对膜-气界面稳定性和演化的作用，我们首先引入了一个近晶-各向同性系统的相场模型。通过对模型的渐近分析，我们推广了经典的局部平衡条件Gibbs-Thomson方程，使其包含了表面弯曲和扭转的贡献以及对界面层取向的依赖。利用相场模型的全数值解，研究了在与各向同性相接触的近晶区域内，局部蒸发和近晶层的冷凝作用下的焦锥结构的演化过程。与实验一样，数值解表明，由于相邻的近晶面蒸发及其相对于界面的取向，在焦点圆锥中心附近出现了金字塔结构。在焦点圆锥域中心附近，要正确描述界面的运动，需要在渐近分析中得到的附加曲率项，从而澄清了仅由平均曲率驱动的双曲曲面运动建模的局限性。
Recent research on interfacial instabilities of smectic films has shown unexpected morphologies that are not fully explained by classical local equilibrium thermodynamics. Annealing focal conic domains can lead to conical pyramids, changing the sign of the Gaussian curvature and exposing smectic layers at the interface. In order to explore the role of the Gaussian curvature on the stability and evolution of the film-vapor interface, we introduce a phase-field model of a smectic-isotropic system as a first step in the study. Through asymptotic analysis of the model, we generalize the classical condition of local equilibrium, the Gibbs-Thomson equation, to include contributions from surface bending and torsion and a dependence on the layer orientation at the interface. A full numerical solution of the phase-field model is then used to study the evolution of focal conic structures in smectic domains in contact with the isotropic phase via local evaporation and condensation of smectic layers. As in experiments, numerical solutions show that pyramidal structures emerge near the center of the focal conic owing to evaporation of adjacent smectic planes and to their orientation relative to the interface. Near the center of the focal conic domain, a correct description of the motion of the interface requires the additional curvature terms obtained in the asymptotic analysis, thus clarifying the limitations in modeling motion of hyperbolic surfaces solely driven by mean curvature.