Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK.
Soft Matter. 2017 Nov 29;13(46):8781-8795. doi: 10.1039/c7sm02017a.
When a nano-drop comprising a single spherical central ion and dielectric solvent is charged above a well-defined threshold, it acquires a stable star morphology. In contrast, conducting droplets, will undergo fission. Here we report combined atomistic molecular dynamics and continuum modelling study of star formation of droplets that contain a highly charged ion. We assume that in the continuum model the dielectric response is linear. In this linear continuum model, which is an extension of Rayleigh model, the energy of the drop is comprised of terms analogous to those in Rayleigh model, which are surface energy and electrostatic energy of dielectric droplet charged by a central point charge. We present the stability analysis of the continuum model to determine the threshold of instability. Indeed we find that the model accounts well for the onset of the instabilities. Molecular dynamics show that the number of points of the star-shaped nano-drops depends only on the surface tension, dielectric constant and size of the droplet, and on the magnitude of the charge of the central ion, but not on its sign. Intuitively, it is expected that when a spherical dielectric drop becomes unstable it would transform into a non-spherical finite shape of the same volume as the initial spherical shape with the point charge located in the drop interior. To test whether the extended Rayleigh model can account for the observed droplet shapes, we performed numerical simulations of the linear continuum model. Contrary to the expectations, the simulations of the extended Rayleigh model does not reproduce the stable star shapes found in the atomistic simulations, not even when we account for the bending rigidity and spontaneous curvature of the surface. We argue that the assumption that the dielectric response is linear breaks down if the droplet surface approaches the central macro-ion, where the electric field strength is such that dielectric saturation sets in. We envisage that for certain solvents, these stars could be made permanent by cross-linking, opening the way to the production of a novel class of highly-non-convex colloids.
当一个由单个球形中心离子和介电溶剂组成的纳米液滴被充电到一个明确的阈值以上时，它会获得一个稳定的星形形态。相比之下，导电液滴会发生裂变。在这里，我们报告了一个关于包含高电荷离子的液滴的星形形成的原子分子动力学和连续体建模研究的综合研究。我们假设在连续体模型中，介电响应是线性的。在这个线性连续体模型中，它是瑞利模型的扩展，液滴的能量由类似于瑞利模型中的那些术语组成，这些术语是由中心点电荷充电的介电液滴的表面能和静电能。我们提出了连续体模型的稳定性分析来确定不稳定性的阈值。事实上，我们发现该模型很好地解释了不稳定性的开始。分子动力学表明，星形纳米液滴的点数仅取决于表面张力、介电常数和液滴的大小，以及中心离子的电荷大小，但与电荷的符号无关。直观地说，当一个球形介电液滴变得不稳定时，它会转变成一个具有相同初始球形形状体积的非球形有限形状，而点电荷位于液滴内部。为了测试扩展的瑞利模型是否可以解释观察到的液滴形状，我们对线性连续体模型进行了数值模拟。与预期相反，扩展的瑞利模型的模拟并不能再现原子模拟中发现的稳定星形形状，即使我们考虑了表面的弯曲刚度和自发曲率。我们认为，如果液滴表面接近中心宏观离子，介电响应线性的假设就会失效，因为在那里电场强度足以使介电饱和。我们设想，对于某些溶剂，通过交联可以使这些恒星永久化，为生产一类新型的高度非凸胶体开辟了道路。
