Schönhöfer Philipp W A, Ellison Laurence J, Marechal Matthieu, Cleaver Douglas J, Schröder-Turk Gerd E
School of Engineering and Information Technology, Mathematics and Statistics, Murdoch University, 90 South Street, Murdoch, Western Australia 6150, Australia.
Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany.
Interface Focus. 2017 Aug 6;7(4):20160161. doi: 10.1098/rsfs.2016.0161. Epub 2017 Jun 16.
We investigate a model of hard pear-shaped particles which forms the bicontinuous Ia[Formula: see text]d structure by entropic self-assembly, extending the previous observations of Barmes (2003 , 021708. (doi:10.1103/PhysRevE.68.021708)) and Ellison (2006 , 237801. (doi:10.1103/PhysRevLett.97.237801)). We specifically provide the complete phase diagram of this system, with global density and particle shape as the two variable parameters, incorporating the gyroid phase as well as disordered isotropic, smectic and nematic phases. The phase diagram is obtained by two methods, one being a compression-decompression study and the other being a continuous change of the particle shape parameter at constant density. Additionally, we probe the mechanism by which interdigitating sheets of pears in these systems create surfaces with negative Gauss curvature, which is needed to form the gyroid minimal surface. This is achieved by the use of Voronoi tessellation, whereby both the shape and volume of Voronoi cells can be assessed in regard to the local Gauss curvature of the gyroid minimal surface. Through this, we show that the mechanisms prevalent in this entropy-driven system differ from those found in systems which form gyroid structures in nature (lipid bilayers) and from synthesized materials (di-block copolymers) and where the formation of the gyroid is enthalpically driven. We further argue that the gyroid phase formed in these systems is a realization of a modulated splay-bend phase in which the conventional nematic has been predicted to be destabilized at the mesoscale due to molecular-scale coupling of polar and orientational degrees of freedom.
我们研究了一种硬梨形颗粒模型，该模型通过熵自组装形成双连续Ia[公式：见正文]d结构，扩展了巴姆斯（2003年，021708。（doi:10.1103/PhysRevE.68.021708））和埃里森（2006年，237801。（doi:10.1103/PhysRevLett.97.237801））之前的观察结果。我们特别给出了该系统的完整相图，以全局密度和颗粒形状作为两个可变参数，其中包括螺旋状相以及无序各向同性相、近晶相和向列相。相图通过两种方法获得，一种是压缩 - 解压研究，另一种是在恒定密度下连续改变颗粒形状参数。此外，我们探究了这些系统中梨形颗粒相互交错的片层形成具有负高斯曲率表面的机制，这是形成螺旋状最小表面所必需的。这是通过使用Voronoi镶嵌实现的，据此可以根据螺旋状最小表面的局部高斯曲率评估Voronoi单元的形状和体积。通过这种方式，我们表明在这个熵驱动系统中普遍存在的机制不同于在自然界中形成螺旋状结构的系统（脂质双层）以及合成材料（二嵌段共聚物）中发现的机制，在这些系统中螺旋状结构的形成是由焓驱动的。我们进一步认为，在这些系统中形成的螺旋状相是调制展曲 - 弯曲相的一种实现，其中传统向列相由于极性和取向自由度的分子尺度耦合在中尺度下被预测是不稳定的。
