Origin of the nucleation barrier in athermal hard spheres

无热硬球中成核势垒的起源

• 批准号: 403607897
• 负责人: Privatdozent Dr. Matthias Schröter, Ph.D.
• 金额: --
• 依托单位: Centre for Mathematics and its Applications
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/403607897?language=en
• 关键词: Origin; nucleation; barrier; athermal; hard

Hard spheres are a seminal model system in condensed matter.Especially their first order phase transition from an ordered solid to an amorphous fluid became the textbook example of entropic forces governing a multi particle system. Both colloids and granular matter are often considered to be experimental realizationsof hard sphere systems. However, while the dynamics of the former is governed by Brownian motion, granular particles are orders of magnitude too large to be in influenced by thermal energies. Granular spheres can therefore be considered as athermal hard spheres.Colloids, as hard spheres, undergo a first order phase transition with a coexistence region with volume fractions between 0.49 and 0.55. The formation of new crystals is well described by the Classical Nucleation Theory (CNT) framework, which assumes that the free energy gain associated with the formation of a crystalline bulk phase has to overcome the free energy costs occurring due to the formation of interface between crystal and amorphous phase. This leads to a critical nucleus size; only above this size it is thermodynamically favorable for the crystal seed to grow. Driven granular packings share some of this phenomenology. They also display transition from an amorphous to a crystalline state characterized by a coexistence region, albeit at volume fractions between 0.64 and 0.74. Moreover, it is also possible to identify a critical nucleus size N necessary for the crystal to grow. However, an analysis of the volume fraction in the transition zone between the nucleus and the amorphous phase shows that the formation of additional interface is energetically favorable for nuclei smaller than N. This failure of the CNT framework demands a new approach to the crystallization in athermal sphere packings.One possible alternative explanation of the critical nucleus size is that the formation of smaller crystals is kinematically inhibited. This proposal aims to test this hypothesis using an already existing setup to cyclic shear a packing of 50000 glass spheres immersed in an index-matched liquid. Using a laser sheet scanning technique, we will identify the positions of all particles. We will then use persistent homology to parameterize the geometrical configurations of groups of particles using the so called persistence diagram PD2. A series of scans made while the system is in the two-phase coexistence region will give us geometrical trajectories of particle groups in PD2. The kinematic inhibition hypothesis stated above corresponds to the existence of a repellent region in PD2. Understanding the nucleation in athermal systems will not only expand our knowledge about granular matter, which is ubiquitous in our daily lives. It might also be the starting point to develop a theory of self-assembly on mesoscopic scales.

硬球是凝聚态中一个开创性的模型系统，特别是它们从有序固体到无定形流体的一级相变，成为多粒子系统熵力的典型例子。胶体和颗粒物质通常被认为是硬球系统的实验实现。然而，虽然前者的动力学由布朗运动控制，但粒状颗粒的数量级太大而不受热能的影响。因此，颗粒球可以被认为是无热的硬球，胶体，作为硬球，经历一级相变，共存区的体积分数在0.49和0.55之间。经典成核理论（CNT）框架很好地描述了新晶体的形成，其假设与结晶体相的形成相关的自由能增益必须克服由于晶体和非晶相之间的界面的形成而发生的自由能成本。这导致了临界核尺寸;只有超过这个尺寸，才有利于晶种生长。驱动颗粒填料共享一些这种现象。它们还显示从非晶态到结晶态的过渡，其特征在于共存区域，尽管体积分数在0.64和0.74之间。此外，还可以确定晶体生长所需的临界核尺寸N。然而，对晶核和非晶相之间过渡区的体积分数的分析表明，对于小于N的晶核，附加界面的形成在能量上是有利的。这种碳纳米管框架的失败需要一种新的方法来结晶在无热球packings.One可能的替代解释的临界核尺寸的形成较小的晶体是运动学抑制。该提案旨在测试这一假设，使用一个已经存在的设置，以循环剪切包装的50000玻璃球浸在一个指数匹配的液体。使用激光片扫描技术，我们将确定所有粒子的位置。然后，我们将使用持久同调来参数化粒子群的几何构型，使用所谓的持久图PD 2。 当系统处于两相共存区时进行的一系列扫描将给我们PD 2中粒子群的几何轨迹。上述运动抑制假说对应于PD 2中存在排斥区。 了解无热化系统中的成核现象不仅可以扩展我们对颗粒物质的认识，因为颗粒物质在我们的日常生活中无处不在。这也可能是发展介观尺度自组装理论的起点。