Origin of the nucleation barrier in athermal hard spheres

硬球是凝聚态物质的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控制多粒子系统的熵力的教科书例子。胶体和颗粒物质通常被认为是硬球系统的实验实现。然而，尽管前者的动力学受布朗运动的支配，但颗粒粒子的数量级太大了，不会受到热能的影响。因此，颗粒球可以被认为是无热硬球，胶体作为硬球经历了一级相变，其共存区域的体积分数在0.49到0.55之间。经典形核理论(CNT)框架很好地描述了新晶体的形成，该框架假设与结晶体相形成相关的自由能增益必须克服由于晶体与非晶相之间形成界面而产生的自由能代价。这导致了一个临界的核大小；只有超过这个大小，才有利于晶体种子的生长。驱动的颗粒状堆积与这一现象有一些相似之处。它们还表现出从非晶态到晶态的转变，其特征是共存区域，尽管体积分数在0.64到0.74之间。此外，还可以确定晶体生长所需的临界核大小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，附加界面的形成对小于N的晶核在能量上是有利的。这种碳纳米管骨架的失效需要一种新的方法来处理非热球堆积中的晶化。对临界晶核尺寸的一种可能的解释是，较小晶体的形成受到运动学上的抑制。这项提议旨在使用已有的装置来验证这一假设，该装置将50000个玻璃球浸入折射率匹配的液体中进行循环剪切。使用激光薄片扫描技术，我们将识别所有粒子的位置。然后，我们将使用持久同调来使用所谓的持久图PD2来参数化粒子组的几何构型。当系统处于两相共存区域时进行的一系列扫描将给出PD2中粒子群的几何轨迹。上述运动抑制假说对应于PD2中存在排斥区域。了解无热系统中的成核现象不仅可以扩展我们对日常生活中普遍存在的颗粒物质的认识。这也可能是发展介观尺度上的自组装理论的起点。

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.