Origin of the nucleation barrier in athermal hard spheres

硬球是凝聚态物质的种子模型系统。特别是它们从有序固体到非晶态流体的一阶相变，成为控制多粒子系统的熵力的教科书范例。胶体和颗粒物质通常被认为是硬球系统的实验实现。然而，前者的动力学是由布朗运动控制的，而颗粒粒子的数量级太大，不受热能的影响。因此，颗粒球可以被认为是非热硬球。胶体作为硬球，发生一阶相变，共存区体积分数在0.49 ~ 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，该框架假设与晶体本体相形成相关的自由能增益必须克服由于晶体和非晶相之间形成界面而产生的自由能成本。这导致了一个临界核大小；只有在这个尺寸以上，才有利于晶体种子的生长。驱动颗粒填料也有这种现象。它们也表现出从无定形到晶态的转变，其特征是共存区域，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，对核和非晶相之间的过渡区体积分数的分析表明，额外界面的形成在能量上有利于小于n的核。这种碳纳米管框架的失败需要一种新的方法来实现非热球填料的结晶。对临界核尺寸的另一种可能的解释是，较小晶体的形成在运动上受到抑制。该提案旨在使用现有的装置来测试这一假设，该装置将50000个玻璃球浸入指数匹配的液体中进行循环剪切。使用激光扫描技术，我们将确定所有粒子的位置。然后，我们将使用持久性同调来参数化粒子群的几何构型，使用所谓的持久性图PD2。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。上述运动学抑制假说对应于PD2中排斥区域的存在。了解非热系统中的成核不仅将扩大我们对颗粒物质的认识，颗粒物质在我们的日常生活中无处不在。这也可能是在介观尺度上发展自组装理论的起点。

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.