Origin of the nucleation barrier in athermal hard spheres

• Applicant: Privatdozent Matthias Schröter, Ph.D.
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2018 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 403607897

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.

• DFG Programme: Research Grants
• International Connection: Australia
• Co-Investigator: Dr. Mohammad Saadatfar