Classical nucleation theory for the crystallization kinetics in sheared liquids

Abstract

While statistical mechanics provides a comprehensive framework for the understanding of equilibrium phase behavior, predicting the kinetics of phase transformations remains a challenge. Classical nucleation theory (CNT) provides a thermodynamic framework to relate the nucleation rate to thermodynamic quantities such as pressure difference and interfacial tension through the nucleation work necessary to spawn critical nuclei. However, it remains unclear whether such an approach can be extended to the crystallization of driven melts that are subjected to mechanical stresses and flows. Here, we demonstrate numerically for hard spheres that the impact of simple shear on the crystallization rate can be rationalized within the CNT framework by an additional elastic work proportional to the droplet volume. We extract the local stress and strain inside solid droplets, which yield size-dependent values for the shear modulus that are about half of the bulk value. Finally, we show that for a complete description one also has to take into account the change of interfacial work between the strained droplet and the sheared liquid. From scaling reasons, we expect this extra contribution to dominate the work formation of small nuclei but become negligible compared to the elastic work for droplets composed of a few hundreds particles.

Homogeneous Nucleation of Sheared Liquids: Advances and Insights from Simulations and Theory

“…Monodisperse hard spheres were studied using this formalism [122]. The authors validated the size-dependence of the shear modulus by showing that the shear modulus of nuclei with sizes less than 100 particles were significantly smaller than the shear modulus of the bulk crystalline phase.…”

“…Richard et al [122] proposed another approach, tying together seeded simulations performed at different shear rates with modified CNT equations. In the framework of Richard et al [122], the reversible elastic work of the solid phase, W S , is not estimated from the shear stress acting on the surrounding liquid phase, ν L = η γ. Instead, W S is calculated from simulations for every shear rate and condition of metastability.…”

“…( 19) that the effective shear modulus can be determined once the solid density, ρ S , shear stress, ν S , and solid strain, γ S , have been estimated. Richard et al [122] proposed a methodology for extracting the required statistics via seeding simulations [98], conducted at each condition of metastability, imposed γ, and seed size considered.…”

“…Deformation of the solid nuclei was not considered, despite the fact that the surface area contribution to the free energy is expected to be dominant for small nuclei. Although the approach of Richard et al [122] is conceptually rigorous, accurate, and less computationally expensive than brute-force methods, the framework may be limited in scope due to the extensive calculations required for the estimation of G ef f at every γ considered.…”

Obtaining A Unified Picture of Heterogeneous and Homogeneous Crystallization with Kinetic Transition Rate

“…Theoretically, due to the competition between interfacial energy and bulk energy, small nuclei have higher free energy than liquid and difficult to grow, [8][9][10] and thus the supercooled liquid may maintain its metastable liquid state over some time blow the freezing point. 11,12 Only after the nuclei exceed a critical size, the interfacial energy becomes less important and the nuclei can grow spontaneously, as described by the classical nucleation theory 5,[13][14][15][16] (CNT). Moreover, the energy barrier overcame to reach this critical nucleus size may reduce substantially at the boundary than in the bulk due to surface wetting, [17][18][19][20] which qualitatively explains why heterogeneous crystallization can occurs much easier than homogeneous crystallization.…”