A fingerprint of surface-tension anisotropy in the free-energy cost of nucleation

Abstract

We focus on the Gibbs free energy $\Delta G$ for nucleating a droplet of the stable phase (e.g. solid) inside the metastable parent phase (e.g. liquid), close to the first-order transition temperature. This quantity is central to the theory of homogeneous nucleation, since it superintends the nucleation rate. We recently introduced a field theory describing the dependence of $\Delta G$ on the droplet volume $V$, taking into account besides the microscopic fuzziness of the droplet-parent interface, also small fluctuations around the spherical shape whose effect, assuming isotropy, was found to be a characteristic logarithmic term. Here we extend this theory, introducing the effect of anisotropy in the surface tension, and show that in the limit of strong anisotropy $\Delta G(V)$ once more develops a term logarithmic on $V$, now with a prefactor of opposite sign with respect to the isotropic case. Based on this result, we argue that the geometrical shape that large solid nuclei mostly prefer could be inferred from the prefactor of the logarithmic term in the droplet free energy, as determined from the optimization of its near-coexistence profile.

arXiv comment41 pages, 9 figures

References in corpus (8)

• Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling and forward flux sampling: A comparison of simulation techniques
• Curvature Dependence of Surface Free Energy of Liquid Drops and Bubbles: A Simulation Study
• Systematic Improvement of Classical Nucleation Theory
• Surface Tension, Surface Stiffness, and Surface Width of the 3-dimensional Ising Model on a Cubic Lattice
• Computing the Roughening Transition of Ising and Solid-On-Solid Models by BCSOS Model Matching
• Physics of Solid and Liquid Alkali Halide Surfaces Near the Melting Point
• Irreducible finite-size effects in surface free energies from crystal-nucleation data
• Effective Hamiltonian of Liquid-Vapor Curved Interfaces in Mean Field

Cited by in corpus (16)

• Pathways to self-organization: crystallization via nucleation and growth
• Shape and area fluctuation effects on nucleation theory
• Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension
• Ground state of weakly repulsive soft-core bosons on a sphere
• Size dependence of the surface tension of a free surface of an isotropic fluid
• The barrier to ice nucleation in monatomic water
• Freezing of soft-core bosons at zero temperature: A variational theory
• Free Energy Barriers for Crystal Nucleation from Fluid Phases
• Shapes of a liquid droplet in a periodic box
• Self-assembly in a model colloidal mixture of dimers and spherical particles
• Do the contact angle and line tension of surface-attached droplets depend on the radius of curvature?
• Aspects of nucleation on curved and flat surfaces
• Droplet condensation in the lattice gas with density functional theory
• Classical and Quantum Gases on a Semiregular Mesh
• A maximum-entropy approach to the adiabatic freezing of a supercooled liquid
• Condensation and crystal nucleation in a lattice gas with a realistic phase diagram