Controlling the Size of Nanoparticles Using a Magnetic Field: A Sphere Packing Approach

TL;DR

This paper introduces an analytical model that predicts and controls nanoparticle size using magnetic fields, combining thermodynamics and sphere packing, validated with silver nanoparticles and applicable to various magnetic materials.

Contribution

The paper presents a novel analytical framework that links magnetic field strength to nanoparticle size, integrating thermodynamics with sphere packing for the first time.

Findings

Model accurately predicts nanoparticle size shifts under magnetic fields.

Field application reduces nucleation barriers, leading to smaller particles.

Robust for particles larger than 3 nm, with limitations discussed for smaller sizes.

Abstract

We present an analytical framework that predicts and controls nanoparticle size through external magnetic fields, uniting first-principles thermodynamics with a sphere packing approach. Calibrated to diamagnetic silver nanoparticles (20 nm at zero field and 5 nm at 250 mT), the model yields a closed-form relation between radius and field that reproduces the observed shift in most-probable size. Within the limits of classical capillarity and spherical demagnetization, the field lowers the nucleation barrier and drives the distribution toward smaller particles. Our results are robust for radii above 3 nm (5740 atoms). Below this scale non-extensive effects likely dominate, as discussed in detail in Supplementary Information. The approach generalizes to both diamagnetic and paramagnetic systems and the limitations expected for very small or ferromagnetically ordered nanoparticles are discussed.