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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\approx 3\)</EquationSource> </InlineEquation> nm (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\approx 5740\)</EquationSource> </InlineEquation> 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.</p>

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Controlling the size of nanoparticles using a magnetic field: a sphere packing approach

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月22日

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  • Yazeed Tawalbeh,
  • Marwa Ghazi,
  • Mauro Fernandes Pereira

摘要

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 \(\approx 3\) nm ( \(\approx 5740\) 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.