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Magnetic field controlled nucleation and size selection of silver nanoparticles

Yazeed Tawalbeh, Mauro F. Pereira

TL;DR

This work addresses how external magnetic fields can actively tune silver nanoparticle (AgNP) size during nucleation. It extends classical nucleation theory (CNT) by incorporating magnetic free-energy contributions and a sphere-packing description of atomic assembly to derive a closed-form relation between NP radius $r$ and field $\\mathcal{B}$, via the work of formation $\\Delta \\mathcal{F}$. The authors demonstrate that the field lowers the nucleation barrier and reproduces the experimentally observed size reductions: from about $245$ nm at zero field to $\\sim170$ nm at $\\mathcal{B} \\\approx 50$ mT in the parallel configuration and to $\\sim155$ nm at $\\mathcal{B} \\\approx 181$ mT in the perpendicular configuration, in agreement with measurements under mechanical stirring. The results show robustness across field orientations, suggesting a thermodynamic mechanism governed by magnetic susceptibility $\\chi_m$ and demagnetization effects, and yield a physically transparent, computationally efficient framework for magnetic-field-controlled NP size selection within the limits of CNT and spherical demagnetization. The framework provides a practical tool for designing field-driven NP synthesis where size distribution is critical for optical and chemical performance."

Abstract

We examine the reduction of silver nanoparticle (AgNP) size under an external magnetic field within a classical nucleation theory framework combined with a sphere-packing description of atomic assembly. The model incorporates magnetic free-energy contributions arising from the coupling between the applied field and the magnetic susceptibility of the nucleating material, yielding a closed-form relation between nanoparticle radius and field strength. Our approach reproduces the experimentally observed decrease in the most-probable particle radius from approximately 170 nm at 49.27 mT when the magnetic field is oriented parallel to the stirring plane, and to 155 nm at 180.78 mT in the perpendicular configuration. Across the investigated field range, the theoretical predictions remain consistent with experimental measurements obtained under continuous mechanical stirring, supporting the interpretation that the observed size reduction originates from a magnetic-field-induced modification of the nucleation free-energy landscape. Within the limits of classical capillarity and spherical demagnetization, the results provide a physically transparent and computationally efficient framework for understanding magnetic-field-controlled nanoparticle size selection.

Magnetic field controlled nucleation and size selection of silver nanoparticles

TL;DR

This work addresses how external magnetic fields can actively tune silver nanoparticle (AgNP) size during nucleation. It extends classical nucleation theory (CNT) by incorporating magnetic free-energy contributions and a sphere-packing description of atomic assembly to derive a closed-form relation between NP radius and field , via the work of formation . The authors demonstrate that the field lowers the nucleation barrier and reproduces the experimentally observed size reductions: from about nm at zero field to nm at mT in the parallel configuration and to nm at mT in the perpendicular configuration, in agreement with measurements under mechanical stirring. The results show robustness across field orientations, suggesting a thermodynamic mechanism governed by magnetic susceptibility and demagnetization effects, and yield a physically transparent, computationally efficient framework for magnetic-field-controlled NP size selection within the limits of CNT and spherical demagnetization. The framework provides a practical tool for designing field-driven NP synthesis where size distribution is critical for optical and chemical performance."

Abstract

We examine the reduction of silver nanoparticle (AgNP) size under an external magnetic field within a classical nucleation theory framework combined with a sphere-packing description of atomic assembly. The model incorporates magnetic free-energy contributions arising from the coupling between the applied field and the magnetic susceptibility of the nucleating material, yielding a closed-form relation between nanoparticle radius and field strength. Our approach reproduces the experimentally observed decrease in the most-probable particle radius from approximately 170 nm at 49.27 mT when the magnetic field is oriented parallel to the stirring plane, and to 155 nm at 180.78 mT in the perpendicular configuration. Across the investigated field range, the theoretical predictions remain consistent with experimental measurements obtained under continuous mechanical stirring, supporting the interpretation that the observed size reduction originates from a magnetic-field-induced modification of the nucleation free-energy landscape. Within the limits of classical capillarity and spherical demagnetization, the results provide a physically transparent and computationally efficient framework for understanding magnetic-field-controlled nanoparticle size selection.
Paper Structure (4 sections, 3 equations, 4 figures, 1 table)

This paper contains 4 sections, 3 equations, 4 figures, 1 table.

Table of Contents

  1. introduction
  2. Methods
  3. Discussion
  4. Conclusion

Figures (4)

  • Figure 1: (a) The Group I experimental configuration where the field is parallel to the stirring direction (b) The Group II experimental configuration where the field is perpendicular to the stirring direction
  • Figure 2: the sphere packing fit $n(x)$. NPs are modeled as a perfectly packed core (blue) with packing fraction $\phi_b=\frac{\pi}{3\sqrt{2}}$ and a defective surface (green) with a packing fraction $\phi_d=0.517$ obtained by fitting the data from packomania pack. $\delta$ is the thickness of the surface.
  • Figure 3: The field radius relation for (a) the parallel configuration and (b) the perpendicular configuration
  • Figure 4: A comparison between the parallel and perpendicular configurations over an extended field. We can see that the radius falls off more rapidly in the parallel configuration.