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Elucidating anisotropic seed-mediated nanorod growth in solution

Junjie Hao1,2,3, Eugenie Pariente1,2, Marie-Helene Delville2, and Jean-Pierre Delville1

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Phys. Rev. Materials 10, 083401 – Published 21 August, 2026

DOI: https://doi.org/10.1103/gcpf-11ks

Abstract

A rod with rounded ends is a noteworthy morphology, naturally encountered from large-scale roots to cells, and synthetically conceived down to nanomaterials. Rod-shaped anisotropic nanocrystals—especially those grown on pre-synthesized spherical seeds—play a major role in areas as different as photonics, cancer therapy, and photocatalysis. Nonetheless, despite decades of intense research, the anisotropic growth laws of nanorods (NRs) remain elusive. Here, we propose a general two-surface tension thermodynamic model that allows determining these axial and radial NR growth rates by reaction and diffusion. Depending on the initial seed size, three growth modes are predicted: either 3d, where both length and diameter grow simultaneously, 1d, where NRs just grow in one direction, and 1d-3d, showing the two growth modes sequentially. Modeling also shows that NRs lengthening and widening are driven by the surface tension ratio between the cylindrical core and the hemispherical tips. The confrontation of this model with kinetics data published on both high-symmetry face-centered-cubic (FCC) and lower-symmetry hexagonal close-packed (HCP) Wurtzite nanocrystals, as well as new experiments on Wurtzite CdSe-CdS NRs, confirms the existence of these three growth modes under reaction-limited conditions. From a practical point of view, they enable the determination of the axial/radial kinetic reaction rates along with surface tensions, and experimentally predict the seed-dependent growth and morphology of the NRs beyond the already well-established synthetic strategies for targeted applications. Finally, the few data published on the growth of Smectic A ligaments in the isotropic phase after a quench in temperature show a qualitative agreement with behaviors expected from a two-surface tension diffusion-limited mechanism.

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Phys. Rev. Materials 10, 083401– Published 21 August, 2026
  • Received 21 January 2026
  • Accepted 22 June 2026
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