Nanorod Pair Complexes Manipulated via Magnetic Casimir Forces

TL;DR

The paper addresses the challenge of controlling Casimir-Lifshitz forces at the nanoscale by embedding anisotropic nanoparticles in a magnetic ferrofluid to achieve tunable interactions. Using semi-classical quantum electrodynamics, it derives the ground-state dispersion energy per unit length, $G(a,R,T)$, for two cylindrical nanorods separated by $R$ and radius $a$, in a ferrofluid with effective permittivity $\,\varepsilon_3\,$ and permeability $\mu_3$, via a Matsubara-frequency scattering approach in the thin-cylinder limit, and also predicts a magnetic contribution to retarded excited-state interactions with $E^{\text{res}}(R)$ scaling as $R^{-3}$. The key finding is that varying the fluid’s magnetic permeability enables transitions between repulsive and attractive CL forces, enabling magnetic Casimir traps whose strength and range depend on magnetite nanoparticle size $D$ and volume fraction $\phi$, with zero-frequency magnetic contributions playing a crucial role. Retardation reduces overall interaction strength but increases the relative weight of magnetic response, and the trapping behavior can be tuned by adjusting $D$ and $\phi$ or by coating magnetite with gold to modify the medium’s dielectric function, offering a route to reversible, field-controlled assembly and enhanced colloidal stability with potential applications in NEMS/MEMS and bio-integrated nanomaterials.

Abstract

Controlling nanoscale interactions to suppress aggregation from short-range attractive forces is a key problem in nanoengineering. Here, we demonstrate a route to modulate Casmir-Lifshitz interactions between anisotropic nanoparticles with the magnetic fluids. By semi-classical quantum electrodynamics, we study ground state dispersion forces for cylindrical dielectric nanorods made of polystyrene (PS), and zinc oxide (ZnO) embedded in toluene-based host media with gold-coated magnetite nanoparticles and also predict magnetic contributions to the non-retarded excited state interaction. The variation in magnetic permeability enables tuning between repulsive and attractive interaction and a thermally unstable and measurable magnetic Casimir traps are predicted between a pair of ZnO-PS nanoparticles whose equilibrium position can be modulated over an order of magnitude with a small variation in the size of the magnetite nanoparticle. This provides an alternative magnetic Casimir-effect pathway to reversibly tune quantum electromagnetic forces at the nanoscale for assembly and enhancement of colloidal stability.

Figures (5)

• Figure 1: Color online: Two cylindrical nanorods, one composed of ZnO with permittivity $\varepsilon_1$ and permeability $\mu_1$, and the other of PS with permittivity $\varepsilon_2$ and permeability $\mu_2$, each having an identical radius $a$, are immersed in a magnetic liquid. The magnetic liquid is composed of toluene and it contains dispersed gold coated (thickness $R_{\rm Au}$) magnetite nanoparticles of diameter $D$ and volume fraction $\phi$ and it has effective permittivity $\varepsilon_3$ and permeability $\mu_3$. The nanorods are separated by a center-to-center distance $R$.
• Figure 2: (Color online): The dielectric functions on the imaginary axis as functions of frequency $\xi$. The parametrized data for PS and toluene are based on optical experiments given by van Zwol et al.Zwol1. The magnetic fluid consists of a mixture of toluene and magnetite particles, using Eq. (\ref{['2mixturedielEqA']}) for a volume fraction of $\phi = 5\%$. The response functions of gold and magnetite are DFT results presented in Ref. Carretero_PRB_2025_PhysRevB.111.085407, whereas the data for ZnO are from present DFT calculations.
• Figure 3: (Color online:) The CL force per unit length between two cylindrical objects (ZnO and PS respectively) with the same radius $a=20$ nm as a function of center-to-center distance $R$ when immersed in a ferrofluid with 5% and 7% concentrations of magnetite nanoparticles of diameter 10, 13, 15 and 17 nm.
• Figure 4: (Color online): The CL force per unit length between two ZnO and PS cylindrical objects was evaluated for volume fraction $\phi = 5\%, 7\%$ and a nanoparticle diameter $D= 17$ nm. The terms "without gold" and "with gold" refer to magnetite nanoparticles without and with a gold coating, respectively. For gold coating, layer thickness was taken to be, $R_{\rm Au} = 2$ nm. Total$_{1}$ is the fully retarded calculation for all frequencies without gold coating whereas Total$_{2}$ reflects the retarded force with gold coating and $p=0$ denotes the zero frequency contribution.
• Figure 5: (Color online:) The CL force per unit length between two cylindrical objects (ZnO and PS respectively) with the same radius $a=20$ nm as a function of center-to-center distance $R$ when immersed in a ferrofluid with different concentrations of ($\phi$=0.01-0.15) magnetite nanoparticles of diameter 17 nm.