Regulation of propulsion in assemblies of thermophoretic nanomotors

Active particles locally transduce energy into motion, leading to unusual and emergent behaviors. However, current synthetic particles lack sensing and adaptation mechanisms. Here, we demonstrate a novel regulation pathway, through the combined use of thermophoretic propulsion and nanometric building blocks. We build an active fluid composed of artificial nanomotors and study its three-dimensional (3D) dynamics. We use laser-induced photo-thermal effect to actuate nanoparticles, and probe their self-propulsion within assemblies. Despite significant thermal fluctuations at the nanoscale, our results reveal a strong dependence of the thermophoretic propulsion on the concentration of nanomotors, leading to ultrafast velocities of up to ~ 800 um/s. This unique behavior originates from a strong coupling of the local concentration of nanomotors and the temperature field, which feeds back on the thermophoretic mobility of the nanoparticles. We rationalize our results from independent modeling of all thermal effects, accounting for nonlinearities of thermophoretic self-propulsion. Our results open novel routes for the design and self-regulation of 3D active fluids by thermal processes.

💡 Research Summary

In this work the authors introduce a novel regulation pathway for active fluids based on thermophoretic nanomotors. They synthesize Au/SiO₂ nano‑heterodimers (NHDs) of about 60 nm overall size, where an absorbing gold nanosphere is asymmetrically coated with a silica lobe. The asymmetry creates a localized temperature gradient when the gold core is illuminated at its plasmon resonance (λ = 532 nm). The resulting self‑thermophoresis drives three‑dimensional propulsion with a velocity v ∝ µ · ⟨∇T⟩, where µ is the thermophoretic mobility and ⟨∇T⟩ the surface temperature gradient.

Because the particles are nanometric, conventional optical tracking is impossible. The authors therefore employ confocal scattering correlation spectroscopy (CSCS) to monitor intensity fluctuations of a weak red probe beam (λ = 632.8 nm) scattered by particles within a ≈ 11 µm³ observation volume. By fitting the autocorrelation function g²(τ) they extract an effective diffusion coefficient D_eff, which contains both Brownian diffusion D and a contribution from self‑propulsion (v² τ_R/6). This method allows them to probe a wide range of particle concentrations, from dilute (c ≈ 6 × 10¹³ NP L⁻¹) to dense (c ≈ 4.7 × 10¹⁴ NP L⁻¹).

In the dilute regime, where inter‑particle interactions are negligible, D_eff increases linearly with laser intensity. The inferred propulsion speed reaches ≈ 150 µm s⁻¹ (≈ 2 × 10³ body lengths per second) at an incident intensity of 40 µW µm⁻². Using Mie calculations (σ_abs ≈ 1650 nm²) and the thermal conductivity of water (κ ≈ 0.20 W m⁻¹ K⁻¹), the authors estimate a surface temperature rise of ~2 K, which yields a thermophoretic mobility µ ≈ 1 µm² s⁻¹ K⁻¹, consistent with literature values for silica particles in water.

When the concentration is increased, the system exhibits a dramatic, nonlinear amplification of D_eff. At the highest concentration studied, D_eff/D_0 reaches ≈ 12, corresponding to propulsion speeds up to ~800 µm s⁻¹. The authors identify two synergistic mechanisms responsible for this boost. First, the collective absorption of laser power raises the bulk temperature of the suspension (Δθ = γ P_abs). By treating the sample as an effective absorbing medium and neglecting convection (Rayleigh number Ra ≲ 1), they find Δθ scales linearly with total absorbed power, with an experimentally determined proportionality factor γ ≈ (1–2) × 10⁻⁴ K W⁻¹. The bulk temperature increase reduces the solvent viscosity η(T), thereby enhancing the Brownian diffusion term in Eq. (1) and also modestly increasing µ.

Second, the reduced inter‑particle distance causes the individual temperature fields of each nanomotor to overlap, effectively amplifying the local temperature gradient experienced by each particle. This “self‑amplification” of ⟨∇T⟩ scales with concentration and laser intensity, leading to a nonlinear dependence of the propulsion term µ · ⟨∇T⟩ on both variables. The authors construct a coupled thermal‑hydrodynamic model that incorporates the concentration‑dependent temperature field and the temperature‑dependent mobility. Numerical solutions of this model reproduce the experimentally observed D_eff versus intensity curves for all concentrations, confirming that the observed acceleration is not due to optical forces or convective flows (which are estimated to be < 100 µm s⁻¹).

Control experiments with isotropic gold nanospheres of identical absorption cross‑section show a much weaker concentration dependence, underscoring the essential role of particle asymmetry in generating strong thermophoretic gradients. Moreover, the authors verify that radiation pressure–induced convection is negligible by measuring the Rayleigh number and performing independent fluid dynamics simulations.

In summary, the paper demonstrates that (i) thermophoretic propulsion of individual nanomotors can be quantitatively measured using CSCS, (ii) the propulsion speed can be dramatically enhanced by increasing particle concentration, due to a feedback loop where the collective heating modifies both bulk viscosity and local temperature gradients, and (iii) this feedback provides a self‑regulating mechanism for active fluids without external feedback control. The findings open new avenues for designing three‑dimensional active matter systems, temperature‑responsive nanorobots, and self‑organizing microfluidic devices that exploit intrinsic thermal coupling rather than external fields.