Regulation of propulsion in assemblies of thermophoretic nanomotors

Abstract

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.

Figures (5)

• Figure 1: Au/SiO$_2$ nano-heterodimers (NHDs) as nanomotors.A) Scheme of the synthesis process. Gold nanospheres are used as a substrate for the asymmetric growth of SiO$_2$. Following the grafting of competing ligands onto the Au surface (4-MBA and PAA, see main text), the silica precursor (TEOS) nucleates a SiO$_2$ lobe on the Au sphere. B)Left: Activation is performed at $\lambda=532$ nm, close to the plasmon resonance of gold, as observed on the extinction spectra of the NHDs, core-shell (CS), and Au nanospheres (Au). Right: Experimental strategy for self-propulsion. The NHDs are activated by photothermal heating. Following laser-light absorption of the Au part, the NHDs propel in 3D by self-thermophoresis. C) Transmission Electron Microscopy (TEM) images of (from left to right): gold nanosphere, Au/SiO$_2$ core-shell nanoparticles (absence of PAA), and Au/SiO$_2$ NHDs (presence of 4-MBA and PAA). Scale bar is 50 nm. D) Large-scale TEM image of a typical sample of NHDs, showing their monodispersity.
• Figure 2: Individual propulsion of nanomotors - dilute regime.A) Scheme of the experimental configuration. Two green collimated laser beams excite the sample (height $H=200$$\mu$m). The scattering from a red laser is used to probe the dynamics, with back-scattered photons collected onto photon detectors. The intensity time-trace (bottom - right panel) is reconstructed, and its auto-correlation informs about the dynamics. B) Representative correlation functions $g^2(\tau)-1$ for equilibrium (black dots), and excited samples (red dots) under $I=30$$\mu$W/$\mu$m$^2$, for (top) 30 nm gold nanospheres, and (bottom) NHDs at identical linear absorption of $40$ m$^{-1}$. A shift is observed for the NHDs, indicative of self-propulsion. Solid lines are fits of the data using Eq.(2). C) Evolution of the normalized diffusion coefficient with the excitation intensity for NHDs (red circles) and 30 nm gold nanospheres (black squares) for identical solvent and absorption $\alpha=100$ m$^{-1}$. The dashed line is a guide for the eye, showing that the diffusion of isotropic gold nanospheres remains roughly constant. D) Estimated propulsion velocity for the NHDs as a function of the incident intensity, using Eq.(1) and constant $D(T)=D_0$ and $\tau_R$, determined from the value at equilibrium. The dashed line is a linear fit to the data, giving a slope of $3.8 \pm 0.4$$\mu$m.s$^{-1}$/$\mu$W/$\mu$m$^2$.
• Figure 3: Dynamics of nanomotors in dense assemblies.A) Evolution of the diffusion coefficient of nanomotors at various concentrations, based on an initial concentration of NHDs $c_0 \approx 4.7\cdot 10^{14}$. particles/L$^{-1}$, corresponding to an absorption $\alpha= 770$ m$^{-1}$. The data correspond to two batches of NHDs (circles and squares). B)Top: Evolution of the diffusion coefficient measured for 30 nm Au nanospheres for different incident power and initial absorption $\alpha$, with $\alpha_0=1385$ m$^{-1}$. All data collapse on the same curve when plotted against the total absorbed power $P_{abs}$. The data are captured by a second-order polynomial fit to the data, given by $f(P_{abs})-1$. Bottom: Plot of the active temperature ratio to the room temperature $T^{a}/T=D^{NHD}_{eff}/D^{NHD}_0f(P_\text{abs})$ as a function of the absorbed power $P_{\text{abs}}$, evidencing a concentration dependency of the active dynamics of the NHDs. C) Estimation of the thermophoretic velocities $v$, using Eq.(5), from the data plotted in A. D) Active Péclet number $\text{Pe}^a=v.R_h/D^{NHD}_0f(P_\text{abs})$ computed for the different concentrations of the NHDs. At identical incident intensity, $\text{Pe}^a$ is higher for higher concentrations of NHDs. Color scales for B-bottom, C, and D are identical to A.
• Figure 4: Quantification of thermal effects from independent measurements.A) Scheme of the experiment to measure the thermophoretic mobility of SiO$_2$ microbeads. A temperature gradient is applied horizontally across the cell, with $\Delta \Theta= T_{hot}-T_{cold} = 39$K. The contribution of osmotic and convective flows is accounted for by simultaneously tracking the motion of $300$ nm gold particles with $3.3$$\mu$m microbeads. B) Snapshots of a typical experiment, showing the thermophilic behavior of SiO$_2$ colloids (in blue). C) Example of extracted velocities for the SiO$_2$ beads (blue circles) and 300 nm Au nanoparticles (red squares) across the channel width, and (Inset) example of reconstructed trajectories of microbeads. D) Computed thermophoretic mobility $\mu_T^{SiO_2}(T)$ for 5 different experiments (dots), and corresponding averaged values (white circles), with $T=T_0+\Delta \theta$ and $T_0=296$K. E) Evolution of $D(T)/D_0$ for passive SiO$_2$ beads (red circles). Blue squares are calculated values from rheometric measurements of the viscosity of the solution. The solid line is a fit of combined data, using an Arrhenius law for the viscosity. F) Computed temperature profile (red line) and corresponding measurement at the center of the capillary, using fluorescent 210 nm fluorescent nanobeads and FCS to obtain their diffusion coefficient (blue circles). G) Analytical modeling: 2D plot of the temperature profile within the capillary, for $P_\text{abs}=1.2$ mW and $\omega_g=40$$\mu$m. H) Temperature increase as a function of absorbed power, for $H=100$$\mu$m and $\omega_g=40$$\mu$m (blue circles), as extracted from the diffusion of Au nanospheres in a laser-heated solution (blue circles, binned average values of [Fig.3B]). The red dashed line shows the results obtained analytically from panel G. The solid blue line is an empirical estimation based on the parameters obtained from the Arrhenius law in [Fig.4E], and using $f(P_\text{abs}).$
• Figure 5: Regulation of self-propulsion with concentration. A) Thermophoretic mobility of the SiO$_2$ microparticles, $\mu_T^{SiO_2}(T)$ (open black squares), and effective mobility of the NHDs, $\mu^{NHD}=|v.R_h/\Delta T_s|$ (circles). Data are plotted at fixed surface temperature elevations (i.e., $\Delta T_S$) from an average of raw data. Both microparticles and NHDs show similar trend with the temperature, with differing amplitude depending on $\Delta T_S$. Inset: Extracted Soret coefficient $\mu_T(T)/D^{SiO_2}(T)$ of the microparticles, which shows a linear trend in the range of investigated temperature. Red solid line is a linear fit to the data, giving $y=\alpha\Delta \theta + \beta$, with $\alpha=-0.28 \pm 0.01$ K$^{-2}$ and $\beta=0.2 \pm 0.1$ K$^{-1}$. B) Péclet number of the NHDs, $\text{Pe}=v\cdot R_h/D^{NHD}(T)$ as a function of the dimensionless number $R_h(\mu_T^{NHD}/D^{NHD}(T))\cdot(\Delta T_S/R_h)\cdot 10^{-6}\approx \Phi (\Delta T_S/\Delta T_c)^2$, with $\Delta T_c= 2.46$ K a constant specific to the system geometry (see main text). All data show universal collapse on the same curve, for which the local slope is given by $\approx\chi\cdot \tilde{\mu}_{\nabla T}\cdot 10^{6}$, representative of the nonlinearity of the thermophoretic velocity with the local gradient. Higher volume fraction $\Phi$ of the NHDs requires lower surface temperature elevation to reach equivalent Péclet, compared to small concentrations. Inset: log-log plot of the main graph, suggesting the linear regime range (dashed black line) for small $\Phi \cdot (\Delta T_S/\Delta T_c)^2$ values with a slope giving $\chi \tilde{\mu}_{\nabla T}= [0.2 \pm 0.1]$. Black and white circles are binned average of all data (showed with red dots). Grey dashed line indicates the transition from linear to non-linear regime, identified for $\Phi (\Delta T_S/\Delta T_c)^2 \sim 10^{-5}$ and $\text{Pe}\approx 1$ (grey dotted line).