Self-Assembly of Colloidal Molecules due to Self-Generated Flow

The emergence of structure through aggregation is a fascinating topic and of both fundamental and practical interest. Here we demonstrate that self-generated solvent flow can be used to generate long-range attractions on the colloidal scale, with subpiconewton forces extending into the millimeter range. We observe a rich dynamic behavior with the formation and fusion of small clusters resembling molecules. The dynamics of this assembly is governed by an effective conservative energy that for large separations $r$ decays as $1/r$. Breaking the flow symmetry, these clusters can be made active.

Figure 1

Long-range interactions through flow. (a) The colloidal particles release hydrogen ions (${\mathrm{H}}^{+}$), which are exchanged with residual cationic impurities (here ${\mathrm{Na}}^{+}$). Different ion mobilities generate local electric fields $E$ that slow the hydrogen ions and accelerate the impurities to maintain overall electroneutrality. (b) In the double layer of the substrate, these fields generate electro-osmotic flow with solvent velocity $v_{\mathrm{eo}}$ towards the particle. In the double layer of the particles, the electric fields lead to electrophoretic flow. (c) Top view of the flow geometry: For two particles a distance $r$ apart, the higher ${\mathrm{H}}^{+}$ concentration in the space between particles reduces the gradient and leads to an asymmetric electro-osmotic flow and thus attraction. (d) Side view sketching the flow away from the substrate.

Figure 2

Effective pair potential. (a) Drift velocity $v(r)$ of two particles with separation $r$ (symbols). The line is the free fit to $v(r)=2u^{\prime }(r)$ with $u^{\prime }(r)$ denoting the derivative of Eq. (2). (b) The resulting effective pair potential $u(r)$. Insets: Histograms of the fluctuating bond length of dimers (left) and trimers (right), where the dashed line indicates the minimum $r_0\simeq 35\mu \mathrm{m}$ of the fitted effective potential.

Figure 3

Dynamics of assembly. (a) Experimental particle traces and the configuration reached after 5 min (disks). (b),(c) Consecutive snapshots from experiment (b) and a single simulation run (c) showing the formation of two clusters in their ground state (middle) and a large cluster with $n=7$ particles (right). The simulations have been initialized with the positions extracted from the first experimental snapshot.

Figure 4

Time evolution of cluster populations $N_n(t)/N$. Solid lines correspond to experimental data (averaged over several experiments), dashed lines to the simulation results of the theoretical model with $N=80$ particles.

Figure 5

Transition to self-propelled motion. Plotted is the center-of-mass speed of three particles, two cationic and one anionic, which accelerate once assembled into a trimer (at $t\approx 50\mathrm{s}$). For times $t=0$, 50, and 150 s, snapshots are shown with cationic particles in red and anionic particles in blue. The field of view is the same for all snapshots. The dashed line indicates the final speed of the trimer.