Tunable Long Range Forces Mediated by Self-Propelled Colloidal Hard Spheres

Using Brownian dynamics simulations, we systematically study the effective interaction between two parallel hard walls in a 2D suspension of self-propelled (active) colloidal hard spheres, and we find that the effective force between two hard walls can be tuned from a long range repulsion into a long range attraction by changing the density of active particles. At relatively high densities, the active hard spheres can form a dynamic crystalline bridge, which induces a strong oscillating long range dynamic wetting repulsion between the walls. With decreasing density, the dynamic bridge gradually breaks, and an intriguing long range dynamic depletion attraction arises. A similar effect occurs in a quasi-2D suspension of self-propelled colloidal hard spheres by changing the height of the confinement. Our results open up new possibilities to manipulate the motion and assembly of microscopic objects by using active matter.

Figure 1

(a) Effective forces $F\sigma /k_{B}T$ as a function of wall-to-wall distance $r$ at density ${\rho }_{\text{bulk}}{\sigma }^2=0.4$ with various activity $f$. (b) $F\sigma /k_{B}T$ and the average density $\overline{\rho }(r)$ inside the confinement $-0.5r\le x\le 0.5r$, $-0.5W\le y\le 0.5W$ as a function of $r$ with $f\sigma /k_{B}T=40$ and ${\rho }_{\text{bulk}}{\sigma }^2=0.4$. (c) $F\sigma /k_{B}T$ as a function of $r$ at ${\rho }_{\text{bulk}}{\sigma }^2=0.4$ with various Gaussian size polydispersities $s$. (d) Reduced density distribution ${\log }_{10}[\rho (x,y)/{\rho }_{\text{bulk}}]$ of active particles with $f\sigma /k_{B}T=40$ at ${\rho }_{\text{bulk}}{\sigma }^2=0.4$, with a wall-to-wall distance $r/\sigma =2.1,5,10$, and 20. (e) Typical snapshots of systems for density distributions in (d), respectively. (f) $F/({\rho }_{\text{bulk}}\sigma k_{B}T)$ for $f\sigma /k_{B}T=40$ as a function of wall-to-wall distance $r$ for various particle densities. (g) $F{\sigma }^2/(W{k}_{B}T)$ for a self-propelled ideal particle system with $f\sigma /k_{B}T=40$ and ${\rho }_{\text{bulk}}{\sigma }^2=0.2$ for various wall sizes $W$. The lines are fits with $\sim -\exp (-r/\xi )$. (h) $F{\sigma }^2/(W{k}_{B}T)$ for ideal particles with density ${\rho }_{\text{bulk}}{\sigma }^2=0.2$ for various self-propulsions and a wall size $W/\sigma =80$. (i) Reduced density distribution ${\log }_{10}[\rho (x,y)/{\rho }_{\text{bulk}}]$ for ideal particle systems with $f\sigma /k_{B}T=40$ and $r/\sigma =2.2,5,10$, and 20, where the wall size is $W/\sigma =10$, and ${\rho }_{\text{bulk}}{\sigma }^2=0.4$.

Figure 2

(a) Simple model with one ideal particle (grey square) moving in a 2D square lattice, with two parallel impenetrable walls (dark squares). (b)–(d) Reduced density distributions $\rho (x,y)/{\rho }_{\text{bulk}}$ for $k_{\text{swap}}=0.2,0.5$, and 1, respectively. (e) Effective force between two walls $F/v_0$ for various $k_{\text{swap}}$ as a function of $r$. The solid lines are the fits with $\sim -\exp (-r/\xi )$. (f) Fitted interaction range $\xi$ in (e) as a function of $1/k_{\text{swap}}$.

Figure 3

(a) Main: $F{\sigma }^2/(W{k}_{B}T)$ as a function of wall-wall separation $r/\sigma$ for $f\sigma /k_{B}T=40$ in quasi-2D confinement with a varying height $H/\sigma$, at fixed 2D number density $N{\sigma }^2/A=0.4$. Inset: a typical system snapshot with two walls as yellow bricks. (b) $F{\sigma }^3/(WH{k}_{B}T)$ as a function of $r/\sigma$ for $f\sigma /k_{B}T=40$ and varying $H/\sigma$, where the 3D number density is fixed at $N{\sigma }^3/(AH)=0.2$.