Antiswarming: Structure and dynamics of repulsive chemically active particles

Chemically active Brownian particles with surface catalytic reactions may repel each other due to diffusiophoretic interactions in the reaction and product concentration fields. The system behavior can be described by a “chemical” coupling parameter ${\mathrm{\Gamma }}_c$ that compares the strength of diffusiophoretic repulsion to Brownian motion, and by a mapping to the classical electrostatic one component plasma (OCP) system. When confined to a constant-volume domain, body-centered cubic (bcc) crystals spontaneously form from random initial configurations when the repulsion is strong enough to overcome Brownian motion. Face-centered cubic (fcc) crystals may also be stable. The “melting point” of the “liquid-to-crystal transition” occurs at ${\mathrm{\Gamma }}_c\approx 140$ for both bcc and fcc lattices.

Figure 1

A schematic for the repulsive diffusiophoretic interaction. Reactant solutes with diffusivity $D_R$ and flux ${\mathit{j}}_R$ are consumed on the surface of catalytic particle 1 with the first-order boundary condition $\mathit{n}·{\mathit{j}}_R=-\kappa c_R$. Product solutes (small red dots) leave the particle surface with flux ${\mathit{j}}_P$ and diffusivity $D_P$. In the vicinity of the particle $1c_P$ is increased while $c_R$ is decreased. When the product is more effective at pushing particle 2 (which occurs when $1-\theta D_R/D_P<0$), particle 2 feels a repulsive diffusiophoretic force $\mathit{F}\sim \nabla c_P$. From the reaction boundary conditions a simple scaling between $c_R$ and $c_P$ holds [24] and only the reaction concentration field needs to be computed, which we denote simply as $c$. The particles then move according to (1).

Figure 2

The distribution of particle reaction $q$ and local volume fraction ${\varphi }_p$, and their correlation. (a) The snapshot of the equilibrium structure of the system in a periodic box of $42a\times 42a\times 42a$, with $\varphi =0.0488$, $\mathrm{Da}=2.0$, $N=864$, $S_D=-15.0,{\mathrm{\Gamma }}_c\approx 20$. Each particle is colored by $q/q_0$. (b) The same system, but equilibrated with stronger repulsion $S_D=-60.0,{\mathrm{\Gamma }}_c\approx 80$.

Figure 3

The measurement of structural change of bcc and fcc crystals, both for $\mathrm{Da}=2.0$. $\varphi =0.0388$ for the bcc system and $\varphi =0.0488$ for the fcc system.

Figure 4

The measurement $Q_6$ of the melting process. (a) The initial configuration is bcc and (b) the initial configuration is fcc. For each combination of $\varphi$ (shape) and $\mathrm{Da}$ (color), simulations of different $S_D$ are conducted so that a range of $100<{\mathrm{\Gamma }}_c<250$ is covered. The melting point for both bcc and fcc is ${\mathrm{\Gamma }}_c\approx 140$.