Transverse Self-Propulsion Enhances the Aggregation of Active Dumbbells

Abstract

We investigate a two-dimensional system of active Brownian dumbbells using molecular dynamics simulations. In this model, each dumbbell is driven by an active force oriented perpendicular to the axis connecting its two constituent beads. We characterize the resulting phase behavior and find that, across all values of activity, the system undergoes phase separation between dilute and dense phases. The dense phase exhibits hexatic order, and for large enough activity, we observe a marked increase in local polarization, with dumbbells predominantly oriented towards the interior of the clusters. Compared to the case of axially self-propelled dumbbells, we find that the binodal region is enlarged towards lower densities at all activities. This shift arises because dumbbells with transverse propulsion can more easily form stable cluster cores, serving as nucleation seeds, and show a highly suppressed escaping rate from the cluster boundary. Finally, we observe that clusters exhibit spontaneous rotation, with the modulus of the angular velocity scaling as ω∼rg-2, where rg is the cluster's radius of gyration. This contrasts with axially propelled dumbbells, where the scaling follows ω∼rg-1. We develop a simplified analytical model to rationalize this scaling behavior.

Keywords: active matter; motility-induced phase separation; phase diagram; self-propelled dumbbells.

Figure 1

Schematic representation of dumbbells with (a) transverse self-propulsion and (b) axial self-propulsion. The active force vector acting on each bead is highlighted with an arrow. These representations depict nucleation events for MIPS, with multiple dumbbells colliding with their self-propulsion directed towards a common center, indicated by a red star. In case (a), a nucleation event can be composed of only two dumbbells, while in case (b), more dumbbells are needed.

Figure 2

Snapshots of transverse self-propelled dumbbells, colored according to the local surface fraction ${\varphi }^{loc}$ of transverse self-propelled dumbbells, defined in the text. Snapshots are shown for Pe $=1,10,100$ (first, middle, and last rows, respectively) and global $\varphi$ values displayed in each snapshot. The range of $\varphi$ spans the region where coexistence occurs between a dense and dilute phase. The range of values of ${\varphi }^{loc}$ is the same for all the snapshots in each row, and is displayed in the color bar on the right side.

Figure 3

Probability distribution of the local surface fraction ${\varphi }^{\mathrm{loc}}$, averaged over independent configurations, across the coexistence region for (a) Pe $=1$, (b) 10, and (c) 100. The values of global surface fraction are displayed in the key.

Figure 4

The $\varphi -$Pe phase diagram of the dumbbell system with transverse propulsion. The black empty and filled square symbols represent the values of the two coexisting densities, ${\varphi }_{low}$ and ${\varphi }_{high}$, respectively. The region in between these points is the binodal region, enclosing the portion of the phase diagram where we observe liquid-hexatic phase separation. The black dashed line indicates the two coexisting densities for axially self-propelled dumbbells, as established in [45], for comparison.

Figure 5

Snapshots for Pe $=1,10,100$ (first, middle, and last rows, respectively) with global $\varphi$ values displayed in each snapshot (same values as Figure 2). Particles are colored according to real component of the local hexatic order parameter ${\psi }_{6,j}$ (Equation (6)). The color code is reported on the right side.

Figure 6

Probability distribution of the local hexatic parameter ${\psi }_6^{\mathrm{loc}}$, computed as the local average of the hexatic parameter (Equation 6) over a square grid of size $2{\sigma }_d$, with coarse-graining length $5{\sigma }_d$, averaged over independent configurations across the coexistence region for Pe $=1$ in (a), Pe $=10$ in (b) and Pe $=100$ in (c). Density values are displayed in the key.

Figure 7

(a) Representative snapshots of the system for Pe $=3,10,30,100$, and global density corresponding to a dense phase occupying 25% of the total surface. Density values are reported over each snapshot. Snapshots are colored according to the local surface fraction (see Figure 2). (b) Same snapshots as in (a), colored according to the modulus of the local average polarization field P, obtained by averaging the local polarization over the coarse-graining length of $5{\sigma }_d$. (c) Polarization field for the same conformations as (a–b), shown enlarged in the high-density region of each snapshot. This enlarged portion is indicated with a black square in the corresponding upper snapshots. For panels (a,b), the coloring code is reported at the right of each figure.

Figure 8

Probability distribution of (a) the modulus of the local polarization, P, and (b) its x-component, $P_x$, for points of the $\varphi$-Pe space indicated in the key. These points are characterized by a dense phase occupying $25\%$ of the total surface (snapshots in Figure 7).

Figure 9

(a) Modulus of the rotating velocity of the clusters as a function of their radius of gyration, see the definition of these quantities in the text, for Pe $=10,30,100$. (b) Modulus of the rotating velocity of the clusters, normalized by the average polarization angle within the cluster, as defined in the text. (c) Graphical representation of a cluster (gray circle), highlighting the vector $\mathbf{r}$ connecting a mass element $dm$ to the cluster’s center of mass, the active force $f_a$ acting on $dm$, and the angle $\theta$ between ${\mathbf{f}}_a$ and $\mathbf{r}$. With the assigned direction of ${\mathbf{f}}_a$, the cluster rotates counter-clockwise (see the direction of the vector $\mathit{\omega }$ in the sketch).