Propulsion dispersion mediated ordering transition in active particles

Abstract

We show that dispersion in propulsion strength qualitatively alters collective behavior of active multi-particle systems interacting via short-range attractive potential, giving rise to novel ordered phases that combine spatial and orientational ordering. Considering a binary mixture of active Brownian particles with two distinct self-propulsion strengths, we find that, the interplay between interaction range, self-propulsion strengths and the relative numbers of the particles with different propulsion strengths can lead to three different phases, namely, a disordered one, and two ordered ones with partial and complete spatial and orientational ordering. The partially ordered phase is characterized by formation of a ring-like assembly of the slower particles while the faster particles diffuse randomly. Two concentric rings, comprising faster and slower particles, form in the fully ordered phase. Using the example of a truncated harmonic potential, we analytically characterize the phase boundaries and identify the associated order parameters. Our results demonstrate that propulsion dispersion provides a robust and novel route to collective ordering in attractive active matter.

Figures (4)

• Figure 1: Ordering transitions: (a) Phase diagram in the $(\phi_{1},\phi_{2},\mu)$ space. (b) Phase diagram on the $(\phi_1, \phi_2)$ plane for a fixed $\mu=1$. (c)-(e) show typical configurations in the O-I, O-II and disordered phases, respectively. (f) Schematic diagram showing the orientational ordering.
• Figure 2: Phase diagram showing the O-I and O-II phases for the truncated harmonic potential: Colour-gradient maps showing the variations of the order parameters $\kappa_{1}$ (a) and $\kappa_{2}$ (b) on the $a_{1}-a_{2}$ plane, obtained from numerical simulations. The dashed and solid lines indicate the phase boundaries [see Eqs. (\ref{['eq:ph_bndry_1']})-\ref{['eq:ph_bndry_3']}] for discontinuous and continuous transitions, respectively. The insets show plots of $\kappa_{1,2}$ as functions of $a_1$ for different values of $a_2$. Symbols indicate data obtained from numerical simulations whereas the solid lines correspond to analytical predictions Eqs. \ref{['eq:OP_KI']}–\ref{['eq:OP_KII_2']} The other parameters used are $N_1=25,N_{2}=37$, i.e., $\mu=0.67$ and $r_0=1.0, k = 0.04, \gamma=1.0, m=0.01, D=0.01$.
• Figure 3: Phase diagram showing the O-I and O-II phases for the truncated Lennard-Jones potential: Colour-gradient maps showing the variations of the order parameters $\kappa_{1}$ (a) and $\kappa_{2}$ (b) on the $a_{1}-a_{2}$ plane, obtained from numerical simulations. The dashed and solid lines indicate the phase boundaries. The insets show plots of $\kappa_{1,2}$ as functions of $a_1$ for different values of $a_2$ obtained from numerical simulations. The other parameters used are $N_1=25,N_{2}=25$, i.e., $\mu=1.0$ and $r_0=0.2, k = 0.04, \sigma = 5.0, \gamma=1.0, m=0.01, D_R=0.01$.
• Figure 4: Schematic diagram showing (a) single ring configuration and (b) two concentric ring configuration.