Effective interactions in active Brownian particles

TL;DR

The study addresses how to extract thermodynamic-like information from non-equilibrium active Brownian particle suspensions by inferring an effective pair potential $u_{ m eff}(r)$ that reproduces the ABP structure via equilibrium-like simulations. It develops a test-particle insertion–based inverse method that matches $g(r)$ from DH and TPI schemes, yielding a density- and activity-dependent $u_{ m eff}(r)$ that combines passive interactions with emergent activity-induced features. The work demonstrates emergent attractions, density-dependent non-additivity, and provides practical routes to compute an effective chemical potential $ ext{mu}_{ m eff}$ and effective pressure $P_{ m eff}$, linking structure to quasi-thermodynamic quantities in active matter. These results offer a framework for interpreting ABP suspensions, informing phase behavior and guiding design of active materials with tunable structure through activity and interactions.

Abstract

We report an approach to obtain effective pair potentials which describe the structure of two-dimensional systems of active Brownian particles. The pair potential is found by an inverse method, which matches the radial distribution function found from two different schemes. The inverse method, previously demonstrated via simulated equilibrium configurations of passive particles, has now been applied to a suspension of active particles. Interestingly, although active particles are inherently not in equilibrium, we still obtain effective interaction potentials which accurately describe the structure of the active system. Treating these effective potentials as if they were those of equilibrium systems, furthermore allows us to measure effective chemical potentials and pressures. Both the passive interactions and active motion of the active Brownian particles contribute to their effective interaction potentials.

Figures (7)

• Figure 1: Zoomed snapshots of the MD (top row) and MC (bottom row) simulations for the studied potentials for selected densities and Péclet numbers. From left to right: From the shoulder potential study at varying $\rho$, we present $\rho=0.4$ (at $\rm{Pe}=120$, see Fig. \ref{['fig:4']}). Then, for the study varying potential type, we present the shoulder, WCA and LJ potentials (all at $\rho=0.3$ and $\rm{Pe}=300$, see Fig. \ref{['fig:1']}). (Snapshots for the complete set of studied parameters are shown in Appendix G.)
• Figure 2: Varying potential type, with fixed $\rm{Pe}=300$ & $\rho=0.3$, for (\ref{['fig:1a']}) LJ, (\ref{['fig:1b']}) WCA and (\ref{['fig:1c']}) shoulder potentials. Each plot shows the passive potential $u(r)$ and $\beta u_{\rm{eff}}(r)$ from the inverse method.
• Figure 3: Varying Péclet number for the WCA potential, with fixed $\rho=0.3$: (\ref{['fig:2a']}) Plot of $\beta u_{\rm{eff}}(r)$ at different $\rm{Pe}$. (\ref{['fig:2b']}) Plot of the magnitude of $\beta u_{\rm{eff}}(r)$’s well depth as a function of $\rm{Pe}$.
• Figure 4: Demonstration of the closeness of $\beta \textcolor{black}{w_{\rm{eff}}(r)}$ to $\beta u_{\rm{eff}}(r)$, using the example of ABPs with a LJ potential, with $\rm{Pe}=300$ & $\rho=0.3$: (\ref{['fig:3a']}) Comparison of $\beta \textcolor{black}{w_{\rm{eff}}(r)}$ with $\beta u_{\rm{eff}}(r)$. (\ref{['fig:3b']}) Comparison of $g_{\rm{DH}}(r)$ from the original data with $g_{\rm{DH,MC}}(r)$ from a MC simulation using $\beta \textcolor{black}{w_{\rm{eff}}(r)}$. These $g(r)$ should not agree perfectly, as they correspond to different $u(r)$, though they are similar due to the closeness of $\beta \textcolor{black}{w_{\rm{eff}}(r)}$ to $\beta u_{\rm{eff}}(r)$.
• Figure 5: Shoulder potential at varying density, with fixed $\rm{Pe}=120$. (\ref{['fig:4a']}) Plot comparing $g_{\rm{DH}}(r)$ and $g_{\rm{TPI}}(r)$, based on the converged $\beta u_{\rm{eff}}(r)$ from the inverse method. (\ref{['fig:4b']}) Plot comparing $\beta u_{\rm{eff}}(r)$ with $\beta \textcolor{black}{w_{\rm{eff}}(r)}$. The colour code in the key of (\ref{['fig:4a']}) also applies to (\ref{['fig:4b']}).