Mechanical theory of nonequilibrium coexistence and motility-induced phase separation.

Nonequilibrium phase transitions are routinely observed in both natural and synthetic systems. The ubiquity of these transitions highlights the conspicuous absence of a general theory of phase coexistence that is broadly applicable to both nonequilibrium and equilibrium systems. Here, we present a general mechanical theory for phase separation rooted in ideas explored nearly a half-century ago in the study of inhomogeneous fluids. The core idea is that the mechanical forces within the interface separating two coexisting phases uniquely determine coexistence criteria, regardless of whether a system is in equilibrium or not. We demonstrate the power and utility of this theory by applying it to active Brownian particles, predicting a quantitative phase diagram for motility-induced phase separation in both two and three dimensions. This formulation additionally allows for the prediction of novel interfacial phenomena, such as an increasing interface width while moving deeper into the two-phase region, a uniquely nonequilibrium effect confirmed by computer simulations. The self-consistent determination of bulk phase behavior and interfacial phenomena offered by this mechanical perspective provide a concrete path forward toward a general theory for nonequilibrium phase transitions.

Kinetic temperature and pressure of an active Tonks gas.

Using computer simulation and analytical theory, we study an active analog of the well-known Tonks gas, where active Brownian particles are confined to a periodic one-dimensional (1D) channel. By introducing the notion of a kinetic temperature, we derive an accurate analytical expression for the pressure and clarify the paradoxical behavior where active Brownian particles confined to 1D exhibit anomalous clustering but no motility-induced phase transition. More generally, this work provides a deeper understanding of pressure in active systems as we uncover a unique link between the kinetic temperature and swim pressure valid for active Brownian particles in higher dimensions.

Dynamic overlap concentration scale of active colloids.

By introducing the notion of a dynamic overlap concentration scale, we identify additional universal features of the mechanical properties of active colloids. We codify these features by recognizing that the characteristic length scale of an active particle's trajectory, the run length, introduces a concentration scale ϕ^{*}. Large-scale simulations of repulsive active Brownian particles (ABPs) confirm that this run-length dependent concentration, the trajectory-space analog of the overlap concentration in polymer solutions, delineates distinct concentration regimes in which interparticle collisions alter particle trajectories. Using ϕ^{*} and concentration scales associated with colloidal jamming, the mechanical equation of state for ABPs collapses onto a set of principal curves that contain several overlooked features. The inclusion of these features qualitatively alters previous predictions of the behavior for active colloids, as we demonstrate by computing the spinodal for a suspension of purely repulsive ABPs. Our findings suggest that dynamic overlap concentration scales should help unravel the behavior of active and driven systems.

The "isothermal" compressibility of active matter.

We demonstrate that the mechanically defined "isothermal" compressibility behaves as a thermodynamic-like response function for suspensions of active Brownian particles. The compressibility computed from the active pressure-a combination of the collision and unique swim pressures-is capable of predicting the critical point for motility induced phase separation, as expected from the mechanical stability criterion. We relate this mechanical definition to the static structure factor via an active form of the thermodynamic compressibility equation and find the two to be equivalent, as would be the case for equilibrium systems. This equivalence indicates that compressibility behaves like a thermodynamic response function, even when activity is large. Finally, we discuss the importance of the phase interface when defining an active chemical potential. Previous definitions of the active chemical potential are shown to be accurate above the critical point but breakdown in the coexistence region. Inclusion of the swim pressure in the mechanical compressibility definition suggests that the interface is essential for determining phase behavior.

Activity-Enhanced Self-Assembly of a Colloidal Kagome Lattice.

Here, we describe a method for the enhanced self-assembly of triblock Janus colloids targeted to form a kagome lattice. Using computer simulations, we demonstrate that the formation of this elusive structure can be significantly improved by self-propelling or activating the colloids along the axis connecting their hydrophobic hemispheres. The process by which metastable aggregates are destabilized and transformed into the favored kagome lattice is quite general, and we argue this active approach provides a systematic pathway to improving the self-assembly of a large number of colloidal structures.

An Active Approach to Colloidal Self-Assembly.

In this review, we discuss recent advances in the self-assembly of self-propelled colloidal particles and highlight some of the most exciting results in this field, with a specific focus on dry active matter. We explore this phenomenology through the lens of the complexity of the colloidal building blocks. We begin by considering the behavior of isotropic spherical particles. We then discuss the case of amphiphilic and dipolar Janus particles. Finally, we show how the geometry of the colloids and/or the directionality of their interactions can be used to control the physical properties of the assembled active aggregates, and we suggest possible strategies for how to exploit activity as a tunable driving force for self-assembly. The unique properties of active colloids lend promise to the design of the next generation of functional, environment-sensing microstructures able to perform specific tasks in an autonomous and targeted manner.

Lipid membrane-assisted condensation and assembly of amphiphilic Janus particles.

Amphiphilic Janus particles self-assemble into complex metastructures, but little is known about how their assembly might be modified by weak interactions with a nearby biological membrane surface. Here, we report an integrated experimental and molecular dynamics simulation study to investigate the self-assembly of amphiphilic Janus particles on a lipid membrane. We created an experimental system in which Janus particles are allowed to self-assemble in the same medium where zwitterionic lipids form giant unilamellar vesicles (GUVs). Janus particles spontaneously concentrated on the inner leaflet of the GUVs. They exhibited biased orientation and heterogeneous rotational dynamics as revealed by single particle rotational tracking. The combined experimental and simulation results show that Janus particles concentrate on the lipid membranes due to weak particle-lipid attraction, whereas the biased orientation of particles is driven predominantly by inter-particle interactions. This study demonstrates the potential of using lipid membranes to influence the self-assembly of Janus particles.