We examine a minimal model for an active colloidal fluid in the form of self-propelled Brownian spheres that interact purely through excluded volume with no aligning interaction. Using simulations and analytic modeling, we quantify the phase diagram and separation kinetics. We show that this nonequilibrium active system undergoes an analog of an equilibrium continuous phase transition, with a binodal curve beneath which the system separates into dense and dilute phases whose concentrations depend only on activity. The dense phase is a unique material that we call an active solid, which exhibits the structural signatures of a crystalline solid near the crystal-hexatic transition point, and anomalous dynamics including superdiffusive motion on intermediate timescales.Active fluids composed of self-propelled units occur in nature on many scales ranging from cytoskeletal filaments and bacterial suspensions to macroscopic entities such as insects, fish and birds [1]. These systems exhibit strange and exciting phenomena such as dynamical self regulation [2], clustering [3], anomalous density fluctuations [4], unusual rheological behavior [5][6][7], and activitydependent phase boundary changes [8]. Motivated by these findings, recent experiments have focused on realizing active fluids in nonliving systems, using chemically propelled particles undergoing self-diffusophoresis [9-11], Janus particles undergoing thermophoresis [12,13], as well as vibrated monolayers of granular particles [14][15][16].In this letter we explore a minimal active fluid model: a system of self-propelled smooth spheres interacting by excluded volume alone and confined to two dimensions. Unlike self-propelled rods [18][19][20][21][22], these particles cannot interchange angular momentum and thus lack a mutual alignment mechanism. Recent simulation and experimental studies have shown that this system exhibits giant number fluctuations [23] and athermal phase separation [23,24] that are characteristic of active fluids [4,25,26]. Here we employ extensive Brownian dynamics simulations to characterize the phase diagram of this system and we develop an analytic model that captures its essential features. We show that this nonequilibrium system undergoes a continuous phase transition, analogous to that of equilibrium systems with attractive interactions, and that the phase separation kinetics demonstrate equilibrium-like coarsening. These structural and dynamic signatures of phase separation and coexistence enable an unequivocal definition of phases in this nonequilibrium, active system. Finally, we find that the dense phase is a dynamic new form of material that we call an "active solid". This material exhibits structural properties consistent with a 2D colloidal crystal near the crystal-hexatic transition point [27,28], but is characterized by such anomalous features as superdiffusive transport at intermediate timescales and a heterogeneous and dynamic stress distribution (see Fig. (1)).Model and Simulation Method : Our system consists of

We develop a class of models with which we simulate the assembly of particles into T1 capsidlike objects using Newtonian dynamics. By simulating assembly for many different values of system parameters, we vary the forces that drive assembly. For some ranges of parameters, assembly is facile; for others, assembly is dynamically frustrated by kinetic traps corresponding to malformed or incompletely formed capsids. Our simulations sample many independent trajectories at various capsomer concentrations, allowing for statistically meaningful conclusions. Depending on subunit (i.e., capsomer) geometries, successful assembly proceeds by several mechanisms involving binding of intermediates of various sizes. We discuss the relationship between these mechanisms and experimental evaluations of capsid assembly processes.

The study of equilibrium liquid crystals has led to fundamental insights into the nature of ordered materials, as well as many practical applications such as display technologies. Active nematics are a fundamentally different class of liquid crystals, which are driven away from equilibrium by the autonomous motion of their constituent rodlike particles1–4. This internally-generated activity powers the continuous creation and annihilation of topological defects, leading to complex streaming flows whose chaotic dynamics appear to destroy long-range order5–11. Here, we study these dynamics in experimental and computational realizations of active nematics. By tracking thousands of defects over centimeter distances in microtubule-based active nematics, we identify a non-equilibrium phase characterized by system-spanning orientational order of defects. This emergent order persists over hours despite defect lifetimes of only seconds. Similar dynamical structures are observed in coarse-grained simulations, suggesting that defect-ordered phases are a generic feature of active nematics.

For experiments on chiral self-assembly, we used a two-component mixture consisting of 880 nm long rod-like fd viruses and the non-adsorbing polymer Dextran. In aqueous suspension, fd viruses alone exhibit purely repulsive interactions 13. Adding non-adsorbing polymer to a dilute isotropic suspension of fd rods induces attractive interactions via the depletion mechanism and leads to their condensation into colloidal membranes, equilibrium structures consisting of one-rod-length thick liquid-like monolayers of aligned rods (Fig. 1a) 11. Despite having different structures on molecular lengthscales, the longwavelength coarse-grained properties of colloidal membranes are identical to those of conventional lipid bilayers. However, unlike their amphiphilic counterparts, colloidal membranes do not form vesicles and are instead observed as freely suspended disks with exposed edges. Here, we investigate the behavior of these exposed edges in a manner analogous to previously studied liquid-liquid domains embedded in lipid bilayers [14][15][16] . For our experiments, it is essential that fd viruses are chiral, i.e. a pair of aligned viruses minimizes their interaction energy when they are slightly twisted in a preferred direction with respect to each other. The strength of chiral interactions can be continuously tuned to zero through either genetic or physical methods ( Supplementary Fig. 1) 13,17 .Before investigating chiral membranes, we determined the structure of a membrane's edge composed of simpler achiral rods using three complimentary imaging techniques, namely 2D and 3D polarization microscopy and electron microscopy. The local tilting of the rods within a membrane was determined using 2D LC-PolScope, which produces images in which the intensity of each pixel represents the local retardance of the membrane (Fig. 1d) 18. Such images can be quantitatively related to the tilting of the rods away from the layer normal, the z-axis 19. Rods in the bulk of a membrane are aligned along the zaxis, so that 2D LC-PolScope images appear black in that region (Fig. 1e). In contrast, the bright birefringent ring along the membrane's periphery reveals local tilting of the rods (Fig. 1e, Supplementary Fig. 2). For achiral rods, this indicates that a membrane has a hemi-toroidal curved edge (Fig. 1b, c). In comparison to an untilted edge, a curved edge structure lowers the area of the rod/polymer interface, thus reducing interfacial tension, at the cost of increasing the elastic energy due to twist distortion. This hypothesis is confirmed by visualizing the 3D membrane structure using electron tomography, whichshows that the viruses' long axis transitions from being parallel to the z-axis in the membrane bulk to perpendicular to the z-axis and tangent to the edge along the membrane periphery ( When viewed with optical microscopy, a membrane's edge exhibits significant thermal fluctuations, the analysis of which yields the line tension γ eff , the energetic cost required to move rods from the membrane interior to the periphe...

Water near hydrophobic surfaces is like that at a liquid–vapor interface, where fluctuations in water density are substantially enhanced compared to those in bulk water. Here we use molecular simulations with specialized sampling techniques to show that water density fluctuations are similarly enhanced, even near hydrophobic surfaces of complex biomolecules, situating them at the edge of a dewetting transition. Consequently, water near these surfaces is sensitive to subtle changes in surface conformation, topology, and chemistry, any of which can tip the balance towards or away from the wet state, and thus significantly alter biomolecular interactions and function. Our work also resolves the long-standing puzzle of why some biological surfaces dewet and other seemingly similar surfaces do not.

Viruses are nanoscale entities containing a nucleic acid genome encased in a protein shell called a capsid, and in some cases surrounded by a lipid bilayer membrane. This review summarizes the physics that govern the processes by which capsids assembles within their host cells and in vitro. We describe the thermodynamics and kinetics for assembly of protein subunits into icosahedral capsid shells, and how these are modified in cases where the capsid assembles around a nucleic acid or on a lipid bilayer. We present experimental and theoretical techniques that have been used to characterize capsid assembly, and we highlight aspects of virus assembly which are likely to receive significant attention in the near future.

We develop a statistical theory for the dynamics of non-aligning, non-interacting self-propelled particles confined in a convex box in two dimensions. We find that when the size of the box is small compared to the persistence length of a particle's trajectory (strong confinement), the steady-state density is zero in the bulk and proportional to the local curvature on the boundary. Conversely, the theory may be used to construct the box shape that yields any desired density distribution on the boundary. When the curvature variations are small, we also predict the distribution of orientations at the boundary and the exponential decay of pressure as a function of box size recently observed in 3D simulations in a spherical box.Active fluids consisting of self-propelled units are found in biology on scales ranging from the dynamically reconfigurable cell cytoskeleton [1] to swarming bacterial colonies [2,3], healing tissues [4,5], and flocking animals [6]. Experiments have begun to achieve the extraordinary capabilities and emergent properties of these biological systems in nonliving active fluids of self-propelled particles, consisting of chemically [7][8][9][10][11][12] or electrically [13] propelled colloids, or monolayers of vibrated granular particles [14][15][16].In contrast to thermal motion, active motion is correlated over experimentally accessible time and length scales. When the persistence length of active motion becomes comparable to the mean free path, uniquely active effects arise that transcend the thermodynamically allowed behaviors of equilibrium systems, including giant number fluctuations and spontaneous flow [3,14,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Importantly, a sufficient active persistence length is the only requirement for macroscopic manifestations of activity, as revealed by athermal phase separation of nonaligning, repulsive self-propelled particles [31][32][33][34][35][36][37][38][39][40][41].When boundaries and obstacles are patterned on the scale of the active correlation length, they dramatically alter the dynamics of the system, and striking macroscopic properties emerge [42][43][44][45][46][47][48][49]; for example, ratchets and funnels drive spontaneous flow in active fluids [42][43][44][45][46]. This effect has been used to direct bacterial motion [50] and harness bacterial power to propel microscopic gears [51][52][53]. However, optimizing such devices for technological applications requires understanding the interaction of an active fluid with boundaries of arbitrary shape. More generally, any real-world device necessarily includes boundaries, and thus the effects of boundary size and shape are essential design parameters. Although recent studies have explored confinement in simple geometries [43,47,[54][55][56], there is no general theory for the effect of boundary shape.In this Letter, we study the dynamics of non-aligning and non-interacting self-propelled particles confined to two-dimensional convex containers, such as ellipses and polygons. We find...

Motivated by recent experiments, we study a system of self-propelled colloids that experience short-range attractive interactions and are confined to a surface. Using simulations we find that the phase behavior for such a system is reentrant as a function of activity: phase-separated states exist in both the low- and high-activity regimes, with a homogeneous active fluid in between. To understand the physical origins of reentrance, we develop a kinetic model for the system's steady-state dynamics whose solution captures the main features of the phase behavior. We also describe the varied kinetics of phase separation, which range from the familiar nucleation and growth of clusters to the complex coarsening of active particle gels.