Diffusion is the principal transport mechanism that controls the motion of solute molecules and other species in solution; however, the random walk process that underlies diffusion is slow and often nonspecific. Although diffusion is an essential mechanism for transport in the biological realm, biological systems have devised more efficient transport mechanisms using molecular motors. Most biological motors utilize some form of chemical energy derived from their surroundings to induce conformational changes in order to carry out specific functions. These small molecular motors operate in the presence of strong thermal fluctuations and in the regime of low Reynolds numbers, where viscous forces dominate inertial forces. Thus, their dynamical behavior is fundamentally different from that of macroscopic motors, and different mechanisms are responsible for the production of useful mechanical motion.There is no reason why our interest should be confined to the small motors that occur naturally in biological systems. Recently, micron and nanoscale motors that use chemical energy to produce directed motion by a number of different mechanisms have been made in the laboratory. These small synthetic motors also experience strong thermal fluctuations and operate in regimes where viscous forces dominate. Potentially, these motors could be directed to perform different transport tasks, analogous to those of biological motors, for both in vivo and in vitro applications. Although some synthetic motors execute conformational changes to effect motion, the ma- * To whom correspondence should be addressed jority do not, and, instead, they use other mechanisms to convert chemical energy into directed motion.In this Account, we describe how synthetic motors that operate by self-diffusiophoresis make use of a self-generated concentration gradient to drive motor motion. A description of propulsion by selfdiffusiophoresis is presented for Janus particle motors comprising catalytic and noncatalytic faces. The properties of the dynamics of chemically powered motors are illustrated by presenting the results of particle-based simulations of sphere-dimer motors constructed from linked catalytic and noncatalytic spheres. The geometries of both Janus and sphere-dimer motors with asymmetric catalytic activity support the formation of concentration gradients around the motors. Because directed motion can occur only when the system is not in equilibrium, the nature of the environment and the role it plays in motor dynamics are described. Rotational Brownian motion also acts to limit directed motion, and it has especially strong effects for very 1 arXiv:1407.6338v2 [cond-mat.soft] 3 Nov 2014 small motors. We address the following question: how small can motors be and still exhibit effects due to propulsion, even if only to enhance diffusion? Synthetic motors have the potential to transform the manner in which chemical dynamical processes are carried out for a wide range of applications.

Active matter, some of whose constituent elements are active agents that can move autonomously, behaves very differently from matter without such agents. The active agents can self-assemble into structures with a variety of forms and dynamical properties. Swarming, where groups of living agents move cooperatively, is commonly observed in the biological realm, but it is also seen in the physical realm in systems containing small synthetic motors. The existence of diverse forms of self-assembled structures has stimulated the search for new applications that involve active matter. We consider active systems where the agents are synthetic chemically powered motors with various shapes and sizes that operate by phoretic mechanisms, especially self-diffusiophoresis. These motors are able to move autonomously in solution by consuming fuel from their environment. Chemical reactions take place on catalytic portions of the motor surface and give rise to concentration gradients that lead to directed motion. They can operate in this way only if the chemical composition of the system is maintained in a nonequilibrium state since no net fluxes are possible in a system at equilibrium. In contrast to many other active systems, chemistry plays an essential part in determining the properties of the collective dynamics and self-assembly of these chemically powered motor systems. The inhomogeneous concentration fields that result from asymmetric motor reactions are felt by other motors in the system and strongly influence how they move. This chemical coupling effect often dominates other interactions due to fluid flow fields and direct interactions among motors and determines the form that the collective dynamics takes. Since we consider small motors with micrometer and nanometer sizes, thermal fluctuations are strong and cannot be neglected. The media in which the motors operate may not be simple and may contain crowding agents or molecular filaments that influence how the motors assemble and move. The collective motion is also influenced by the chemical gradients that arise from reactions in the surrounding medium. By adopting a microscopic perspective, where the motors, fluid environment, and crowding elements are treated at the coarse-grained molecular level, all of the many-body interactions that give rise to the collective behavior naturally emerge from the molecular dynamics. Through simulations and theory, this Account describes how active matter made from chemically powered nanomotors moving in simple and more complicated media can form different dynamical structures that are strongly influenced by interactions arising from cooperative chemical reactions on the motor surfaces.

Collections of chemically propelled nanomotors free to move in solution can form dynamic clusters with diverse properties as a result of interactions through hydrodynamic flow and concentration fields, as well as direct intermolecular interactions between motors. Here, we study the collective rotational behavior of pinned sphere-dimer motors where direct motor-motor interactions play no role. Since the centers of mass of the motors are pinned, they cannot execute directed translational motion, but they can pump fluid and rotate; thus, the rotors remain coupled through hydrodynamic and chemical fields. Using a microscopic simulation method that accounts for coupling through both these fields, we show that different rotor configurations with a high degree of correlation exist and their forms depend on the nature of the fluid-rotor interactions. The correlations are greatly reduced or completely destroyed when the chemical interactions are removed, indicating that hydrodynamic coupling, while present, plays a lesser role in determining the collective rotor dynamics. These conclusions are supported by Langevin dynamics simulations that neglect hydrodynamics and include an approximate form of coupling through chemical fields.

Synthetic nanomotors powered by chemical reactions have potential uses as cargo transport vehicles in both in vivo and in vitro applications. In many situations, motors will have to operate in out-of-equilibrium complex chemically reacting media, which supply fuel to the motors and remove the products they produce. Using molecular simulation and mean-field theory, this paper describes some of the new features that arise when a chemically powered nanomotor, operating through a diffusiophoretic mechanism, moves in an environment that supports an oscillatory chemical reaction network. It is shown how oscillations in the concentrations in chemical species in the environment give rise to oscillatory motor dynamics. More importantly, since the catalytic reactions on the motor that are responsible for its propulsion couple to the bulk phase reaction network, the motor can change its local environment. This process can give rise to distinctive spatiotemporal structures in reaction-diffusion media that occur as a result of active motor motion. Such locally induced nonequilibrium structure will play an important role in applications that involve motor dynamics in complex chemical media.

Active colloidal particles that are propelled by a self-diffusiophoretic mechanism are often described by Langevin equations that are either postulated on physical grounds or derived using the methods of fluctuating hydrodynamics. While these descriptions are appropriate for colloids of micrometric and larger size, they will break down for very small active particles. A fully microscopic derivation of Langevin equations for self-diffusiophoretic particles powered by chemical reactions catalyzed asymmetrically by the colloid is given in this paper. The derivation provides microscopic expressions for the translational and rotational friction tensors, as well as reaction rate coefficients appearing in the Langevin equations. The diffusiophoretic force and torque are expressed in terms of nonequilibrium averages of fluid fields that satisfy generalized transport equations. The results provide a description of active motion on small scales where descriptions in terms of coarse grained continuum fluid equations combined with boundary conditions that account for the presence of the colloid may not be appropriate.