Active rotational dynamics of a self-diffusiophoretic colloidal motor.

The dynamics of a spherical chemically-powered synthetic colloidal motor that operates by a self-diffusiophoretic mechanism and has a catalytic domain of arbitrary shape is studied using both continuum theory and particle-based simulations. The motor executes active rotational motion when self-generated concentration gradients and interactions between the chemical species and colloidal motor surface break spherical symmetry. Local variations of chemical reaction rates on the motor catalytic surface with catalytic domain sizes and shapes provide such broken symmetry conditions. A continuum theoretical description of the active rotational motion is given, along with the results of particle-based simulations of the active dynamics. From these results a detailed description of the factors responsible for the active rotational dynamics can be given. Since active rotational motion often plays a significant part in the nature of the collective dynamics of many-motor systems and can be used to control motor motion in targeted cargo transport, our results should find applications beyond those considered here.

Chemical micromotors self-assemble and self-propel by spontaneous symmetry breaking.

Self-propelling chemical motors have thus far required the fabrication of Janus particles with an asymmetric catalyst distribution. Here, we demonstrate that simple, isotropic colloids can spontaneously assemble to yield dimer motors that self-propel. In a mixture of isotropic titanium dioxide colloids with photo-chemical catalytic activity and passive silica colloids, light illumination causes diffusiophoretic attractions between the active and passive particles and leads to the formation of dimers. The dimers constitute a symmetry-broken motor, whose dynamics can be fully controlled by the illumination conditions. Computer simulations reproduce the dynamics of the colloids and are in good agreement with experiments. The current work presents a simple route to obtain large numbers of self-propelling chemical motors from a dispersion of spherically symmetric colloids through spontaneous symmetry breaking.

Diffusiophoretically induced interactions between chemically active and inert particles.

In the presence of a chemically active particle, a nearby chemically inert particle can respond to a concentration gradient and move by diffusiophoresis. The nature of the motion is studied for two cases: first, a fixed reactive sphere and a moving inert sphere, and second, freely moving reactive and inert spheres. The continuum reaction-diffusion and Stokes equations are solved analytically for these systems and microscopic simulations of the dynamics are carried out. Although the relative velocities of the spheres are very similar in the two systems, the local and global structures of streamlines and the flow velocity fields are found to be quite different. For freely moving spheres, when the two spheres approach each other the flow generated by the inert sphere through diffusiophoresis drags the reactive sphere towards it. This leads to a self-assembled dimer motor that is able to propel itself in solution. The fluid flow field at the moment of dimer formation changes direction. The ratio of sphere sizes in the dimer influences the characteristics of the flow fields, and this feature suggests that active self-assembly of spherical colloidal particles may be manipulated by sphere-size changes in such reactive systems.

Autophoretic motion in three dimensions.

Janus particles with the ability to move phoretically in self-generated chemical concentration gradients are model systems for active matter. Their motion typically consists of straight paths with rotational diffusion being the dominant reorientation mechanism. In this paper, we show theoretically that by a suitable surface coverage of both activity and mobility, translational and rotational motion can be induced arbitrarily in three dimensions. The resulting trajectories are in general helical, and their pitch and radius can be controlled by adjusting the angle between the translational and angular velocity. Building on the classical mathematical framework for axisymmetric self-phoretic motion under fixed-flux chemical boundary conditions, we first show how to calculate the most general three-dimensional motion for an arbitrary surface coverage of a spherical particle. After illustrating our results on surface distributions, we next introduce a simple intuitive patch model to serve as a guide for designing arbitrary phoretic spheres.

Swimming with a cage: low-Reynolds-number locomotion inside a droplet.

Inspired by recent experiments using synthetic microswimmers to manipulate droplets, we investigate the low-Reynolds-number locomotion of a model swimmer (a spherical squirmer) encapsulated inside a droplet of a comparable size in another viscous fluid. Meditated solely by hydrodynamic interactions, the encaged swimmer is seen to be able to propel the droplet, and in some situations both remain in a stable co-swimming state. The problem is tackled using both an exact analytical theory and a numerical implementation based on a boundary element method, with a particular focus on the kinematics of the co-moving swimmer and the droplet in a concentric configuration, and we obtain excellent quantitative agreement between the two. The droplet always moves slower than a swimmer which uses purely tangential surface actuation but when it uses a particular combination of tangential and normal actuations, the squirmer and droplet are able to attain the same velocity and stay concentric for all times. We next employ numerical simulations to examine the stability of their concentric co-movement, and highlight several stability scenarios depending on the particular gait adopted by the swimmer. Furthermore, we show that the droplet reverses the nature of the far-field flow induced by the swimmer: a droplet cage turns a pusher swimmer into a puller, and vice versa. Our work sheds light on the potential development of droplets as self-contained carriers of both chemical content and self-propelled devices for controllable and precise drug deliveries.

Microscopic and continuum descriptions of Janus motor fluid flow fields.

Active media, whose constituents are able to move autonomously, display novel features that differ from those of equilibrium systems. In addition to naturally occurring active systems such as populations of swimming bacteria, active systems of synthetic self-propelled nanomotors have been developed. These synthetic systems are interesting because of their potential applications in a variety of fields. Janus particles, synthetic motors of spherical geometry with one hemisphere that catalyses the conversion of fuel to product and one non-catalytic hemisphere, can propel themselves in solution by self-diffusiophoresis. In this mechanism, the concentration gradient generated by the asymmetric catalytic activity leads to a force on the motor that induces fluid flows in the surrounding medium. These fluid flows are studied in detail through microscopic simulations of Janus motor motion and continuum theory. It is shown that continuum theory is able to capture many, but not all, features of the dynamics of the Janus motor and the velocity fields of the fluid.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Structured light enables biomimetic swimming and versatile locomotion of photoresponsive soft microrobots.

Microorganisms move in challenging environments by periodic changes in body shape. In contrast, current artificial microrobots cannot actively deform, exhibiting at best passive bending under external fields. Here, by taking advantage of the wireless, scalable and spatiotemporally selective capabilities that light allows, we show that soft microrobots consisting of photoactive liquid-crystal elastomers can be driven by structured monochromatic light to perform sophisticated biomimetic motions. We realize continuum yet selectively addressable artificial microswimmers that generate travelling-wave motions to self-propel without external forces or torques, as well as microrobots capable of versatile locomotion behaviours on demand. Both theoretical predictions and experimental results confirm that multiple gaits, mimicking either symplectic or antiplectic metachrony of ciliate protozoa, can be achieved with single microswimmers. The principle of using structured light can be extended to other applications that require microscale actuation with sophisticated spatiotemporal coordination for advanced microrobotic technologies.

Multiple external field effects on diffusion-limited reversible reactions for a geminate pair with no interparticle interactions.

Kinetics of a geminate particle pair with no interparticle interactions controlled by diffusion-limited reversible reactions is investigated in the presence of various possible external fields such as electric or gravitational fields based on continuum theory. Diffusion equations subject to multiple external fields are analytically solved with Green functions and the physical quantities such as the binding and survival probabilities are derived. Particularly, the local binding probabilities at the specific location on the reaction surface depending on the initial distance and orientation and the field directions are calculated. The variations of the binding probabilities due to the change of the field directions are predicted at long times and it shows that the binding probabilities tend to shift along the sum of individual field directions.

Catalytic dimer nanomotors: continuum theory and microscopic dynamics.

Synthetic chemically-powered motors with various geometries have potentially new applications involving dynamics on very small scales. Self-generated concentration and fluid flow fields, which depend on geometry, play essential roles in motor dynamics. Sphere-dimer motors, comprising linked catalytic and noncatalytic spheres, display more complex versions of such fields, compared to the often-studied spherical Janus motors. By making use of analytical continuum theory and particle-based simulations we determine the concentration fields, and both the complex structure of the near-field and point-force dipole nature of the far-field behavior of the solvent velocity field that are important for studies of collective motor motion. We derive the dependence of motor velocity on geometric factors such as sphere size and dimer bond length and, thus, show how to construct motors with specific characteristics.

Chemistry in motion: tiny synthetic motors.

CONSPECTUS: 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 majority 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 self-diffusiophoresis 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 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.

Effect of an external electric field on the diffusion-influenced geminate reversible reaction of a neutral particle and a charged particle in three dimensions. IV. Excited-state ABCD reaction.

In the presence of an external electric field, an excited-state A + B(*q) <−> C(*q) + D diffusion-influenced geminate reversible reaction of a neutral particle and a charged particle, with two unimolecular decay rates and contact quenching processes, is investigated in three dimensions. The probability density functions to find individual particles, rates of reactions, and survival probabilities are analytically derived in the Laplace domain and the long-time kinetics is resolved. The probability density functions to find the particles and the rates of reactions in a scaled form exhibit a kinetic transition behavior from a t(-3/2) power law to t(-3/2)e(t) increase with the increase of external fields. The scaled survival probabilities present a kinetic transition behavior of t(-3/2) → constant → exponential with the increase of field strengths. The critical fields are found to determine the kinetic transition behaviors.

Effect of an external electric field on the diffusion-influenced geminate reversible reaction of a neutral particle and a charged particle in three dimensions. III. Ground-state ABCD reaction.

In the presence of an external electric field, the ground-state A+B(q)<->C(q)+D diffusion-influenced reversible reaction for a geminate pair, a neutral and a charged particle, is investigated in three dimensions. The probability density functions, the rates of reactions, and the survival probabilities of individual particles are analytically derived in the Laplace domain in terms of series solutions. The long-time kinetics of probability density functions and rates of reactions in rescaled forms shows a kinetic transition behavior from a t(-3∕2) power law to a t(-3∕2)e(t) increase when the condition D1F1 (2)≤D2F2 (2), which depends on the diffusivities of particles and the external electric fields, changes to D1F1 (2)>D2F2 (2). In the transition region D1F1 (2)=D2F2 (2), the long-time behavior also shows a t(-3∕2) power law decay but with a different value of the prefactor. The rescaled survival probabilities only exhibit an exponentially increasing behavior at long times with no dependence on the various values of parameters.

Synchronization, slippage, and unbundling of driven helical flagella.

Peritrichous bacteria exploit bundles of helical flagella for propulsion and chemotaxis. Here, changes in the swimming direction (tumbling) are induced by a change of the rotational frequency of some flagella. Employing coarse-grained modeling and simulations, we investigate the dynamical properties of helical flagella bundles driven by mismatched motor torques. Over a broad range of distances between the flagella anchors and applied torque differences, we find a stable bundled state, which is important for a robust directional motion of a bacterium. With increasing torque difference, a phase lag in the flagellar rotations develops, followed by slippage and ultimately unbundling, which sensitively depends on the anchoring distance of neighboring flagella. In the slippage and drift states, the different rotation frequencies of the flagella generate a tilting torque on the bacterial body, which implies a change of the swimming direction as observed experimentally.

Concentration Dependence of Ring Polymer Conformations from Monte Carlo Simulations.

The concentration dependence of the conformations of ring polymers is investigated by lattice Monte Carlo simulations and compared with that of linear polymers. The relative radii of gyration of linear polymers follow a universal master curve as a function of the scaled concentration for various chain lengths, with a scaling relationship ⟨Rg2⟩ ∼ ϕ-0.25, which is consistent with scaling theory and neutron scattering experiments. Ring polymers of different lengths also follow a universal behavior with a broad crossover to a scaling behavior ⟨Rg2⟩ ∼ ϕ-0.59 for long chains. The scaling relationship between the concentration dependence and the chain-length dependence of the radius of gyration implies ⟨Rg2⟩ ∼ N0.72, indicating highly collapsed conformations for long-chain ring polymers in the melt.

Effect of an external field on the reversible reaction of a neutral particle and a charged particle in three dimensions. II. Excited-state reaction.

The excited-state reversible reaction of a neutral particle and a charged particle in an external electric field is studied in three dimensions. This work extends the previous investigation for the ground-state reaction [S. Y. Reigh et al., J. Chem. Phys. 129, 234501 (2008)] to the excited-state reaction with two different lifetimes and quenching. The analytic series solutions for all the fundamental probability density functions are obtained with the help of the diagonal approximation. They are found to be in excellent agreement with the exact numerical solutions of anisotropic diffusion-reaction equations. The analytical solutions for reaction rates and survival probabilities are also obtained. We find that the long-time kinetic transition from a power-law decrease to an exponential increase can be controlled by the external field strength or excited-state decay rates or both.

Monte-carlo method for simulations of ring polymers in the melt.

A detailed analysis of the efficiency of a Monte-Carlo (MC) method employing non-local moves for simple lattice ring polymers is presented. While the introduction of kink-translocation moves for linear chains results in the expected speedup by a factor of the order of the number of sites, this is significantly reduced for a melt of rings.

Effect of an external electric field on the diffusion-influenced reversible reaction of a neutral particle and a charged particle in three dimensions.

The diffusion-influenced reversible reaction of a neutral particle and a charged particle in an external field is analytically solved in three dimensions. A generalized nonisotropic boundary condition is used and a kinetic equation for the probability density function is set up. A tridiagonal matrix equation is derived for the coefficients of the series solution and we obtain the solution within the diagonal approximation in the Laplace domain. We also find that the long time asymptotic behavior of the first term solution shows a kinetic transition from a power law to an exponential behavior as the field strength is increased. The full numerical calculation reveals that the first term solution deviates slightly at short times but gives good result at long times. Thus it contributes dominantly to the kinetic transition behavior at long times. For the irreversible limit, we find a different kinetic transition behavior from a power law to an exponential increase through a constant in the transition region for the initially bound state.