Thermodynamic approach to the self-diffusiophoresis of colloidal Janus particles

Diffusion coefficient and power spectrum of active particles with a microscopically reversible mechanism of self-propelling

Catalytically active macromolecules are envisioned as key building blocks in development of artificial nanomotors. However, theory and experiments report conflicting findings regarding their dynamics. The lack of consensus is mostly caused by a limited understanding of specifics of self-propulsion mechanisms at the nanoscale. Here, we study a generic model of a self-propelled nanoparticle that does not rely on a particular mechanism. Instead, its main assumption is the fundamental symmetry of microscopic dynamics of chemical reactions: the principle of microscopic reversibility. Significant consequences of this assumption arise if we subject the particle to an action of an external time-periodic force. The particle diffusion coefficient is then enhanced compared to the unbiased dynamics. The enhancement can be controlled by the force amplitude and frequency. We also derive the power spectrum of particle trajectories. Among new effects stemming from the microscopic reversibility are the enhancement of the spectrum at all frequencies and sigmoid-shaped transitions and a peak at characteristic frequencies of rotational diffusion and external forcing. The microscopic reversibility is a generic property of a broad class of chemical reactions, therefore we expect that the presented results will motivate new experimental studies aimed at testing of our predictions. This could provide new insights into dynamics of catalytic macromolecules.

Enhanced diffusivity in microscopically reversible active matter

The physics of self-propelled objects at the nanoscale is a rapidly developing research field where recent experiments have focused on the motion of individual catalytic enzymes. Contrary to the experimental advancements, theoretical understanding of the possible self-propulsion mechanisms at these scales is limited. A particularly puzzling question concerns the origins of the reportedly high diffusivities of the individual enzymes. Here we start with the fundamental principle of microscopic reversibility (MR) of chemical reactions powering self-propulsion and demonstrate that MR can lead to an increase of the particle mobility and of the short- and long-time diffusion coefficients as compared to dynamics where MR is neglected. Furthermore, the derived diffusion coefficients are enhanced due to the action of an external force. These results can shed new light on interpretations of the measured diffusivities and help to test the relevance of MR for the active motion of individual nanoswimmers.

Asymmetry-induced order in multilayer networks

Symmetries naturally occur in real-world networks and can significantly influence the observed dynamics. For instance, many synchronization patterns result from the underlying network symmetries, and high symmetries are known to increase the stability of synchronization. Yet here we find that general macroscopic features of network solutions such as regularity can be induced by breaking their symmetry of interactions. We demonstrate this effect in an ecological multilayer network where the topological asymmetries occur naturally. These asymmetries rescue the system from chaotic oscillations by establishing stable periodic orbits and equilibria. We call this phenomenon asymmetry-induced order and uncover its mechanism by analyzing both analytically and numerically the absence of dynamics on the system's synchronization manifold. Moreover, the bifurcation scenario describing the route from chaos to order is also disclosed. We demonstrate that this result also holds for generic node dynamics by analyzing coupled paradigmatic Rössler and Lorenz systems.

High-order simulation scheme for active particles driven by stress boundary conditions

We study the dynamics and interactions of elliptic active particles in a two dimensional solvent. The particles are self-propelled through prescribing a fluid stress at one half of the fluid-particle boundary. The fluid is treated explicitly solving the Stokes equation through a discontinuous Galerkin scheme, which allows to simulate strictly incompressible fluids. We present numerical results for a single particle and give an outlook on how to treat suspensions of interacting active particles.

Shaping the gradients driving phoretic micro-swimmers: influence of swimming speed, budget of carbonic acid and environment

pH gradient-driven modular micro-swimmers are investigated as a model for a large variety of quasi-two-dimensional chemi-phoretic self-propelled entities. Using three-channel micro-photometry, we obtain a precise large field mapping of pH at a spatial resolution of a few microns and a pH resolution of [Formula: see text] units for swimmers of different velocities propelling on two differently charged substrates. We model our results in terms of solutions of the three-dimensional advection-diffusion equation for a 1:1 electrolyte, i.e. carbonic acid, which is produced by ion exchange and consumed by equilibration with dissolved [Formula: see text]. We demonstrate the dependence of gradient shape and steepness on swimmer speed, diffusivity of chemicals, as well as the fuel budget. Moreover, we experimentally observe a subtle, but significant feedback of the swimmer's immediate environment in terms of a substrate charge-mediated solvent convection. We discuss our findings in view of different recent results from other micro-fluidic or active matter investigations. We anticipate that they are relevant for quantitative modelling and targeted applications of diffusio-phoretic flows in general and artificial micro-swimmers in particular.

Active Matter, Microreversibility, and Thermodynamics

Active matter, comprising many active agents interacting and moving in fluids or more complex environments, is a commonly occurring state of matter in biological and physical systems. By its very nature, active matter systems exist in nonequilibrium states. In this paper, the active agents are small Janus colloidal particles that use chemical energy provided by chemical reactions occurring on their surfaces for propulsion through a diffusiophoretic mechanism. As a result of interactions among these colloids, either directly or through fluid velocity and concentration fields, they may act collectively to form structures such as dynamic clusters. A general nonequilibrium thermodynamics framework for the description of such systems is presented that accounts for both self-diffusiophoresis and diffusiophoresis due to external concentration gradients, and is consistent with microreversibility. It predicts the existence of a reciprocal effect of diffusiophoresis back onto the reaction rate for the entire collection of colloids in the system, as well as the existence of a clustering instability that leads to nonequilibrium inhomogeneous system states.