Intermediate scattering function of an anisotropic active Brownian particle

We present a mode-coupling theory (MCT) for the high-density dynamics of two-dimensional spherical active Brownian particles (ABP). The theory is based on the integration-through-transients (ITT) formalism and hence provides a starting point for the calculation of non-equilibrium averages in active-Brownian particle systems. The ABP are characterized by a self-propulsion velocity v0, and by their translational and rotational diffusion coefficients, Dt and Dr. The theory treats both the translational and the orientational degrees of freedom of ABP explicitly. This allows to study the effect of self-propulsion of both weak and strong persistence of the swimming direction, also at high densities where the persistence length p = v0/Dr is large compared to the typical interaction length scale. While the low-density dynamics of ABP is characterized by a single Péclet number, Pe = v 2 0 /DrDt, close to the glass transition the dynamics is found to depend on Pe and p separately. At fixed density, increasing the self-propulsion velocity causes structural relaxation to sped up, while decreasing the persistence length slows down the relaxation. The theory predicts a nontrivial idealized-glass-transition diagram in the three-dimensional parameter space of density, selfpropulsion velocity and rotational diffusivity. The active-MCT glass is a nonergodic state where correlations of initial density fluctuations never fully decay, but also an infinite memory of initial orientational fluctuations is retained in the positions.

show abstract

“…(12). The formal solution, S( q, t) = exp[−ω( q)t], reproduces the exact solution as discussed in 3D [30].…”

Section: Mode-coupling Theorysupporting

confidence: 67%

Mode-coupling theory for active Brownian particles

2017

View full text Add to dashboard Cite

show abstract

“…A first step would be to consider rotationally symmetric shape-anisotropic particles such as rods 17,48 or spheroids. [49][50][51] For these systems, the description has to be adapted accordingly, but the underlying physics is basically the same. This is different for particles without any symmetry axis.…”

Section: Discussionmentioning

confidence: 99%

Helical paths, gravitaxis, and separation phenomena for mass-anisotropic self-propelling colloids: Experiment versus theory

Campbell

Wittkowski

Hagen

et al. 2017

The Journal of Chemical Physics

View full text Add to dashboard Cite

The self-propulsion mechanism of active colloidal particles often generates not only translational but also rotational motion. For particles with an anisotropic mass density under gravity, the motion is usually influenced by a downwards oriented force and an aligning torque. Here we study the trajectories of self-propelled bottom-heavy Janus particles in three spatial dimensions both in experiments and by theory. For a sufficiently large mass anisotropy, the particles typically move along helical trajectories whose axis is oriented either parallel or antiparallel to the direction of gravity (i.e., they show gravitaxis). In contrast, if the mass anisotropy is small and rotational diffusion is dominant, gravitational alignment of the trajectories is not possible. Furthermore, the trajectories depend on the angular self-propulsion velocity of the particles. If this component of the active motion is strong and rotates the direction of translational self-propulsion of the particles, their trajectories have many loops, whereas elongated swimming paths occur if the angular self-propulsion is weak. We show that the observed gravitational alignment mechanism and the dependence of the trajectory shape on the angular self-propulsion can be used to separate active colloidal particles with respect to their mass anisotropy and angular self-propulsion, respectively.

show abstract

“…Only recently the intermediate scattering function has been computed analytically for simple run-andtumble particles [40] and for active Brownian agents [41]. Whereas it has also been measured for Chlamydomonas reinhardtii by light scattering experiments [17,18], and within the recently developed image based framework of differential dynamic microscopy [19], only approximations of the intermediate scattering function of circle swimmers valid at rather small length scales have been worked out [18,19].…”

Section: Introductionmentioning

confidence: 99%

Intermediate scattering function of an anisotropic Brownian circle swimmer

Kurzthaler

Franosch

2017

Soft Matter

Self Cite

View full text Add to dashboard Cite

Microswimmers exhibit noisy circular motion due to asymmetric propulsion mechanisms, their chiral body shape, or by hydrodynamic couplings in the vicinity of surfaces. Here, we employ the Brownian circle swimmer model and characterize theoretically the dynamics in terms of the directly measurable intermediate scattering function. We derive the associated Fokker-Planck equation for the conditional probabilities and provide an exact solution in terms of generalizations of the Mathieu functions. Different spatiotemporal regimes are identified reflecting the bare translational diffusion at large wavenumbers, the persistent circular motion at intermediate wavenumbers and an enhanced effective diffusion at small wavenumbers. In particular, the circular motion of the particle manifests itself in characteristic oscillations at a plateau of the intermediate scattering function for wavenumbers probing the radius.

show abstract

Intermediate scattering function of an anisotropic active Brownian particle

Cited by 98 publications

References 44 publications

Mode-coupling theory for active Brownian particles

Mode-coupling theory for active Brownian particles

Helical paths, gravitaxis, and separation phenomena for mass-anisotropic self-propelling colloids: Experiment versus theory

Intermediate scattering function of an anisotropic Brownian circle swimmer

Contact Info

Product

Resources

About