Chiral diffusion of rotary nanomotors

Nourhani, Amir; Lammert, Paul E.; Borhan, Ali; Crespi, Vincent H.

doi:10.1103/physreve.87.050301

Cited by 36 publications

(35 citation statements)

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“…Effects of chirality about a fixed direction Consideration of chirality in the locomotion behavior of active particles is justified in many observed patterns of motion of biological organisms or artificial active particles [53,83]. Due to different mechanisms, chirality breaks rotational symmetry which makes diffusion anisotropic, in the simple case in which the rotational symmetry is broken about a fixed, arbitrary direction, diffusion is split into diffusion along that direction and along the perpendicular plane.…”

Section: Resultsmentioning

confidence: 99%

“…A simple effective-force model, that leads to circular patterns of motion, is the inclusion of an effective constant "torque" in the Langevin equations that drive the orientation of the self-propulsive force [52]. Such constant torque exerts the particle to rotate with constant angular velocity [37,38,50,53], leading to circular trajectories in two dimensions and to helical ones in three dimensions. Such torque, for instance, may be externally caused by a magnetic field that act over the magnetic moment of magnetic bacteria or used over nanorods to steer them [54].…”

Section: Introductionmentioning

confidence: 99%

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Diffusion of active chiral particles

Sevilla

2016

Phys. Rev. E

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The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the directionv at time t, and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around an uniformly-distributed random axis, it is found evidence of the so called effect "anomalous, yet Brownian, diffusion", for which particles follow a non-Gaussian distribution for the positions yet the mean squared displacement is a linear function of time.PACS numbers: 02.50.-r 05.40.-a 05.10.Gg

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Diffusion of active chiral particles

Sevilla

2016

Phys. Rev. E

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“…Artificial swimmers of this sort have been fabricated in a variety of forms such as tadpoles [8,9], Janus sphere dimers [10,11], nanorods [12,13], and acoustically-activated swimmers [14]. Stochastic perturbations in the form of unbiased orientational diffusion or random chirality-reversal resulting from flipping about the direction of motion have significant effects on the long term motion: an effective translational diffusion is generated [15][16][17], the infinite-time limit of the mean position conditioned on the initial position and velocity is non-zero and chirality-dependent [5], and the mean approach to the limit is a logarithmic spiral [17,18].In this Letter, we experimentally and theoretically demonstrate "spiral diffusion" as a general finite-time behavior of the conditional mean position in circle swimmers. First, we expose the phenomenon in experimental data for both tadpole-like [9] and Janus-sphere dimer [10] rotary microswimmers (see Fig.…”

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Spiral diffusion of rotating self-propellers with stochastic perturbation

et al. 2016

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Translationally diffusive behavior arising from the combination of orientational diffusion and powered motion at microscopic scales is a known phenomenon, but the peculiarities of the evolution of expected position conditioned on initial position and orientation have been neglected. A theory is given of the spiral motion of the mean trajectory depending upon propulsion speed, angular velocity, orientational diffusion and rate of random chirality reversal. We demonstrate the experimental accessibility of this effect using both tadpole-like and Janus sphere dimer rotating motors. Sensitivity of the mean trajectory to the kinematic parameters suggest that it may be a useful way to determine those parameters.Active colloids such as microswimmers and nanomotors are a class of non-equilibrium systems which has been the subject of intense research in recent years [1][2][3]. At the sub-micron length scale, stochastic effects significantly perturb a self-propeller's deterministic motion, and the coupling of such noise to a steady motion can lead to unexpected emergent phenomena such as motilityinduced phase separation [4], chiral diffusion [5], and phenomena with biological relevance [6] which can now be modelled by artificial active colloids. In the absence of noise a circle swimmer, confined to a plane with a strong rotational component to its powered motion, travels on a fixed circle with a steady clockwise or counterclockwise chirality [7]. Artificial swimmers of this sort have been fabricated in a variety of forms such as tadpoles [8,9], Janus sphere dimers [10,11], nanorods [12,13], and acoustically-activated swimmers [14]. Stochastic perturbations in the form of unbiased orientational diffusion or random chirality-reversal resulting from flipping about the direction of motion have significant effects on the long term motion: an effective translational diffusion is generated [15][16][17], the infinite-time limit of the mean position conditioned on the initial position and velocity is non-zero and chirality-dependent [5], and the mean approach to the limit is a logarithmic spiral [17,18].In this Letter, we experimentally and theoretically demonstrate "spiral diffusion" as a general finite-time behavior of the conditional mean position in circle swimmers. First, we expose the phenomenon in experimental data for both tadpole-like [9] and Janus-sphere dimer [10] rotary microswimmers (see Fig. 1), and present fits to the model. Then, we explain the theory for spiral diffusion of circle swimmers subjected to both orientational diffusion and flipping (change of chirality). The expected position of the swimmer, conditioned on its initial position, velocity direction and chirality, evolves along a converging spiral. The theory serves as a sensitive and accurate utility for determining kinematic parameters such as angular velocity and orientational diffusivity. Supplementary Material contains the details of fabrication and experimental protocols, as well as movies of simulated ensembles of swimmers for a variety of noise par...

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“…Nevertheless, as stated in our Letter [2], effective forces and torques [3][4][5][6][7] can be used together with the grand resistance matrix (GRM) [8] to describe the self-propulsion of forceand torque-free swimmers [9]. To prove this, we perform a hydrodynamic calculation based on slender-body theory for Stokes flow [10,11].…”

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confidence: 99%

Kümmelet al.Reply:

et al. 2014

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Kümmel et al. Reply: In a Comment [1] on our Letter on self-propelled asymmetric particles [2], Felderhof claims that our theory based on Langevin equations would be conceptually wrong. In this Reply we show that our theory is appropriate, consistent, and physically justified.The motion of a self-propelled particle (SPP) is forceand torque-free if external forces and torques are absent. Nevertheless, as stated in our Letter [2], effective forces and torques [3][4][5][6][7] can be used together with the grand resistance matrix (GRM) [8] to describe the self-propulsion of forceand torque-free swimmers [9]. To prove this, we perform a hydrodynamic calculation based on slender-body theory for Stokes flow [10,11]. This approach has been applied successfully to model, e.g., flagellar locomotion [12,13] and avoids a general Faxén theorem for asymmetric particles. A key assumption of slender-body theory is that the width 2ϵ of the arms of the L-shaped particle is much smaller than the total arc length L ¼ a þ b, where a and b are the arm lengths.The centerline position of the slender particle is xðsÞHere, r is the center-of-mass position of the particle in the laboratory frame of reference and r S ¼ ða∥ Þ=ð2LÞ is a vector in the particle's framedefined by the unit vectorsû ∥ ,û ⊥ -such that r − r S is the point where the two arms meet at right angles. The fluid velocity on the particle surface is approximated by _ x þ v sl with a prescribed slip velocity v sl ðsÞ. According to the leading-order slender-body approximation [10], the fluid velocity is related to the local force per unit length fðsÞ on the particle surface byÞf with c ¼ logðL=ϵÞ=ð4πηÞ, the solvent viscosity η, the identity matrix I, x 0 ¼ ∂x=∂s, and the dyadic product ⊗. The force density f satisfies the integral constraints of vanishing net force, R a −b fds ¼ 0, and vanishing net torque relative to the center of mass,T . First, we consider a passive particle driven by an external force F ext , which is constant in the particle's frame, and torque M ext . For this case, we assume no-slip conditions for the fluid on the entire particle surface. Then the integral constraints with net force F ext and torque M ext givewhereÞ=ð12L 2 Þ is the GRM that depends on the particle shape [8,14].In the self-propelled case, motivated by the slip flow generated near the Au coating in the experiments, we setthe arm of length b and no slip (v sl ¼ 0) along the other arm. This results inWe emphasize that the tensor H in Eq. (3) is identical to the GRM in Eq. (1). Formally, both equations are exactly the same ifû ∥ · F ext ¼ 0,û ⊥ · F ext ¼ bV sl =c, and M ext ¼ −ab 2 V sl =ð2cLÞ. This shows that the motion of a SPP with v sl ¼ −V slû⊥ along the arm of length b is identical to the motion of a passive particle driven by a net external force F ext ¼ Fû ⊥ and torque M ext ¼ lF with the effective self-propulsion force F ¼ bV sl =c and effective lever arm l ¼ −ab=ð2LÞ. By transforming Eq. (3) from the particle's frame to the laboratory frame and introducing the generalized diffusi...

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Chiral diffusion of rotary nanomotors

Cited by 36 publications

References 23 publications

Diffusion of active chiral particles

Diffusion of active chiral particles

Spiral diffusion of rotating self-propellers with stochastic perturbation

Kümmelet al.Reply:

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