Critical dynamics of ballistic and Brownian particles in a heterogeneous environment

Höfling, Felix; Munk, Tobias; Frey, Erwin; Franosch, Thomas

doi:10.1063/1.2901170

Cited by 75 publications

(127 citation statements)

References 63 publications

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“…Recently, it was shown that the diffusion coefficient for an all-cluster average vanishes as D(n) ∼ (n * c − n * ) µ with a value µ = 2.88 [30,31]. Since only particles that are located in the percolating clusters can contribute to diffusion, we anticipate D(n) ∼ D ∞ (n)P ∞ (n) and infer the scaling relation µ ∞ = µ − β = 2.47.…”

Section: Diffusion Coefficientsmentioning

confidence: 59%

“…4. Choosing C ∞ = −0.53 t y 0 the data nicely collapse on a single master curve although the improvement is less satisfactory than for the all-cluster average [30,31] or in two-dimensional transport on a lattice [34]. The reason may be traced back to the slower convergence of the diffusion coefficients identified in the inset of Fig.…”

Section: Scaling Behaviormentioning

confidence: 93%

“…On the other hand, for large rescaled time the mean-square displacement increases linearly implying δr 2 ∞ (t 1) ∼t 1−2/d w . Furthermore, one expects that the crossover from subdiffusive to linear increase of the Earlier it has been demonstrated that the all-cluster averaged mean-square displacement also displays subdiffusive behavior δr 2 (t) ∼ t 2/z at the critical obstacle density [30,31], yet with a different dynamic exponent z = 6.25. Here the self-similar hierarchy of finite clusters contributes to the mean-square displacement.…”

Section: Scaling Behaviormentioning

confidence: 99%

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Anomalous transport of a tracer on percolating clusters

Spanner¹,

Höfling²,

Schröder‐Turk³

et al. 2011

J. Phys.: Condens. Matter

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Abstract. We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport, which extends to infinite times precisely at the critical obstacle density. The slowing down of the diffusion coefficient exhibits power-law behavior for densities close to the critical point and we show that the mean-square displacement fulfills a scaling hypothesis. Furthermore, we calculate the dynamic conductivity as response to an alternating electric field. Last, we discuss the non-gaussian parameter as an indicator for heterogeneous dynamics.

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Section: Diffusion Coefficientsmentioning

confidence: 59%

Section: Scaling Behaviormentioning

confidence: 93%

Section: Scaling Behaviormentioning

confidence: 99%

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Anomalous transport of a tracer on percolating clusters

Spanner¹,

Höfling²,

Schröder‐Turk³

et al. 2011

J. Phys.: Condens. Matter

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“…24 Hydrodynamic interactions are ignored in DMD and the dynamics is ballistic between collisions. Recent simulations 25 have shown, however, that the long time behavior is not affected by the short time dynamics. We use DMD because it is more efficient than…”

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confidence: 99%

Effect of Polydispersity on Diffusion in Random Obstacle Matrices

et al. 2012

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“…(1) with an event-driven algorithm to detect the collisions between rod and obstacles [21][22][23]. The MSDs in fig.…”

mentioning

confidence: 99%

Effective Perrin theory for the anisotropic diffusion of a strongly hindered rod

Munk¹,

Höfling²,

Frey³

et al. 2009

Europhys. Lett.

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Abstract. -Slender rods in concentrated suspensions constitute strongly interacting systems with rich dynamics: transport slows down drastically and the anisotropy of the motion becomes arbitrarily large. We develop a mesoscopic description of the dynamics down to the length scale of the interparticle distance. Our theory is based on the exact solution of the Smoluchowski-Perrin equation; it is in quantitative agreement with extensive Brownian dynamics simulations in the dense regime. In particular, we show that the tube confinement is characterised by a power law decay of the intermediate scattering function with exponent 1/2.Brownian motion of highly anisotropic particles is considerably more complex than the diffusion of spherical objects, the basic understanding of which is founded on the seminal works by Einstein and von Smoluchowski. A shape anisotropy results in diffusion coefficients that depend on the direction of motion in the body frame, thus inducing a coupling of translation to the orientation. This anisotropic dynamics has been investigated in recent experiments measuring diffusion coefficients of micrometre sized ellipsoids and rods by single particle tracking [1-3]; in particular, non-Gaussian statistics has been observed [1]. Likewise in dynamic light scattering, the rotational and translational diffusion coefficients were determined simultaneously [4]. For these dilute systems, the ratio of diffusion parallel and perpendicular to the long symmetry axis was limited to values up to D /D ⊥ ≈ 4 in quasi two-dimensional (2D) confinement.Considerably higher values of this ratio have been observed in simulations of semi-dilute suspensions of slender rods, yielding D /D ⊥ up to values of 50 [5,6]. This increase in anisotropy is caused by the steric constraints imposed by surrounding rods; thereby the transverse and rotational motion is suppressed, whereas the longitudinal transport is barely influenced [7]. An intermediate regime of anisotropic diffusion has been derived for ballistic needles within kinetic theory [8] and was observed in simulations [9].For a finite width b, the rods undergo a phase transition to the nematic phase at densities of the order of 1/bL 2 as predicted by Onsager [10]. The dynamics in this ordered phase becomes trivially anisotropic and splits into a fast diffusion along the nematic director axis and slower diffusion perpendicular to it. Such a pronounced anisotropic diffusion has been observed in simulations of nematic elongated ellipsoids [11] and spherocylinders [12,13]. Experiments have also clearly demonstrated orientation-dependent diffusion in colloidal nanorods in the isotropic and nematic phase [14] and in various liquid crystalline phases of fd viruses [15,16]. The phenomena connected with the nematic phase transition are essentially understood and will not be discussed in this work.In the isotropic phase, experiments and computer simulations have been restricted to determine the diffusion coefficients from the mean-square displacements. The complex interplay of tra...

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Critical dynamics of ballistic and Brownian particles in a heterogeneous environment

Cited by 75 publications

References 63 publications

Anomalous transport of a tracer on percolating clusters

Anomalous transport of a tracer on percolating clusters

Effect of Polydispersity on Diffusion in Random Obstacle Matrices

Effective Perrin theory for the anisotropic diffusion of a strongly hindered rod

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