Splitting of the Universality Class of Anomalous Transport in Crowded Media

Abstract

We investigate the emergence of subdiffusive transport by obstruction in continuum models for molecular crowding. While the underlying percolation transition for the accessible space displays universal behavior, the dynamic properties depend in a subtle nonuniversal way on the transport through narrow channels. At the same time, the different universality classes are robust with respect to introducing correlations in the obstacle matrix as we demonstrate for quenched hard-sphere liquids as underlying structures. Our results confirm that the microscopic dynamics can dominate the relaxational behavior even at long times, in striking contrast to glassy dynamics.

Active Brownian particles moving in a random Lorentz gas

“…Above a critical obstacle density, the test particle can no longer explore the whole environment but stays trapped and long-range transport is effectively suppressed. Höfling et al have observed that in two dimensions and close to the critical density diffusive and ballistic particles show the same subdiffusive motion in a random Lorentz gas [44,[47][48][49][50].…”

Complex dynamics induced by strong confinement – From tracer diffusion in strongly heterogeneous media to glassy relaxation of dense fluids in narrow slits

“…The statistics of having a narrow channel can be modified by introducing structural correlations into the system. Relying on a quenched hard-sphere host structure the probability to find such narrow channels becomes larger than for the uncorrelated Lorentz gas [55]. This observation holds both for the infinite cluster only as well as averaged over all pores of the system.…”

“…Yet, apart from changing the value of this probability density the changes induced by the packing are smooth deformations with respect to the original Lorentz model. Simulation results for the mean-square displacement δr 2 ∞ (t) for ballistic tracers confined to the infinite cluster reveal that the walk dimension d w remains the same for all packing fractions [55]. Therefore the conclusion is that the statistics of the narrow channel is irrelevant as long as the probability density extrapolates to a constant for small channel widths.…”

“…Upon increasing the packing fraction the critical obstacle density decreases, and as a peculiarity in 2D systems a minimum emerges at η ≈ 0.5 and increases again for even higher packing fractions [76]. This feature is not present in the corresponding 3D analog [55]. The percolation transition is present for all packing fractions and universality suggests that the underlying geometrical properties are characterized by the same universal exponents, say ν for the growth of the correlation length ξ ∼ | | −ν and β for the weight of the infinite cluster ϕ ∞ ∼ (− ) β , < 0.…”

“…This incipient percolating cluster ceases to exist beyond a certain density n * c known as the percolation threshold. Computer simulations yield n * c ≈ 0.359 [51] in the twodimensional case, and n * c ≈ 0.838 [52][53][54][55] in 3D. The volume fraction ϕ ∞ of the incipient percolating cluster plays the role of an order parameter here and is anticipated to vanish as ϕ ∞ ∼ (− ) β for → 0, < 0, where = (n − n c )/n c denotes the separation parameter.…”