Single-file diffusion of interacting particles in a finite-sized channel

Abstract

We study the dynamics of charged macroscopic particles (millimetric steel balls) confined in a linear channel of finite length, sufficiently narrow to avoid particles crossing. We show that their individual response to thermal fluctuations strongly depends either on their position in the channel or the local potential they experience. Three different dynamical regimes are identified. At small times, a "free regime" takes place, with the outermost particles exhibiting the highest diffusion coefficient. This effect results from an "echo" of the thermal fluctuations reflected by the channel wall. Then, forbidden crossing induces a correlated regime similar to single file diffusion. Surprisingly, the corresponding mobility increases with the local potential. Lastly, the finite length of the channel induces the saturation of fluctuations. We show that those behaviors may be described heuristically with the help of models for N hard-core interacting particles diffusing in a finite channel of length L, provided that we replace the uniform interparticle distance L/N by a characteristic distance (k(B)T/K)(1/2) built upon the temperature T and the stiffness K of the local potential. It provides a very satisfactory estimate for the fluctuations sizes, whereas they are greatly overestimated assuming hard-core interactions.

Single-file diffusion of particles in a box: Transient behaviors

“…All simulations are done with a system of 33 interacting particles (N = 17) confined in a channel of length L = 60 mm, and a length scale λ 0 = 0.48 mm. These values have been selected in order to compare the simulations with our previous experiments [27]. The dimensionless mean density L/(2Nλ 0 ) is of the same order of magnitude as in other numerical [24,25,31] and experimental [15,[17][18][19][32][33][34][35] studies.…”

“…6 of Ref. [27]) and that the longest saturation times t sat are always associated to the inner balls. This is somewhat paradoxical since the latter are the more confined particles and are submitted to the strongest interparticle forces; we should therefore expect the quickest saturation for these particles.…”

“…Only a few experimental studies [27] and no complete theory are devoted to the SFD for particles with soft-core interactions in a finite channel [6,28,29]. In a previous paper [27], we have presented experimental results performed with a system of millimetric metallic balls, with soft-core screened electrostatic interactions. This system is put in an effective thermal bath insured by a random mechanical vibration [20][21][22].…”

Single-file diffusion in an interval: First passage properties

“…Although the overall density of particles in such a system evolves as if there is no interaction, 1 the diffusion of one specific particle (a tagged particle, or a tracer) is slowed down by the exclusion interactions with neighboring particles. Experimentally SFD is observed for instance in narrow biological pores, 2 inside zeolites, 3,4 during the sliding of proteins along DNA, 5,6 and in many other either natural or artificial systems [7][8][9][10][11][12][13][14][15][16][17] .…”

Evolution equation for tagged-particle density and correlations in single-file diffusion

“…To have a better understanding of the processes that take place at the atomic scale, there have been experiments carried out by Lutz et al [20] and Delfau et al [21]. The former studied the diffusion of particles constrained in a circular optical trap; the latter analyzed the dynamics of particles confined in a linear channel of finite length.…”