Single-File Diffusion of Colloids in One-Dimensional Channels

Abstract

We study the diffusive behavior of colloidal particles which are confined to one-dimensional channels generated by scanning optical tweezers. At long times t, the mean-square displacement is found to scale as t 1=2 , which is expected for systems where single-file diffusion occurs. In addition, we experimentally obtain the long-time, self-diffusive behavior from the short-time collective density fluctuations of the system as suggested by a recent analytical approach [M. Kollmann, Phys. Rev. Lett. 90, 180602 (2003)]. DOI: 10.1103/PhysRevLett.93.026001 PACS numbers: 83.50.Ha, 82.70.Dd, 83.80.Hj Single-file diffusion (SFD), prevalent in many physical, chemical, and biological processes, refers to the onedimensional (1D) motion of interacting particles in pores which are so narrow that the mutual passage of particles is excluded. Since the sequence of particles in such a situation remains unaffected over time t, this leads to strong deviations from normal diffusion. One of the most striking features of SFD is that the mean-square displacement (MSD) Wt of a tracer particle for t much larger than the direct interaction time (i.e., the time a particle needs to move a significant fraction of the mean particle distance) is given by [1][2][3][4][5] where F is the SFD mobility. While most of the results for SFD are limited to hard-rod systems [6 -8], only recently has it been demonstrated by one of us that Eq. (1) remains valid for colloidal and atomic systems with arbitrary interaction potentials, provided the correlation length between the particles is of finite range and collisions are associated with some energy dissipation [9]. In addition, it was shown that the SFD mobility F can be determined by the compressibility and the short-time collective diffusion coefficient of the system. This is an interesting result, because it relates in a unique way a long-time feature, i.e., the SFD mobility to the short-time collective diffusional properties of the system. Although the asymptotic t 1=2 behavior of SFD systems was predicted almost 40 years ago, experimental studies of such non-Fickian diffusion processes were lacking for a long time. However, due to recent progress in the synthesis of zeolitic materials which consist of long quasicylindrical pores with diameters of several angstroms [10], experimentally accessible SFD systems are now available. By means of pulsed force gradient nuclear magnetic resonance (PFG-NMR) experiments, it was demonstrated that the transport of methane and ethane in such molecular sieves can indeed be described by SFD [2,3]. Experimental evidence for the occurrence of SFD as provided by different authors, however, remains contradictory [11]. In addition, some of the results obtained with PFG-NMR are not in agreement with recent quasielastic neutron scattering studies, which show that both methane and ethane exhibit normal diffusion in AlPO 4 molecular sieves [12]. Several possible reasons have been suggested to account for this discrepancy: First, due to almost inevitable deviations of the ...

Single-file diffusion of particles with long-range interactions: Damping and finite-size effects

“…The temperature and interaction strength are such that Γ ranges as in experiments [9,15,16,24] and numerical simulations [26,27,32]. The interest of the simulations is to get acces to parameter values that are difficult or impossible to obtain experimentally.…”

“…4-a) and Fig. 4-b)], being replaced by a Dt scaling with D given by (16), and the collective regime begins by a t 2 evolution [see III C and (17)]. The time τ coll may thus be estimated by…”

“…This is the initial assumption in the existing models for long range interacting particles [22,23]. The relevant experiments were generally done with solutions of colloïds [9][10][11][12][13][14][15][16] for which overdamping is a safe assumption. The simulations [26,27] are shown in [24] to be in good agreement with the theoretical prediction of Kollmann, but they also assume overdamping in the choice of the simulation algorithm.…”

“…This phenomenon called Single File Diffusion was first noticed in 1955 by Hodgkin and Keynes [1] who were studying water transport through molecular-sized channels in biological membranes. Since then, SFD also appeared in the diffusion of molecules in porous materials like zeolites [2][3][4], of charges along polymer chains [5], of ions in electrostatic traps [6], of vortices in band superconductors [7,8] and of colloids in nanosized structures [9][10][11][12][13][14] or optically generated channels [15,16]. Even though SFD can be encountered in a lot of various physical systems, most of the theoretical studies devoted to it are generally restricted to the simplest case : an infinite overdamped system with hard core interactions.…”

Particle diode: Rectification of interacting Brownian ratchets

“…Many-particle systems may exhibit some features not found in the single-particle counterparts, such as phase transitions, spontaneous ratchet effects, and negative mobility [9][10][11][12][13][14]. The interacting Brownian ratchets been proposed for a variety of applications, including molecular motors [2], friction [16], diffusion of dimers on surfaces [17], diffusion of colloidal particles [18], DNA translocation through a nanopore [19], charge density waves [20], and arrays of Josephson junctions [21].…”