Single file dynamics in soft materials

The term single file (SF) dynamics refers to the motion of an assembly of particles through a channel with cross-sections comparable to the particles' diameter. Single file diffusion (SFD) is then the diffusion of a tagged particle in a single file, i.e., under the condition that particle passing is not allowed. SFD accounts for a large variety of processes in nature, including diffusion of colloids in synthetic and natural channels, biological motors along molecular chains, electrons in proteins and liquid helium, ions through membranes, just to mention a few examples. Albeit introduced in 1965s, over the last decade the classical notion of SF dynamics has been generalised to account for a more realistic modelling of the particle properties, file geometry, particle-particle and channel-particle interactions, which paves the way to remarkable applications of the SF model, for instance, in the technology of bio-integrated nanodevices. We provide here a comprehensive review of the recent advances in the theory of SF dynamics with the purpose of spurring further experimental work.

Insights from Single-File Diffusion into Cooperativity in Higher Dimensions

Diffusion in colloidal suspensions can be very slow due to the cage effect, which confines each particle within a short radius on one hand, and involves large-scale cooperative motions on the other. In search of insight into this cooperativity, here the authors develop a formalism to calculate the displacement correlation in colloidal systems, mainly in the two-dimensional (2D) case. To clarify the idea for it, studies are reviewed on cooperativity among the particles in the one-dimensional (1D) case, i.e. the single-file diffusion (SFD). As an improvement over the celebrated formula by Alexander and Pincus on the mean-square displacement (MSD) in SFD, it is shown that the displacement correlation in SFD can be calculated from Lagrangian correlation of the particle interval in the one-dimensional case, and also that the formula can be extended to higher dimensions. The improved formula becomes exact for large systems. By combining the formula with a nonlinear theory for correlation, a correction to the asymptotic law for the MSD in SFD is obtained. In the 2D case, the linear theory gives description of vortical cooperative motion.

Linear instability of a zigzag pattern

Interacting particles confined in a quasi-one-dimensional channel are physical systems which display various equilibrium patterns according to the interparticle interaction and the transverse confinement potential. Depending on the confinement, the particles may be distributed along a straight line, in a staggered row (zigzag), or in a configuration in which the linear and zigzag phases coexist (distorted zigzag). In order to clarify the conditions of existence of each configuration, we have studied the linear stability of the zigzag pattern. We find an acoustic transverse mode that destabilizes the zigzag configuration for short-range interaction potentials, and we calculate the interaction range above which this instability disappears. In particular, we recover the unconditional stability of zigzag patterns for Coulomb interactions. We show that the domain of existence for the distorted zigzag patterns is accurately described by our linear stability analysis. We also emphasize the complexity of finite size effects. Last, we provide a criterion for the onset of instability in the thermodynamic limit and propose a biphasic model that explains some characteristics of the distorted zigzag patterns.