Single-file diffusion and kinetics of template-assisted assembly of colloids

Heterogeneity of dynamics in a modulated colloidal liquid

We study the dynamics of a system of two dimensional colloidal particles subjected to a spatially periodic external potential using Brownian dynamics simulations. We characterize the dynamics in the system by the mean square displacements and the self-van Hove function. The static density plots suggest that system gets into modulated liquid phase in presence of the external potential. We find that diffusion coefficients, obtained from long time mean sqaure displacements, decay exponentially with increasing potential strength. The self-van Hove functions computed from the distribution of particle displacemets in a given time interval show non-gaussian behaviour in directions both parallel and transverse to the external modulation. This suggests heterogeneous dynamics and is supported by particle mobilities and residence times.

Crystalline Bis-urea Nanochannel Architectures Tailored for Single-File Diffusion Studies

Urea is a versatile building block that can be modified to self-assemble into a multitude of structures. One-dimensional nanochannels with zigzag architecture and cross-sectional dimensions of only ∼3.7 Å × 4.8 Å are formed by the columnar assembly of phenyl ether bis-urea macrocycles. Nanochannels formed by phenylethynylene bis-urea macrocycles have a round cross-section with a diameter of ∼9.0 Å. This work compares the Xe atom packing and diffusion inside the crystalline channels of these two bis-ureas using hyperpolarized Xe-129 NMR. The elliptical channel structure of the phenyl ether bis-urea macrocycle produces a Xe-129 powder pattern line shape characteristic of an asymmetric chemical shift tensor with shifts extending to well over 300 ppm with respect to the bulk gas, reflecting extreme confinement of the Xe atom. The wider channels formed by phenylethynylene bis-urea, in contrast, present an isotropic dynamically average electronic environment. Completely different diffusion dynamics are revealed in the two bis-ureas using hyperpolarized spin-tracer exchange NMR. Thus, a simple replacement of phenyl ether with phenylethynylene as the rigid linker unit results in a transition from single-file to Fickian diffusion dynamics. Self-assembled bis-urea macrocycles are found to be highly suitable materials for fundamental molecular transport studies on micrometer length scales.

Analytical calculation of four-point correlations for a simple model of cages involving numerous particles

Dynamics of a one-dimensional system of Brownian particles with short-range repulsive interaction (diameter σ) is studied with a liquid-theoretical approach. The mean square displacement, the two-particle displacement correlation, and the overlap-density-based generalized susceptibility are calculated analytically by way of the Lagrangian correlation of the interparticulate space, instead of the Eulerian correlation of density that is commonly used in the standard mode-coupling theory. In regard to the mean square displacement, the linear analysis reproduces the established result on the asymptotic subdiffusive behavior of the system. A finite-time correction is given by incorporating the effect of entropic nonlinearity with a Lagrangian version of mode-coupling theory. The notorious difficulty in derivation of the mode-coupling theory concerning violation of the fluctuation-dissipation theorem is found to disappear by virtue of the Lagrangian description. The Lagrangian description also facilitates analytical calculation of four-point correlations in the space-time, such as the two-particle displacement correlation. The two-particle displacement correlation, which is asymptotically self-similar in the space-time, illustrates how the cage effect confines each particle within a short radius on one hand and creates collective motion of numerous particles on the other hand. As the time elapses, the correlation length grows unlimitedly, and the generalized susceptibility based on the overlap density converges to a finite value which is an increasing function of the density. The distribution function behind these dynamical four-point correlations and its extension to three-dimensional cases, respecting the tensorial character of the two-particle displacement correlation, are also discussed.

Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings

We numerically examine colloidal particles driven over a muffin tin substrate. Previous studies of this model identified a variety of commensurate and incommensurate static phases in which topological defects can form domain walls, ordered stripes, superlattices, or disordered patchy regimes as a function of the filling fraction. Here, we show that the addition of an external drive to these static phases can produce distinct dynamical responses. At incommensurate fillings the flow occurs in the form of localized pulses or solitons correlated with topological defect structures. Transitions between different modes of motion can occur as a function of increasing drive. We measure the average particle velocity for specific ranges of external drive and show that changes in the velocity response correlate with changes in the topological defect arrangements. We also demonstrate that in the different dynamic phases, the particles have distinct trajectories and velocity distributions. Dynamic transitions between ordered and disordered flows exhibit hysteresis, while in strongly disordered regimes there is no hysteresis and the velocity-force curves are smooth. When stripe patterns are present, transport can occur at an angle to the driving direction.

Everlasting effect of initial conditions on single-file diffusion

We study the dynamics of a tagged particle in an environment of point Brownian particles with hard-core interactions in an infinite one-dimensional channel (a single-file model). In particular, we examine the influence of initial conditions on the dynamics of the tagged particle. We compare two initial conditions: equal distances between particles and uniform density distribution. The effect is shown by the differences of mean-square-displacement and correlation function for the two ensembles of initial conditions. We discuss the violation of Einstein relation, and its dependence on the initial condition, and the difference between time and ensemble averaging. More specifically, using the Jepsen line, we will discuss how transport coefficients, like diffusivity, depend on the initial state. Our work shows that initial conditions determine the long time limit of the dynamics, and in this sense the system never forgets its initial state in complete contrast with thermal systems (i.e., a closed system that attains equilibrium independent of the initial state).

Non-monotonic crossover from single-file to regular diffusion in micro-channels

The diffusion behavior of interacting particles determines the behavior of a large number of systems ranging from pedestrians crossing a road to ions passing through channels in living cells. Here we present a system in which the nature of the diffusion process varies with changes in the external conditions. We find this special behavior in a colloidal model system, consisting of micron sized particles which are confined to narrow channels and interact via induced magnetic dipoles. When the density of these particles is changed, diffusion alternates between normal Fickian behavior and single-file diffusion. This anomalous behavior is induced by the order of the particles in the restricted geometry and does not depend on the exact nature of the inter-particle interactions.