Ordering and single-file diffusion in colloidal systems

Single-file diffusion of active Brownian particles

Single-file diffusion (SFD) is a key mechanism underlying transport phenomena in confined physical and biological systems. In a typical SFD process, microscopic particles are restricted to moving in a narrow channel where they cannot pass one another, resulting in constrained motion and anomalous long-time diffusion. In this study, we use Brownian dynamics simulations and analytical theory to investigate the SFD of athermal active Brownian particles (ABPs)-a minimal model of active colloids. Building on prior work [Schiltz-Rouse et al., Phys. Rev. E 108, 064601 (2023)], where the kinetic temperature, pressure, and compressibility of the single-file ABP system were derived, we develop an accurate analytical expression for the mean square displacement (MSD) of a tagged particle. We find that the MSD exhibits ballistic behavior at short times, governed by the reduced kinetic temperature of the system. At long times, the characteristic subdiffusive scaling of SFD, [⟨(Δx)2⟩∼ t1/2], is preserved. However, self-propulsion introduces significant changes to the 1D-mobility, which we directly relate to the system's compressibility. Furthermore, we demonstrate that the generalized 1D-mobility, originally proposed by Kollmann for equilibrium systems [M. Kollmann, Phys. Rev. Lett. 90, 180602 (2003)], can be extended to active systems with minimal modification. These findings provide a framework for understanding particle transport in active systems and for tuning transport properties at the microscale, particularly in geometries where motion is highly restricted.

Colloidal transport in periodic potentials: the role of modulated-crowding

The transport properties of colloids in external potentials are often studied at low concentrations to avoid particle-particle interactions. However, the impact of concentration on colloidal dynamics under external potentials has received limited attention. We examine the effect of concentration on the diffusivity of a quasi-2D colloidal dispersion subjected to a light-induced sinusoidal potential (interference fringes). By measuring particle diffusivity perpendicular to the fringes at various concentrations and laser powers, we find how the particle transport is governed by concentration and the structural organization induced by the external potential. Specifically, we introduce the concept of modulated-crowding for this physical scenario and characterize its influence on the long-time self-diffusion coefficient. These findings are confirmed using Brownian dynamics simulations.

Ordering and Dynamics of Interacting Colloidal Particles under Soft Confinement

Confinement can induce substantial changes in the physical properties of macromolecules in suspension. Soft confinement is a particular class of restriction where the boundaries that constraint the particles in a region of the space are not well-defined. This scenario leads to a broader structural and dynamical behavior than observed in systems enclosed between rigid walls. In this contribution, we study the ordering and diffusive properties of a two-dimensional colloidal model system subjected to a one-dimensional parabolic trap. Increasing the trap strength makes it possible to go through weak to strong confinement, allowing a dimensional transition from two- to one-dimension. The non-monotonic response of the static and dynamical properties to the gradual dimensionality change affects the system phase behavior. We find that the particle dynamics are connected to the structural transitions induced by the parabolic trap. In particular, at low and intermediate confinement regimes, complex structural and dynamical scenarios arise, where the softness of the external potential induces melting and freezing, resulting in faster and slower particle diffusion, respectively. Besides, at strong confinements, colloids move basically along one direction, and the whole system behaves structurally and dynamically similar to a one-dimensional colloidal system.

Active noise-driven particles under space-dependent friction in one dimension

We study a Langevin equation describing the stochastic motion of a particle in one dimension with coordinate x, which is simultaneously exposed to a space-dependent friction coefficient γ(x), a confining potential U(x) and nonequilibrium (i.e., active) noise. Specifically, we consider frictions γ(x)=γ_{0}+γ_{1}|x|^{p} and potentials U(x)∝|x|^{n} with exponents p=1,2 and n=0,1,2. We provide analytical and numerical results for the particle dynamics for short times and the stationary probability density functions (PDFs) for long times. The short-time behavior displays diffusive and ballistic regimes while the stationary PDFs display unique characteristic features depending on the exponent values (p,n). The PDFs interpolate between Laplacian, Gaussian, and bimodal distributions, whereby a change between these different behaviors can be achieved by a tuning of the friction strengths ratio γ_{0}/γ_{1}. Our model is relevant for molecular motors moving on a one-dimensional track and can also be realized for confined self-propelled colloidal particles.

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.

One-dimensional Gaussian-core fluid: ordering and crossover from normal diffusion to single-file dynamics

The peculiarity of a bounded pair potential in combination with strong confinement brings some quite interesting new phenomenology in the structure and dynamics of one-dimensional colloidal systems. Such behaviour is atypical in comparison with colloidal systems interacting with potentials that diverge at the origin. In this contribution, by means of molecular dynamics simulations, a confined one-dimensional model of particles interacting via a Gaussian-core pair potential is studied. We explore the effects of confinement, density and temperature on the structural and dynamical correlation functions. Our findings indicate that the static and dynamic liquid-state anomalies already reported in open systems are also present in this 1D model system. Using the radial distribution function and the static structure factor to characterise the spatial ordering, it is observed that the system remains fluid at all densities. However, when the reduced temperature is above 0.03, it displays typical features of a liquid regime, i.e., there exist short-range spatial correlations among particles. In contrast, at lower temperatures and densities, where the particle-particle interaction dominates, the system behaves structurally and dynamically similar to a hard-core repulsive system. In such a region, interestingly, there is a crossover from a liquid to a solid-like regime. At any given temperature, the system undergoes a sort of reentrant structural behaviour as the density increases. At either high densities or temperatures, particle correlations vanish, thus, the system exhibits structural and dynamical properties similar to those of an ideal gas. To examine a possible correlation between the structural anomalies and the diffusive behaviour, the mean-square displacement and the self-intermediate scattering function are also computed. From these observables, we establish the thermodynamic phase-space points where the dynamical behaviour is non-monotonic. In conjunction with the observed anomalous diffusion, we have found a dynamical crossover from single-file diffusion, which is characteristic of one-dimensional systems with a well-defined hard-core, to the ordinary Fickian diffusion present in open systems.

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.

Single-file diffusion in periodic energy landscapes: the role of hydrodynamic interactions

We report on the dynamical properties of interacting colloids confined to one dimension and subjected to external periodic energy landscapes. We particularly focus on the influence of hydrodynamic interactions on the mean-square displacement. Using Brownian dynamics simulations, we study colloidal systems with two types of repulsive interparticle interactions, namely, Yukawa and superparamagnetic potentials. We find that in the homogeneous case, hydrodynamic interactions lead to an enhancement of the particle mobility and the mean-square displacement at long times scales as t(α), with α=1/2+ε and ε being a small correction. This correction, however, becomes much more important in the presence of an external field, which breaks the homogeneity of the particle distribution along the line and, therefore, promotes a richer dynamical scenario due to the hydrodynamical coupling among particles. We provide here the complete dynamical scenario in terms of the external potential parameters: amplitude and commensurability.

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

We report computer simulation studies of the kinetics of ordering of a two-dimensional system of particles on a template with a one-dimensional periodic pattern. In equilibrium, one obtains a reentrant liquid-solid-liquid phase transition as the strength of the substrate potential is varied. We show that domains of crystalline order grow as ~t(1/z), with z~4, with a possible crossover to z~2 at late times. We argue that the t(1/4) law originates from single-file motion and annihilation of defect pairs of opposite topological charge along channels created by the template.