Single-File Nanochannel Persistence Lengths from NMR

Scaling laws for single-file diffusion of adhesive particles

Single-file diffusion refers to the Brownian motion in narrow channels where particles cannot pass each other. In such processes, the diffusion of a tagged particle is typically normal at short times and becomes subdiffusive at long times. For hard-sphere interparticle interaction, the time-dependent mean squared displacement of a tracer is well understood. Here we develop a scaling theory for adhesive particles. It provides a full description of the time-dependent diffusive behavior with a scaling function that depends on an effective strength of adhesive interaction. Particle clustering induced by the adhesive interaction slows down the diffusion at short times, while it enhances subdiffusion at long times. The enhancement effect can be quantified in measurements irrespective of how tagged particles are injected into the system. Combined effects of pore structure and particle adhesiveness should speed up translocation of molecules through narrow pores.

Solitons in Overdamped Brownian Dynamics

Solitons are commonly known as waves that propagate without dispersion. Here, we show that they can occur for driven overdamped Brownian dynamics of hard spheres in periodic potentials at high densities. The solitons manifest themselves as periodic sequences of different assemblies of particles moving in the limit of zero noise, where transport of single particles is not possible. They give rise to particle currents at even low temperature that appear in bandlike structures around certain hard-sphere diameters. At high temperatures, the bandlike structures are washed out by the noise, but the particle transport is still dominated by the solitons. All these predicted features should occur in a broad class of periodic systems and are amenable to experimental tests.

Driven transport of soft Brownian particles through pore-like structures: Effective size method

Single-file transport in pore-like structures constitutes an important topic for both theory and experiment. For hardcore interacting particles, a good understanding of the collective dynamics has been achieved recently. Here, we study how softness in the particle interaction affects the emergent transport behavior. To this end, we investigate the driven Brownian motion of particles in a periodic potential. The particles interact via a repulsive softcore potential with a shape corresponding to a smoothed rectangular barrier. This shape allows us to elucidate effects of mutual particle penetration and particle crossing in a controlled manner. We find that even weak deviations from the hardcore case can have a strong impact on the particle current. Despite this fact, knowledge about the transport in a corresponding hardcore system is shown to be useful to describe and interpret our findings for the softcore case. This is achieved by assigning a thermodynamic effective size to the particles based on the equilibrium density functional of hard spheres.

Single-file transport in periodic potentials: The Brownian asymmetric simple exclusion process

Single-file Brownian motion in periodic structures is an important process in nature and technology, which becomes increasingly amenable for experimental investigation under controlled conditions. To explore and understand generic features of this motion, the Brownian asymmetric simple exclusion process (BASEP) was recently introduced. The BASEP refers to diffusion models where hard spheres are driven by a constant drag force through a periodic potential. Here we derive general properties of the rich collective dynamics in the BASEP. Average currents in the steady state change dramatically with the particle size and density. For an open system coupled to particle reservoirs, extremal current principles predict various nonequilibrium phases, which we verify by Brownian dynamics simulations. For general pair interactions we discuss connections to single-file transport by traveling-wave potentials and prove the impossibility of current reversals in systems driven by a constant drag and by traveling waves.

Brownian Asymmetric Simple Exclusion Process

We study the driven Brownian motion of hard rods in a one-dimensional cosine potential with a large amplitude compared to the thermal energy. In a closed system, we find surprising features of the steady-state current in dependence of the particle density. The form of the current-density relation changes greatly with the particle size and can exhibit both a local maximum and minimum. The changes are caused by an interplay of a barrier reduction, blocking, and exchange symmetry effect. The latter leads to a current equal to that of noninteracting particles for a particle size commensurate with the period length of the cosine potential. For an open system coupled to particle reservoirs, we predict five different phases of nonequilibrium steady states to occur. Our results show that the particle size can be of crucial importance for nonequilibrium phase transitions in driven systems. Possible experiments for demonstrating our findings are pointed out.

Tracer counterpermeation analysis of diffusivity in finite-length nanopores with and without single-file dynamics

We perform a tracer counterpermeation (TCP) analysis for a stochastic model of diffusive transport through a narrow linear pore where passing of species within the pore is inhibited or even excluded (single-file diffusion). TCP involves differently labeled but otherwise identical particles from two decoupled infinite reservoirs adsorbing into opposite ends of the pore, and desorbing from either end. In addition to transient behavior, we assess steady-state concentration profiles, spatial correlations, particle number fluctuations, and diffusion fluxes through the pore. From the profiles and fluxes, we determine a generalized tracer diffusion coefficient D_{tr}(x), at various positions x within the pore. D_{tr}(x) has a plateau value in the pore center scaling inversely with the pore length, but it is enhanced near the pore openings. The latter feature reflects the effect of fluctuations in adsorption and desorption, and it is also associated with a nontrivial scaling of the concentration profiles near the pore openings.

A Tunable Magnetic Domain Wall Conduit Regulating Nanoparticle Diffusion

We demonstrate a general and robust method to confine on a plane strongly diffusing nanoparticles in water by using size tunable magnetic channels. These virtual conduits are realized with pairs of movable Bloch walls located within an epitaxially grown ferrite garnet film. We show that once inside the magnetic conduit the particles experience an effective local parabolic potential in the transverse direction, while freely diffusing along the conduit. The stiffness of the magnetic potential is determined as a function of field amplitude that varies the width of the magnetic channel. Precise control of the degree of confinement is demonstrated by tuning the applied field. The magnetic conduit is then used to realize single files of nonpassing particles and to induce periodic condensation of an ensemble of particles into parallel stripes in a completely controllable and reversible manner.

Squeezing xenon into phenylether bis-urea nanochannels

One-dimensional nanochannels, hundreds of microns in persistence length but with elliptical cross-sectional dimensions of only ∼3.7 Å × 4.8 Å, are formed by the columnar assembly of phenylether bis-urea macrocycles. Hyperpolarized Xe-129 NMR is utilized to investigate the Xe atom packing and Xe diffusion inside the needle shaped crystals. The elliptical channel structure produces a Xe-129 powder pattern characteristic of an asymmetric chemical shift tensor extending to well over 300 ppm with respect to the gas phase, reflecting the highly anisotropic electronic environment and extreme confinement of the atom. Consistent with the simple geometrical criterion, hyperpolarized tracer exchange NMR data reveals single-file diffusion in the bis-urea nanochannels.

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.

Relationship between single-file diffusion of mixed and pure gases in dipeptide nanochannels by high field diffusion NMR

Under single-file confinement, the relationship between diffusion rates of mixed and pure gases is studied experimentally for the first time and observed to differ from that for normal diffusion.

Hydrophobic dipeptide crystals: a promising Ag-free class of ultramicroporous materials showing argon/oxygen adsorption selectivity

The adsorption isotherms of nitrogen, oxygen and argon in four VA-class hydrophobic dipeptides are presented.