Crossover from normal diffusion to single-file diffusion of particles in a one-dimensional channel: LJ particles in zeolite zsm-22

In Situ Encapsulation of Pt Nanoparticles within Pure Silica TON Zeolites for Space-Confined Selective Hydrogenation

Straightforward encapsulation of Pt clusters (∼2 nm) into the pure silica TON-type zeolite (ZSM-22) was reached in a dry gel conversion route, where the ionic liquid template was removed via the hydrocracking-calcination-reduction approach. The obtained Pt@ZSM-22 series possessed high crystallinity, large surface area, and ultrafine Pt clusters inside the zeolite crystals. They exhibited remarkable activity in the semi-hydrogenation of phenylacetylene into styrene; the lead sample with 0.2 wt % Pt loading afforded a large turnover number up to 117,787. The preferential high affinity of the pure silica ZSM-22-encapsulated Pt clusters toward the substrate phenylacetylene rather than the hydrogenated product was derived from the unique space-confinement effect of zeolite microchannels, which is responsible for such excellent performance.

Mapping diffusivity of narrow channels into one dimension

The diffusion of particles trapped in long narrow channels occurs predominantly in one dimension. Here, a molecular-dynamics simulation is used to study the inertial dynamics of two-dimensional hard disks confined to long, narrow, structureless channels with hard walls in the no-passing regime. We show that the diffusion coefficient obtained from the mean-squared displacement can be mapped onto the exact results for the diffusion of the strictly-one-dimensional hard rod system through an effective occupied volume fraction obtained from either the equation of state or a geometric projection of the particle interaction diameters.

The effect of soft repulsive interactions on the diffusion of particles in quasi-one-dimensional channels: A hopping time approach

Fluids confined to quasi-one-dimensional channels exhibit a dynamic crossover from single file diffusion to normal diffusion as the channel becomes wide enough for particles to hop past each other. In the crossover regime, where hopping events are rare, the diffusion coefficient in the long time limit can be related to a hopping time that measures the average time it takes for a particle to escape the local cage formed by its neighbors. In this work, we show that a transition state theory (TST) that calculates the free energy barrier for two particles attempting to pass each other in the small system isobaric ensemble is able to quantitatively predict the hopping time in a system of two-dimensional soft repulsive disks [U(r_ij)=(σ/r_ij)^α] confined to a hard walled channel over a range of channel radii and degrees of particle softness measured in terms of 1/α. The free energy barrier exhibits a maximum at intermediate values of α that moves to smaller values of 1/α (harder particles) as the channel becomes narrower. However, the presence of the maximum is only observed in the hopping times for wide channels because the interaction potential dependence of the kinetic prefactor plays an increasingly important role for narrower channels. We also begin to explore how our TST approach can be used to optimize and control dynamics in confined quasi-one-dimensional fluids.

Effect of Ionic Strength and Surface Charge Density on the Kinetics of Cellulose Nanocrystal Thin Film Swelling

This work explores cellulose nanocrystal (CNC) thin films (<50 nm) and particle-particle interactions by investigating film swelling in aqueous solutions with varying ionic strength (1-100 mM). CNC film hydration was monitored in situ via surface plasmon resonance, and the kinetics of liquid uptake were quantified. The contribution of electrostatic double-layer forces to film swelling was elucidated by using CNCs with different surface charges (anionic sulfate half ester groups, high and low surface charge density, and cationic trimethylammonium groups). Total water uptake in the thin films was found to be independent of ionic strength and surface chemistry, suggesting that in the aggregated state van der Waals forces dominate over double-layer forces to hold the films together. However, the rate of swelling varied significantly. The water uptake followed Fickian behavior, and the measured diffusion constants decreased with the ionic strength gradient between the film and the solution. This work highlights that nanoparticle interactions and dispersion are highly dependent on the state of particle aggregation and that the rate of water uptake in aggregates and thin films can be tailored based on surface chemistry and solution ionic strength.

Diffusion in quasi-one-dimensional channels: A small system n, p, T, transition state theory for hopping times

Particles confined to a single file, in a narrow quasi-one-dimensional channel, exhibit a dynamic crossover from single file diffusion to Fickian diffusion as the channel radius increases and the particles begin to pass each other. The long time diffusion coefficient for a system in the crossover regime can be described in terms of a hopping time, which measures the time it takes for a particle to escape the cage formed by its neighbours. In this paper, we develop a transition state theory approach to the calculation of the hopping time, using the small system isobaric-isothermal ensemble to rigorously account for the volume fluctuations associated with the size of the cage. We also describe a Monte Carlo simulation scheme that can be used to calculate the free energy barrier for particle hopping. The theory and simulation method correctly predict the hopping times for a two-dimensional confined ideal gas system and a system of confined hard discs over a range of channel radii, but the method breaks down for wide channels in the hard discs' case, underestimating the height of the hopping barrier due to the neglect of interactions between the small system and its surroundings.