Applications of a general random-walk theory for confined diffusion

Lithium and Sodium Ion Binding Mechanisms and Diffusion Rates in Lignin-Based Hard Carbon Models

Hard carbons are the primary candidate for the anode of next-generation sodium-ion batteries for large-scale energy storage, as they are sustainable and can possess high charge capacity and long cycle life. These properties along with diffusion rates and ion storage mechanisms are highly dependent on nanostructures. This work uses reactive molecular dynamics simulations to examine lithium and sodium ion storage mechanisms and diffusion in lignin-based hard carbon model systems with varying nanostructures. It was found that sodium will preferentially localize on the surface of curved graphene fragments, while lithium will preferentially bind to the hydrogen dense interfaces of crystalline and amorphous carbon domains. The ion storage mechanisms are explained through ion charge and energy distributions in coordination with snapshots of the simulated systems. It was also revealed that hard carbons with small crystalline volume fractions and moderately sized sheets of curved graphene will yield the highest sodium-ion diffusion rates at ∼10-7 cm2/s. Self-diffusion coefficients were determined by mean square displacement of ions in the models with extension through a confined random walk theory.

Impact of confined geometries on hopping and trapping of motile bacteria in porous media

We use a random walk particle-tracking (RWPT) approach to elucidate the impact of porous media confinement and cell-cell interactions on bacterial transport. The model employs stochastic alternating motility states consisting of hopping movement and trapping reorientation. The stochastic motility patterns are defined based on direct visualization of individual trajectory data. We validate our model against experimental data, at single-cell resolution, of bacterial E. coli motion in three-dimensional confined porous media. Results show that the model is able to efficiently simulate the spreading dynamics of motile bacteria as it captures the impact of cell-cell interaction and pore confinement, which marks the transition to a late-time subdiffusive regime. Furthermore, the model is able to qualitatively reproduce the observed directional persistence. Our RWPT model constitutes a meshless simple method which is easy to implement and does not invoke ad hoc assumptions but represents the basis for a multiscale approach to the study of bacterial dispersal in porous systems.

Nonempirical Free Volume Viscosity Model for Alkane Lubricants under Severe Pressures

Viscosities η and diffusion coefficients D_{s} of linear and branched alkanes at pressure 0<P<0.7  GPa and temperature T=500-600  K are calculated from molecular dynamics simulations. Combining Stokes-Einstein, free volume, and random walk concepts results in an accurate viscosity model for the considered P and T. All model parameters (hydrodynamic radius, random walk step size, and step frequency) are extracted from equilibrium molecular dynamics via microscopic ensemble averages rendering η(P,T) a parameter-free predictor for lubrication simulations.

A molecular dynamics study of nuclear quantum effect on diffusivity of hydrogen molecule

In this paper, the nuclear quantum effect of the hydrogen molecule on its diffusivity was analyzed using the molecular dynamics (MD) method. The centroid MD (CMD) method was applied to reproduce the time evolution of the molecules. The diffusion coefficient of hydrogen was calculated using the Green-Kubo method over a wide temperature region, and the temperature dependence of the quantum effect of the hydrogen molecule on its diffusivity was addressed. The calculated results were compared with classical MD results based on the principle of corresponding state (PCS). It was confirmed that the difference in the diffusion coefficient calculated in the CMD and classical MD methods was small, and the PCS appears to be satisfied on the temperature dependence of the diffusion coefficient, even though the quantum effect of the hydrogen molecules was taken into account. It was clarified that this result did not suggest that the quantum effect on the diffusivity of the hydrogen molecule was small but that the two changes in the intermolecular interaction of hydrogen due to the quantum effect offset each other. Moreover, it was found that this tendency was related to the temperature dependence of the ratio of the kinetic energy of the quantum fluctuational motion to the classical kinetic energy.

Molecular mobility on graphene nanoribbons

Graphene nanoribbons (GNRs) have been proposed to be used as nanoscale mass-conveyor highways. However, how factors such as edge confinement, edge rippling, ribbon twisting, and thermal fluctuations affect the mobility of admolecules on GNRs for such application remains unknown. Using molecular dynamics (MD) simulations, we address these issues by investigating the surface mobility of a physisorbed C60 admolecule on pristine GNRs. We show that the absorption energy and edge energy barrier of a GNR are able to keep and confine the admolecule motion only on one side of the GNR. The twisting of narrow GNRs in combination with thermal fluctuations causes the admolecule to move in a helical trajectory, and thus markedly affects its mobility. As the GNR width increases, its twisting is gradually inhibited, and the motion of the admolecule becomes planar. A comparison between the results from our MD simulations and those from the confined Langevin model indicates that the distinct behavior of molecular mobility on narrow GNRs is due to their twisting rather than geometrical confinement. These findings shed light on the important factors that control the characteristics of the GNR-based mass transport highways.

Molecular dynamics simulations of water sorption in a perfluorosulfonic acid membrane

Atomistic molecular dynamics simulations are reported over a wide range of water contents and temperatures to obtain a better understanding of the structural and transport aspects of water sorption in Nafion, a perfluorosulfonic acid membrane, under equilibrium conditions. For the short Nafion chains studied, good agreement is found between the water sorption isotherms from simulations and experiments at intermediate hydration (2 ≲ λ ≲ 7, where λ is the number of water molecules per sulfonate group), suggesting that, in that range, the isotherm is insensitive to effects of polymer chain relaxation. If polymer chain relaxation were important for water sorption at these conditions, then the water uptake of experimental membranes, which contain very long chains, might be far from equilibrium, making it difficult to obtain agreement with equilibrated, short-chain simulations. At λ ≲ 7, strong water-sulfonate interactions, rather than chain relaxation, may control water sorption, despite the fact that chain relaxation time increases dramatically with decreasing hydration. Evidence for strong water-sulfonate interactions is found in the observation that sulfonate groups share water molecules in their first coordination shells at λ ≲ 7. Strong water-sulfonate interactions are also observed to influence transport properties like water diffusivity, and are as important for understanding these transport properties as larger-scale phenomena like morphology and percolation transitions. Finally, at low humidity (λ ≈ 1-2), rod-like hydrophilic clusters are observed, as well as a mechanism of water diffusion that differs qualitatively from that of water at high hydration (λ ≳ 7) and in the bulk, pure-component phase.

Extraction of self-diffusivity in systems with nondiffusive short-time behavior

We consider a toy model that captures the short-time nondiffusive behavior seen in many physical systems, to study the extraction of self-diffusivity from particle trajectories. We propose and evaluate a simple method to automatically detect the transition to diffusive behavior. We simulate the toy model to generate data sets of varying quality and test different methods of extracting the self-diffusion coefficient and characterizing its uncertainty. We find that weighted least-squares with statistical bootstrap is the most accurate and efficient means for analyzing the trajectory data. The analysis suggests an iterative recipe for designing simulations to conform to a specified level of accuracy.

Mechanism of diffusion slowdown in confined liquids

With the aid of molecular dynamics simulation, we consider why the diffusivity of liquid becomes slower as the liquid is confined to a narrower space. The diffusion coefficient of octamethylcyclotetrasiloxane liquid confined between two mica surfaces was calculated for a range of surface separations from 64 to 23 Å. The resulting separation dependence of the diffusion coefficient can be explained by considering that the molecular diffusion is an activated process. In particular, we find that the increase in the activation energy is closely correlated with the decrease of the potential energy per molecule, from which we propose a molecular-level mechanism of this confined-induced diffusion slowdown.