Diffusion of chain molecules and mixtures in carbon nanotubes: The effect of host lattice flexibility and theory of diffusion in the Knudsen regime

Connecting theory and simulation with experiment for the study of diffusion in nanoporous solids

Nanoporous solids are ubiquitous in chemical, energy, and environmental processes, where controlled transport of molecules through the pores plays a crucial role. They are used as sorbents, chromatographic or membrane materials for separations, and as catalysts and catalyst supports. Defined as materials where confinement effects lead to substantial deviations from bulk diffusion, nanoporous materials include crystalline microporous zeotypes and metal–organic frameworks (MOFs), and a number of semi-crystalline and amorphous mesoporous solids, as well as hierarchically structured materials, containing both nanopores and wider meso- or macropores to facilitate transport over macroscopic distances. The ranges of pore sizes, shapes, and topologies spanned by these materials represent a considerable challenge for predicting molecular diffusivities, but fundamental understanding also provides an opportunity to guide the design of new nanoporous materials to increase the performance of transport limited processes. Remarkable progress in synthesis increasingly allows these designs to be put into practice. Molecular simulation techniques have been used in conjunction with experimental measurements to examine in detail the fundamental diffusion processes within nanoporous solids, to provide insight into the free energy landscape navigated by adsorbates, and to better understand nano-confinement effects. Pore network models, discrete particle models and synthesis-mimicking atomistic models allow to tackle diffusion in mesoporous and hierarchically structured porous materials, where multiscale approaches benefit from ever cheaper parallel computing and higher resolution imaging. Here, we discuss synergistic combinations of simulation and experiment to showcase theoretical progress and computational techniques that have been successful in predicting guest diffusion and providing insights. We also outline where new fundamental developments and experimental techniques are needed to enable more accurate predictions for complex systems.

Cosine law for the atomically rough nanopore: Modeling lattice vibrations with a modified Lowe-Andersen thermostat

This work proposes a simulation technique that can be used to compute the thermal interaction between a rarefied gas and an atomically rough nanopore. A standard pore geometry, the slit pore, is used to derive the correct version of the cosine law in case the wall consists out of individual atoms. Having the correct cosine law drastically reduces the computational cost of calculating the gas-wall pair interaction in the rarefied gas regime since it is no longer necessary to consider a fully flexible crystal lattice. By considering only a small modification of the Lowe-Andersen thermostat, a well-known simulation technique that uses diffusive gas-heatbath collisions, we show how it can be used to incorporate lattice flexibility even if the wall is modeled as a rigid lattice.

Ultrabreathable and Protective Membranes with Sub-5 nm Carbon Nanotube Pores

Small-diameter carbon nanotubes (CNTs) are shown to enable exceptionally fast transport of water vapor under a concentration gradient driving force. Thanks to this property, membranes having sub-5 nm CNTs as conductive pores feature outstanding breathability while maintaining a high degree of protection from biothreats by size exclusion.

Transport diffusivity of propane and propylene inside SWNTs from equilibrium molecular dynamics simulations

The gas transport of two model gases (propane and propylene) inside the single-walled nanotubes (SWNTs) of various diameters was systematically investigated using the molecular dynamics (MD) simulations. The thermodynamic factor can be obtained directly from equilibrium MD simulations following the newly-minted method proposed by Schnell et al. (Chem. Phys. Lett., 2011, 504, 199-201). This process eliminates the need to implement the tedious and challenging Monte Carlo simulations for the adsorption isotherm, from which the thermodynamic factor is usually extracted. The satisfactory agreement between simulation and the literature is found for self-diffusivity, corrected diffusivity and transport diffusivity, as well as for the thermodynamic factor. The ideal selectivity for a propane-propylene mixture through SWNT membranes could be optimized through adjusting the concentration gradient. This method can be readily extended to the binary and multiple-component systems.

Influence of Structural Heterogeneity on Diffusion of CH4 and CO2 in Silicon Carbide-Derived Nanoporous Carbon

We investigate the influence of structural heterogeneity on the transport properties of simple gases in a Hybrid Reverse Monte Carlo (HRMC) constructed model of silicon carbide-derived carbon (SiC-DC). The energy landscape of the system is determined based on free energy analysis of the atomistic model. The overall energy barriers of the system for different gases are computed along with important properties, such as Henry constant and differential enthalpy of adsorption at infinite dilution, and indicate hydrophobicity of the SiC-DC structure and its affinity for CO₂ and CH₄ adsorption. We also study the effect of molecular geometry, pore structure and energy heterogeneity considering different hopping scenarios for diffusion of CO₂ and CH₄ through ultramicropores using the Nudged Elastic Band (NEB) method. It is shown that the energy barrier of a hopping molecule is very sensitive to the shape of the pore entry. We provide evidence for the influence of structural heterogeneity on self-diffusivity of methane and carbon dioxide using molecular dynamics simulation, based on a maximum in the variation of self-diffusivity with loading. A comparison of the MD simulation results with self-diffusivities from quasi-elastic neutron scattering (QENS) measurements and, with macroscopic uptake-based low-density transport coefficients, reveals the existence of internal barriers not captured in MD simulation and QENS experiments. Nevertheless, the simulation and macroscopic uptake-based diffusion coefficients agree within a factor of 2-3, indicating that our HRMC model structure captures most of the important energy barriers affecting the transport of CH₄ in the nanostructure of SiC-DC.

Smoluchowski thermostat: a realistic introduction of the tangential momentum accommodation coefficient

This work presents a simulation technique that can be used to compute the thermal interaction between a gas and a cylindrically shaped wall. The method is computationally simple and is based on the Maxwell-Smoluchowski thermal wall scenario often used for the slit pore geometry. A geometric argument is used to find the corresponding thermalization mechanism for the cylindrical confinement. The algorithm serves as a thermostat, which enables one to perform constant-temperature simulations. By means of simple numerical simulations, Smoluchowski's expression for self-diffusivity D s is then recovered in reduced units. The tangential momentum accommodation coefficient is interpreted as a coupling constant for the thermostat similar to the one used for the ordinary Andersen thermostat but applied locally onto the boundary crossing particles.

Diffusion and separation of CO2 and CH4 in silicalite, C168 schwarzite, and IRMOF-1: a comparative study from molecular dynamics simulation

Recently we have investigated the storage and adsorption selectivity of CO(2) and CH(4) in three different classes of nanoporous materialssilicalite, IRMOF-1, and C(168) schwarzite through Monte Carlo simulation (Babarao, R.; Hu, Z.; Jiang, J. Langmuir, 2007, 23, 659). In this work, the self-, corrected, and transport diffusivities of CO(2) and CH(4) in these materials are examined using molecular dynamics simulation. The activation energies at infinite dilution are evaluated from the Arrhenius fits to the diffusivities at various temperatures. As loading increases, the self-diffusivities in the three frameworks decrease as a result of the steric hindrance; the corrected diffusivities remain nearly constant or decrease approximately linearly depending on the adsorbate and framework; and the transport diffusivities generally increase except for CO(2) in IRMOF-1. The correlation effects are identified to reduce from MFI, C(168) to IRMOF-1, in accordance with the porosity increasing in the three frameworks. Predictions of self-, corrected, and transport diffusivities for pure CO(2) and CH(4) from the Maxwell-Stefan formulation match the simulation results well. In a CO(2)/CH(4) mixture, the self-diffusivities decreases with loading, and good agreement is found between simulated and predicted results. On the basis of the adsorption and self-diffusivity in the mixture, the permselectivity is found to be marginal in IRMOF-1, slightly enhanced in MFI, and greatest in C(168) schwarzite. Although IRMOF-1 has the largest storage capacity for CH(4) and CO(2), its selectivity is not satisfactory.