Multiscale modeling of transport and residence times in nanostructured membranes

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.

Analytic description of anomalous diffusion in heterogeneous environments: Fokker-Planck equation without fractional derivatives

This article presents a one-dimensional model of diffusion in a heterogeneous environment, which qualitatively reflects the transport properties of a polymeric membrane with carbon nanotube areas. We derive the Fokker-Planck equation from a system of stochastic equations using a diffusion regime in polymers and a ballistic diffusion regime in nanotube areas. We demonstrate how the probability density function changes in the presence of nanotubes. The mean-square displacement of nonlinear time dependence is observed, indicating anomalous diffusion. This model explains the mechanism of anomalous diffusion in a ballistic-diffusion regime. Our approach does not suppose any type of distribution and does not use a fractional differentiate apparatus.

Heterogeneous Diffusion of Alkanes in the Hierarchical Metal-Organic Framework NU-1000

The metal-organic framework (MOF) NU-1000 is a hierarchical material that comprises both micropores and mesopores in its crystalline structure. Because the pore structure is perfectly defined, NU-1000 is an interesting material for improving our understanding of diffusion in hierarchically structured materials. Here, we present molecular dynamics simulations aimed at probing the transport properties of n-alkanes in NU-1000 and introduce methods from the microrheology literature for analyzing the mean-squared displacements and their spatial heterogeneity. Adsorption occurs initially in the smaller channels, and diffusion at low loading is limited by interaction between adsorbate and framework atoms. The larger channels provide a region of low density where molecules are able to diffuse at higher rates predominantly along the channel axes. The disparate size of the channels gives rise to heterogeneity in the diffusivity of the guest molecules, whereas the asymmetry of the channels leads to anisotropic diffusion. Together, the channels form a network of "highways" and "side streets" that provide enhanced diffusion in one dimension.

Ballistic and non-ballistic gas flow through ultrathin nanopores

We show that ultrathin porous nanocrystalline silicon membranes exhibit gas permeance that is several orders of magnitude higher than other membranes. Using these membranes, gas flow obeying Knudsen diffusion has been studied in pores with lengths and diameters in the tens of nanometers regime. The components of the flow due to ballistic transport and transport after reflection from the pore walls were separated and quantified as a function of pore diameter. These results were obtained in pores made in silicon. We demonstrate that changing the pore interior to carbon leads to flow enhancement resulting from a change in the nature of molecule-pore wall interactions. This result confirms previously published flow enhancement results obtained in carbon nanotubes.

Mechanical reinforcement of nanoparticle thin films using atomic layer deposition

Thin films composed of nanoparticles exhibit synergistic properties, making them useful for numerous advanced applications. Nanoparticle thin films (NTFs), however, have a very low resistance to mechanical loading and abrasion, presenting a major bottleneck to their widespread use and commercialization. High-temperature sintering has been shown to improve the mechanical durability of NTFs on inorganic substrates; however, these high-temperature processes are not amenable to organic substrates. In this study, we demonstrate that the mechanical durability of TiO(2)/SiO(2) nanoparticle layer-by-layer (LbL) films on glass and polycarbonate substrates can be drastically improved using atomic layer deposition (ALD) at a relatively low temperature. The structure and physical properties of ALD-treated TiO(2)/SiO(2) nanoparticle LbL films are studied using spectroscopic ellipsometry, UV-vis spectroscopy, contact angle measurements, and nanoindentation. The composition of TiO(2)/SiO(2) LbL films as a function of ALD-cycle number is determined through solution ellipsometry, enabling the determination of the characteristic pore size of nanoparticle thin films. Mechanical durability is also investigated by abrasion tests, showing that the robustness of ALD-treated nanoparticle films is comparable to that of thermally calcined films. More importantly, ALD-treated nanoparticle films retain the original functionality of the TiO(2)/SiO(2) LbL films, such as superhydrophilicity and antireflection properties, demonstrating the utility of ALD as a reinforcement method for nanoparticle thin films.

Water desalination using carbon-nanotube-enhanced membrane distillation

Carbon nanotube (CNT) enhanced membrane distillation is presented for water desalination. It is demonstrated that the immobilization of the CNTs in the pores of a hydrophobic membrane favorably alters the water-membrane interactions to promote vapor permeability while preventing liquid penetration into the membrane pores. For a salt concentration of 34 000 mg L(-1) and at 80 °C, the nanotube incorporation led to 1.85 and 15 times increase in flux and salt reduction, respectively.

TEM-BASED INVESTIGATIONS ON CVD-ASSISTED GROWTH OF ZnO NANOWIRES INSIDE NANOCHANNELS OF ANODIZED ALUMINUM OXIDE TEMPLATE

The role of Chemical Vapor Deposition's (CVD) temperature and time duration on the mass transport properties and repercussions of these properties on the crystalline growth of ZnO nanowires inside Anodic Aluminum Oxide (AAO) nanotubes (aspect ratio = 1500) have been investigated.

CVD assisted growth of nanowires in AAO nanochannels was carried out for 27 min at deposition temperature of 813 K (A1) and for 180 min at 903 K (A2) under identical gas flow rates ( Ar : 23 sccm and O2 : 0.45 sccm) under a chamber pressure of 4.45 torr.

Electron diffraction patterns (SAED) of the ZnO diffused inside A1 nanotube (exposed in Focused Ion Beam milled cross-sections) showed a ringed pattern, signifying polycrystalline morphology at the tip as well as the channel bottom. For A2, a single crystal formation at least in the tip region was confirmed by the SAED pattern while the corresponding High Resolution TEM image (HRTEM) revealed a lattice spacing of 0.24 nm corresponding to the (1 0 1) growth direction of zincite (JCPDS-36-1451).

Chemical composition of the nanowires, reflected the inherent stoichiometry of preferentially nucleated ZnO in the grooved orifices of individual nanopores. Data points of normalised values of the Zn concentration (TEM-EDS line scan) versus penetration depth (~ 0.6 μm), were empirically fitted with solutions of modified Fickian diffusion equation in 1-D. The Diffusion coefficient values of the order of 0.06 nm2 s-1 and 0.22 nm2 s-1 were obtained for ZnO flow inside nanochannels of A1 and A2, respectively. Observed variations, in diffusivity and relative density, have been explained qualitatively by considering the transport of ZnO inside the nanochannels as arising from superposition of the temperature dependent contributions of the convectional viscous creep and surface diffusion components.

Cosine law at the atomic scale: toward realistic simulations of Knudsen diffusion

We propose to reconsider the diffusion of atoms in the Knudsen regime in terms of a complex dynamical reflection process. By means of molecular dynamics simulations, we emphasize the asymptotic nature of the cosine law of reflection at the atomic scale, and carefully analyze the resulting strong correlations in the reflection events. A dynamical interpretation of the accommodation coefficient associated with the slip at the wall interface is also proposed. Finally, we show that the first two moments of the stochastic process of reflection depend nonuniformly on the incident angle.