Dynamic Monte-Carlo simulations of diffusion limited reactions in rough nanopores

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.

Effective rate constant for nanostructured heterogeneous catalysts

There is a great deal of interest in the use of nanostructured heterogeneous catalysts, particularly those based on expensive precious metals, in order to maximise the surface to volume ratio of the catalyst, potentially reducing the cost without sacrificing performance. When there is an abundance of reactants available, the effective reactivity will depend on the surface density of the catalytically active sites. However, under diffusion-limited conditions, catalytically active sites may compete for reactants, potentially leading to diminishing returns from the use of nanostructures. In this paper we apply a mathematical homogenization approach to investigate the effect of scale and patterning on the effective activity of catalytic sites on a heterogeneous catalyst operating under diffusion-limited conditions. We test these theoretical results numerically using Monte Carlo simulations, and show that in the continuum limit the theory works well. In particular, in the limit where the mean free path is much less than the scale of patterning of catalytically active sites, the effective rate constant is found to be equal to the area-weighted harmonic mean of the rate constants on the surface. However, as the length scale of the patterns becomes comparable to the mean free path length, the simulations show that the effective activity of the system can exceed the theoretical limit suggested by the continuum theory.

Controlling the adsorption kinetics via nanostructuring: Pd nanoparticles on TiO2 nanotubes

Activity and selectivity of supported catalysts critically depend on transport and adsorption properties. Combining self-organized porous oxide films with different metal deposition techniques, we have prepared novel Pd/TiO(2) catalysts with a new level of structural control. It is shown that these systems make it possible to tune adsorption kinetics via their nanostructure. Self-organized TiO(2) nanotubular arrays (TiNTs) prepared by electrochemical methods are used as a support, on which Pd particles are deposited. Whereas physical vapor deposition (PVD) in ultrahigh vacuum (UHV) allows us to selectively grow Pd particles at the tube orifice, Pd/TiNT systems with homogeneously distributed Pd aggregates inside the tubes are available by particle precipitation (PP) from solution. Both methods also provide control over particle size and loading. Using in-situ infrared reflection absorption spectroscopy (IRAS) and molecular beam (MB) methods, we illustrate the relation between the nanostructure of the Pd/TiNT systems and their adsorption kinetics. Control over the metal nanoparticle distribution in the nanotubes leads to drastic differences in adsorption probability and saturation behavior. These differences are rationalized based on differences in surface and gas phase transport resulting from their nanostructure. The results suggest that using carefully designed metal/TiNT systems it may be possible to tailor transport processes in catalytically active materials.