The demand for subnanometer control for nanomaterial fabrication and applications has refocused attention on microporous materials (e.g., zeolites). Their ordered crystalline microstructure and finely tuned nanometer-sized pores, coupled with well-established techniques for fabricating thin, oriented films, makes them attractive for a wide range of current and future applications. Despite decades of research leveraging microporous materials for catalytic (e.g., hydrocarbon cracking, shape-selective catalysis) and non-catalytic applications (e.g., pressure swing adsorption, gas separation), rational design of new microporous films and fine tailoring of current materials demand a comprehensive understanding of these materials over a wide range of scales.

Research in our group is focused on development of such a comprehensive, fundamental understanding of zeolites and nanomaterial applications. This requires a multifaceted, multiscale approach involving research on understanding and controlling:

• Silica phase behavior and self assembly of nanoparticle zeolite precursors
• Nucleation and mechanisms of zeolite growth
• Zeolite particle morphology
• Growth and preferential thin film (membrane) orientation
• Multiscale modeling of diffusion, separation, and reaction of interacting guest molecules in zeolite thin films under non-equilibrium conditions
• Non-destructive characterization of polycrystalline zeolite thin films
• Multiscale modeling of quantum dot formation

We employ an integrated experimental (e.g., SAXS, SANS, DLS, FTIR, TGA, SEM, XRD, fluorescence confocal optical microscopy) and theoretical (e.g., molecular dynamics, kinetic Monte Carlo, hierarchical parameterization techniques, continuum mesoscopic theories) approach to elucidate critical understanding at each scale.

Silica phase behavior

One area of study has been the phase behavior of silica in aqueous solutions. Conductivity and pH measurements display a critical point at a 1:1 molar ratio of SiO2:[OH-]initial for systems containing both organic structure directing agents (quaternary ammonium cations) and inorganic cations (Na+ and Cs+). Three phases (left) have been discovered with small-angle scattering techniques: a monomer-oligomer phase, a stable suspension of silica nanoparticles, and a gel phase. For the nanoparticle phase, small-angle x-ray and neutron scattering pair distance distribution functions have been modeled using a simulated annealing MC algorithm to determine the silica structure as well as the cation amount and location (right, particle tested with tetramethylammonium hydroxide). We have found that the particles are ellipsoidal in shape, with cations located primarily on the ends. Simulations also exhibit the presence of internal cations (yellow).

Figure 1: Phase behavior of silica in aqueous solutions. For details see Fedeyko, Vlachos, and Lobo , Langmuir 21 5197-5206 (2005).

Multiscale modeling of diffusion through zeolite membranes

Molecular modeling has emerged as a powerful tool, providing deep fundamental insight into equilibrium and non-equilibrium dynamics of molecules within complex microporous materials. The current modeling paradigm focuses on host-guest systems characterized by relatively weak adsorbate-adsorbate forces, and on the inter-crystalline diffusion through perfect single-crystal membranes.

Figure 2:Comparison of equilibrium experiments with predictions of a hierarchially parameterized, complex molecular model of adsorption and diffusion in microporous materials (shown here for benzene in NaX zeolite). For details, see Snyder and Vlachos., Molecular Simulation 30 561-577 (2004).

Our multiscale approach toward modeling diffusion through zeolite membranes involves:

• Rational, hierarchical parameterization of complex host-guest (e.g., benzene in NaX zeolite) molecular models via a coupled series of mean field models, sensitivity analysis, surface response techniques, and simulated annealing.
• Enforcement of thermodynamic consistency in parameterizing molecular models simultaneously with multiple sets and types (e.g., adsorption isotherms and self-diffusivity) of equilibrium experimental data.
• Gradient KMC simulation of molecular diffusion through thin, single crystal zeolite films with appropriate crystal termination, and dynamic exchange of adsorbate molecules between the membrane surface and adjacent bulk fluid phase
• Acceleration of gradient KMC simulation of stiff molecular systems aimed at pushing the limits of computational accessibility
• Extension of gradient KMC simulations to diffusion through thin polycrystalline microporous thin films, revealing molecular level insight into the role of crystal terminations, strong adsorbate-adsorbate potentials, underlying diffusion mechanisms, and nanoscopic defects in permeation
• Development of topology-specific continuum mesoscopic theories via rigorous coarse-graining of the molecular-level description (i.e., master equation). The resulting continuum framework is capable of accessing large length and time scales characteristic of realistic membranes while retaining molecular level detail of adsorbate interactions and diffusion dynamics.

A challenge in the development of theory and detailed simulation of diffusion through microporous thin films has been the prediction of permeation performance for real membranes that exhibit permeation anomalies (e.g., unexpectedly low selectivities and deviations from single-crystal theory). Our gradient KMC simulations predict substantial sensitivity of permeation to only moderate membrane polycrystallinity. This underscores the need for quantitative characterization of microporous membrane polycrystallinity for development of predictive models of membrane permeation. Fluorescence confocal optical microscopy (FCOM) studies involving selective adsorption of dye molecules in polycrystalline features have highlighted the extent of this polycrystallinity in zeolite membranes.

Quantitative interpretation of FCOM images, however, has remained relatively elusive. Consequently, we are developing new protocols to more quantitatively characterize confocal images of dye-saturated zeolite membranes, including:

• Employing reflectance imaging to conclusively link fluorescing features observed via FCOM with the specific crystal structures and grain boundaries observed with SEM.
• Rational screening of dye molecules via molecular mechanics calculations for a priori assessment of steric compatibility and energetic interactions with zeolitic (e.g., silicalite-1 and NaX) pores and dominant crystal surfaces.
• Sequential and time-dependent adsorption studies revealing distribution of grain boundary and defect sizes through the thickness of zeolite membranes.
• Fabrication and FCOM imaging of novel standards with nanometer scale features of varying size and density for image calibration based upon fluorescence intensity and its spatial decay.
• Application of established image segmentation techniques and subsequent calculation of n-point correlation functions for quantitative comparison of differences in membrane polycrystallinity arising from preferential crystal orientation and growth conditions.

Fabrication techniques employed to grow nanoparticles (quantum dots) and nanowires on substrates follow either the top-down or the bottom-up approach. The bottom-up approach, which relies on the strain fields developing during the deposition process via the Stranski-Krastanow growth mode, has been most successful. Even though it has been possible to fabricate quantum dots with relatively narrow size and shape distribution, understanding the inherent stochastic nature of deposition and nucleation has remained elusive. For novel opto-electronic devices applications, such as lasers and optical transistors, there is a need for greater control of shape, size, and packing density. In our group we use multiscale simulation methods to model and understand such self-organization processes.