Thermodynamic and Dynamic Models for Directed Assembly of Small Ensembles of Colloidal Particles

Self and directed assembly of finite clusters (10 to 1000) of colloidal particles into crystalline objects is an emerging area of scientific interest that finds applica- tions in manufacturing of photonic crystals and other meta-materials. Such assembly problems are also of fundamental scientific interest because they involve thermodynamically small systems, with a number of particles that is far below the bulk limit. Robust methods for assembling defect-free target structures will ultimately require reduced-dimension process models that link the particle-level dynamics of the colloids to the actuator states. We have developed a three-part strategy for developing such process models. First, we employ diffusion mapping (DMaps), a machine learning technique, on raw trajectory data to identify slow, low-dimensional manifolds in the system dy- namics. Second, we identify convenient observables, or order parameters (OPs), that strongly correlate with low-dimensional DMap coordinates; this step may involve a feedback loop with the DMap process itself. Third, we use a Fokker-Planck or Smoluchowski formalism to build free energy and diffusivity landscapes in the OPs, which serve as our reduced-dimension process models. We have applied this technique to two model systems in this work. The first system comprises 32 silica particles, which interact via a temperature-tunable depletion interaction potential. This system shows transitions between an expanded and condensed phase when the pair interaction strength is changed by a few kBT . The second system comprises 210 quasi-2D silica particles confined within quadrupole electrodes and the interaction strength, which is of the order of few kBT , is tuned by an externally applied electric field. This system shows interesting features like the formation and annealing of polycrystalline microstructures as the magnitude of the applied field is changed. We systematically compare and contrast the DMap analysis on both these model systems. We construct an optimal control policy map in the low-dimensional DMap coordinates using dynamic programming. The free energy and diffusivity landscapes along with the control policy map is used to robustly assemble perfect colloidal crystals. We have also examined the phase behavior of the depletion potential system via a histogram-based simulation approach. We conducted replica exchange Monte Carlo simulations of these small colloidal clusters and generated potential energy histograms for various levels of the osmotic pressure that controls the interaction strength. By carefully tuning the osmotic pressure, we observed bimodal distributions in the potential energy space, which is indicative of coexistence between fluid-like and solid-like configurations. Quantitative analysis of these histograms yield phase coexistence curves for these small clusters and we report comparisons with bulk colloidal phase diagrams

Hierarchical ZIF‑8 Materials via Acid Gas-Induced Defect Sites: Synthesis, Characterization, and Functional Properties

Microporous metal-organic frameworks (MOFs) have been widely studied for molecular separation and catalysis. The uniform micropores of MOFs (<2 nm) can introduce diffusion limitations and render the interiors of the crystal inaccessible to target molecules. The introduction of hierarchical porosity (interconnected micro and mesopores) can enhance intra-crystalline diffusion while maintaining the separation/catalytic selectivity. Conventional hierarchical MOF synthesis involves complex strategies such as elongated linkers, soft templating, and sacrificial templates. Here, we demonstrate a more general approach using our controlled acid gas-enabled degradation and reconstruction (Solvent-Assisted Crystal Redemption) strategy. Selective linker labilization of ZIF-8 is shown to generate a hierarchical pore structure with mesoporous cages (∼50 nm) while maintaining microporosity. Detailed structural and spectroscopic characterization of the controlled degradation, linker insertion, and subsequent linker thermolysis is presented to show the clustering of acid gas-induced defects and the generation of mesopores. These findings indicate the generality of controlled degradation and reconstruction as a means for linker insertion in a wider variety of MOFs and creating hierarchical porosity. Enhanced molecular diffusion and catalytic activity in the hierarchical ZIF-8 are demonstrated by the adsorption kinetics of 1-butanol and a Knoevenagel condensation reaction

How Reproducible Are Surface Areas Calculated from the BET Equation?

Porosity and surface area analysis play a prominent role in modern materials science, where their determination spans the fields of natural sciences, engineering, geology and medical research. At the heart of this sits the Brunauer-Emmett-Teller (BET) theory,[1] which has been a remarkably successful contribution to the field of materials science. The BET method was developed in the 1930s for open surfaces but is now the most widely used metric for the estimation of surface areas of micro- and mesoporous materials.[2] Since the BET method was first developed, there has been an explosion in the field of nanoporous materials with the discovery of synthetic zeolites,[3] nanostructured silicas,[4–6] metal-organic frameworks (MOFs),[7] and others. Despite its widespread use, the manual calculation of BET surface areas causes a significant spread in reported areas, resulting in reproducibility problems in both academia and industry. To prove this, we have brought together 60 labs with strong track records on the study of nanoporous materials. We provided eighteen already measured raw adsorption isotherms and asked these researchers to calculate the corresponding BET areas. This round-robin exercise resulted in a wide range of values for each isotherm. We demonstrate here that the reproducibility of BET area determination from identical isotherms is a largely ignored issue, raising critical concerns over the reliability of reported BET areas in micro- and mesoporous materials in the literature. To solve this major issue, we have developed a new computational approach to accurately and systematically determine the BET area of nanoporous materials. Our software, called BET Surface Identification (BETSI), expands on the well-known Rouquerol criteria and makes, for the first time, an unambiguous BET area assignment possible

How Reproducible are Surface Areas Calculated from the BET Equation?

Funder: Sandia National Laboratories; Id: http://dx.doi.org/10.13039/100006234Funder: U.S. Department of Energy; Id: http://dx.doi.org/10.13039/100000015Funder: Office of Energy Efficiency and Renewable Energy; Id: http://dx.doi.org/10.13039/100006134Funder: Hydrogen and Fuel Cell Technologies Office; Id: http://dx.doi.org/10.13039/100010268Funder: Active Co. ResearchFunder: Spanish MICINNPorosity and surface area analysis play a prominent role in modern materials science. At the heart of this sits the Brunauer-Emmett-Teller (BET) theory, which has been a remarkably successful contribution to the field of materials science. The BET method was developed in the 1930s for open surfaces but is now the most widely used metric for the estimation of surface areas of micro- and mesoporous materials. Despite its widespread use, the calculation of BET surface areas causes a spread in reported areas, resulting in reproducibility problems in both academia and industry. To prove this, for this analysis, 18 already-measured raw adsorption isotherms were provided to sixty-one labs, who were asked to calculate the corresponding BET areas. This round-robin exercise resulted in a wide range of values. Here, the reproducibility of BET area determination from identical isotherms is demonstrated to be a largely ignored issue, raising critical concerns over the reliability of reported BET areas. To solve this major issue, a new computational approach to accurately and systematically determine the BET area of nanoporous materials is developed. The software, called "BET surface identification" (BETSI), expands on the well-known Rouquerol criteria and makes an unambiguous BET area assignment possible