The past decade has seen researchers develop and apply novel technologies for biomolecular detection, at times approaching hard limits imposed by physics and chemistry. In nearly all sensors, the transport of target molecules to the sensor can play as critical a role as the chemical reaction itself in governing binding kinetics, and ultimately performance. Yet rarely does an analysis of the interplay between diffusion, convection and reaction motivate experimental design or interpretation. Here we develop a physically intuitive and practical understanding of analyte transport for researchers who develop and employ biosensors based on surface capture. We explore the qualitatively distinct behaviors that result, develop rules of thumb to quickly determine how a given system will behave, and derive order-of-magnitude estimates for fundamental quantities of interest, such as fluxes, collection rates and equilibration times. We pay particular attention to collection limits for micro- and nanoscale sensors, and highlight unexplained discrepancies between reported values and theoretical limits.

Crystalline mesoporous molecular sieves have long been sought as solid acid catalysts for organic reactions involving large molecules. We synthesized a series of mesoporous molecular sieves that possess crystalline microporous walls with zeolitelike frameworks, extending the application of zeolites to the mesoporous range of 2 to 50 nanometers. Hexagonally ordered or disordered mesopores are generated by surfactant aggregates, whereas multiple cationic moieties in the surfactant head groups direct the crystallization of microporous aluminosilicate frameworks. The wall thicknesses, framework topologies, and mesopore sizes can be controlled with different surfactants. The molecular sieves are highly active as catalysts for various acid-catalyzed reactions of bulky molecular substrates, compared with conventional zeolites and ordered mesoporous amorphous materials.

Identifying and characterizing defects in crystalline solids is a challenging problem, particularly for lithium-ion intercalation materials, which often exhibit multiple stable oxidation and spin states as well as local ordering of lithium and charges. Here, we reveal the existence of characteristic lithium defect environments in the crystalline lithium-ion battery electrode LiVPO 4 F and establish the relative sub-nanometer-scale proximities between them. Well-crystallized LiVPO 4 F samples were synthesized with the expected tavorite-like structure, as established by X-ray diffraction (XRD) and scanning transmission electron microscopy (STEM) measurements. Solidstate 7 Li nuclear magnetic resonance (NMR) spectra reveal unexpected paramagnetic 7 Li environments that can account for up to 20% of the total lithium content. Multi-dimensional and site-selective solid-state 7 Li NMR experiments using finite-pulse radio-frequency-driven recoupling (fp-RFDR) establish unambiguously that the unexpected lithium environments are associated with defects within the LiVPO 4 F crystal structure, revealing the existence of dipole-dipole-coupled defect pairs. The lithium defects exhibit local electronic environments that are distinct from lithium ions in the crystallographic LiVPO 4 F site, which result from altered oxidation and/or spin states of nearby paramagnetic vanadium atoms. The results provide a general strategy for identifying and characterizing lithium defect environments in crystalline solids, including paramagnetic materials with short 7