Not all nanopores are created equal. By definition, nanopores have characteristic diameters or conduit widths between ∼1 and 100 nm. However, the narrowest of such pores, perhaps best called Single Digit Nanopores (SDNs) and defined as those with regular diameters less than 10 nm, have only recently been accessible experimentally for precision transport measurements. This Review summarizes recent experiments on pores in this size range that yield surprising results, pointing toward extraordinary transport efficiencies and selectivities for SDN systems. These studies have identified critical gaps in our understanding of nanoscale hydrodynamics, molecular sieving, fluidic structure, and thermodynamics. These knowledge gaps are, in turn, an opportunity to discover and understand fundamentally new mechanisms of molecular and ionic transport at the nanometer scale that may inspire a host of new technologies, from novel membranes for separations and water purification to new gas-permeable materials and energy storage devices. Here we highlight seven critical knowledge gaps in the study of SDNs and identify the need for new approaches to address these topics.

Transition metal dichalcogenides (TMDs) like molybdenum disulfide (MoS2) and tungsten disulfide (WS2) are layered materials capable of growth to one monolayer thickness via chemical vapor deposition (CVD). Such CVD methods, while powerful, are notoriously difficult to extend across different reactor types and conditions, with subtle variations often confounding reproducibility, particularly for 2D TMD growth. In this work, we formulate the first generalized TMD synthetic theory by constructing a thermodynamic and kinetic growth mechanism linked to CVD reactor parameters that is predictive of specific geometric shape, size, and aspect ratio from triangular to hexagonal growth, depending on specific CVD reactor conditions. We validate our model using experimental data from Wang et al. (Chem. Mater. 2014, 26, 6371-6379) that demonstrate the systemic evolution of MoS2 morphology down the length of a flow CVD reactor where variations in gas phase concentrations can be accurately estimated using a transport model (CSulfur = 9-965 μmol/m(3); CMoO3 = 15-16 mmol/m(3)) under otherwise isothermal conditions (700 °C). A stochastic model which utilizes a site-dependent activation energy barrier based on the intrinsic TMD bond energies and a series of Evans-Polanyi relations leads to remarkable, quantitative agreement with both shape and size evolution along the reactor. The model is shown to extend to the growth of WS2 at 800 °C and MoS2 under varied process conditions. Finally, a simplified theory is developed to translate the model into a "kinetic phase diagram" of the growth process. The predictive capability of this model and its extension to other TMD systems promise to significantly increase the controlled synthesis of such materials.

Due to its atomic thickness, porous graphene with sub-nanometer pore sizes constitutes a promising candidate for gas separation membranes that exhibit ultrahigh permeances. While graphene pores can greatly facilitate gas mixture separation, there is currently no validated analytical framework with which one can predict gas permeation through a given graphene pore. In this work, we simulate the permeation of adsorptive gases, such as CO and CH, through sub-nanometer graphene pores using molecular dynamics simulations. We show that gas permeation can typically be decoupled into two steps: (1) adsorption of gas molecules to the pore mouth and (2) translocation of gas molecules from the pore mouth on one side of the graphene membrane to the pore mouth on the other side. We find that the translocation rate coefficient can be expressed using an Arrhenius-type equation, where the energy barrier and the pre-exponential factor can be theoretically predicted using the transition state theory for classical barrier crossing events. We propose a relation between the pre-exponential factor and the entropy penalty of a gas molecule crossing the pore. Furthermore, on the basis of the theory, we propose an efficient algorithm to calculate CO and CH permeances per pore for sub-nanometer graphene pores of any shape. For the CO/CH mixture, the graphene nanopores exhibit a trade-off between the CO permeance and the CO/CH separation factor. This upper bound on a Robeson plot of selectivity versus permeance for a given pore density is predicted and described by the theory. Pores with CO/CH separation factors higher than 10 have CO permeances per pore lower than 10 mol s Pa, and pores with separation factors of ∼10 have CO permeances per pore between 10 and 10 mol s Pa. Finally, we show that a pore density of 10 m is required for a porous graphene membrane to exceed the permeance-selectivity upper bound of polymeric materials. Moreover, we show that a higher pore density can potentially further boost the permeation performance of a porous graphene membrane above all existing membranes. Our findings provide insights into the potential and the limitations of porous graphene membranes for gas separation and provide an efficient methodology for screening nanopore configurations and sizes for the efficient separation of desired gas mixtures.

β-Nickel oxyhydroxide (β-NiOOH) is a promising electrocatalyst for the oxygen evolution reaction (OER), which is the more difficult half-reaction involved in water splitting. In this study, we revisit the OER activities of the two most abundant crystallographic facets of pristine β-NiOOH, the (0001) and ( 1010) facets, which expose 6-fold-lattice-oxygen-coordinated and 5-foldlattice-oxygen-coordinated Ni sites, respectively. To this end, we model various active sites on these two facets using hybrid density functional theory, which includes a fraction of the exact nonlocal Fock exchange in the electronic description of the system. By evaluating thermodynamic OER overpotentials, we show that the two active sites considered on each crystallographic facet demonstrate OER activities remarkably different from each other. However, the lowest OER overpotentials calculated for the two facets were found to be similar to each other and comparable to the overpotential for the 4-fold-lattice-oxygen-coordinated Ni site on the (1211) facet of β-NiOOH previously examined in J. Am. Chem. Soc. 2019, 141, 1, 693−705. This finding shows that all of the low-index facets investigated so far could be responsible for the experimentally observed OER activity of pristine β-NiOOH. However, the lowest overpotential active sites on these three crystallographic facets operate via different mechanisms, underscoring the importance of considering multiple OER pathways and intermediates on each crystallographic facet of a potential electrocatalyst. Specifically, our work demonstrates that consideration of previously overlooked active sites, transition-metal-ion oxidation states, reaction intermediates, and lattice-oxygen-stabilization are critical to reveal the lowest overpotential OER pathways on pristine β-NiOOH.

Atomically thin MoS2 is of great interest for electronic and optoelectronic applications because of its unique two-dimensional (2D) quantum confinement; however, the scaling of optoelectronic properties of MoS2 and its junctions with metals as a function of layer number as well the spatial variation of these properties remain unaddressed. In this work, we use photocurrent spectral atomic force microscopy (PCS-AFM) to image the current (in the dark) and photocurrent (under illumination) generated between a biased PtIr tip and MoS2 nanosheets with thickness ranging between n = 1 to 20 layers. Dark current measurements in both forward and reverse bias reveal characteristic diode behavior well-described by Fowler-Nordheim tunneling with a monolayer barrier energy of 0.61 eV and an effective barrier scaling linearly with layer number. Under illumination at 600 nm, the photocurrent response shows a marked decrease for layers up to n = 4 but increasing thereafter, which we describe using a model that accounts for the linear barrier increase at low n, but increased light absorption at larger n creating a minimum at n = 4. Comparative 2D Fourier analysis of physical height and photocurrent images shows high spatial frequency spatial variations in substrate/MoS2 contact that exceed the frequencies imposed by the underlying substrates. These results should aid in the design and understanding of optoelectronic devices based on quantum confined atomically thin MoS2.