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.

Nanoparticles offer clear advantages for both passive and active penetration into biologically important membranes. However, the uptake and localization mechanism of nanoparticles within living plants, plant cells, and organelles has yet to be elucidated.1 Here, we examine the subcellular uptake and kinetic trapping of a wide range of nanoparticles for the first time, using the plant chloroplast as a model system, but validated in vivo in living plants. Confocal visible and near-infrared fluorescent microscopy and single particle tracking of goldcysteine-AF405 (GNP-Cys-AF405), streptavidin-quantum dot (SA-QD), dextran and poly(acrylic acid) nanoceria, and various polymer-wrapped single-walled carbon nanotubes (SWCNTs), including lipid-PEG-SWCNT, chitosan-SWCNT and 30-base (dAdT) sequence of ssDNA (AT) 15 wrapped SWCNTs (hereafter referred to as ss(AT) 15 -SWCNT), are used to demonstrate that particle size and the magnitude, but not the sign, of the zeta potential are key in determining whether a particle is spontaneously and kinetically trapped within the organelle, despite the negative zeta potential of the envelope. We develop a mathematical model of this lipid exchange envelope and penetration (LEEP) mechanism, which agrees well with observations of this size and zeta potential dependence. The theory predicts a critical particle size below which the mechanism fails at all zeta potentials, explaining why nanoparticles are critical for this process. LEEP constitutes a powerful particulate transport and localization mechanism for nanoparticles within the plant system.

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.

It is well-known that atoms in a substrate placed in contact with a polar solvent like water experience a finite electric field from the solvent molecules. Nevertheless, the effect of this electric field on the wetting properties of the substrate remains unknown. In this study, by carrying out molecular dynamics (MD) simulations with force field parameters derived from ab initio simulations, we develop a theoretical framework to quantify the role of the polarization of graphene in the wetting of graphitic surfaces by water. Our study shows that a self-consistent modeling of the polarization of graphene yields a water contact angle on graphite that is remarkably different from the contact angle that results if the polarization energy is instead modeled implicitly using a Lennard-Jones potential, a typical approximation used in all previous MD simulation studies on the wetting of graphitic surfaces. Our findings reveal that polarization has a more pronounced effect on the interfacial entropy of water compared to dispersion interaction. Consequently, polarization and dispersion interactions contribute differently to the wetting of graphitic surfaces. Our study significantly advances our understanding of the water–graphene interface, which is important for practical applications of graphene-based nanomaterials in osmotic power harvesting and seawater desalination.

Nanoporous graphene is a promising candidate material for gas separation membranes, due to its atomic thickness and low cross-membrane transport resistance. The mechanisms of gas permeation through graphene nanopores, in both the large and small pore size limits, have been reported in the literature. However, mechanistic insights into the crossover from the small pore size limit to the large pore size limit are still lacking. In this study, we develop a comprehensive theoretical framework to predict gas permeance through graphene nanopores having a wide range of diameters using analytical equations. We formulate the transport kinetics associated with the direct impingement from the bulk and with the surface diffusion from the adsorption layer on graphene and then combine them to predict the overall gas permeation rate using a reaction network model. We also utilize molecular dynamics simulations to validate and calibrate our theoretical model. We show that the rates of both the direct impingement and the surface diffusion pathways need to be corrected using different multiplicative factors, which are functions of temperature, gas kinetic diameter, and pore diameter. Further, we find a minor spillover pathway that originates from the surface adsorption layer, but is not included in our theoretical model. Finally, we utilize the corrected model to predict the permeances of CO2, CH4, and Ar through graphene nanopores. We show that as the pore diameter increases, gas transport through graphene nanopores can transition from being translocation dominated (pore diameter < 0.7 nm), to surface pathway dominated (pore diameter 1–2 nm), and finally to direct pathway dominated (pore diameter > 4 nm). The various gas permeation mechanisms outlined in this study will be particularly useful for the rational design of membranes made out of two-dimensional materials such as graphene for gas separation applications.