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.

Ions in ionic liquids and concentrated electrolytes reside in a crowded, strongly interacting environment, leading to the formation of discrete layers of charges at interfaces and spin-glass structure in the bulk. Here, we propose a simple theory that captures the coupling between steric and electrostatic forces in ionic liquids. The theory predicts the formation of discrete layers of charge at charged interfaces. Further from the interface, or at low polarization of the electrode, the model outputs slowly decaying oscillations in the charge density with a wavelength of a single ion diameter, as shown by analysis of the gradient expansion. The gradient expansion suggests a new structure for partial differential equations describing the electrostatic potential at charged interfaces. We find quantitative agreement between the theory and molecular simulations in the differential capacitance and concentration profiles.

Agricultural development, extensive industrialization, and rapid growth of the global population have inadvertently been accompanied by environmental pollution. Water pollution is exacerbated by the decreasing ability of traditional treatment methods to comply with tightening environmental standards. This review provides a comprehensive description of the principles and applications of electrochemical methods for water purification, ion separations, and energy conversion. Electrochemical methods have attractive features such as compact size, chemical selectivity, broad applicability, and reduced generation of secondary waste. Perhaps the greatest advantage of electrochemical methods, however, is that they remove contaminants directly from the water, while other technologies extract the water from the contaminants, which enables efficient removal of trace pollutants. The review begins with an overview of conventional electrochemical methods, which drive chemical or physical transformations via Faradaic reactions at electrodes, and proceeds to a detailed examination of the two primary mechanisms by which contaminants are separated in nondestructive electrochemical processes, namely electrokinetics and electrosorption. In these sections, special attention is given to emerging methods, such as shock electrodialysis and Faradaic electrosorption. Given the importance of generating clean, renewable energy, which may sometimes be combined with water purification, the review also discusses inverse methods of electrochemical energy conversion based on reverse electrosorption, electrowetting, and electrokinetic phenomena. The review concludes with a discussion of technology comparisons, remaining challenges, and potential innovations for the field such as process intensification and technoeconomic optimization.

The standard model for diffuse charge phenomena in colloid science, electrokinetics, and biology is the Poisson−Boltzmann mean-field theory, which breaks down for multivalent ions and large surface charge densities because of electrostatic correlations. In this paper, we formulate a predictive continuum theory of correlated electrolytes based on two extensions of the Bazant− Storey−Kornyshev (BSK) framework: (i) a physical boundary condition enforcing continuity of the Maxwell stress at a charged interface, which upholds the contact theorem for dilute primitivemodel electrolytes, and (ii) scaling relationships for the correlation length, for a one-component plasma at a charged plane and around a cylinder, as well as a dilute z:1 electrolyte screening a planar surface. In these cases, the theory accurately reproduces Monte Carlo simulation results from weak to strong coupling, and extensions are possible for more complex models of electrolytes and ionic liquids.

Aqueous electrolyte solutions containing multivalent ions exhibit various intriguing properties, including attraction between like-charged colloidal particles, which results from strong ion–ion correlations. In contrast, the classical Derjaguin–Landau–Verwey–Overbeek theory of colloidal stability, based on the Poisson–Boltzmann mean-field theory, always predicts a repulsive electrostatic contribution to the disjoining pressure. Here, we formulate a general theory of surface forces, which predicts that the contribution to the disjoining pressure resulting from ion–ion correlations is always attractive and can readily dominate over entropic-induced repulsions for solutions containing multivalent ions, leading to the phenomenon of like-charge attraction. Ion-specific short-range hydration interactions, as well as surface charge regulation, are shown to play an important role at smaller separation distances but do not fundamentally change these trends. The theory is able to predict the experimentally observed strong cohesive forces reported in cement pastes, which result from strong ion–ion correlations involving the divalent calcium ion.