Fluctuation-induced quantum friction in nanoscale water flows.

The flow of water in carbon nanochannels has defied understanding thus far1, with accumulating experimental evidence for ultra-low friction, exceptionally high water flow rates and curvature-dependent hydrodynamic slippage2-5. In particular, the mechanism of water-carbon friction remains unknown6, with neither current theories7 nor classical8,9 or ab initio molecular dynamics simulations10 providing satisfactory rationalization for its singular behaviour. Here we develop a quantum theory of the solid-liquid interface, which reveals a new contribution to friction, due to the coupling of charge fluctuations in the liquid to electronic excitations in the solid. We expect that this quantum friction, which is absent in Born-Oppenheimer molecular dynamics, is the dominant friction mechanism for water on carbon-based materials. As a key result, we demonstrate a marked difference in quantum friction between the water-graphene and water-graphite interface, due to the coupling of water Debye collective modes with a thermally excited plasmon specific to graphite. This suggests an explanation for the radius-dependent slippage of water in carbon nanotubes4, in terms of the electronic excitations of the nanotubes. Our findings open the way for quantum engineering of hydrodynamic flows through the electronic properties of the confining wall.

Atomic rheology of gold nanojunctions.

Despite extensive investigations of dissipation and deformation processes in micro- and nano-sized metallic samples1-7, the mechanisms at play during the deformation of systems with ultimate (molecular) size remain unknown. Although metallic nanojunctions, which are obtained by stretching metallic wires down to the atomic level, are typically used to explore atomic-scale contacts5,8-11, it has not been possible until now to determine the full equilibrium and non-equilibrium rheological flow properties of matter at such scales. Here, by using an atomic-force microscope equipped with a quartz tuning fork, we combine electrical and rheological measurements on ångström-size gold junctions to study the non-linear rheology of this model atomic system. By subjecting the junction to increasing subnanometric deformations we observe a transition from a purely elastic regime to a plastic one, and eventually to a viscous-like fluidized regime, similar to the rheology of soft yielding materials12-14, although orders of magnitude different in length scale. The fluidized state furthermore exhibits capillary attraction, as expected for liquid capillary bridges. This shear fluidization cannot be captured by classical models of friction between atomic planes15,16 and points to an unexpected dissipative behaviour of defect-free metallic junctions at ultimate scales. Atomic rheology is therefore a powerful tool that can be used to probe the structural reorganization of atomic contacts.

Collective modes and quantum effects in two-dimensional nanofluidic channels.

Nanoscale fluid transport is typically pictured in terms of atomic-scale dynamics, as is natural in the real-space framework of molecular simulations. An alternative Fourier-space picture, that involves the collective charge fluctuation modes of both the liquid and the confining wall, has recently been successful at predicting new nanofluidic phenomena such as quantum friction and near-field heat transfer, that rely on the coupling of those fluctuations. Here, we study the charge fluctuation modes of a two-dimensional (planar) nanofluidic channel. Introducing confined response functions that generalize the notion of surface response function, we show that the channel walls exhibit coupled plasmon modes as soon as the confinement is comparable to the plasmon wavelength. Conversely, the water fluctuations remain remarkably bulk-like, with significant confinement effects arising only when the wall spacing is reduced to 7 Å. We apply the confined response formalism to predict the dependence of the solid-water quantum friction and thermal boundary conductance on channel width for model channel wall materials. Our results provide a general framework for Coulomb interactions of fluctuating matter under nanoscale confinement.

Electronic screening using a virtual Thomas-Fermi fluid for predicting wetting and phase transitions of ionic liquids at metal surfaces.

Of relevance to energy storage, electrochemistry and catalysis, ionic and dipolar liquids display unexpected behaviours-especially in confinement. Beyond adsorption, over-screening and crowding effects, experiments have highlighted novel phenomena, such as unconventional screening and the impact of the electronic nature-metallic versus insulating-of the confining surface. Such behaviours, which challenge existing frameworks, highlight the need for tools to fully embrace the properties of confined liquids. Here we introduce a novel approach that involves electronic screening while capturing molecular aspects of interfacial fluids. Although available strategies consider perfect metal or insulator surfaces, we build on the Thomas-Fermi formalism to develop an effective approach that deals with any imperfect metal between these asymptotes. Our approach describes electrostatic interactions within the metal through a 'virtual' Thomas-Fermi fluid of charged particles, whose Debye length sets the screening length λ. We show that this method captures the electrostatic interaction decay and electrochemical behaviour on varying λ. By applying this strategy to an ionic liquid, we unveil a wetting transition on switching from insulating to metallic conditions.

Enhanced nanofluidic transport in activated carbon nanoconduits.

Carbon has emerged as a unique material in nanofluidics, with reports of fast water transport, molecular ion separation and efficient osmotic energy conversion. Many of these phenomena still await proper rationalization due to the lack of fundamental understanding of nanoscale ionic transport, which can only be achieved in controlled environments. Here we develop the fabrication of 'activated' two-dimensional carbon nanochannels. Compared with nanoconduits with 'pristine' graphite walls, this enables the investigation of nanoscale ionic transport in great detail. We show that activated carbon nanochannels outperform pristine channels by orders of magnitude in terms of surface electrification, ionic conductance, streaming current and (epi-)osmotic currents. A detailed theoretical framework enables us to attribute the enhanced ionic transport across activated carbon nanochannels to an optimal combination of high surface charge and low friction. Furthermore, this demonstrates the unique potential of activated carbon for energy harvesting from salinity gradients with single-pore power density across activated carbon nanochannels, reaching hundreds of kilowatts per square metre, surpassing alternative nanomaterials.

Concluding remarks: Iontronics, from fundamentals to ion-controlled devices - Random access memories.

Is this the dawn of iontronics? Iontronics underpins the notion of devices and ionic machines, whereby ion and water also act as information carriers. Thinking about iontronics gives a vision and a road map, with applications in the water-energy nexus.

Disentangling 1/f noise from confined ion dynamics.

Ion transport through biological and solid-state nanochannels is known to be a highly noisy process. The power spectrum of current fluctuations is empirically known to scale like the inverse of frequency, following the long-standing yet poorly understood Hooge's law. Here, we report measurements of current fluctuations across nanometer-scale two-dimensional channels with different surface properties. The structure of fluctuations is found to depend on the channel's material. While in pristine channels current fluctuations scale like 1/f1+a with a = 0-0.5, the noise power spectrum of activated graphite channels displays different regimes depending on frequency. Based on these observations, we develop a theoretical formalism directly linking ion dynamics and current fluctuations. We predict that the noise power spectrum takes the form 1/f × Schannel(f), where 1/f fluctuations emerge in fluidic reservoirs on both sides of the channel and Schannel describes fluctuations inside it. Deviations to Hooge's law thus allow direct access to the ion transport dynamics of the channel - explaining the entire phenomenology observed in experiments on 2D nanochannels. Our results demonstrate how current fluctuations can be used to characterize nanoscale ion dynamics.

Nanofluidics at the crossroads.

Nanofluidics, the field interested in flows at the smallest scales, has grown at a fast pace, reaching an ever finer control of fluidic and ionic transport at the molecular level. Until now, artificial pores are far from reaching the wealth of functionalities of biological channels that regulate sensory detection, biological transport, and neurostransmission-all while operating at energies comparable to thermal noise. Here, we argue that artificial ionic machines can be designed by harnessing the entire wealth of phenomena available at the nanoscales and exploiting techniques developed in various fields of physics. As they are generally based on solid-state nanopores, rather than soft membranes and proteins, they should, in particular, aim at taking advantage of their specific properties, such as their electronic structure or their ability to interact with light. These observations call for the design of new ways of probing nanofluidic systems. Nanofluidics is now at the crossroads, there are new avenues to build complex ionic machines, and this may allow to develop new functionalities inspired by nature.

Unified non-equilibrium simulation methodology for flow through nanoporous carbon membrane.

The emergence of new nanoporous materials, based, e.g., on 2D materials, offers new avenues for water filtration and energy. There is, accordingly, a need to investigate the molecular mechanisms at the root of the advanced performances of these systems in terms of nanofluidic and ionic transport. In this work, we introduce a novel unified methodology for Non-Equilibrium classical Molecular Dynamic simulations (NEMD), allowing to apply likewise pressure, chemical potential, and voltage drops across nanoporous membranes and quantifying the resulting observables characterizing confined liquid transport under such external stimuli. We apply the NEMD methodology to study a new type of synthetic Carbon NanoMembranes (CNM), which have recently shown outstanding performances for desalination, keeping high water permeability while maintaining full salt rejection. The high water permeance of CNM, as measured experimentally, is shown to originate in prominent entrance effects associated with negligible friction inside the nanopore. Beyond, our methodology allows us to fully calculate the symmetric transport matrix and the cross-phenomena, such as electro-osmosis, diffusio-osmosis, and streaming currents. In particular, we predict a large diffusio-osmotic current across the CNM pore under a concentration gradient, despite the absence of surface charges. This suggests that CNMs are outstanding candidates as alternative, scalable membranes for osmotic energy harvesting.

Ion filling of a one-dimensional nanofluidic channel in the interaction confinement regime.

Ion transport measurements are widely used as an indirect probe for various properties of confined electrolytes. It is generally assumed that the ion concentration in a nanoscale channel is equal to the ion concentration in the macroscopic reservoirs it connects to, with deviations arising only in the presence of surface charges on the channel walls. Here, we show that this assumption may break down even in a neutral channel due to electrostatic correlations between the ions arising in the regime of interaction confinement, where Coulomb interactions are reinforced due to the presence of the channel walls. We focus on a one-dimensional channel geometry, where an exact evaluation of the electrolyte's partition function is possible with a transfer operator approach. Our exact solution reveals that in nanometer-scale channels, the ion concentration is generally lower than in reservoirs and depends continuously on the bulk salt concentration, in contrast to the conventional mean-field theory that predicts an abrupt filling transition. We develop a modified mean-field theory taking into account the presence of ion pairs that agrees quantitatively with the exact solution and provides predictions for experimentally relevant observables, such as the ionic conductivity. Our results will guide the interpretation of nanoscale ion transport measurements.

Massive radius-dependent flow slippage in carbon nanotubes.

Measurements and simulations have found that water moves through carbon nanotubes at exceptionally high rates owing to nearly frictionless interfaces. These observations have stimulated interest in nanotube-based membranes for applications including desalination, nano-filtration and energy harvesting, yet the exact mechanisms of water transport inside the nanotubes and at the water-carbon interface continue to be debated because existing theories do not provide a satisfactory explanation for the limited number of experimental results available so far. This lack of experimental results arises because, even though controlled and systematic studies have explored transport through individual nanotubes, none has met the considerable technical challenge of unambiguously measuring the permeability of a single nanotube. Here we show that the pressure-driven flow rate through individual nanotubes can be determined with unprecedented sensitivity and without dyes from the hydrodynamics of water jets as they emerge from single nanotubes into a surrounding fluid. Our measurements reveal unexpectedly large and radius-dependent surface slippage in carbon nanotubes, and no slippage in boron nitride nanotubes that are crystallographically similar to carbon nanotubes, but electronically different. This pronounced contrast between the two systems must originate from subtle differences in the atomic-scale details of their solid-liquid interfaces, illustrating that nanofluidics is the frontier at which the continuum picture of fluid mechanics meets the atomic nature of matter.

Interaction confinement and electronic screening in two-dimensional nanofluidic channels.

The transport of fluids at the nanoscale is fundamental to manifold biological and industrial processes, ranging from neurotransmission to ultrafiltration. Yet, it is only recently that well-controlled channels with cross sections as small as a few molecular diameters became an experimental reality. When aqueous electrolytes are confined within such channels, the Coulomb interactions between the dissolved ions are reinforced due to dielectric contrast at the channel walls: We dub this effect "interaction confinement." Yet, no systematic way of computing these confined interactions has been proposed beyond the limiting cases of perfectly metallic or perfectly insulating channel walls. Here, we introduce a new formalism, based on the so-called surface response functions, that expresses the effective Coulomb interactions within a two-dimensional channel in terms of the wall's electronic structure, described to any desired level of precision. We use it to demonstrate that in few-nanometer-wide channels, the ionic interactions can be tuned by the wall material's screening length. We illustrate this approach by implementing these interactions in Brownian dynamics simulations of a strongly confined electrolyte and show that the resulting ionic conduction can be adjusted between Ohm's law and a Wien effect behavior. Our results provide a quantitative approach to tuning nanoscale ion transport through the electronic properties of the channel wall material.

Chemisorbed vs physisorbed surface charge and its impact on electrokinetic transport: Carbon vs boron nitride surface.

The possibility of controlling electrokinetic transport through carbon and hexagonal boron nitride (hBN) nanotubes has recently opened new avenues for nanofluidic approaches to face outstanding challenges such as energy production and conversion or water desalination. The pH-dependence of experimental transport coefficients points to the sorption of hydroxide ions as the microscopic origin of the surface charge and recent ab initio calculations suggest that these ions behave differently on carbon and hBN, with only physisorption on the former and both physisorption and chemisorption on the latter. Using classical non-equilibrium molecular dynamics simulations of interfaces between an aqueous electrolyte and three models of hBN and graphite surfaces, we demonstrate the major influence of the sorption mode of hydroxide ions on the interfacial transport properties. Physisorbed surface charge leads to a considerable enhancement of the surface conductivity as compared to its chemisorbed counterpart, while values of the ζ-potential are less affected. The analysis of the MD results for the surface conductivity and ζ-potential in the framework of Poisson-Boltzmann-Stokes theory, as is usually done to analyze experimental data, further confirms the importance of taking into account both the mobility of surface hydroxide ions and the decrease in the slip length with increasing titratable surface charge density.

Mechanically activated ionic transport across single-digit carbon nanotubes.

Fluid and ionic transport at the nanoscale has recently demonstrated a wealth of exotic behaviours1-14. However, artificial nanofluidic devices15-18 are still far from demonstrating the advanced functionalities existing in biological systems, such as electrically and mechanically activated transport19,20. Here, we focus on ionic transport through 2-nm-radius individual multiwalled carbon nanotubes under the combination of mechanical and electrical forcings. Our findings evidence mechanically activated ionic transport in the form of an ionic conductance that depends quadratically on the applied pressure. Our theoretical study relates this behaviour to the complex interplay between electrical and mechanical drivings, and shows that the superlubricity of the carbon nanotubes4-8,21 is a prerequisite to attaining mechanically activated transport. The pressure sensitivity shares similarities with the response of biological mechanosensitive ion channels19,20, but observed here in an artificial system. This paves the way to build new active nanofluidic functionalities inspired by complex biological machinery.

Dramatic pressure-sensitive ion conduction in conical nanopores.

Ion transporters in Nature exhibit a wealth of complex transport properties such as voltage gating, activation, and mechanosensitive behavior. When combined, such processes result in advanced ionic machines achieving active ion transport, high selectivity, or signal processing. On the artificial side, there has been much recent progress in the design and study of transport in ionic channels, but mimicking the advanced functionalities of ion transporters remains as yet out of reach. A prerequisite is the development of ionic responses sensitive to external stimuli. In the present work, we report a counterintuitive and highly nonlinear coupling between electric and pressure-driven transport in a conical nanopore, manifesting as a strong pressure dependence of the ionic conductance. This result is at odds with standard linear response theory and is akin to a mechanical transistor functionality. We fully rationalize this behavior on the basis of the coupled electrohydrodynamics in the conical pore by extending the Poisson-Nernst-Planck-Stokes framework. The model is shown to capture the subtle mechanical balance occurring within an extended spatially charged zone in the nanopore. The pronounced sensitivity to mechanical forcing offers leads in tuning ion transport by mechanical stimuli. The results presented here provide a promising avenue for the design of tailored membrane functionalities.

Resonant osmosis across active switchable membranes.

To overcome the traditional paradigm of filtration, where separation is essentially performed upon steric sieving principles, we explore the concept of dynamic osmosis through active membranes. A partially permeable membrane presents a time-tuneable feature that changes the effective pore interaction with the solute and thus actively changes permeability with time. In general, we find that slow flickering frequencies effectively decrease the osmotic pressure and large flickering frequencies do not change it. In the presence of an asymmetric membrane, we find a resonant frequency where pumping of the solute is performed and can be analyzed in terms of ratchet transport. We discuss and highlight the properties of this resonant osmotic transport. Furthermore, we show that dynamic osmosis allows us to pump the solute at the nanoscale using less energy than reverse osmosis. This opens new possibilities to build advanced filtration devices and design artificial ionic machinery.

Osmosis, from molecular insights to large-scale applications.

Osmosis is a universal phenomenon occurring in a broad variety of processes and fields. It is the archetype of entropic forces, both trivial in its fundamental expression - the van 't Hoff perfect gas law - and highly subtle in its physical roots. While osmosis is intimately linked with transport across membranes, it also manifests itself as an interfacial transport phenomenon: the so-called diffusio-osmosis and -phoresis, whose consequences are presently actively explored for example for the manipulation of colloidal suspensions or the development of active colloidal swimmers. Here we give a global and unifying view of the phenomenon of osmosis and its consequences with a multi-disciplinary perspective. Pushing the fundamental understanding of osmosis allows one to propose new perspectives for different fields and we highlight a number of examples along these lines, for example introducing the concepts of osmotic diodes, active separation and far from equilibrium osmosis, raising in turn fundamental questions in the thermodynamics of separation. The applications of osmosis are also obviously considerable and span very diverse fields. Here we discuss a selection of phenomena and applications where osmosis shows great promises: osmotic phenomena in membrane science (with recent developments in separation, desalination, reverse osmosis for water purification thanks in particular to the emergence of new nanomaterials); applications in biology and health (in particular discussing the kidney filtration process); osmosis and energy harvesting (in particular, osmotic power and blue energy as well as capacitive mixing); applications in detergency and cleaning, as well as for oil recovery in porous media.

Adsorption Kinetics in Open Nanopores as a Source of Low-Frequency Noise.

Ionic current measurements through solid-state nanopores consistently show a power spectral density that scales as 1/f α at low frequency f, with an exponent α ∼ 0.5-1.5, but strikingly, the physical origin of this behavior remains elusive. Here, we perform simulations of particles reversibly adsorbing at the surface of a nanopore and show that the fluctuations in the number of adsorbed particles exhibit low-frequency pink noise. We furthermore propose theoretical modeling for the time-dependent adsorption of particles on the nanopore surface for various geometries, which predicts a frequency spectrum in very good agreement with the simulation results. Altogether, our results highlight that the low-frequency noise takes its origin in the reversible adsorption of ions at the pore surface combined with the long-lasting excursions of the ions in the reservoirs. The scaling regime of the power spectrum extends down to a cutoff frequency which is far smaller than simple diffusion estimates. Using realistic values for the pore dimensions and the adsorption-desorption kinetics, this predicts the observation of pink noise for frequencies down to the hertz for a typical solid-state nanopore, in good agreement with experiments.

MicroMegascope based dynamic surface force apparatus.

Surface force apparatus (SFA) allows accurate resolving of the interfacial properties of fluids confined between extended surfaces. The accuracy of the SFA makes it an ubiquitous tool for the nanoscale mechanical characterization of soft matter systems. The SFA traditionally measures force-distance profiles through interferometry with subnanometric distance precision. However, these techniques often require a dedicated and technically demanding experimental setup, and there remains a need for versatile and simple force-distance measurement tools. Here we present a MicroMegascope based dynamic SFA capable of accurate measurement of the dynamic force profile of a liquid confined between a millimetric sphere and a planar substrate. Normal and shear mechanical impedance is measured within the classical frequency modulation framework. We measure rheological and frictional properties from micrometric to molecular confinement. We also highlight the resolution of small interfacial features such as ionic liquid layering. This apparatus shows promise as a versatile force-distance measurement device for exotic surfaces or extreme environments.

Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube.

New models of fluid transport are expected to emerge from the confinement of liquids at the nanoscale, with potential applications in ultrafiltration, desalination and energy conversion. Nevertheless, advancing our fundamental understanding of fluid transport on the smallest scales requires mass and ion dynamics to be ultimately characterized across an individual channel to avoid averaging over many pores. A major challenge for nanofluidics thus lies in building distinct and well-controlled nanochannels, amenable to the systematic exploration of their properties. Here we describe the fabrication and use of a hierarchical nanofluidic device made of a boron nitride nanotube that pierces an ultrathin membrane and connects two fluid reservoirs. Such a transmembrane geometry allows the detailed study of fluidic transport through a single nanotube under diverse forces, including electric fields, pressure drops and chemical gradients. Using this device, we discover very large, osmotically induced electric currents generated by salinity gradients, exceeding by two orders of magnitude their pressure-driven counterpart. We show that this result originates in the anomalously high surface charge carried by the nanotube's internal surface in water at large pH, which we independently quantify in conductance measurements. The nano-assembly route using nanostructures as building blocks opens the way to studying fluid, ionic and molecule transport on the nanoscale, and may lead to biomimetic functionalities. Our results furthermore suggest that boron nitride nanotubes could be used as membranes for osmotic power harvesting under salinity gradients.