Mechanisms and models for water transport in reverse osmosis membranes: history, critical assessment, and recent developments

Water scarcity is one of the greatest societal challenges facing humanity. Reverse osmosis (RO) desalination, a widely used membrane-based technology, has proven to be effective to augment water supply in water-stressed regions of our planet. However, progress in the design and development of RO membranes has been limited. To significantly enhance the performance of RO membranes, it is essential to acquire a deep understanding of the membrane separation and transport mechanisms. In this tutorial review, we cover the pivotal historical developments in RO technology, examine the chemical and physical properties of RO membrane materials, and critically review the models and mechanisms proposed for water transport in RO membranes. Based on recent experimental and computational findings, we conduct a thorough analysis of the key transport models-the solution-diffusion and pore-flow models-to assess their validity for accurately describing water transport in RO membranes. Our analysis involves examining the experimental evidence in favor of the solution-diffusion mechanism. Specifically, we explain whether the water content gradient within the membrane, cited as evidence for the key assumption in the solution-diffusion model, can drive a diffusive transport through RO membranes. Additionally, we review the recent molecular dynamics simulations which support the pore-flow mechanism for describing water transport in RO membranes. We conclude by providing future research directions aimed at addressing key knowledge gaps in water transport phenomena in RO membranes, with the goal of advancing the development of next-generation RO membranes.

Water transport in reverse osmosis membranes is governed by pore flow, not a solution-diffusion mechanism

We performed nonequilibrium molecular dynamics (NEMD) simulations and solvent permeation experiments to unravel the mechanism of water transport in reverse osmosis (RO) membranes. The NEMD simulations reveal that water transport is driven by a pressure gradient within the membranes, not by a water concentration gradient, in marked contrast to the classic solution-diffusion model. We further show that water molecules travel as clusters through a network of pores that are transiently connected. Permeation experiments with water and organic solvents using polyamide and cellulose triacetate RO membranes showed that solvent permeance depends on the membrane pore size, kinetic diameter of solvent molecules, and solvent viscosity. This observation is not consistent with the solution-diffusion model, where permeance depends on the solvent solubility. Motivated by these observations, we demonstrate that the solution-friction model, in which transport is driven by a pressure gradient, can describe water and solvent transport in RO membranes.

Modified Lucas-Washburn theory for fluid filling in nanotubes

Ultrafast water transport in carbon nanotubes (CNTs) has drawn a great deal of attention in a number of applications, such as water desalination, power generation, and biomolecule detection. With the recent experimental advances in water filling of isolated CNTs, the Lucas-Washburn theory for capillary rise in tubes needs to be revisited for a better understanding of the physics and dynamics of water filling in CNTs. Here, the Lucas-Washburn theory is corrected for the hydrodynamic entrance effects as well as the variation of capillary pressure and hydrodynamic properties with the radius and length of CNTs. Due to the large slippage in CNTs, inclusion of the entrance effects is important particularly for the initial stages of filling where a L∝t scaling, as opposed to L^{2}∝t, is observed in our molecular dynamics (MD) simulations. The corrected Lucas-Washburn theory is shown to predict the water filling dynamics in CNTs as observed in MD simulations. With the corrected theory, we achieve a better understanding of capillary rise and water filling dynamics in CNTs.

Molecular Simulations to Elucidate Transport Phenomena in Polymeric Membranes

Despite decades of dominance in separation technology, progress in the design and development of high-performance polymer-based membranes has been incremental. Recent advances in materials science and chemical synthesis provide opportunities for molecular-level design of next-generation membrane materials. Such designs necessitate a fundamental understanding of transport and separation mechanisms at the molecular scale. Molecular simulations are important tools that could lead to the development of fundamental structure-property-performance relationships for advancing membrane design. In this Perspective, we assess the application and capability of molecular simulations to understand the mechanisms of ion and water transport across polymeric membranes. Additionally, we discuss the reliability of molecular models in mimicking the structure and chemistry of nanochannels and transport pathways in polymeric membranes. We conclude by providing research directions for resolving key knowledge gaps related to transport phenomena in polymeric membranes and for the construction of structure-property-performance relationships for the design of next-generation membranes.

Designing polymeric membranes with coordination chemistry for high-precision ion separations

State-of-the-art polymeric membranes are unable to perform the high-precision ion separations needed for technologies essential to a circular economy and clean energy future. Coordinative interactions are a mechanism to increase sorption of a target species into a membrane, but the effects of these interactions on membrane permeability and selectivity are poorly understood. We use a multilayered polymer membrane to assess how ion-membrane binding energies affect membrane permeability of similarly sized cations: Cu²⁺, Ni²⁺, Zn²⁺, Co²⁺, and Mg²⁺. We report that metals with higher binding energy to iminodiacetate groups of the polymer more selectively permeate through the membrane in multisalt solutions than single-salt solutions. In contrast, weaker binding species are precluded from diffusing into the polymer membrane, which leads to passage proportional to binding energy and independent of membrane thickness. Our findings demonstrate that selectivity of polymeric membranes can markedly increase by tailoring ion-membrane binding energy and minimizing membrane thickness.

Ultrasensitive Detection of Dopamine, IL-6 and SARS-CoV-2 Proteins on Crumpled Graphene FET Biosensor

Universal platforms for biomolecular analysis using label-free sensing modalities can address important diagnostic challenges. Electrical field effect-sensors are an important class of devices that can enable point-of-care sensing by probing the charge in the biological entities. Use of crumpled graphene for this application is especially promising. It is previously reported that the limit of detection (LoD) on electrical field effect-based sensors using DNA molecules on the crumpled graphene FET (field-effect transistor) platform. Here, the crumpled graphene FET-based biosensing of important biomarkers including small molecules and proteins is reported. The performance of devices is systematically evaluated and optimized by studying the effect of the crumpling ratio on electrical double layer (EDL) formation and bandgap opening on the graphene. It is also shown that a small and electroneutral molecule dopamine can be captured by an aptamer and its conformation change induced electrical signal changes. Three kinds of proteins were captured with specific antibodies including interleukin-6 (IL-6) and two viral proteins. All tested biomarkers are detectable with the highest sensitivity reported on the electrical platform. Significantly, two COVID-19 related proteins, nucleocapsid (N-) and spike (S-) proteins antigens are successfully detected with extremely low LoDs. This electrical antigen tests can contribute to the challenge of rapid, point-of-care diagnostics.

Selective Fluoride Transport in Subnanometer TiO2 Pores

Synthesizing nanopores which mimic the functionality of ion-selective biological channels has been a challenging yet promising approach to advance technologies for precise ion-ion separations. Inspired by the facilitated fluoride (F^-) permeation in the biological fluoride channel, we designed a highly fluoride-selective TiO₂ film using the atomic layer deposition (ALD) technique. The subnanometer voids within the fabricated TiO₂ film (4 Å < d < 12 Å, with two distinct peaks at 5.5 and 6.5 Å), created by the hindered diffusion of ALD precursors (d = 7 Å), resulted in more than eight times faster permeation of sodium fluoride compared to other sodium halides. We show that the specific Ti-F interactions compensate for the energy penalty of F^- dehydration during the partitioning of F^- ions into the pore and allow for an intrapore accumulation of F^- ions. Concomitantly, the accumulation of F^- ions on the pore walls also enhances the transport of sodium (Na⁺) cations due to electrostatic interactions. Molecular dynamics simulations probing the ion concentration and mobility within the TiO₂ pore further support our proposed mechanisms for the selective F^- transport and enhanced Na⁺ permeation in the TiO₂ film. Overall, our work provides insights toward the design of ion-selective nanopores using the ALD technique.

Dynamic and weak electric double layers in ultrathin nanopores

The unique properties of aqueous electrolytes in ultrathin nanopores have drawn a great deal of attention in a variety of applications, such as power generation, water desalination, and disease diagnosis. Inside the nanopore, at the interface, properties of ions differ from those predicted by the classical ionic layering models (e.g., Gouy-Chapman electric double layer) when the thickness of the nanopore approaches the size of a single atom (e.g., nanopores in a single-layer graphene membrane). Here, using extensive molecular dynamics simulations, the structure and dynamics of aqueous ions inside nanopores are studied for different thicknesses, diameters, and surface charge densities of carbon-based nanopores [ultrathin graphene and finite-thickness carbon nanotubes (CNTs)]. The ion concentration and diffusion coefficient in ultrathin nanopores show no indication of the formation of a Stern layer (an immobile counter-ionic layer) as the counter-ions and nanopore atoms are weakly correlated in time compared to the strong correlation observed in thick nanopores. The weak correlation observed in ultrathin nanopores is indicative of a weak adsorption of counter-ions onto the surface compared to that of thick pores. The vanishing counter-ion adsorption (ion-wall correlation) in ultrathin nanopores leads to several orders of magnitude shorter ionic residence times (picoseconds) compared to the residence times in thick CNTs (seconds). The results of this study will help better understand the structure and dynamics of aqueous ions in ultrathin nanopores.

Ultrasensitive detection of nucleic acids using deformed graphene channel field effect biosensors

Field-effect transistor (FET)-based biosensors allow label-free detection of biomolecules by measuring their intrinsic charges. The detection limit of these sensors is determined by the Debye screening of the charges from counter ions in solutions. Here, we use FETs with a deformed monolayer graphene channel for the detection of nucleic acids. These devices with even millimeter scale channels show an ultra-high sensitivity detection in buffer and human serum sample down to 600 zM and 20 aM, respectively, which are ∼18 and ∼600 nucleic acid molecules. Computational simulations reveal that the nanoscale deformations can form 'electrical hot spots' in the sensing channel which reduce the charge screening at the concave regions. Moreover, the deformed graphene could exhibit a band-gap, allowing an exponential change in the source-drain current from small numbers of charges. Collectively, these phenomena allow for ultrasensitive electronic biomolecular detection in millimeter scale structures.

Ultrasensitive detection of nucleic acids using deformed graphene channel field effect biosensors

Field-effect transistor (FET)-based biosensors allow label-free detection of biomolecules by measuring their intrinsic charges. The detection limit of these sensors is determined by the Debye screening of the charges from counter ions in solutions. Here, we use FETs with a deformed monolayer graphene channel for the detection of nucleic acids. These devices with even millimeter scale channels show an ultra-high sensitivity detection in buffer and human serum sample down to 600 zM and 20 aM, respectively, which are ∼18 and ∼600 nucleic acid molecules. Computational simulations reveal that the nanoscale deformations can form 'electrical hot spots' in the sensing channel which reduce the charge screening at the concave regions. Moreover, the deformed graphene could exhibit a band-gap, allowing an exponential change in the source-drain current from small numbers of charges. Collectively, these phenomena allow for ultrasensitive electronic biomolecular detection in millimeter scale structures.

Nanofluidic Transport Theory with Enhancement Factors Approaching One

High performance water transport in nanopores has drawn a great deal of attention in a variety of applications, such as water desalination, power generation, and biosensing. High water transport enhancement factors in carbon-based nanopores have been reported over the classical Hagen-Poiseuille (HP) equation which does not account for the physics of transport at molecular scale. Instead, comparing the experimentally measured transport rates to that of a theory, that accounts for the microscopic physics of transport, would result in enhancement factors approaching unity. Such a theory is currently missing. Here, molecular corrections are introduced into the HP equation by considering the variation of key hydrodynamical properties (viscosity and friction) with thickness and diameter of pores in ultrathin graphene and finite-length carbon nanotubes (CNTs) using Green-Kubo relations and molecular dynamics (MD) simulations. The corrected HP (CHP) theory successfully predicts the permeation rates from nonequilibrium MD pressure driven flows. The previously reported enhancement factors over no-slip HP (of the order of 1000) approach unity when the permeations are normalized by the CHP flow rates. The results of our study will help better understand nanoscale flows in carbon-based pores and tubes.

Electrical Double Layer of Supported Atomically Thin Materials

The electrical double layer (EDL), consisting of two parallel layers of opposite charges, is foundational to many interfacial phenomena and unique in atomically thin materials. An important but unanswered question is how the "transparency" of atomically thin materials to their substrates influences the formation of the EDL. Here, we report that the EDL of graphene is directly affected by the surface energy of the underlying substrates. Cyclic voltammetry and electrochemical impedance spectroscopy measurements demonstrate that graphene on hydrophobic substrates exhibits an anomalously low EDL capacitance, much lower than what was previously measured for highly oriented pyrolytic graphite, suggesting disturbance of the EDL ("disordered EDL") formation due to the substrate-induced hydrophobicity to graphene. Similarly, electrostatic gating using EDL of graphene field-effect transistors shows much lower transconductance levels or even no gating for graphene on hydrophobic substrates, further supporting our hypothesis. Molecular dynamics simulations show that the EDL structure of graphene on a hydrophobic substrate is disordered, caused by the disruption of water dipole assemblies. Our study advances understanding of EDL in atomically thin limit.

Molybdenum disulfide and water interaction parameters

Understanding the interaction between water and molybdenum disulfide (MoS₂) is of crucial importance to investigate the physics of various applications involving MoS₂ and water interfaces. An accurate force field is required to describe water and MoS₂ interactions. In this work, water-MoS₂ force field parameters are derived using the high-accuracy random phase approximation (RPA) method and validated by comparing to experiments. The parameters obtained from the RPA method result in water-MoS₂ interface properties (solid-liquid work of adhesion) in good comparison to the experimental measurements. An accurate description of MoS₂-water interaction will facilitate the study of MoS₂ in applications such as DNA sequencing, sea water desalination, and power generation.

Strain Modulation of Graphene by Nanoscale Substrate Curvatures: A Molecular View

Spatially nonuniform strain is important for engineering the pseudomagnetic field and band structure of graphene. Despite the wide interest in strain engineering, there is still a lack of control on device-compatible strain patterns due to the limited understanding of the structure-strain relationship. Here, we study the effect of substrate corrugation and curvature on the strain profiles of graphene via combined experimental and theoretical studies of a model system: graphene on closely packed SiO₂ nanospheres with different diameters (20-200 nm). Experimentally, via quantitative Raman analysis, we observe partial adhesion and wrinkle features and find that smaller nanospheres induce larger tensile strain in graphene; theoretically, molecular dynamics simulations confirm the same microscopic structure and size dependence of strain and reveal that a larger strain is caused by a stronger, inhomogeneous interaction force between smaller nanospheres and graphene. This molecular-level understanding of the strain mechanism is important for strain engineering of graphene and other two-dimensional materials.

Antibody Subclass Detection Using Graphene Nanopores

Solid-state nanopores are promising for label-free protein detection. The large thickness, ranging from several tens of nanometers to micrometers and larger, of solid-state nanopores prohibits atomic-scale scanning or interrogation of proteins. Here, a single-atom thick graphene nanopore is shown to be highly capable of sensing and discriminating between different subclasses of IgG antibodies despite their minor and subtle variation in atomic structure. Extensive molecular dynamics (MD) simulations, rigorous statistical analysis with a total aggregate simulation time of 2.7 μs, supervised machine learning (ML), and classification techniques are employed to distinguish IgG2 from IgG3. The water flux and ionic current during IgG translocation reveal distinct clusters for IgG subclasses facilitating an additional recognition mechanism. In addition, the histogram of ionic current for each segment of IgG can provide high-resolution spatial detection. Our results show that nanoporous graphene can be used to detect and distinguish antibody subclasses with good accuracy.

Adsorption Kinetics Dictate Monolayer Self-Assembly for Both Lipid-In and Lipid-Out Approaches to Droplet Interface Bilayer Formation

The droplet interface bilayer (DIB)--a method to assemble planar lipid bilayer membranes between lipid-coated aqueous droplets--has gained popularity among researchers in many fields. Well-packed lipid monolayer on aqueous droplet-oil interfaces is a prerequisite for successfully assembling DIBs. Such monolayers can be achieved by two different techniques: "lipid-in", in which phospholipids in the form of liposomes are placed in water, and "lipid-out", in which phospholipids are placed in oil as inverse micelles. While both approaches are capable of monolayer assembly needed for bilayer formation, droplet pairs assembled with these two techniques require significantly different incubation periods and exhibit different success rates for bilayer formation. In this study, we combine experimental interfacial tension measurements with molecular dynamics simulations of phospholipids (DPhPC and DOPC) assembled from water and oil origins to understand the differences in kinetics of monolayer formation. With the results from simulations and by using a simplified model to analyze dynamic interfacial tensions, we conclude that, at high lipid concentrations common to DIBs, monolayer formation is simple adsorption controlled for lipid-in technique, whereas it is predominantly adsorption-barrier controlled for the lipid-out technique due to the interaction of interface-bound lipids with lipid structures in the subsurface. The adsorption barrier established in lipid-out technique leads to a prolonged incubation time and lower bilayer formation success rate, proving a good correlation between interfacial tension measurements and bilayer formation. We also clarify that advective flow expedites monolayer formation and improves bilayer formation success rate by disrupting lipid structures, rather than enhancing diffusion, in the subsurface and at the interface for lipid-out technique. Additionally, electrical properties of DIBs formed with varying lipid placement and type are characterized.

Electromechanical Signatures for DNA Sequencing through a Mechanosensitive Nanopore

Biological nanopores have been extensively used for DNA base detection since these pores are widely available and tunable through mutations. Distinguishing bases of nucleic acids by passing them through nanopores has so far primarily relied on electrical signals-specifically, ionic currents through the nanopores. However, the low signal-to-noise ratio makes detection of ionic currents difficult. In this study, we show that the initially closed mechanosensitive channel of large conductance (MscL) protein pore opens for single-stranded DNA (ssDNA) translocation under an applied electric field. As each nucleotide translocates through the pore, a unique mechanical signal is observed-specifically, the tension in the membrane containing the MscL pore is different for each nucleotide. In addition to the membrane tension, we found that the ionic current is also different for the four nucleotide types. The initially closed MscL adapts its opening for nucleotide translocation due to the flexibility of the pore. This unique operation of MscL provides single nucleotide resolution in both electrical and mechanical signals. Finally, we also show that the speed of DNA translocation is roughly 1 order of magnitude slower in MscL compared to Mycobacterium smegmatis porin A (MspA), suggesting MscL to be an attractive protein pore for DNA sequencing.