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At least 451 records · Page 25

Evaluation of Electrodialysis Desalination Performance of Novel Bioinspired and Conventional Ion Exchange Membranes with Sodium Chloride Feed Solutions

Electrodialysis (ED) desalination performance of different conventional and laboratory-scale ion exchange membranes (IEMs) has been evaluated by many researchers, but most of these studies used their own sets of experimental parameters such as feed solution compositions and concentrations, superficial velocities of the process streams (diluate, concentrate, and electrode rinse), applied electrical voltages, and types of IEMs. Thus, direct comparison of ED desalination performance of different IEMs is virtually impossible. While the use of different conventional IEMs in ED has been reported, the use of bioinspired ion exchange membrane has not been reported yet. The goal of this study was to evaluate the ED desalination performance differences between novel laboratory‑scale bioinspired IEM and conventional IEMs by determining (i) limiting current density, (ii) current density, (iii) current efficiency, (iv) salinity reduction in diluate stream, (v) normalized specific energy consumption, and (vi) water flux by osmosis as a function of (a) initial concentration of NaCl feed solution (diluate and concentrate streams), (b) superficial velocity of feed solution, and (c) applied stack voltage per cell-pair of membranes. A laboratory‑scale single stage batch-recycle electrodialysis experimental apparatus was assembled with five cell‑pairs of IEMs with an active cross-sectional area of 7.84 cm2. In this study, seven combinations of IEMs (commercial and laboratory-made) were compared: (i) Neosepta AMX/CMX, (ii) PCA PCSA/PCSK, (iii) Fujifilm Type 1 AEM/CEM, (iv) SUEZ AR204SZRA/CR67HMR, (v) Ralex AMH-PES/CMH-PES, (vi) Neosepta AMX/Bare Polycarbonate membrane (Polycarb), and (vii) Neosepta AMX/Sandia novel bioinspired cation exchange membrane (SandiaCEM). ED desalination performance with the Sandia novel bioinspired cation exchange membrane (SandiaCEM) was found to be competitive with commercial Neosepta CMX cation exchange membrane.

42 ENGINEERING↗

Life Cycle Assessment of Innovative Carbon Dioxide Selective Membranes from Low Carbon Emission Sources: A Comparative Study

Carbon capture has been an important topic of the twenty-first century because of the elevating carbon dioxide (CO2) levels in the atmosphere. CO2 in the atmosphere is above 420 parts per million (ppm) as of 2022, 70 ppm higher than 50 years ago. Carbon capture research and development has mostly been centered around higher concentration flue gas streams. For example, flue gas streams from steel and cement industries have been largely ignored due to lower associated CO2 concentrations and higher capture and processing costs. Capture technologies such as solvent-based, adsorption-based, cryogenic distillation, and pressure-swing adsorption are under research, but many suffer from higher costs and life cycle impacts. Membrane-based capture processes are considered cost-effective and environmentally friendly alternatives. Over the past three decades, our research group at Idaho National Laboratory has led the development of several polyphosphazene polymer chemistries and has demonstrated their selectivity for CO2 over nitrogen (N2). Poly[bis((2-methoxyethoxy)ethoxy)phosphazene] (MEEP) has shown the highest selectivity. A comprehensive life cycle assessment (LCA) was performed to determine the life cycle feasibility of the MEEP polymer material compared to other CO2-selective membranes and separation processes. The MEEP-based membrane processes emit at least 42% less equivalent CO2 than Pebax-based membrane processes. Similarly, MEEP-based membrane processes produce 34–72% less CO2 than conventional separation processes. In all studied categories, MEEP-based membranes report lower emissions than Pebax-based membranes and conventional separation processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

LES simulations of a vacuum membrane distillation channel with geometric alterations

3D LES simulations were carried out to study the performance of a vacuum membrane distillation module. A wiggly wall profile with/without embedded stiffeners was considered to alleviate axial and radial temperature polarization, the cause of performance decrease in membrane distillation. Results of the flow field show the wiggles create unsteady vortex shedding inducing intense mixing in the channel. Vortex shedding intensity increases as the Reynolds number increases or stiffeners are added. 3D results show a 56% improvement in flux when moving from a flat sheet membrane to a wiggly membrane with stiffeners at a constant Reynolds number, corresponding to an improvement from 11.7 to 41.7 in the Nusselt number, showing that the alterations improved the flux performance by enhancing the heat transfer along the membrane surface and therefore alleviating temperature polarization, a critical bottleneck in membrane distillation systems. Further, a merit criterion was defined based on the Nusselt number and friction factor, and a 40% increase in merit was shown switching from a flat to a wiggly channel, while a 97% merit increase was seen going from flat to wiggly with stiffeners. A 42% enhancement in the flux was also seen moving from a straight channel to a wiggly channel at a higher Reynolds number which highlights the importance of strategically choosing the mass flow rate, as well as inducing flow separation and vortex shedding in the channel to promote mixing and dissipate the thermal boundary layer. The variation in results between the wiggly module with stiffeners and the wiggly module at high Reynolds numbers suggests enhancing mixing structures can be more impactful on flux for this geometry than increasing the flow rate to a turbulent/transitional regime. However, both are preferable for peak system flux performance. Furthermore, a 2D approximation was used to perform simulations on more extended channels to examine the length degradation. The modules with wiggly channels performed at the same flux level with a doubling of the length. On the other hand, the flat sheet modules experienced length degradation by temperature polarization and dropped in flux yield by around 13% of the short-channel value. This work illustrates that modeling the system and understanding how the performance decreases as the membrane surface area increases are critical for a larger module (scaling up from a lab to a prototype module) to maintain high flux performance.

42 ENGINEERING↗

Project Final Report - Advanced Oxygen Separation from Air Using a Novel Mixed Matrix Membrane

This report describes a summary of the findings of the project. The technical work was divided into three activities: 1) technoeconomic analysis; 2) membrane component development (support layer, selective layer development, and gutter layer formulation); and 3) hollow fiber formation. The technoeconomic analysis includes operating, capital, and materials costs of an oxygen enrichment system with 1-3 stages. The analysis concluded that the desired gas quality (90-95% O2) cannot be reached with a single stage. The triple stage system yielded the best overall product quality at lower membrane performance levels but with the highest cost. For the membrane development activities, functionalized nanodiamonds have been shown to slightly improve membrane formation behaviors and gas permeability performance. For example, support layers based on polysulfone-nanodiamond composites have been formed that increase the material’s O2 permeability by over a factor of 150, however, at the cost of selectivity that suggests a change in transport mechanism. Furthermore, nanodiamonds have been found to improve membrane durability. Improvements in selective and gutter layers also have been accomplished. An additional accomplishment is the demonstration of phase inversion of polysulfone-nanodiamond composites that ensures that hollow fiber formation can be performed. Finally, the interfaces between support, gutter, and selective layers were briefly examined and the resulting membrane material consisting of all three layers gave good performance in an O2 separation from N2. The three-layer prototype membrane gave permeability of 29.2-32.2 Barrers, which equates to permeance of approximately 290-320 GPU, which is lower than the TEA informed goal of 500 GPU. O2/N2 selectivity ranged from 5.2-6.2, which is consistent with the less costly two-stage implementation of the technology. In summary, new materials have been developed for O2 concentration from air and are well-suited to a hollow fiber format.

20 FOSSIL-FUELED POWER PLANTS↗

Hydrogen production with seawater-resilient bipolar membrane electrolyzers

Generation of H 2 and O 2 from untreated water sources represents a promising alternative to ultrapure water required in contemporary proton exchange membrane-based electrolysis. Bipolar membrane-based devices, often used in electrodialysis and CO 2 electrolysis, facilitate impure water electrolysis via the simultaneous mediation of ion transport and enforcement of advantageous microenvironments. Herein, we report their application in direct seawater electrolysis; we show that upon introduction of ionic species such as Na + and Cl - from seawater, bipolar membrane electrolyzers limit the oxidation of Cl - to corrosive OCl - at the anode to a Faradaic efficiency (FE) of 0.005%, while proton exchange membrane electrolyzers under comparable operating conditions exhibit up to 10% FE to Cl oxidation. In conclusion, the effective mitigation of Cl - oxidation by bipolar membrane electrolyzers underpins their ability to enable longer-term seawater electrolysis than proton exchange membrane assemblies by a factor of 140, suggesting a path to durable seawater electrolysis.

08 HYDROGEN↗

Enhancing CO 2 Transport Across a PEEK‐Ionene Membrane and Water‐Lean Solvent Interface

Abstract Efficient direct air capture (DAC) of CO 2 will require strategies to deal with the relatively low concentration in the atmosphere. One such strategy is to employ the combination of a CO 2 ‐selective membrane coupled with a CO 2 capture solvent acting as a draw solution. Here, the interactions between a leading water‐lean carbon‐capture solvent, a polyether ether ketone (PEEK)‐ionene membrane, CO 2 , and combinations were probed using advanced NMR techniques coupled with advanced simulations. We identify the speciation and dynamics of the solvent, membrane, and CO 2 , presenting spectroscopic evidence of CO 2 diffusion through benzylic regions within the PEEK‐ionene membrane, not spaces in the ionic lattice as expected. Our results demonstrate that water‐lean capture solvents provide a thermodynamic and kinetic funnel to draw CO 2 from the air through the membrane and into the bulk solvent, thus enhancing the performance of the membrane. The reaction between the carbon‐capture solvent and CO 2 produces carbamic acid, disrupting interactions between the imidazolium (Im + ) cations and the bistriflimide anions within the PEEK‐ionene membrane, thereby creating structural changes through which CO 2 can diffuse more readily. Consequently, this restructuring results in CO 2 diffusion at the interface that is faster than CO 2 diffusion in the bulk carbon‐capture solvent.

Walter, Eric D.↗

Water transport through monolayer fullerene membrane

Water transport through nanoporous materials is important in water treatment, desalination, and nanofiltration. Two-dimensional (2D) membranes such as porous graphene have been explored for high-permeance water transport. However, water transport through a new class of 2D membranes based on two-dimensional covalently linked fullerene monolayers has not been fully explored. Here we use classical molecular dynamics simulations to investigate both vapor and liquid water transport through a monolayer fullerene membrane. We find that a quasi-tetragonal phase fullerene membrane possesses the right pore size and geometry that allows fast water vapor transport (∼ 50 g m −2 day −1 Pa −1 ) and water liquid transport (∼ 2.0 g m −2 day −1 Pa −1 ). Furthermore, simulation of sea water transport through the fullerene membrane shows 100 % salt rejection. The much faster vapor transport rate is attributed to the funnel-shaped pore and the optimal size that allows free rotation of water molecules permeating through, while the slower liquid transport is due to the need to desolvate a water molecule to break its hydrogen-bond network across the hydrophobic pore. This work shows the great potential of using monolayer fullerene membranes as 2D membranes for fast and selective water transport.

Desalination↗

Ion-gated carbon molecular sieve gas separation membranes

Membrane technology lies at the heart of many industrial gas separation processes and applications. Molecular sieving membranes that break the Robeson limit are desirable for energy-efficient gas separation. In this paper, we report a facile strategy of directly integrating ionic liquids (ILs) into porous membranes. Particularly, the ILs form an ultra-thin layer on the carbon molecular sieve (CMS) membranes rather than penetrating into the pores, acting as a smart gate for gas entry to boost the selectivity. The hybrid membrane exhibits CO 2 permeability >600 barrer and enhanced CO 2 /N 2 selectivity >50, which surpasses the Robeson limit and shows potential in CO 2 /N 2 separation process. Molecular dynamics simulations confirm the gating effect of the IL layer of molecular thickness. In conclusion, this work demonstrates a universal strategy to improve CMS membrane performance by creating an IL-membrane interface and tuning the ion-pore interaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Boric acid removal with polyol-functionalized polyether membranes

Poor selectivity of conventional desalination membranes for boron often necessitates multi-stage treatment trains to achieve desired boron removal for end uses such as irrigation. One approach to membrane design for improved single-pass boric acid removal is via incorporation of chelating ligands that selectively sorb boron. In this study, membranes based on epoxy-amine cross-linked poly(glycidyl glycidyl ether) (PGGE) were synthesized and functionalized with N-methyl-d-glucamine (NMDG), a polyol known to interact selectively with boron. PGGE and PGGE-NMDG membranes exhibited boron sorption isotherms that were well-described by dual mode isotherms. PGGE-NMDG sorbed 2.5 mmol B/g dry polymer from a neutral aqueous solution containing 100 mmol B/L, which was almost three times the adsorption density of a commercial boron selective resin, Amberlite IRA743. Further, the membranes were regenerated in acid without a significant loss of boron sorption capacity over four cycles. Interactions between boron and NMDG and PGGE sites (e.g., epoxides) impacted boron diffusion in both membranes. The use of ligand functionalized membranes to capture target solutes such as boron requires high loading of interacting sites to maximize uptake capacity. Establishing fundamental structure/property rules for boron selectivity could lead to new material designs with improved boron separation properties for water purification.

36 MATERIALS SCIENCE↗

Preparation of defect-free asymmetric gas separation membranes with dihydrolevoglucosenone (Cyrene TM ) as a greener polar aprotic solvent

Nonsolvent-induced phase separation (NIPS) is widely used to prepare asymmetric gas separation membranes. Most industrial NIPS casting solution formulations are limited to a small group of glassy polymers and, importantly, require toxic polar aprotic solvents such as N,N-dimethylacetamide (DMAc), N,N-dimethylformamide (DMF), or N-methyl-2-pyrrolidone (NMP). Growing restrictions on the use of such solvents are spurring the search for more benign casting solution formulations that do not compromise membrane performance. Herein this study reports high-flux, defect-free asymmetric polysulfone (PSf) gas separation membranes prepared using dihydrolevoglucosenone (Cyrene TM ), a polar aprotic solvent that is believed to be safer than DMAc, DMF, and NMP, as the majority casting solution component. Optimized formulations and casting conditions produce membranes with hydrogen permeances exceeding 100 gas permeance units (GPU) and selectivities at or above those of dense PSf films. Dry/wet NIPS membrane performance improved with shorter dry step times and increased Cyrene TM loadings relative to the volatile solvent, tetrahydrofuran (THF), in the casting solution. The high water-Cyrene TM Flory-Huggins interaction parameter, $\mathcal{X}12$ , and high casting solution viscosities help suppress the formation of skin layer defects and sublayer macrovoids. In some cases, membrane selectivities were influenced by substructure resistance, providing insight into the relationship between sublayer morphology and membrane performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Linking water quality, fouling layer composition, and performance of reverse osmosis membranes

Fouling of polyamide membranes during reverse osmosis (RO) is a major challenge for adopting membrane technologies to treat highly contaminated waters, especially those containing organic foulants (e.g., natural organic matter (NOM), polysaccharides) and dominant cations (e.g., sodium, magnesium, calcium). Here, this work combines bench-scale membrane fouling experiments with detailed characterization of feedwater chemistry and fouling layer composition/morphology to reveal fundamental mechanisms of (in)organic fouling during RO. Divalent cations are shown to promote fouling by hydrophobic NOM containing aromatic and carboxyl groups, while NOM fouling in the presence of a monovalent cation, sodium, occurs by smaller fulvic acids containing larger fractions of carboxyl groups and other oxygen-rich moieties. Calcium-carboxyl bridging occurs in solution and near the membrane surface to induce NOM aggregation on nanometer length scales. In complex waters containing foulant mixtures, co-fouling by calcium-carboxyl bridging and CaCO 3 precipitation influence membrane performance at longer timeframes. However, the flux decline observed for the co-fouling mechanism was less significant than the sum of its parts, suggesting both synergistic and antagonistic fouling mechanisms should be considered in membrane design/operation. These results encourage the design of pretreatment processes to reduce concentrations of multivalent ions and hydrophobic NOM in RO feedwaters, and of membrane materials to limit attachment/deposition of aggregates to/on polyamide surfaces.

42 ENGINEERING↗

Anion exchange membranes: The effect of reinforcement in water and electrolyte

Alkaline anion-conducting polymer-based CO 2 electrolysis and water electrolysis are among two emerging renewable energy conversion technologies. Their system design and integration offer promise of lower capital cost due to utilization of low-cost catalysts, in contrast to platinum group metal catalysts required for cation-conducting polymer-based devices. However, a critical component, the polymer electrolyte membrane, remains an obstacle hampering system performance and durability. In this study, commercially-available Sustainion® membranes with and without PTFE-reinforcement were investigated to understand previously unreported origins of improved device performance when compared to alternative membrane chemistries. We report critical membrane properties, such as morphology, thermal stability, as well as temperature-, hydration-, and counter-ion dependent ion conductivity. Moveover, the changes in uptake and conductivity of membranes in supporting electrolytes of K 2 CO 3 and KOH investigated as a function of their concentration. Presence of reinforcement and supporting electrolyte type alter the membrane's transport functionality, which could help guide device design for improved performance. In conclusion, the obtained results not only show how Sustainion® properties change with operating environment for CO 2 and water electrolysis applications, but also provide understanding for internal and external factors controlling anion-exhcnage membrane functionality in electrochemical devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Non-equilibrium simulations of hydraulic permeation: Role of mechanical boundary conditions in dense membranes

Understanding the mechanisms of water transport in reverse osmosis membranes is critical for improving membrane performance and guiding material design. While classical models describe transport as either solution-diffusion (SD)—involving concentration-driven diffusion through a homogeneous medium—or pore-flow (PF)—involving pressure-driven convection through percolated water channels—their applicability to crosslinked polyamide membranes remains debated. Here, using non-equilibrium molecular dynamics simulations, we investigate the impact of mechanical support conditions on pressure-driven water transport in polyamide membranes across varying crosslink densities and pressure differentials (1000–5000 bar). Two support conditions are considered: graphene-restrained, representing experimentally relevant supported membranes, and freeze-restrained, mimicking a self-supported structure. In graphene-restrained systems, water concentration gradients and constant pressure profiles emerge, consistent with SD theory and incompatible with PF assumptions due to the absence of percolated pores and sub-nanometer voids. In contrast, freeze-restrained systems display uniform water concentration and linearly decreasing pressure at 1000 bar, and exhibit compressibility-induced water gradients and partial percolation at 5000 bar, resembling PF-like behavior. However, the underlying assumptions of PF theory—continuous solvent pathways and pressure transmission through water-filled pores—are not met under most conditions. Our results demonstrate that accurate modeling of reverse osmosis membranes must incorporate realistic mechanical boundary conditions to distinguish between transport mechanisms. For dense polyamide membranes supported by porous substrates, graphene-restrained simulations best reflect experimental setups and support the SD model as the dominant mechanism of water permeation.

molecular dynamics↗

Insights into determining pore size properties of ultrafiltration membranes

The selectivity of porous membranes is often characterized using solute rejection tests, where membranes are challenged with dilute aqueous solutions of neutral solutes at operating conditions that minimize concentration polarization and fouling. In single solute tests, a membrane is challenged with one molecular weight (MW) solute at a time from low to high MW. Since single solute methods are time-intensive, mixed solute tests have become more common, where a mixture of several MW solutes challenges a membrane at once. However, the presence of large solutes in a mixture increases the rejection of smaller solutes. Furthermore, there are no universally accepted operating conditions or standard methods used by membrane manufacturers or researchers for the experiments, leading to difficulty in pore size and pore characteristic comparisons. In this paper, commercial ultrafiltration membranes were challenged with single and mixed solute polyethylene glycol (PEG) and dextran aqueous solutions. First, rejection values determined using total organic carbon (TOC) and high-performance liquid chromatography (HPLC) from single solute filtration experiments are compared. Differences in rejection curves obtained by the two techniques are attributed to solute polydispersity. Mixed solute filtration experiments with binary mixtures of solutes showcased co-solute interactions, which increase with both the size and weight percent of large solute in the mixture. Mixed solute filtration experiments at varying operating conditions (i.e., stir speed and flux) were conducted to determine operating conditions that mitigate co-solute interactions. Stir speed had a minimal effect on co-solute interactions. In contrast, low flux conditions can help minimize co-solute interactions, leading to pore size distributions that closely resemble results observed in single solute filtration using narrowly dispersed solutes. Additionally, at low flux conditions, the predicted membrane pore size distributions utilizing mixed solute experiments with PEG and dextran were similar.

36 MATERIALS SCIENCE↗

Nondestructive In Operando Imaging of Thin Film Composite Membrane Compaction Enhanced by AI-Based Segmentation

Reverse osmosis (RO) membranes are essential for desalination and water reuse, yet their permeability declines in high-pressure applications due to membrane compaction. This study investigates the structural and functional responses of commercial brackish, seawater, and high-pressure RO membranes at applied pressures up to 120 bar using a multiscale, nondestructive in operando scanning electron microscopy (iSEM) imaging platform. The iSEM technique reveals progressive densification across the composite membrane structure, which correlates with observed declines in water and solute permeance. To quantify these structural changes with greater fidelity, we combined X-ray computed tomography with AI-based segmentation enabling precise analysis of pore size distribution and thickness of the polysulfone support layer. Compared to traditional thresholding, AI segmentation accurately delineates material phases and void spaces, enhancing the reproducibility and resolution of morphological assessments. The results demonstrate that compaction-induced reductions in porosity and thickness strongly impact membrane transport properties. These findings provide mechanistic insights into the compaction behavior of RO membranes and underscore the potential for advanced imaging and AI-driven data analysis to guide the design of next-generation membranes with improved mechanical resilience and operational longevity.

13 HYDRO ENERGY↗

Dense, continuous membrane labeling and expansion microscopy visualization of ultrastructure in tissues

Abstract Lipid membranes are key to the nanoscale compartmentalization of biological systems, but fluorescent visualization of them in intact tissues, with nanoscale precision, is challenging to do with high labeling density. Here, we report ultrastructural membrane expansion microscopy (umExM), which combines an innovative membrane label and optimized expansion microscopy protocol, to support dense labeling of membranes in tissues for nanoscale visualization. We validate the high signal-to-background ratio, and uniformity and continuity, of umExM membrane labeling in brain slices, which supports the imaging of membranes and proteins at a resolution of ~60 nm on a confocal microscope. We demonstrate the utility of umExM for the segmentation and tracing of neuronal processes, such as axons, in mouse brain tissue. Combining umExM with optical fluctuation imaging, or iterating the expansion process, yields ~35 nm resolution imaging, pointing towards the potential for electron microscopy resolution visualization of brain membranes on ordinary light microscopes.

Science & Technology - Other Topics↗

A reverse-selective ion exchange membrane for the selective transport of phosphates via an outer-sphere complexation–diffusion pathway

Specific-ion selectivity is a highly desirable feature for the next generation of membranes. However, existing membranes rely on differences in charge, size and hydration energy, which limits their ability to target individual ion species. Here we demonstrate a nanocomposite ion-exchange membrane material that enables a reverse-selective transport mechanism that can selectively pass a single ion species. Here we demonstrate this transport mechanism with phosphate ions selectively transporting across negatively charged cation exchange membranes. Selective transport is enabled by the in situ growth of hydrous manganese oxide nanoparticles throughout a cation exchange membrane that provide a diffusion pathway via phosphate-specific, reversible outer-sphere interactions. On incorporating the hydrous manganese oxide nanoparticles, the membrane’s phosphate flux increased by a factor of 27 over an unmodified cation exchange membrane, and the selectivity of phosphorous over sulfate, nitrate and chloride reaches 47,100 and 20, respectively. By pairing ion-specific outer-sphere interactions between the target ions and appropriate nanoparticles, these nanocomposite ion-exchange materials can, in principle, achieve selective transport for a range of ions.

42 ENGINEERING↗

Scaling of ionic conductance in a fluctuating single-layer nanoporous membrane

Abstract Single-layer membranes have emerged as promising candidates for applications requiring high transport rates due to their low resistance to molecular transport. Owing to their atomically thin structure, these membranes experience significant microscopic fluctuations, emphasizing the need to explore their impact on ion transport processes. In this study, we investigate the effects of membrane fluctuations on the elementary scaling behavior of ion conductance $$G$$ G as a function of ion concentration $$c_{0}$$ c 0 , represented as $$G = \beta c_{0}^{\alpha }$$ G = β c 0 α , using molecular dynamics simulations. Our findings reveal that membrane fluctuations not only alter the conductance coefficient $$\beta$$ β but also the power-law exponent $$\alpha$$ α . We identify two distinct frequency regimes of membrane fluctuations, GHz-scale and THz-scale fluctuations, and examine their roles in conductance scaling. Furthermore, we demonstrate that the alteration of conductance scaling arises from the non-linearity between ion conductance and membrane shape. This work provides a fundamental understanding of ion transport in fluctuating membranes.

42 ENGINEERING↗