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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

The role of temperature on defect diffusion and nanoscale patterning in graphene

Graphene is of great scientific interest due to a variety of unique properties such as ballistic transport, spin selectivity, the quantum hall effect, and other quantum properties. Nanopatterning and atomic scale modifications of graphene are expected to enable further control over its intrinsic properties, providing ways to tune the electronic properties through geometric and strain effects, introduce edge states and other local or extended topological defects, and sculpt circuit paths. The focused beam of a scanning transmission electron microscope (STEM) can be used to remove atoms, enabling milling, doping, and deposition. Utilization of a STEM as an atomic scale fabrication platform is increasing; however, a detailed understanding of beam-induced processes and the subsequent cascade of aftereffects is lacking. Here, we examine the electron beam effects on atomically clean graphene at a variety of temperatures ranging from 400 to 1000 °C. We find that temperature plays a significant role in the milling rate and moderates competing processes of carbon adatom coalescence, graphene healing, and the diffusion (and recombination) of defects. The results of this work can be applied to a wider range of 2D materials and introduce better understanding of defect evolution in graphite and other bulk layered materials.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Influences of Hydrogen Bonding-Based Stabilization of Bolaamphiphile Layers on Molecular Diffusion within Organic Nanotubes Having Inner Carboxyl Groups

This paper reports molecular diffusion behavior in two bolaamphiphile-based organic nanotubes having inner carboxyl groups with different inner dimeters (10 and 20 nm) and wall structures, COOH-ONT 10nm and COOH-ONT 20nm , using imaging fluorescence correlation spectroscopy (imaging FCS). Here, the results were compared to those previously obtained in a similar nanotube with inner amine groups (NH 2 -ONT 10nm ). COOH-ONT 10nm , as with NH 2 -ONT 10nm , were formed from a rolled bolaamphiphile layer incorporating triglycine moieties, whereas COOH-ONT 20nm consisted of four stacks of triglycine-free bolaamphiphile layers. Imaging FCS measurements were carried out for anionic sulforhodamine B (SRB), zwitterionic/cationic rhodamine B (RB) and cationic rhodamine-123 (R123) diffusing within ONTs (1–9 µm long) at different pH (3.4–8.4) and ionic strengths (1.6–500 mM). Diffusion coefficients (D) of these dyes in the ONTs were very small (0.01–0.1 µm 2 /s), reflecting the significant contributions of molecule-nanotube interactions to diffusion. The D of SRB was larger at higher pH and ionic strength, indicating the essential role of electrostatic repulsion that was enhanced by the deprotonation of the inner carboxyl groups. Importantly, the D of SRB was virtually independent of nanotube inner diameter and wall structure, indicating the diffusion of the hydrophilic molecule was controlled by short timescale adsorption/desorption processes onto the inner surface. In contrast, pH effects on D were less clear for relatively hydrophobic R123 and RB, suggesting the significant contributions of non-Coulombic interactions. Interestingly, the diffusion of these molecules in COOH-ONT 20nm was slower than in COOH-ONT 10nm . Slower diffusion in COOH-ONT20nm was attributable to relatively efficient partitioning of the hydrophobic dyes into the bolaamphiphile layers, which was reduced in COOH-ONT 10nm due to the stabilization of its layer by polyglycine-II-type hydrogen bonding networks. These results show that, by tuning the bolaamphiphile structures and their intermolecular interactions, unique environments can be created within the nanospaces for enhanced molecular separations and reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Thermal properties of simulated Hanford waste glasses

Abstract The Hanford Tank Waste Treatment and Immobilization Plant will vitrify the mixed hazardous wastes generated from 45 years of plutonium production at the Hanford Site in Washington State. The molten glasses will be poured into stainless steel containers or canisters and subsequently cooled for storage and disposal. For appropriate facility design and operations to handle such highly energy‐consuming processes, knowledge of the material properties is required. The thermal properties (heat capacity, thermal diffusivity, and thermal conductivity) of representative high‐level and low‐activity waste glasses were studied as functions of temperature in the range of 200°C‐800°C (relevant to the cooling process). Simultaneous differential scanning calorimetry‐thermal gravimetry (DSC‐TGA), Xe‐flash diffusivity, pycnometry, and dilatometry were implemented. The study showed that simultaneous DSC‐TGA would be a reliable method for obtaining the heat capacity of various glasses in the temperature range of interest. Accurate thermal properties from this study were shown to provide a more realistic guideline for capacity and time constraints of the heat removal process when compared to the original conservative design‐basis engineering estimates. The estimates, though useful for design in the absence of measured physical properties, can now be supplanted and the measured thermal properties can be used in design verification activities.

Rodriguez, Carmen P.↗
DOE OSTI2017

A strong diffusive ion mode in dense ionized matter predicted by Langevin dynamics

We determined the state and evolution of planets, brown dwarfs and neutron star crusts by the properties of dense and compressed matter. Furthermore, due to the inherent difficulties in modelling strongly coupled plasmas, however, current predictions of transport coefficients differ by orders of magnitude. Collective modes are a prominent feature, whose spectra may serve as an important tool to validate theoretical predictions for dense matter. With recent advances in free electron laser technology, X-rays with small enough bandwidth have become available, allowing the investigation of the low-frequency ion modes in dense matter. Here, we present numerical predictions for these ion modes and demonstrate significant changes to their strength and dispersion if dissipative processes are included by Langevin dynamics. Notably, a strong diffusive mode around zero frequency arises, which is not present, or much weaker, in standard simulations. These results have profound consequences in the interpretation of transport coefficients in dense plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Roll-to-Roll Advanced Materials Manufacturing DOE Laboratory Collaboration - FY2018 Final Report

High-value R2R processing is used to support a wide range of products in applications which span many industrial business sectors. The overall R2R process technology can be considered as “mature” as the process methodology and has been in use for decades. This continuous processing technique traditionally involves deposition of material(s) onto moving webs or carriers or other continuous R2R, belt-fed, or conveyor-based processes that enable successive steps to build a final version which serves to support the deposited materials. Current process technologies, which typify “roll to roll”, include tape casting, silk-screen printing, reel-to-reel vacuum deposition/coating and R2R lithography. Products supported by R2R manufacturing include micro-electronics, electro-chromic window films, PVs, fuel cells for energy conversion, battery electrodes for energy storage, and barrier materials. Due to innovation in materials and process equipment, high-quality yet very low-cost multi-layer technologies can be manufactured on a very cost-competitive basis. To move energy-related products from high-cost niche applications to the commercial sector, a means must be available to enable manufacture of these products in a cost-competitive manner that is affordable by the general consumer. Fortunately, products such as fuel cells, thin- and mid-film PVs, batteries, electrochromic and piezoelectric films, water separation membranes, and other energy saving technologies readily lend themselves to manufacture using R2R approaches.Within the DOE EERE AMO, it was recognized that establishment of a program supported at the DOE National Laboratories, along with their immense design of materials and equipment modelling capabilities enabled with use of high-performance computing, could take advantage of available R2R infrastructure to manufacture new technologies. In FY 2016, a R2R Consortium was established and provided with initial “seed” funding to take an approach that was envisioned to be supportable by advanced manufacturing R2R processes. This collaborative approach was designed to foster identification and development of materials and processes related to R2R for clean-energy product development. Using computational and experimental capabilities by acknowledged subject matter experts within the supported National Laboratory system, this collaborative project would leverage the capabilities and expertise at each of four laboratories to further the development of an enabling high-volume cost-competitive platform technology. The collaboration team that is comprised of ORNL, ANL, NREL and LBNL, coordinating with EPB and other selected industry partners, was formed in April 2016 to initially address enhancing battery electrode performance and R2R manufacturing challenges. The research efforts were to predict and measure changes and results in electrode morphology and performance based on process condition changes; to evaluate mixed, active, particle size deposition and drying for novel electrode materials; to model various process condition changes and the resulting morphology and electrode performance; and to develop and validate NDE techniques for in-line measurement of battery electrode material properties. These efforts carried through FY 2017 and completed at the end of FY 2018.The approach was to look at compositions of materials with different particle sizes to make electrode samples using a R2R manufacturing process. The shape, size, and morphology of the materials, the chemistry of the formulation, the nature of slurries, their coating rate, the rate of drying all play a role in determining the final coating architecture, quality, and performance. A commercial cathode material was selected to make a series of cathodes and anodes by single pass, dual pass and slot die methods. Analysis of all the compiled results for this battery electrode development were that the best performing cathodes included: dual-pass electrode with large particles near the foil, mixed small and large particles, and small particles only. Whereas, the best performing anodes were with a mix of small and large graphite particles. An additional core project was added in FY 2017 to conduct studies of fuel cell materials that can be produced using R2R processes. The goal of this project is to explore, understand and optimize material and process parameters to support increased throughput, increased quality, and reduced cost for high volume production of gas-diffusion electrodes (GDEs) for PEMFCs. Project work in FY 2018 were to use a R2R process to fabricate electrodes without ionomer overlayer that can produce the equivalent mass activity as spray-coated electrodes with an ionomer overlayer. Oxygen-limiting current measurements were utilized to optimize oxygen mass transport. Alcohol-rich solvents were investigated, and results were that the alcohol and water ratio can be tuned to control ionomer distribution. Water-rich solvents produce a more dispersed ink which results in better high-current density performance.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Technological diffusion trends suggest a more equitable future for rooftop solar in the United States

Abstract Equity has become central in the academic and regulatory discourse shaping the future of residential-scale clean energy technologies in the United States, particularly rooftop solar. Here, we develop a holistic perspective on these issues by analyzing rooftop solar adoption trends using two alternative forecasting methods: an inside-view forecast based on historical solar adoption data, and an outside-view forecast based on adoption data for other emerging consumer technologies. We show how rooftop solar, like other emerging consumer technologies, has become more equitably adopted over time. We show that solar diffusion patterns are largely consistent with those of other technologies. Both forecasting methods suggest that clean energy technologies should be expected to become more equitably adopted over time. Policy could accelerate this process by supporting low-income adoption without unduly curbing overall diffusion.

14 SOLAR ENERGY↗
DOE OSTI2019

SnO 2 -Catalyzed Oxidation in High-Efficiency CdTe Solar Cells

Interfaces at the front of superstrate CdTe-based solar cells are critical to carrier transport, recombination, and device performance, yet determination of the chemical structure of these nanoscale regions has remained elusive. This is partly due to changes that occur at the front interfaces during high temperature growth and substantive changes occurring during postdeposition processing. In addition, these buried interfaces are extremely difficult to access in a way that preserves chemical information. In this work, we use a recently developed thermomechanical cleaving technique paired with X-ray photoelectron spectroscopy to probe oxidation states at the SnO 2 interface of CdTe solar cells. We show that the tin oxide front electrode promotes the formation of nanometer-scale oxides of tellurium and sulfur. Most oxidation occurs during CdCl 2 /O 2 activation. Surprisingly, we show that relatively low-temperature anneals (180-260 degrees C) used to diffuse and activate copper acceptors in a doping/back contact process also cause significant changes in oxidation at the front of the cell, providing a heretofore missing aspect of how back contact processes can modify device transport, recombination, and performance. Device performance is shown to correlate with the extent of tellurium and sulfur oxidation within this nanometer-scale region. Mechanisms responsible for these beneficial effects are proposed.

14 SOLAR ENERGY↗
DOE OSTI2021

Superior photo-carrier diffusion dynamics in organic-inorganic hybrid perovskites revealed by spatiotemporal conductivity imaging

Abstract The outstanding performance of organic-inorganic metal trihalide solar cells benefits from the exceptional photo-physical properties of both electrons and holes in the material. Here, we directly probe the free-carrier dynamics in Cs-doped FAPbI 3 thin films by spatiotemporal photoconductivity imaging. Using charge transport layers to selectively quench one type of carriers, we show that the two relaxation times on the order of 1 μs and 10 μs correspond to the lifetimes of electrons and holes in FACsPbI 3 , respectively. Strikingly, the diffusion mapping indicates that the difference in electron/hole lifetimes is largely compensated by their disparate mobility. Consequently, the long diffusion lengths (3~5 μm) of both carriers are comparable to each other, a feature closely related to the unique charge trapping and de-trapping processes in hybrid trihalide perovskites. Our results unveil the origin of superior diffusion dynamics in this material, crucially important for solar-cell applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Two-dimensional Radiative Magnetohydrodynamic Simulations of Partial Ionization in the Chromosphere. II. Dynamics and Energetics of the Low Solar Atmosphere

We investigate the effects of interactions between ions and neutrals on the chromosphere and overlying corona using 2.5D radiative MHD simulations with the Bifrost code. We have extended the code capabilities implementing ion–neutral interaction effects using the generalized Ohm’s law, i.e., we include the Hall term and the ambipolar diffusion (Pedersen dissipation) in the induction equation. Our models span from the upper convection zone to the corona, with the photosphere, chromosphere, and transition region partially ionized. Our simulations reveal that the interactions between ionized particles and neutral particles have important consequences for the magnetothermodynamics of these modeled layers: (1) ambipolar diffusion increases the temperature in the chromosphere; (2) sporadically the horizontal magnetic field in the photosphere is diffused into the chromosphere, due to the large ambipolar diffusion; (3) ambipolar diffusion concentrates electrical currents, leading to more violent jets and reconnection processes, resulting in (3a) the formation of longer and faster spicules, (3b) heating of plasma during the spicule evolution, and (3c) decoupling of the plasma and magnetic field in spicules. Our results indicate that ambipolar diffusion is a critical ingredient for understanding the magnetothermodynamic properties in the chromosphere and transition region. The numerical simulations have been made publicly available, similar to previous Bifrost simulations. This will allow the community to study realistic numerical simulations with a wider range of magnetic field configurations and physics modules than previously possible.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Computational framework for modeling membrane processes without process and solution property simplifications

Accurately modeling membrane processes is critical to evaluating novel process configurations, designing scalable membrane systems, informing process cost estimates, and directing future research. Most membrane process models trade accuracy for computational efficiency by employing simplified approximations of the process (i.e. no salt flux, no pressure drop) and solution properties (i.e. ideal solution, and constant density, viscosity, and diffusivity). Our report introduces a detailed one-dimensional finite difference model for evaluating membrane processes that avoids these common simplifications. We apply this model to quantify the error introduced by these simplifications for case studies of reverse osmosis, osmotically assisted reverse osmosis, forward osmosis, and pressure retarded osmosis. While the magnitude of error introduced by these simplifications is reliant on the case study parameters and specifications, we find that existing model formulations can underestimate or overestimate average water flux by nearly 50% for some membrane processes operating under standard conditions. Lastly we investigate the error introduced by simplified inlet-outlet models that do not solve the governing system of differential equations, and we assess the accuracy of novel inlet-outlet formulations that use a log and geometric mean, instead of the typical arithmetic mean, to represent non-linear water flux profiles.

42 ENGINEERING↗
DOE OSTI2018

Methane production and emissions in trees and forests

Forest ecosystem methane (CH 4 ) research has focused on soils, but trees are also important sources and sinks in forest CH 4 budgets. Living and dead trees transport and emit CH 4 produced in soils; living trees and dead wood emit CH 4 produced inside trees by microorganisms; and trees produce CH 4 through an abiotic photochemical process. Here, we review the state of the science on the production, consumption, transport, and emission of CH 4 by living and dead trees, and the spatial and temporal dynamics of these processes across hydrologic gradients inclusive of wetland and upland ecosystems. Emerging research demonstrates that tree CH 4 emissions can significantly increase the source strength of wetland forests, and modestly decrease the sink strength of upland forests. Scaling from stem or leaf measurements to trees or forests is limited by knowledge of the mechanisms by which trees transport soil-produced CH 4 , microbial processes produce and oxidize CH 4 inside trees, a lack of mechanistic models, the diffuse nature of forest CH 4 fluxes, complex overlap between sources and sinks, and extreme variation across individuals. Understanding the complex processes that regulate CH 4 source–sink dynamics in trees and forests requires cross-disciplinary research and new conceptual models that transcend the traditional binary classification of wetland vs upland forest.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

State-variable model of porous electrode batteries 1-D electrochemical/thermal behavior

Compared to full-order numerical models, the state-variable model (SVM) achieves multiple orders of reduction in computation time for simulation of electrochemical/thermal transport and reaction processes occurring inside lithium-ion and similar batteries with porous electrode construction. The model efficiently describes Li diffusion dynamics in active material and electrolyte phases, charge transfer kinetics, charge balance, and electron transport processes. The model requires a separate pre-processing step to identify SVM parameters.

Kim, Gi-Heon↗
DOE OSTI2021

Enhanced Diffusive Transport in Fluctuating Porous Media

Mass transport within porous structures is a ubiquitous process in biological, geological, and technological systems. Despite the importance of these phenomena, there is no comprehensive theory that describes the complex and diverse transport behavior within porous environments. While the porous matrix itself is generally considered a static and passive participant, many porous environments are in fact dynamic, with fluctuating walls, pores that open and close, and dynamically changing cross-links. While diffusion has been measured in fluctuating structures, notably in model biological systems, it is rarely possible to isolate the effect of fluctuations because of the absence of control experiments involving an identical static counterpart, and it is generally impossible to observe the dynamics of the structure. In this paper, we present a direct comparison of the diffusion of nanoparticles of various sizes within a trackable, fluctuating porous matrix and a geometrically equivalent static matrix, in conditions spanning a range of regimes from obstructed to highly confined. The experimental system comprised a close-packed layer of colloidal spheres that were either immobilized to a planar surface or allowed to fluctuate locally, within the space defined by their nearest neighbors. Interestingly, the effective long-time diffusion coefficient was approximately 35–65% greater in the fluctuating porous matrix than in the static one (depending on the size of the nanoparticle probes), regardless of the geometric regime. This was explained by considering the enhancing effects of matrix fluctuations on the short-time diffusion coefficient and cooperative “gate-opening” motions of matrix particles and nanoparticle probes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

State-selective probing of CO 2 autoionizing inner valence Rydberg states with attosecond extreme ultraviolet four-wave-mixing spectroscopy

Nonlinear spectroscopies can disentangle spectra that are congested due to inhomogeneous broadening. Here, in conjunction with theoretical calculations, attosecond extreme ultraviolet (XUV) four-wave-mixing (FWM) spectroscopy is utilized to probe the dynamics of autoionizing inner valence excited Rydberg states of the polyatomic molecule, CO 2 . This tabletop nonlinear technique employs a short attosecond XUV pulse train and two noncollinear, few-cycle near-infrared pulses to generate background-free XUV wave-mixing signals. FWM emission is observed from the n=5-7 states of the Henning sharp ndσ g Rydberg series that converges to the ionic $\widetilde{B}$ 2 Σ$^{+}_{u}$ state. However, these transient emission signals decay with lifetimes of 33 ± 6, 53 ± 2, and 94 ± 2 fs, respectively, which calculations show are consistent with the lifetimes of the short-lived n=6-8 members of the nsσ g character Henning diffuse Rydberg series. The oscillator strengths of transitions between states involved in all possible resonant FWM processes are calculated, verifying that the nonlinear spectra are dominated by pathways described by an initial excitation to the diffuse nsσ g Rydberg series and emission from the sharp ndσ g Rydberg series. The results substantiate not only that attosecond XUV FWM spectroscopy produces rigorous and meaningful measurements of ultrafast dynamics in polyatomic systems, but also that nonlinear spectroscopic techniques are versatile tools to selectively probe dynamics that are otherwise difficult to access.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

IR spectroscopic quantification of small molecule transport and desorption phenomena in polymers

The application, continued performance, and degradation behavior of polymers often depends on their interaction with small organic or gaseous volatiles. Understanding the underlying permeation and diffusion properties of materials is crucial for predicting their barrier properties (permeant flux), drying behavior, solvent loss or tendency to trap small molecules, as well as their interaction with materials in the vicinity due to off-gassing phenomena, perhaps leading to compatibility concerns. Further, the diffusion of low Mw organics is also important for mechanistic aspects of degradation processes. Based on our need for improved characterization methods, a FTIR-based spectroscopic gas/volatile quantification setup was designed and evaluated for determination of the diffusion, desorption and transport behavior of small IR-active molecules in polymers. At the core of the method, a modified, commercially available IR transmission gas cell monitors time-dependent gas concentration. Appropriate experimental conditions, e.g. desorption or permeation under continuous flow or static gas conditions, are achieved using easily adaptable external components such as flow controllers and sample ampoules. This study presents overview approaches using the same IR detection methodology to determine diffusivity (desorption into a static gas environment, continuous gas flow, or intermittent desorption) and permeability (static and dynamic flow detection). Further, the challenges encountered for design and setup of IR gas quantification experiments, related to calibration and gas interaction, are presented. These methods establish desorption and permeation behavior of solvents (water and methanol), CO 2 off-gassing from foam, and offer simultaneous measurements of the permeation of several gases in a gas mixture (CO 2 , CO and CH 4 ) through polymer films such as epoxy and Kapton. They offer complementary guidance for material diagnostics and understanding of basic properties in sorption and transport behavior often of relevance to polymer degradation or materials reliability phenomena.

36 MATERIALS SCIENCE↗
DOE OSTI2026

15.3% AM1.5G Efficiency GaAs Solar Cells Fabricated via an Epitaxy-Free Process

Here, we report simple and potentially low-cost techniques for creating high-quality n-type gallium arsenide (GaAs) and GaAs p/n junctions and fabricate GaAs p/n junction solar cells. Detailed-balance modeling suggests that 20% AM1.5G efficiency p/n homojunction devices may be possible if the surface doping concentration can be limited to values less than ∼ 5 × 10 19 cm −3 . Our process exploits an open-tube, vapor-phase, deposition-free, zinc diffusion technique for forming p-type layers in melt-grown n-GaAs substrates that results in sheet resistances less than 1 kΩ/$\square$. In addition, we have improved the minority carrier diffusion lengths of melt-grown GaAs from less than one micron to over five microns using an open-tube, vacuum-free, annealing process which reduces the density of EL2 midgap defects. Finally, we have combined these advances to fabricate epitaxy-free, GaAs solar cells with a validated AM1.5G efficiency of 15.3%.

14 SOLAR ENERGY↗
DOE OSTI2017

Analysis of a Wave-Powered, Reverse-Osmosis System and Its Economic Availability in the United States: Preprint

A wave energy converter (WEC) system has the potential to convert the wave energy resource directly into the high-pressure flow that is needed by the desalination system to permeate saltwater through the reverse-osmosis membrane to generate clean water. In this study, a wave-to-water numerical model was developed to investigate the potential use of a wave-powered desalination system (WPDS) for water production in the United States. The model was developed by coupling a time-domain radiation-and-diffraction-method-based numerical tool (WEC-Sim) for predicting the hydrodynamic performance of WECs with a solution-diffusion model that was used to simulate the reverse-osmosis process. To evaluate the feasibility of the WPDS, the wave-to-water numerical model was applied to simulate a desalination system that used an oscillating surge WEC device to pump seawater through the system. The annual water production was estimated based on the wave resource at a reference site on the coast of northern California to investigate the potential cost of water in that area, where the cost of water and electricity is high compared to other regions. In the scenario evaluated, for a 100-unit utility-scale electricity-producing array, the estimated levelized cost of energy for these WECs is about 3-6 times the U.S.'s current, unsubsidized electricity rates. However, with clean water as an end product and by directly producing pressurized water with WECs, rather than electricity as an intermediary, it is presently only 12 percent greater than typical water cost in California. This study suggests that a WEC array that produces water may be a viable, near-term solution to the nation's water supply, and the niche application of the WPDS may also provide developers with new opportunities to further develop technologies that benefit both the electric and drinking water markets.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Capacitive response of biological membranes

We present a minimal model to analyze the capacitive response of a biological membrane subjected to a step voltage via blocking electrodes. Through a perturbative analysis of the underlying electrolyte transport equations, we show that the leading-order relaxation of the transmembrane potential is governed by a capacitive timescale, τ_{C}=λ_{D}L/D(2+Γδ^{M}/L/4+Γδ^{M}/λ_{D}), where λ_{D} is the Debye screening length, L is the electrolyte width, Γ is the ratio of the permittivity of the electrolyte to the membrane, δ^{M} is the membrane thickness, and D is the ionic diffusivity. This timescale is considerably shorter than the traditional RC timescale λ_{D}L/D for a bare electrolyte due to the membrane's low permittivity and finite thickness. Beyond the linear regime, however, salt diffusion in the bulk electrolyte drives a secondary, nonlinear relaxation process of the transmembrane potential over a longer timescale τ_{L}=L^{2}/4π^{2}D. A simple equivalent-circuit model accurately captures the linear behavior, and the perturbation expansion remains applicable across the entire range of observed physiological transmembrane potentials. Together, these findings underscore the importance of the faster capacitive timescale and nonlinear effects on the bulk diffusion timescale in determining transmembrane potential dynamics for a range of biological systems.

Farhadi, Jafar↗