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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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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Confocal Raman Microscopy as a Probe of Material Deconstruction in Processed Low-Density Polyethylene Particles

Confocal Raman microscopy was applied to detect structural change within individual particles of low-density polyethylene (LDPE) following chemical and electrochemical processing steps that aimed to facilitate material decomposition. A high numerical aperture (NA) oil-immersion objective enabled depth-profiling through the near surface region (20 μm–40 μm) of irregularly shaped particles with an axial spatial resolution < 2 μm estimated from measurements of instrument detection efficiency profiles. Changes in vibrational bands sensitive to polyethylene crystallinity were evident following treatments and linked to the release of low molecular weight compounds present as additives and products of processing. Effects of processing were probed by monitoring the rise of Raman scattering intensity in vibrational modes associated with polyethylene chains in a zig-zag (trans) conformation near 1128 cm –1 , 1294 cm –1 , and 1418 cm –1 , signaling chain clustering and development of organized, crystalline-like assemblies. Pristine LDPE particles displayed a uniform structure across the near surface region, while particles treated initially with chemical extractant and then further processed displayed increasingly enhanced crystallinity up to the maximum depth probed (40 μm). As a step toward measurements on ensembles of particles, least squares modeling was adapted to derive pure component spectra reflecting crystallinity change within spectral datasets. The work demonstrates high spatial resolution Raman depth-profiling for the characterization of processed polymers using a high NA immersion objective to overcome the limitations of air-objectives often used for confocal Raman microscopy.

Wahiduzzaman, Md. [Department of Chemistry and Bio↗
DOE OSTI2026

Synergistic Evolution of Segmental Motion and Cooperative Relaxation within the Amorphous Phase of Organic Mixed Ionic-Electronic Conductors

Organic mixed ionic-electronic conductors (OMIECs) facilitate a variety of electrochemical processes and feature a heterogeneous microstructure composed of both crystalline and amorphous phases. However, structural evolution in amorphous regions during electrochemical doping remains poorly understood, limiting our understanding of mixed conduction mechanisms. Here, in this work, we develop operando chip calorimetry to probe amorphous phase evolution in poly­(3,4-ethylenedioxythiophene):poly­(styrenesulfonate) (PEDOT:PSS) under swelling and electrochemical (de)­doping. Our results reveal that amorphous regions providing ionic transport pathways and those within electronic transport channels undergo heterogeneous, yet synergistic, evolution during electrochemical modulation. The cooperative interplay between segmental motion and relaxation maintains ionic conductivity and intergrain electronic transport upon electrowetting and doping, while facilitating efficient ion hopping and adaptable chain conformations during dedoping. Such synergies are more pronounced in loose structures featuring a fibrillar morphology, which exhibit lower glass transition temperatures (T g ) and higher fragility (m). High-throughput robotic screening further establishes a strong correlation between elevated m/T g ratios and enhanced mixed conduction. These findings elucidate the role of the amorphous phase in the synthesis of OMIECs and underscore the potential of operando chip calorimetry in uncovering structure–property relationships in electroactive polymers.

amorphous phase↗
NASA NTRS2017

Modeling for Battery Prognostics

For any battery-powered vehicles (be it unmanned aerial vehicles, small passenger aircraft, or assets in exoplanetary operations) to operate at maximum efficiency and reliability, it is critical to monitor battery health as well performance and to predict end of discharge (EOD) and end of useful life (EOL). To fulfil these needs, it is important to capture the battery's inherent characteristics as well as operational knowledge in the form of models that can be used by monitoring, diagnostic, and prognostic algorithms. Several battery modeling methodologies have been developed in last few years as the understanding of underlying electrochemical mechanics has been advancing. The models can generally be classified as empirical models, electrochemical engineering models, multi-physics models, and molecular/atomist. Empirical models are based on fitting certain functions to past experimental data, without making use of any physicochemical principles. Electrical circuit equivalent models are an example of such empirical models. Electrochemical engineering models are typically continuum models that include electrochemical kinetics and transport phenomena. Each model has its advantages and disadvantages. The former type of model has the advantage of being computationally efficient, but has limited accuracy and robustness, due to the approximations used in developed model, and as a result of such approximations, cannot represent aging well. The latter type of model has the advantage of being very accurate, but is often computationally inefficient, having to solve complex sets of partial differential equations, and thus not suited well for online prognostic applications. In addition both multi-physics and atomist models are computationally expensive hence are even less suited to online application An electrochemistry-based model of Li-ion batteries has been developed, that captures crucial electrochemical processes, captures effects of aging, is computationally efficient, and is of suitable accuracy for reliable EOD prediction in a variety of operational profiles. The model can be considered an electrochemical engineering model, but unlike most such models found in the literature, certain approximations are done that allow to retain computational efficiency for online implementation of the model. Although the focus here is on Li-ion batteries, the model is quite general and can be applied to different chemistries through a change of model parameter values. Progress on model development, providing model validation results and EOD prediction results is being presented.

Prognostics↗
DOE OSTI2026

Mixed-anion electrolytes: from bulk speciation to interfacial dynamics in divalent metal electrodeposition

Mixing anions is emerging as a promising strategy for multivalent electrolyte design, allowing for adjustment of the solvation structure of bulk cations and enhancing the efficiency of electrochemical processes (e.g. metal deposition for batteries and catalysis). Further progress in electrolyte development requires a fundamental understanding of how tailored electrolyte speciation in mixed anion systems can modify the dynamic electrochemical interface during metal cycling. In this study, we present an anode-focused mechanistic study of exemplar Mg electrolytes containing three different secondary anions, correlating electrochemical behavior with bulk speciation and operando interfacial dynamics. Electrospray Ionization-Mass Spectrometry (ESI-MS) results reveal a general trend of forming mixed anion contact ion pairs (CIPs) across various anions, with the extent of ion pairing influenced by the association strength of the secondary anion. Operando multiharmonic electrochemical quartz crystal microbalance with dissipation (EQCM-D) reveals how these bulk species influence interfacial mass uptake, viscoelasticity, and solvent-coupled hydrodynamic behavior during deposition and stripping. The results indicate that Mg-containing ion pairs and solvated complexes shape adsorption, nucleation, and deposit growth, leading to distinct anion-dependent interphases ranging from more permeable, solvent-coupled layers to relatively compact and rigid deposits. This work establishes a quantitative link between bulk speciation and interfacial dynamics in divalent metal electrodeposition and provides mechanistic guidance for electrolyte design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Polarons are probes of the dynamic nanoscale environments found in electrochemically doped π-conjugated polymers

Charge carriers (i.e., polarons) in electrochemically doped organic (semi)conductors are proposed to be regulated by several physicochemical features, including the chemical compositions and structures of the π-conjugated frameworks of the semiconductor building blocks, the chemistry of the electrolyte (considering both the salt and solvent), multiscale and time-dependent morphology variations across the material as a function of electrochemical processes, and assorted permutations of these and other factors. To address these hypotheses, we investigate the energetic, optoelectronic, chemical, and local structural properties of negative polarons (radical anions) as a function of electrochemical doping in the donor–acceptor, π-conjugated redox copolymer P(NDI2OD-T2), also referred to as N2200. A critical finding is that there is not just “one type” of polaron in electrochemically doped P(NDI2OD-T2). Rather, an ensemble of polarons exists, with the polarons having optoelectronic signatures that are defined by their nanoscale environments. Importantly, the polaron optical signatures serve as local probes for how the operando electrochemical environments are dynamically working in concert to facilitate charge transport. Collectively, the distinctive and extensive integration of theory and measurement science presented here establishes a baseline for the roles that semiconductor and electrolyte chemistries and dynamic structural features have on polarons in electrochemically doped organic semiconductors and how these factors influence the energetics and rates of polaron transport.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Membrane Characterization For Rare Earth Element Separations

The scope of this work is to gain a baseline in membrane characterization for common rare earth elements. Electrochemical processes and techniques for rare earth elements have already been implemented in some cases, but the fundamental behavior has not been thoroughly investigated. With an understanding of the behavior that occurs within the membrane, a better electrochemical device can be developed.

36 MATERIALS SCIENCE↗
DOE OSTI2026

How to Minimize Faradaic Efficiency Error in Electrochemical CO 2 Reduction for Gas Products

Faradaic efficiency (FE) is an important metric for evaluating electrochemical processes, such as carbon dioxide reduction, that is often used for performance comparisons. Although the equation to calculate FE is well-known, details needed to yield accurate values are often overlooked, potentially leading to errors exceeding 100%. Avoiding any errors is crucial for drawing correct conclusions, especially during a catalysis optimization process. Factors with high potential for FE errors include incorrect mass flow rates and temperature values, imprecise gas chromatography calibrations, and uncorrected gas viscosities, while factors with less potential are also identified. In conclusion, this manuscript presents FE calculation guidelines intended for both newcomers and experts in the field of electrochemical fuel production.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Porous transport electrodes for oxygen evolution reaction in proton exchange membrane water electrolysis -cells: Materials, designs, and diagnoses

H 2 production using proton exchange membrane (PEM) water electrolysis (PEMWE) cells has received considerable attention because of the high efficiencies of these cells and no harmful emissions from the related process. In PEMWE cells, porous transport electrodes (PTEs) composed of a catalyst layer (CL) comprising O 2 evolution reaction (OER) catalysts, porous transport layer (PTL), and PEM play key roles in the stack performance and lifetime. Herein, Ir-based and non-precious-metal OER catalysts that are highly active and stable at low pH values and high anodic potentials are reviewed to understand their OER mechanisms. Various strategies are proposed for engineering CLs and PTLs to improve the interfacial properties and mass transfers of reactants and products to and from the active sites. Additionally, diagnoses of PTEs is significantly crucial for interpreting electrochemical processes and addressing their current challenges. Therefore, half-cell analyses, including diffusion electrode (DE), floating electrode (FE), and modified rotating disk electrode (MRDE) techniques, are explored, and membrane electrode assembly (MEA)-based analyses, such as the polarization technique, electrochemical impedance spectroscopy, and magnetic field analysis, are established. In conclusion, this study aims to provide an overview of recent technologies used for the engineering and diagnostic tools of PEMWE cells and insights into the advanced components and systems to be developed in this field.

Diagnosis of PEMWE Cells↗
DOE OSTI2025

MARIE: A Python-Based Framework for Comprehensive Fuel Recycling Modeling

One of the most pressing challenges to the continued deployment of nuclear energy systems is in the ultimate management and disposition of discharged fuel assemblies. While reprocessing and recovery of valuable materials from UNF assemblies has been considered as part of an overall strategy for minimization of the volume of reactor-based wastes to be managed, the deployment of commercial-scale reprocessing facilities presents an enormous economic challenge. The MARIE software package has been developed as a means of confronting this challenge. Representing components of a generic fuel reprocessing operation as individual physical processes, MARIE is designed as a modular framework intended to allow for analysis and cost-optimization for a hypothetical reprocessing facility while realistically accounting for the physical characteristics of the used fuel source term, such as decay heat, activity, and radiation dose (informing corresponding shielding requirements). Capabilities supported by MARIE include head-end operations such as fuel shearing, voloxidation, and dissolution; generic solvent extraction operations informed by available open-literature data; a suite of unit operations intended to represent electrochemical processing of used fuel assemblies (i.e., oxide reduction, electrorefining, and electrowinning); and finally, accounting for both costs and physical features of discharged waste streams, which can be used to inform follow-on analyses such as the feasibility of deep-borehole disposal of HLW. This paper presents an overview of the MARIE software capabilities, including how individual unit operations are implemented to enable a larger-scale optimization of a hypothetical reprocessing operation on aspects such as cost and recovery of valuable materials.

Skutnik, Steve [ORNL] (ORCID:000000016441135X)↗
DOE OSTI2026

Modular multi-interface nanocrystals for enhanced ethanol oxidation electrocatalysis

Electrochemical processes that utilize biomass-derived ethanol as a source of electrons and protons offer a sustainable energy strategy, yet their practical implementation is limited by sluggish ethanol oxidation reaction (EOR) kinetics and catalyst poisoning. Here, in this study, we report a modular multi-interface nanocrystal catalyst comprising core/shell Co 2 P/Pd and Pd-Au heterostructured interfaces that exhibit complementary functions for the enhanced EOR catalysis. The Co 2 P/Pd interface boosts Pd atom utilization and lowers the kinetic barriers for ethanol-to-acetate conversion, while the Pd-Au interface effectively alleviates CO poisoning caused by C–C bond cleavage of ethanol. In-depth analyses using in situ attenuated total reflectance-surface-enhanced infrared absorption spectroscopy, differential electrochemical mass spectrometry, and density functional theory calculations elucidate the mechanistic roles of these interfaces. The optimized Co 2 P/Pd-Au 0.08 nanorods achieve an excellent mass activity, underscoring the potential of modular, multi-interface nanocrystals for advancing EOR catalysis and offering a generalizable strategy for broader catalytic innovations.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Molecular insights into CO 2 -to-bicarbonate transformation in functionalized anion exchange ionomers for electrochemical separations

Bipolar membrane (BPM) electrochemical processes are a promising platform for carbon dioxide (CO 2 ) separations, but the molecular level thermodynamic and kinetic understanding of CO 2 -to-bicarbonate (HCO 3 − ) transformation remain poorly understood. This study employs a multiscale computational approach to systematically explore the adsorption and reactive transformation of CO 2 in five anion exchange ionomer systems. Classical molecular dynamics (MD) simulation results demonstrate that polymers with imidazolium groups significantly reduce CO 2 diffusion and enhance (OH − )–CO 2 interactions due to stronger electrostatic and π-interactions. Compared to the commonly used quaternary ammonium ionomers, imidazolium-functionalized ionomers show improved CO 2 proximity and interaction strength. Ab initio MD and density functional theory (DFT) calculations reveal that the benzyl-substituted imidazolium (IM-Ben) substantially reduces the energy barrier for HCO 3 − formation (∼72 meV lower) compared to the alkyl-substituted IM-nBu, while also mitigating imidazolium deprotonation under moderate hydration conditions. Transition state analysis shows IM-Ben forms more extensive hydrogen-bonding networks, which stabilize the transition state structure and contribute to a lower energy barrier for bicarbonate formation. These findings highlight the advantage of the adjacent benzyl moiety in enabling efficient CO 2 -to-bicarbonate transformation via hydrated hydroxide ion counterions, offering mechanistic insights and clear molecular design principles for optimizing anion exchange ionomers at bipolar membrane interfaces for electrochemical CO 2 separation applications.

Bipolar membranes, Reactive transformation of CO2,↗
DOE OSTI2025

Electroplated Polymer‐Modified Carbon Fiber for Performance‐Enhancing Composite Interfaces

Carbon fiber composite performance relies on the fiber-matrix interface for effective load transfer. To enhance interfacial properties between the fiber and matrix, often carbon fiber surfaces are oxidatively and covalently modified to incorporate chemical functional groups. By contrast, here, noncovalent electrodeposition of functional polyelectrolyte is applied onto conducting carbon fibers from aqueous solutions. A natural polymer, chitosan (CS), is electro-deposited onto the fiber surface, which undergoes multi-scale physical interactions. The bound CS layer with abundant amine functionalities reacts with epoxy moieties within the matrix to improve the interfacial properties. The scalable and energy-efficient electrodeposition eliminates traditional functionalization and sizing requirements of carbon fiber while delivering significantly higher mechanical performance with enhanced consistency. For continuous fiber reinforced composites, compared to conventional fibers, apparent interlaminar shear strength increases by 27%, reaching ≈86 MPa. The short fiber composites with only 2–11 wt.% fibers exhibit ≈20% increase in tensile strength with a peak performance of 120 MPa. Unlike traditionally treated and sized carbon fiber, this approach delivers coated fibers with long shelf-life and allows recovery of both CS in electrolyte form and carbon fiber by continuous electrochemical processing of the modified fibers with inverse polarity; thus, it promotes overall fiber recyclability.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Numerical and experimental analysis of mechanically induced failure in electric vehicle battery modules

Mitigating thermal runaway and cell-to-cell propagation is essential for improving the safety of electric and hybrid vehicles. Enhancing digital twin capabilities to predict battery mechanical abuse is particularly critical for automotive and aerospace applications, where crashworthiness is a key concern. Understanding failure conditions and propagation in battery modules during mechanical abuse is complex due to interactions between structural deformation, heat transfer, electrochemical processes, exothermic reactions and mechanical fracture. While prior studies have focused on modeling cell-level behavior, extending these models to module or pack level is necessary for a system level understating of electric vehicle safety. This study develops coupled large deformation finite element models that simultaneously solve for electrochemistry, material failure, internal short circuit and thermal runaway propagation. The models account for mechanical and thermal interactions between lithium-ion cells and other battery components while the contact interfaces are evolving with time. Model-predicted voltage, temperature and force responses are compared with experimental data for validation. The results demonstrate that the approach captures key failure mechanisms, including thermal propagation through heat transfer, electrical propagation from short circuits in parallel-connected cells, and mechanical propagation via penetration and crack formation. These findings show that computational models are valuable tools for understanding battery module failure and providing insight that can reduce the need for extensive experimental testing.

25 ENERGY STORAGE↗
DOE OSTI2026

Electrochemo-mechanics unlocks hidden dynamics of lithium plating under stacking pressure

Understanding and mitigating lithium plating remains one of the most pressing challenges in advancing the safety and longevity of lithium-ion batteries (LIBs). Here, we present a novel integrative framework that combines in-operando swelling force measurements with a physics-based electro-chemo-mechanical model to uncover previously inaccessible insights into lithium plating dynamics under mechanical constraints. Unlike existing approaches that focus primarily on electrochemical signatures, our approach captures the coupled mechanical responses of commercial pouch cells during cycling, revealing how mechanical constraints fundamentally alter degradation pathways. We demonstrate that the use of a moderate stacking pressure suppresses lithium plating and enhances lithium stripping. This mechanically driven structural effect, coupled with the electrochemical process, significantly extends the linear aging regime in LIBs. Intriguingly, intermittent capacity recovery events that were observed during the battery cycling suggest dynamic lithium reactivation, a phenomenon rarely captured in real-time. This study pioneers a stress-aware methodology for diagnosing and managing lithium plating, establishing a new paradigm for real-time battery health monitoring. The findings offer transformative implications for the design of durable, high-performance LIB systems, opening new avenues for intelligent control strategies in battery management systems.

Bhowmick, Amit↗
DOE OSTI2026

Spatiotemporal and Statistical Mapping of Transition Metal Equilibria in Alkaline Media

Transition metal dissolution and redeposition (D/R) kinetics in alkaline media play a critical role in various chemical and electrochemical processes. Competitive reaction kinetics between different transition metals can modulate individual metal behavior in these processes. To date, these phenomena have remained largely unmeasured, and even when captured, they are difficult to statistically characterize due to their dynamic nature, simultaneous occurrence, and spatially heterogeneous nature. Here, in this study, we develop a statistical analysis framework based on in situ and operando X-ray fluorescence microscopy (XFM) to investigate the relative D/R kinetics of multiple transition metals in alkaline media. By employing statistical analysis, we quantify the spatial distribution of D/R species and assess the rate at which the system reaches equilibrium under varying reaction conditions. We show that pH does not simply change the rate of dissolution and redeposition, but reorganizes the cross-element kinetic correlations among Ni, Fe, and Mn and accelerates the spatial equilibration of D/R events, as quantified through correlation analysis, reaction-rate estimation, probability function distributions, and texture-based monitoring statistics. Additionally, we demonstrate how modifying the solvent environment can influence D/R kinetics, providing a pathway for tuning materials synthesis and process optimization. Our study offers valuable insights into the complex interplay between different transition metals and provides a reliable statistical framework for spatial analysis of diverse imaging data sets, enabling deeper extraction of latent information across multiple modalities.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Solvent Stabilization of Protic Oxonium/Ammonium Intermediates in Cation Radical Cyclization Reactions Investigated via Computational Approaches

Anodic intramolecular cyclization reactions have substantial synthetic utility for formation of cyclic carbon–carbon or carbon–heteroatom bonds. For cases of intramolecular trapping of a cation radical by a protic nucleophile, the cyclization step coincides with a substantial increase in substrate acidity and thus may exhibit particularly pronounced solvent effects. In this computational work, we employ both quantum chemical (QM) and quantum mechanics/molecular mechanics (QM/MM) methods to compute solvent effects on free energy profiles for cyclization and deprotonation reaction steps for cation radical intermediates of substrates representative for anodic intramolecular cyclizations. We find substantial solvent contribution to the thermodynamic driving force for cation radical cyclization; for example, methanol and tetrahydrofuran solvents provide ∼30–35 kJ/mol driving force to form cyclic oxonium cation radicals and ∼15–25 kJ/mol driving force to form cyclic ammonium cation radicals, compared to baseline reactions in dichloromethane solvent. Given that these solvent shifts are on par with the innate cyclization reaction thermodynamics, the choice of solvent plays a crucial role in promoting/driving the cation radical cyclization step. Methanol is particularly effective at facilitating rapid deprotonation of the cyclic cation radical intermediate, which may lead to the full electrochemical process (e.g., second electron transfer) proceeding heterogeneously at the anode.

Khan, Shahriar [ORNL] (ORCID:0000000289138430)↗
DOE OSTI2025

Stability of Mn-Doped TiO 2 Thin-Film Anodes during Water Oxidation Reactions

Incorporating manganese atoms into TiO 2 has been shown to improve its activity for water oxidation. However, its activity has been observed to steadily degrade under constant applied potential, especially at more oxidizing applied potentials. Here, the compositional profile and electrochemical stability of Mn-doped TiO 2 (Mn:TiO 2 ) thin-film electrodes precisely fabricated by atomic layer deposition (ALD) were evaluated to elucidate the mechanisms of electrode degradation. Although ALD enables the deposition of Mn dopants throughout the film thickness, only Mn within 1.5 nm of the surface was observed to be redox active. Annealing Mn:TiO 2 films in air leads to the diffusion of Mn toward the electrode surface and oxidation of the Mn and alters the redox behavior. Annealing endows greater stability to Mn redox behavior but does not fully stabilize the water oxidation current, suggesting that the two electrochemical processes are not precisely correlated. In situ inductively coupled plasma mass spectrometry reveals that Mn is lost from Mn:TiO 2 films at potentials greater than 1.8 V vs RHE. However, the initial Mn loss is equivalent to less than a single ALD layer of MnO x . Longer-term constant potential experiments suggest that Mn is lost from up to 1 nm of the electrode surface but that this loss may account for only a portion of the diminished water oxidation activity.

atomic layer deposition↗
DOE OSTI2025

Anodized Aluminum Oxide Membrane Ionic Memristors

Memory effect in ion transport (IT) at the solid–solution interface is uniquely attractive in that the conductance depends on or “memorizes” the previous states. Hysteretic and rectified transport properties offer exciting potential to developing advanced iontronics and neuromorphic functions, improving the efficiency of energy conversion and electrochemical processes, and overcoming the selectivity-throughput bottleneck in the enrichment of low abundant species for environment- and energy-friendly separations, among others. Herein, memory effects are discovered in the rectified electrokinetic IT through anodized aluminum oxide (AAO) membranes containing densely packed highly ordered nanochannels (10 10 per cm 2 ). Characteristic memristor responses of pinched current–potential loops are resolved in voltammetric experiments and successfully reproduced through finite element simulation. Excitatory and inhibitory conductance states are shown to arise from the enrichment and depletion of mobile charge carriers. Structurewise, the transport symmetry is broken by the barrier oxide layer (BOL) on the one end of the cylindrical nanochannels across the AAO membranes. Charge selectivity is attributed to the gradient(s) of the space charge density across the BOL characterized by depth profiling via X-ray photoelectron spectroscopy analysis. The space charge gradient(s) overcomes the fundamental limitation of widely exploited surface charge effects to enable intense rectification and hysteresis prevailing at very high ionic concentrations up to 1–2 M. A new strategy is developed for controlling the preferential IT direction and selectivity via counterion intercalation and extraction/exchange. Mechanistic understanding is further confirmed through parameter variations such as potential scan rate and ionic strength, which also demonstrates convenient controls of the related functions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗