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At least 55 records · Page 3

Dynamic Shaping of Grid Response of Multi-Machine Multi-Inverter Systems Through Grid-Forming IBRs: Preprint

We consider the problem of controlling the frequency response of weakly-coupled multi-machine multi-inverter low-inertia power systems via grid-forming inverter-based resources (IBRs). In contrast to existing methods, our approach relies on dividing the larger system into multiple strongly-coupled subsystems, without ignoring either the underlying network or approximating the subsystem response as an aggregate harmonic mean model. Rather, through a structured clustering and recursive dynamic shaping approach, the frequency response of the overall system to load perturbations is shaped appropriately. We demonstrate the proposed approach for a three-node triangular configuration and a small-scale radial network. Furthermore, for small-scale radial microgrids, we demonstrate the ability of IBRs to tune the effective transfer functions of synchronous machines. This enables us to relax the uniform turbine time-constant assumptions and widen the scope of existing synchronization results for proportionally heterogeneous machines.

frequency-shaping control↗

Effect of Molecular Conformation on Intermolecular Interactions and Photovoltaic Performances of Giant Molecule Acceptors

The molecular conformation of giant molecule acceptors (GMAs) plays a significant role in regulating the intermolecular interactions and their photovoltaic performances in organic solar cells (OSCs). For the linear GMA GT‐l, the stronger homo‐molecular interaction causes its aggregation being weakly affected by the donor, thus forming an ordered molecular stacking and proper phase separation in its blend film. The star‐shaped GMA GT‐s‐based blend film shows a dominant hetero‐molecular interaction that suppresses the aggregation of the donor and acceptor, resulting in smaller phase separation and more uniform vertical phase distribution. While for another star‐shaped GMA GTs, the weakest hetero‐molecular interaction causes its blend film to form larger phase separation. Therefore, the GT‐l based OSC with PM6 as donor shows the highest charge mobilities, the fastest charge transfer (CT) process, reduced energy loss and less charge recombination, contributing to a higher power conversion efficiency (PCE) of 19.03%. Comparatively, the PCEs of the OSCs based on GTs and GT‐s are 18.05% and 17.58% respectively. Notably, all the three GMAs based OSCs show excellent thermal stability and long‐term storage stability. This study provides a facile strategy by tuning the linking unit and its connecting mode for designing highly efficient and stable organic photovoltaic materials.

Chemistry↗

New Phosphoranylideneketenes and Phosphoranylidenethioketenes‐Synthesis, Structure, Spectroscopy, and Lewis Base Properties

Posphoranylideneketene Ph 3 PCCO and its sulfur analogue, Ph 3 PCCS, are cumulated ylides that exhibit diverse reactivity and distinct structural features. Herein, we present the first systematic study of substituent effects on the structures and bonding of a series of aryl- and alkyl-substituted phosphoranylideneketenes, R 3 PCCO [R = Et, cyclohexyl, NMe 2 , 4-Me 2 N-C 6 H 4 , 4-MeO-C 6 H 4 , 4-CF 3 -C 6 H 4 , 3,5-(CF 3 ) 2 -C 6 H 3 ], prepared from the corresponding phosphonium salts, [R 3 PCH 2 COOEt]X (X = Br, I) and two equivalents of Na[N(SiMe 3 ) 2 ]. Multinuclear NMR and IR spectroscopy, supported by single-crystal X-ray diffraction, revealed that the bond strength within the central P═C═C═O fragment increases with the electron-deficiency of the aryl substituents at phosphorus. The corresponding phosphoranylidenethioketenes, R 3 PCCS (R = Et, cyclohexyl, NMe 2 , 4-Me 2 N-C 6 H 4 , 4-MeO-C 6 H 4 , 4-CF 3 -C 6 H 4 ), were obtained by reactions of R 3 PCCO with CS 2 . Here, the rate of conversion of R 3 PCCO into R 3 PCCS decreases with increasing electron deficiency at phosphorus. Both R 3 PCCO and R 3 PCCS act as relatively weak ambidentate Lewis donors, yet they form stable acid-base adducts with strong Lewis acids such as B(C 6 F 5 ) 3 and Al(C 6 F 5 ) 3 .

Lewis acid-base adduct↗

Anion–Cation–Anion Ion Triplet Characterization by Computation and Photoelectron Spectroscopy

Ion triplets of the chloride salts of two commonly used weakly coordinating cations are reported (i.e., Cl – ·NMe 4 + Cl – (1 – ) and Cl – ·PPh 4 + Cl – (2 – )). Negative ion photoelectron spectra at 20 K afford vertical and adiabatic detachment energies of 5.18 and 5.00 eV (1 – ) and 5.03 and 4.70 eV (2 – ), respectively. These results are well reproduced by coupled cluster calculations with single, double, and perturbative triple excitations (CCSD(T)) whereas M06-2X is systematically too small by ~0.3 eV (i.e., 7 kcal mol –1 ). The structures of both 1 – and 2 – have five or six C–H···Cl – interactions that stabilize these cluster anions by 32 (1 – ) and 27 (2 – ) kcal mol –1 as given by their chloride dissociation enthalpies. In conclusion, these values drop to 7.4 and 3.8 kcal mol –1 in dichloromethane based up conductor-like polarizable continuum model calculations and suggest that X – ·M + X – ion triplets with a weakly coordinating cation maybe the reactive form of salts under some conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optimizing semi-hydrogenation of unsaturated hydrocarbons by electrolyte engineering approach

Electrochemical hydrogenation of unsaturated hydrocarbons, when powered by renewables, represents a unique opportunity to substitute current energy-intensive synthetic routes. Modulation of adsorption energies of the organic substrate and key intermediates of the reaction is critical for fine tuning of the yield, selectivity and kinetics of the reaction. Interestingly, mounting evidence exists regarding the role of electrolyte composition in the outcome of semi-hydrogenation reactions. Nevertheless, electrolyte optimization is a complex task, owing to its hybrid nature. Indeed, it is composed of water serving as a proton source, an organic solvent necessary to dissolve the organic substrate and a conducting salt. Herein, we demonstrate that varying conducting salt and organic solvent has a dramatic impact on the outcomes of semi-hydrogenation of alkynes. By varying salt and water concentrations, we demonstrate that water does not serve as a proton source, and instead addition of an acid is necessary. While increasing the acid concentration increases the yield of the reaction, at too large concentrations the hydrogen evolution reaction becomes predominant. Furthermore, by combining electrochemical measurements with spectroscopic techniques including Fourier transform infrared (FTIR) spectroscopy and small angle X-ray spectroscopy (SAXS), we demonstrate that the electrolyte solvation structure dramatically impacts the yield of the reaction. Organic solvents weakly interacting with water, including acetonitrile, form aqueous nanoheterogeneities that prevent the organic substrate from accessing the catalyst interface and thus lead to limited yields. Instead, solvents such as dimethylformamide form homogeneous mixtures with which all reactants can access the interface, leading to yields greater than 80% for optimized compositions.

Zhang, Rongyu↗

The 650 °C Tensile Deformation of Graded IN718-René41 Superalloy Fabricated by Laser Blown-Powder Directed Energy Deposition

The microstructure and 650 °C tensile properties of a compositionally graded IN718-René41 (718-R41) superalloy fabricated by laser blown-powder directed energy deposition (DED-LB/M) are investigated to understand structure–property relationships and baseline tensile properties. Digital Image Correlation (DIC), in situ neutron diffraction, and conventional characterization techniques are performed to study the as-built and heat-treated states. The applied heat treatment generates static recrystallization and equiaxed grains in 718-rich compositions, while R41-rich compositions remain partially or un-recrystallized possibly influenced by a higher MC carbide fraction (>0.5%). The yield strengths of the 718 and R41 sections in the heat-treated state are comparable to wrought forms but the graded compositions show weakness due to unoptimized heat treatment. Diffraction elastic constants first decrease and then increase along the 718-R41 composition gradient, while a small difference is observed between the as-built and heat-treated states and γ, γ′ phases. Overall, the compositionally graded region shows a smooth transition in the elastic properties. Grain-level load transfer from the (220) to (200) grains shows compositional dependence, and qualitatively agrees with DIC-measured macroscopic yield strength. Within the (200) grains, the γ/γ′ phases deform elastically until the γ phase yields and afterwards, the γ′ phase takes load from the γ phase.

Huang, Shenyan (ORCID:0000000196528114)↗

Synergistic Anion and Solvent-Derived Interphases Enable Lithium-Ion Batteries under Extreme Conditions

Lithium-ion batteries (LIBs) face increasingly stringent demands as their application expands into new areas, including extreme temperatures and fast charging. To meet these demands, the electrolyte should enable fast lithium-ion transport and form stable interphases on electrodes simultaneously. In practice, however, improving one aspect often compromises another. For instance, the trend toward electrolytes forming anion-derived interphases typically reduces transport efficiency due to weak-solvating solvents. Here, we propose that instead of relying on anions to form the interphase, leveraging both solvents and anions to form interphases can potentially lead to a balancing point between robust interphase formation and effective ion transport. Guided by this design principle, 2,2-difluoroethyl ethyl carbonate (DFDEC) was identified as the promising solvent. With the new electrolyte using DFDEC as the major solvent and lithium bis(fluorosulfonyl) imide (LiFSI) as the salt, graphite||LiNi 0.8 Mn 0.1 Co 0.1 O 2 (NMC811) full cells are capable of fast charging and demonstrate long-term cycling stability with a cutoff voltage of 4.5 V. Notably, the battery shows a capacity retention of 84.3% after 500 cycles with an average Coulombic efficiency (CE) as high as 99.93%. This new electrolyte also enables stable battery cycling across a wide temperature range (-20 to 60 °C), with excellent capacity retention.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

In situ transmission electron microscopy observations of CaCO 3 crystallization onto polysaccharide-coated nanoparticles

Polysaccharides and proteoglycans are widely associated with the organic matrix at sites of CaCO 3 biomineralization, and previous studies indicate that these macromolecules may confer greater roles in mineral nucleation than previously recognized. This investigation uses in situ liquid-phase transmission electron microscopy (LP-TEM) to observe CaCO 3 nucleation onto aminated silica (SiO 2 –NH 3 + ) nanoparticles treated with a layer of chitosan (near-neutral derivative of chitin) or heparin (a carboxylated and highly sulfated glycosaminoglycan). In the absence of polysaccharides, few CaCO 3 particles formed and exhibited mobility. However, the SiO 2 –NH 3 + nanoparticles were enveloped in a region of higher mass density relative to the bulk solution, suggesting the development of a local solute-rich environment that surrounds the charged NH 3 + groups. The heparin- or chitosan-coated silica particles also exhibited regions of higher mass density around the nanoparticles. In the presence of these polysaccharide coatings, we observed the nucleation of abundant CaCO 3 particles whereby the polyanionic heparin promoted more nucleation than the weakly cationic chitosan. Many crystallites appeared to form at the polysaccharide–TEM cell membrane–solution interface, further indicating interfacial and macromolecule-specific control on crystallization. The combined results demonstrate that chitosan and heparin have an appreciable effect on the timing, size, and location of CaCO 3 nucleation compared to the polysaccharide-free nanoparticles.

15 GEOTHERMAL ENERGY↗

Application of Weak-Beam Dark-Field STEM for Dislocation Loop Analysis

Nanoscale dislocation loops formed by irradiation can significantly contribute to both irradiation hardening and embrittlement of materials when subjected to extreme nuclear reactor environments. Here, this study explores the application of weak-beam dark-field (WBDF) scanning transmission electron microscopy (STEM) methods for quantitative irradiation-induced defect analysis in crystalline materials, with a specific focus on dislocation loop imaging and analysis. A high-purity Fe-5 wt% Cr model alloy was irradiated with 8 MeV Fe 2+ ions at 450°C to a fluence of 8.8 × 10 19 m -2 , inducing dislocation loops for analysis. While transmission electron microscopy (TEM) has traditionally been the primary tool for dislocation imaging, recent advancements in STEM technology have reignited interest in using STEM for defect imaging. This study introduces and compares three WBDF STEM methods, demonstrating their effectiveness in suppressing background contrasts, isolating defect information for dislocation loop type classification, providing finer dislocation line images for small loop analysis, and presenting inside–outside contrast for identifying loop nature. Experimental findings indicate that WBDF STEM methods surpass traditional TEM approaches, yielding clearer and more detailed images of dislocation loops. The study concludes by discussing the potential applications of WBDF STEM techniques in defect analysis, emphasizing their adaptability across various material systems beyond nuclear materials.

36 MATERIALS SCIENCE↗

Time evolution of a pumped molecular magnet—A time-resolved inelastic neutron scattering study

Introducing an experimental technique of time-resolved inelastic neutron scattering (TRINS), we explore the time-dependent effects of resonant pulsed microwaves on the molecular magnet Cr 8 F 8 Piv 16 . The octagonal rings of magnetic Cr 3+ atoms with antiferromagnetic interactions form a singlet ground state with a weakly split triplet of excitations at 0.8 meV. A 4.6 tesla field was applied to tune the splitting between two members of the triplet excited level |1$\rangle$ ↔ |2$\rangle$ to resonance with 105 GHz (0.434 meV) microwaves. The time-dependent occupations of the ground state |0$\rangle$, lower lying levels |1$\rangle$ and |2$\rangle$, and higher energy states |λ ≥ 3$\rangle$ were extracted during and after 20 s long microwave pulses incident along the (101) direction of a Cr 8 F 8 Piv 16 crystal held at 1.9 K. At significantly elevated spin temperatures, we found underpopulation relative to thermal equilibrium of |2$\rangle$ and spin-lattice thermalization time scales ranging from 1.6(2) s to 5.7(2) s depending on the power level. This contrasts with the relaxation time τ 1 (T → 0) = 27(5) 𝛍 s inferred for |2$\rangle$ from in situ Electron Spin Resonance measurements. By probing a broad range of excited states during intense microwave pumping, TRINS thus provides a first view of long lived excited states in a molecular antiferromagnet.

Science & Technology - Other Topics↗

Dynamical phase transition in a strongly hybridized phonon-triplon chain

In this article, we study a dimerized spin-1/2 chain, such as CuGeO 3 , hosting triplon excitations coupled to optical phonons under weak terahertz laser driving. Both phonons and triplons weakly lose energy into the surrounding baths, forming a non-equilibrium steady state. In the strong phonon-triplon coupling regime, phonons near the two-triplon continuum hybridize strongly with triplons. Using mean-field Lindblad dynamics, we show that strong hybridization induces sharp first-order phase transitions—either single or simultaneous double—in the emission spectrum, mainly due to nonlinearities in the chain and the instantaneous breaking of spatial inversion symmetry, as captured by the phonon displacement. Using mean-field Floquet analysis of harmonic modes in both sectors, we analytically confirm the existence of these phase transitions. Furthermore, we map the complete steady-state phase diagram by varying key control parameters and provide experimentally relevant parameters for observing these transitions in laser-driven CuGeO 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

In situ coherent x-ray scattering reveals polycrystalline structure and discrete annealing events in strongly coupled nanocrystal superlattices

Solution-phase bottom up self-assembly of nanocrystals into superstructures such as ordered superlattices is an attractive strategy to generate functional materials of increasing complexity, including very recent advances that incorporate strong interparticle electronic coupling. While the self-assembly kinetics in these systems have been elucidated and related to the product characteristics, the weak interparticle bonding interactions suggest the superstructures formed could continue to order within the solution long after the primary nucleation and growth have occurred, even though the mechanism of annealing remains to be elucidated. Here, we use a combination of Bragg coherent diffractive imaging and x-ray photon correlation spectroscopy to create real-space maps of supercrystalline order along with a real-time view of the strain fluctuations in aging strongly coupled nanocrystal superlattices while they remain suspended and immobilized in solution. By combining the results, we deduce that the self-assembled superstructures are polycrystalline, initially comprising multiple nucleation sites, and that shear avalanches at grain boundaries continue to increase crystallinity long after growth has substantially slowed. This multimodal approach should be generalizable to characterize a breadth of materials in their native chemical environments, thus extending the reach of high-resolution coherent x-ray characterization to the benefit of a much wider range of physical systems. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

Non-thermal atmospheric pressure plasma–liquid synthesis of organic acids in aqueous solution from carbon monoxide

This work aims at understanding the conversion of CO to organic acids, namely oxalic acid and formic acid, using non-thermal atmospheric pressure plasma over aqueous solutions. CO exhibited significantly higher conversion to organic acids (more than 15×) compared to CO 2 under the same reaction conditions. The result bolsters a proposed two-step process for CO 2 fixation, whereby CO 2 is first converted to CO, and then CO is converted to organic acids. The organic acids produced from CO are intermediates in the water–gas shift (WGS) reaction of CO in the presence of an aqueous solution to dissolved CO 2 and hydrogen gas. Based on a simple thermodynamic analysis, the organic acid yield was increased by lowering the plasma–liquid reaction temperature using an ice bath to cool the reaction flask. The composition of the organic acids could be varied by changing the pH of the solution. Oxalate was formed in higher concentrations with increasing solution pH above the pK a of the radical species (CO 2 )˙ − . Below the pK a value, formate was the exclusive organic acid formed. The production of formate has a rather weak pH dependence but is enhanced slightly at a basic pH above 10. Furthermore, at basic pH, the effect of electrolyte concentration comes into play. Higher electrolyte concentrations, leading to shorter electrolyte Debye lengths, resulted in lowered organic acid yields. The highest yields of organic acids obtained in our system were 122 mg L −1 for oxalate and 77 mg L −1 for formate at an optimum 1 mM NaOH concentration in the starting solution. This work is a successful pioneering example of CO to organic acids conversion using non-thermal plasmas, which opens the pathway for a promising two-step conversion process of CO 2 to organic acids.

Sudagar, Alcina Johnson [Washington University in ↗

Modulating metal-centered dimerization of a lanthanide chaperone protein for separation of light lanthanides

Elucidating details of biology’s selective uptake and trafficking of rare earth elements, particularly the lanthanides, has the potential to inspire sustainable biomolecular separations of these essential metals for myriad modern technologies. Here, we biochemically and structurally characterize Methylobacterium (Methylorubrum) extorquens LanD, a periplasmic protein from a bacterial gene cluster for lanthanide uptake. This protein provides only four ligands at its surface-exposed lanthanide-binding site, allowing for metal-centered protein dimerization that favors the largest lanthanide, La III . However, the monomer prefers Nd III and Sm III , which are disfavored lanthanides for cellular utilization. Structure-guided mutagenesis of a metal-ligand and an outer-sphere residue weakens metal binding to the LanD monomer and enhances dimerization for Pr III and Nd III by 100-fold. Selective dimerization enriches high-value Pr III and Nd III relative to low-value La III and Ce III in an all-aqueous process, achieving higher separation factors than lanmodulins and comparable or better separation factors than common industrial extractants. Finally, we show that LanD interacts with lanmodulin (LanM), a previously characterized periplasmic protein that shares LanD’s preference for Nd III and Sm III . Our results suggest that LanD’s unusual metal-binding site transfers less-desirable lanthanides to LanM to siphon them away from the pathway for cytosolic import. The properties of LanD show how relatively weak chelators can achieve high selectivity, and they form the basis for the design of protein dimers for separation of adjacent lanthanide pairs and other metal ions.

lanthanide biochemistry↗

Using Eye Tracking to Elucidate the Mechanisms Underlying Stimulation-Enhanced Visual Target Detection

Transcranial direct current stimulation (tDCS) is a noninvasive form of brain stimulation that involves passing a weak electrical current between electrodes on the scalp to modulate underlying neural tissue. TDCS has been shown to modulate cognition in a variety of domains, including memory, attention, and visual processing. Prior work from our laboratory has shown positive effects of tDCS on learning to detect target objects hidden in complex naturalistic visual scenes and learn rules for categorizing images, though the mechanism for these benefits remains unknown. One possibility is that tDCS optimizes visual search by modulating visual attention or via the reduction in search errors. One method of quantifying visual attention is to use eye tracking to record search patterns to determine if and how visual search is adjusted under verum stimulation conditions. Eye tracking data allows classification of errors into error types, including sampling errors (failing to look in the relevant region), recognition errors (looking at the critical portion of a scene, but failing to recognize it as such as evidenced by visual fixation), and decision-making errors (fixating on the relevant portion of a scene, but making the wrong determination). Our results indicate that the benefit tDCS confers on visual search for targets stems from the reduction in decision-making errors when targets are present (Cohen’s d = 0.86). Also reported is a replication of previous findings showing a tDCS-dependent improvement in learning this task, learning score (Cohen’s d = 0.88); d’ (Cohen’s d = 1.00). This provides support for moving tDCS into the application space by pairing it with analysts who are concerned with the type of search error that is corrected via stimulation.

attention↗

Emergent interaction-induced topology in Bose-Hubbard ladders

We investigate the quantum many-body dynamics of bosonic atoms hopping in a two-leg ladder with strong on-site contact interactions. We observe that when the atoms are prepared in a staggered pattern with pairs of atoms on every other rung, singlon defects, i.e., rungs with only one atom, can localize due to an emergent topological model, even though the underlying model in the absence of interactions admits only topologically trivial states. This emergent topological localization results from the formation of a zero-energy edge mode in an effective lattice formed by two adjacent chains with alternating strong and weak hoping links (Su-Schrieffer-Heeger chains) and opposite staggering which interface at the defect position. Our findings open the opportunity to dynamically generate nontrivial topological behaviors without the need for complex Hamiltonian engineering. Published by the American Physical Society 2025

Wellnitz, David (ORCID:0000000349788938)↗

Stripe and bubble ratchets on asymmetric substrates

We show that various nonmonotonic ratchet effects can arise when mesophase pattern-forming systems, which exhibit anisotropic crystal, stripe, and bubble regimes, are coupled to one-dimensional asymmetric substrates under ac driving. The patterns emerge in the absence of a substrate when the ratio of attraction to repulsion is varied for particles with competing short-range attraction and long-range repulsion potentials. In the presence of the substrate, we find that the ratchet efficiency varies nonmonotonically with increasing attraction, depending upon how well the mesophase morphology matches the substrate spacing and periodicity. For strong repulsion, there is a weak but finite ratchet effect, while at intermediate attraction, there is a robust ratchet effect in which the system forms stripes aligned with the substrate symmetry direction. For strong attraction, large bubbles appear that have weak or no ratchet effects when the bubble width exceeds the substrate lattice spacing, causing the bubble to be only weakly coupled to the substrate. For very strong attraction, small bubbles form and undergo a strong ratchet effect with an efficiency that oscillates as a function of ac drive amplitude. Although the small bubble regime is a strongly correlated regime in which each bubble contains many particles, the system behaves as if it is in a single-particle regime since the bubble width is much smaller than the substrate lattice spacing. We map out the different rectification phases as a function of the pattern morphology, substrate strength, and ac drive amplitude. The pronounced ratchet effects that we observe in some regimes can be exploited for pattern sorting in hard and soft matter systems. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Elucidating Phosphate and Cadmium Cosorption Mechanisms on Mineral Surfaces with Direct Spectroscopic and Modeling Evidence

The simultaneous sorption of cations and anions at the mineral–water interface can substantially alter their individual sorption characteristics; however, this phenomenon lacks a mechanistic understanding. Our study provides direct spectroscopic and modeling evidence of the molecular cosorption mechanisms of the cadmium ion (Cd 2+ ) and phosphate (P) on goethite and layered manganese (Mn) oxide of birnessite, through in situ attenuated total reflection Fourier-transform infrared (ATR-FTIR), P K-edge X-ray absorption near-edge structure (XANES) spectroscopy, and surface complexation modeling. Phosphate synergistically cosorbed with Cd on goethite predominantly through P-bridged ternary complexes (≡Fe–P–Cd) and electrostatic interactions at wide pH conditions. Likewise, P and Cd exhibited synergistic cosorption on birnessite by forming P-bridged ternary complexes (≡Mn–P–Cd) and weak competitive sorption at the layer edge sites. As pH and Cd loading increased, the surface P species transitioned from a binary complex to a ternary complex and/or Cd 3 (PO 4 ) 2 precipitate for both goethite and birnessite. Compared to that in solution at pH 8, the formation of Cd 3 (PO 4 ) 2 was inhibited by the presence of goethite and birnessite, ascribed to the specific adsorption of P and Cd, more pronounced in birnessite due to the stronger sorption of Cd at its vacant sites. Finally, the discovered cosorption mechanisms of P and Cd have important implications for understanding and predicting their mobility and availability in Cd-contaminated settings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗