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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Shifting the MLCT of d 6 metal complexes to the red and NIR

Light-active d 6 -coordination compounds hold great promise for light energy conversion, sensors and therapeutic applications. However, the activity in the red-to-NIR spectral region is highly desirable to convert solar light more efficiently, use low-cost red-light sources and activate these chromophores in biological tissue environment. Due to their versatility, tunability and broad intense absorption, d 6 -coordination compounds with metalto-ligand charge transfer (MLCT) transitions are especially interesting. This review article offers a comprehensive collection of strategies to tune MLCT excited states in d 6 metal complexes and gives insights on group 6 to group 9 transition metals and their respective state-of-the-art MLCT engineering towards red-shifted absorption and emission properties with long-lived excited states. Strategies comprise lowering the π* level of the ligands, destabilizing and mixing of the metal-based HOMO, switching within a group of transition metals, matrix effects and insights into dealing with excited state deactivation in the context of the energy gap law.

Metal to ligand charge transfer (MLCT)↗
DOE OSTI2022

Tailoring Redox Active Ligands for Probing the Reactivity of Actinides

With this project, we aim to further enhance our understanding of fundamental f-element chemistry, including electronic structure and bonding behaviors. Key project goals include the characterization of actinide complexes bearing redox-active ligands, including those of lower-oxidation state uranium, and examining how structural changes to the ligand and coordination sphere affect structure and bonding. Redox-active and redox non-innocent ligands have been used widely in transition metal chemistry, but uranium complexes with redox-active ligands are surprisingly rare. We recently reported the synthesis of the redox-active ligand, “phen-BIAN” (N,N’-bis(iminophenol)acenaphthene), in an investigation of the electronic behavior of uranium and other actinides. This ligand framework borrows features from two classes of Schiff base ligands—the tetradentate O-N-N-O binding pocket from salens, and the redox-active α-diimine unit and backbone from Ar-BIANs (N,N’-bis[(aryl)imino]acenaphthenes, which can accept up to four electrons upon reduction. To continue this work, the electronics of uranyl and thorium complexes will be probed using the reduced forms of these ligands, using these in the preparation of lower-oxidation state and non-oxo uranium complexes. Additional members of the phen-BIAN family will be synthesized, including naphthol and thiol derivative. With these we can characterize the influence of substitutent groups on the redox activity, coordination geometry, and covalent interactions. The work proposed here entails extensive preparation, structural and spectroscopic characterization, of an array of actinide complexes. This will allow us to address probative questions about the nature of actinide bonding, the degree of covalency, the validity of lanthanides as models for the actinides, hard-soft interactions, magnetic interactions between metals in bimetallic complexes and what combination of electronic and steric affects produce an actinide selective ligand. The latter will assist greatly in providing a benchmark against which to compare and evaluate the distinct behaviors exhibited by 5f-element complexes. This will enable us to learn about the differences in binding between the 4f lanthanides and the 5f elements like uranium and plutonium. Such difference in binding can be exploited in separations and the development of new materials.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

How novel is protactinium: Insights into the structure and properties of (PaO) 2 (SO 4 ) 3 (H 2 O) 2

Because of the scarcity of protactinium and the challenges associated with its separation and crystallization, even in sulfuric acid media where protactinium is relatively stable, there has been an incomplete understanding of the structural features of protactinium complexes. The characterization of protactinium sulfate complexes has been limited to those in solution, which have left key details unaddressed since the 1960s. This report describes a synthetic strategy to crystallize a protactinium complex using boric acid and sulfuric acid. Herein, the authors detail the results of hydrothermal synthesis and the single-crystal analysis of a novel protactinium sulfate complex, (PaO) 2 (SO 4 ) 3 (H 2 O) 2 . This work has elucidated structural features, providing groundwork for accurate computational analysis and clarifying previously unknown details on the coordination, denticity, and binding properties of protactinium sulfate complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Tracking the Light-Induced Excited-State Dynamics and Structural Configurations of an Extraordinarily Long-Lived Metastable State at Room Temperature

Time-resolved X-ray (Tr-XAS) and optical transient absorption (OTA) spectroscopy in the pico-microsecond time scale coupled with Density Functional theory calculations are applied to study the light-induced spin crossover processes of a Fe-based macrocyclic complex in solution. Tr-XAS analysis after light illumination shows the formation of a seven-coordinated high spin quintet metastable state which relaxes to a six-coordinated high spin configuration before decaying to ground state. Kinetic analysis of the macrocyclic complex reveals an unprecedented long-lived decay lifetime of ~42.6 µs. Comparative studies with a non-macrocyclic counterpart illustrate a significantly shortened ~568-old decay lifetime of ~75 ns, and highlight the importance of the ligand arrangement in stabilizing the reactivity of the excited state. Lastly, OTA analysis shows the seven-coordinated high spin state to be formed within ~6.2 ps. Finally, these findings provide a complete understanding of the spin crossover reaction and relaxation pathways of the macrocyclic complex, and reveal the importance of a flexible coordination environment for their rational design.

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

Molecular structures of dissolved and colloidal As V –Fe III complexes and their roles in the mobilization of As V under strongly acidic conditions

The effect of high concentration of iron (Fe III ) on the speciation and mobility of arsenic (As) under strongly acidic conditions remains unclear. This work studied the redistribution and speciation of As V and Fe III at Fe/As molar ratio of 1–14 and pH 1.5–2.0 in the dissolved, colloidal, and solid phases. Results showed that the elevated Fe III induced the decomposition of the precipitated poorly crystalline ferric arsenate by forming dissolved (< 3 kDa) and colloidal (3 kDa–0.1 µm) As–Fe complexes. The fraction of particulate As (> 0.1 µm) decreased from 70–90% to less than 20% when the Fe/As molar ratio increased from 1 to 14. The particle size of the bulk samples decreased significantly with the increase of Fe III concentration. The FTIR results suggested that AsV in dissolved/colloidal As–Fe complexes dominantly occurred as HAsO 4 2– species. The EXAFS results indicated that each HAsO 4 2– coordinated with approximately two Fe atoms in dissolved/colloidal As–Fe complexes at Fe/As ≥ 2. Furthermore, the findings suggest that high aqueous Fe III concentration can promote the mobility of As by forming dissolved/colloidal Fe–As complexes in acidic waters, potentially accelerating As transport from source to downstream in acid mine drainage systems.

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

Slow Electron Spin Relaxation at Ambient Temperatures with Copper Coordinated by a Rigid Macrocyclic Ligand

Paramagnetic transition metal complexes can serve as quantum bits, storing phase information through unpaired electrons. Despite their promise, these systems often require low temperatures and tend to rapidly decohere. Recent efforts have sought to improve longitudinal relaxation (T 1 ), which provides an upper limit for phase coherence (T m ), by investigating existing literature compounds with reduced vibrational coupling and orbital angular momentum. However, synthetic strategies for improving T 1 through novel ligand design have remained scant. Here, we disclose the synthesis of a new modular macrocyclic ligand framework with four nitrogen donors (N 4 ) derived from phenanthroline that supports room-temperature coherent Cu(II) spin centers. The optimized complex more than doubles the T 1 over the next best Cu(II)-N 4 compound and exhibits a room temperature coherence time (T m ) of 0.28 μs, close to previously reported values. This performance enhancement arises from a tight binding site with short Cu–N distances, resulting in a stronger ligand field and reduced thermal accessibility of symmetric vibrational modes. This work demonstrates a practical approach to enabling spin coherence at room temperature, a factor critical to accessing relevant quantum bits and biological sensors, through a designer macrocyclic ligand platform.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1990

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 1 is the Analysis Description, and describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Towne, Charles E.↗
NASA NTRS1990

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 2 is the User's Guide, and describes the program's general features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Towne, Charles E.↗
NASA NTRS1990

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

A new computer code was developed to solve the 2-D or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating-direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 3 is the Programmer's Reference, and describes the program structure, the FORTRAN variables stored in common blocks, and the details of each subprogram.

Towne, Charles E.↗
DOE OSTI2024

Comprehensive Synthesis and Structural Trends in Tetramethyl Diglycolamide (TMDGA) Nitrate Complexes with Lanthanides and Americium

Complexes of N,N,N',N'-tetramethyl diglycolamide (TMDGA), a hydrophilic diglycolamide (DGA) proposed as an aqueous phase holdback reagent, have been crystallized for the majority of the lanthanide series (excluding promethium), yttrium, and americium to deepen our structural understanding of trivalent metal ion (M 3+ ) DGA coordination compounds in the presence of nitrate counter-anions. The presented collection of 16 complexes with accompanying single-crystal structures, taking formulas [M(TMDGA) 3 ][M(NO 3 ) 6 ] (M = La, Ce, Pr, Nd, Sm, Am), [M(TMDGA) 3 ][M(NO 3 ) 5 (H 2 O)] 1–x [M(NO 3 ) 4 (H 2 O) 2 ] x (NO 3 ) 1+x (M = Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb), [M(TMDGA) 3 ] 2 [M(NO 3 ) 4 (H 2 O) 2 ] 0.75 [M(NO 3 ) 5 (H 2 O)] 1.25 (NO 3 ) 2.75 ·H 2 O (M = Lu), and [M(TMDGA) 3 ][M(NO 3 ) 5 (H 2 O)](NO 3 )·CH 3 OH (M = Y) were all synthesized via solvent diffusion of reaction mixtures containing the metal nitrate M(NO 3 ) 3 ·nH 2 O and TMDGA. Single-crystal X-ray diffraction analyses of these new structures show that each TMDGA complex comprises of three TMDGA ligands coordinating the metal ion via carbonyl and etheric oxygen atoms forming [M(TMDGA) 3 ] 3+ cations. Spectroscopy measurements under high pressure displayed notable differences in the f → f transition shifting between that of Nd(III) and Am(III). Shifting of transitions by 2.0 nm were observed in Nd up to 8.50 ± 0.09 GPa, while Am saw shifting between 11.0 to 13.5 nm at pressures up to 20.06 ± 1.90 GPa. The local geometry in these complexes is a distorted spherical capped square antiprism (CSAPR-9) except for of the yttrium complex, which exhibits a distorted spherical tricapped trigonal prismatic (TCTPR-9) geometry. Further, the anions that form concomitantly with the TMDGA complexes are composed of hexanitrato species for the early lanthanide ions (lanthanum to samarium); whereas the remaining smaller lanthanides did not possess sufficiently large ionic radii to coordinate six bidentate nitrate anions, instead, one or two nitrate anions are situated in the outer sphere. The systematic progression of changes in the anionic environments of these complexes outlines the changing coordination habits afforded by the lanthanide contraction.

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

Integrated Experimental and Computational K-Edge X-ray Absorption Near-Edge Structure Analysis of Vanadium Catalysts

X-ray Absorption Near-Edge Structure (XANES) spectroscopy is a powerful tool to reveal key structural and electronic features of isolated catalytic sites, yet insights into molecular structure and more detailed orbital analysis through a combination of experimental and computed XANES analysis are necessary for accurate interpretation of the spectra, especially when significant heterogeneity exits among the catalytic sites. Herein, we present an integrated computational and experimental strategy to determine both primary and secondary bonding interactions within the XANES pre-edge region for organovanadium complexes, which was developed using a series of well-defined molecular vanadium complexes and then applied to the characterization of a supported organovanadium olefin hydrogenation catalyst. Time-dependent density functional theory is used to predict the energy of pre-edge XANES features for a series of vanadium complexes with a variety of oxidation states and local coordination environments. Further, a calibration scheme incorporating different density functionals and basis sets is established, resulting in an optimized scheme that accurately predicts pre-edge energies with a mean absolute error of 0.40 eV. Second-shell coordination (e.g., V---V) effects within XANES are identified through the analysis of the computed dominant orbital contributions for multi-vanadium complexes. Orbital analysis also provided confirmation that the vanadium-hydride formation combined with the heterogeneity of the catalytic active species in ole-fin hydrogenation caused the energy shift and broadening of the pre-edge peak after hydrogen treatment of the silica-supported organovanadium pre-catalyst. This work further elucidates computational XANES simulations and techniques potentially guiding characterization in surface organometallic chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Dinuclear Ligand-to-Ligand Charge Transfer Complexes

The synthesis and characterization of dinuclear ligand-to-ligand charge transfer complexes are described. Each complex is comprised of square-planar platinum(II) coordinated to a 3-tert-butyl-orthocatecholate donor and a 4,4’-di-tert-butyl-2,2’-bipyridine acceptor. Both complexes exhibit donor x acceptor ligand-to-ligand charge transfer (LL’CT) bands in the visible spectrum. The platinum complexes are covalently attached at the catecholate 5-position to either a meta- or para-phenylene bridge fragment. Both cyclic voltammetry and electronic absorption spectroscopy exhibit features characteristic of intramolecular interaction between the platinum centres. The LL’CT excited state lifetimes are ~twofold longer than the mononuclear parent complex. Here, the properties of these complexes are discussed and compared to similar complexes in the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Synthesis and characterization of the rare-earth chloride complexes with N,N,N',N' -tetramethylmalonamide

Exploration of the solid-state chemistry of the f-elements and their coordination chemistry can assist in understanding the speciation of these elements in solution, which, in turn, can aid in the interpretation of their chemical behavior in complex liquid-liquid separations. Within these separation processes, malonamides are common organic extractants that are used for complexing both lanthanides and actinides, thus it is relevant to understand the malonamide ligand complexation under various conditions. In this work, we investigate solid-state complexes of the rare-earth chlorides with N,N,N',N' -tetramethylmalonamide (TMMA) across the entire lanthanide series. Here, we isolated two structural families of compounds Ln(TMMA) 2 Cl 3 Ln = La–Dy and [Ln(TMMA) 2 (H 2 O) 4 ]Cl 3 • x H 2 O x = 0,4 Ln = Ho–Lu, showing differences in chloride coordination from the inner-sphere complex for early lanthanides to outer-sphere for the late lanthanides. Both structural series were additionally analyzed by both IR and Raman spectroscopy confirming similarities in malonamide ligand coordination modes, while showing differences in vibrational features associated with chloride and aqua ligand coordination.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Benzenesulfonamide Derivatives as Complexants and Extractants for Addressing the Mercury Problem at the Savannah River Site

Mercury (Hg) is a major global pollutant arising from both natural and anthropogenic sources. Its widespread use in medicinal and industrial applications makes it a common chemical exposure and environmental pollutant. It can exist in several forms which include: Metallic mercury (Hg{sup 0}), mercurous (Hg{sub 2}{sup 2+}), mercuric salts (Hg{sup 2+}), and organic mercury (e.g. CH{sub 3}Hg{sup +}), with the latter being the most toxic of all the species. Due to mercury's high toxicity, new approaches towards its detection has received significant attention in the scientific community. Mercury exposure at the Savannah River Site (SRS) has been a recent concern especially with increasing amounts of organic mercury in the saltstone. It originates mainly from its use as an acidic dissolution catalyst of aluminum cladding from target fuels within the uranium and plutonium processing operations [1]. It is present to an amount of about 60 metric tons in the high-level waste (HLW) tanks. Organic Mercury species have been found in low activity waste (LAW) at the site that eventually ends up in the saltstone. Therefore, there is a need for: i) Converting organic mercury to other less toxic forms and ii) Complexation and removal of Hg prior of disposal of LAW in saltstone. Various methods have been developed for selective sensing of mercury in the presence of other toxic metals. These methods include using ligands that can form organo-soluble metal complexes with different optical and spectroscopic properties that can be used for toxic metal sensing. In 2005, our group pioneered an ion-exchange extraction method, in which o-phenylenediamine-derived disulfonamides were used to complex and selectively extract and sense Pb{sup 2+} from aqueous solutions into an organic phase [2,3]. Herein, a disulfonamide and a bis-dansylamide have been shown to extract, complex and sense Hg(II). Ligand 1: The crystal structure of the disulfonamide-Hg complex confirms the complexation of Hg(II) with the ligand. Complexation was corroborated by the {sup 1}H-NMR spectra obtained after contacting solutions of various concentrations of Hg{sup 2+} with 2 mM ligand in chloroform. Distinct resonances are observed at Hg/L ratio of 0.5 that are also observed for the isolated 1:2 complex. In the presence of excess mercury, new resonances, as well as the movement of Et{sub 3}N resonances indicate the formation of a different Hg-sulfonamide-triethylamine complex, presumably having 1:1 Hg:L stoichiometry. The electronic spectra of aqueous phases after extraction show that there was no free ligand absorption at 0.5 eq of Hg, indicating a complete complexation. Complexation was also confirmed by the UV-visible titrations with Hg{sup 2+} at constant ligand concentration. pH-dependent extraction carried out shows that extraction of Hg(II) by ligand 1 was over 90% for most alkaline pHs. Ligand 2: The crystal structure of the Ligand 2 complex formed with Hg(OAc){sub 2} shows a remarkable coordination pattern with 4:2 metal:ligand stoichiometry. The fluorescent bis-dansyl disulfonamide derivative was found to complex and sense HgCl{sub 2} and Hg(OAc){sub 2} by demonstrating fluorescence quenching upon Hg(II) addition in comparison with other metals (Zn(II), Cd(II), Pb(II)). No were observed for Cu(II), Ag(I) and Co(II). We have shown the complexation of Hg(II) by a disulfonamide and a bis-dansyl disulfonamide ligand using several spectroscopic methods. Ligand 1 was able to extract mercury into chloroform and form a complex in the presence of excess mercury by synergistic complexation with triethylamine acting as a co-ligand. X-ray and NMR both confirm a 1:2 HgL{sub 2} stoichiometry. Ligand 2 can be used for sensing of Hg(II) as fluorescence quenching was observed after addition of Hg(II)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Lanthanide binding peptide surfactants at air–aqueous interfaces for interfacial separation of rare earth elements

Rare earth elements (REEs) are critical materials to modern technologies. They are obtained by selective separation from mining feedstocks consisting of mixtures of their trivalent cation. We are developing an all-aqueous, bioinspired, interfacial separation using peptides as amphiphilic molecular extractants. Lanthanide binding tags (LBTs) are amphiphilic peptide sequences based on the EF-hand metal binding loops of calcium-binding proteins which complex selectively REEs. We study LBTs optimized for coordination to Tb 3+ using luminescence spectroscopy, surface tensiometry, X-ray reflectivity, and X-ray fluorescence near total reflection, and find that these LBTs capture Tb 3+ in bulk and adsorb the complex to the interface. Molecular dynamics show that the binding pocket remains intact upon adsorption. We find that, if the net negative charge on the peptide results in a negatively charged complex, excess cations are recruited to the interface by nonselective Coulombic interactions that compromise selective REE capture. If, however, the net negative charge on the peptide is −3, resulting in a neutral complex, a 1:1 surface ratio of cation to peptide is achieved. Surface adsorption of the neutral peptide complexes from an equimolar mixture of Tb 3+ and La 3+ demonstrates a switchable platform dictated by bulk and interfacial effects. The adsorption layer becomes enriched in the favored Tb 3+ when the bulk peptide is saturated, but selective to La 3+ for undersaturation due to a higher surface activity of the La 3+ complex.

Ortuno Macias, Luis E. (ORCID:0000000284342192)↗
NASA NTRS2016

Three-Dimensional Modeling of Aircraft High-Lift Components with Vehicle Sketch Pad

Vehicle Sketch Pad (OpenVSP) is a parametric geometry modeler that has been used extensively for conceptual design studies of aircraft, including studies using higher-order analysis. OpenVSP can model flap and slat surfaces using simple shearing of the airfoil coordinates, which is an appropriate level of complexity for lower-order aerodynamic analysis methods. For three-dimensional analysis, however, there is not a built-in method for defining the high-lift components in OpenVSP in a realistic manner, or for controlling their complex motions in a parametric manner that is intuitive to the designer. This paper seeks instead to utilize OpenVSP's existing capabilities, and establish a set of best practices for modeling high-lift components at a level of complexity suitable for higher-order analysis methods. Techniques are described for modeling the flap and slat components as separate three-dimensional surfaces, and for controlling their motion using simple parameters defined in the local hinge-axis frame of reference. To demonstrate the methodology, an OpenVSP model for the Energy-Efficient Transport (EET) AR12 wind-tunnel model has been created, taking advantage of OpenVSP's Advanced Parameter Linking capability to translate the motions of the high-lift components from the hinge-axis coordinate system to a set of transformations in OpenVSP's frame of reference.

Olson, Erik D.↗
DOE OSTI2020

Medium amplitude parallel superposition (MAPS) rheology. Part 2: Experimental protocols and data analysis

An experimental protocol is developed to directly measure the new material functions revealed by medium amplitude parallel superposition (MAPS) rheology. This protocol measures the medium amplitude response of a material to a simple shear deformation composed of three sine waves at different frequencies, revealing a rich dataset consisting of up to 19 measurements of the third-order complex modulus at distinct three-frequency coordinates. We discuss how the choice of input frequencies influences the features of the MAPS domain studied by the experiment. A polynomial interpolation method for reducing the bias of measured values from spectral leakage and reducing variance due to noise is discussed, including a derivation of the optimal range of amplitudes for the input signal. This leads to the conclusion that conducting the experiment in a stress-controlled fashion possesses a distinct advantage to the strain-controlled mode. The experimental protocol is demonstrated through measurements of the MAPS response of a model complex fluid: a surfactant solution of wormlike micelles. The resulting dataset is indeed large and feature-rich, while still acquired in a time comparable to similar medium amplitude oscillatory shear (MAOS) experiments. We demonstrate that the data represent measurements of an intrinsic material function by studying its internal consistency, compatibility with low-frequency predictions for Coleman–Noll simple fluids, and agreement with data obtained via MAOS amplitude sweeps. Finally, the data are compared to predictions from the corotational Maxwell model to demonstrate the power of MAPS rheology in determining whether a constitutive model is consistent with a material’s time-dependent response.

Lennon, Kyle R. (ORCID:0000000212515461)↗