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At least 289 records · Page 16

Specific ion effects on ion transport in charged polymer membranes

Selective separation of like-charged ions is a central challenge in applications such as critical mineral recovery. Electrochemical membrane–based separations offer promising pathways to address this need, but a limited fundamental understanding of ion transport in charged polymer membranes hampers the development of highly selective materials. This study elucidates the role of specific ion effects (SIEs) in ion transport through charged polymer membranes by integrating experimental measurements of ion mobility and in situ ion/ion and ion/water interactions in model charged polymer membranes with results from molecular dynamics simulations on analogous systems. We demonstrate that solvent-mediated ion interactions drive pronounced SIEs within the studied membranes, with the ion softness, i.e., the malleability of ion hydration shells, from hard/soft acid/base (HSAB) theory emerging as a key predictor of transport properties. HSAB theory also explains the observed mechanism of solvent-mediated ion interactions. Our findings offer a mechanistic framework for designing membranes with tailored ion selectivity, potentially enabling efficient separations of chemically similar ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The structure of CaO–MgO–Al 2 O 3 –SiO 2 melts and glasses doped with FeO X –NiO

Neutron and x-ray diffraction measurements have been performed on CaO–MgO–Al 2 O 3 –SiO 2 (CMAS) glasses doped with NiO–Fe X O at room temperature, along with x-ray measurements on aerodynamically levitated liquids at ≥2000 K. The disordered structures have been modeled using empirical potential structure refinement to investigate the relation between the aluminosilicate network and the modifying cations. The SiO 4 and AlO 4 tetrahedra are found to have wider Si–O and Al–O bond distance distributions in the glass, and the first Ca–O n coordination shell is highly distorted, redistributing different populations of long and short bonds between the liquid and the glass. The addition of Fe and Ni at low aluminosilicate content increases the number of free oxygens not bonded to AlO 4 or SiO 4 . Mg–O and Fe–O are both found to be predominantly fourfold and fivefold in the liquid and glassy states. Despite these low coordination numbers, their bond angle distributions indicate that they are predominantly in nontetrahedral-type geometries, with ferrous and ferric iron possessing similar coordination environments. The Ca–O and Mg–O average coordination numbers and enthalpies of solution are consistent with their higher reactivity within relatively acidic aluminosilicate melts.

36 MATERIALS SCIENCE↗

A Theory of Ultrafast Charge Transfer Relaxation with Non-Innocent Solvent Molecules

In this work we revisit the photodynamics of tetracyanoethylene-hexamethylbenzene (TCNE- HMB), the molecular complex studied by Hochstrasser et al. [J. Chem. Phys. 100, 4797–4810, 1994] that has long challenged the applicability of Marcus’s theory of elec- tron transfer for predicting photochemical reactions. Using a novel black-box electronic structure algorithm (time-dependent density functional theory with one double, TD- DFT-1D) to efficiently run molecular dynamics that can treat charge recombination, we run ab initio surface hopping molecular dynamics and confirm that, for a polar solvent, charge recombination rates can be incredibly fast (indeed faster than the sol- vent relaxation time); for non-polar solvents, the rate is much slower. We demonstrate that, although Marcus theory cannot be directly applied, these nonequilibrium (and sometimes incredibly fast) photoexcited dynamics can be effectively explained within a two-state model without any evidence of a transition through a conical intersection. Most importantly, for this paradigmatic model system, we are able to identify two nuclear coordinates of interest (rather than the single coordinate predicted by Marcus or a full set of internal quantum modes studied by Bixon and Jortner): the solvent relaxation in the first shell (that strongly modulates the energies of the charge trans- fer state and differentiates time scales for relaxation) and a nuclear displacement in the TCNE-HMB complex arising from a handful of vibrations that induces non-Born Oppenheimer motion and eventually facilitates an abrupt electronic transition to the ground state. Altogether, these findings suggest a tractable generalization of Marcus theory for future simulations of photochemistry with non-innocent solvent environ- ments in the spirit of a Hamiltonian suggested by Stuchebrukhov (J. Chem. Phys. 107, 3821, 1997).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

PIXE – State of the Art, Systems, Challenges

Particle-induced X-ray emission (PIXE) is an analytical technique for elemental analysis in which a charged-particle beam (most commonly protons, but also alpha particles or heavier ions) ionizes inner-shell electrons in target atoms. When these vacancies are filled by outer-shell electrons, the atom emits characteristic X-rays (e.g., Kα, Kβ, L-series) whose energies are unique to each element. Measuring the X-ray spectrum therefore enables identification of the elements present and, with appropriate calibration and modeling, their concentration. PIXE provides rapid, simultaneous, quantitative multi-element detection with trace-level sensitivity for many mid- to high-Z elements, often with minimal sample preparation. It is widely used across materials science (thin films, alloys, corrosion), geology (mineral chemistry, provenance) and environmental monitoring (aerosols, particulates, soils); semiconductor contamination analysis (wafer surface/trace metals), cultural heritage (pigments, inks, archaeological artifacts) and forensics (gunshot residue, glass/pain), and biological/medical studies (tissue/biomaterial trace-element mapping).

47 OTHER INSTRUMENTATION↗

Electrochemical Oxidation in Garnet-Type Solid Electrolyte by Formation of Point Defects

All-solid-state batteries hold greater promise for improving safety and energy density over conventional battery technology employing organic liquid electrolytes. One of the required features of a Li + conducting solid electrolyte is electrochemical stability, attained thermodynamically or kinetically, within the targeted operating voltage and temperature ranges. Therefore, understanding of the oxidative or reductive degradation mechanism is important to allow the design of stable solid electrolyte materials. This work contributes to building an understanding of the oxidative degradation mechanism in lithium solid electrolytes at cell operating conditions. Here, we have focused on resolving the oxidative decomposition mechanism of Al-doped lithium garnet Li 6.28 Al 0.24 La 3 Zr 2 O 12 (LLZO) as a state-of-the-art inorganic ceramic electrolyte. By combining experimental and computational analyses, we show that oxidation of LLZO occurs by simultaneous loss of oxygen and lithium from the structure, resulting in substoichiometric LLZO, at a moderate temperature (80 °C) and a high electrode potential (4.3 V vs Li/Li + ). Based on X-ray absorption and diffraction analyses, we find that the zirconium coordination shells in LLZO contract while the crystal structure experiences positive chemical strain upon electrochemical oxidation. The results from ex situ structural characterization of both the local structure and crystal symmetry are supported by a substoichiometric LLZO with lithium and oxygen vacancies, modeled by density functional theory (DFT) calculations. These chemical and structural changes in LLZO suppress effective lithium-ion conductivity by an order of magnitude. Formation of lithium and oxygen vacancies in LLZO upon electrochemical oxidation is different from prior thermodynamic predictions of phase decomposition of LLZO. The difference here is that the experiments were conducted at near-room temperature, which can hinder the kinetics of phase separation, and thus, the resultant LLZO solid electrolyte is still single-phase but substoichiometric in Li and O. In conclusion, these findings contribute an important degradation mechanism of the electrolyte, relevant for practical operational conditions of solid-state batteries.

36 MATERIALS SCIENCE↗

Minimal implicit-solvent coarse-grained simulation of Pluronic block copolymers with ionic liquids

Pluronic block copolymers, composed of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) in a triblock structure (PEO–PPO–PEO), are well known for their amphiphilic character and ability to self‐assemble into micelles in aqueous solution. The addition of ionic liquids (ILs) can further modulate the core–shell structures of these copolymers, influencing their stability, critical micellization temperature, and size. However, fully atomistic simulations often become prohibitively expensive due to the size and complexity of these systems. In this work, coarse‐grained simulations using a minimal implicit‐solvent model were performed to examine how two classes of ILs, namely, 1‐alkyl‐3‐methylimidazolium ([C n C 1 im]) and 1‐alkyl‐3‐methylpyrrolidinium ([C n C 1 pyrr]), change the micellization of Pluronic block copolymers in aqueous solution. The effects of IL concentration and alkyl group length were investigated, and the model greatly improved the efficiency of simulating large‐scale micelle systems. Furthermore, the numerical simulations are qualitatively compared with experimental investigations. Our results show that adding ILs expands the micelle core by embedding IL tails among the PPO blocks, thereby increasing overall micelle size. Less polar ILs generally induce more pronounced micellar growth. However, the effect of IL tail length on conformation and micellar packing is non‐monotonic. Up to moderate chain lengths (around C8–C10), the IL tails can extend sufficiently to increase local separation within the micelle; at longer tail lengths, enhanced hydrophobic clustering and steric hindrance cause the tails to bend or fold, capping further expansion. In addition, although block copolymer chains tend to pack more closely in the presence of longer‐tailed ILs, the random coil size of an individual polymer chain does not necessarily shrink. Meanwhile, these insights provide a deeper understanding of how Pluronic/IL systems interact, informing applications in drug delivery, cosmetics, food, and environmental engineering. Finally, our minimal implicit‐solvent model can be applied to larger systems and longer timescales, substantially reducing computational cost while reproducing key structural trends observed experimentally.

Atomistic simulations↗

Unraveling the solvation phenomena of Ln 3+ cations in room-temperature ionic liquids: A computational study

Rare-earth elements (REEs), classified as critical materials, are difficult to separate due to their similar chemical properties and slight differences in ionic radius. Room-temperature ionic liquids (RTILs) have gained significant attention for REE separation because of their unique physicochemical properties and environmental advantages. In this study, we have investigated the solvation mechanisms of two RE cations (Ln 3+ ), Nd 3+ (light REE) and Yb 3+ (heavy REE), in two 1-butyl-3-methylimidazolium ([BMIM] + )-based RTILs using bis(trifluoromethylsulfonyl)imide ([NTf 2 ] − ) and acetate ([OAc] − ) as the respective anions, employing classical molecular dynamics (MD) simulations and density functional theory (DFT) techniques. From MD simulations, it is evident that Ln 3+ cations are primarily solvated by RTIL anions in the first solvation shell, while [BMIM] + cations form the second solvation shell with their numbers depending on the size and composition of the first solvation shell. The neutralizing [NO 3 − ] counterions are mainly solvated by [BMIM] + cations in their first solvation shell. Relative free energy change of solvation calculations using thermodynamic integration (TI) method indicate that Yb 3+ is more strongly solvated than Nd 3+ in both RTILs, a trend further supported by DFT calculations. While both methods predict consistent qualitative behavior, differences in models and energy evaluations lead to variations in absolute values. Overall, this study provides a comprehensive understanding of the solvation behavior of Ln 3+ cations in RTILs, demonstrating a stronger solvation preference for the heavy Ln 3+ cation (Yb 3+ ). In conclusion, these findings have implications for the design of RTIL-based separation processes for REEs.

Ash, Tamalika [Ames Lab., and Iowa State Univ., Am↗

Density Functional Tight Binding Insights into Plasmonic Silver–Platinum Nanoparticles and Alloys for Enhanced Photocatalysis

Developing accurate and efficient Slater-Koster (SK) tight-binding parameter sets is essential for quantum plasmonic studies of alloyed metal nanoparticles, as conventional time dependent density functional theory (TD-DFT) calculations are computationally prohibitive for larger clusters. In this work, we develop and validate density functional tight binding (DFTB) parameter sets for both ground state (GS-SK) and excited state (ES-SK) calculations to study the structural, electronic, and optical properties of silver (Ag), platinum (Pt), and Ag–Pt nanoalloys. Our investigation of the ground state properties demonstrates that the GS-SK parameters enable DFTB to closely reproduce the electronic structures of platinum clusters with diverse sizes and geometries – showing qualitative agreement with DFT for density of states (DOS) profiles and energy levels. The ES-SK parameters accurately describe excited-state properties compared to TD-DFT reference calculations, including the broad, featureless absorption profiles of Pt that are dominated by interband transitions. Using the ES-SK parameters within a real-time TD-DFTB framework, we compute size-dependent optical absorption spectra of Ag, Pt and Ag-Pt nanocubes containing up to 1099 atoms (size ∼4.18 nm). A detailed study of Ag–Pt and Pt-Ag core–shell nanoparticles shows quenching of the Ag plasmon resonance even at monolayer coverage for Ag-Pt, but not for Pt-Ag. We also show how to define submonolayer Ag-core Pt-shell cubic structures that have similar optical properties to those generated experimentally for much larger particles, which offers potential for describing plasmon-enhanced photocatalysis. Collectively, the GS-SK and ES-SK parameter sets provide an accurate, computationally efficient approach for modeling the complex optical and electronic behavior of noble–transition metal nanostructures and their alloys.

SPR↗

Inverse Lieb materials: altermagnetism and more

The Lieb lattice, originally proposed for cuprate superconductors, has gained new attention in the emerging field of altermagnetism as a minimal analytical model for the latter. While the inverse Lieb lattice (ILL) was once considered purely theoretical, several materials with this motif have recently been discovered. Its unique geometry supports complex magnetic orders driven by geometric frustration, offering high tunability. In this work, we provide comprehensive insights into ILL magnetic phases and establish guidelines for identifying altermagnets. Using a Heisenberg model, we first construct phase diagrams to elucidate the mechanisms underlying experimental magnetic phases. We then bridge theory and experiment via density functional theory (DFT) calculations on existing ILL compounds, finding results consistent with experimental data. Notably, we identified a trend linking d-shell filling to magnetic order, where d x (x≤5) configurations show a propensity for altermagnetism. We also highlight Sr 2 CrO 2 Cr 2 OAs 2 as a promising metallic altermagnet with highly anisotropic J 2 exchange and a high Néel temperature (~600 K). Finally, our magnon spectra calculations confirm that chiral splittings correlate directly with anisotropies between inequivalent J 2 interactions.

36 MATERIALS SCIENCE↗

𝐵⁡(𝐸⁢2) measurements in the yrast band of 28 Mg: Implications for the 𝑁 = 20 island of inversion

High-precision lifetime measurements in 28 Mg were performed to study neutron shell evolution in Mg isotopes and the onset of the N = 20 island of inversion. Here, using both the recoil distance and Doppler shift attenuation methods, five lifetimes were measured in addition to six upper limits. The observation of two long-lived, negative-parity states demonstrate the importance of studying Mg isotopes for the contribution of intruder configurations to sd-shell nuclei. Lifetimes of the $2^+_1$ and $4^+_1$ states of 1.81(5) ps and 172⁢($^{+11}_{–10}$) stat.⁢ (4) stop. ⁢(8) feed.⁢ (4) targ. fs, respectively, demonstrate a loss of collectivity with increasing spin in the yrast band, permitting for distinguishing between current theoretical models. These measurements also highlight the progression of yrast structure across the Mg isotopic chain from rotational at N = 12 to large shape mixing at N = 16 and back to collective behavior at N = 20 but with dominating intruder configurations.

20 ≤ A ≤ 38↗

Charge Radii of Neutron-Rich Scandium Isotopes and the Seniority Symmetry in the 0⁢𝑓 7/2 Shell

Nuclear charge radii of neutron-rich 47–49 Sc isotopes were measured using collinear laser spectroscopy at CERN-ISOLDE. The new data reveal that the charge radii of scandium isotopes exhibit a distinct trend between 𝑁 = 20 and 𝑁 = 28, with 41 Sc and 49 Sc isotopes having similar values, mirroring the closeness of the charge radii of 40 Ca and 48 Ca. Theoretical models that successfully interpret the radii of calcium isotopes could not account for the observed behavior in scandium radii, in particular the reduced odd-even staggering. Remarkably, the inclusion of the new 49 Sc radius data has unveiled a similar trend in the charge radii of 𝑁 = 28 isotones and 𝑍 = 20 isotopes when adding the protons atop the 48 Ca core and the neutrons atop the 40 Ca core, respectively. We demonstrate that this trend is consistent with the prediction of the seniority model.

Nuclear charge distribution↗

Primary biomolecular adsorption energetics of core–shell nanocomplexes: Implications for biological interactions

Molecular organization at the nano-bio interface governing the colloidal stability, reactivity, immune recognition, and drug delivery performance of nanoparticles remains difficult to predict. Quantifying the primary hydration energetics of biomolecule-coated nanomaterials can determine those interactions and provide a basis for engineered nanocarriers with tailored behavior in biological systems. Here, we measured the thermodynamics of water adsorption on patchy dry magnetite (Fe 3 O 4 ) nanoparticles coated with three model biomolecules, bovine serum albumin, potato starch, and lauric acid and compared these properties to the hydration energetics of the corresponding free dry biomolecules. The results demonstrate how the surface functionalization alters the hydrophilicity, the accessible hydrophilic surface, and the interaction potential of the nanocomplex surface with biological media. The protein coating increases the interaction potential of the surface of the nanocomplex. The weaker interaction potential of the polysaccharide coating and the relatively large hydrophilic surface area allow dynamic and reversible binding, while the fatty acid rearranges into a partial bilayer with very strong hydrophilicity. The findings establish the hydration enthalpy as a quantitative basis to determine and interpret nanoparticle interactions with proteins, membranes, and biological fluids, and provide a thermodynamic foundation for designing nanocarriers with predictable biological reactivity.

59 BASIC BIOLOGICAL SCIENCES↗

High-Fidelity and High-Performance Computational Simulations for Rapid Design Optimization of Sulfur Thermal Energy Storage

Industrial process heating (IPH) accounts for approximately 70% of US manufacturing energy use and is primarily produced by fossil fuel combustion. Approximately 1500 TWht (approximately 60%) of IPH demand is in the temperature range of 100-300. Industrial applications in this temperature range include drying, hydrothermal processing, thermal enhanced oil recovery, food and beverage, bioethanol production, etc. Cost-effective thermal energy storage (TES) that increases the utilization of waste and renewable heat (solar, geothermal, etc.) could provide significant energy savings and reliable heat sources, decrease emissions, and increase US manufacturing competitiveness through reductions in fuel consumption. TES development has historically been dominated by technologies suitable for deployment with concentrating solar power (CSP). State-of-the-art thermal storage deployed commercially with power tower CSP plants uses a 60%/40% NaNO3/KNO3 molten salt and operates between temperatures of approximately 280 degrees Celsius and 570 degrees Celsius using a two-tank configuration. However, these nitrate salts are unsuitable for operation outside of this temperature range due to a high freezing point of approximately 220 degrees Celsius, and limits on high-temperature salt stability and corrosion resistance of containment alloys. Other materials being investigated for TES include those based on: (1) sensible energy storage (various molten salt compositions, inert solid particles, rocks or pebble beds, sulfur, water, concrete, graphite, etc.), (2) latent energy storage in materials that undergo solid-liquid phase change at relevant temperatures (organic materials for low-temperature applications, inorganic salts and/or metals for high-temperature applications), or (3) thermochemical energy storage (hydrides, hydroxides, carbonates, metal oxides, etc.). The application temperature and challenges pertaining to storage material and/or containment cost, energy density, long-term thermal and cyclic stability, and charge/discharge heat transfer effectiveness drive material selection for a given IPH or electricity generation application. Sulfur is a cheap commodity at $80/ton compared to $1100 - 1300/ton for conventional salts. When using a metric of storage cost per kWh, sulfur costs around 2-3 $/kWh. Previous sulfur TES development focused on high temperature (>600 degrees) concentrated solar power applications with sulfur encapsulated in pipes and flow of gaseous HTF (air) in the shell side. However, for lower-temperature IPH applications in the range of approximately 100-300 degrees Celsius Element 16 adopted a compact and scalable TES design with molten sulfur in the shell and HTF pipes submerged in the molten sulfur bath. The low-cost molten sulfur TES for dispatchable IPH has deployment potential for broad applications. The spatial and temporal evolution of the HTF and sulfur temperature is critical to the TES system performance, and thus detailed modeling can improve understanding of the performance and facilitate design improvements. Using high performance computing and computational fluid dynamics (CFD) a low-cost molten sulfur thermal energy storage (TES) system for industrial process heating (IPH) applications was developed. The unique challenges in CFD modeling of sulfur TES are the sharp property changes of sulfur relevant to the working temperatures. Above 159, liquid sulfur undergoes polymerization, and the viscosity of sulfur rapidly increases by several orders of magnitude between 159 degrees Celsius and 188 degrees Celsius, followed by a decrease in viscosity beyond 188 degrees Celsius due to thermal bound dissociation. In addition, various concentrations of H2S impurities can also modify sulfur viscosity. This numerical challenge is especially relevant to transient simulation of the sulfur TES charging and discharging processes as the extreme property variations limit the applicability of traditional heat transfer correlations. Transient CFD simulations including the temperature-dependent sulfur properties and geometric complexity of the TES design were used to predict the effect of natural convection during charging and discharging on the heat transfer process, sulfur temperature uniformity, charge/discharge rates, and performance of the storage devices. The CFD model was validated with experimental results for a full charge and discharge cycle. The work will show 3D and 2D simulation comparisons aimed to facilitate rapid design iterations and a machine learning based design optimization approach.

CFD↗

Novel Full-Ceramic Multi-Tubular Membrane Systems for Pre-Combustion CO2 Capture with Simultaneous H2 Production: Fabrication, Performance Testing, and 3D CFD Modeling

Inorganic membranes show promise for application in pre-combustion CO2 capture with simultaneous H2 production. State-of-the-art systems for use under high temperature and pressure conditions consist of multiple membrane tube bundles prepared in a "candle-filter" configuration, in which the membrane tubes are open at one end and sealed at the other. This configuration is used for practical reasons, specifically the need to minimize potential problems due to thermal expansion mismatch, at high temperatures, between the ceramic tube bundle and the steel housing. The primary technical problem with the candle-filter configuration for use in commercial-scale installations is the inability to purge the permeate side (typically the tube side), a feature that is crucial for high H2 recovery. In this study, we fabricated dual-end open, commercial-size ceramic multiple-tube bundles made of zeolite, palladium (Pd), and carbon molecular sieve (CMS) membranes that enable permeate-side (tube-side) purge for gas separation applications. Experimental gas separation data with these membrane bundles under harsh operating conditions (temperatures up to 350 and pressures up to 800 psig), to be presented at the meeting, manifest excellent performance. Parallel to the membrane bundle construction and testing efforts, we have also developed a detailed 3D CFD modeling package using COMSOL Multiphysics software to gain more insight into the effect on the H2 purity and recovery of the detailed geometry of the multi-tubular membrane system, including the number of tubes used, their dimensions, and placement in the bundle, as well as the number, type, and positioning of internal baffles and other flow-enhancement accessories. The CFD package is validated with experimental data from different systems (1-tube, 3-tube, and 19-tube bundles), and shows high accuracy in predicting the experimental results (<5 % error in all cases). The results of our study show that the detailed internal geometry of these multi-tubular membrane systems has a considerable impact on the performance of the system as the flow maldistribution within the shell-side can substantially decrease (>40%) the H2 recovery.

20 FOSSIL-FUELED POWER PLANTS↗

Charge Radii Measurements of Exotic Tin Isotopes in the Proximity of 𝑁 =50 and 𝑁 =82

We report nuclear charge radii for the isotopes 104–134 Sn , measured using two different collinear laser spectroscopy techniques at ISOLDE-CERN. These measurements clarify the archlike trend in charge radii along the isotopic chain and reveal an odd-even staggering that is more pronounced near the 𝑁 =50 and 𝑁 =82 shell closures. The observed local trends are well described by both nuclear density functional theory and valence space in-medium similarity renormalization group calculations. Both theories predict appreciable contributions from beyond-mean-field correlations to the charge radii of the neutron-deficient tin isotopes. The models, however, fall short of reproducing the magnitude of the known 𝐵⁡(𝐸⁢2) transition probabilities, highlighting the remaining challenges in achieving a unified description of both ground-state properties and collective phenomena.

laser spectroscopy↗

Charge radii measurements of exotic tin isotopes in the proximity of $N=50$ and $N=82$

We report nuclear charge radii for the isotopes $^{104-134}$Sn, measured using two different collinear laser spectroscopy techniques at ISOLDE-CERN. These measurements clarify the archlike trend in charge radii along the isotopic chain and reveal an odd-even staggering that is more pronounced near the $N=50$ and $N=82$ shell closures. The observed local trends are well described by both nuclear density functional theory and valence space in-medium similarity renormalization group calculations. Both theories predict appreciable contributions from beyond-mean-field correlations to the charge radii of the neutron-deficient tin isotopes. The models fall short, however, of reproducing the magnitude of the known $B(E2)$ transition probabilities, highlighting the remaining challenges in achieving a unified description of both ground-state properties and collective phenomena.

FOS: Physical sciences↗

All-loop soft theorem for pions

In this paper we discuss a generalization of the Adler zero to loop integrands in the planar limit of the S U ( N ) nonlinear sigma model (NLSM). The Adler zero for integrands is violated starting at the two-loop order and is only recovered after integration. Here we propose a soft theorem satisfied by loop integrands with any number of loops and legs. This requires a generalization of NLSM integrands to an off shell framework with certain deformed kinematics. Defining an , we identify a simple nonvanishing soft behavior of integrands, which we call the . We find that the proposed soft theorem is satisfied by the “surface” integrand of Arkani-Hamed and Figueiredo [], which is obtained from the shifted Tr φ 3 surfacehedron integrand. Finally, we derive an on shell version of the algebraic soft theorem that takes an interesting form in terms of self-energy factors and lower-loop integrands in a mixed theory of pions and scalars. Published by the American Physical Society 2024

Astronomy & Astrophysics↗