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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 595 records · Page 33

Multiplicity dependence of (multi-)strange hadrons in oxygen-oxygen collisions at $\sqrt{s_{NN}}$ TeV using EPOS4 and AMPT

It is anticipated that the Large Hadron Collider (LHC) will collect data from oxygen-oxygen (O+O) collisions at a center-of-mass energy of $\sqrt{s_{NN}}$ = 7 TeV to explore the effects observed in high multiplicity proton-proton (p+p) and proton-lead (p+pb) collisions that closely related to lead-lead (Pb+Pb) collisions. Furthermore, these effects include azimuthal asymmetries in particle production, as well as variations in the abundances and momentum distributions across different hadron species, which are indicative of collective particle production mechanisms induced by the interactions in the presence of a QGP. The upcoming data on O+O collisions at the LHC are expected to constrain the model parameters and refine our understanding of theoretical models. In this work, the predicted transverse momentum (p T ) spectra, rapidity density distributions (dN/dy), particle yield ratios, and p T -differential ratios of (multi)strange hadrons produced in O+O collisions at $\sqrt{s_{NN}}$ = 7 TeV using AMPT and EPOS4 models are presented. AMPT focuses on preformed hadronic interactions, while EPOS4 incorporates a QGP phase. Stronger radial flow in EPOS4 as compared to AMPT is also observed. AMPT incorporates some flow effects, but the implementation of full hydrodynamic flow in EPOS4 appears to be significantly more effective in reproducing the existing experimental data. Both models predict the final state multiplicity overlap with p+p, p+pb, and Pb+Pb collisions.

Heavy-ion collisions↗

Non-intrusive reduced-order modeling for dynamical systems with spatially localized features

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains that exhibit fast and slow singular value decay. The dynamics of the subdomain exhibiting slow singular value decay are learned with sFOM while the dynamics with intrinsically low dimensionality on the complementary subdomain are learned with OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high resolution of sFOM, and thus enables fast non-intrusive predictions for conditions beyond those sampled in the training data set. A novel regularization technique with a closed-form solution based on the Gershgorin disk theorem is introduced to promote stable sFOM and OpInf models. We also provide a data-driven indicator for subdomain selection and ensure solution smoothness over the interface via a post-processing interpolation step. We evaluate the efficiency of the approach in terms of offline and online speedup through a quantitative, parametric computational cost analysis. We demonstrate the coupled OpInf-sFOM formulation for two test cases: a one-dimensional Burgers’ model for which accurate predictions beyond the span of the training snapshots are presented, and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics, for which the OpInf-sFOM model achieves an average prediction error on the order of 1% with an online speedup factor of approximately 8$\times$ compared to the numerical simulation.

42 ENGINEERING↗

Personalized and uncertainty-aware coronary hemodynamics simulations: From Bayesian estimation to improved multi-fidelity uncertainty quantification

Non-invasive simulations of coronary hemodynamics have improved clinical risk stratification and treatment outcomes for coronary artery disease, compared to relying on anatomical imaging alone. However, simulations typically use empirical approaches to distribute total coronary flow amongst the arteries in the coronary tree, which ignores patient variability, the presence of disease, and other clinical factors. Further, uncertainty in the clinical data often remains unaccounted for in the modeling pipeline. We present an end-to-end uncertainty-aware pipeline to (1) personalize coronary flow simulations by incorporating vessel-specific coronary flows as well as cardiac function; and (2) predict clinical and biomechanical quantities of interest with improved precision, while accounting for uncertainty in the clinical data. We assimilate patient-specific measurements of myocardial blood flow from clinical CT myocardial perfusion imaging to estimate branch-specific coronary artery flows. Simulated noise in the clinical data is used to estimate the joint posterior distributions of the model parameters using adaptive Markov Chain Monte Carlo sampling. Additionally, the posterior predictive distribution for the relevant quantities of interest is determined using a new approach combining multi-fidelity Monte Carlo estimation with non-linear, data-driven dimensionality reduction. This leads to improved correlations between high- and low-fidelity model outputs. Our framework accurately recapitulates clinically measured cardiac function as well as branch-specific coronary flows under measurement noise uncertainty. We observe substantial reductions in confidence intervals for estimated quantities of interest compared to single-fidelity Monte Carlo estimation and state-of-the-art multi-fidelity Monte Carlo methods. This holds especially true for quantities of interest that showed limited correlation between the low- and high-fidelity model predictions. In addition, the proposed multi-fidelity Monte Carlo estimators are significantly cheaper to compute than traditional estimators, under a specified confidence level or variance. The proposed pipeline for personalized and uncertainty-aware predictions of coronary hemodynamics is based on routine clinical measurements and recently developed techniques for CT myocardial perfusion imaging. The proposed pipeline offers significant improvements in precision and reduction in computational cost.

Bayesian parameter estimation↗

Enabling end-to-end secure federated learning in biomedical research on heterogeneous computing environments with APPFLx

Facilitating large-scale, cross-institutional collaboration in biomedical machine learning (ML) projects requires a trustworthy and resilient federated learning (FL) environment to ensure that sensitive information such as protected health information is kept confidential. Specifically designed for this purpose, this work introduces APPFLx - a low-code, easy-to-use FL framework that enables easy setup, configuration, and running of FL experiments. APPFLx removes administrative boundaries of research organizations and healthcare systems while providing secure end-to-end communication, privacy-preserving functionality, and identity management. Furthermore, it is completely agnostic to the underlying computational infrastructure of participating clients, allowing an instantaneous deployment of this framework into existing computing infrastructures. Experimentally, the utility of APPFLx is demonstrated in two case studies: (1) predicting participant age from electrocardiogram (ECG) waveforms, and (2) detecting COVID-19 disease from chest radiographs. Here, ML models were securely trained across heterogeneous computing resources, including a combination of on-premise high-performance computing and cloud computing facilities. By securely unlocking data from multiple sources for training without directly sharing it, these FL models enhance generalizability and performance compared to centralized training models while ensuring data remains protected. In conclusion, APPFLx demonstrated itself as an easy-to-use framework for accelerating biomedical studies across organizations and healthcare systems on large datasets while maintaining the protection of private medical data.

Biomedical Research↗

Geologic hydrogen: From natural occurrences to anthropogenic generation – A review of fundamentals, potential, challenges and prospects

Growing demand for hydrogen is exposing the environmental and economic limits of reforming-based and carbon-managed supply chains, while the scale-up of electrolytic capacity remains capital-constrained. Geologic hydrogen, defined as molecular H₂ generated and stored within the Earth's crust offers a complementary, potentially lower-cost resource, yet exploration is still ad hoc. This review (1) revisits a global inventory of confirmed hydrogen seeps and subsurface occurrences; (2) analyzes the controlling reactions, migration pathways, and trapping conditions governing these occurrences; (3) proposes a process-based geologic hydrogen system concept analogous to, yet distinct from, the petroleum system; and (4) evaluates potential geologic hydrogen systems within the United States as a representative case study. Here, we contrast natural systems powered by serpentinization, mantle degassing or radiolysis with anthropogenic systems that stimulate the same reactions or convert in-situ hydrocarbons. Stable hydrogen accumulations require generation rates that outpace combined physical, chemical and microbial losses; the Bourakébougou field (Mali) exemplifies a self-recharging, free-gas reservoir sustained by meteoric-water serpentinization beneath an efficient caprock. Prospective geologic hydrogen resources are likely to occur in regions where iron-rich lithologies, deep-seated faults, and low-permeability sealing formations coexist. Applying this principle, we highlight three promising hydrogen play types in U.S. geological terrains: ophiolite belts (Appalachian and Californian regions), the Midcontinent Rift and the Lake Superior banded‑iron formations. Multiphysics numerical models and positive-unlabeled machine-learning workflows help to accelerate play screening and de-risk future production; yet, reaction kinetics, stimulation strategies, and full techno-economic and life-cycle assessments remain pivotal knowledge gaps.

Anthropogenic hydrogen generation↗

Siting bioenergy facilities in the United States: Measuring participation in decisions and distribution of effects

Scientists and stakeholders can inform the process of siting renewable energy facilities in ways that do not perpetuate socioeconomic disparities associated with fossil fuel industries or create new ones. Procedural justice indicators and distributional justice indicators that incorporate environmental, social, and economic objectives can be used to site energy facilities in ways that increase benefits and reduce negative impacts to disadvantaged and underserved populations. A generic list of potential energy justice indicators for siting bioenergy facilities was developed collaboratively between U.S. bioenergy researchers and diverse agriculture, energy, and energy and environmental justice stakeholders and experts. From this list smaller numbers of indicators can be selected or modified with communities for local siting of bioenergy facilities. Groups of indicators can be used to guide biorefinery or biopower siting and permitting decisions, e.g., to compare siting options, to draw early attention to key problems, or to track progress toward justice-related targets.

09 BIOMASS FUELS↗

Anion exchange membranes based on (3-acrylamidopropyl) trimethylammonium chloride (APTA) and phenyl Acrylate: Impact of crosslinker and crosslinker content on physiochemical properties and transport behavior of acetate and formate

CO 2 reduction cells are innovative devices that convert CO 2 into valuable chemicals, such as formate (OFm - ) and acetate (OAc - ), at the cathode. One of the key challenges in these devices is the development of ion exchange membranes that enable the transport of charge carriers between electrodes while minimizing the transfer of CO 2 reduction products. This study focuses on the preparation and characterization of crosslinked anion exchange membranes (AEMs) made of phenyl acrylate (PA) and (3-acrylamidopropyl) trimethylammonium chloride (APTA), crosslinked with either poly(ethylene glycol) diacrylate (PEGDA) or N,N’-methylenebisacrylamide (MBAA). Here, the membranes are characterized to understand their physiochemical properties and corresponding transport behavior through characterization of water volume fraction, mechanical properties, ionic conductivity, ion exchange capacity, water contact angle, glass transition temperature as well as their permeability and solubility to formate and acetate. MBAA crosslinked membranes exhibit higher Young’s modulus and lower strain at break compared to PEGDA-crosslinked membranes, which is attributed to their shorter chain length. Within a series of membranes of varied comonomer content, for either PEGDA or MBAA as crosslinker, permeabilities generally follow free volume theory (increasing permeability with increasing water content where water content increases with decreasing crosslinker content). Interestingly, for membranes with different crosslinkers but analogous water volume fraction significant differences (∼2 orders of magnitude) in permeability are observed which we attribute to differences in chain mobility as characterized through the glass transition temperature.

25 ENERGY STORAGE↗

MOOSE-based Tritium Migration Analysis Program, Version 8 (TMAP8) for advanced open-source tritium transport and fuel cycle modeling

Tritium management is critical for the safety, sustainability, and economics of fusion energy systems, and advanced and reliable modeling tools help accelerate the development of tritium technologies. This paper presents the Tritium Migration Analysis Program, Version 8 (TMAP8), an open-source, MOOSE-based application developed to provide state-of-the-art tritium transport and fuel cycle modeling capabilities. TMAP8 aims to expand the capabilities of previous versions (i.e., TMAP4 and TMAP7) by leveraging modern computational techniques, ensuring high software quality assurance standards (key to building trust), and enabling multispecies, multiscale, and multiphysics simulations for integrated tritium transport modeling in complex geometries. This paper outlines TMAP8’s scope and rigorous development practices, emphasizing its transparency, accessibility, modularity, and reliability. We present the current suite of verification and validation cases based on those from TMAP4, demonstrating TMAP8’s accuracy and reliability against analytical solutions and experimental data. Additionally, the paper showcases TMAP8’s integrated fuel cycle modeling capabilities, highlighting its applicability at various scales and levels. The TMAP8 code and documentation are openly available, promoting collaborative development and widespread adoption within the fusion community. Future work will soon expand TMAP8’s verification and validation suite to include those from TMAP7 and other recent experimental studies for validation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Numerical simulation of asteroid geometry variance on airburst threat

For an atmospheric airburst the primary source of concern when assessing uncertainty is the size and velocity. Determining these properties provides the basis for threat assessment, as the total energy of the asteroid may then be estimated, and the threat investigated thoroughly. Even with clarity as to how much energy an asteroid may deposit, a great deal of uncertainty still exists for the actual energy deposition process. One such source of uncertainty is the geometry of the incoming asteroid. The geometry of an asteroid will alter the stress distribution during entry, which adds uncertainty to when fracture will occur. Here, in this study, we use Smoothed Particle Hydrodynamics to model the atmospheric airburst of Tunguska-scale asteroids with varying geometric profiles, including a sphere, ellipsoid, binary and superellipsoid. Each asteroid is modeled as a homogenous structure with strength. We assess uncertainty through a series of planar 2D simulation cases for each geometry, comparing the source of stochasticity across geometries. A single 3D airburst simulation for each geometry is also analyzed. Additionally, the 3D cases are compared to the highly uncertain Tunguska event, predicting variance in burst height across geometries, but all bounded by theoretical burst heights proposed for Tunguska.

Airburst↗

Deep learning model for fast, science-based forecasting of fluid migration along faults in geologic carbon storage scenarios

Effective long-term geologic storage depends on robust site selection and credible, science-based forecasting of subsurface behavior to ensure storage integrity. For this work, we develop a deep learning–based reduced-order model (ROM) to quantify potential carbon dioxide (CO₂) and brine migration through geological faults. The ROM combines a Transformer model for binary classification and a Stacked Ensemble for regression, trained on a comprehensive dataset generated from 1400 physics-based reservoir simulations. Key geologic and operational parameters—including fault geometry, reservoir structure, and injection conditions—were systematically varied to capture a wide range of fluid migration scenarios. The ROM accurately predicts the onset of migration, cumulative migration volumes of both CO₂ and brine, and associated migration rates, as compared to an independent set of validation simulations, while significantly reducing computational cost compared to traditional simulation methods. Model performance was evaluated across diverse fault configurations, revealing that shallow reservoir geometry and fault angle are among the most influential factors governing migration behavior. Sensitivity analysis using SHapley Additive exPlanations (SHAP) provided interpretability, revealing distinct patterns in how geological and operational features drive transient versus cumulative migration outcomes. The ROM’s ability to rapidly simulate fault migration scenarios enables efficient sensitivity analyses, scenario evaluations, and decision support for site selection and monitoring design. This approach enhances the safety, scalability, and long-term operational performance of geologic carbon storage (GCS) systems by providing a robust, interpretable tool for predicting subsurface fluid migration and assessing fault-related migration potential.

42 ENGINEERING↗

MOOSE ProbML: Parallelized probabilistic machine learning and uncertainty quantification for computational energy applications

Here, this paper presents the development and demonstration of massively parallel probabilistic machine learning (ML) and uncertainty quantification (UQ) capabilities within the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source computational platform for parallel finite element and finite volume analyses. In addressing the computational expense and uncertainties inherent in complex multiphysics simulations, this paper integrates Gaussian process (GP) variants, active learning, Bayesian inverse UQ, adaptive forward UQ, Bayesian optimization, evolutionary optimization, and Markov chain Monte Carlo (MCMC) within MOOSE. It also elaborates on the interaction among key MOOSE systems — Sampler, MultiApp, Reporter, and Surrogate — in enabling these capabilities. The modularity offered by these systems enables development of a multitude of probabilistic ML and UQ algorithms in MOOSE. Example code demonstrations include parallel active learning and parallel Bayesian inference via active learning. The impact of these developments is illustrated through five applications relevant to computational energy applications: UQ of nuclear fuel fission product release, using parallel active learning Bayesian inference; very rare events analysis in nuclear microreactors using active learning; advanced manufacturing process modeling using multi-output GPs (MOGPs) and dimensionality reduction; fluid flow using deep GPs (DGPs); and tritium transport model parameter optimization for fusion energy, using batch Bayesian optimization. These capabilities are part of the MOOSE framework.

97 - MATHEMATICS AND COMPUTING↗

CoRE MOF DB: A curated experimental metal-organic framework database with machine-learned properties for integrated material-process screening

Here, we present an updated version of the Computation-Ready, Experimental (CoRE) Metal-Organic Framework (MOF) database, which includes a curated set of computation-ready MOF crystal structures designed for high-throughput computational materials discovery. Data collection and curation procedures were improved from the previous version to enable more frequent updates in the future. Machine-learning-predicted properties, such as stability metrics and heat capacities, are included in the dataset to streamline screening activities. An updated version of MOFid was developed to provide detailed information on metal nodes, organic linkers, and topologies of an MOF structure. DDEC6 partial atomic charges of MOFs were assigned based on a machine-learning model. Gibbs ensemble Monte Carlo simulations were used to classify the hydrophobicity of MOFs. The finalized dataset was subsequently used to perform integrated material-process screening for various carbon-capture conditions using high-fidelity temperature-swing adsorption (TSA) simulations. Our workflow identified multiple MOF candidates that are predicted to outperform CALF-20 for these applications.

CoRE MOF database↗

An overview of HR-EBSD techniques for mapping local stress and dislocations in crystalline materials at sub-micron resolution

High resolution electron backscatter diffraction (HR-EBSD) is a technique used to map elastic strain, crystallographic orientation and dislocation density in a scanning electron microscope. Here, this review covers the background and mathematics of this technique, contextualizing it within the broader landscape of EBSD techniques and other materials characterization methods. Several case studies are presented showing the application of HR-EBSD to the study of plasticity in metals, failure analysis in microelectronics and defect quantification in thin films. This is intended to be a comprehensive resource for researchers developing this technique as well as an introduction to those wishing to apply it.

Ruggles, Timothy J. [Sandia National Laboratories ↗

Design and full core fuel performance assessment of high burnup cores for 4-loop PWRs

Increasing the fuel discharge burnup of current light water reactors (LWRs) promises reductions in fuel cycle and/or operations costs. By assuming a constant core power density, the economic gain is enabled by better fuel utilization and/or an increased capacity factor. In this effort to investigate greater than 62 MWd/kgU maximum rod average burnup for 110+ kW/l core power density, two core designs have been developed for a standard 17x17, 193 fuel assemblies pressurized water reactor (PWR). The levelized unit cost methodology is employed to evaluate fuel cycle, operation and maintenance, and capital cost impacts and to examine the economic viability of both core design pathways. Core design and optimization are performed using the commercial STUDSVIK code package. Fuel performance analysis is realized in full core configuration via auditing FRAPCON4.1, FAST1.2, and the high-fidelity code BISON. To provide a realistic assessment, the core design process takes into consideration best practices in current PWR core design. It features acceptable performance in terms of various core design constraints on maximum allowable peaking and boron concentration. Gadolinia (Gd2O3) is used as a burnable poison with a maximum of 9 wt% concentration while feeding 89 or 77 fuel assemblies in a 3-batch refueling scheme. Full core fuel performance simulation, which allows for characterization of relevant fuel temperatures, plenum pressures, stresses, and strains, is performed with respect to two bounding burnup levels. Such performance is potentially licensable for the 18-month high burnup core (<68 MWd/kgU peak pin), while it is more challenging for the 24-month high burnup core design pathway (<75 MWd/kgU peak pin). Maximum rod plenum pressure is identified as the most limiting fuel performance parameter. Here, while the scope of the present study focuses on the steady-state plus overpower conditions, the acceptability of the new discharge burnup has to be further assessed by considering uncertainties and impacts under accident scenarios in the future.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Characterization of Gulf Stream energy resources: A 30-year high-resolution simulation study

The strength and proximity of the Gulf Stream (GS) along the U.S. coast offers opportunities for marine energy extraction. Leveraging high-resolution (up to 400 m) long-term (30-year) hindcasts based on an unstructured grid model, this study characterizes the energy potential of the GS in two viable locations: the Florida Straits (FS) and Cape Hatteras (CH). Results reveal distinct characteristics in the kinetic energy flux (KEF) and kinetic energy density (KED) for the two regions. The 30-year mean KEF at CH is 27.50 GW, surpassing the 19.74 GW estimated for the FS, which is attributed to the wider cross-section of the GS in CH. Additionally, CH exhibits higher KEF variability due to GS’s larger path shifts and meanders. Estimated KEDs at ADCP site locations reach up to 2,908 W/m 2 in the FS and 1,512 W/m 2 in the CH at a depth of 20 m. High-energy zones are closer to shore in the FS, whereas energy-rich areas at CH are located further offshore. A depth-based KED analysis shows significant decreases across typical energy extraction depths (20 to 100 m), with reductions up to 44%. Finally, this study provides high-resolution resource characterization, forming a foundation for optimized site selection and marine hydrokinetic system design.

16 TIDAL AND WAVE POWER↗

A mathematical design framework for membrane pre-concentration in energy-efficient recovery of fermentation products

Due to the dilute nature of products manufactured via fermentation and cell-free bioprocessing, dewatering is a common unit operation in downstream processing (DSP) for bioproduct recovery, but it is typically energy intensive. To improve DSP energy efficiency for bio-based small molecules, integrating high-pressure membrane pre-concentration is a promising process option. However, this approach is typically constrained by a tradeoff between concentration factor (CF) and product recovery (PR), namely increasing the CF typically results in greater product loss, and vice versa. Here we developed a model that enables process design guidelines to: (i) identify scenarios in which the additional energy consumption and product loss from membrane pre-concentration are justified for use in DSP, and (ii) determine the optimal CF that minimizes process specific energy consumption. We compared the energy consumption of high-pressure membrane-integrated processes to evaporation-only processes and applied the model to an experimental case study for the separation and purification of butyric acid from Clostridium tyrobutyricum fermentation using an in situ product recovery (ISPR) process. The model estimated that integrating a tangential-flow reverse osmosis (RO) pre-concentration unit could reduce process energy consumption up to 45%. The use of advanced membrane pre-concentration technologies, such as negative rejection membranes and organic solvent reverse osmosis (OSRO), have the potential to further reduce the overall process specific energy consumption up to 96%, projected based on modeling. Overall, membrane pre-concentration, especially when strategically integrated prior to an evaporation step with optimized process conditions, holds significant potential for improving DSP energy efficiency, particularly in applications requiring substantial solvent removal for product recovery from dilute mixtures.

09 BIOMASS FUELS↗

Essential barrier height and a probabilistic approach in characterizing potential landscape

In this work we propose a probabilistic approach to investigate the shape of landscapes of multi-dimensional potential functions. Under a suitable coupling scheme, two copies of the overdamped Langevin dynamics associated with the potential function are coupled, and the coupling times are collected. Assuming a set of intuitive yet technically challenging conditions on the coupling scheme, it is shown that the tail distributions of the coupling times exhibit qualitatively different dependencies on the noise magnitude for single-well versus multi-well potential functions. More specifically, for convex single-well potentials, the negative tail exponent of the coupling time distribution is uniformly bounded away from zero by the convexity parameter and is independent of the noise magnitude. In contrast, for multi-well potentials, the negative tail exponent decreases exponentially as the noise vanishes, with the decay rate governed by the essential barrier height, a quantity introduced in this paper to characterize the non-convex nature of the potential function. Numerical investigations are conducted for a variety of examples, including the Rosenbrock function, interacting particle systems, and loss functions arising in artificial neural networks. These examples not only illustrate the theoretical results in various contexts but also provide crucial numerical validation of the conjectured assumptions, which are essential to the theoretical analysis yet lie beyond the reach of standard technical tools.

97 MATHEMATICS AND COMPUTING↗

pH Regulates Ion Dynamics in Carboxylated Mixed Conductors

Coupled ionic and electronic transport underpins processes as diverse as electrochemical energy conversion, biological signaling, and soft adaptive electronics. Yet, how chemical environments such as pH modulate this coupling at the molecular scale remains poorly understood. Here, we show that the protonation state of carboxylated polythiophenes provides precise chemical control over ion dynamics, doping efficiency, solvent uptake, and mechanical response. Using a suite of multimodal operando techniques, supported by simulations, we reveal that pH dictates the balance of cation/anion uptake during electrochemical doping. Mapping across pH uncovers a quasi-nonswelling regime (≈pH 3–3.5) where charge compensation proceeds with minimal volumetric change yet pronounced stiffening. These findings establish molecular acidity as a general strategy to program ionic preference and mechanical stability, offering design principles for pH-responsive mixed conductors and soft electronic materials that couple ionic, electronic, and mechanical functionality.

PH↗