Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Numerical stability”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Learning Stochastic Parametric Differentiable Predictive Control Policies

We present a scalable unsupervised learning-based method for obtaining explicit control policies for model predictive control problems for stochastic linear systems with additive uncertainties subject to nonlinear chance constraints. We call the proposed method stochastic parametric differentiable predictive control (SP-DPC), which extends the recently proposed deterministic DPC policy optimization algorithm. We formulate the SP-DPC as a deterministic approximation to the stochastic parametric constrained optimal control problem via independent sampling of the problem's parameters and uncertainties. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the problem's value function is backpropagated through the finite-time closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy. We also provide theoretical probabilistic guarantees on closed-loop stability and chance constraints satisfaction for systems controlled by learned neural policies. We demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.

Drgona, Jan↗
DOE OSTI2020

Sorbmatech{sup R}Cs, an Innovative Highly Selective Cs Sorbent for Wastewater Decontamination - 20065

The treatment of radioactive wastewater from the operating nuclear industry (energy production, reprocessing of spent fuel, decommissioning of shut-down facilities, etc.) or in case of incidental or accidental situation (such as Fukushima Daichii NPP accident) is an important issue requiring constant improvement of the technologies and techniques used to prevent radioactive releases into the environment and/or to reduce the production of secondary waste. CEA, Orano and CTI are collaborating since 2014, with the support of the French government's program 'investments for the future', to develop Sorbmatech{sup R}Cs, an innovative and patented selective sorbent (Grandjean and Barre 2014) to deal with the removal of radioactive {sup 137}Cs, one of the most hazardous isotope to be managed in nuclear waste, highly efficient either in agitated reactor or in column process. Sorbmatech{sup R}Cs sorbent consists of mesoporous silica particles loaded with potassium-copper hexacyanoferrate nanoparticles (KCu-HCF). This peculiar structure enables much faster sorption kinetics compared to denser crystalline structures, such as Silicotitanate or Zeolite sorbents, whose drawback consists in hindering the diffusion process through the material, and whose larger sorbent particles slow down the ion exchange process. The equilibrium of Sorbmatech{sup R}Cs is reached in few minutes, even at high flow rates in a fixed-bed column process (up to 10 m.h{sup -1} Darcy velocity) with low drop pressure. Moreover, Sorbmatech{sup R}Cs can be used over a wide pH range from 2 to 10 and has a very high selectivity towards {sup 137}Cs even in brine solution (saline, mineral or sea water). This new sorbent also has a K{sub d} higher than 10{sup 5} mL.g{sup -1} depending on the salinity of the wastewater, enabling a highly efficient removal of Cs trace in radioactive wastewater compared to Cs selective sorbent such as Zeolites and Silicotitanates. Its radiological resistance enables the treatment of high, medium and low activity wastewater. The CEA-Orano-CTI/ALSYS partnership leads to the development of a simple and low-cost synthetic route, which demonstrated large-scale manufacturing of the product on a batch of 100 kg. Two products have been developed and are ready for short run market introduction so far with grain size well adapted either for column processes or agitated reactors.. Finally, the industrial implementation has been studied and largely benefits from the properties of the sorbent. Indeed, its high sorption kinetics enable high flow rates resulting in a decrease of operation times, unit sizes, and volumes of secondary waste produced. Moreover, Sorbmatech{sup R}Cs is designed to be combined into a full and integrated solution, ranging from preliminary optimization of operating conditions through numerical dimensioning model, industrial implementation and treatment of the wastewater (through cartridge or preconditioned columns systems developed thanks to Orano's extensive expertise), to long-term stabilization of generated waste (under progress). (authors)

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

Chapter 7: Learning Stable Local Volt/Var Controllers in Distribution Grids

This chapter describes a framework to synthesize provably stable local Volt/Var controllers for distributed energy resources (DERs) in power distribution grids (DGs). The goal is to control the reactive power injections of DERs to improve the system performance as quantified by a generic optimal reactive power flow (ORPF) problem. To achieve this, we jointly design for each DER the control function, which prescribes the reactive power update rule, and the equilibrium function, which approximates the ORPF solutions from local measurements of voltages and powers. We provide conditions on the equilibrium functions and the control parameters ensuring the stability of the closed-loop system. In particular, we discuss the trade-offs between each set of conditions accounting for practical considerations, like fully exploiting the DERs' generation capabilities and reducing the optimality gap. These conditions are then translated into learning constraints on the neural networks' parameters that are enforced in the training phase. We validate our framework with numerical simulations on the IEEE 37-bus network and through a comparison with an optimized version of standard piece wise linear control rules.

closed-loop asymptotic stability↗
DOE OSTI2021

Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion

Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation method for nonlocal diffusion models with Dirichlet boundary condition. The numerical scheme is shown to be convergent to both nonlocal diffusion and its corresponding local limit as nonlocal interaction vanishes. The analysis is carried out on a special family of rectilinear Cartesian grids for a linear RK method with designed kernel support. The key idea for the stability of the RK collocation scheme is to compare the collocation scheme with the standard Galerkin scheme, which is stable. In addition, assembling the stiffness matrix of the nonlocal problem requires costly computational resources because high-order Gaussian quadrature is necessary to evaluate the integral. We thus provide a remedy to the problem by introducing a quasi-discrete nonlocal diffusion operator for which no numerical quadrature is further needed after applying the RK collocation scheme. The quasi-discrete nonlocal diffusion operator combined with RK collocation is shown to be convergent to the correct local diffusion problem by taking the limits of nonlocal interaction and spatial resolution simultaneously. The theoretical results are then validated with numerical experiments. We additionally illustrate a connection between the proposed technique and an existing optimization based approach based on generalized moving least squares.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A statistical mechanics approach to macroscopic limits of car-following traffic dynamics

Herein we study the derivation of macroscopic traffic models from car-following vehicle dynamics by means of hydrodynamic limits of an Enskog-type kinetic description. We consider the superposition of Follow-the-Leader (FTL) interactions and relaxation towards a traffic-dependent Optimal Velocity (OV) and we show that the resulting macroscopic models depend on the relative frequency between these two microscopic processes. If FTL interactions dominate then one gets an inhomogeneous Aw–Rascle–Zhang model, whose (pseudo) pressure and stability of the uniform flow are precisely defined by some features of the microscopic FTL and OV dynamics. Conversely, if the rate of OV relaxation is comparable to that of FTL interactions then one gets a Lighthill–Whitham–Richards model ruled only by the OV function. We further confirm these findings by means of numerical simulations of the particle system and the macroscopic models. Unlike other formally analogous results, our approach builds the macroscopic models as physical limits of particle dynamics rather than assessing the convergence of microscopic to macroscopic solutions under suitable numerical discretisations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Numerical assessment of fault impact on caprock seals during CO 2 sequestration

Coupled fluid-flow and geomechanical analysis of caprock integrity has gained a lot of attention among scientists and researchers investigating the long-term performance of geologic carbon storage systems. Reactivation of pre-existing fractures within the caprock or re-opening of faults can create permeable pathways which can influence the seal integrity. Stability of the caprock during and after injection of super-critical CO 2 , and the impact of pre-existing fractures in the presence or absence of one or multiple faults have been investigated in this study. The impact of the wellbore orientation and the injection rate are among other key factors in understanding the structural trapping mechanisms within such geological formations. In this study, we numerically investigated the impact of each of these factors. This study revealed the interplay between joints and faults and how different leakage pathways are formed and under which scenario they play a dominant role in terms of CO 2 leakage. Finally, this study also highlights the role of one versus multiple faults in the domain and the importance of the fault hydrological property in forming leakage pathway.

58 GEOSCIENCES↗
DOE OSTI2025

Predictive numerical modeling of plasma-induced surface roughness and wettability evolution in LM-PAEK/CF tape

Plasma surface modification effectively enhances adhesion in thermoplastic composites, yet its impacts on high-performance polymers like low-melting polyaryletherketone (LM-PAEK) remain inadequately quantified. Here, this study integrates experimental analysis and numerical modeling to characterize surface roughness and wettability changes in LM-PAEK/carbon fiber composites treated with atmospheric plasma. Atomic Force Microscopy quantified surface topography (n = 10 per condition for contact angles), while static contact-angle assessments measured wettability. Roughness rapidly increased from ∼0.2 nm to 1.6 nm, and contact angle reduced from ∼90° to 24°, both stabilizing after 25–30 s of exposure. A semi-empirical, physics-informed framework was calibrated to these data, coupling surface chemistry via the Owens–Wendt decomposition with topography via the Wenzel roughness factor, and evaluated using out-of-sample (cross-validated) tests, while static contact angle assessments measured wettability. Numerical predictions matched experimental results closely (RMSE <5%, R 2 > 0.95). Incorporating material-specific parameters, the calibrated model supports plasma-treatment optimization and provides quantitative guidance for improving interfacial adhesion in thermoplastic composite manufacturing.

Atomic Force Microscopy↗
DOE OSTI2020

Learning how structures form in drift-wave turbulence

Drift-wave turbulence produces anomalous transport via cross-correlations between fluctuations. This transport has profound implications for confinement, structure formation, and virtually all aspects of the non-linear turbulent dynamics. Herein, we use a data-driven method based on deep learning in order to study turbulent transport in the 2D Hasegawa–Wakatani system and infer a reduced mean-field model from numerical solution. In addition to the usual turbulent diffusion, we find an effect which couples the particle flux to the local gradient of vorticity, which tends to modulate the density profile. The direct coupling to the shear is relatively weak. In addition, the deep learning method finds a model for spontaneous zonal flow generation by negative viscosity, stabilized by non-linear and hyperviscous terms. We compare these results to analytic calculations using quasilinear theory and wave kinetics, finding qualitative agreement, though the calculations miss certain higher-order effects. A simplified, 1-D model for the evolution of the profile, flow, and intensity based on the deep learning results is solved numerically and compared to previous models for staircasing based on bistability. We see that the physics uncovered by the deep learning method provided simple explanations for the formation of zonal structures in the density, flow, and turbulence fields. We highlight the important role of symmetry in the deep learning method and speculate on the portability of the method to other applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Predicting metal-binding proteins and structures through integration of evolutionary-scale and physics-based modeling

Metals are essential elements in all living organisms, binding to approximately 50% of proteins. They serve to stabilize proteins, catalyze reactions, regulate activities, and fulfill various physiological and pathological functions. While there have been many advancements in determining the structures of protein-metal complexes, numerous metal-binding proteins still need to be identified through computational methods and validated through experiments. Here, to address this need, we have developed the ESMBind workflow, which combines evolutionary scale modeling (ESM) for metal-binding prediction and physics-based protein-metal modeling. Our approach utilizes the ESM-2 and ESM-IF models to predict metal-binding probability at the residue level. In addition, we have designed a metal-placement method and energy minimization technique to generate detailed 3D structures of protein-metal complexes. Our workflow outperforms other models in terms of residue and 3D-level predictions. To demonstrate its effectiveness, we applied the workflow to 142 uncharacterized fungal pathogen proteins and predicted metal-binding proteins involved in fungal infection and virulence.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Removal of Surface Carbonate from Lithium-Ion Battery Cathode Materials via Vapor-Phase Fluorination

Herein, ultrathin metal-fluoride barrier coatings on the surface of lithium-ion battery (LIB) cathodes can improve cycling stability and prevent corrosion by acidic byproducts in the electrolyte. Atomic layer deposition (ALD) is an effective method to deposit ultrathin metal fluoride coatings on LIB cathodes. Although numerous studies have demonstrated the benefit of ALD metal fluoride coatings to LIB performance, comparatively few works have examined the effect of individual ALD precursors on the cathode surface. This paper uses X-ray photoelectron spectroscopy (XPS) measurements to elucidate the surface chemical changes on LIB cathode material surfaces upon exposure to the ALD metal fluoride precursor, hydrogen fluorine pyridine (HFPy). We found a decrease in surface carbonate and an increase in surface fluoride after HFPy exposure suggesting the conversion of lithium carbonate (Li 2 CO 3 ) to lithium fluoride (LiF). This conversion is desirable given that Li 2 CO 3 degrades LIB performance, whereas LiF provides an excellent physio-chemical barrier against chemical attack during cycling. Scanning transmission electron microscopy, X-ray energy dispersive spectroscopy, and XPS measurements following HFPy exposure to Li 2 CO 3 powder revealed the formation of a conformal LiF shell around the Li 2 CO 3 particles. Finally, we confirmed the complete conversion of similar to 7 nm ALD Li 2 CO 3 films on silicon from HFPy exposure using XPS and spectroscopic ellipsometry. The elimination of problematic Li 2 CO 3 from LIB cathode surfaces and conversion into a protective LiF coating via a single precursor vapor treatment may provide a cost-effective method for enhancing LIB performance.

25 ENERGY STORAGE↗
DOE OSTI2020

Timescales and Processes of Methane Hydrate Formation and Breakdown, With Application to Geologic Systems

Abstract Gas hydrate is an ice‐like form of water and low molecular weight gas stable at temperatures of roughly −10°C to 25°C and pressures of ~3 to 30 MPa in geologic systems. Natural gas hydrates sequester an estimated one sixth of Earth's methane and are found primarily in deepwater marine sediments on continental margins, but also in permafrost areas and under continental ice sheets. When gas hydrate is removed from its stability field, its breakdown has implications for the global carbon cycle, ocean chemistry, marine geohazards, and interactions between the geosphere and the ocean‐atmosphere system. Gas hydrate breakdown can also be artificially driven as a component of studies assessing the resource potential of these deposits. Furthermore, geologic processes and perturbations to the ocean‐atmosphere system (e.g., warming temperatures) can cause not only dissociation, but also more widespread dissolution of hydrate or even formation of new hydrate in reservoirs. Linkages between gas hydrate and disparate aspects of Earth's near‐surface physical, chemical, and biological systems render an assessment of the rates and processes affecting the persistence of gas hydrate an appropriate Centennial Grand Challenge. This paper reviews the thermodynamic controls on methane hydrate stability and then describes the relative importance of kinetic, mass transfer, and heat transfer processes in the formation and breakdown (dissociation and dissolution) of gas hydrate. Results from numerical modeling, laboratory, and some field studies are used to summarize the rates of hydrate formation and breakdown, followed by an extensive treatment of hydrate dynamics in marine and cryospheric gas hydrate systems.

58 GEOSCIENCES↗
DOE OSTI2025

Anomalous entropy-driven kinetics of dislocation nucleation

The kinetics of dislocation reactions, such as dislocation multiplication, controls the plastic deformation in crystals beyond their elastic limit, therefore critical mechanisms in a number of applications in materials science. We present a series of large-scale molecular dynamics simulations that shows that one such type of reactions, the nucleation of dislocation at free surfaces, exhibit unconventional kinetics, including unexpectedly large nucleation rates under compression, very strong entropic stabilization under tension, as well as strong non-Arrhenius behavior. These unusual kinetics are quantitatively rationalized using a variational transition state theory approach coupled with an efficient numerical scheme for the estimation of vibrational entropy changes. These results highlight the need for a variational treatment of the kinetics to quantitatively capture dislocation reaction kinetics, especially at low-to-moderate strains where large deformations are required to activate reactions. These observations suggest possible explanations to previously observed unconventional deformation kinetics in both molecular dynamics simulations and experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

The 2022 solar fuels roadmap

Abstract Renewable fuel generation is essential for a low carbon footprint economy. Thus, over the last five decades, a significant effort has been dedicated towards increasing the performance of solar fuels generating devices. Specifically, the solar to hydrogen efficiency of photoelectrochemical cells has progressed steadily towards its fundamental limit, and the faradaic efficiency towards valuable products in CO 2 reduction systems has increased dramatically. However, there are still numerous scientific and engineering challenges that must be overcame in order to turn solar fuels into a viable technology. At the electrode and device level, the conversion efficiency, stability and products selectivity must be increased significantly. Meanwhile, these performance metrics must be maintained when scaling up devices and systems while maintaining an acceptable cost and carbon footprint. This roadmap surveys different aspects of this endeavor: system benchmarking, device scaling, various approaches for photoelectrodes design, materials discovery, and catalysis. Each of the sections in the roadmap focuses on a single topic, discussing the state of the art, the key challenges and advancements required to meet them. The roadmap can be used as a guide for researchers and funding agencies highlighting the most pressing needs of the field.

08 HYDROGEN↗
DOE OSTI2025

Poster Abstract: Leveraging Large Language Models to Reveal Interpretable Cooling Behaviors from Smart Thermostat Data

Frequent heatwaves and hot summers increasingly challenge occupant comfort, health, and energy grid stability. Addressing these challenges requires a detailed understanding of household cooling behaviors, such as thermostat adjustments and adaptive responses to extreme conditions. Traditional analyses often rely on aggregated numerical metrics that overlook subtle but important household-specific variations. In this study, we introduce a generalizable methodology that integrates large language models (LLMs) with vision capabilities to enable scalable and detailed analysis of residential thermostat data. Using Ecobee's Donate Your Data (DYD) dataset—which provides five-minute records of indoor temperatures, thermostat setpoints, and HVAC runtimes—we focus on two U.S. cities with contrasting summer climates : Austin (TX) and Phoenix (AZ). Because raw time-series data are not well suited for direct LLM analysis, we transform them into visual representations, such as daily indoor temperature trajectories and weekly runtime histograms, to better capture behavioral variations. Leveraging LLMs' visual interpretation, we extract descriptive behavioral features, including temperature preferences, time-of-day cooling orientation, anticipatory versus reactive heatwave responses, and behavioral consistency. These semantic features support unsupervised clustering to identify distinct occupant archetypes at scale, revealing differences—such as morning-centric anticipatory coolers versus households that shift toward warmer setpoints during heatwaves—that can inform demand response, resilience planning, and health-aware interventions. By converting raw numerical data into interpretable behavioral patterns, this methodology enables scalable and practical analysis of occupant behavior, supporting actionable insights for comfort, resilience, and energy management.

Nihar, Kopal↗
DOE OSTI2024

Spectral Analysis of Regular Material Point Method and its Application to Study High Pressure Reverse Osmosis Membrane Compaction and Embossing

Material Point Method (MPM) is gaining widespread interest in applied continuum mechanics. The fact that all the continuum properties are stored on the particles (or material points) and the governing equations are solved on these material points makes MPM extremely suited to problems involving severe material deformations, such as crack propagation, soil movement, and fluid flows. Despite its popularity, only a few studies have focused on the numerical properties of MPM. This presentation introduces a global spectral analysis of the regular material point method. Contrary to previous studies, the analysis focuses on the numerical properties of the method in the spectral space. The amplification factor is derived as a function of the non- dimensional wave numbers. It provides insights into the stability and dissipative properties of the method for various CFL and Fourier numbers. The effect of the grid shape functions, number of particles per cell and their locations inside the grid cell are also analyzed. The EXAGOOP MPM solver (https://github.com/NREL/Exagoop.git) is developed at the National Renewable Energy Laboratory as a part of the NAWI UHPRO project and is based on the AMReX framework. A single-level, uniform cartesian grid is used as the background mesh, while the particle class in AMReX is used to manage the material point operations. Linear hat and B-splines are used as grid shape functions, while the time integration is performed using explicit Euler time integration. EXAGOOP is both CPU and GPU compatible and has been demonstrated to work well on multiple compute architectures. The performance of EXAGOOP on various computing architectures is presented along with its application to study compaction and embossing of high-pressure reverse osmosis membranes. The MPM solution accurately reproduces the membrane deformation. The deformed pore size and structure simulated using MPM also agree well with experimental SEM images.

material point method↗
DOE OSTI2025

Stability analysis of the Eulerian–Lagrangian finite volume methods for nonlinear hyperbolic equations in one space dimension

In this paper, we construct a novel Eulerian–Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the initial conditions are smooth, and direct numerical methods may suffer from restricted time step sizes. To relieve the restriction, we propose an ELFV method, where the space-time domain was separated by the partition lines originated from the cell interfaces whose slopes are obtained following the Rakine–Hugoniot junmp condition. Unfortunately, to avoid the intersection of the partition lines, the time step sizes are still limited. To fix this gap, we detect effective troubled cells (ETCs) and carefully design the influence region of each ETC, within which the partitioned space-time regions are merged together to form a new one. Then with the new partition of the space-time domain, we theoretically prove that the proposed first-order scheme with Euler forward time discretization is total-variation-diminishing and maximum-principle-preserving with at least twice larger time step constraints than the classical first order Eulerian method for Burgers’ equation. Numerical experiments verify the optimality of the designed time step sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Innovations in underground hydrogen storage with multiphysics simulations, optimization, and monitoring: A review

Underground Hydrogen Storage (UHS) is a promising solution for large-scale energy storage and a critical component in advancing low-carbon energy system. Ensuring the safety and efficiency of UHS necessitates a comprehensive understanding of multiphysical interactions driven by cyclic pore fluid pressure fluctuations and coupled physicochemical processes. Here, this review examines the key geomechanical responses in UHS, including rock property variations under cyclic loading, fracture evolution and propagation, reservoir stress sensitivity, and fault stability. It also explores the impact of geochemical and microbial reactions on geomechanical characteristics. We provide an in-depth analysis of Thermal-Hydraulic-Mechanical-Chemical (THMC) coupled numerical simulations, highlighting their potential for future multi-scale modeling. Limitations of current machine learning (ML) approaches in addressing UHS challenges are highlighted, emphasizing the need for innovative ML-based methodologies. Operational strategies for hydrogen injection and production are reviewed, focusing on safety, efficiency, and economic viability. The necessity for multi-objective optimization (MOO) to balance storage efficiency, risk mitigation, and cost-effectiveness is also discussed. Current monitoring technologies are evaluated to ensure safe and efficient UHS operations. Finally, this review identifies critical knowledge gaps and underscores the importance of advancing geomechanical understanding under multiphysics-coupling. We highlight the need for ML-driven multiphysics theories, enhanced modeling techniques, and robust optimization strategies to improve UHS performance. This study serves as a comprehensive reference for future research and the large-scale implementation of UHS systems.

25 ENERGY STORAGE↗
DOE OSTI2020

Synthesis and Electrocatalytic HER Studies of Carbene-Ligated Cu 3– x P Nanocrystals

N-heterocyclic carbenes (NHCs) are an important class of ligands capable of making strong carbon-metal bonds. Recently, there has been a growing interest in the study of carbene-ligated nanocrystals, primarily coinage metal nano-crystals, which have found application as catalysts for numerous reactions. The general ability of NHC ligands to positively affect the catalytic properties of other types of nanocrystal catalysts remains unknown. Furthermore, we present the first carbene-stabilized Cu 3–x P nanocrystals. Inquiries into the mechanism of formation of NHC-ligated Cu 3-x P nanocrystals suggest that crystalline Cu 3–x P forms directly as a result of a high-temperature metathesis reaction be-tween a tris(trimethylsilyl)phosphine precursor and an NHC-CuBr precursor, the latter of which behaves as a source of both carbene ligand and Cu + . To study the effect of the NHC surface ligands on catalytic performance, we tested the electrocatalytic hydrogen evolving ability of the NHC-ligated Cu 3–x P nanocrystals and found they possess superior activity to analogous oleylamine-ligated Cu 3–x P nanocrystals. Density functional theory calculations suggest that the NHC ligands minimize unfavorable electrostatic interactions between the copper phosphide surface and H + during the first step of the hydrogen evolution reaction, which contributes to the superior performance of NHC-ligated Cu 3–x P catalysts as compared to oleylamine-ligated Cu 3–x P catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗