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At least 199 records · Page 11

Multiscale modeling high-order methods and data-driven modeling

Projection-based reduced-order models (ROMs) comprise a promising set of data-driven approaches for accelerating the simulation of high-fidelity numerical simulations. Standard projection-based ROM approaches, however, suffer from several drawbacks when applied to the complex nonlinear dynamical systems commonly encountered in science and engineering. These limitations include a lack of stability, accuracy, and sharp a posteriori error estimators. This work addresses these limitations by leveraging multiscale modeling, least-squares principles, and machine learning to develop novel reduced-order modeling approaches, along with data-driven a posteriori error estimators, for dynamical systems. Theoretical and numerical results demonstrate that the two ROM approaches developed in this work - namely the windowed least-squares method and the Adjoint Petrov - Galerkin method - yield substantial improvements over state-of-the-art approaches. Additionally, numerical results demonstrate the capability of the a posteriori error models developed in this work.

97 MATHEMATICS AND COMPUTING↗

Pronghorn: A Multidimensional Coarse Mesh Application for Advanced Reactor Thermal-Hydraulics

This paper presents an overview of Pronghorn, a multiscale thermal-hydraulic (T/H) application developed by Idaho National Laboratory and the University of California, Berkeley. Pronghorn, built on the open-source finite element Multiphysics Object-Oriented Simulation Environment (MOOSE), leverages state-of-the-art physical models, numerical methods, and nonlinear solvers to deliver fast-running advanced reactor T/H simulation capabilities within a modern software engineering environment. This work summarizes the physical models, multiphysics and multiscale coupling, and numerical discretization in Pronghorn with emphasis on our initial target application to pebble bed reactors (PBRs). A diverse set of applications are shown to depressurized natural circulation in the SANA experiments, forced convection in the Pebble Bed Modular Reactor, three-dimensional (3-D)/one-dimensional coupling of Pronghorn and RELAP-7 systems T/H for loop analysis in the High Temperature Reactor Power Module, and forced convection in the Mark-1 Pebble Bed Fluoride-Salt-Cooled High-Temperature Reactor. A multiphysics coupling of Pronghorn, RELAP-7, and Griffin deterministic neutronics for a gas-cooled PBR demonstrates the capability of the MOOSE framework for reactor design calculations. These applications highlight the verification and validation underlying Pronghorn’s software development while emphasizing features that improve upon capabilities offered by legacy tools in areas such as 3-D unstructured meshing, physics modeling, and multiphysics coupling.

97 MATHEMATICS AND COMPUTING↗

Micro-cantilever beam experiments and modeling in porous polycrystalline UO 2

Understanding the impact of microstructure on the thermo-mechanical behavior of oxide nuclear fuels is vital to predicting their performance through multiscale models. Evaluating the mechanical properties at the sub-grain length scale is key to developing these multiscale models. In this work, 3D finite element (FE) models were constructed to simulate the micrometer-scale bending of micro-cantilever beams fabricated using porous polycrystalline uranium dioxide (UO 2 ) and tested at room temperature. Here, the results showed that the porosity and elastic anisotropy of individual grains can play a significant role in determining the effective mechanical properties of the material deduced from the tests. Specifically, the porosity had a non-negligible effect, given that the pore size was of the same order of magnitude as the dimensions of the micro-beams. Correlations between load-deflection data, pore location, and elastic properties (effective Young's modulus) were investigated using UO 2 micro-beam FE models, where pore clusters were included and placed at different locations along the length of the beam. Results indicated that the presence of pore clusters near the substrate, i.e., the clamp of the micro-cantilever beam, has the strongest effect on the load-deflection behavior, with the porosity leading to a reduction of stiffness that is the largest for any location of the pore clusters. Furthermore, it was also found that pore clusters located towards the middle of the span and close to the end of the beam have a comparatively small effect on the load-deflection behavior. Therefore, it is concluded that accurate estimates of Young's modulus can be obtained from micro-cantilever experiments after accounting for porosity on the one third of the beam length close to the clamp. This, in turn, provides an avenue to improve microscale experiments and their analysis in porous, anisotropic elastic materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Multiscale Ecosystem for solving Maxwell-Schrodinger equations of open quantum systems (OpenMS)

Light-matter interactions play an important role in many branches of physics, chemistry, energy, and materials science. In the strong coupling regime, light-matter interactions are able to tune the materials properties via the formation of new quasiparticles, such as plasmons and polaritons. However, theoretical and numerical modeling of the light-matter interaction-mediated processes remain a big challenge because light-matter interactions are fundamentally multiscale and multiphysics problems involving multiple interactions between electrons, nuclei, and photons at different time/length scales. In the current community, light-matter interactions were treated at different levels of theoretical complexity in quantum chemistry and quantum optics. In quantum optics or quantum photonics, the matter is usually simplified as a few-level system, and the light is treated quantum-mechanically. On the other hand, quantum chemistry explores first-principles methods, including both single-particle and many-body-based techniques, to describe the electronic properties of matter in detail. However, light is usually prescribed as a classical electromagnetic field, and the light-matter interaction is taken into account as an external potential via classical approximations. This software is designed to fill current modeling shortcomings by delivering a first-ever scalable multiscale platform for simulating light-matter interactions in realistic electromagnetic environments. The software solves Maxwell and Schrodinger equations self-consistent on the heterogeneous platforms. It implements HF/DFT, TDDFT, and coupled-cluster counterparts for light-matter interactions and adopts modular programming to offload massively parallel algorithms on a large number of CPU/GPUs.

Zhang, Yu↗

C-FOG: Life of Coastal Fog

C-FOG is a comprehensive bi-national project dealing with the formation, persistence, and dissipation (life cycle) of fog in coastal areas (coastal fog) controlled by land, marine, and atmospheric processes. Given its inherent complexity, coastal-fog literature has mainly focused on case studies, and there is a continuing need for research that integrates across processes (e.g., air–sea–land interactions, environmental flow, aerosol transport, and chemistry), dynamics (two-phase flow and turbulence), microphysics (nucleation, droplet characterization), and thermodynamics (heat transfer and phase changes) through field observations and modeling. Central to C-FOG was a field campaign in eastern Canada from 1 September to 8 October 2018, covering four land sites in Newfoundland and Nova Scotia and an adjacent coastal strip transected by the Research Vessel Hugh R. Sharp . An array of in situ, path-integrating, and remote sensing instruments gathered data across a swath of space–time scales relevant to fog life cycle. Satellite and reanalysis products, routine meteorological observations, numerical weather prediction model (WRF and COAMPS) outputs, large-eddy simulations, and phenomenological modeling underpin the interpretation of field observations in a multiscale and multiplatform framework that helps identify and remedy numerical model deficiencies. An overview of the C-FOG field campaign and some preliminary analysis/findings are presented in this paper.

58 GEOSCIENCES↗

Efficacy of the Cell Perturbation Method in Large-Eddy Simulations of Boundary Layer Flow over Complex Terrain

A challenge to simulating turbulent flow in multiscale atmospheric applications is the efficient generation of resolved turbulence motions over an area of interest. One approach is to apply small perturbations to flow variables near the inflow planes of turbulence-resolving simulation domains nested within larger mesoscale domains. While this approach has been examined in numerous idealized and simple terrain cases, its efficacy in complex terrain environments has not yet been fully explored. Here, we examine the benefits of the stochastic cell perturbation method (CPM) over real complex terrain using data from the 2017 Perdigão field campaign, conducted in an approximately 2-km wide valley situated between two nearly parallel ridges. Following a typical configuration for multiscale simulation using nested domains within the Weather Research and Forecasting (WRF) model to downscale from the mesoscale to a large-eddy simulation (LES), we apply the CPM on a domain with horizontal grid spacing of 150 m. At this resolution, spurious coherent structures are often observed under unstable atmospheric conditions with moderate mean wind speeds. Results from such an intermediate resolution grid are often nested down for finer, more detailed LES, where these spurious structures adversely affect the development of turbulence on the subsequent finer grid nest. We therefore examine the impacts of the CPM on the representation of turbulence within the nested LES domain under moderate mean flow conditions in three different stability regimes: weakly convective, strongly convective, and weakly stable. In addition, two different resolutions of the underlying terrain are used to explore the role of the complex topography itself in generating turbulent structures. We demonstrate that the CPM improves the representation of turbulence within the LES domain, relative to the use of high-resolution complex terrain alone. During the convective conditions, the CPM improves the rate at which smaller-scales of turbulence form, while also accelerating the attenuation of the spurious numerically generated roll structures near the inflow boundary. During stable conditions, the coarse mesh spacing of the intermediate LES domain used herein was insufficient to maintain resolved turbulence using CPM as the flow develops downstream, highlighting the need for yet higher resolution under even weakly stable conditions, and the importance of accurate representation of flow on intermediate LES grids.

17 WIND ENERGY↗

Predicting secondary organic aerosol phase state and viscosity and its effect on multiphase chemistry in a regional-scale air quality model

Atmospheric aerosols are a significant public health hazard and have substantial impacts on the climate. Secondary organic aerosols (SOAs) have been shown to phase separate into a highly viscous organic outer layer surrounding an aqueous core. This phase separation can decrease the partitioning of semi-volatile and low-volatile species to the organic phase and alter the extent of acid-catalyzed reactions in the aqueous core. A new algorithm that can determine SOA phase separation based on their glass transition temperature (T g ), oxygen to carbon (O:C) ratio and organic mass to sulfate ratio, and meteorological conditions was implemented into the Community Multiscale Air Quality Modeling (CMAQ) system version 5.2.1 and was used to simulate the conditions in the continental United States for the summer of 2013. SOA formed at the ground/surface level was predicted to be phase separated with core–shell morphology, i.e., aqueous inorganic core surrounded by organic coating 65.4 % of the time during the 2013 Southern Oxidant and Aerosol Study (SOAS) on average in the isoprene-rich southeastern United States. Our estimate is in proximity to the previously reported ~70 % in literature. The phase states of organic coatings switched between semi-solid and liquid states, depending on the environmental conditions. The semi-solid shell occurring with lower aerosol liquid water content (western United States and at higher altitudes) has a viscosity that was predicted to be 10 2 –10 12 Pa s, which resulted in organic mass being decreased due to diffusion limitation. Organic aerosol was primarily liquid where aerosol liquid water was dominant (eastern United States and at the surface), with a viscosity <10 2 Pa s. Phase separation while in a liquid phase state, i.e., liquid–liquid phase separation (LLPS), also reduces reactive uptake rates relative to homogeneous internally mixed liquid morphology but was lower than aerosols with a thick viscous organic shell. The sensitivity cases performed with different phase-separation parameterization and dissolution rate of isoprene epoxydiol (IEPOX) into the particle phase in CMAQ can have varying impact on fine particulate matter (PM 2.5 ) organic mass, in terms of bias and error compared to field data collected during the 2013 SOAS. This highlights the need to better constrain the parameters that govern phase state and morphology of SOA, as well as expand mechanistic representation of multiphase chemistry for non-IEPOX SOA formation in models aided by novel experimental insights.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development of Dynamic Sub-Grid Models for Variational Multiscale Methods

A dynamic Variational Multiscale Method (Hughes et al. 1998) is developed by leveraging the Germano procedure from classical Large-eddy Simulations (LES). The similarity between the classical and variational approaches is analyzed in the context of incompressible flow. This analysis leads to a consistent modeling approach for both incompressible and compressible flows, the latter being demonstrated in a priori testing for low-speed attached and separated boundary layers. Similar to the classical LES procedure from which it is derived, the variational dynamic procedure does not guarantee a positive semi-definite coefficient in the general case. However, reproducing the behavior of the classical LES dynamic approach is seen as a necessary first step to develop a VMM that automatically adjusts to the local resolution and flow physics.

Variational multiscale↗

Selection and Ranking of Experiments from the Halden Database in support of Multiscale Model Validation

Validating fuel performance codes, such as BISON, requires an extensive amount of experiments covering a wide range of operating conditions and fuel types. Within the light-water reactor (LWR) space, there have been several international experimental programs that have contributed to the wealth of available experimental data available for use. One of those international programs, the Halden Reactor Project (HRP), began in 1958 and utilized the Halden Boiling Water Reactor to conduct many highly instrumented experiments until the reactor closed in 2018. Idaho National Laboratory, through the U.S. Department of Energy, has utilized several Halden experiments to perform the initial validation of the BISON code based upon their inclusion in international modeling and simulation benchmarks. Recently, the HRP has provided member organizations a complete copy of all available data, reports, and presentations since the HRP began. This report provides an initial exploration of the data available in the database for use in validating the multiscale models under development in the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program for LWR applications. Ranking tables that identify potential validation cases are provided for the high priority models of interest. It was found that some of the recommended high priority experiments correspond to additional rods in existing assemblies already available in the BISON validation suite. It is expected that several of these cases will be incorporated into future NEAMS milestones in the fuels technical area for increased validation of BISON.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Stochastic nonlinear analysis of unidirectional fiber composites using image-based microstructural uncertainty quantification

Here, we present a data-driven nonlinear uncertainty quantification and propagation framework to study the microstructure-induced stochastic performance of unidirectional (UD) carbon fiber reinforced polymer (CFRP) composites. The proposed approach integrates (1) microscopic image characterization, (2) stochastic microstructure reconstruction, and (3) efficient multiscale finite element simulations enabled by self-consistent clustering (SCA) analysis. To model the complex microstructural variability, the proposed UQ methods take the non-Gaussian uncertainty sources into account through a distribution-free sampling approach leveraging nonparametric and asymptotic statistical tools. A hierarchical conditional sampling strategy enables the simultaneous sampling of multiple sources of uncertainties. Our approach provides insights into the impact of microstructural variabilities, which are shown to have an increasing impact on the nonlinear responses of UD CFRP parts under progressive compression loading and ultimately on the failure rate over time. We discover that before CFRP parts start to fail, a characteristic time period emerges with distinctive uncertainty distributions specific to the microstructure variability and the probability of failure. Identifying the failure time period is crucial to the reliability prediction, which is an essential component of CFRP design.

36 MATERIALS SCIENCE↗

Effects of organized convection parameterization on the MJO and precipitation in E3SMv1. Part I: Mesoscale heating

Mesoscale organization of convection is typically not represented in global circulation models, and hence its influence on the global circulation is not accounted for. The heating component of a parameterization that represents the dynamical and physical effects of circulations associated with organized convection, referred to as the multiscale coherent structure parameterization (MCSP), is implemented in the Energy Exascale Earth System Model version 1 (E3SMv1). Numerical simulations are conducted to assess its impact on the simulated climate. Besides E3SMv1 simulations, we performed high-resolution (1 km) simulations using the Weather Research and Forecasting (WRF) Model to determine the temperature tendencies induced by mesoscale convective systems embedded in deep convection. We tuned the free parameters of the MCSP based on the WRF simulations. MCSP heating enhances Kevin wave spectra in E3SMv1, improves the representation of the Madden-Julian Oscillation, and impacts on mean precipitation that vary with locations and seasons, including a reduction of biases over the tropical Pacific.

Climate Modeling↗

Multiscale modeling of microwave-heated multiphase systems

Modeling of microwave heating of multiphase systems requires resolving the electromagnetic field from the single particle to the entire cavity. We introduce a multiscale methodology for computationally affordable simulations of microwave heating of multiphase systems consisting of one phase dispersed in a continuum phase. The methodology homogenizes the original multiphase system, by taking advantage of the large separation of length scales, to calculate the effective permittivity, effective thermal conductivity, and volumetric power absorbed in each phase. The methodology is rigorously assessed against particle-resolved detailed numerical simulations of model systems. We demonstrate a significant reduction in computational cost while retaining the accuracy of detailed simulations. Lastly, the present methodology enables high throughput exploration of novel multiphase system designs utilizing microwave heating.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Critical Stack Pressure to Alter Void Generation at Li/Solid-Electrolyte Interfaces during Stripping

The lithium stripping process generates vacancies, which may accumulate as voids and lead to uneven current distribution and dendrite growth in the following plating cycles. A stack pressure is typically required during stripping, but how to optimize the stack pressure is not clear. In this work, extremely lithiophilic Li/Li 2 O and lithiophobic Li/LiF interfaces were used to reveal the combining effect of interface interaction and stack pressure induced lithium creep on the stripping critical current density (CCD). A multiscale simulation scheme with Density Functional Theory (DFT), kinetic Monte Carlo (KMC) simulations, and an analytical model was developed. The analytical model predicted lithiophobic interfaces require a higher stack pressure than lithiophilic interfaces to reach the same CCD. The KMC simulations also showed higher stack pressure is needed at lithiophobic interfaces to accelerate Li vacancy diffusion into the bulk and maintain a flat surface. This stack pressure needs to be high enough to alter the Li forward-and-backward hopping barriers at the interface. This multiscale simulation scheme illustrates the importance to include the chemical-mechanical effects during Li stripping morphology evolution. It can be used to design ideal interlayer coating materials to maintain a flat Li surface during cycling.

25 ENERGY STORAGE↗

Materials Informatics at NASA GRC: Machine Learning Surrogate Modeling, Data Management, and Integrated Toolsets for Establishing/Maintaining the Digital Thread

Integrated Computational Materials Engineering (ICME) has recently received widespread attention due to its promises in reducing dependence on physical testing for engineering design by relying on simulation, reducing both time and cost to market for various applications. ICME however requires validated multiscale material models, which heavily depend on available test data with full material and test pedigree, including material processing, test and measurement equipment, raw data collection, and analysis methodology and results that is findable and usable, along with integrated, efficient toolsets for effectively passing information across various length and time scales across such models. At the NASA Glenn Research Center under the Transformational Tools and Technologies Project, significant recent efforts have been directed towards establishing the required cyberinfrastructure to enable optimized ICME processes and the design of “fit-for-purpose” materials to achieve the goals outlined in the NASA Vision 2040 report. Such efforts include development of multiscale physics-based material models, which can be used to train highly efficient surrogate machine learning models, development of best practices and infrastructure for effective, traceable materials information management, and development of toolsets that integrate with physics-based codes, machine learning models, and an information management system to enable high throughput of materials data collection and analysis, establishment of digital twins and the digital thread, and automation of the ICME design process for material optimization.

Machine Learning↗

Multiscale simulations for multi-continuum Richards equations

In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation (for pressure head), and these equations are coupled to one another by transfer terms. On its own, Richards equation is already a nonlinear partial differential equation, and it is exceedingly difficult to solve numerically due to the extra nonlinear dependencies involving the soil water. To deal with multiple scales, our strategy is that starting from a microscopic scale, we upscale the coupled system of dual-continuum Richards equations via homogenization by the two-scale asymptotic expansion, to obtain a homogenized system, at an intermediate scale (level). Based on a hierarchical approach, the homogenization’s effective coefficients are computed through solving the arising cell problems. Furthermore, to tackle the nonlinearity, after time discretization, we use Picard iteration procedure for linearization of the homogenized Richards equations. At each Picard iteration, some degree of multiscale still remains from the intermediate level, so we utilize the generalized multiscale finite element method (GMsFEM) combining with a multi-continuum approach, to upscale the homogenized system to a macroscopic (coarse-grid) level. This scheme involves building uncoupled and coupled multiscale basis functions, which are used not only to construct coarse-grid solution approximation with high accuracy but also (with the coupled multiscale basis) to capture the interactions among continua. These prospects and convergence are demonstrated by several numerical results for the proposed method.

97 MATHEMATICS AND COMPUTING↗

Solvation Thermodynamics of Solutes in Water and Ionic Liquids Using the Multiscale Solvation-Layer Interface Condition Continuum Model

We report molecular assembly processes are generally driven by thermodynamic properties in solutions. Atomistic modeling can be very helpful in designing and understanding complex systems, except that bulk solvent is very inefficient to treat explicitly as discrete molecules. The SLIC/CDC multiscale model combines continuum solvent electrostatics based on the solvent layer interface condition (SLIC) with statistical thermodynamic models for hydrogen bonding and nonpolar modes: cavity formation, dispersion interactions, combinatorial mixing (CDC). The SLIC/CDC model predicts Gibbs energies of solvation for a database of 500 solutes in water with average accuracy better than 1 kcal/mol both for experimental measurements and for explicit-solvent molecular dynamics simulations. The separate SLIC/CDC energy mode values agree quantitatively with those computed from explicit-solvent molecular dynamics. The SLIC/SASA multiscale model combines the SLIC continuum electrostatic model with the solvent accessible surface area (SASA) nonpolar energy mode. The SLIC/SASA model predicts Gibbs energies of solvation with better than 1.4 kcal/mol average accuracy in aqueous systems and better than 1.6 kcal/mol average accuracy in ionic liquids. Both models predict solvation entropies, and are the first implicit-solvation models capable of predicting solvation heat capacities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multi-scale fission product release model with comparison to AGR data

TRistructural ISOtropic (TRISO) particle fuel is central to several advanced, high-temperature reactor designs. Each particle consists of a fuel kernel encapsulated by three layers of carbon and ceramics that prevent the release of fission products and ensure physical integrity. Despite outstanding retention properties, fission product release has been observed from intact particles. To better understand and quantify fission product release from TRISO particles, a multiscale, mechanistic model of fission product transport is being developed by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. Previous work focused on silver (Ag) transport and improved Ag release predictions. The work described in this report builds on this experience to better understand cesium (Cs) transport in silicon carbide (SiC), the main barrier to the release of fission products. Atomistic simulations provide bulk and grain boundary (GB) Cs diffusivities in SiC, which are used by phase field simulations in the mesoscale code Marmot to determine the temperature, microstructure, and irradiation-dependent Cs diffusivity at the mesoscale in SiC. This approach attributes the different temperature regimes experimentally observed for Cs diffusivities in SiC to a transition from bulk-dominated diffusivity at high temperatures to a GB-dominated regime at low temperatures, providing new insight. The multiscale, mechanistic effective diffusivity is then implemented in the fuel performance code BISON and further validated by comparing Cs release predictions from Advanced Gas Reactor (AGR)-1 and AGR-2 post-irradiation measurements. The new model improves BISON’s predictability. This document also reports improvements made on Ag transport modeling by accounting for different GB types having different diffusivities. Moreover, this report details preliminary efforts to model palladium (Pd) attack of the SiC at the mesoscale using a phase field approach. Pd attack and its impact on accelerated Ag transport remains a misunderstood phenomenon, and we use the model to demonstrate that the formation of lamellae that has been observed in experiments can be explained by the reaction of Pd with SiC to form alternating layers of graphite and Pd 2 Si. This effort aims to improve our understanding of the reaction and eventually provide a model for BISON to account for Pd penetration and its effects on fission product release.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Theoretical Investigation of the Oxygen Reduction Reaction over Platinum Catalysts Supported by Multi-Edged Vertically Aligned Carbon Nanofiber for Electrocatalyst Preparation

Vertically aligned carbon nanofibers (VACNFs) are promising supports for oxygen reduction reaction (ORR) electrocatalysts in fuel cells. Although experimentally these catalytic systems have shown great potential, there is lack of molecular understanding of the catalytic sites and reaction mechanisms. This work investigated the origin of the ORR reactivities of the platinum catalysts on multi-edged VACNFs (Pt/VACNF) using a multiscale modeling approach combining Density Functional Theory (DFT) and classical Molecular Dynamics (MD) simulations. Based on the ReaxFF potential, here all nanoscale Pt particles (Pt 55 , P 100 , and Pt 147 ) are stabilized by the open edges located axially along the VACNF walls. The calculated first-shell coordination numbers, CN, of surface Pt atoms are 6.63, 7.27, and 7.85, respectively, suggesting that the percentage of low coordination sites increases as the particle size decreases. The adsorption energies of OOH, O, and OH on Pt-55 were systematically probed using DFT calculations. These adsorption energies retain a linear correlation against the generalized coordination numbers ($\overline{CN}$). For Pt nanoparticles supported on VACNF, we found that the OOH and OH bind stronger than on Pt (111) by 0.14 and 0.17 eV, respectively, which can hinder the ORR activity with lower limiting potential than Pt (111). Our theoretical prediction is in good agreement with the linear sweeping voltammetry that revealed a left shift of the half-wave potential.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗