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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Global Free-tropospheric NO2 Abundances Derived Using a Cloud Slicing Technique from AURA OMI

We derive free-tropospheric NO2 volume mixing ratios (VMRs) by applying a cloud-slicing technique to data from the Ozone Monitoring Instrument (OMI) on the Aura satellite. In the cloud-slicing approach, the slope of the above-cloud NO2 column versus the cloud scene pressure is proportional to the NO2 VMR. In this work, we use a sample of nearby OMI pixel data from a single orbit for the linear fit. The OMI data include cloud scene pressures from the rotational-Raman algorithm and above-cloud NO2 vertical column density (VCD) (defined as the NO2 column from the cloud scene pressure to the top of the atmosphere) from a differential optical absorption spectroscopy (DOAS) algorithm. We compare OMI-derived NO2 VMRs with in situ aircraft profiles measured during the NASA Intercontinental Chemical Transport Experiment Phase B (INTEX-B) campaign in 2006. The agreement is generally within the estimated uncertainties when appropriate data screening is applied. We then derive a global seasonal climatology of free-tropospheric NO2 VMR in cloudy conditions. Enhanced NO2 in the free troposphere commonly appears near polluted urban locations where NO2 produced in the boundary layer may be transported vertically out of the boundary layer and then horizontally away from the source. Signatures of lightning NO2 are also shown throughout low and middle latitude regions in summer months. A profile analysis of our cloud-slicing data indicates signatures of lightning-generated NO2 in the upper troposphere. Comparison of the climatology with simulations from the global modeling initiative (GMI) for cloudy conditions (cloud optical depth less than10) shows similarities in the spatial patterns of continental pollution outflow. However, there are also some differences in the seasonal variation of free-tropospheric NO2 VMRs near highly populated regions and in areas affected by lightning-generated NOx.

NO2↗
NASA NTRS2014

Biological Water Processor and Forward Osmosis Secondary Treatment

The goal of the Biological Water Processor (BWP) is to remove 90% organic carbon and 75% ammonium from an exploration-based wastewater stream for four crew members. The innovative design saves on space, power and consumables as compared to the ISS Urine Processor Assembly (UPA) by utilizing microbes in a biofilm. The attached-growth system utilizes simultaneous nitrification and denitrification to mineralize organic carbon and ammonium to carbon dioxide and nitrogen gas, which can be scrubbed in a cabin air revitalization system. The BWP uses a four-crew wastewater comprised of urine and humidity condensate, as on the ISS, but also includes hygiene (shower, shave, hand washing and oral hygiene) and laundry. The BWP team donates 58L per day of this wastewater processed in Building 7.

Shull, Sarah↗
NASA NTRS2014

Relationship Between Column-Density and Surface Mixing Ratio: Statistical Analysis of O3 and NO2 Data from the July 2011 Maryland DISCOVER-AQ Mission

To investigate the ability of column (or partial column) information to represent surface air quality, results of linear regression analyses between surface mixing ratio data and column abundances for O3 and NO2 are presented for the July 2011 Maryland deployment of the DISCOVER-AQ mission. Data collected by the P-3B aircraft, ground-based Pandora spectrometers, Aura/OMI satellite instrument, and simulations for July 2011 from the CMAQ air quality model during this deployment provide a large and varied data set, allowing this problem to be approached from multiple perspectives. O3 columns typically exhibited a statistically significant and high degree of correlation with surface data (R(sup 2) > 0.64) in the P- 3B data set, a moderate degree of correlation (0.16 < R(sup 2) < 0.64) in the CMAQ data set, and a low degree of correlation (R(sup 2) < 0.16) in the Pandora and OMI data sets. NO2 columns typically exhibited a low to moderate degree of correlation with surface data in each data set. The results of linear regression analyses for O3 exhibited smaller errors relative to the observations than NO2 regressions. These results suggest that O3 partial column observations from future satellite instruments with sufficient sensitivity to the lower troposphere can be meaningful for surface air quality analysis.

nitrogen dioxide↗
NASA NTRS2015

Consolidating NASA's Arc Jets

The paper describes the consolidation of NASA's high powered arc-jet testing at a single location. The existing plasma arc-jet wind tunnels located at the Johnson Space Center were relocated to Ames Research Center while maintaining NASA's technical capability to ground-test thermal protection system materials under simulated atmospheric entry convective heating. The testing conditions at JSC were reproduced and successfully demonstrated at ARC through close collaboration between the two centers. New equipment was installed at Ames to provide test gases of pure nitrogen mixed with pure oxygen, and for future nitrogen-carbon dioxide mixtures. A new control system was custom designed, installed and tested. Tests demonstrated the capability of the 10 MW constricted-segmented arc heater at Ames meets the requirements of the major customer, NASA's Orion program. Solutions from an advanced computational fluid dynamics code were used to aid in characterizing the properties of the plasma stream and the surface environment on the calorimeters in the supersonic flow stream produced by the arc heater.

Consolidation↗
NASA NTRS2016

Comparison of OMI NO2 Observations and Their Seasonal and Weekly Cycles with Ground-Based Measurements in Helsinki

We present the comparison of satellite-based OMI (Ozone Monitoring Instrument) NO2 products with ground-based observations in Helsinki. OMI NO2 total columns, available from standard product (SP) and DOMINO algorithm, are compared with the measurements performed by the Pandora spectrometer in Helsinki in 2012. The relative difference between Pandora 21 and OMI SP retrievals is 4 and 6 for clear sky and all sky conditions, respectively. DOMINO NO2 retrievals showed slightly lower total columns with median differences about 5 and 14 for clear sky and all sky conditions, respectively. Large differences often correspond to cloudy autumn-winter days with solar zenith angles above 65. Nevertheless, the differences remain within the retrieval uncertainties. Furthermore, the weekly and seasonal cycles from OMI, Pandora and NO2 surface concentrations are compared. Both satellite- and ground-based data show a similar weekly cycle, with lower NO2 levels during the weekend compared to the weekdays as result of reduced emissions from traffic and industrial activities. Also the seasonal cycle shows a similar behavior, even though the results are affected by the fact that most of the data are available during spring-summer because of cloud cover in other seasons. This is one of few works in which OMI NO2 retrievals are evaluated in an urban site at high latitudes (60N). Despite the city of Helsinki having relatively small pollution sources, OMI retrievals have proved to be able to describe air quality features and variability similar to surface observations. This adds confidence in using satellite observations for air quality monitoring also at high latitudes.

Validation↗
NASA NTRS2016

Impact of the 2008 Global Recession on Air Quality over the United States: Implications for Surface Ozone Levels from Changes in NOx Emissions

Satellite and ground observations detected large variability in nitrogen oxides (NOx) during the 2008 economic recession, but the impact of the recession on air quality has not been quantified. This study combines observed NOx trends and a regional chemical transport model to quantify the impact of the recession on surface ozone (O3) levels over the continental United States. The impact is quantified by simulating O3 concentrations under two emission scenarios: business-as-usual (BAU) and recession. In the BAU case, the emission projection from the Cross-State Air Pollution Rule is used to estimate the would-be NOx emission level in 2011. In the recession case, the actual NO2 trends observed from Air Quality System ground monitors and the Ozone Monitoring Instrument on the Aura satellite are used to obtain realistic changes in NOx emissions. The model prediction with the recession effect agrees better with ground O3 observations over time and space than the prediction with the BAU emission. The results show that the recession caused a 12ppbv decrease in surface O3 concentration over the eastern United States, a slight increase (0.51ppbv) over the Rocky Mountain region, and mixed changes in the Pacific West. The gain in air quality benefits during the recession, however, could be quickly offset by the much slower emission reduction rate during the post-recession period.

NOx emissions↗
NASA NTRS2016

Prebiotic Chemistry and Atmospheric Warming of Early Earth by an Active Young Sun

Nitrogen is a critical ingredient of complex biological molecules. Molecular nitrogen, however, which was outgassed Into the Earth's early atmosphere, is relatively chemically inert and nitrogen fixation into more chemically reactive compounds requires high temperatures. Possible mechanisms of nitrogen fixation include lightning, atmospheric shock heating by meteorites, and solar ultraviolet radiation. Here we show that nitrogen fixation in the early terrestrial atmosphere can be explained by frequent and powerful coronal mass ejection events from the young Sun -- so-called superflares. Using magnetohydrodynamic simulations constrained by Kepler Space Telescope observations, we find that successive superflare ejections produce shocks that accelerate energetic particles, which would have compressed the early Earth's magnetosphere. The resulting extended polar cap openings provide pathways for energetic particles to penetrate into the atmosphere and, according to our atmospheric chemistry simulations, initiate reactions converting molecular nitrogen, carbon dioxide and methane to the potent greenhouse gas nitrous oxide as well as hydrogen cyanide, an essential compound for life. Furthermore, the destruction of N2, C02 and CH, suggests that these greenhouse gases cannot explain the stability of liquid water on the early Earth. Instead, we propose that the efficient formation of nitrous oxide could explain a warm early Earth.

Airapetian, V. S.↗
NASA NTRS2014

Identification of Flights for Cost-Efficient Climate Impact Reduction

The aircraft-induced climate impact has drawn attention in recent years. Aviation operations affect the environment mainly through the release of carbon-dioxide, nitrogen-oxides, and by the formation of contrails. Recent research has shown that altering trajectories can reduce aviation environmental cost by reducing Absolute Global Temperature Change Potential, a climate assessment metric that adapts a linear system for modeling the global temperature response to aviation emissions and contrails. However, these methods will increase fuel consumption that leads to higher fuel costs imposed on airlines. The goal of this work is to identify ights for which the environmental cost of climate impact reduction outweighs the increase in operational cost on an individual aircraft basis. Environmental cost is quanti ed using the monetary social cost of carbon. The increase in operational cost is considering cost of additional fuel usage only. For this paper, an algorithm has been developed that modi es the trajectories of ights to evaluate the e ect of environ- mental cost and operational cost of ights in the United States National Airspace System. The algorithm identi es ights for which the environmental cost of climate impact can be reduced and modi es their trajectories to achieve maximum environmental net bene t, which is the di erence between reduction in environmental cost and additional operational cost. The result shows on a selected day, 16% of the ights among eight major airlines, or 2,043 ights, can achieve environmental net bene t using weather forecast data, resulting in net bene t of around $500,000. The result also suggests that the long-haul ights would be better candidates for cost-ecient climate impact reduction than the short haul ights. The algorithm will help to identify the characteristics of ights that are capable of applying cost-ecient climate impact reduction strategy.

climate impact reduction↗
NASA NTRS2019

Trends and Seasonal Variability of Atmospheric NO2 and HNO3 Concentrations Across Three Major African Biomes Inferred from Long-Term Series of Ground-Based and Satellite Measurements

In the framework of the INDAAF (International Network to study Deposition and Atmospheric chemistry in AFrica) programme, part of the ACTRIS (Aerosols, Clouds, and Trace gases Research InfraStructure), European Research Infrastructure for the long-term observation of Aerosol, Cloud, and Trace gases, this paper aims to study trends and seasonal variability of surface atmospheric NO2 and HNO3 concentrations, and OMI (Ozone Monitoring Instrument) NO2 over 6 sites in tropical Africa. Sites are located in west and central Africa to represent the major African biomes: dry savanna (Banizoumbou, Niger and Katibougou, Mali), wet savanna (Djougou, Benin and Lamto, Côte d’Ivoire) and forest (Bomassa, Republic of Congo and Zoétélé, Cameroon). Ground-based NO2 and HNO3 concentrations were obtained over the period 1998–2015 using INDAAF passive samplers at a monthly basis, and NO2 Vertical Column Densities (VCDs) from OMI for a 1-degree grid cell around each sites were obtained from 2005 to 2015. Mean annual NO2 concentrations ranged from 2.3 plus or minus 1.2 to 0.9 plus or minus 0.4 parts per billion (ppb) from dry savannas to forests, representing a north-south gradient. In dry savannas, we observe two concentration peaks of NO2 appearing at the beginning and the end of the wet season both for ground-based and satellite measurements, whereas at wet savannas and forest sites, NO2 concentrations are highest in the dry season. The seasonality of surface NO2 observations provide further evidence for a large role of microbial soil NOx emissions in dry savannas and of biomass burning NOx emissions in wet savanna and forest sites. Mean annual HNO3 concentrations ranged from 0.4 to 0.5 ppb in dry and wet savannas to 0.2 to 0.3 ppb in forest. In dry ecosystems, higher HNO3 concentrations are measured in the early wet season, consistent with NO2 results. The analysis of a long-term dataset of surface O3 concentrations indicates that HNO3 production can mainly be explained by the photo-oxidation of NOx. Mann-Kendall and Seasonal Kendall statistical tests showed that NO2 surface concentrations have a significant decreasing seasonal and annual trends at multiple sites (p-value less than 0.05) ranging from -2.96 percent per year (at Zoétélé) to -0.64 percent per year (at Banizoumbou). HNO3 results indicate no trends except at Bomassa (1.07 percent per year). The decreasing NO2 ground-based concentration trends observed in wet savannas sites are correlated with OMI NO2 decreasing trends at these sites. Trends obtained for NO2 concentrations in wet savanna and forest ecosystems are consistent with trends of NOₓ biomass burning emissions.

Trends↗
NASA NTRS2021

Challenges and opportunities for enhancing food security and greenhouse gas mitigation in smallholder farming in sub-Saharan Africa. A review

Smallholder farmers struggle to achieve food security in many countries of sub-Saharan Africa (SSA). It is urgently required to find appropriate practices for enhancing crop production while avoiding large increases in greenhouse gas (GHG) emissions in SSA. This review aims to identify common smallholder farming practices for enhancing crop production, to assess how these affect GHG emissions and to identify strategies that not only enhance crop production but also mitigate GHG emissions in SSA. To increase crop production and ensure food security, smallholder farmers usually expand agricultural land, develop water harvesting and irrigation techniques and increase cropping intensity and fertilizer use. These practices may result in changing carbon stocks and GHG emissions, potentially creating trade-offs between food security and GHG mitigation. Agricultural land expansion at the expense of forests is the most dominant source of GHG emissions in SSA. While water harvesting and irrigation can increase soil organic carbon, they can trigger GHG emissions. Increasing cropping intensity can enhance the decomposition of soil organic matter, thus releasing carbon dioxide. Increasing nitrogen fertilizer use can enhance soil organic carbon, but also leads to increasing nitrous oxide emissions. An integrated land, water and nutrient management strategy is necessary to enhance crop production and mitigate GHG emissions. Among the most relevant strategies found, agroforestry practices in degraded and marginal lands could replace expanding agricultural croplands. In addition, water management, via adequate rainwater harvesting and irrigation techniques, together with appropriate nutrient management should be considered. Therefore, a land-water-nutrient nexus (LWNN) approach will enable an integrated and sustainable solution to increasing crop production and mitigating GHG emissions. Various technical, economic and policy barriers hinder implementing the LWNN approach on the ground, but these may be overcome through developing appropriate technologies, disseminating them through farmer to farmer approaches and developing specific policies to address smallholder land tenure issues and motivate long-term investment.

Sub-Sahara Africa↗
NASA NTRS2022

Plasma Assisted Nutrient Recovery from Inedible Biomass via Ash Leaching

Sustaining a human presence on the Moon, Mars, or deep space will require closing loops on many life support systems. Some form of agriculture will be required because plants produce the vitamins, antioxidants, and essential oils in our diets that degrade over time in stored foods. In addition, they provide dietary fiber, restore air, and purify water. Growing plants will require recycling nutrients trapped in inedible vegetation. Researchers at KSC have investigated the use of a thermal plasma with various carrier gases to thermally degrade inedible plant biomass for nutrient recovery. Previous work demonstrated a thermally degrading environment such as a muffle furnace improved nutrient recovery from inedible biomass prior to an acid leaching process. However, a muffle furnace is an inefficient process. We have explored the use of a small scale, thermal plasma for degradation of pellets to enhance the breakdown of plant stems, leaves, and debris to further close the nutrient loop. Plasma carrier gases such as carbon dioxide (CO2), nitrogen (N2), and air were used to explore variations in recovery and potential chemical by-products. Plasma processed inedible biomass was added to varying concentrations of acid solution for leaching of nutrients (e.g. potassium (K) , magnesium (Mg), calcium (Ca), and phosphorus (P)) for reuse in the crop production cycle. We also examined total N2 recovery. Results are presented showing the impact of plasma processing prior to acid leaching on recovery of plant nutrients.

Kenneth Engeling↗
NASA NTRS2023

Tracking NO2 Pollution Changes Over Texas: Synthesis of In Situ and Satellite Observations

Nitrogen oxides (NO x ) are major air pollutants that play a crucial role in atmospheric chemistry. We compare Ozone Measuring Instrument's (OMI) NO 2 records with the in situ surface measurements from the Air Quality System of the US Environmental Protection Agency and the Texas Commission on Environmental Quality network in the state of Texas with the goal of understanding the correspondence of satellite and in situ surface observations and identifying the potential synergies between the two observing systems. Our analysis of over 40 in situ daily surface site observations, mostly from urban areas, and OMI daily observed data suggests a correlation ( r ) ranging between 0.2 and 0.8. The correlation improves considerably ( r > 0.5) for monthly average data. Weekly variation of surface NO 2 with a Sunday minimum is well captured by OMI tropospheric NO 2 column observations with similar weekend reductions. NO 2 trend in Texas during 2005–2019 is characterized by significant reductions of 20%–36% in highly populated cities and urban centers. However, a significant (up to 80%) increase was observed in oil and gas producing regions of the Permian and Eagle Ford Basins over the same period. In March–April of 2020, like the other US and global cities, Texas experienced up to 60% reduction in NO 2 levels in major cities due to travel restrictions imposed at local and national levels to contain the spread of COVID-19. Though such reduction is temporary, these reductions were significantly larger than those achieved in the past 16 years of OMI record suggesting that technological advancement can curtail NO x emissions.

Nitrogen dioxide (NO2)↗
NASA NTRS2023

Formation of Amino Acids and Carboxylic Acids in Weakly Reducing Planetary Atmospheres by Solar Energetic Particles from the Young Sun

Life most likely started during the Hadean Eon; however, the environmental conditions which contributed to the complexity of its chemistry are poorly known. A better understanding of various environmental conditions, including global (heliospheric) and local (atmospheric, surface, and oceanic), along with the internal dynamic conditions of the early Earth, are required to understand the onset of abiogenesis. Herein, we examine the contributions of galactic cosmic rays (GCRs) and solar energetic particles (SEPs) associated with superflares from the young Sun to the formation of amino acids and carboxylic acids in weakly reduced gas mixtures representing the early Earth’s atmosphere. We also compare the products with those introduced by lightning events and solar ultraviolet light (UV). In a series of laboratory experiments, we detected and characterized the formation of amino acids and carboxylic acids via proton irradiation of a mixture of carbon dioxide, methane, nitrogen, and water in various mixing ratios. These experiments show the detection of amino acids after acid hydrolysis when 0.5% (v/v) of initial methane was introduced to the gas mixture. In the set of experiments with spark discharges (simulation of lightning flashes) performed for the same gas mixture, we found that at least 15% methane was required to detect the formation of amino acids, and no amino acids were detected in experiments via UV irradiation, even when 50% methane was used. Carboxylic acids were formed in non-reducing gas mixtures (0% methane) by proton irradiation and spark discharges. Hence, we suggest that GCRs and SEP events from the young Sun represent the most effective energy sources for the prebiotic formation of biologically important organic compounds from weakly reducing atmospheres. Since the energy flux of space weather, which generated frequent SEPs from the young Sun in the first 600 million years after the birth of the solar system, was expected to be much greater than that of GCRs, we conclude that SEP-driven energetic protons are the most promising energy sources for the prebiotic production of bioorganic compounds in the atmosphere of the Hadean Earth.

Kensei Kobayashi↗
NASA NTRSDate not supplied

How Can We Harness the Power of Machine Learning With TEMPO Data?

There are many potential applications of machine learning for TEMPO data that include - Improve retrievals by reducing the effect of random instrument noise - Expand coverage by producing data in moderately cloudy conditions (see also Fasnacht et al. poster) - Help diagnose impacts of instrumental artifacts - Produce value-added products quickly by training on existing products from other sensors (land and ocean) - Speed up processing by training on products produced with full-physics algorithms (e.g., NO 2 slant column fitting may take ~1 hour/orbit but with a neural net it may take only minutes)

NO2↗
DOE OSTI2020

Environmental impact of national and subnational carbon policies in China based on a multi-regional dynamic CGE model

Carbon policies are important not only for mitigating global climate change, but also for controlling local and regional air pollution. The large regional disparities in economic development and air pollution across China calls for regionally differentiated policies. Previous studies have not systematically investigated the environmental impacts of regional carbon policies in China covering different spatial scales. This study constructs a multi-regional dynamic computable general quilibrium (CGE) model covering 30 provinces of China to assess the impacts of national and subnational carbon polices on CO2 emissions and co-emitted air pollutants from 2020 to 2050. We consider one national carbon policy which aims to achieve China’s 2030 national CO2 abatement target, as well as three regional policies with the same policy stringency as the national one but only applied to eastern China (EP), the Jiangsu-Shanghai-Zhejiang area (JSZP), and the Beijing-Tianjin-Hebei area (BTHP), respectively. We find that regional policies (EP, JSZP, and BTHP) are as effective in reducing CO2 emissions in their targeted regions as the national policy. However, they lead to an increase in CO2 emissions in untargeted regions (the so-called “emissions leakage”). The CO2 leakage rates, which depend on the policy spatial coverage, are 4%, 13%, and 65% for EP, JSZP, and BTHP, respectively, in 2050. Compared with CO2, changes in air pollutant emissions, including sulfur dioxide (SO2), nitrogen oxides (NOx), volatile organic compounds (VOC), and fine particulate matter (PM2.5), exhibit a similar pattern under all policy scenarios, but the magnitude of change is significantly smaller. Transportation, thermal power, and some energy intensive industries are the three largest contributors to CO2 and air pollutant emission reductions. Our results suggest that regional carbon policy is effective in reducing CO2 and air pollutant emissions in the targeted regions, and extending the spatial coverage or increasing policy stringency can largely inhibit emissions leakage.

Zhang, Wenwen↗
DOE OSTI2023

Effect of feed composition on the production of off-gases during vitrification of simulated low-activity nuclear waste

During the vitrification of nuclear waste, hazardous and radioactive emissions are generated from the feed-to-glass conversion reactions, in addition to discharges from forced air bubbling and air inleakage. Although the major gaseous emissions are water vapor, nitrogen, and carbon dioxide, various monitored environmental pollutants are also released, such as nitrogen oxides or sulfur dioxide. In addition, reactions between organics and nitrates in the feed may also form products of incomplete combustion such as carbon monoxide and acetonitrile. Although off-gas emissions are commonly measured during both laboratory- and pilot-scale melter testing, no predictive tool is currently available to a priori estimate the composition of gaseous emissions during nuclear waste vitrification. This work forms a basis for the development of such predictive tool by measuring gas evolution from a broad range of simulated low-activity waste melter feeds using evolved gas analysis data and developing correlations between the feed and off-gas compositions. Using reaction stoichiometry and regression analysis, we demonstrate that next to the content of nitrogen and organic carbon in the feed, the gaseous emissions are affected by the feed reduction-oxidation conditions – the more the feed is reduced, the less nitrogen monoxide, and more carbon monoxide and acetonitrile evolves. In conclusion, the results presented in this work provide a first step towards reducing the amount of expensive physical melter testing and the regression analysis provides a simple tool for rapid optimization of feed composition with respect to off-gas composition.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

A metal-supported single-atom catalytic site enables carbon dioxide hydrogenation

Nitrogen-doped graphene-supported single atoms convert CO 2 to CO, but fail to provide further hydrogenation to methane – a finding attributable to the weak adsorption of CO intermediates. To regulate the adsorption energy, here we investigate the metal-supported single atoms to enable CO 2 hydrogenation. We find a copper-supported iron-single-atom catalyst producing a high-rate methane. Density functional theory calculations and in-situ Raman spectroscopy show that the iron atoms attract surrounding intermediates and carry out hydrogenation to generate methane. The catalyst is realized by assembling iron phthalocyanine on the copper surface, followed by in-situ formation of single iron atoms during electrocatalysis, identified using operando X-ray absorption spectroscopy. The copper-supported iron-single-atom catalyst exhibits a CO 2 -to-methane Faradaic efficiency of 64% and a partial current density of 128 mA cm –2 , while the nitrogen-doped graphene-supported one produces only CO. The activity is 32 times higher than a pristine copper under the same conditions of electrolyte and bias.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗