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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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Prolonged Stability of Pb-Catalyzed CO 2 Electroreduction to Methyl Formate in Acidic Methanol

Electrochemical CO 2 reduction from renewable energy is a promising route to mitigate greenhouse gas emissions from waste sources while generating value-added products. CO 2 electroreduction in methanol is particularly interesting due to the increased CO 2 solubility compared to water and the propensity to form methyl formate, a product absent in aqueous electrolysis. Here, four factors have been identified as critical to achieving prolonged high selectivity for methyl formate production on a Pb cathode in methanol: high pH near the electrode, low bulk pH, low water content, and regeneration of Pb 2+ sites. Increasing concentration of the formic acid product was observed to induce a selectivity shift towards hydrogen, which was mitigated by the in-situ conversion of the formic acid to methyl formate via an esterification reaction. Furthermore, co-electrolysis of CO 2 with dilute molecular oxygen (4% O 2 ) led to Pb catalyst repair through in-situ surface oxidation. Using CO 2 and dilute O 2 along with single-pass catholyte flow to maintain a low formic acid concentration, sustained high selectivity for methyl formate was attained at ~60% faradaic efficiency at -20 mA cm -2 for over 72 hours.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Electrochemical Conversion of CO 2 to Methyl Formate in a Flow Electrolyzer with Mixed Propylene Carbonate/Methanol Catholyte

Despite the promise of electrochemical carbon dioxide reduction as a technology for the production of clean fuels and decarbonization of the chemical industry, research has mostly focused on aqueous systems with a relatively limited set of products that have been achieved via electrosynthesis. Increasingly, CO 2 electroreduction in nonaqueous solvents is being pursued to develop new avenues for expanding the suite of products that can be made with high selectivity. CO 2 reduction in alcohols coupled with in situ esterification to produce esters is one such route that utilizes nonaqueous electrolyte. To be practical, such electrochemical syntheses need to be translated to a high-performance reactor such as a flow electrolyzer. However, many organic solvents, such as alcohols, wet and flood porous electrodes, thus impeding reactor performance. In this work, methanol was mixed with propylene carbonate as a catholyte for a gas-fed CO 2 flow electrolyzer that avoided cathode flooding. Simultaneously, a dual aqueous anolyte was used for water oxidation as a scalable and sustainable anodic half-reaction. The performance effect of methanol concentration, catholyte acidity, CO 2 flow rate, and dilute water in the catholyte were investigated. With 10 vol % methanol in 90 vol % propylene carbonate, 63% faradaic efficiency for methyl formate ester product was sustained without cathode flooding. However, improvements are still needed to lower the cell resistance and further increase the operating current density.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Atomically Dispersed Iron–Nitrogen Sites on Hierarchically Mesoporous Carbon Nanotube and Graphene Nanoribbon Networks for CO 2 Reduction

Atomically dispersed metal and nitrogen co-doped carbon (M-N/C) catalysts hold great promise for electrochemical CO 2 conversion. However, there is a lack of cost-effective synthesis approaches to meet the goal of economic mass production of single-atom M-N/C with desirable carbon support architecture for efficient CO 2 reduction. Herein, we report facile transformation of commercial carbon nanotube (CNT) into isolated Fe-N 4 sites anchored on carbon nanotube and graphene nanoribbon (GNR) networks (Fe-N/CNT@GNR). The oxidization-induced partial unzipping of CNT results in the generation of GNR nanolayers attached to the remaining fibrous CNT frameworks, which reticulates a hierarchically mesoporous complex and thus enables a high electrochemical active surface area and smooth mass transport. The Fe residues originating from CNT growth seeds serve as Fe sources to form isolated Fe-N-4 moieties located at the CNT and GNR basal plane and edges with high intrinsic capability of activating CO 2 and suppressing hydrogen evolution. The Fe-N/CNT@GNR delivers a stable CO Faradaic efficiency of 96% with a partial current density of 22.6 mA cm -2 at a low overpotential of 650 mV, making it one of the most active M-N/C catalysts reported. This work presents an effective strategy to fabricate advanced atomistic catalysts and highlights the key roles of support architecture in single-atom electrocatalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Copper Tantalate by a Sodium-Driven Flux-Mediated Synthesis for Photoelectrochemical CO 2 Reduction

Copper-tantalate, Cu 2 Ta 4 O 11 (CTO), shows significant promise as an efficient photocathode for multi-carbon compounds (C 2+ ) production through photoelectrochemical (PEC) CO 2 reduction, owing to its suitable energy bands and catalytic surface. However, synthesizing CTO poses a significant challenge due to its metastable nature and thermal instability. In this study, this challenge is addressed by employing a flux-mediated synthesis technique using a sodium-based flux to create sodium-doped CTO (Na-CTO) thin films, providing enhanced nucleation and stabilization for the CTO phase. To evaluate the PEC performance and catalytic properties of the films, copper(II) oxide (CuO) at the Na-CTO surface is selectively etched. The etched Na-CTO shows a lower dark current, with decreased contribution from photocorrosion, unlike the non-etched Na-CTO which has remaining CuO on the surface. Furthermore, Na-CTO exhibits 7.3-fold ethylene selectivity over hydrogen, thus highlighting its promising potential as a photocathode for C 2+ production through PEC CO 2 reduction.

copper tantalate↗
DOE OSTI2020

Pore-Edge Tailoring of Single-Atom Iron–Nitrogen Sites on Graphene for Enhanced CO 2 Reduction

Hosting atomically dispersed nitrogen-coordinated iron sites (Fe-N 4 ) on graphene offers unique opportunities for driving electrochemical CO 2 reduction reaction (CO 2 RR) to CO. However, the strong adsorption of *CO on the Fe-N 4 site embedded in intact graphene limits current density due to slow CO desorption process. Herein, we report how the manipulation of pore edges on graphene alters the local electronic structure of isolated Fe-N 4 sites and improves their intrinsic reactivity for prompting CO generation. We demonstrate that constructing holes on graphene basal plane to support Fe-N 4 can significantly enhance its CO 2 RR compared to the pore-deficient graphene-supported counterpart, exhibiting a CO Faradaic efficiency of 94% and a turnover frequency of 1630 h -1 at 0.58 V vs RHE. Mechanistic studies reveal that the incorporation of pore edges results in the downshifting of the d-band center of Fe sites, which weakens the strength of the Fe-C bond when the *CO intermediate adsorbs on edge-hosted Fe-N 4 , thus boosting the CO desorption and evolution rates. These findings suggest that engineering local support structure renders a way to design high-performance single-atom catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Carbon dioxide and nitrogen reduction reactions using 2D transition metal dichalcogenide (TMDC) and carbide/nitride (MXene) catalysts

Improving the carbon dioxide and nitrogen reduction reactions (CO 2 RR and NRR) can reduce anthropogenic greenhouse gas emissions while selectively producing chemicals needed for the fuel, plastic, and chemical industries. Efficient CO 2 RR can be used to replace fossil fuels as well as repurpose captured CO 2 , while new NRR pathways can be used to supplement or replace the energy intensive Haber–Bosch process for NH 3 generation with no CO 2 emissions. Therefore, this review article focuses on (photo)electrocatalytic and photocatalytic conversion of CO 2 and N 2 molecules into useful products, such as carbon monoxide, methanol, formic acid, and ammonia, using 2D transition metal dichalcogenides (TMDCs) and metal carbides/nitrides (MXenes). Additionally, these highly tunable 2D catalysts will be evaluated for their ability to selectively and efficiently undergo CO 2 RR and NRR by controlling defects, phases, edge sites, interfaces, and functional groups. We first address the CO 2 RR and NRR challenges, with a particular focus on theoretical mechanisms and minimum energy pathways. We follow this discussion with a detailed review of state-of-the-art 2D TMDC and MXene experimental catalysts for CO 2 RR and NRR (photo)electrocatalytic and photocatalytic reactions, and then address areas of opportunity for these catalytic reactions.

14 SOLAR ENERGY↗
DOE OSTI2022

Vapor–Fed Electrolyzers for Carbon Dioxide Reduction Using Tandem Electrocatalysts: Cuprous Oxide Coupled with Nickel–Coordinated Nitrogen–Doped Carbon

We report ethylene is particularly attractive due to its major importance as a feedstock for various applications including the polymer industry. As such, catalyst and electrolyzer developments are crucial to achieve industrially relevant ethylene production and efficiency levels. In this work, a tandem electrocatalyst composed of copper nanocubes and nickel-coordinated nitrogen-doped carbon (NiNC) is presented, which is integrated into gas diffusion electrodes (GDEs) for direct conversion of vapor-fed CO 2 into ethylene. Evaluation of tandem GDEs in the vapor-fed flow electrolyzer shows significantly increased ethylene selectivity in terms of faradaic efficiency and C 2 H 4 /CO ratio compared to a non-tandem copper GDE. The enhancements are attributed to the increased local CO availability near the copper surface via effective CO 2 to CO conversion on neighboring NiNC. The experimental results are validated by 3D resolved continuum simulations, which show increased flux of higher-order prod-ucts with the added CO flux from NiNC. The practical viability of Cu/NiNC catalyst is further evaluated in a membrane electrode assembly electrolyzer, achieving 40% FE toward ethylene at 150 mA cm -2 and 3.2 V. These find-ings highlight the high selectivity and formation rate of ethylene achieved by successful device integration of the Cu/NiNC catalyst, demonstrating the potential for implementation in large-scale sustainable CO 2 electrolyzers.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Two‐Membrane Dual Non‐Aqueous/Aqueous Electrolyte Flow Cell Operation for Electrochemical Conversion of CO 2 to Methyl Formate

Recently, tandem cathodic reactions have been demonstrated in non-aqueous solvents to couple CO 2 reduction to a secondary reaction to create novel species that are not produced in aqueous CO 2 electrolysis. One reaction that can be performed with high selectivity and durability is the electrochemical conversion of CO 2 to formic acid and in-situ esterification with methanol to produce methyl formate. However, the translation to a high-performance flow electrolyzer is far from trivial, as the non-aqueous catholyte leads to reactor challenges including flooding the gas diffusion electrode. Here, in this study, a two-membrane flow electrolyzer with both anion and cation exchange membranes was used with flowing methanol catholyte and aqueous anolyte. This design prevented methanol from flooding the cathode, which was a pervasive limiting issue for electrolyzers with a single membrane. Methyl formate production at 42.9 % faradaic efficiency was achieved with pure methanol in a flow electrolyzer with stable performance beyond 80 min. However, low-water-content catholyte compositions also led to increased cell resistance and lower operating current densities. Thus, with the present ionomer materials there is a tradeoff between methyl formate selectivity and current density depending on water concentration, highlighting a need for new ionomers tailored for desirable non-aqueous solvents such as methanol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Efficient electrocatalytic conversion of CO 2 to ethanol enabled by imidazolium-functionalized ionomer confined molybdenum phosphide

An effective electrochemical carbon dioxide reduction reaction (eCO 2 RR) requires the discovery of a catalytic system that is highly active and selective for multi-carbon products together with superior CO 2 diffusion at a catalyst layer to minimize the reduction barriers. Here, we found a catalytic system that uses molybdenum phosphide (MoP) nanoparticles covered by imidazolium-functionalized ionomer (Im) that promotes CO 2 diffusion at the catalyst layer toward the catalyst surface, where CO 2 is reduced to ethanol (C 2 H 5 OH). The electrochemical results with the MoP-Im co-catalyst show a C 2 H 5 OH production Faradaic efficiency and a cathodic energy efficiency of 77.4% and 63.3%, respectively, at a potential as low as - 200 mV vs. RHE. The electrochemical experiments along with our physicochemical characterizations indicate that the Im improves CO 2 diffusion and balances water content resulting in a higher CO 2 -to-water ratio at the catalyst layer and fine-tunes the electronic properties of Mo atoms at the MoP surface. Finally, in-situ Raman spectroscopy reveals that a high number of adsorbed *CO intermediates on the surface and a higher binding strength of *CO intermediates on the Mo surface sites in the presence of imidazolium molecules are the main reasons for a superior C-C coupling and thereby the improved C 2 H 5 OH formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Pore-Scale Transport Effects in Electrochemical CO 2 Reduction on Gold via Coupled Microkinetic-Transport Modeling

A pore-resolved modeling framework is developed to quantify how pore-scale transport affects the intrinsic microkinetics of CO 2 -to-CO on Au. A DFT-informed microkinetic model is coupled self-consistently to a Generalized-Modified Poisson–Nernst–Planck (GMPNP) transport description in a single, electrolyte-filled cylindrical pore, allowing local concentrations and potential to feed back into site-specific reaction rates. FIB-SEM is used to determine pore sizes within realistic electrode materials. Across pore diameters, d p = 10–6000 nm, the surface-averaged CO 2 reduction rate is systematically reduced relative to the ideal microkinetic baseline where mass transport is not accounted for; the effectiveness factor 𝜂 𝑠,CO 2 , which quantifies this ratio, decreases rapidly at more negative potentials and is about 1% near −1.0 V vs SHE due to reactant depletion. Spatial maps reveal pore-bulk alkalization that emerges at higher cathodic bias, with a small, near-wall pH dip due to electrostatic repulsion of hydroxide at the cathode interface. For a fixed aspect ratio L p /d p , narrower pores exhibit larger 𝜂 𝑠,CO 2 by shortening diffusion paths, whereas variations in the aspect ratio L p /d p play a secondary role. A dimensionless analysis (surface/bulk Damköhler numbers) delineates operating regimes. In conclusion, this work offers a concept for incorporating microkinetic models into homogenized porous-electrode models through effectiveness factors and pore-size distribution.

Au-catalyst↗
DOE OSTI2025

Electrochemical reduction of ammonia-captured CO 2 to CO over a nickel single-atom catalyst

Carbon reactive capture and conversion offers a sustainable route to valuable chemicals and fuels while aiding Green House Gas (GHG) reduction. Direct electrochemical conversion of capture solutions like bicarbonate avoids the energy demands of conventional CO 2 regeneration. Ammonium bicarbonate (NH 4 HCO 3 ) is particularly attractive due to its low decomposition temperature and ability to supply in situ CO 2 from dilute sources without requiring purified CO 2 . Meanwhile, single-atom catalysts (SACs) with nitrogen-coordinated metal sites further enhance CO 2 reduction efficiency using Earth-abundant materials. In this study, we demonstrate a nickel single-atom catalyst (Ni-SAC)-based electrolyzer that utilizes NH 4 HCO 3 as the CO 2 source, achieving significantly improved CO production performance compared to the conventional silver cathodes used in the CO 2 reduction reaction (CO 2 RR) to produce CO. The Ni-SAC cathode exhibited a Faradaic efficiency of 60.1% for CO production at −200 mA cm −2 , while the silver cathode achieved a Faradaic efficiency of only 2%, likely due to ammonium-induced poisoning. Furthermore, the integration of a customized microporous layer onto the electrode significantly increased the Faradaic efficiency from 64% to 83% at −100 mA cm −2 , emphasizing the crucial role of electrode structure optimization in enhancing CO selectivity. These findings demonstrate a sustainable and economically viable strategy for green CO production directly from CO 2 capture solutions.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2025

Net-Zero Ethylene: On the Sustainability, Economics, and Scalability of Synthetic and Fossil Production Pathways

The ethylene industry has contributed over 260 million tons of CO 2 annually, warranting a more sustainable approach. The conversion of CO 2 and H 2 O into ethylene is an appealing technology capable of decoupling chemical production from fossil fuels. However, the large energy demand from this process can potentially lead to adverse environmental impacts. Here, in this article, we critically analyze the economic viability, environmental impact, and scalability of the conversion of CO 2 to ethylene via electrochemical reduction (CO 2 R) and compare this with those of CO 2 -neutral fossil routes utilizing carbon capture and direct air capture. Ethylene derived from CO 2 may be economically competitive under optimistic conditions; however, its large energy requirements pose environmental and scalability challenges. Meeting forecast 2050 ethylene demand using CO 2 R would require half of all electricity produced globally today, and, if powered by solar PV, may have greater CO 2 emissions than current petrochemical ethylene production, negating the purpose of this technology. Using Carbon Capture and Storage and Direct Air Capture to decarbonize petrochemical pathways would require roughly an order of magnitude less energy but would have disproportionate health and climate impacts. Lastly, the analysis highlights the importance of low-carbon energy sources to ensure sustainable CO 2 R ethylene production.

CO2R↗
DOE OSTI2026

CO (2) Electroreduction on Borated Copper Surfaces: Boron Active Sites, Not Copper

Boron-doped copper has recently emerged as an active and stable catalyst for the electrochemical reduction of CO 2 to value-added C 2 products. Here, in this work, we develop a realistic model of CO electroreduction on surface borides of copper under operational conditions, taking into account the effects of electrode potential, electrolyte environment, and pH. We study the possible reconstruction of the electrocatalyst surface using grand canonical DFT and global optimization to obtain a potential-dependent grand canonical ensemble description of metastable, hydrogen-covered catalyst surfaces. Two key surface configurations, low H coverage (LC, −0.6 V SHE ) and high H coverage (HC, −0.8 V SHE ), dominate this ensemble, with the former being kinetically persistent and C 2 selective under strongly reducing conditions. Nonmetallic boron sites on the surface copper boride are found to bind CO more strongly than copper sites, and mechanistic investigation of CO electroreduction pathways presents a surprisingly unconventional case of boron-centered reactivity in contrast to typical copper-centered reactivity. Neighboring boron sites present along boron chains on the surface copper boride are found to facilitate C−C coupling, thereby driving the high C 2 selectivity of this electrocatalyst.

boron-doped copper↗
DOE OSTI2026

Selective CO 2 Reduction by Bis(bipyridine)cobalt(II) Catalysts: The Role of Pendant Pyridine as a Proton Acceptor

Electrochemical CO 2 reduction reaction (CO 2 RR) catalyzed by molecular earth-abundant metal catalysts is a promising strategy to convert CO 2 into value-added products. One recent trend in this field has been focusing on the rational design of catalysts by incorporating redox-active ligands and modifying the secondary coordination sphere (SCS) to achieve efficient and selective CO 2 RR. Herein, we report a series of Co bis­(bipyridine) catalysts featuring various dangling groups, such as pyridine, tertiary amine, or butyl, in the secondary coordination sphere (Co-PyMe, Co-Py, Co-PrN, and Co-Bu). Efficient, selective electrocatalytic CO 2 RR was achieved by the complexes after the generation of triply reduced intermediate consisting of a Co I center and a dianionic ligand, producing CO as the major product and trace amount of H 2 . Strong correlations with the identity of dangling groups and turnover frequency (TOF) have been observed, in which Co-PyMe displayed the highest TOF (1086 s –1 in MeCN/H 2 O). Mechanistic studies indicated that the acceleration of CO 2 RR with pyridine-functionalized catalysts were derived from the protonation of pyridine dangling groups which participated as weak acids in the H-bonding network with exogenous proton sources, stabilizing CO 2 -bound intermediates and facilitating proton transfer. In addition, precatalytic CO 2 binding and activation at the third reduction (−2.1 V) was revealed by CV and SEC-IR studies. The resultant doubly reduced CO-bound species acted as a trapping state which inhibited CO 2 RR electrocatalysis. Regeneration of active species was accessed via reductive dissociation of CO at a more negative potential. In conclusion, this study highlights the combined effects of redox-active ligands and pyridine/pyridinium as SCS groups on CO 2 RR catalysis and provides design principles for future development of CO 2 RR catalysts utilizing pyridine/pyridiniums as SCS functional groups to fine-tune the catalytic activity.

CO2 reduction↗
DOE OSTI2021

Binary Atomically Dispersed Metal-Site Catalysts with Core–Shell Nanostructures for O 2 and CO 2 Reduction Reactions

Engineering atomically dispersed metal site catalysts with controlled local coordination environments and 3D nanostructures effectively improves the catalytic performance for the oxygen reduction reaction (ORR) and the carbon dioxide reduction reaction (CO 2 RR), which are critical for clean energy conversion and chemical production. Herein, an innovative approach for preparing core-shell nanostructured catalysts with different single-metal sites in the core and the shell, respectively, is developed. In particular, as the shell precursors, covalent organic polymers with a thin layered structure that is polymerized in situ and coated on a metal-doped ZIF-derived carbon core are used, followed by a controlled thermal activation. The selective combination and construction of different metal sites increase active site density in the surface layers, promote structural robustness, facilitate mass/charge transfer, and yield a possible synergy of active sites in the core and the shell. The p-FeNC(shell)@CoNC(core), consisting of a polymerized FeTPPCl-derived carbon layer (p-FeNC) on a Co-doped ZIF-derived carbon (CoNC), exhibits remarkable ORR activity and stability in acidic media along with encouraging durability in H 2 –air fuel cells. Likewise, a p-FeNC(shell)@NiNC(core) catalyst demonstrates outstanding CO 2 RR activity and stability. Hence, integrating two appropriate single-metal sites in core and shell precursors, respectively, can modulate morphological and catalytic properties for a possible synergy toward different electrocatalysis processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Photoelectrocatalytic reduction of CO 2 to formate using immobilized molecular manganese catalysts on oxidized porous silicon

The reduction of carbon dioxide (CO 2 ) to formate using molecular catalysts immobilized on high surface area porous silicon is described. Manganese complexes of the type ( R bpy)Mn(CO) 3 Br (bpy = 2,2′-bipyridine) were prepared with silatrane groups on the bpy ligand for attachment to oxide-coated porous silicon (SiO x -porSi). SiO x -porSi wafers were formed by heating hydrogen-terminated p-type porous silicon wafers under air, and the manganese complexes were immobilized on SiO x -porSi by heating at 80°C. The resulting hybrid photoelectrodes are photoelectrocatalysts for CO 2 reduction in acetonitrile containing 2.0 M triethylamine and 2.0 M isopropanol, yielding formate with high selectivity (>96%) and current density (∼0.6 mA/cm 2 ), excellent reproducibility, and a photovoltage of 280 mV at −1.75 V (versus ferrocenium/ferrocene) under 1 sun illumination. Here, the applied potential is close to the equilibrium potential for CO 2 reduction to formate. This work presents rare examples of immobilized molecular catalysts for CO 2 reduction to formate and the first on semiconducting silicon.

13 HYDRO ENERGY↗
DOE OSTI2022

Comparative Technoeconomic Analysis of Pathways for Electrochemical Reduction of CO 2 with Methanol to Produce Methyl Formate

Electrochemical CO 2 reduction has promise as a technology that could help society reach carbon neutrality while producing valuable fuels and chemicals. Herein, the electrochemical synthesis of methyl formate, a product not observed in aqueous CO 2 electrolysis, has been analyzed by a rigorous technoeconomic model to evaluate its commercial viability. Methyl formate synthesis has been demonstrated with high faradaic efficiency through the electroreduction of CO 2 in methanol. Four competing approaches were analyzed: (1) Electroreduction of captured CO 2 in a dual CH 3 OH/H 2 O electrolyzer, (2) Direct electroreduction of flue gas CO 2 in a dual CH 3 OH/H 2 O electrolyzer, (3) Electroreduction of captured CO 2 in a CH 3 OH/CH 3 OH electrolyzer, and (4) Electroreduction of captured CO 2 in a H 2 O/H 2 O electrolyzer with a downstream CH 3 OH reactor. Sensitivity analyses, cost contour plots, and comparison plots were generated. The dual methanol/water electrolysis approach was the most cost-competitive, with a levelized cost of methyl formate below the present market price. Here, the all-methanol electrolysis route was more expensive due to increased methanol consumption and greater distillation costs. Methyl formate production through aqueous CO 2 electrolysis to formic acid with a secondary esterification reaction was by far the most expensive approach, primarily due to the energy-intensive nature of distilling formic acid from water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗