SELF-CLEANING CO2 REDUCTION SYSTEM AND RELATED METHODS
20240076790 ยท 2024-03-07
Inventors
- Edward Sargent (Toronto, CA)
- David SINTON (Toronto, CA)
- Yi XU (Toronto, CA)
- Jonathan P. EDWARDS (Toronto, CA)
Cpc classification
C25B9/23
CHEMISTRY; METALLURGY
C25B11/052
CHEMISTRY; METALLURGY
International classification
C25B9/17
CHEMISTRY; METALLURGY
C25B11/052
CHEMISTRY; METALLURGY
Abstract
A self-cleaning CO.sub.2 reduction strategy is proposed herein including alternating operation and regeneration of the CO.sub.2 electrolysis system. The strategy includes application of short and periodic reductions in applied voltage, thereby avoiding saturation and prevention of carbonate salt formation.
Claims
1-32. (canceled)
33. A method for reducing CO.sub.2 in an electrolytical system and/or for self-cleaning a gas diffusion electrode in an electrolytical system operating CO.sub.2 reduction, the method comprising: applying an operational voltage to the electrolytical system to operate CO.sub.2 reduction for a first period of time defining an operation cycle, thereby forming carbonate ions at a cathode side of the electrolytical system and having a local carbonate ion concentration; and subsequently applying a regeneration voltage to the electrolytical system for a second period of time defining a regeneration cycle to force electromigration of the formed carbonate ions to an anode side of the electrolytical system; characterized in that the regeneration voltage is lower than the operational voltage and the operational voltage is between 3.0 and 4.5 V.
34. The method of claim 33, characterized in that the duration of the operation cycle is chosen to maintain the local carbonate ion concentration at the cathode side below a carbonate salt solubility limit.
35. The method of claim 33, characterized in that the first period of time is at between 1 second and 1200 seconds.
36. The method of claim 33, characterized in that the first period of time is at between 60 seconds and 300 seconds.
37. The method of claim 33, characterized in that the second period of time is between 1 second and 60 seconds.
38. The method of claim 33, characterized in that said method further comprises repeating the operation cycle and the regeneration cycle by alternating a voltage applied to the electrolytic system between the operational voltage and the lower regeneration voltage.
39. The method of claim 38, characterized in that each operation cycle is performed for the same duration.
40. The method of claim 38, characterized in that each regeneration cycle is performed for the same duration.
41. The method of claim 38, characterized in that the duration of each operation cycle varies between 1 second and 1200 seconds.
42. The method of claim 38, characterized in that the duration of each regeneration cycle varies between 1 second and 60 seconds.
43. The method of claim 33, characterized in that the regeneration voltage is chosen to obtain a CO.sub.2 reduction rate below 1 mA.Math.cm.sup.2.
44. The method of claim 33 characterized in that the operational voltage is between 3.2 and 4.0 V.
45. The method of claim 33, characterized in that the regeneration voltage is between 2.5 V and 5.0 V.
46. The method of claim 33, characterized in that the electrolytical system is a membrane electrode assembly (MEA) comprising a gas diffusion electrode serving as a cathode.
47. The method of claim 33, characterized in that the electrolytical system is a flow cell system comprising a liquid catholyte and a gas diffusion electrode serving as a cathode.
48. The method of claim 46, characterized in that the cathode comprises a metal layer deposited on substrate.
49. The method of claim 48, characterized in that the cathode comprises a silver layer deposited on a carbon paper substrate.
50. The method of claim 48, characterized in that the cathode comprises a copper layer deposited on a PTFE substrate.
51. The method of claim 33, characterized in that the electrolytical system comprises an anolyte.
52. The method of claim 51, characterized in the anolyte is an aqueous solution of one or more alkaline compounds, said one or more alkaline compounds comprising one alkali metal cations selected from lithium, sodium, potassium, rubidium, caesium and any combination thereof.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0100] The figures describe various aspects and information regarding the techniques described and claimed herein.
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DETAILED DESCRIPTION
[0148] The descriptions, examples, methods and materials presented in the claims and the specification are not to be construed as limiting but rather as illustrative only.
[0149] Meanings of technical and scientific terms used herein are to be commonly understood as by one of ordinary skill in the art to which the invention belongs, unless otherwise defined.
[0150] It is understood that whether the term about is used explicitly or not, every quantity given herein is meant to refer to an actual given value, and it is also meant to refer to the approximation to such given value that would reasonably be inferred based on the ordinary skill in the art, including approximations due to the experimental and/or measurement conditions for such given value. It is commonly accepted that a 10% precision measure is acceptable and encompasses the term about.
[0151] Although various implementations of the invention may be described in the context of a single embodiment, these implementations may also be provided separately or in any suitable combination. Conversely, although the invention may be described herein in the context of separate embodiments for clarity, the implementations of the techniques described herein may also be implemented in a single embodiment, unless incompatible.
[0152] Any publications, including patens, patent applications and articles, referenced or mentioned in this specification are herein incorporated in their entirety into the specification, to the same extent as if each individual publication was specifically and individually indicated to be incorporated herein. In addition, citation or identification of any reference in the description of some embodiments of the invention shall not be construed as an admission that such reference is available as prior art to the present invention.
[0153] The present techniques relate to self-cleaning of a gas diffusion electrode in an electrolytical cell operating CO.sub.2 reduction at an applied cell voltage where carbonate ions are formed. The self-cleaning techniques involve alternating the applied cell voltage between an operational voltage and a lower regeneration voltage. An operational cycle is defined by application of the operational voltage for an operational duration, and the regeneration cycle is defined by application of the regeneration voltage for a regeneration duration. Duration of each operational cycle and regeneration cycle can be tailored to reduce or avoid carbonate salt precipitation at the gas diffusion electrode side (e.g., cathode side for CO.sub.2RR) of the electrolytical cell. Carbonate ions that are formed at the cathode side during the operational cycle can be transferred to an anode side of the electrolytical cell via electromigration during the subsequent regeneration cycle. Once migrated to the anode side, the carbonate ions are further changed to CO.sub.2. The techniques proposed herein can be referred to as an alternating voltage approach, an alternating approach, an alternating voltage strategy, an alternating strategy or an unsteady electrochemical forcing strategy.
[0154] Different alternating voltage and pulsed electrolysis strategies have been employed in CO.sub.2 electrolyzers with a range of duty cycles. Depending on the specific conditions, these strategies can be used to adjust the surface CO:H.sub.2 ratio (see Kumar B., et al.ACS Catal. 2016, 6 (7), 4739-4745), increase C.sub.2+ production (see Arn-Ais, R. M. et al.Nat. Energy 2020, 5 (4), 317-325), and decrease H.sub.2 generation (see Kimura K. W. et al.ChemSusChem 2018, 11 (11), 1781-1786). Computational modelling was used to illustrate that steady state operation of electrolyzers for CO.sub.2 reduction can yield high carbonate concentrations, which further lead to inevitable salt formations. The present salt formation prevention strategy includes avoiding reaching the steady state conditions. To do so, the present techniques include varying the applied cell voltage between two values, and more specifically, applying cyclically an operation voltage for an operation duration, and a regeneration voltage for a regeneration duration. The resulting regeneration potential lowers the reaction rate to nearly 0 mA cm.sup.2, eliminating hydroxide formation, while maintaining a sufficiently negative polarization at the cathode to transport carbonate ions to the anode under electromigration (
[0155] Based on experimentation using carbon paper and PTFE-based electrodes for silver and copper catalysts, respectively, CO.sub.2 electrolysis was performed in a membrane electrode assembly (MEA) electrolyzer, using the present alternating voltage approach. A similar product distribution to that of constant voltage operation was obtained, but demonstrated enhanced stability. The copper-PTFE electrodes were able to sustain the product distribution when operated alternatively for 157 hours of operation over 236 hours of total duration, as compared to 10 hours of operation when the same copper-PTFE electrodes were operated continuously.
[0156] In some implementations, selection of a duration for each operation cycle and regeneration cycle is based on the variation of a local carbonate ion concentration at the cathode side. To avoid any salt precipitation, the local carbonate ion concentration can be maintained below the carbonate salt solubility limit during operation. Additionally, the local carbonate ion concentration can be reduced sufficiently (via electromigration), e.g., by at least 80%, during the regeneration cycle to ensure that the local carbonate ion concentration will not reach the carbonate salt solubility limit during a subsequent operation cycle. For example, selecting the duration for each operation cycle and regeneration cycle can include simulating the local carbonate ion concentration variation history for a specific voltage application scenario.
[0157] To better understand the present salt prevention strategy, a computational model of CO.sub.2RR was developed to assess concentration profiles of key species during operation (
[0158] Another series of simulations, including the use of multiple regeneration periods during which a regeneration voltage of 2.0 V was applied, allowed to analyze concentration changes immediately after 60 seconds of operation (
[0159] A cycle with 60-second operation followed by 30-second regeneration (
[0160] To further demonstrate that the alternating strategy was successful in reducing carbonate salt formation, a cathode was fabricated by spraying a carbon gas diffusion layer with silver nanoparticles on a substrate and carbon monoxide (CO) was produced from CO.sub.2 in a CO.sub.2RR MEA electrolyzer including the fabricated cathode. The anolyte was 0.1 M potassium bicarbonate and the anode was an iridium-based catalyst that was used to perform oxygen. Referring to
[0161] In order to apply the present alternating strategy, also referred to as an unsteady electrochemical forcing strategy, the system was cyclically operated with the application of the same operational voltage of 3.6 V for an operation duration of 60 seconds, and further application of a regeneration voltage of 2.0 V for a regeneration duration of 30 seconds (
TABLE-US-00002 TABLE 2 Product distribution for alternating voltage experiments with silver and copper cathodes. Full cell Faradaic Efficiency (%) Potential Formate Acetate N- Sample (V) H.sub.2 CO CH.sub.4 C.sub.2H.sub.4 Acid Acid Ethanol propanol Acetaldehyde Carbon paper 3.40 4.2 2.9 92.1 4.6 0.2 0.0 0.1 0.0 0.7 0.3 sprayed with 3.60 4.3 1.7 93.5 5.7 0.2 0.1 0.1 0.0 0.9 0.2 silver 3.80 4.7 2.0 93.2 5.1 0.4 0.1 0.2 0.0 0.7 0.2 nanoparticles 4.00 8.9 5.7 88.7 3.7 0.5 0.2 0.2 0.1 1.2 0.4 4.20 19.2 6.1 77.4 10.0 0.7 0.2 0.2 0.0 1.4 0.2 PTFE with 3.40 6.1 3.2 .sup.54 9.1 0.2 0.1 25.2 3.9 4.1 2.0 1.1 0.1 7.2 0.9 0.6 0.2 0.4 0.0 sputtered 3.60 6.3 2.9 36.2 5.4 0.3 0.1 37.1 3.7 3.2 1.1 2.9 0.4 10.9 3.7 0.9 0.2 0.7 0.2 copper & 3.80 5.9 2.1 10.6 3.4 0.7 0.3 56.7 5.5 1.9 0.2 4.7 1.4 15.6 3.1 1.8 0.9 1.4 0.4 sprayed copper 4.00 13.2 5.8 9 1.9 2.6 0.9 43 7.2 1.8 0.7 7.5 1.3 16.2 1.9 2.1 0.6 1.6 0.4 nanoparticles 4.20 17.9 12.0 6.1 1.7 4.9 0.7 32.1 6.1 2.1 0.5 9.2 2.4 17.1 5.7 2.4 0.7 1.8 0.5
[0162] The test was stopped after 18 hours (total duration) for direct comparison with the continuously operated system.
[0163] To validate that enhancement of the stability was due to the use of a regeneration period as per the proposed method, and not from the lower average current density, another series of tests was performed including operation of a silver cathode sample at a slightly lower constant operational voltage (3.4 V shown in
[0164] To demonstrate the versatility of the alternating strategy, another series of tests was performed using an electrode including a copper-based catalyst on a PTFE-based substrate as reported in the experimental section (see study of Gabardo et al., entitled Continuous Carbon Dioxide Electroreduction to Concentrated Multi-Carbon Products Using a Membrane Electrode Assembly (Joule 2019, 3 (11), 2777-2791). It was noted that despite the change in both the catalyst material and electrode substrate, the stability was maintained. When the copper electrode was operated continuously, there was much salt precipitation visible after 48 hours (
[0165] The current density of the copper-PTFE system fluctuated during the 236-hour experiment (
[0166] When comparing
TABLE-US-00003 TABLE 3 The copper on PTFE electrode presented in this work is the longest demonstration in existing literature operated at industrially relevant current densities. j.sub.C2 Operational Catalysts (mA cm.sup.2) Time C.sub.2 FE Cell type References 1 CuNP/Cu/PTFE 138 157 h 81% MEA This work 2 3D catalyst ~120 60 h ~60% MEA Science 367, 661-666 (2020) 3 Cu.sub.3N 101 20 h 60% Flow cell Nano Lett. 19, 8658-8663 (2019) 4 Molecular tuned ~79 180 h ~70% MEA Nature. 577 (7791), 509-513 Cu (2020) 5 Graphite/NP/Cu/ 100 h ~80% MEA Joule. 3, 2777-2791 (2019) PTFE 6 Graphite/NP/Cu/ ~55 150 h 83% Flow cell Science. 360, 783-787 (2018).sup.8 PTFE 7 Ordered ~0.15 24 h 77% H cell Angew. Chemie. 129, Mesoporous NC 10980-10984 (2017)
[0167] An activation voltage refers herein to the voltage required to reach an onset potential for both cathodic and anodic reactions, thereby generating a current density in accordance with an activation energy of the triggered redox event. The regeneration voltage is selected to be below the activation voltage, and thus the regeneration period operates at a negligible current density, which is a much lower current density than during the operational period. Therefore, there is minimal additional energy required to power the regeneration period since the regeneration period can consume less than 1% of the system energy requirements (
[0168] In summary, when CO.sub.2 electrolysis is performed at industrially relevant current densities, the steady state alkaline conditions lead, inevitably, to carbonate salt formation. The self-cleaning CO.sub.2 reduction method implementations that are proposed herein can circumvent steady state by cycling the applied voltage between an operational voltage and a regeneration voltage. The regeneration voltage is applied during the regeneration period in order to maintain an electric field for carbonate ions to migrate to the anode, thereby lowering carbonate ions concentrations at the cathode and avoiding damaging of the cathode via salt formation and plugging. The alternating approach was applied to silver and copper catalysts on carbon paper and PTFE based electrodes, respectively. The product selectivity resulting from the cyclically operated system was shown to be similar to that of the continuously operated system, with the advantage that alternating operation with regeneration yielded no detectable carbonate formation. More specifically, using the alternating strategy, the copper-PTFE sample in a MEA-based electrolyzer was operated in alternate for 157 hours (236 hours total duration), while maintaining a C.sub.2 product selectivity of 80% and a C.sub.2 partial current density of 138 mA cm.sup.2 with a cost of <1% additional system energy input.
Test and Determination Methods
Raman Spectroscopy
[0169] Potassium carbonate (John Wiley & Sons, I. SpectraBase Compound ID=DepkjwUOQKb SpectraBase Spectrum ID=JXEQ5H3aIck https://spectrabase.com/spectrum/JXEQ5H3aIck (accessed Dec. 19, 2020) and potassium bicarbonate (John Wiley & Sons, I. S. SpectraBase Compound ID=DBxdA3hFcsM SpectraBase Spectrum ID=E0IHiW8WWv5 https://spectrabase.com/spectrum/E0IHiW8WWv5 (accessed Dec. 19, 2020) were both detected, but potassium carbonate had a much higher intensity.
X-Ray Photoelectron Spectroscopy
[0170] X-Ray Photoelectron Spectroscopy (XPS) measurements were performed with a Thermo Fisher ESCALAB 250 Xi XPS.
Experimental Parts
[0171] The following part includes information related to the COMSOL Multiphysics simulation results and model mechanism; current density plots of the different regeneration voltages; current density and selectivity plots of continuous operation of silver and copper catalysts; electrochemical performance comparison between continuous and alternating voltage with the same average current density; current density and selectivity of continuous operation of silver catalyst; electrode preparation; operation of the electrochemical MEA cell; and product analysis.
Solubility Calculation
[0172] The solubility product constant of potassium carbonate (K.sub.sp) describes the equilibrium between the solid and its constituent ions in a solution. The value of the constant identifies the degree to which the compound can dissociate in water. The K.sub.sp value of potassium carbonate is 2073 at 20 C..sup.1
K.sub.2CO.sub.3(s)2K.sup.+(aq)+CO.sub.3.sup.2(aq)(E1)
K.sub.sp=[K.sup.+].sup.2[CO.sub.3.sup.2].sup.1(E2)
[0173] Applying the solubility product constant of potassium carbonate equation (E2) into the 1D MEA COMSOL model, the simulation time of the continuous operation run reached K.sub.sp=2073 at 1200 s of continuous operation at 3.8 V, where [CO.sub.3.sup.2]=7.8 M, [K.sup.+]=16.6 M.
[0174] Moreover, due to the charge neutrality of the local cathode electrolyte, the concentrations of the constituent ions can be expressed in E3. The basic condition around the cathode (pH 14), the concentrations of the [H.sup.+], [HCO.sub.3.sup.] and [OH.sup.] were relatively small and negligible, as compared to [K.sup.+] and [CO.sub.3.sup.2]. Therefore, the concentrations of [K.sup.+] and [CO.sub.3.sup.2] maintained the approximate ratio of 2:1.
[K.sup.+]+[H.sup.+]=[HCO.sub.3.sup.]+[OH.sup.]+[CO.sub.3.sup.2](E3)
Electrode Preparation
[0175] The carbon papersilver gas diffusion electrode (GDE) was prepared by airbrushing catalyst inks with a nitrogen carrier gas. The catalyst silver ink was prepared with 12 mL ethanol (Greenfield Global Inc., >99.8%), 150 L Nafion (Fuel Cell Store D521 Alcohol-based 1100 EW, 5 wt %), and 15 mg silver nanoparticles (Sigma-Aldrich 576832-5G, <100 nm particle size). The catalyst ink mixtures were sonicated for two hours, and then sprayed on a gas diffusion carbon paper (Fuel Cell Store Sigracet 39 BC, with a microporous layer) with a spray density of 0.15 mL cm.sup.2. After airbrushing, the GDE was dried for 24 hours at room temperature (20 C.). The polytetrafluoroethylene (PTFE) based copper electrode used was prepared by plasma sputtering and then airbrushing catalyst inks with a nitrogen carrier gas. Approximately 300 nm of copper catalyst was sputtered onto the PTFE substrate using an AJA International ATC Orion 5 Sputter Deposition System (Toronto Nanofabrication Centre, University of Toronto). An additional copper layer was sprayed on top of the sputtered layer. The copper ink was prepared with 12 mL ethanol, 150 L Nafion, and 15 mg of copper nanoparticles (Sigma-Aldrich 774081-5G, 25 nm particle size). Catalyst inks were sonicated for two hours and then sprayed on the sputtered PTFE sample with a spray density of 0.15 mL cm.sup.2. After airbrushing, the GDE was dried for 24 hours at room temperature (20 C.). A Sustainion anion exchange membrane (Dioxide Materials Sustainion 37) was used in the electrolyzer. The anode electrode was prepared by spraying iridium chloride (Alfa Aesar, IrCl3.Math.xH2O 99.8%) on a titanium support (Fuel Cell Store 592795-1, Titanium Felt). The coated electrode was treated by a thermal decomposition method.sup.10.
Operation of the Electrochemical MEA Cell
[0176] All electrochemical experiments were performed in an anion exchange membrane-based MEA electrolyzer (Fuel Cell Store, 72500322, AEM Water Electrolyzer5 cm.sup.2). The electrolyte was pumped through the cell by a peristaltic pump. The CO.sub.2 inlet gas flow rate was approximately 80 standard cubic centimeters per minute (sccm). The constant voltage electrochemical tests were performed by running one fresh cathode sample at multiple voltages of interest sequentially (3.4 V, 3.6 V, 3.8 V, 4.0 V, and 4.2 V). The alternating voltage electrochemical tests were performed using the same sequential operational voltage above for 60 seconds, followed by a 30 second 2.0 V regeneration voltage. The voltages reported are full cell voltages with no iR compensation.
Product Analysis
[0177] The gas products from CO.sub.2 reduction were analyzed in 1 mL volumes using a gas chromatograph (PerkinElmer Clarus 680), possessing a thermal conductivity detector (TCD) and a flame ionization detector (FID). Using argon as the carrier gas (Praxair, 99.999%), the gas chromatograph was equipped with a Molecular Sieve 5A capillary column and a packed Carboxen-1000 column. The flow rate of the gas was measured before each 1 mL volume was collected. The gas sample was collected by water displacement for one operational and regenerational iteration for alternating voltage tests. Then, we used the integration of total charge passing over the iteration to calculate the gas product Faradaic efficiency.
[0178] The liquid products were quantified using nuclear magnetic resonance spectroscopy (NMR). .sup.1H NMR spectra of freshly acquired samples were collected on an Agilent DD2 500 spectrometer using water suppression mode with dimethyl sulfoxide (DMSO) as an internal standard.
1D MEA COMSOL Multiphysics Model:
[0179] The one-dimensional was modelled by COMSOL Multiphysics version 5.5, incorporating both the carbon dioxide reduction reaction (CO.sub.2RR) on the cathode and the oxygen evolution reaction (OER) on the anode in 0.1M KHCO.sub.3 anolyte. An anion exchange membrane (AEM) was sandwiched between the cathode and anode. The major focus of this study was to compare the local carbonate concentration with and without the alternating voltage salt prevention strategy. The Secondary Current Distribution and Transport of Diluted Species physics modules within COMSOL were used to model the chemical reactions between aqueous CO.sub.2, HCO.sub.3.sup., CO.sub.3.sup.2, H.sup.+, OH.sup. and K.sup.+ in a time-dependent study. This model was a modified version of previous reports, see for example the study of McCallum C., et al., entitled Reducing the crossover of carbonate and liquid products during carbon dioxide electroreduction (Cell Reports Physical Science, 2021, 2, 100522). There were several general assumptions for this simulation. Firstly, a constant concentration of CO.sub.2 was supplied at the humidified GDE/CL interface, and constant concentrations of chemical species were set at the right-hand boundary of the anolyte layer. Secondly, a Cu/Nafion layer was directly deposited on top of the porous Cu catalyst layer to serve as a current collector. Thirdly, the cathode and anode were separated by an AEM, and an electrolyte was distributed through the porous media.
[0180] The geometry (
CO.sub.2 Solubility in 0.1M KHCO.sub.3 Electrolyte:
[0181] The CO.sub.2 Solubility in pure water was determined by Henry's Law (E4-E5). Solubility in water depends on the temperature and pressure..sup.16,17
[0182] Where K.sub.0 is the Henry volatility constant, which can be influenced by temperature T. However, due to the Salting out effect as explained by the Sechenov Equation,.sup.18 the Solubility of CO.sub.2 in a 0.1M KHCO.sub.3 electrolyte decreases as the salt concentration increases (E6-E8). As such, CO.sub.2 Solubility can be calculated using the sets of equations are shown below.
[0183] The K.sub.s represents the Sechenov constant, and C.sub.s is the molar concentration of the electrolyte solution. The Solubility is determined based on K.sup.+, HCO.sub.3.sup., CO.sub.3.sup.2 and OH.sup. ions concentration and the specific parameters which are shown in table 4.
TABLE-US-00004 TABLE 4 Corresponding Sechenov constants in 0.1M KHCO.sub.3 electrolyte - see study of Weisenberger S., et al., entitled Estimation of gas solubilities in salt solutions at temperatures from 273 K to 363 K (AIChE J., 1996, 42 (1), 298-300. Ion h.sub.ion K.sup.+ 0.0922 OH.sup. 0.0839 CO.sub.3.sup.2 0.1423 HCO.sub.3.sup. 0.0967 h.sub.G, 0 for CO.sub.2 0.0172 h.sub.T for CO.sub.2 0.000338
Catalyst Electrochemical Reactions:
[0184] Electrochemical reactions were applied within the respective catalyst layers (E9-E12): CO.sub.2 reduction to CO, H.sub.2, C.sub.2H.sub.4, C.sub.2H.sub.5OH on the cathode and oxygen evolution on the anode catalyst layer (E13).
CO.SUB.2.RR:
[0185]
2H.sub.2O+2e.sup..fwdarw.H.sub.2+2OH.sup.(E9)
CO.sub.2+H.sub.2O+2e.sup..fwdarw.CO+2OH.sup.(E10)
2CO.sub.2+8H.sub.2O+12e.sup..fwdarw.C.sub.2H.sub.4+12OH.sup.(E11)
2CO.sub.2+9H.sub.2O+12e.sup..fwdarw.C.sub.2H.sub.5OH+12OH.sup.(E12)
OER:
2H.sub.2O.fwdarw.O.sub.2+4H.sup.++2e.sup.(E13)
Ohm's Law and Poisson Equation:
[0186] The electrode and electrolyte potentials were governed by Ohm's Law (E14). The electromigration of the charged species (HCO.sub.3.sup., CO.sub.3.sup.2, H.sup.+, OH.sup. and K.sup.+) (E15) was controlled by the electrolyte potential and the combination of electroneutrality and induced space charge for ion-exchange membrane, which is governed by the Poisson equation (E16).
Where was the electrical conductivity of different media as listed in Table 5. .sub.l was the electrolyte potential. was the combination of electroneutrality and induced space charge for the ion-exchange membrane. .sub.0 and .sub.r were the permittivity of vacuum and the relative permittivity of water, respectively. .sub.aem was the space charge for the membrane that exists exclusively in the membrane domain. The detailed values for AEM are listed in Table 6.
TABLE-US-00005 TABLE 5 Electrical conductivity of different domains. (see study of Gabardo C. M. et al., cfr supra) Domain electrical conductivity [S/m] Copper cathode catalyst 0.8e5 Current collector 1.7e6 Anion exchange membrane 8.0 IrO.sub.x Anode catalyst 1.4e7 Anolyte 4.56
TABLE-US-00006 TABLE 6 Parameters for AEM. Parameters Value (unit) Permittivity of vacuum 8.8542e12 (F/m) Relative permittivity of water 80 (1) Membrane space charge 1 (M)
Porous Medium Effective Diffusion
[0187] All layers except the electrolyte diffusion boundary layer were considered as a porous medium. The effective diffusivity was governed by the Bruggeman model. The porosity was 0.6 in the Cu cathode catalyst and current collector. The porosity was 0.9 in the IrOx Anode catalyst. The porosity was 0.1 for the AEM with a 90% reduction in diffusion coefficients for the cations (see studies of Dinh C. T. et al., entitled CO.sub.2 Electroreduction to Ethylene via Hydroxide-Mediated Copper Catalysis at an Abrupt Interface (Science, 2018, 360 (6390), 783-787) and of Singh M. R. et al., entitled Mechanistic Insights into Electrochemical Reduction of CO.sub.2 over Ag Using Density Functional Theory and Transport Models (Proc. Natl. Acad. Sci., 2017, 114 (42), E8812-E8821).
Butler-Volmer Equations:
[0188] The electrode kinetics of CO.sub.2 reduction and water oxidation were modelled by the Butler-Volmer equation (E17-E21)
[0189] The exchange current density (i.sub.o,i) and charge transfer coefficient (.sub.c,i) were obtained from experimental results, determined in the same way as previous works (see Burdyny T. et alACS Sustain. Chem. Eng. 2017, 5 (5), 4031-4040). The overpotential () was determined by the difference between the applied voltage V.sub.app and the equilibrium voltage (E.sub.0,i) (E22). The kinetics constants are listed in Table 7.
TABLE-US-00007 TABLE 7 Experimental electrode kinetics for CO.sub.2RR and HER. Reaction i.sub.0, i (A m.sup.2) E.sub.0, i (V vs RHE) .sub.c, i() COER 9.7e7 0.51 0.136 C.sub.2H.sub.4ER 1.1e6 0.33 0.17 HER 5.3e6 0.41 0.136 EtOHER 5.4e5 0.32 0.119 OER 1e1 0.82 1.02
Species Transport:
[0190] In the reaction-diffusion model, the species transport equations (E23-E24) were governed by the Nernst-Planck equations. Diffusion and electromigration terms were considered for the transportation of chemical species.
[0191] C.sub.i,D.sub.i and z.sub.i represent the species concentration, diffusion coefficient, and charge number, respectively. The diffusion coefficient and charge number are listed below in Table 8.
TABLE-US-00008 TABLE 8 Diffusion coefficients and charge in the MEA system (see Vansek, P - CRC Handb. Chem. Phys. 1996, 96 (73), 5-98). Diffusion coefficient Species (m.sup.2s.sup.1) Charge number CO.sub.2 1.91e9 0 CO.sub.3.sup.2 0.923e9 2 HCO.sub.3.sup. 1.185e9 1 H.sup.+ 9.31e9 +1 OH.sup. 5.26e9 1 K.sup.+ 1.96e9 +1
Carbonate Equilibrium Equation:
[0192] The model predicted a steady-state equilibrium between aqueous CO.sub.2, HCO.sub.3.sup., CO.sub.3.sup.2, H.sup.+, and OH.sup. by considering several chemical reactions in alkaline conditions (E25-E28). Water dissociation (E29) was also considered in this system. The reaction rate constants were determined by the temperature and salinity.sup.4. The corresponding equations are listed below:
CO.sub.2+H.sub.2O.Math.H.sup.++HCO.sub.3.sup.(E25)
HCO.sub.3.Math.H.sup.++CO.sub.3.sup.2(E26)
CO.sub.2+OH.sup..Math.CO.sub.3.sup.2(E27)
HCO.sub.3.sup.+OH.sup..Math.CO.sub.3.sup.2+H.sub.2O(E28)
H.sub.2O.Math.H.sup.++OH.sup.(E29)