Probing dissolved CO2(aq) in aqueous solutions for CO2 electroreduction and storage.

CO2 dissolved in aqueous solutions CO2(aq) is important to CO2 capture, storage, photo-/electroreduction in the fight against global warming and to CO2 analysis in drinks. Here, we developed microscale infrared (IR) spectroscopy for in situ dynamic quantitating CO2(aq). The quantized CO2(g) rotational state transitions were observed to quench for CO2(aq), accompanied by increased H2O IR absorption. An accurate CO2 molar extinction coefficient ε was derived for in situ CO2(aq) quantification up to 58 atm. We directly measured CO2(aq) concentrations in electrolytes under CO2(g) bubbling and high-pressure conditions with high spectral and time resolutions. In KHCO3 electrolytes with CO2(aq) > ~1 M, CO2 electroreduction (CO2RR) to formate reached >98% Faradaic efficiencies on copper (Cu2O/Cu)-based electrocatalyst. Furthermore, CO2 dissolution/desolvation kinetics showed large hysteresis and ultraslow reversal of CO2(aq) supersaturation in aqueous systems, with implications to CO2 capture, storage, and supersaturation phenomena in natural water bodies.

INTRODUCTION

Analyzing dissolved CO2(aq) in aqueous solutions is of fundamental importance and has wide implications from environment and energy fields to consumer industries (–). As a greenhouse gas, excessive CO2 emissions from burning of fossil fuels have led to negative environmental and social consequences (, ). Absorption of CO2(g) by aqueous solvents or natural waterbodies (, , ) is a promising approach to CO2 capture and storage. CO2(aq) is also a popular flavoring molecule in many types of consumer drinks (, , ). Dissolved carbon species in aqueous systems were typically probed by titration (–) or total carbon measurements (, , ) and analyzed by chemical equilibria analysis (–). Tracking of gas phase pressure (), composition (), and electrical (, ) or thermal () conductivity were able to glean the kinetics of CO2 dissolution. However, direct in situ CO2(aq) probing with a high time resolution is rarely reported, especially under high pressures (, , ) in closed systems.

Conversion of CO2 into fuels and value-added products via CO2 electroreduction reaction (CO2RR) is an attractive approach to combating climate change and closing the carbon cycle (, ). During CO2RR, it is widely accepted that the dissolved CO2(aq) is the active carbon species (–) reduced to CO, hydrocarbons, and oxygenates (–), and the reduction products are influenced by CO2(aq) concentration in the electrolytes (, –). However, quantitative probing of CO2(aq) to correlate with CO2RR products is rare. For example, in widely performed CO2RR experiments under CO2 gas bubbling in electrolytes, CO2(aq) was inferred from diffusion and equilibria analysis (, , ), indirect pH probing (), or sampled at a given time point for total carbon (), without direct kinetic measurements of CO2(aq) in a quantitative manner.

In this work, we performed in situ Fourier transform infrared (FTIR) spectroscopy for dynamic CO2(aq) monitoring in various aqueous systems relevant to CO2 capture, storage, and CO2RR conditions at up to 58 atm of pressure. A thin (<~100 μm) liquid micro-infrared (IR) cell for transmission FTIR measurements circumvented the overwhelming IR absorption of H2O, enabling the probing of CO2 features (–) over water background (, ). Dynamic tracking of CO2(aq) with time resolutions down to 30 s per spectrum revealed the evolution of convoluted CO2(g) rotational-vibrational absorption bands (, ) to a single CO2(aq) vibrational peak (, ), which was accompanied by significant strengthening of H2O IR absorption especially under high pressures, suggesting considerable interactions between CO2 and H2O molecules that led to the quenching of CO2 molecular rotations during aqueous dissolution. We derived a CO2(aq) molar extinction coefficient ε of ~1.74 × 104 M−1·cm−2 for quantitating CO2(aq) in various solutions and beverages dynamically with a detection limit of ~1 mM (~44 mg/liter). CO2(aq) supersaturation levels at various CO2(g) bubbling rates in solutions were quantified. We correlated the CO2RR products with CO2(aq) concentrations in KHCO3 electrolytes under bubbling and various pressures up to 58 atm, establishing a relation between CO2(aq) concentration and CO2 electrochemical conversion products. Kinetic CO2(aq) probing over time showed faster CO2 dissolution kinetics than desolvation in aqueous solutions, with the finding of an unexpectedly long time needed to fully reversed CO2 supersaturation in water, which could be related to the observed CO2 supersaturation in lakes (, ).

RESULTS AND DISCUSSION

IR spectroscopy of CO2 in microscale liquid cells

A micro-IR cell with two borosilicate glass (or CaF2) windows sandwiching a thin (thickness d of ~10 to 100 μm, set by thin polytetrafluoroethylene spacers) aqueous layer (Fig. 1A and fig. S1) was used in our FTIR experiments. The microscale path lengths were critical to revealing CO2 ν3 band (C═O asymmetric stretching vibration at ~2350 cm−1) (, , ) without diminished by IR adsorption of H2O bending-libration combination mode in ~1900 to 2400 cm−1 region (, ). With 0.5 M NaHCO3 solution in 51.5-μm-thick micro-IR cell equilibrated under 1 atm of CO2(g) or at continuous CO2(g) bubbling (see Materials and Methods for details), we observed a dip in the spectrum at ~2350 cm−1 (IR resolution = 0.96 cm−1; Fig. 1A and fig. S2). Upon background subtraction of high-resolution (0.06 cm−1) spectrum, we obtained a symmetric peak at 2343.1 cm−1 (Fig. 1B), attributed to the main solvated carbon species CO2(aq) (–, , ). Calculation based on Conductor-like Screening Model for Real Solvents (COSMO-RS) () revealed a slight Gibbs-free energy (ΔG) decrease of 0.149 kcal/mol for CO2 dissolution in water (Fig. 1C and see Materials and Methods for details) close to the experimental value of 0.24 kcal/mol (), providing the thermodynamic driving force for CO2(g) to CO2(aq) (, ). CO2(aq) peak exhibited a 4.4 cm−1 redshift from fundamental CO2 ν3 vibrational frequency () f0 = 2347.5 cm−1 (marked by dashed line in Fig. 1, B, D, and E), consistent with density functional theory (DFT) result of the decreasing trend in ν3 frequency due to CO2 interactions with H2O molecules (fig. S3 and see Materials and Methods for details). For comparison, CO2 fully hydrated to H2CO3 resulted in an increased ΔG of 10.254 kcal/mol based on COSMO-RS calculation (fig. S4 and see Materials and Methods for details), suggesting thermodynamically disfavored formation of H2CO3 and corroborating the reported H2CO3 concentration ≤ 0.3% of CO2(aq) in aqueous solutions (, , ). The C═O asymmetric stretching frequency of H2CO3 would show a peak ~1770 cm−1 based on previous reports (–) and DFT calculation (fig. S4 and see Materials and Methods for details) but was not observed in the current work due to the low concentration and the signal was buried in the strong H─O─H bending absorption peak.

Fig. 1.

CO2 solvation in aqueous solutions monitored in micro-IR optical cells.

(A) Transmittance FTIR spectrum (resolution = 0.96 cm−1) of H2O after bubbling with 30 sccm Ar and of 0.5 M NaHCO3 solution after bubbling with 30 sccm of CO2(g), both for 30 min. Inset: Zoom-in of 2300 to 2400 cm−1 range, showing CO2(aq) ν3 (C═O asymmetric stretching) IR absorption band; a schematic of the micro-IR cell that was used, with thin (< ~100 μm) aqueous sample films sandwiched between borosilicate glass windows for FTIR measurements. (B) Background subtracted CO2(aq) ν3 peak at f = 2343.1 cm−1 (resolution = 0.06 cm−1) measured in water equilibrated with 1 atm of CO2(g), showing a 4.4 cm−1 redshift from fundamental ν3 vibrational frequency f0 = 2347.5 cm−1 due to interactions with H2O. (C) COSMO-RS simulation of Gibbs-free energy change ΔG = −0.149 kcal/mol during CO2 solvation in atmosphere at room temperature, suggesting the high reversibility between CO2(g) and CO2(aq). (D) FTIR spectrum of 12CO2(g) (resolution = 0.06 cm−1), revealing the coupling of quantized molecular rotational transitions with C═O vibration. Sharp peaks correspond to transitions of increasing (ΔJ > 0, R branch) and decreasing (ΔJ < 0, P branch) rotational energy levels located at each side of fundamental ν3 frequency f0 following Boltzmann distribution. Small 13CO2(g) signals corresponding to ~1.1% natural abundance of 13C are observed near 2270 cm−1. (E) Dynamic monitoring of CO2 solvation in 0.5 M NaHCO3 solution under 30 sccm of CO2(g) bubbling (resolution = 0.06 cm−1; see Materials and Methods for details). Sharp CO2(g) absorption peaks diminished from ~2 min and disappeared after ~20 min, suggesting the quenching of CO2 molecular rotations by solvating H2O molecules during CO2(g) to CO2(aq) elevation.

In contrast to CO2(aq), gaseous CO2(g) showed two broad asymmetric branches at 2336 and 2362 cm−1 in FTIR spectrum (resolution = 0.96 cm−1; fig. S5 and see Materials and Methods for details). The branches exhibited sharp narrowly spaced peaks on the two sides of the pure ν3 fundamental frequency f0 = 2347.5 cm−1 (Fig. 1D and fig. S6) recorded at a resolution of 0.06 cm−1, corresponding to the R branch and P branch of CO2(g) rotational-vibrational spectrum with molecular rotational transitions ΔJ > 0 and ΔJ < 0, respectively (). A much weaker 13CO2(g) P branch (corresponding to ~1.1% natural abundance of 13C) were observed in the 2500 to 2800 cm−1 range, with its R branch merging/overlapping with 12CO2(g) P branch. Comparison of high-resolution CO2(g) spectrum with the single narrow CO2(aq) peak observed at 2343.1 cm−1 without P/R branch signal suggested quenching of rotational transitions and inhibition of solvated CO2(aq) molecular rotations by the surrounding H2O molecules.

The dynamics of CO2 dissolution were monitored in micro-IR cell for 0.5 M NaHCO3 solution under 30 standard cubic centimeter per minute (sccm) of CO2(g) bubbling (see Materials and Methods for details). When bubbling started, the initial CO2(aq) peak (~5 mM formed via HCO3− equilibria; see Materials and Methods for details) increased, accompanied by rotational P and R branches due to coexistence of CO2(g) (Fig. 1E). The CO2(g) P/R branch disappeared after 20 min of bubbling, leaving a symmetric single peak at 2343.1 cm−1 corresponding to CO2(aq) in equilibrium with NaHCO3 solution under the 30 sccm of bubbling condition. To our knowledge, this was the first time that the kinetic evolution of the rotational-vibrational IR spectrum of CO2(g) to CO2(aq) (Fig. 1E) were reported at a high resolution. Similar high-resolution dynamic monitoring was done in pure water and 1 M NaHCO3 solutions under bubbling with 30 sccm of CO2(g). Different to the 0.5 M NaHCO3 case, we noticed that CO2(g) signals were weaker in pure water at the same time points and disappeared after >10 min. In 1 M NaHCO3, CO2(g) signals were much stronger and persisted over >30 min (fig. S7), suggesting the slowdown of CO2 solvation in solutions with increasing ionic strength.

We derived a calibration curve for CO2(aq) quantification by correlating the integrated absorbance A of CO2(aq) ν3 peak (peak integrated over wave number in the unit of centimeter−1; Fig. 2A and fig. S8) with calculated CO2(aq) concentrations [CO2(aq)] in water and NaHCO3 solutions equilibrated with air or 1 atm of CO2(g) based on CO2 dissolution equilibria () and Henry’s law (, ) (see Materials and Methods for details). High linearities in A versus solution thickness d (12.2 to 103 μm; Fig. 2B) and versus [CO2(aq)] (Fig. 2C) were observed. The molar extinction coefficient ε of CO2(aq) was derived from Beer’s law () A = ε·[CO2(aq)]·d to be 1.74 × 104 M−1·cm−2 (fig. S9), giving CO2(aq) concentrations of 34.2 and 23.1 mM in 1 atm of CO2(g) equilibrated H2O and 0.5 M NaHCO3 solutions, respectively, which were within 5% of established literature results (, ). Note that the integrated absorbance A was found superior to peak absorbance (peak height) in yielding a constant ε independent to FTIR resolution (fig. S10). CO2(aq) detection limit by micro-IR was determined to be ~1 mM (~44 mg/liter; see Materials and Methods for details) at an IR resolution of 0.96 cm−1.

Fig. 2.

CO2(aq) quantification based on Beer’s law.

(A) Background subtracted CO2(aq) ν3 IR absorbance spectra (resolution = 0.96 cm−1) measured in a 0.5 M NaHCO3 solution equilibrated with 1 atm of CO2(g) for 30 min in micro-IR cells with thicknesses d = 12.2, 24.7, 51.5, and 103.0 μm, respectively (gas-liquid interphase area of ~1.5 cm2). (B) Integrated CO2(aq) IR absorbance A plotted against cell thickness d, showing a high linearity (R2 = 0.998). Error bars were obtained from three parallel measurements. (C) Calibration curves for CO2(aq) integrated absorbance A versus calculated concentrations [CO2(aq)] in micro-IR cells with different cell thicknesses d. The pure H2O and 0.5 and 1.0 M NaHCO3 solutions were equilibrated with air or 1 atm of CO2(g) for 30 min before micro-IR measurements. Integrated absorbance A in micro-IR cells of d = 12.2, 24.7, 51.5, and 103.0 μm was correlated with [CO2(aq)] under corresponding equilibrating condition for linear regression. Error bars were obtained from three parallel experiments. Derived CO2(aq) molar extinction coefficient ε was 1.74 × 104 M−1·cm−2 according to Beer’s law. (D) Quantitation of CO2(aq) in commercial drinks by micro-IR. CO2(aq) concentration in brut champagne may be underestimated due to its high packaging pressure (see Materials and Methods for details).

Dissolved CO2 is an important determinant of beverage taste (). CO2 level in commercial beverages was routinely quantified in industry by tracking the electrical () or thermal () signals of released CO2(g) from the liquids. We performed micro-IR measurements of CO2(aq) in sparkling water, coke, grape wine, and brut champagne, applying the above calibration curve, and the various solutes in these drinks (including ethanol, sugars, minerals, and flavoring agents) did not interfere with acquiring clear and quantifiable CO2(aq) peaks in micro-IR spectra (fig. S11 and see Materials and Methods for details). We obtained a lowest CO2(aq) concentration of ~0.4 g/liter in grape wine, highest of ~10 g/liter in champagne, and similar concentrations of ~6 g/liter in sparkling water and coke (Fig. 2D), matching well with reported CO2 levels (, ) in these beverages.

Probing CO2(aq) in solutions under CO2 bubbling and correlation with CO2RR

CO2(g) bubbling into electrolytes has been widely used to provide CO2(aq) feedstocks for CO2RR. Our in situ micro-IR measurements revealed that with 30, 50, and 100 sccm of CO2(g) bubbling for 30 min, equilibrium CO2(aq) concentration in pure water reached 39.4, 50.1, and 59.9 mM, respectively, ~1.2, 1.5, and 1.8 times higher than that in water equilibrated with 1 atm of CO2(g) without bubbling (Fig. 3A). Correspondingly, solution pH decreased from 3.8 to 3.6 when the bubbling rate increased from 0 to 100 sccm (Fig. 3A). In addition with dynamic tracking at 30 sccm of CO2(g) bubbling (fig. S12), [CO2(aq)] versus time were fit to phenomenological exponential functions (see Materials and Methods for details), showing a faster CO2 dissolution kinetics under bubbling than simply equilibrating in 1 atm of CO2(g) (time constant ts1 < ts2; Fig. 3B). Note that quantitating CO2(aq) kinetically under various bubbling conditions has not been done previously and should be considered when analyzing the CO2RR performance.

Fig. 3.

Dynamic CO2(aq) monitoring and CO2RR.

(A) CO2(aq) concentrations and solution pH measured in H2O after CO2(g) bubbling at 0 [i.e., steady 1 atm of CO2(g) equilibrating] to 100 sccm of for 30 min. [CO2(aq)] showed a linearly increasing trend along CO2(g) bubbling rate with solution pH decreasing. Error bars were obtained from three parallel experiments. (B) Dynamic monitoring of CO2 solvation in H2O under 30 sccm of CO2(g) bubbling or 1 atm of CO2(g) equilibrating. With [CO2(aq)] versus time fitting by a phenomenological exponential function y = y0 + a * exp (−x/ts), a faster solvation kinetics and ~1.2 times higher equilibrium CO2(aq) concentration were observed under bubbling than equilibrating in 1 atm of CO2(g) after 40 min. Error bars were obtained from three parallel experiments. (C) Dynamic monitoring of CO2 solvation in 0.5 M KHCO3 solution under 30 sccm of CO2(g) bubbling and 1 atm of CO2(g) equilibrating. CO2 in KHCO3 solutions showed slower solvation kinetics and lower CO2(aq) equilibrium concentrations than pure water. After 30 min of bubbling/equilibrating followed by 30 min of CO2RR at −1.3 V versus Ag/AgCl using a SW-Cu2O/Cu catalyst, CO2(aq) concentration maintained in the bubbling case while significantly decreased in the equilibrating case. Error bars were obtained from three parallel experiments. (D) CO2RR performance of SW-Cu2O/Cu in 0.5 M KHCO3 under 30 sccm of CO2(g) bubbling or 1 atm of CO2(g) equilibrating. CO2RR started after 30 min bubbling/equilibrating at −1.3 V versus Ag/AgCl in H cell with total current densities of ~8 mA/cm. Higher formate production FE was obtained under the bubbling case, suggesting the strong correlation between CO2(aq) concentration and CO2RR performance. Error bars were obtained from three parallel experiments.

For 0.5 M KHCO3 solutions under CO2(g) bubbling or 1 atm equilibrating, CO2(g) peaks were observed in the initial ~10 to 20 min (fig. S13). Deconvolution of the overlapping CO2(g) and CO2(aq) absorption bands showed significantly slower CO2 dissolution kinetics in the KHCO3 solution than in pure water (fig. S13 and see Materials and Methods for details). After 30 min, CO2(aq) concentration reached 29.3 mM under bubbling and 22.8 mM under 1 atm equilibrating (Fig. 3C). Similar micro-IR measurements were conducted for KHCO3, KCl, K2SO4, and KOH solutions of various concentrations as well as seawater, revealing a general trend of CO2(g) dissolution slowdown and CO2(aq) equilibrium concentration decreasing when the solutions became saltier (figs. S13 to S15). These results corroborated the salting-out effect () and suggested reduced CO2 dissolution in the presence of strong ion-H2O interactions in aqueous solutions (, ). The CO2 dissolution equilibrium times and varying CO2(aq) concentrations in different electrolytes should be considered in CO2RR investigations.

In the commonly used 0.5 M KHCO3 electrolyte for CO2RR, we performed 30-min CO2RR using a square-wave treated Cu2O/Cu catalyst (SW-Cu2O/Cu) () in an H cell after bubbling CO2(g) at 30 sccm or after equilibrating in 1 atm of CO2(g) environment for 30 min (see Materials and Methods for details). This catalyst was prepared under cycling square-wave oxidation/reduction potentials to form abundant Cu2O (111) facet covering the catalyst surface (fig. S16) (). When the electrolyte was under continuous bubbling through the 30-min CO2RR reaction, the measured CO2(aq) concentration in the solution maintained at ~30 mM (Fig. 3C), and the Faradaic efficiency (FE) of formate production was 35.7% at −1.3 V versus Ag/AgCl, with a total current density of 8.2 mA/cm2 (Fig. 3D and fig. S17). In contrast, CO2(aq) in the electrolyte equilibrated under 1 atm of CO2(g) without bubbling decreased to 14.1 mM after 30-min CO2RR, and the corresponding formate FE decreased to 12.5% under the same CO2RR condition (Fig. 3D). Clearly, lower CO2(aq) concentration in the electrolyte led to a reduced FE for formate production by CO2RR.

Probing CO2(aq) under high pressures and correlation with CO2RR

High CO2(g) pressure conditions are widely used for CO2 capture, storage, and electroreduction in aqueous solutions (, , , ). However, dynamic probing of CO2(aq) under these conditions is rarely reported, especially for CO2RR. We equipped a micro-IR cell with a stainless steel frame and 6-mm-thick CaF2 windows for CO2(aq) monitoring in fully sealed aqueous samples under high CO2(g) pressures up to 58 atm at room temperature. For pure H2O equilibrated under 15 to 58 atm of CO2(g) partial pressures for 30 min, FTIR spectra (d = 6.0 μm; Fig. 4A and fig. S18; see Materials and Methods for details) were used to derive CO2(aq) concentration [CO2(aq)] at each CO2(g) partial pressure p(CO2) based on the integrated absorbance A (Fig. 4B) and molar extinction coefficient ε. A reciprocal fitting led to [CO2(aq)]−1 = 30.18 × p(CO2)−1 + 0.1550 with R2 = 0.9997 (Fig. 4C), corroborating previous experimental data and the ECO2N module analysis (an extended Henry’s law) developed for CO2 aquifers (, , ).

Fig. 4.

Dynamic CO2(aq) monitoring and correlation with high-pressure CO2RR.

(A) CO2 ν3 IR band dynamic evolution in H2O under 58 atm of CO2(g) (resolution = 0.96 cm−1, d = 6 μm, and gas-liquid interphase ~1.5 cm2). 12CO2(g) branches diminished from ~1 min, with tiny 13CO2(aq) signals observed. Inset: Micro-IR cell equipped with stainless steel frame for high pressures. (B) CO2(aq) ν3 IR spectra of H2O equilibrated with 15 to 58 atm of CO2(g) for 30 min (resolution = 0.96 cm−1 and d = 6.0 μm), showing stronger absorbance at higher pressures. (C) CO2(aq) quantification calibration curve under 1 to 58 atm. Measured CO2(aq) concentration was correlated with pressure p(CO2), affording a reciprocal fitting [CO2(aq)]−1 = 30.18 * p(CO2)−1 + 0.1550 with R = 0.9997, closely agreeing with ECO2N model (, ). Error bars were obtained from three parallel experiments. (D) [CO2(aq)] in 0.5 M KHCO3 under various pressures correlating with SW-Cu2O/Cu CO2RR performances. A reciprocal fitting of measured CO2(aq) concentration resulted in [CO2(aq)]−1 = 43.76 * p(CO2)−1 + 0.03457 with R2 = 0.9996. With CO2(aq) increasing from 0.0232 to 1.25 M along pressure, formate FE increased from 27.1 to 98.2%, and H2 decreased from 64.1 to 0% as previously reported (). Error bars were obtained from three parallel experiments. (E) Formate FE during CO2RR increased linearly along [CO2(aq)] and flattened out after [CO2(aq)] > ~1 M, which potentially revealed saturated CO2(aq) absorption on Cu2O (111). H2 FE decreased along [CO2(aq)] but with a weaker linearity. (F) CO2 solvation kinetics in water under 30 and 58 atm of CO2(g). With [CO2(aq)] fitting by phenomenological exponential functions, we observed faster solvation kinetics under high pressures (ts ~5.4 and 6.3 min) than the 1 atm condition in Fig. 3B (red curve) (ts ~14.1 min). Error bars were obtained from three parallel experiments.

Under elevating CO2(g) pressure, we observed continuous increasing of water IR absorption intensity in the whole measured range of ~1000 to 4000 cm−1 (fig. S18) that resulted from increased interactions between CO2(aq) and H2O molecules (, ). This enhanced H2O IR absorption was not observed in Ar-H2O and O2-H2O systems () due to much weaker interactions between Ar/O2 and H2O molecules than CO2.

We also measured CO2(aq) concentration in 0.5 M KHCO3 equilibrated under 15 to 58 atm of CO2(g) and noticed lower equilibrium concentration than pure water under the same pressures. A reciprocal fitting of [CO2(aq)] over p(CO2) gave [CO2(aq)]−1 = 43.76 * p(CO2)−1 + 0.03457 with R2 (coefficient of determination) = 0.9996 (Fig. 4D) in the 0.5 M KHCO3 electrolyte widely used for CO2RR. Correlating with our previously reported CO2RR to high yield formate production up to ~98.2% FE catalyzed by SW-Cu2O/Cu30, we found that CO2(aq) concentration increased from 23.2 mM to 1.25 M as pressure increased from 1 to 58 atm, while the FE for formate production over 1 hour of CO2RR increased from 27.1% to an impressive 98.2%, with the FE for H2 generation decreased from 64.1 to ~0% (Fig. 4D). A high linearity of formate FE to CO2(aq) concentration was observed up to ~1 M CO2(aq) under 45 atm of CO2(g) [independent of pH change from 7.66 to 6.01 reported earlier ()], beyond which the formate FE flattened out with little further increase under 58 atm of CO2(aq) (Fig. 4E). Since the average distance between CO2(aq) at 1 M concentration in the electrolyte was ~1.18 nm (see Materials and Methods for details), which is on the same order as the distance between coordinatively unsaturated Cu+ (CuCUS) () sites on Cu2O (111) surface, this flattening was attributed to the saturation of CO2(aq) species binding to CuCUS sites through oxygen atoms (, ) at above 45 atm. Together, our results here confirmed that high CO2(aq) concentrations in CO2RR electrolyte was responsible for up to 98.2% FE of formate production on copper-based electrocatalysts under high pressures.

Probing CO2 dissolution/desolvation hysteresis and supersaturation in aqueous solutions

Dynamic monitoring of CO2 dissolution in water under high CO2(g) pressures showed much faster kinetics than under 1 atm of CO2(g) (i.e., smaller ts; Fig. 4F). COSMO-RS simulation derived ΔG = −0.106 kcal/mol for CO2 dissolution under 58 atm, more positive than that of −0.149 kcal/mol under 1 atm, indicating reduced thermodynamic driving forces for CO2 dissolution at higher CO2(aq) concentrations, which led to deviation of Henry’s law from linearity in the high-pressure range (, ). Redshifts of the H2O bending-libration combination IR absorption band were observed under elevating CO2(g) pressures (fig. S19), and signaling increased disruption of H2O hydrogen bonding network when more CO2(g) dissolved (, ), corroborating with the positively shifted ΔG.

CO2 supersaturation in aqueous solutions has been widely investigated (, , , ), but quantitative, dynamic, and in situ monitoring of CO2(aq) supersaturated solutions is rare. To this end, we used micro-IR to quantitatively investigate CO2(aq) desolvation back to CO2(g) in supersaturated aqueous systems. Upon bubbling H2O with 30 sccm of CO2(g) for 30 min and exposing it to air (see Materials and Methods for details), we noticed tiny gas bubbles released from the supersaturated solution during ~3 hours of standing. Continuous probing of CO2 ν3 band (Fig. 5A) found that CO2(aq) concentration in the solution decreased from 39.9 mM (0.0721% in molar fraction) to 17.2 mM [14 μM, i.e., the equilibrium level of CO2(aq) in 1 atm of air] in 3 hours, still in a highly supersaturated state. This process was accompanied by the solution pH increase from 3.71 to 5.67 (Fig. 5B). CO2 solvation and desolvation in aqueous systems are a complex process with solute effects and mass transport adding more complexities (). We used exponential functions as phenomenological fittings of CO2 solvation/desolvation kinetics in the time frame of 0 to a few hours to glean the solvation/desolvation speeds in various cases. By fitting [CO2(aq)] versus time to an exponential function (R2 = 0.985), we observed a much slower desolvation kinetics than dissolution of CO2 molecule in water (tds = 46.1 min > ts = 9.8 min).

Fig. 5.

Dynamic monitoring of CO2(aq) desolvation in aqueous solutions.

(A) CO2 ν3 IR band dynamic evolution in H2O after CO2(g) bubbling stopped and solution exposed to air (resolution = 0.96 cm−1, d = 51.5 μm, and gas-liquid interphase ~1.5 cm2). CO2(aq) absorbance decreased and CO2(g) appeared over time, suggesting CO2 desolvation from water. (B) CO2 desolvation in supersaturated water after bubbling stopped. With pH increasing from 3.71 to 5.67 (near equilibrium) over 3 hours standing in air, [CO2(aq)] decreased from 40 to 17 mM, far from reversing supersaturation. [CO2(aq)] evolution fitting by y = y0 + a * exp (−x/tds) suggested slower desolvation kinetics than solvation (tds = 46.1 min > ts = 9.8 min, CO2 hysteresis). Error bars were obtained from three parallel experiments. (C) Surface [CO2(aq)] long-term tracking in supersaturated water and seawater. While [CO2(aq)] in seawater decreased below 1 mM (detection limit) after 3 days standing in air, ~ 1.1 mM CO2(aq) was still observed in water after 10 days and was only removable by boiling, suggesting slow desolvation in water and implying the widely observed CO2 level difference between surface lakes and oceans. (D) With tds plotted versus initial equilibrium [CO2(aq)] in H2O (conditions indicated), seawater and KHCO3 [1 atm of CO2(g)], and commercial beverages (under/near packaged pressures), we noticed slower desolvation in H2O (purple line/points) than all other solutions and beverages (orange points). (E) Bending-libration combination IR absorption of water [in air and 15 to 58 atm of CO2(g)], seawater and KHCO3 (in air), and commercial beverages (under/near packaged pressures) (resolution = 0.96 cm−1; absorbance normalized for clear comparison). Systematic redshifts from H2O bending-libration peak at 2144 cm−1 in air revealed weakening of hydrogen bonding network in all solute-rich solutions, where strong solute-H2O interactions outcompeted CO2 solvation and accelerated desolvation.

We observed that it is much slower to reverse CO2(aq) supersaturation in pure water than in seawater (Fig. 5C). Upon exposure to air after CO2 bubbling, the CO2(aq) micro-IR signal in seawater decreased from 29.7 mM (0.0526% in molar fraction) () to below detection limit after 3 days; however, in pure water, there was still a measurable ~1.1 mM CO2(aq) after 10 days, which was reduced to baseline only by boiling the solution (Fig. 5C). The observed CO2 hysteresis (fast dissolution and slow desolvation) and very slow supersaturation reversal in water could be related to the observed supersaturation of dissolved CO2 levels in freshwater lakes (, ), more so than that in oceans (). Note that slower CO2(aq) desolvation kinetics than dissolution were also observed in KHCO3 solutions and water-equilibrated with high-pressure CO2(g) (fig. S20).

Last, we measured CO2(aq) desolvation kinetics in beverages including sparkling water, grape wine, coke, and brut champagne upon opening seals, and the derived desolvation time constants were tds = 22.5, 15.5, 9.6, and 7.4 min, respectively (fig. S20 and see Materials and Methods for details). In general, compared with 1 atm of CO2(g) equilibrated pure water, we observed accelerated CO2(aq) desolvation kinetics for all the rest solutions and conditions tested (Fig. 5D), suggesting decreased favorability of CO2 dissolution in the presence of salts/ions, sugar, alcohol, and other solutes (even including solvated CO2 itself). That is, the solvated solutes in aqueous solutions outcompeted the dissolution of CO2(g). Interactions of these solutes with H2O were reflected by obvious redshifts of H2O bending-libration combination band from f = 2144 cm−1 (for pure water with no solute) (Fig. 5E and fig. S21), suggesting weakened hydrogen bonding network in the presence of solvated solutes () that led to disfavored CO2-H2O molecular interactions slowing down CO2 dissolution (Fig. 3, B and C, and fig. S13) and accelerating desolvation (Fig. 5, C and D, and fig. S20).

In summary, IR spectroscopy through <100-μm-thick aqueous solutions allowed in situ dynamic CO2(aq) quantitation and dissolution/desolvation kinetics probing in various aqueous systems important to CO2 capture, storage, electroreduction, and environmental monitoring. High-resolution spectral kinetic evolution from CO2(g) to CO2(aq) were obtained. An accurate CO2(aq) molar extinction coefficient ε was determined to be 1.74 × 104 M−1·cm−2, which could facilitate CO2(aq) quantitation by other researchers. Electrochemical CO2RR on our Cu2O/Cu catalyst showed strong correlations to CO2(aq) concentration in the commonly used KHCO3 electrolyte under bubbling and high-pressure conditions, exhibiting a high linearity of formate FE over CO2(aq) until a saturation point of ~1 M CO2(aq). The kinetics of CO2 dissolution/desolvation were determined dynamically with a high time resolution down to 30 s in various solutions, revealing significant CO2 hysteresis (faster solvation and slow desolvation) in aqueous systems. CO2 dissolution slowed down, and desolvation accelerated when solutions became saltier or contained more solutes due to stronger solute (salts/ions, sugar, alcohol, etc.)—H2O interactions than CO2-H2O interactions and the interruption of H2O-hydrogen bonding network. We also observed that > 10 days, and unexpectedly long time, were needed to reverse CO2(aq) supersaturation in water compared to ~3 days in seawater.

MATERIALS AND METHODS

Transmission FTIR spectroscopy and micro-IR optical cell

Transmission FTIR spectra of all liquid samples were obtained on a Nicolet iS50 FTIR Spectrometer using the micro-IR cell connecting with a sample reservoir (fig. S1). Borosilicate glass disc windows for the cell were purchased from McMaster-Carr Supply Company. The stainless steel cell frame, CaF2 disc windows, and PTFE spacers for the cell were purchased from Harrick Scientific Products Inc. The stainless steel frame was screwed tightly with O-rings onto the cell windows to ensure good sealing under high pressures. During FTIR measurements, the optical cell was fixed in the FTIR chamber with continuous N2 purging at 30 standard cubic feet per hour (scfh). Background subtraction was applied before sample testing to exclude the IR absorption of instrument, gas phase in the FTIR chamber, and cell windows (fig. S2).

FTIR measurements of CO2(g)

We purged FTIR chamber by 30 scfh N2 for >2 hours to remove air from the chamber. Then, with continuous N2 purging, we flowed CO2(g) into the chamber at 10 sccm for 5 min and recorded IR spectra at resolutions of 0.06 and 0.96 cm−1.

Micro-IR measurements of NaHCO3 solutions equilibrating with air

Five milliliters of 0.5 and 1.0 M NaHCO3 solutions were prepared and transferred into 15-ml vials with gas-liquid interphase area of ~1.5 cm2, and the headspace in the vials was filled with air. After standing still for 1 hour, 0.5 ml of top surface liquid samples in the vials was transferred by pipette into the micro-IR optical cell, with 1.1-mm-thick borosilicate glass windows and 12.2-, 24.7-, 51.5-, and 103.0-μm-thick PTFE spacers. This sampling process was finished in ~15 s to avoid potential changes in the liquid samples. FTIR spectra were recorded at a resolution of 0.96 cm−1.

Micro-IR measurements of H2O, seawater, NaHCO3, and KHCO3 solutions equilibrating with 1 atm of CO2(g)

Five milliliters of deionized water, seawater (collected in November 2020 from San Gregorio State Beach, California, US), 0.5 and 1.0 M NaHCO3 solutions, and 0.5 M KHCO3 solution were prepared and transferred into 15-ml vials with gas-liquid interphase area of ~1.5 cm2, and the headspace in the vials was filled with 1 atm of CO2(g). After every 10 min, 0.5 ml of top surface liquid samples in the vials was transferred by pipette into the micro-IR optical cell, with 1.1-mm-thick borosilicate glass windows and 12.2-, 24.7-, 51.5-, 103.0-, and 204.2-μm-thick PTFE spacers. This sampling process was finished in ~15 s to avoid potential changes in the liquid samples, and CO2(g) was refilled into the headspace of the vials after sampling. FTIR spectra were recorded at resolutions of 0.06, 0.24, and 0.96 cm−1.

Micro-IR measurements of H2O, NaHCO3, KHCO3, KCl, K2SO4, and KOH solutions under CO2(g) or Ar bubbling

Five milliliters of deionized water; 0.5 and 1 M NaHCO3 solutions; 0.1, 0.5, 1.0, and 2.0 M KHCO3 solutions; 0.1, 0.5, 1.0, and 2.0 M KCl solutions; 0.05, 0.25, and 0.5 M K2SO4 solutions; and 0.1, 0.5, 1.0, and 2.0 M KOH solutions were prepared and transferred into the sample reservoir connected with micro-IR optical cell (gas-liquid interphase area of ~1.5 cm2; fig. S1). With a CO2(g) or Ar tubing reaching deep inside the reservoir, we kept valve V2 closed and bubbled solutions with 30, 50, and 100 sccm of CO2(g) or Ar. After every 10 min, valve V2 and V3 were opened for the CO2(g) bubbled liquid entering and filling the 51.5-μm-thick micro-IR cell equipped with 1.1-mm-thick borosilicate glass windows. The valves were quickly closed after >300 μl of liquid flowed out of V3 (for flushing the channels with fresh samples), and FTIR spectra were then recorded at resolutions of 0.06 and 0.96 cm−1. The time it took for CO2(g) vibration-rotation signatures disappearing from the spectra indicated the time of CO2(g) bubbles evolving to solvated CO2(aq) measured in the spectra.

Micro-IR measurements of sparkling water, coke, grape wine, and brut champagne

Since sparkling water (500 ml; S.Pellegrino Sparkling Natural Mineral Water, PRD 02.12.21 02), coke (500 ml; Coca-Cola Original Taste, AUG1621UVD1249), and brut champagne (750 ml; Kirkland Signature Champagne Brut, MA 3761-01-00666) were packed under pressures higher than 1 atm, we stored these drinks at 4°C for 24 hours before transferring 0.5 ml of them into 12.2-μm-thick micro-IR cell equipped with 6-mm-thick CaF2 windows and quickly sealed the cell within ~30 s of opening the cooled drinks to minimize escaping of dissolved CO2. After ~5 to 10 min of the liquids warming to room temperature, FTIR spectra were recorded at a resolution of 0.96 cm−1. CO2 solubility increases by ~2 times in water with temperature decreasing from 25° to 4°C (); however, the measured CO2(aq) concentration in carbonated drinks, especially champagne, could still be underestimated due to the very high concentration of CO2(aq) and some inevitable escaping during sample transfer. For the measurement of grape wine (750 ml; Sparrow Hawk 2018 Reserve Chardonnay Napa Valley, 2107 B3 1 20190227 17 41), 0.5 ml of sample was transferred into the micro-IR cell without cooling, and FTIR spectrum was recorded at a resolution of 0.96 cm−1.

Preparation of SW-Cu2O/Cu electrode

A constant oxidation current of 5 mA/cm2 was applied on Cu foil (99.999%, 1 cm by 1 cm; Thermo Fisher Scientific) with graphite as counter electrode in an electrolyte consisting of 0.375 M NaOH, 0.236 M Na2CO3, and 0.066 M Na2SiO3. After 15 min of oxidation, the foil was transferred into 25% H2SO4 and soaked for 2 hours to remove the surface oxidation layer. Then, the Cu foil was washed by ultrapure water for three times before usage. A typical square-wave redox cycling was conducted in an H-type glass cell, with two electrolyte zones being separated by a Nafion 117 membrane (Chemours, DuPont). The electrolyte contained 2.3 M lactic acid and 3.2 M KOH at 40°C water bath, with the saturated calomel electrode (SCE) being used as reference electrode and graphite being used as counter electrode. For a typical synthesis of SW-Cu2O/Cu, the oxidation and reduction potentials were set to be −0.45 and −0.75 V (versus SCE), with an alternating frequency of 5 Hz and a cycling time of 0.5 hours. As-prepared SW-Cu2O/Cu electrode was rinsed by ultrapure water and stored in vacuum before CO2RR.

Characterization of the SW-Cu2O/Cu catalyst

The morphology of as-prepared SW-Cu2O/Cu was characterized using a field-emission scanning electron microscope (JEOL JSM6335) operating at 20 kV. Annular dark-field transmission electron microscopy measurements of a single nanoparticle on the sample was carried out on a Nion HERMES-100.

Electrochemical measurements and CO2RR product analysis

Electrochemical measurements were carried out in a three-electrode H-type glass cell connected to an electrochemical workstation (CHI 760E). During the CO2RR testing, SW-Cu2O/Cu electrode was used as the working electrode, silver/silver chloride electrode (Ag/AgCl) as reference electrode, and carbon paper (1 cm by 3 cm; Sigracet SGL 39 BC) as counter electrode. With 0.5 M KHCO3 solutions as electrolyte, the anodic and cathodic zones were separated by a neutralized Nafion 117 film (Fuel Cell Store). For CO2RR under 30 sccm of CO2(g) continues bubbling, the gaseous outlet in cathodic zone was connected to a gas chromatograph (SRI multiple gas analyzer no. 5) for online gaseous product analysis. In addition, for the nonbubbling (1 atm equilibrating) case, gas samples were collected by a syringe from the headspace of sealed cathodic zone after the 30-min reaction at −1.3 V versus Ag/AgCl and then injected into the gas chromatograph. For liquid product analysis, 0.2 ml of catholyte was collected, and one-dimensional 1H nuclear magnetic resonance (NMR) was performed on Inova 600-MHz NMR spectrometer using a water suppression method.

Micro-IR measurements of 0.5 M KHCO3 solutions after CO2RR

After 30 min of CO2RR in H cell, 0.5 ml of liquid samples was collected from the cathodic zone (near cathode surface) and transferred by pipette into the micro-IR optical cell with 1.1-mm-thick borosilicate glass windows and 51.5-μm-thick PTFE spacer. This sampling process was finished in ~15 s to avoid potential changes in the liquid samples. FTIR spectra were recorded at a resolution of 0.96 cm−1.

Micro-IR measurements of H2O and 0.5 M KHCO3 equilibrating with high-pressure CO2(g)

Deionized water or 0.5 M KHCO3 solutions (2 ml) were transferred into the sample reservoir connected with micro-IR optical cell (with 6-mm CaF2 windows and cell thickness d = 6.0 μm; fig. S1). The stainless steel cell frame was screwed tightly with O-rings onto CaF2 windows to ensure good sealing under high pressures. With valve V2 opened, V3 closed, and V1 connected to CO2 cylinder, 15 to 58 atm of CO2(g) were applied to the reservoir with a gas-liquid interphase area of ~1.5 cm2. IR spectra were recorded from 0.5 to 30 min at a resolution of 0.96 cm−1.

Micro-IR measurements of CO2 desolvation in H2O, seawater, and 0.5 M KHCO3 solution after bubbled by CO2(g) or equilibrated with 1 atm of CO2(g) and from commercial drinks

The liquid [5 ml; saturated with CO2(aq) under respective conditions] was stored in 15-ml vials with the headspace filled with air (gas-liquid interphase area of ~1.5 cm2). At various times after standing for 20 to 180 min, 0.5 ml of top surface liquid samples in the vials was transferred by pipette into the micro-IR optical cell, with 1.1-mm-thick borosilicate glass windows and 51.5-μm-thick PTFE spacers for measuring CO2(aq) concentration. This sampling process was finished in ~15 s to avoid potential changes in the liquid samples. FTIR spectra were recorded at a resolution of 0.96 cm−1.

Micro-IR measurements of CO2 desolvation in H2O after equilibrated with 30 and 60 atm of CO2(g)

After 2 ml of H2O was equilibrated with 30 or 60 atm of CO2(g) for 30 min in 6.0-μm-thick micro-IR cell equipped with 6-mm-thick CaF2 windows, we released the gas pressure, opened the sample reservoir, and exposed the liquids to air. FTIR spectra were recorded at a resolution of 0.96 cm−1 after 10 and 20 min of standing. We then switched the micro-IR cell to 51.5-μm-thick PTFE spacers and 1.1-mm-thick borosilicate glass windows for CO2 desolvation monitoring after 30 to 180 min of exposure to air. This was done since CO2(aq) decayed quickly to much lower levels in the initial ~30 min, after which switching to a thicker cell/longer optical path gave higher signals and provided more accurate quantification of CO2(aq) at lower concentrations. FTIR spectra were recorded at a resolution of 0.96 cm−1.

Long-term micro-IR measurement of surface CO2(aq) in supersaturated pure water and seawater

Deionized water and seawater (5 ml each) were transferred into plastic tubes with a cross-section area of ~1.5 cm2 and bubbled by 30 sccm of CO2(g) for 30 min. The tubes were then kept together with 50 ml of deionized water in another container (for maintaining humidity) in a ~20-liter chamber filled with 1 atm of air. After every 24 hours, 0.5 ml of top surface liquid samples in the tubes was transferred by pipette into the micro-IR optical cell equipped with 1.1-mm-thick borosilicate glass windows and 51.5-μm-thick PTFE spacers. This sampling process was finished in ~15 s to avoid potential changes in the liquid samples. FTIR spectra were recorded at a resolution of 0.96 cm−1. After 10 days of continues tracking, the supersaturated pure water sample was transferred into a beaker and boiled, and then the micro-IR measurement with the same setup was conducted for the last time once the sample cooled down to room temperature.

Micro-IR measurements of water, seawater, and 0.5 M KHCO3 solution for probing H2O bending-libration combination IR absorption band

Deionized water, seawater, or 0.5 M KHCO3 solutions (0.5 ml) were transferred by pipette into the micro-IR optical cell equipped with 6-mm-thick CaF2 windows and 6.0- or 12.2-μm-thick PTFE spacers. FTIR spectra were recorded at a resolution of 0.96 cm−.

Data processing of FTIR spectra

Raw FTIR spectra obtained from the instrument with a scale of transmittance T (%) on Y axis were converted to absorbance A by

For further quantitative analysis, to obtain background subtracted CO2 ν3 (C═O asymmetric stretching) IR absorption bands in ~2300- to 2400-cm−1 range for liquid samples, baselines [interference () and H2O bend + libration combination peaks] in absorbance spectra were fitted by polynomial functions and subtracted using OriginPro (version 2017b 9.4).

For CO2 ν3 bands with single CO2(aq) peaks at 2343.1 cm−1, the absorbance peaks were fitted by Voigt functions and integrated over wave number to obtain peak areas (in the unit of centimeter−1) for quantification. In addition, for CO2 ν3 bands with convoluted CO2(aq) and CO2(g) signals at an IR resolution of 0.96 cm−1 (fig. S11), we fitted each convoluted ν3 band with one Voigt function and two Asymmetric double Sigmoidal (Asym2Sig) functions in representing the single peak of CO2(aq) and two asymmetric branches of CO2(g), with fixed peak width and position parameters. CO2(aq) peak width and position parameters were obtained from previous Voigt fitting of pure CO2(aq) ν3 peak in water at the same IR resolution, and CO2(g) parameters were from the fitting of CO2(g) FTIR spectra by Asym2Sig functions. CO2(aq) peaks obtained from deconvolution were integrated over wave number for quantitative kinetics analysis.

Determination of detection limit in micro-IR measurements by SD analysis of parallel experiments

During micro-IR quantification of CO2(aq), liquid samples were measured parallelly for three times, and the three integrated absorbance peak areas were averaged. The SD of the three parallel measurements was calculated bywhere xi refers to the integrated peak area in each parallel experiment and refers to the average value. The detection limit φ of CO2(aq) was then derived bywhere ε refers to molar extinction coefficient of CO2(aq) derived from working curve (fig. S7). Parallel measurements of 0.5 M NaHCO3 solution equilibrated with air were used for determining CO2(aq) detection limit at an IR resolution of 0.96 cm−1 using a 51.5-μm-thick micro-IR cell.

Calculation of equilibrium concentrations of CO2(aq), H2CO3, HCO3−, CO32−, H+, and OH− in H2O equilibrated with air or 1 atm of CO2(g) and in 0.5 M NaHCO3 solution equilibrated with 1 atm of CO2(g)

CO2 dissolving in aqueous systems leads to the existing of multiple carbon species including CO2(aq), H2CO3, HCO3−, and CO32− in liquid phase at equilibrium states. The relationship between equilibrium concentrations of these species can be derived from the dissociation equations of carbonic acid (, , )

In addition, because of the high reversibility of conversions between H2CO3 and CO2(aq), the first dissociation process of H2CO3 can be described with an apparent dissociation constant involving CO2(aq) ()

Since aqueous solutions are electrically neutral, we have charge conservation equation of ion species in H2Oand in sodium bicarbonate solution

In addition, according to the dissociation equilibrium of water, the relationship of [H+] and [OH−] in liquid phase can be described as

According to Henry’s law, the concentration of dissolved CO2(aq) in pure water or dilute solutions (< ~2 M) is linearly dependent on the partial pressure of CO2(g) in the gas phasewhere p(CO2) refers to CO2(g) partial pressure and kp refers to Henry’s constant of CO2 in specific liquids at 25°C. For pure water, kp = 0.034 M/atm at room temperature (), and for the 0.5 M NaHCO3 solution, kp = 0.024 M/atm (). Note that these constants are applicable under near atmospheric conditions and deviate under very high pressures (, ).

On the basis above, we calculated equilibrium concentrations of species involved in CO2 dissolving in H2O and NaHCO3 solution under air or 1 atm of CO2(g) conditions using the dissociation equilibrium (Eqs. 1 to 3 and 5), ionic charge conservation (Eq. 4, A and B), and Henry’s law (Eq. 6). MATLAB (version R2016a) codes for the calculations above are provided in Supplementary Text.

Calculation of equilibrium concentrations of CO2(aq), H2CO3, HCO3−, CO32−, H+, and OH− in 0.5 and 1.0 M NaHCO3 solutions equilibrated with air

For bicarbonate or carbonate solutions equilibrating with a gas phase that has very low CO2(g) partial pressures (such as air), species equilibria suggests CO2(aq) mainly coming from the conversion of bicarbonate or carbonate ions instead of CO2(g) dissolution (, ). From Eqs. 1 and 3, we can obtain

Thus, equilibrium CO2(aq) concentration increases with increasing bicarbonate concentration when NaHCO3 solutions are equilibrating with air. Instead of applying Henry’s law, we introduce a carbon conservation equation for those caseswhere c(carbon) refers to the initial concentration of the bicarbonate or carbonate salt added for preparing the solution.

We calculated equilibrium concentrations of species involved in CO2 dissolving in NaHCO3 solutions under air based on dissociation equilibrium (Eqs. 1 to 3 and 5), ionic charge conservation (Eq. 4, A and B), and carbon conservation (Eq. 8). MATLAB codes for the calculations above are provided in Supplementary Text.

COSMO-RS calculations of Gibbs-free energy changes during CO2 solvation

Gibbs-free energy change (ΔG) during CO2 solvation in pure water under atmosphere and 58 atm of CO2(g) was calculated using Amsterdam Modeling Suite (AMS) software package (version 2019.307). Geometry optimization of the CO2 molecule was performed in Amsterdam Density Functional (ADF) package using generalized gradient approximation (GGA) in the scheme of Perdew-Burke-Ernzerhof (PBE) at triple-zeta polarized (TZP) basis sets (). A single CO2 molecule after geometry optimization was surrounded by 134 H2O molecules introduced based on COSMO-RS () for simulating the solvated CO2(aq) under atmosphere. Internal energy (U) and entropy (S) of CO2 and CO2·(H2O)134 were calculated, respectively, at room temperature (T = 298.15 K) in the software. To derive ΔG, we assumed no volume change (ΔV = 0) during CO2 solvationwhere p refers to the system pressure, U1 and S1 refer to the internal energy and entropy of CO2, respectively, and U2 and S2 refer to those of CO2·(H2O)134.

For CO2 solvation under 58 atm of CO2(g), we assumed a uniform distribution of dissolved CO2(aq) in equilibrated H2O. Since equilibrium CO2(aq) concentration in H2O under 58 atm of CO2(g) was derived to be 1.452 M according to the ECO2N module (), an average distance d between two dissolved CO2 molecules in the liquid phase at this concentration is

Thus, we introduced two CO2 molecules (geometry optimized) of C─C atomic distance d = 1.05 nm in the software, with 131 H2O molecules surrounded (based on COSMO-RS) to simulate the solvation in water. U and S of (CO2)2 and (CO2)2·(H2O)131 were then calculated accordingly at room temperature to derive ΔG under the 58 atm condition.

DFT simulations of the redshift in CO2 ν3 vibrational frequency after solvation

CO2 ν3 (C═O asymmetric stretching) vibrational frequency before and after solvation was calculated on the basis of DFT using AMS software package. Geometry optimization of CO2 molecule was performed in ADF package at GGA/PBE/TZP level before the calculation of fundamental CO2 ν3 vibrational frequency f0. For solvated CO2(aq), we introduced one and four H2O molecules around a single CO2 molecule to simulate the solvation in liquid phase, since CO2 with one H2O coordinated (coordination number n = 1) was reported as the simplest structure of solvated CO2(aq) and n = 4 as the most probable coordination according to energy analysis (). We performed geometry optimizations using Grimme’s dispersion correction method D3 with Becke-Jonson (BJ) damping () for simulating the weak noncovalent interactions between CO2 and H2O molecules during solvation. Calculations of ν3 vibrational frequency, internal energy, and entropy of CO2·H2O and CO2·(H2O)4 molecular clusters at room temperature were performed at the same GGA/PBE-D3(BJ)/TZP level after geometry optimizations.

COSMO-RS calculations of Gibbs-free energy changes during CO2 hydration to H2CO3

The ΔG during CO2 hydration to H2CO3 was calculated using AMS software package. Geometry optimization of CO2, H2O, and H2CO3 molecules was performed in ADF package using GGA in the scheme of PBE at TZP basis sets. A single CO2, H2O, or H2CO3 molecule after geometry optimization was surrounded by 134 H2O molecules introduced based on COSMO-RS for simulating corresponding solvated molecules under atmosphere. Internal energy (U) and entropy (S) of CO2·(H2O)134, H2O·(H2O)134, and H2CO3·(H2O)134 were calculated, respectively, at room temperature (T = 298.15 K) in the software, and the Gibbs-free energy change during CO2 hydration to H2CO3 was calculated to be: ΔG = ΔU − T * ΔS = (UΗ − UCO − UH) − T * (SΗ − SCO − SH).

DFT simulations of C═O asymmetric stretching frequency in H2CO3

C═O asymmetric stretching frequency of H2CO3 was calculated on the basis of DFT using AMS software package. Geometry optimization and frequency calculation of H2CO3 molecule were performed in ADF package at GGA/PBE/TZP level at room temperature.

Phenomenological exponential fitting of CO2 solvation/desolvation kinetics

CO2 solvation and desolvation in aqueous systems are complicated processes, with solute effects and mass transport adding more complexities (). A single function may not be able to fit the processes in the whole time scale range. We chose exponential functions for phenomenal fitting of CO2 solvation and desolvation kinetics in the time frame of 0 to a few hours in our experiments, and the obtained time constants ts and tds are merely convenient indicators to show the speed of CO2 solvation and desolvation in different cases.

Absorption density of CO2(aq) on Cu2O (111) surface

At 45 atm of CO2(g), equilibrium CO2(aq) concentration in 0.5 M KHCO3 solution was measured to be 1.01 M, so an average distance d between two dissolved CO2 molecules in the liquid phase at this concentration is

Since a SW-Cu2O/Cu catalyst with abundant Cu2O (111) facet on the catalyst surface was used in CO2RR (), and CO2(aq) species were binding to the coordinately unsaturated Cu+ (CuCUS) sites on the surface through oxygen atoms (), we calculated the distance D between two CuCUS sitesand noticed that D ~ d/2. This suggested that half of the active CuCUS sites responsible for formate production were occupied by CO2(aq) at 45 atm in 0.5 M KHCO3. Combining with the CO2RR results that formate FE flattened out at more than 45 atm (main Fig. 4, D and E), one-half of the occupation of CuCUS sites should be a saturation level for CO2(aq) absorption on Cu2O (111) plane. In addition, the molecular diameter of CO2 is 0.334 nm > D/2 (), supporting the above calculation that one-half of the CuCUS sites alternatively occupied by CO2(aq) is the maximum absorption density of CO2(aq) on Cu2O (111) surface.