Low energy carbon capture via electrochemically induced pH swing with electrochemical rebalancing

We demonstrate a carbon capture system based on pH swing cycles driven through proton-coupled electron transfer of sodium (3,3′-(phenazine-2,3-diylbis(oxy))bis(propane-1-sulfonate)) (DSPZ) molecules. Electrochemical reduction of DSPZ causes an increase of hydroxide concentration, which absorbs CO2; subsequent electrochemical oxidation of the reduced DSPZ consumes the hydroxide, causing CO2 outgassing. The measured electrical work of separating CO2 from a binary mixture with N2, at CO2 inlet partial pressures ranging from 0.1 to 0.5 bar, and releasing to a pure CO2 exit stream at 1.0 bar, was measured for electrical current densities of 20–150 mA cm−2. The work for separating CO2 from a 0.1 bar inlet and concentrating into a 1 bar exit is 61.3 kJ molCO2−1 at a current density of 20 mA cm−2. Depending on the initial composition of the electrolyte, the molar cycle work for capture from 0.4 mbar extrapolates to 121–237 kJ molCO2−1 at 20 mA cm−2. We also introduce an electrochemical rebalancing method that extends cell lifetime by recovering the initial electrolyte composition after it is perturbed by side reactions. We discuss the implications of these results for future low-energy electrochemical carbon capture devices.

Liquid pumping rate is 50 mL min -1 for all the cycles. Note that, the pH measurements for high current densities are inaccurate, as the pH should never be able to reach pH > 14 for 0. 11 Figure 10| Five CO2 concentrating cycles with 0.05 bar inlet pCO2 and 1 bar exit pCO2 at 40 mA cm -2 . Same cell was used as in Fig. 2. Fresh negolyte and posolyte were used. The liquid pumping rate is 150 mL min -1 , which is 50% faster than for capture at higher inlet pressure. a, Voltage profile. b, Current density. c, pH of the negolyte. d, N2 and CO2 percentage in the upstream source gas, controlled by mass flow controllers. e, CO2 partial pressure. f, Total gas flow rate.   ΔDICflow,xày change in DIC between states "x" and "y" (DICy -DICx), measured by flow meter and CO2 sensor ΔDICTA-pH,xày change in DIC between states "x" and "y" (DICy -DICx), measured by known total alkalinity and measured pH ΔDICTA-eq,xày change in DIC between states "x" and "y" (DICy -DICx), measured by by known total alkalinity and assuming gas-solution equilibrium DOC direct ocean capture DSPZ sodium 3,3'-(phenazine-2,3-diylbis(oxy))bis(propane-1-sulfonate) DSPZH2 reduced DSPZ EMAR electrochemically mediated amine regeneration K3Fe(CN) 6 potassium ferricyanide (oxidized form of Fe(CN)6) K4Fe(CN) 6 potassium ferrocyanide (reduced form of Fe(CN)6) MFC mass flow controller p1 CO2 partial pressure in bar during CO2 capture (inlet) p3 CO2 partial pressure in bar during CO2 outgassing (exit) PCET proton-coupled electron transfer pHmea pH measured by pH probe pHTA-eq pH calculated using known total alkalinity and assuming gas-solution equilibrium TA total alkalinity TAx concentration of total alkalinity in state "x" ΔTAxày change in TA between states "x" and "y" (TAy -TAx), measured by counting charges during deacidification or acidification, which is equivalent to twice the concentration of DSPZ.

CO2 Molar Ideal Cycle Work
For a system with given TA3'i and ΔTA3à1, i.e. DSPZ concentration, the ideal cycle work is defined as the work input for driving the system through electrochemical deacidification at p1 and a subsequent electrochemical acidification at p3, at an infinitesimal current. In the ideal cycle, gassolution equilibrium is assumed at every point and because TA is known, pHTA-eq and DICTA-eq at every point can be calculated. The CO2 molar ideal cycle work, which we denote as ( !"#$% , is obtained from dividing the ideal cycle work by expected ΔDIC3à1, i.e. ΔDICTA-eq,3à1. This section explains how ( !"#$% is calculated in detail. Both of the ideal cycle work and ΔDICTA-eq,3à1 are governed by these parameters: initial TA (ΤΑ3'i or simply TA3' because TA3'i and TA3'f will be the same in an ideal cycle), ΔTA3à1 and pCO2 at p1, and the following equations: (S1) where the K1 and K2 used here are 1.1 × 10 -6 M and 4.1 × 10 -10 M, [1] resulting in the first and second pKa for carbonic acid being 6.0 and 9.4, respectively. Eq. S4 is the definition of TA of the solution under consideration and eq. S5 arises from the charge neutrality constraint in solution (S + and Scorrespond to the cationic and anionic species of the electrolyte salt). During deacidification, [S + ] increases in the negolyte reservoir, so TA increases as well (eq. S5), which means an increase of hydroxide concentration or [HCO3 -] or [CO3 2-] given nonzero pCO2 (eq. S4). The reverse happens during acidification. The expressions for the concentration of each constituent of DIC can be derived by rearranging the above equations: TA3' is calculated using eq. S7, measured pH and assumed gas-solution equilibrium, i.e.
[CO 2 (aq)] = 0.035 × CO -. (S10) where 0.035 comes from Henry's Law constant of 35 mM bar -1 at room temperature and the units of [CO2(aq)] and pCO2 are Molar and bars, respectively. For example, in Table 1, pHmeas at state 3'i was 7.4, and pCO2 was 0.1 bar, so DIC can be derived from eq. S7 and S10, and subsequently [HCO3 -] and [CO3 2-] from eq. S8 and S9, respectively. TA3'i is then obvious from eq. S4. Because ΔTA3'ià1, which is determined by the concentration of DSPZ, is equal to ΔTA3à1, and -ΔTA1'à3 (or -ΔTA1à3) in the ideal cycle, TA at states 1, 1' and 3 can be derived from TA3'i and ΔTA values. Because TA and pCO2 is known for each state, pHTA-eq and DICTA-eq can be calculated. Then ΔDICTA-eq,3à1 is simply DICTA-eq,1 minus DICTA-eq,3. In fact, we can calculate TA, pHTA-eq and DICTA-eq of every point in between the states as well, and hence construct the ideal cycles. Because of the 2H + /2eredox processes of DSPZ, [2] its reduction potential, and overall cell potential decreases 59 mV for every unit of increase in pH. This allows us to calculate the ideal cycle work using the following equation: (S11) ,where n is the index, TA increases by ΔTA Molar when n increases by 1, pH is a function of TA and the process, 0.059 (V/pH) is the conversion factor between pH and cell voltage, F is the Faraday constant (96485 C mole--1 ) and the unit of wcycle,ideal is J L -1 . Then ( !"#$% follows naturally by dividing wcycle,ideal by ΔDIC3à1. (S12) As mentioned in the main text, ΔDIC values vary as p1, TA3' and ΔTA3à1 change. Fig. 4 e, f and g show the ideal cycles for various p1 given fixed p3, TA3' and ΔTA3à1. The amount of CO2 captured in process 3'ià1 and monitored by the flow meter and the CO2 sensor is around 50 mL, which translates to 0.21 M ΔDICflow,3'ià1, assuming T = 293 K and p = 1 bar, across all different p1 values (Fig. 4a). This similarity is consistent with the ideal cycle behavior, illustrated in Fig. 4 c and the alignment of measured ΔDICflow,3'ià1 with the theoretical ΔDICTA-eq,3'à1 vs. pCO2 curve. The similar amount of CO2 captured and released, i.e. ΔDICflow,3'ià1 and ΔDICflow,1'à3, is caused by the coincidental resemblance of the slopes of the two-stage deacidification+CO2 invasion and the two-stage acidification+CO2 outgassing processes under the experimental conditions (Fig. 4  c). The agreement of ΔDICTA-eq,3'à1 vs. pCO2 and ΔDICTA-eq,1'à3 vs. pCO2 curves at high p1 values also corroborates the flow measurements. If the p1 were 0.4 mbar instead, the deacidification and acidification processes would have significantly different slopes so the amounts of CO2 captured during deacidification and released during acidification would be different, as shown in Supplementary Figure 1 e.

Supplementary
With the same reasoning, if a PCET molecule that undergoes 2-etransfer and has 10 M solubility is developed, the ideal cycle work could be as low as 24 kJ molCO2 -1 , leading to an actual cycle work of 59.8 kJ molCO2 -1 .

Non-Linear Fit of Molar Cycle Work With Tafel Model
This section interprets the origin of the non-linear trend of the molar cycle work and describes in detail the Tafel model that fits the non-linear behavior.
The molar cycle work values shown in Fig. 5e and f are composed of ideal molar cycle work at given inlet CO2 partial pressure p1 and TA3'i, and work loss associated with cell inefficiencies, i.e. ( = ( !"#$% + ( .#%% ; (S13) where ( is the experimental molar cycle work (eq. 4 in the method section of main text), ( !"#$% is the ideal molar cycle work (eq. S12) and ( .#%% is the molar cycle work loss associated with cell inefficiency beyond the irreversibilities inherent in the ideal cycle. ( .#%% is expressed as: where q is the charge passed in a half-cycle; V is the electrolyte volume; ΔDIC3à1 is the DIC difference between state 1 and state 3; ηohmic is the ohmic overpotential; ηet is the electron transfer, or sometimes called activation or kinetic, overpotential; and ηmt is the mass transport overpotential. ηohmic arises from ohmic resistance, such as membrane resistance, and is proportional to the applied current, i.e.
where i is the applied current density and rohmic is the area specific ohmic resistance, which is 1.4 W cm 2 , measured by electrochemical impedance spectrometry, in the cell we used. We also assume that the losses caused by under-pressure during CO2 invasion and over-pressure during CO2 outgassing [ref Jin et al.] are proportional to current and consequently are included in the ohmic overpotential term; we find that adding 0.1 W cm 2 for these effects permits us to fit the data reasonably well by the process described below. ηohmic is the sum of the absolute values of the overpotentials during acidification and deacidification. Because ηohmic is proportional to current and ηmt is usually negligible within a flow battery system at modest current densities like our case, [3] we interpret the cause of the non-linear behavior in Fig. 5e and 5f to be ηet. The electron transfer overpotential consists of a deacidification and an acidification contribution, i.e: where ηdeacidification is the electron transfer overpotential during the deacidification process, which has a positive value, and ηacidification is the electron transfer overpotential during the acidification process, which has a negative value, as discussed below. Both deacidification and acidification reactions involve an anodic half reaction and a cathodic half reaction, so each of ηdeacidification and ηacidification has an anodic and a cathodic contribution. In our cell, the participating half reactions in deacidification are: Anodic: Fe(CN) 6 4( →Fe(CN) 6 3( +e ( (S17) Assuming that the backward reactions in eq. S17 and S18 are negligible, which is a good approximation when the electron transfer overpotential is large (>118 mV), ηdeacidification is expressed as: where ηanodic,Fe and ηcathodic,DSPZ represent, respectively, the overpotentials from the electron transfer process of the anodic half reaction in the Fe(CN)6 4-/Fe(CN)6 3posolyte, i.e. eq. S17, and the cathodic half reaction in the DSPZ/DSPZH2 negolyte, i.e. eq. S18.
Similarly, the participating half reactions in acidification are: Again, assuming the backward reactions in eq. S20 and S21 are negligible, ηacidification is expressed as where ηcathodic,Fe and ηanodic,DSPZ represent, respectively, the overpotentials from the cathodic and anodic half reactions. These ηcathodic and ηanodic values are well modelled by the Tafel equations for the large overpotential region [4]: .$@>="!. = ln Substituting eq. S23 and S24 into eq. S22, S19 and S16, we obtain the expression of ηet as: Because eq. S25 describes the overpotential associated with a composite of four electron transfer processes, it is difficult to disentangle the contribution from each process. Therefore, for simplicity, we modelled it with the constraint that all i0 values are equal and we set both αFe and αDSPZ to be 0.5, supported by the symmetric shapes of the cyclic voltammograms of both species. [2,5] So eq. S25 is simplified to: The inputs for eq. S26 are ηet calculated from eq. S11-13 and the applied current density, and a non-linear least squares method is applied to fit for i0 For high partial pressure capture data presented in Fig. 5e, ( !"#$% values are calculated using eq. S1-12 with p3 = 1 bar and TA3'i = 0.11 M, and the resulting values are 6.85, 3.4 and 1.88 kJ molCO2 -1 for p1 = 0.1, 0.3 and 0.5 bar, respectively. Other parameters q and ΔDIC3à1 are available from Supplementary Figure 8 and Fig. 5b and V is 10 mL. The fitted curves are shown in Supplementary Figure 12.  (Supplementary Figure 2 a). The similar behavior for the two conditions of ηet plus ηohmic suggests the dramatic difference in molar cycle work in Fig. 5f is caused by the difference in ΔDIC3à1 and ( !"#$% (eq. S11-12).  Fig. 1b lists all the reactions related to carbon capture in our system. When all reactions involving CO2 are removed, the system is the same as an aqueous organic redox flow battery (AORFB). [6][7][8] The electrochemical rebalancing method is also applicable to AORFB when there is an oxygen leakage. Fig. 6 demonstrates the application of the electrochemical rebalancing method in an AORFB and carbon capture flow cell, which both are organic PCET systems that have pH swing ranging from neutral to basic. Supplementary Figure 15 shows that there are no new peaks generated in the aromatic region in the NMR spectra, indicating the absence of side reactions during electrochemical rebalancing. Based on the result in Fig. 6, the electrochemical rebalancing of a completely out-of-balance cell consumes roughly three times the cycle work of a single carbon capture cycle at 40 mA cm -2 . Therefore, performing one rebalancing step per 30 cycles increases the cycle work per cycle by 10%, which is approximately an acceptable upper limit. Therefore, each cycle is allowed to have 3.3% of the reduced PCET molecule oxidized by oxygen. We also calculated a target capture duration to be 8 hours for DAC (we used equations in Stolaroff et al. [9] Uncycled DSPZ Cycled DSPZ DSPZ after electrochemical rebalancing and assumed 2 M KOH. The calculation indicates that an 8-hour capture period is achievable with a 2mm thick sorbent bed). So the max-tolerable oxidation rate is 0.4% hr -1 under air. Note that the energy cost of the rebalancing step will be reduced if a smaller current density is applied or an electrode that facilitates oxygen evolution reaction is used. As a result, the oxidation rate requirement on the PCET molecule may be loosened.
Here we suggest that the electrochemical rebalancing method also applies to other aqueous based electrochemical systems, including organic and inorganic, PCET or non-PCET, acidic or basic, dissolved or solid redox active materials. If no side reaction is triggered by the oxidative voltage, which is the case for DSPZ as shown in Supplementary Figure 16, the electrochemical rebalancing method can be applied. Here are several examples.

Organic Non-PCET system in neutral aqueous solution: Fe(CN)6 (posolyte) | Viologen (negolyte) Flow Battery
When the viologen-based redox flow battery [5,10,11] is charged: oxygen can chemically oxidize the reduced viologen to the oxidized state, accumulating hydroxide in the negolyte, leading to the negolyte to discharged state and the posolyte active species maintaining the oxidized state. Because the redox active core of viologens have two positive charges, we denote their oxidized form as Vi 2+ and the single-electron reduced form as Vi + . The negolyte side is discharged when oxygen is present, i.e. : 1 The electrochemical rebalancing method can remove the accumulated hydroxide, repelling O2 in the negolyte reservoir: 2 ( à 1 2 -+ -+ 2 ( During the electrochemical rebalancing process, the electrons are transferred to the posolyte side, which has accumulated Fe(CN)6 3-, and eventually both negolyte and posolyte sides are recover the their initial composition, i.e. Fe(CN)6 4in posolyte and Vi 2+ in negolyte, rebalancing the system.

Inorganic Non-PCET system in strongly acidic aqueous solution: VO
When a vanadium redox flow battery [12] negolyte contains the charged form, i.e. V 2+ : if oxygen diffuses into the negolyte, it can chemically oxidize V 2+ to V 3+ , and hydroxide is accumulated in the negolyte, 1 2 The electrochemical rebalancing method can remove the accumulated hydroxide, repelling O2: Because the electrolyte of a vanadium redox flow battery is strongly acidic, the hydroxide is readily neutralized and forming water. Hence the oxidation reaction is the following: 1 2 -+ 2 -+ + 2 + à 2 4+ + -Therefore, instead of generating two hydroxides in the negolyte, the oxidation by oxygen reaction causes the loss of two protons. And the electrochemical rebalancing method in such scenario is as follows: During the electrochemical rebalancing process, the electrons are transferred to the posolyte side, which has accumulated the oxidized form VO 2+ , through 2 -+ + 2 ( à 2 -+ , and eventually both negolyte and posolyte sides are fully discharged (VO2 + in posolyte and V 3+ in negolyte), thus rebalancing the system.

Inorganic Non-PCET system in basic aqueous solution: air (posolyte) | S4 2-/S4 4-(negolyte) Battery
When a sulfur-air flow battery [13] is charged: if oxygen diffuses into polysulfide negolyte, oxygen can chemically oxidize polysulfide, and hydroxide is accumulated in the negolyte, Liu et al. [14] demonstrated a solid quinone aqueous carbon capture system, where the cathode is LiFePO4 and the anode is polyquinone (PAQ) tethered to a carbon electrode. The authors utilized a 20 molal LiTFSI aqueous solution to ensure that the reduced PAQ are deprotonated, i.e. PAQ 2-, which then binds with CO2 to form PAQ-CO2 adduct. Although the influence of oxygen in this system is rather small, but side reaction still happens and can cause long term imbalance (accumulation of oxidized cathode material and accumulated LiOH in the anode side).
When the anode is charged: oxygen can chemically oxidize the air-sensitive anode, and hydroxide is accumulated in the negolyte, The electrochemical rebalancing method can remove the accumulated hydroxide, repelling O2: 2 ( à 1 2 -+ -+ 2 ( During the electrochemical rebalancing process, the electrons are transferred to the cathode side externally, eventually both anode and cathode are discharged, rebalancing the system. Benzene-1,2-diamine (1 equiv.) was mixed with 2,5-dihydroxycyclohexa-2,5-diene-1,4-dione (1.03 equiv.) in water to achieve 0.2 M benzene-1,2-diamine solution in a pressure vessel. The reaction mixture was refluxed at 80 °C and stirred overnight. The resulting slurry was filtered, and the black precipitate was crude product phenazine-2,3-diol (DHPZ). The black precipitate was then dissolved in 0.1 M KOH solution to make a 0.02 M DHPZ solution. The solution was filtered again and the filtrate was acidified with HCl solution until pH reached 7. Red precipitates formed and were filtered to give pure DHPZ (81% yield).
DHPZ (1 equiv. ) was dissolved in DMF to make 0.05 M DHPZ solution. NaH (60 wt. % in mineral oil) (2.2 equiv. NaH) was added to the DHPZ solution under N2. After all bubbles disappeared, 2.05 equiv. propane sultone was then added into the solution. The reaction mixture was stirred overnight at 80 °C to give a red slurry. The slurry was then cooled and filtered. The red precipitates were washed thoroughly with ethyl acetate to remove residual DMF. The final DSPZ products were red solids (65% yield)