Size-Dependent Sigmoidal Reaction Kinetics for Pyruvic Acid Condensation at the Air–Water Interface in Aqueous Microdroplets

The chemistry of pyruvic acid (PA) under thermal dark conditions is limited in bulk solutions, but in microdroplets it is shown to readily occur. Utilizing in situ micro-Raman spectroscopy as a probe, we investigated the chemistry of PA within aqueous microdroplets in a relative humidity- and temperature-controlled environmental cell. We found that PA undergoes a condensation reaction to yield mostly zymonic acid. Interestingly, the reaction follows a size-dependent sigmoidal kinetic profile, i.e., an induction period followed by reaction and then completion. The induction time is linearly proportional to the surface area (R2), and the maximum apparent reaction rate is proportional to the surface-to-volume ratio (1/R), showing that both the induction and reaction occur at the air–water interface. Furthermore, the droplet size is shown to be dynamic due to changes in droplet composition and re-equilibration with the relative humidity within the environmental cell as the reaction proceeds. Overall, the size-dependent sigmoidal kinetics, shown for the first time in microdroplets, demonstrates the complexity of the reaction mechanism and the importance of the air–water interface in the pyruvic acid condensation reaction.


Data Analysis
Ratiometric approach for determining PA concentration.To analyze the in-situ reaction kinetics of PA in microdroplets, the peak area ratio of PA (ν(C-C) at 785 cm -1 ) and H2O (OH band from 3180 to 3750 cm -1 ) (A !" /A # !$ ) is used to calibrate and determine PA concentration in units of molality (mPA, mol kg -1 ).The calibration curve is obtained by relating mPA to A !" /A # !$ using bulk solutions with known PA concentrations, and an excellent linear correlation is observed over a wide PA concentration range (0.5 to 15 mol kg -1 ) (Figure S7).The changes in mPA during PA reactions in microdroplets are determined by converting the A !" /A # !$ of microdroplets obtained from the Raman spectra to mPA, using the calibration curve.This ratiometric approach offers two key advantages.First, it can normalize changes in droplet size and laser power fluctuations.Second, it excludes the contribution of PA evaporation to the decrease in PA concentration, as the A !" /A # !$ reflects the molality of PA, i.e., the molar amount of PA per unit mass of H2O.Evaporation of PA under a constant RH condition will result in a corresponding evaporation of H2O, maintaining a constant PA molality.In other words, a decrease in A !" /A # !$ explicitly reflects the decrease of PA concentration caused by reactions.
Boltzmann sigmoidal fitting.The PA reaction kinetics in aqueous microdroplets can be fitted by a Boltzmann sigmoidal equation 2 Where Ai and Af are the initial and final values of the curve, respectively.In eqn.(1), x0 is the abscissa of the curve's central inflection point and a is a constant.The maximum slope (Smax) of the curve is at x0 and determined by  -,( = ( & −  % )/(4) (2)  The maximum reaction rate (Rmax) for the PA dark reaction is determined by  -,( = − -,( Changes in droplet size.During the induction period, the droplet size slowly decreases while the mPA remains constant.This is because PA is semi-volatile and evaporates from the droplet to the gas phase.Since the microdroplet is in equilibrium with the surrounding RH in the environmental cell, a corresponding amount of H2O also evaporates from the droplet.Consequently, the microdroplet decreases in size while maintaining a constant mPA.Our analysis shows that all the investigated droplets (113 μm ≤ Ri ≤ 415 μm) exhibit a similar ratio of the size at the end of induction to the initial size, with an average value of 0.79 and a standard deviation of 0.037 (Figure S11).This result indicates that ~50% of PA and H2O partition from the droplet to the gas phase.During the reaction period, in addition to the evaporation of PA, the formation of less hygroscopic products (mostly ZA) through the reaction of PA, and the reequilibration with the RH inside the environmental cell, lead to a decrease in water content, further contributing to droplet size reduction.Since ZA has low volatility, it does not evaporate significantly during the completion period, leading to a stable size, in agreement with a recent study. 3The ratio of the droplet size at the end of reaction to the initial droplet size has an average value of 0.45 with a standard deviation of 0.023 (Figure S11).

Figure S6.
Raman spectra of sodium pyruvate aqueous microdroplet with a radius of 212 μm at 0 h (black), 2 h (red) and 12 h (blue).The peaks of pyruvate (CH3COCOO -) from the low wavenumber to high wavenumber are assigned to COO -wag (619 cm -1 ), C-C stretch (841 cm - 1 ), C-CH3 stretch (1175 cm -1 ), sym.CH3 bending (1356 cm -1 ), sym.COO -stretch (1399 cm -1 ), asym.CH3 bending (1423 cm -1 ), asym.COO -stretch (1613 cm -1 ), C=O stretch (1708 cm -1 ), sym.CH3 stretch (2928 cm -1 ), asym.6][7] Note no changes in spectra were detected after 12 hours, indicating that no reaction occurred during that period.The microdroplet was generated from a sodium pyruvate solution with a concentration of 1.8 mol kg -1 .The solution had a pH of 6.77±0.02,as measured by the pH meter, and this pH was used to indicate the droplet pH.We are aware that the droplet pH may not be exactly the same as the bulk solution.Nevertheless, the droplet was in equilibrium with a high RH (95%) of in the environmental chamber.The uncertainty of droplet pH caused by using bulk pH as a surrogate in this case should not be significant.

Figure S8
. Time evolution of the peak area ratio of PA (at 785 cm -1 ) and H2O (from 3180 to 3750 cm -1 ) (A !" /A # !$ ) (black) and the peak area ratio of the product (at 796 cm -1 ) and H2O (from 3180 to 3750 cm -1 ) (A !./0123 /A # !$ ) (red) in droplets with Ri of (a) 170 μm and (b) 313 μm.Due to the lack of a standard for the product, we used A !./0123 /A # !$ to reflect the concentration of the product.Similarly, we also used A !" /A # !$ to reflect PA concentration, even though we have the PA concentration values (Figure 2a and 2b).The similar shape between the evolution of A !" /A # !$ here and mPA in Figures 2a and 2b, suggests that the peak area ratio is a good choice to reflect the concentration., and (e) 141.9 mol kg -1 in the dark from 0 to 7 days.][10] To explore if the potential higher mPA at the interface is the underlying reason for the surface reaction, we measured bulk solutions with mPA ranging from 4.7 mol kg -1 , which is slightly higher than the droplet interior mPA (mostly in the range of 4−4.6 mol kg -1 Figure 2a and 2b), to an extremely high value of 141.9 mol kg -1 .No significant bulk reactions were observed after 7 days even at these higher concentrations, suggesting that the potential enrichment of PA the at the interface alone cannot trigger the PA condensation reaction, and the reaction is likely initiated by the unique environment and potential the solute orientation/ structures at the air-water interface.) determined for 65% and 75% RH might not be as precise as that less than 15 mol kg -1 .This is because the PA concentration calibration curve covers a range of 0.5 to 15 mol kg -1 (Figure S7) and the curve was extrapolated to determine the PA concentration greater than 15 mol kg -1 .

Figure S2 .
Figure S2.The contact angle of the hydrophobic coverslip.3 μL of water droplets were used for the contact angle measurements.The contact angle is 94.1±4.8°.

Figure S3 .
Figure S3.The correlation between the pH and the concentration of PA solution (mPA).The solution pH was measured by a pH meter (Oakton pH 700).The droplet in Figure1had an initial mPA of 4.3 mol kg -1 , thus, the initial droplet pH is determined to be 0.9 based on the correlation between pH and concentration.

Figure S4. 1 H
Figure S4.1 H NMR spectrum (500 MHz) of the products from PA microdroplet reaction dissolved in DMSO-d6.The peaks at 1.57, 6.29 and 10.08 ppm are assigned to methyl proton (H1), alkene proton (H2) and the enol proton (H3) in zymonic acid (ZA).4The ratios of the peaks H1:H2:H3 are 3.14:1:1.05.The absence of the acid proton (H4) is likely due to the exchange of the acid proton with water in the DMSO.

Figure S5 .
Figure S5.Mass spectrum of the products obtained from PA reaction in microdroplets.

Figure S9 .
Figure S9.Raman spectra of PA bulk solutions with concentrations of (a) 4.7, (b) 7.1, (c) 14.2, (d) 42.6, and (e) 141.9 mol kg -1 in the dark from 0 to 7 days.As it has been reported that PA is surface active and mPA at the air/water interface may be higher than that of the interior of the microdroplets.[8][9][10]To explore if the potential higher mPA at the interface is the underlying reason for the surface reaction, we measured bulk solutions with mPA ranging from 4.7 mol kg -1 , which is slightly higher than the droplet interior mPA (mostly in the range of 4−4.6 mol kg -1 Figure2aand 2b), to an extremely high value of 141.9 mol kg -1 .No significant bulk reactions were observed after 7 days even at these higher concentrations, suggesting that the potential enrichment of PA the at the interface alone cannot trigger the PA condensation reaction, and the reaction is likely initiated by the unique environment and potential the solute orientation/ structures at the air-water interface.

Figure S10 .
Figure S10.Comparison of the induction time (a) and reaction time (b) of PA reaction obtained from the evolution of droplet size (black) and the evolution of PA concentration (red).

Figure S11 .
Figure S11.The ratio of the droplet size to the initial droplet size at the end of induction (R_end of induction/Ri) and at the end of reaction (R_end of reaction/Ri).R_end of induction/Ri has an average value of 0.79 with a standard deviation of 0.037, while R_end of reaction/Ri has an average value of 0.45 with a standard deviation of 0.023.The dashed lines, y=0.79 and y=0.45, indicate the average values of these two ratios.

Figure S12 .
Figure S12.Time evolution of mPA under different RH conditions: 65% (black), 75% (red), 85% (blue) and 95% (green) for droplets with Ri of (a) 210±5 μm, (b) 320±5 μm, and (c) 417±5 μm.(d) Changes of maximum apparent reaction rate (Rmax) and induction time of droplets with different sizes as a function of RH.FigureS12ais the same as Figure4in the main text.It is worth noting that the accuracy of the high PA concentration (>15 mol kg -1 ) determined for 65% and 75% RH might not be as precise as that less than 15 mol kg -1 .This is because the PA concentration calibration curve covers a range of 0.5 to 15 mol kg -1 (FigureS7) and the curve was extrapolated to determine the PA concentration greater than 15 mol kg -1 .