Interfacial Water Structure of Binary Liquid Mixtures Reflects Nonideal Behavior

The evaporation of molecules from water–organic solute binary mixtures is key for both atmospheric and industrial processes such as aerosol formation and distillation. Deviations from ideal evaporation energetics can be assigned to intermolecular interactions in solution, yet evaporation occurs from the interface, and the poorly understood interfacial, rather than the bulk, structure of binary mixtures affects evaporation kinetics. Here we determine the interfacial structure of nonideal binary mixtures of water with methanol, ethanol, and formic acid, by combining surface-specific vibrational spectroscopy with molecular dynamics simulations. We find that the free, dangling OH groups at the interfaces of these differently behaving nonideal mixtures are essentially indistinguishable. In contrast, the ordering of hydrogen-bonded interfacial water molecules differs substantially at these three interfaces. Specifically, the interfacial water molecules become more disordered (ordered) in mixtures with methanol and ethanol (formic acid), showing higher (lower) vapor pressure than that predicted by Raoult’s law.


Evaporation Rate Measurement
We prepared various concentrations of the aqueous binary mixtures samples in a trough with a diameter of 2 cm and total volume 3.5 mL, and placed the samples in a N 2 -purged chamber.
After the relative humidity in the chamber reached below 10%, we evaluated the evaporation  indicates the 95% confidence interval of the estimation of the evaporation rate.

Estimation of Vapor Pressure of Formic Acid at 333 K
The vapor pressure at 333 K for the water-formic acid mixture was extrapolated from those at 388 K and 398 K in ref 1, using a simple semi-empirical Antoine equation 2,3 , , = + where represents the vapor pressure corresponding to ith component in the system at the temperature T. Based on the values at 388 K and 398 K, we determined the values at 333 K for the data with various molar fraction of water (x 1 ) and formic acid (x 2 ) in the liquid phase. Here, we assume that, upon changing the temperature, the molecular compositions in the gas-and liquid-phases do not vary. These data are displayed in Table S1. Table S1. The partial vapor pressure of water ( ) and formic acid ( ) calculated from 1 2 Antoine equation and estimated deviations from Raoult's law for . 1 Figure S2 shows the total vapor pressure and partial water vapor pressure of aqueous binary mixtures of methanol, ethanol, and formic acid at 333 K.  and 5, respectively. The data for (c) were extrapolated in the previous section 1 using the Antoine equation.

N 2 Purging Effect on the SFG Measurements
It was argued that the evaporation with and without carrier gas might affect the evaporation process by affecting the diffusion of the evaporated molecules 6,7 . As such, purging with N 2 as required for the SFG experiments at the free-OH stretching frequency, the interfacial composition may not be in equilibrium. To explore the effect of N 2 purging on the SFG spectra, we compared the C-H stretching mode signal with and without N 2 purging. Fig. S3 S6 shows that the signals of both 2% methanol and pure methanol samples do not change by using N 2 purging. Therefore, the SFG spectra when purging can be approximated to represent the equilibrium conditions and it is reasonable to compare equilibrium vapor pressures to our SFG results.  Figure S4 shows the measured SFG spectra at the interface of the air-aqueous binary mixture of methanol. We extracted the amplitude of the symmetric C-H stretching mode of CH 3 group by fitting the SFG spectra of the water-methanol mixtures. The SFG signal ( ) consists of the second-order susceptibilities; where is non-resonant contribution, are the symmetric and  (2) NR  (2) ss and  (2) as antisymmetric C-H stretching modes of the CH 3 groups 8,9 , respectively, and  (2) Fermi represents the Fermi resonance between the symmetric stretching mode and the overtone of the H-C-H bending mode (~1455 cm −1 ). 8, 10 We assumed that the second-order susceptibilities have a Lorentzian lineshape; where X denotes a vibrational mode, and indicate the amplitude and the characteristic X X frequency of the vibrational mode X, respectively, and is the full width at half maximum 2 X (FWHM). The fits are shown in Fig. S4, and the obtained fitting parameters are summarized in Table S2.
This assignment has been done based on polarization-dependent SFG intensities (Ref. 11), assuming a delta function for the orientational distribution function for the CH 3 vibrational chromophores. However, previous MD simulations have shown that the orientational distribution markedly differs from a delta function. Rather, the orientational distribution function decays exponentially. 14 The different orientational distributions also result in different ssp and ppp intensities, as we have shown in our previous work. 15 Based on these considerations, the peak assignment given in Ref. 11 should be reconsidered. Our previous post vibrational self-consistent field calculation for methanol beyond the classical/harmonic vibration approach (Refs. 8 and 9), which can accurately predict Fermi resonances, indicates that the 2950 cm -1 contribution can be assigned to the antisymmetric stretching mode of the S8 CH 3 group. As such, we assign the 2950 cm -1 peak to the antisymmetric stretching mode in the present study.   Figure S5 shows the measured SFG data at the interface of the air-aqueous binary mixture of ethanol. Similarly, the SFG spectra of the water-ethanol mixture samples were fitted via;  Table S3.   Figure S6 shows the measured SFG data at the interface of the air-aqueous binary mixture of formic acid. The spectra of the water-formic acid mixtures were fitted via; by assuming the Lorentzian lineshape expressed by Eq.
stretching mode peaked at ~2930 cm −1 . 17 The fits are shown in Fig. S6. The obtained fitting parameters are summarized in Table S4.
by assuming that and have a Lorentzian lineshape (S2). The shoulder peak of water is used for the water-formic acid mixture, while it was not used for water-methanol and water-ethanol mixtures. The fit lines are also plotted in Figs. S7, S8, and S9, and the fitting parameters are summarized in Tables S5, S6, and S7 accordingly.     Figure S10 shows the measured SFG spectra at the interfaces of the air-aqueous binary mixtures with methanol, which display a broad band ranging from 3000 to 3500 cm -1 .

S21
For the aqueous-binary mixture of formic acid, we found that the C=O stretching mode (~1720 cm -1 ) of formic acid overwhelms the H-O-H bending mode contributions spectrally ( Figure S12). To avoid this complication, we measured the H-O-D bending mode with isotopically diluted water-formic acid mixtures. Figure S13 displays the measured S22 spectra in this frequency region, one can see the C-H bending (~1380 cm -1 ) and the C-O-H bending mode (~1490 cm -1 ) features of formic acid. 26,27 Although the band assignment at ~1490 cm -1 is controversial, it was reported that the formic acid dimmer in gas phase and crystal forms show C-O-H in-plane bending mode at 1450 and 1560 cm -1 respectively. 26 We didn't observe this band for low formic acid concentration, while it's easy to form transconformation structure or even dimmer at high concentration. We therefore chose to assign it to the C-O-H bending mode. These modes may slightly change in water-formic acid mixture.
Therefore, to determine the modes' parameters further precisely for isotopically diluted water-formic acid system, we performed a global fit for the spectra of isotopically diluted water-formic acid and H 2 O-formic acid simultaneously.  resolve the weak negative contribution of bend 1 for the isotopic mixtures. Therefore, in the current work, we neglect the bend 1 contribution for the isotopic mixtures. The obtained fitting parameters are displayed in Tables S10 and S11.
Table S10. The spectral fitting parameters for the SFG spectra at the interfaces of isotopically diluted water-formic acid mixtures given in Fig. 3c. The values of , and are the concentration before mixing. Table S11. The spectral fitting parameters for the SFG spectra at the interfaces of H 2 Oformic acid mixtures given in Figure S13.

Estimation of Water Mole Fraction in the Water-Formic Acid Mixture
The equilibria of the isotopically labeled water-formic acid binary mixture can be written as The equilibration constant for expression (S8) is known to be , 29 while the = 3.86 equilibrium constant for expression (S9) was assumed to be , based on the rule of the = 1 geometric mean. 30 The obtained , , , and are listed in Table S12.

MD Simulation Details
We carried out the molecular dynamics (MD) simulation for the interfaces of the air-aqueous binary mixture. We used the GROMACS software for performing the MD simulations. 31 The equation of motion was integrated with a time step of 2 fs. The bond lengths of all the molecules were fixed through the LINCS algorithm. 32 MD simulation was run in the canonical ensemble, and the temperature of the system was controlled through the canonical sampling through velocity rescaling method. 33 The target temperature was set to 300 K. We ran 10 ns MD simulations for equilibrating the systems and sequentially obtained total 70 ns MD trajectories which were used for analyzing the data.
For the water-methanol mixture, we used two different combinations of the force field models: The OPLS-AA force field model for methanol 34 and TIP4P/2005 model for water 35 as well as the Kirkwood-Buff derived force field model for methanol 36  OPLS-AA force field tends to reproduce the experimental data (see section 9 in Supporting Information), we showed the data using the OPLS-AA force field in the main text. The data of the Kirkwood-Buff derived force field model is given in this Supporting Information.
For the water-ethanol mixture, we used two different combinations of the force field models: The OPLS-AA force field model for ethanol 34 and TIP4P/2005 model for water 35 as well as the Kirkwood-Buff derived force field model for ethanol 38,39 with the SPC/E model for water. 37 We prepared the solutions with of 0.15, 0.58, 0.76, 0.91, 0.95, 0.98, and 1.00.
Since the OPLS-AA force field tends to reproduce the experimental data, we showed the data using the OPLS-AA force field model in the main text. The data of the Kirkwood-Buff derived force field model is given in this Supporting Information.
For the water-formic acid mixture, we used two different combinations of the force field models: the original and modified OPLS-AA force field model for formic acid 34  Furthermore, we modified the 1-4 electrostatic interaction of the formic acid. It is known that the trans-conformation is favored when a formic acid molecule is in the gas-phase, while the cis-conformation is more favored when a water molecule interacts with formic S28 acid. 43 Thus, the cis-trans energy barrier would be essential to determine the ratio of the cisand trans-conformations in the water-formic acid solutions. In fact, the frequency shift of the C-H stretching SFG feature at the water-formic acid interface (see Fig. 2a of the main text, Figure S6 and Table S4) indicates the transition from cis-conformation (2922 cm -1 ) to the trans-conformation (2933 cm -1 ) of the formic acid. We scaled the 1-4 electrostatic interaction down to 30%, rather than 50% which is used for the OPLS-AA force field model. With the scaling down of the 1-4 interactions by 70%, the force field model could reproduce the energy difference of ~4.3 between the cis-and trans-conformation. 44 Thus, we scaled the 1-4 electrostatic interaction down by 70%.
Here, we note that the accurate force field model of formic acid was developed by Jedlovszky and Turi, 45 while it was not used in this study, because the model of Jedlovsky and Turi assumed the trans-conformation of formic acid. As is evident from the experiment, the cis-conformation is more favored than the trans-conformation, and thus the fixed transconformation geometry of formic acid is not suitable for the water-formic acid mixture. In fact, we observed 70% cis-conformation for the < 20% formic acid aqueous solution, while we observed < 50% cis-conformation for the ~70% formic acid aqueous solution.

Water
We calculated the depth profiles of aqueous binary mixture density and orientations of methyl  Fig. 2b and d (solid lines) in the main text were obtained by integrating these depth profiles and normalized by the maximum value among these concentrations.

Depth Profiles of Density and Orientation
We calculated the depth profiles of aqueous binary mixture density and orientations for the interfacial water molecules. The origin point of the profiles is set to the center of mass for the whole system. The depth profiles of are given in Figure S14. The data shown in Fig.  〈 cos 〉 3d in the main text are obtained by integrating these depth profiles. To compute the orientation of the interfacial molecules, we defined the interfacial regions. This was given as the FWHM region of the depth profiles of . 〈 cos 〉 Note that here we cannot exclude the possibility that the variation of the number of water molecules ( ) upon the addition of organic molecules affects the variation at 〈 cos 〉 the air-binary mixture interface. However, the discussion on the variation of itself may mislead the conclusion, while the number of molecules located in the interfacial region is critically affected by the surface nanoroughness, which differs significantly between the three S30 binary mixtures considered here ( Figure S14 and S15). In fact, arbitrary decomposition of and terms has resulted in a different interpretation of the binary mixture. 12,47,48 Thus, cos here, we do not discuss the impact of on the SFG signal. Figure S14. The depth profiles of of the interfacial water. 〈 cos 〉 S31 Figure S15. The density profiles of the interfacial water.