Synthesis and hydrolysis of atmospherically relevant monoterpene-derived organic nitrates

Abstract

The partition of gas-phase organic nitrates (ONs) to aerosols and subsequent hydrolysis is regarded as an important loss mechanism for ON species. However, the hydrolysis mechanisms and the major factors controlling the hydrolysis lifetime are not fully understood. In this work, we synthesized seven monoterpene-derived ONs and systematically investigated their hydrolysis in bulk solutions at different pH. The hydrolysis lifetimes ranged from 13.9 min to 8.5 h for allylic primary ON and tertiary ONs, but secondary ONs were stable at neutral pH. The alkyl substitution numbers, functional groups, and carbon skeleton were three important factors controlling hydrolysis rates. Tertiary and secondary ONs were found to hydrolyze via the acid-catalyzed unimolecular (S_N1) mechanism, while a competition of S_N1 and bimolecular (S_N2) mechanisms accounted for the hydrolysis of primary ONs. The consistency of experimental and theoretical hydrolysis rates calculated by density functional theory (DFT) further support the proposed mechanisms. Reversible reactions including hydrolysis and esterification were first reported to explain the hydrolysis of ONs, highlighting the possibility that particulate nitric acid can participate in esterification to generate new nitrogen-containing compounds. These findings demonstrate that ON hydrolysis is a complex reaction which proceeds via different mechanisms and are controlled by various parameters.

Graphical Abstract

1. Introduction

Biogenic volatile organic compounds (BVOCs), such as isoprene, monoterpenes, and sesquiterpenes, contribute significantly to the global secondary organic aerosols (SOA) budget.^1,2 In the presence of high anthropogenic emissions, the conversion of BVOCs to SOA can be substantially promoted.^3–6 One such pathway is the interaction of BVOC oxidation products with nitrogen oxides (NO_x = NO₂ + NO) leading to formation of organic nitrate (ON) compounds, which is an important component of reactive oxidized nitrogen.^7–10 In the past decade, improvements in measuring both total and speciated gas-phase and particle-phase ONs^11–16 have demonstrated their contribution to a large fraction of ambient OA.^6,12,16–21 ONs can either retain or release NO_x upon further reactions to act as permanent sink or temporary reservoir of NO_x.^19–36 Therefore, it is important to thoroughly evaluate the kinetics and chemical mechanisms of different ON loss processes in the atmosphere to understand their roles in NO_x cycling, ozone and SOA formation.

The partition of gas-phase ONs to aerosols and subsequent hydrolysis removes the oxidized nitrogen from further atmospheric processing. Condensed phase hydrolysis has been identified as an important sink for ON species^{28,30,34,39,40}, supported by large ONs uptake to aerosols^11,15,37,41 and proposed short hydrolysis lifetimes^{28,30,34,39,40}. Simultaneously, nitric acid (HNO₃) generated from ON hydrolysis in hydrated aerosols can be further removed via dry and wet deposition^36,42,43, making hydrolysis an efficient sink for NO_x compared to other potential loss processes (e.g., photolysis) that recycle NO_x. Despite the importance of hydrolysis, there is still a very limited number of studies focusing on the hydrolysis of ONs, especially for monoterpene-derived ONs.

The paucity of commercially available ON standards presents a significant obstacle to study hydrolysis processes. The majority of studies in the literature estimated hydrolysis rates using synthetic alkyl nitrates with 2–5 carbon numbers in bulk solutions^22,23,33,38. Only one study investigated the hydrolysis rate of a tertiary α-pinene hydroxynitrate³⁸. These previous studies revealed that the number of alkyl substitutions is an important factor in controlling hydrolysis rates since particle-phase hydrolysis of tertiary (3°) nitrate is fast with a lifetime of minutes to hours, while primary (1°) and secondary (2°) nitrates are stable. Based on this simple alkyl substitution number-based rule, the different magnitudes of ON hydrolysis lifetimes in laboratory chamber studies, field measurements, and model simulations^{29,30,34,39,43,44} have been attributed to differences in the relative amount of primary, secondary, and tertiary nitrates. However, the observation of highly functionalized ONs^{16,39,45–47} rather than mono-functional ONs in the ambient atmosphere warrants additional studies on how factors such as functional groups (e.g., hydroxyl group, carbonyl group, etc.) and carbon skeletons (e.g., isoprene or monoterpene-derived ONs) impact the ON hydrolysis lifetime.

In this study, we deployed two synthetic approaches for synthesizing seven monoterpene-derived ONs with high purity. These synthetic ONs were employed to explore the hydrolysis processes in bulk solutions. By comparing hydrolysis rate constants determined from in situ nuclear magnetic resonance (NMR) and high-resolution time-of-flight chemical-ionization mass spectrometer coupled with the filter inlet for gases and aerosols (FIGAERO-HR-ToF-CIMS), we provided new insights into how various factors influence hydrolysis rates of monoterpene-derived ONs and extended the previously reported hydrolysis mechanisms. Lastly, we confirmed the final degraded products by ultra-high performance liquid chromatography-ultrahigh resolution mass spectrometry (UHPLC-UHRMS). The consistency of the theoretical mechanisms predicted by density functional theory (DFT) calculations with the proposed mechanisms further shed light on the results.

2. Experimental Section

2.1. ON synthesis.

A total of seven monoterpene-derived ONs were synthesized in this study. Their molecular structures and abbreviations were shown in Scheme S1. The synthetic methods were partially reported in our recent work⁴⁸. Here, we expanded the synthetic approaches to synthesize ketone nitrates (KNs) derived from α-pinene and limonene. Briefly, two synthetic strategies (Scheme S2) were employed to prepare the ONs from the respective monoterpenes (i.e., β-pinene (Bp) and limonene (Lm)) or monoterpene oxide (i.e., α-pinene (Ap) and limonene oxides). The first route involved epoxide opening^49–51 of monoterpene oxide with fuming HNO₃ to form four hydroxynitrates (HNs) (i.e., 2°_ApHN, 3°_ApHN and a mixture of 3°_LmHN and 2°_LmHN). The second route explored halohydrination of monoterpenes with N-bromosuccinimide (NBS)^52,53 followed by nucleophilic substitution of the bromide with nitrate (NO₃⁻)^41,54,55 to generate 1°_BpHN and 2°_LmHN. Further oxidation of the hydroxyl group of 2°_ApHN and 3°_LmHN by Dess-Martin oxidation⁵⁶ resulted in the formation of 2°_ApKN and 3°_LmKN, respectively. The purities of the synthetic ONs were higher than 95% based on ¹H NMR spectra (Sections S1 and S2 in SI). All synthetic standards were stored in clear bottles at −20 °C in a freezer until use.

2.2. Hydrolysis experiments.

NMR and FIGAERO-HR-ToF-CIMS were utilized to study ON hydrolysis in aqueous solutions of different pH values. For the NMR based technique, around 20 mg of ONs and 1 mg of dimethyl-2-silapentane-5-sulfonate sodium salt (DSS as an internal standard) were added to 1 mL of D₂O (pH = 7.44) or D₂O buffered solvent. The D₂O solution was buffered with either a sulfate, acetate, phthalate, or citrate buffer system to control the pH at 0.33, 2.38, 3.13–3.33, 4.12, or 5.15 (Table 1 and Table S3). The pH values were measured by a calibrated pH meter (HI 5522, HANNA instruments). The solution was stirred for approximately 1–2 min and 0.5 mL of supernatant was loaded into an NMR tube, and spectral collection was started. Hydrolysis kinetic measurements were obtained by collecting sequential ¹H NMR spectra over the course of the experiment and measuring the depletion of proton peaks unique to each ON (Table S1). In order to increase the accuracy of quantification in ¹H spectra, we deployed spin-lattice relaxation (T₁-relaxation) experiments⁵⁷ to obtain the delay time (d₁ = 5×T₁ time) (Section S3.1, and Figure S3 in SI). The start time of each ¹H NMR data collection period was taken as the start of the reaction time. Depending on the rate of hydrolysis of each ON, the solution was monitored for different periods of time. Specifically, the experiment was run for a total time period of about 10 h (¹H spectra taken every 20 min) for 3°_LmKN and 0.6–1.5 h for 1°_BpHN and 3°_LmHN (¹H spectra taken every 1.5 min) or monitored intermittently over seven days for slow-hydrolyzable secondary ONs (i.e., 2°_LmHN, 2°_ApHN, and 2°_ApKN, ¹H spectra taken every day). The ON unique proton peak area was used for quantification of each ON, with DSS serving as an internal standard (Table S1).

Table 1.

Hydrolysis lifetimes of synthetic organic nitrates in this work.

Hydrolysis lifetimes
ONs		1°_BpHN	3°_LmHN	3°_ApHN	3°_LmKN	2°_LmHN	2°_ApKN	2°_ApHN
Structures
NMR	pH = 7.44	13.9 min	18.1 min	/a	7.5 h	Stable	Stable	Stable
	pH = 5.15c	12.3 min	9.0 min		4.1 h	/b	/b	/b
	pH = 4.12c	11.4 min	10.8 min		/b	/b	/b	/b
	pH = 3.33c	12.2 min	10.9 min		/b	/b	/b	/b
	pH = 2.38c	12.5 min	6.6 min		/b	/b	/b	/b
	pH = 0.33	11.6 min	5.7 min		2.7 h	9.4 days	10.6 days	16.6 days
CIMS	pH = 7.44	12.9 min	13.1 min	2.5 h	8.5 h	/b
	pH = 5.86	12.4 min	9.4 min	2.5 hd	6.4 h

^a.NMR cannot detect 3°_ApHN hydrolysis rate because of the overlap of the proton peaks of 3°_ApHN and its degradation products;

^b.Hydrolysis experiments were not conducted under these conditions;

^c.Buffer: acetic acid and/or sodium acetate;

^d.Decrease to 9 min if use ApDo to fit the hydrolysis curve (Section S3.9 in SI).

Hydrolysis of selected ONs were also measured using FIGAERO-HR-ToF-CIMS with iodide (I⁻) as the reagent ion (Aerodyne Research Inc.), which is capable of detecting a large suite of gaseous and particulate oxidized organics⁵⁸, including hydroxy and ketone nitrates. The setting and operation of the instrument were detailed in our previous studies^25,29. Experiments were conducted under two pH conditions. Unlike the NMR experiments, after stirring the ONs in D₂O (pH 7.44) or deionized-water (DI-water, pH 5.86), 0.5 mL of supernatant was first transferred to a new bottle. For each FIGAERO-HR-ToF-CIMS measurement, 1 μL of supernatant was loaded onto the polytetrafluoroethylene (PTFE) filter. A gradually heated nitrogen gas flowed over the filter, evaporated the ON sample as well as its degradation products, and transported them into the CIMS for detection. Each desorption cycle lasted for 15 min and consisted of two parts: a linear increase of the desorbing gas temperature (~25 °C → ~170 °C in 5 min) and a cooling period to decrease the gas temperature to room temperature (~170 °C → ~25 °C in 10 min). The start time of each desorption cycle was recorded as the start time of the reaction time. Before and after each hydrolysis experiment, a blank measurement was conducted by loading 1 μL of solvent (DI-water or D₂O) onto the PTFE filter and followed the same thermal desorption cycle. All data were analyzed using Tofware v2.5.11 and all the masses presented in this study were I⁻ adducts.

2.3. LC/MS analysis.

Vanquish Horizon UHPLC (Thermo Scientific, USA) coupled to an Orbitrap mass spectrometer (Q-Exactive Hybrid Quadrupole mass spectrometer, Thermo Scientific, USA) was used to detect the synthetic ONs and their degradation products in DI-water after 5 hours. Chromatographic separation was performed on an Acquity UPLC BEH C18 column (2.1 mm×100 mm, 1.7 μm particle size; Waters, Milford, MA, USA) with Van Guard column (BEH C18, 1.7 μm) at a flow rate of 0.4 mL min⁻¹. The mobile phase consisted of water (eluent A) and methanol (eluent B), each containing 0.1% acetic acid. The gradient elution program was carried out as follows: eluent B was set at 8% at the beginning, increased to 100% in 7.0 min and held for 3 min, decreased to 8% in 0.7 min and held for 1.3 min. The injection volume was 2 μL.

The Orbitrap mass spectrometer was operated in positive ESI mode under the following conditions: the heated electrospray ionization (HESI) source was operated at a vaporizer temperature of 425 °C, a spray voltage of 3.0 kV, and sheath, auxiliary, and sweep gas flows of 60, 18, and 4 L min⁻¹, respectively. The m/z range was 100–1000 Da for full MS scan with 120,000 as mass resolution. Compounds were detected as their Na⁺ and/or NH₄⁺ adducts and molecular formulas were assigned within 5 ppm error.

2.4. DFT calculations.

Potential and free energy surfaces of the hydrolysis of four different monoterpene-derived ONs (i.e., 1°_BpHN, 3°_ApHN, 3°_LmHN, and 3°_LmKN) exhibiting a range of lifetimes were computed using the Gaussian 16 (G16) electronic structure program by invoking the default convergence criteria and the ultrafine integration grid⁵⁹. Calculations were carried out using the M062x density functional which has been extensively and successfully applied in estimating barriers in both the gas and condensed phases^60–62. The SMD continuum solvation model^63,64 was used to describe bulk water solvation effects.

In order to map reaction trajectories and determine mechanisms, lengthy calculations were conducted that mapped the potential energy surface of the reaction coordinate using the nudged elastic band (NEB) method⁶⁵ with the 6–31+G(d) basis set. G16 was interfaced with software that implements the NEB which is essentially a modified version of the original program from Alfonso and Jordan⁶⁶. For each NEB calculation, 20–40 intermediate images were generated using Materials Studio (version 7.0, Biovia, Dassault Systemes). Materials Studio uses the method of Halgren and Lipscomb⁶⁷ to interpolate between the defined reactants and products. The NEB computer program has been modified to include variable spring constants, climbing image, and the FIRE optimizer⁶⁸. The FIRE optimizer improves the rate of convergence of an NEB calculation and it was the optimizer of choice in all NEB calculations. The NEB calculations were stopped when all important maxima along the NEB trajectory had gradients in the range of 1.0×10⁻³ to 5.0×10⁻³ Hartrees/Bohr. This technique was used on molecular clusters to explore the potential energy surface of the acid-catalyzed hydrolysis of atmospherically relevant epoxides in aqueous aerosols⁶⁰. In a similar fashion, it was applied here to find all reactive intermediates and transition states in the reaction coordinate. For acid-catalyzed hydrolysis, clusters were constructed to satisfy all reaction requirements: (1) H₃O⁺ addition to the leaving nitrate group, (2) attack of the H₂O nucleophile along the axis opposite the nitrate leaving group, and (3) an additional water molecule that receives the proton from the protonated alcohol generated after the attacking H₂O bonds with the monoterpene. The simplest cluster to satisfy these requirements involved the ON, H₃O⁺, and two water molecules where the H₃O⁺ hydrogen bonds with the nitrate group and the two water molecules form a hydrogen bond chain with the H₃O⁺ in order to make a backside attack by the lower water molecule possible (Figure S11). An additional four water molecules were added to the cluster to solvate the nitrate and H₃O⁺ as a way of more explicitly accounting for local solvation effects. The H₃O⁺ was replaced with an H₂O molecule for neutral calculations.

Once mechanisms were established using the NEB calculations, more detailed calculations using the larger 6–311++G(d,p) basis set were subsequently conducted on smaller molecular clusters to compute the Gibbs free energies of activation in solution in order to rationalize the pH dependence for different monoterpene-derived ONs. For 1°_BpHN, the neutral cluster consisted of 1°_BpHN and an attacking H₂O molecule below the nitrate function group. In the acid-catalyzed mechanism, H₃O⁺ was hydrogen bonded with the nitrate group. For all tertiary nitrates, the attacking water molecule was removed because it maintains a great distance (> 2.7 Å) in the transition state of the unimolecular (S_N1) mechanism. To estimate the free energies of these smaller clusters immersed in a water dielectric continuum, the ideal gas/rigid rotor/harmonic oscillator (IGRRHO) was invoked. While this theoretical method is designed to account for free energies of gas phase reactions, it has also been successfully applied to the liquid phase reactions without corrections or invoking minor corrections at most⁶⁹. It is likely that the largest uncertainties of the method involve the entropic term because bulk solvation effects are accounted for with continuum models. G16 outputs the Gibbs free energies within the IGRRHO approximation and this was used to compute the liquid phase rate constants within the SMD solvation model.

3. Results and Discussion

3.1. ON hydrolysis results.

The addition of synthetic ON standards to an aqueous solution resulted in hydrolysis of the nitrate functionality. Seven monoterpene-derived ONs (i.e., 1°_BpHN, 2°_ApHN, 2°_ApKN, 2°_LmHN, 3°_ApHN, 3°_LmHN, and 3°_LmKN) were employed to explore hydrolysis processes in bulk solutions. During hydrolysis, as water is in large excess compared to the ONs, the processes can be described by pseudo first-order rate equations (Section S3.4 in SI). For 1°_BpHN, 3°_LmHN, 2°_ApHN, 2°_ApKN, and 2°_LmHN, pseudo first-order decay rate constants (and thus the inverse of lifetimes) were obtained by fitting the monotonically decreasing ON concentration versus time (Figures 1a, 2a, 2b, and S4a). However, the degradation of 3°_LmKN and 3°_ApHN decelerated and reached a constant level in the observed reaction time (Figures S5a and 2c). For these compounds, we employed reversible reaction rate equations to obtain the hydrolysis rate constants and lifetimes (Section S3.4 in SI).

Figure 1.

(a) Pseudo first-order kinetics analysis for hydrolysis of 3°_LmHN in different pH based on NMR results; (b) The hydrolysis rate (min⁻¹) for 3°_LmHN as a function of solution pH. The error bars correspond to 1 standard deviation of measurement.

Figure 2.

(a) Pseudo first-order kinetics analysis for hydrolysis of 1°_BpHN in different pH and formation of BpDo under pH = 5.9; (b) Pseudo first-order kinetics analysis for hydrolysis of 3°_LmHN in different pH and formation of LmDo under pH = 5.9; (c) Reversible kinetics analysis for hydrolysis of 3°_ApHN in different pH and formation of ApDo under pH = 5.9; (d) Pseudo first-order kinetics analysis for hydrolysis of 3°_LmKN in different pH and formation of LkAlc and LkDim under pH = 5.9. All data are from FIGAERO-HR-ToF-CIMS measurements.

The hydrolysis lifetimes under different pH for the ON species studied were shown in Figure S6 and Table 1. A wide range of hydrolysis lifetimes was observed. NMR technique was utilized to measure the hydrolysis rates for all synthetic ON species except 3°_ApHN, due to the overlap of unique proton peak of 3°_ApHN and its product in ¹H NMR. Thus, we used FIGAERO-HR-ToF-CIMS to measure the hydrolysis rate for 3°_ApHN. A subset of compounds were measured by both NMR and FIGAERO-HR-ToF-CIMS: 1°_BpHN, 3°_LmHN, and 3°_LmKN. From NMR measurements, hydrolysis rate constants for fast- hydrolyzable ON (i.e., 1°_BpHN, 3°_LmHN, and 3°_LmKN) ranged from 0.002–0.07 min⁻¹ at neutral pH 7.4 to 0.006–0.18 min⁻¹ at low pH 0.33. The corresponding hydrolysis lifetimes were 13.9 min, 18.1 min, and 7.5 h for 1°_BpHN, 3°_LmHN, and 3°_LmKN in neutral condition, respectively. The difference in hydrolysis lifetime for ONs measured by both NMR and FIGAERO-HR-ToF-CIMS in neutral condition ranged from 8% to 25%, which was within measurement uncertainties of these two techniques⁵⁸ (Figure S7). 3°_ApHN is another fast-hydrolyzable ON with hydrolysis rates of 0.007 min⁻¹ (lifetime 2.5 h) at both neutral pH 7.4 and acidic pH 5.9. Except these fast-hydrolyzable ONs, a number of ONs were observed to be stable under our experimental conditions. Specifically, we did not observe a noticeable depletion of slow-hydrolyzable secondary ONs (i.e., 2°_ApHN, 2°_ApKN, and 2°_LmHN) in NMR for seven days in neutral condition. The degradation of these secondary ONs only took place at low pH with hydrolysis rates up to 7.6×10⁻⁵ min⁻¹ (average lifetime ~10 days), which was slower by up to 4 orders of magnitude relative to the fast-hydrolyzable ONs.

3.2. Factors influencing the rate of hydrolysis.

The acid-catalyzed S_N1 mechanism^22,23,33,38 has been proposed to explain the pH dependence of ON hydrolysis rate constants, in which carbocations were recognized to be the most important intermediate in this mechanism. Carbocations are sp2 hybridized with an empty ‘p’ orbital sitting perpendicular to the molecule. Alkyl substitutions are weak electron donating groups to provide extra electrons to ‘p’ orbital of carbocation to stabilize it. Tertiary carbocation is the most stable carbocation followed by secondary and primary carbocation. Carbocation stability drives the rate of S_N1 hydrolysis reaction⁷⁰. Therefore, the number of alkyl substitution has been suggested to be an important factor influencing the hydrolysis processes with the observation that tertiary ONs have the fastest hydrolysis rates followed by secondary and primary ONs^{22,23,29,33,38,39,43,44}. In our work, the hydrolysis rate constants for most of the ONs (i.e., 2°_ApHN, 2°_ApKN, 2°_LmHN, 3°_LmHN, and 3°_LmKN) showed a linear correlation with pH (Figure 1b and Figure S5b for example), confirming the acid-catalyzed S_N1 mechanism. However, we did not observe pH dependence of the hydrolysis rate constants for 3°_ApHN and 1°_BpHN (Figure S4b). Simultaneously, we found that secondary ONs showed much slower hydrolysis rates than tertiary ONs. This observation demonstrated that the number of alkyl substitution^22,23 is an important factor for ON hydrolysis processes in some extent. However, the observation that the hydrolysis rate for 1°_BpHN was much faster than secondary ONs and even faster than some tertiary ONs (e.g., 3°_LmKN), was not in line with the trend one would expect based on the number of alkyl substitution. These exceptions indicated that other than acid-catalyzed S_N1 mechanism, there are additional factors or mechanisms controlling the hydrolysis processes of monoterpene-derived ONs. In the following, we explore different parameters to explain these unexpected observations.

Carbon skeleton is a possible controlling factor for hydrolysis processes. The short hydrolysis lifetime of 1°_BpHN’s (14 min) compared to other primary ON (several months)^22,23,38 suggested that the allyl skeleton can promote hydrolysis. The same phenomenon was observed in Jacob et al.³³ In their study, the hydrolysis lifetime for C₅ primary allylic HN is 3 min in neutral condition, which is much shorter than primary alkyl HN with same carbon number (>2500 h)²² (Table S2). In addition to their explanation that resonance stabilization of a primary carbocation increased the rate of nucleophilic substitution reaction, we hypothesized that the allyl carbocation promotes the conjugated effect to carbocation. The delocalized electrons in the double bond are conjugated to the ‘p’ orbital of carbocation intermediate to stabilize carbocation and further conduce hydrolysis (Figure 3). The two isomers of β-pinene diol (BpDo) (Figure S8d) formed by Wagner-Meerwein rearrangement⁷¹ further confirmed our proposed mechanism.

Figure 3.

The proposed hydrolysis mechanisms in this work.

Beyond the constraint that the allyl skeleton can stabilize the carbocation to promote hydrolysis of 1°_BpHN via the S_N1 mechanism, the bimolecular mechanism (S_N2) can also contribute to the processes (Figure 3b). In S_N2 reaction, water is the nucleophile to attack the backside of carbon atom to substitute the nitrooxy group directly. Since the rate constants in S_N2 reaction are controlled by steric hindrance, primary alkyl compounds are expected to have the fastest rate constants. Without the participation of the proton, the S_N2 reaction is independent of pH. This is consistent with a lack of correlation between the hydrolysis rate of 1°_BpHN and pH (Figure S4b). This finding suggested that S_N1 reaction and S_N2 reaction are competitive and concurrent for primary ONs.

For secondary and tertiary ONs, acid-catalyzed S_N1 mechanism is the only dominant mechanism to explain the hydrolysis processes with the defining characteristic of the linear correlation between hydrolysis rates and pH. However, we observed the deviation of hydrolysis rates of 3°_LmHN around pH 3–5 from the linear fitting, indicating that the use of buffer can influence hydrolysis as well (Figure 1b). Therefore, we tested three buffer systems with different carbon numbers (acetate, phthalate, and citrate) with pH around 3 for 3°_LmHN to verify our hypothesis (Table S3). We found that even with very similar pH, the hydrolysis lifetimes were different with different buffer solutions: buffer systems with larger carbon numbers had slower hydrolysis rates and longer lifetimes. This observation indicated that water or hydronium (H₃O⁺) is not the only factor to influence hydrolysis rates of ONs. Our results suggested that the hydrolysis processes might not be a simple reaction between water and ONs in the atmosphere, and that organic species (e.g., SOA) in the particle phase might also play a role. More work is warranted to investigate the possible solute effects on hydrolysis.

Since highly functionalized ONs^{16,39,45–47} rather than mono-functional ONs are often detected in the atmosphere, there is a need to evaluate the influence of functional groups on hydrolysis rates of ONs. Here, we systematically compared the hydrolysis rates of monoterpene-derived ONs with similar carbon skeleton but different functionality. This included three tertiary ONs (3°_ApHN, 3°_LmHN, and 3°_LmKN). We found that the hydrolysis rate of 3°_LmHN is the fastest followed by 3°_ApHN and 3°_LmKN. This result indicated that the presence of a hydroxyl group adjacent to the nitrooxy group can conduce but carbonyl group in the same position can slow down hydrolysis processes of ONs. Based on our proposed mechanism (Figure 3 and Scheme S3), although the hydroxyl group is an electron-withdrawing group to destabilize carbocation, the existence of hydroxyl group can introduce both inter- and intra-molecular reactions to promote hydrolysis. For example, 3°_LmHN can undergo both intermolecular reaction to form limonene diol (LmDo) and intramolecular reaction to generate limonene oxide (Figure 3). The increasing LmDo signal detected by FIGAERO-HR-ToF-CIMS (Figure 2b) over the course of the experiment and the three isomers of LmDo (Figure S8b) identified by LC/Orbitrap MS provided the evidence to support our hypothesis. The condition was different for 3°_LmKN: a carbonyl group is an electron-withdrawing group to destabilize carbocation by decreasing the electron density around carbocation to inhibit hydrolysis. Interestingly, we observed the formation of not only limonketone alcohol (LkAcl) but also the dimer of LkAlc (LkDim) from aldol condensation⁷² in both FIGAERO-HR-ToF-CIMS and LC/MS (Figure 2d and Figure S8h). We did not find any evidence to support that the hydrolysis process of 3°_ApHN proceed through intra-molecular reaction producing pinol, which differed from previous work³⁸. We only detected the increase of α-pinene diol (ApDo) signal in FIGAERO-HR-ToF-CIMS and one isomer of α-pinene diol in LC/MS (Figure 2c and Figure S8f). Furthermore, since monoterpene-derived alcohol is the major product of monoterpene-derived ON hydrolysis, the hydrolysis of ONs can potentially increase SOA mass as these alcohols can further undergo sulfation to generate organosulfates⁷³. Meanwhile, HNO₃ is another major product from ON hydrolysis, as confirmed by FIGAERO-HR-ToF-CIMS (Figure S9). HNO₃ can be removed from the atmosphere by wet and dry deposition easily^36,42,43.

Hydrolysis of ONs is first reported to be reversible in this work. We found that the hydrolysis processes for 3°_LmKN and 3°_ApHN were reversible (Figures 3c and S5a). The hydrolysis and esterification of alcohol with HNO₃ can occur simultaneously at comparable rates. Previous work³⁸ reported that the hydrolysis lifetime of 3°_ApHN is 8.8 h by fitting simple pseudo first-order rate equations in neutral condition (pH 6.9). We obtained the same hydrolysis lifetime for 3°_ApHN (8.8 h) by fitting our data (pH 7.4) with pseudo first-order rate equations. However, when we considered this process as reversible with both forward hydrolysis and backward esterification, the hydrolysis lifetime decreased to 2.5 h. By employing the same reversible reaction rate equations to track the degradation process of 3°_ApHN, the hydrolysis lifetime of 3°_ApHN was 2.5 h under pH 5.9. This hydrolysis lifetime further decreased to 9 min when we used the increase of ApDo, which is the major product for hydrolysis, to fit the reversible hydrolysis curve (Section S3.9 in SI). Further work is needed to explore new methods with higher time resolution to verify hydrolysis lifetime of 3°_ApHN in different pH conditions.

3.3. DFT evidence.

In order to further support the proposed ON hydrolysis mechanisms, we employed DFT for two objectives: (1) to classify the reactions for different ONs as S_N1 or S_N2 mechanisms and (2) to predict the pH dependence of hydrolysis for different ONs. For reaction classifications, molecular complexes were constructed and reaction trajectories were computed using the NEB method, which is capable of discerning S_N1 versus S_N2 mechanisms by computing how close the attacking water molecule can approach the monoterpene-derived ONs in the transition state. In this manner, it was shown that the transition state involved the dissociation of the nitrate with a close association of H₃O⁺. For 1°_BpHN, the approach of the attacking water nucleophile was much closer than for 3°_ApHN and its potential energy surface was sharper in the region of the transition state with no discernable carbocation intermediate (Figure S11) which indicated that it exhibited S_N2 character while 3°_ApHN experienced the S_N1 mechanism. The NEB calculations therefore confirmed the general observation that primary and tertiary carbons react via S_N2 and S_N1 mechanisms, respectively.

The second objective of the DFT calculations was to rationalize the pH dependence of the hydrolysis of different ONs. Based on the observation that the lifetimes of different monoterpene-derived ONs may or may not be affected by the pH of the solution, two competing hydrolysis mechanisms (acid-catalyzed or neutral where the nitrate ion dissociates without the assistance of acid) were invoked in DFT calculations. Alkaline-based hydrolysis was not considered here for pH values less than 7.5. The estimated Gibbs free energies of activation for hydrolysis reactions in both neutral and acid conditions for four monoterpene-derived ONs are summarized in Figure 4 and show that the reaction barriers are essentially the same for 3°_ApHN and 1°_BpHN and different for 3°_LmHN and 3°_LmKN. This calculation was consistent with experimental measurements as shown in Figure S6. The absence of a strong pH dependence for 3°_ApHN and 1°_BpHN was attributed to the low neutral barriers relative to the H⁺ barriers indicating that the neutral (pH independent) mechanism will dominate at all pH. However, for 3°_LmHN and 3°_LmKN, the neutral barriers were much larger relative to the H⁺ barriers indicating that at lower pH, the H⁺ mechanism may be favored.

Figure 4.

Estimated Gibbs free energies for four fast-hydrolyzable ONs (i.e., 1°_BpHN, 3°_ApHN, 3°_LmHN, and 3°_LmKN) under neutral and acidic conditions.

For primary nitrates the rate for neutral and acid conditions are respectively given by

$$rat{e}_{1°, \mathit{\text{neutral}}}=k_{2nd \mathit{\text{order}}}\left[ON\right]\left[H_{2}O\right]$$ (1)

$$rat{e}_{1°, H+}=k_{3rd \mathit{\text{order}}}\left[ON\right]\left[H_{2}O\right]\left[H^{+}\right]$$ (2)

The rate is third order for the acid-catalyzed hydrolysis of primary nitrates because the mechanism is S_N2 and also depends on the close interaction of H₃O⁺ where the proton starts to transfer to the nitrate in the transition state. Interestingly, the NEB calculations showed that this does not occur prior to nitrate dissociation. The rates for the tertiary nitrates are similar to primary nitrates except the nucleophile (H₂O) is removed in the expressions:

$$rat{e}_{3°, \mathit{\text{neutral}}}=k_{1st \mathit{\text{order}}}\left[ON\right]$$ (3)

$$rat{e}_{3°, H+}=k_{2nd \mathit{\text{order}}}\left[ON\right]\left[H^{+}\right]$$ (4)

By knowing the pH and water concentration in dilute solutions (~ 55.5 M), the effective first-order rate constants for all mechanisms may be computed and compiled as a function of pH. The inverse of these rate constants yielded the monoterpene-derived ON hydrolysis lifetimes. pH dependent lifetime data was converted to effective first-order rate constants (k_eff) and the logarithm of these were plotted versus pH (Figure S12). The utility of this plot is that in the acid dominated regime, the slope of log(k_eff) versus pH is −1 while it is 0 if the neutral mechanism dominates. In competitive regimes, the slope continuously transitions from −1 to 0. Experimental lifetime data was to fit using the above mechanisms with the only adjustable parameters being the barrier heights for both neutral and acid-catalyzed reactions. Fit and computed barrier heights were compared to analyze discrepancies between experimental and computational results (Figure S13). Figures S12 and S13 show that the computed pH dependent hydrolysis rates and reaction barriers are remarkably close to the fit for 1°_BpHN, reasonably close for 3°_LmHN, and diverge for 3°_ApHN and 3°_LmKN. The computed barriers to hydrolysis are under-predicted for 3°_ApHN (indicating fast reaction rates) although the larger measured values may be caused by the limitation of our measured method. As discussed above, the hydrolysis lifetime can decrease to 9 min by fitting the formation of ApDo instead of the decay of 3°_ApHN.

4. Atmospheric implication

In this study, we systematically investigated hydrolysis of seven synthetic monoterpene-derived ONs. In addition to the number of alkyl substitutions which was the only factor considered in prior studies to control hydrolysis rates of ONs^22,23,33,38, we found that carbon skeleton and the type of the functional group are influential factors controlling hydrolysis rates of ON species. For example, the hyper-conjugation effect in an allyl skeleton can shorten the hydrolysis lifetime of ONs. As benzene-related skeleton contains three delocalized π orbitals which increases the hyper-conjugation effect and stabilizes the carbocation, our results implied that the hydrolysis lifetimes of aromatic-derived nitrates would likely be short. Based on our results, for ONs with the same carbon skeleton and number of alkyl substitutions, those with hydroxyl group adjacent to the nitrooxy group will have a shorter hydrolysis lifetimes than those with carbonyl group in the same position. Overall, the combination of these three influential factors will allow for more accurate predictions of the hydrolysis rates for ambient ONs, which are highly functionalized^{16,39,45–47} with different carbon skeletons. In this work, we confirmed that hydrolysis can be explained via the acid-catalyzed S_N1 mechanism^22,23,33,38. In addition, we found that the competition of S_N1 and S_N2 mechanisms can explain the hydrolysis of primary ONs. Reversible reactions including hydrolysis (forward) and esterification (backward) were also reported to explain the hydrolysis processes of ONs. While HNO₃^74–78 is considered to be the chemical endpoint of the NO_x life cycle in the atmosphere prior to wet or dry deposition, our observation highlighted the possibility that HNO₃ in the particle phase can participate in esterification to generate new nitrogen-containing species⁷⁹. Our results suggested that the hydrolysis process is not a simple reaction that can be explained by a single mechanism in the atmosphere, more work is warranted to investigate the kinetics and mechanisms.

Although ONs are expected to be degraded through different loss processes, hydrolysis is regarded as one of the dominant loss pathways of ONs in atmospheric models by using ambient data as constraints^{16,28,30,34,39,40}. The current regional and global chemical transport models evaluate hydrolysis of monoterpene-derived ONs by two approaches. The first approach³⁹ assumed all ONs are hydrolyzable with a short hydrolysis lifetime (several hours), which overestimated the hydrolysis rates for slow-hydrolyzable ONs. The second approach assumed a hydrolyzable fraction of ONs based on the number of alkyl substitutions. For example, the hydrolyzable fractions of ONs from photooxidation of α-pinene and β-pinene were assumed to be 62% and 92% with 3 or 6 h as the overall hydrolysis lifetimes^28,43. A recent study by Takeuchi and Ng²⁹ reported experimentally constrained parameters for hydrolysis of monoterpene ONs and found that the hydrolyzable fractions of ONs in these systems are much lower than what have been assumed in these prior modeling studies. Specifically, the hydrolyzable fractions and hydrolysis lifetimes were determined to be 23–32% and 27–34% with less than 30 min for α-pinene and β-pinene photooxidation systems, respectively²⁹. In this work, we provided new experimental constraints and insights into hydrolysis mechanisms and how chemical structures impact hydrolysis, facilitating a more explicit representation of monoterpene-derived ON hydrolysis in atmospheric models³⁰. Specifically, monoterpene-derived ONs with different functional groups (e.g., hydroxyl or carbonyl nitrates) or carbon skeleton (e.g., saturated or unsaturated nitrates) can be represented in models with different hydrolysis lifetimes. The loss of ONs through hydrolysis depends on the specific ON isomer and global atmospheric photochemistry can be remarkably sensitive to the hydrolysis of an individual ON. For instance, a recent study by Vasquez at el.⁴⁰ reported that the hydrolysis of a single isoprene-derived HN (1,2-isoprene-derived HN) resulted in the decrease of 40% of NO and 5 ppb of O₃ in a global model. Our work highlighted the importance of considering structural diversity in monoterpene ONs to accurately evaluate their role in global atmospheric chemistry, with respect to nitrogen budget, ozone and SOA formation. We also demonstrated that the capability of DFT calculations to simulate hydrolysis processes for ONs. With limited laboratory measurements with authentic ON standards, DFT calculation will be the crucial tool for studying hydrolysis processes for highly functionalized ONs.

In our measurements, we identified the hydrolysis lifetimes of fast-hydrolyzable ONs ranged from 13.9 min to 8.5 h. However, the hydrolysis lifetimes for slow-hydrolyzable ONs were in the range of 9–17 days even in highly acidic condition. The lifetimes of atmospherically relevant ONs are estimated to be a few hours^{16,28,30,34,39} through field and laboratory analyses, which implies that other potential loss mechanisms of ONs can also be important. To evaluate the role of hydrolysis of ONs in NO_x recycling, we used the Master Chemical Mechanism (MCM, version 3.3.1) and estimation program interface suite (EPI Suite^™, https://www.epa.gov/tsca-screening-tools/epi-suitetm-estimation-program-interface) to estimate lifetimes of both fast and slow-hydrolyzable monoterpene-derived ONs in other processes and compared with our measured hydrolysis lifetimes. Specifically, we evaluated the lifetimes of these ONs with respect to OH photooxidation and ozonolysis in gas phase and they are found to be 1.9–3.2 h and 0.5–18.6 h, respectively (Table S4). Therefore, our reported hydrolysis lifetimes for these fast-hydrolyzable ONs are generally comparable with these other potential loss processes. In contrast, the photochemical lifetime (3.1–26.8 h) and ozonolysis lifetime (18.6 h for 2°_LmHN) for slow-hydrolyzable ONs are much shorter than their hydrolysis lifetime (9–17 days under acidic condition). Therefore, hydrolysis is not the main loss process for these slow-hydrolyzable ONs. As there are currently no experimental measurements on photolysis and oxidation rate constants of monoterpene-derived ONs in gas and particle phases, more work is warranted to investigate the potential loss processes of these ONs including photolysis, photooxidation, hydrolysis, and wet and dry deposition to obtain a comprehensive evaluation of their role in NO_x recycling under ambient conditions.

Synopsis:

This work systematically investigated hydrolysis of synthetic monoterpene-derived ONs and provided new insights into how various factors influence their hydrolysis rates and extended the previously reported hydrolysis mechanisms.