Volatile organic compound conversion by ozone, hydroxyl radicals, and nitrate radicals in residential indoor air: Magnitudes and impacts of oxidant sources

Abstract

Indoor chemistry may be initiated by reactions of ozone (O₃), the hydroxyl radical (OH), or the nitrate radical (NO₃) with volatile organic compounds (VOC). The principal indoor source of O₃ is air exchange, while OH and NO₃ formation are considered as primarily from O₃ reactions with alkenes and nitrogen dioxide (NO₂), respectively. Herein, we used time-averaged models for residences to predict O₃, OH, and NO₃ concentrations and their impacts on conversion of typical residential VOC profiles, within a Monte Carlo framework that varied inputs probabilistically. We accounted for established oxidant sources, as well as explored the importance of two newly realized indoor sources: (i) the photolysis of nitrous acid (HONO) indoors to generate OH and (ii) the reaction of stabilized Criegee intermediates (SCI) with NO₂ to generate NO₃. We found total VOC conversion to be dominated by reactions both with O₃, which almost solely reacted with d-limonene, and also with OH, which reacted with d-limonene, other terpenes, alcohols, aldehydes, and aromatics. VOC oxidation rates increased with air exchange, outdoor O₃, NO₂ and d-limonene sources, and indoor photolysis rates; and they decreased with O₃ deposition and nitric oxide (NO) sources. Photolysis was a strong OH formation mechanism for high NO, NO₂, and HONO settings, but SCI/NO₂ reactions weakly generated NO₃ except for only a few cases.

1. Introduction

Indoor volatile organic compounds (VOCs) are oxidized by ozone (O₃), the hydroxyl radical (OH), or the nitrate radical (NO₃). Indoor chemistry research has mostly focused on O₃/terpene reactions, both because O₃ is easy to generate, manipulate, and measure compared to OH and NO₃ and because terpenes are emitted indoors by building materials and consumer products and are often present at significant indoor concentrations (Baumann et al., 1999; Logue et al., 2011; Singer et al., 2006; Toftum et al., 2008). Also, since O₃/terpene reaction rate constants are about 10⁻⁴–10⁻² ppb⁻¹ h⁻¹, when viewed within the context of typical indoor O₃ concentrations of ~1–50 ppb, reactions with terpenes compete with loss due to air exchange and influence indoor pollutant loadings (Atkinson and Arey, 2003; Weschler, 2000).

While OH/ and NO₃/terpene reaction rate constants are generally four to five orders of magnitude faster, typical indoor OH concentrations (~10⁻⁷–10⁻⁵ ppb) and NO₃ concentrations (~10⁻⁶–10⁻³ ppb) suggest terpenes may react meaningfully with NO₃ as well as O₃ but that reactions of terpenes with OH are too slow to influence terpene conversion for most settings (Nazaroff and Weschler, 2004; Nojgaard, 2010). However, impacts of all three of these oxidants should be considered because OH and NO₃ can react with many VOCs, in contrast with alkene-only O₃ reactions (Atkinson and Arey, 2003). Therefore, the purpose of this work is to challenge the (perhaps implicit) assumption of a limited indoor reaction scheme based mostly on O₃ and NO₃ reactions with terpenes (and alkenes) and explore total VOC conversion by O₃, OH, and NO₃ in typical indoor environments.

Excellent reviews and investigative research on indoor oxidants are available (e.g. Carslaw, 2007; Drakou et al., 2000; Nazaroff and Weschler, 2004; Sarwar et al., 2002; Weschler, 2000, 2011; Weschler and Shields, 1996, 1997). We recount a brief distillation of this literature regarding the influence of O₃, OH, and NO₃ on VOC conversion and indoor chemistry due to gas-phase reactions. After that, we discuss some new, possibly influential advances in our understanding of sources of oxidants indoors, for both OH and NO₃. Finally, we use a modeling analysis within a Monte Carlo framework to estimate the magnitudes and determinants of gas-phase conversion rates of VOCs due to O₃, OH, and NO₃ in typical residences, and explore the impacts of both the established and newer sources of these oxidants.

1.1. Established background on O₃, OH, and NO₃ sources and reactions

The initiator and main driver of indoor chemistry is O₃, which is largely the result of outdoor-to-indoor transport, and indoor O₃ concentrations are often 20–70% of ambient values (Weschler, 2000). Ozone reacts in the gas-phase with alkenes, or it reacts heterogeneously with building materials or surface-sorbed alkenes, such as squalene or monoterpenes (Atkinson and Arey, 2003; Springs et al., 2011; Wang and Morrison, 2006; Wang and Waring, 2014; Waring and Siegel, 2013; Wells et al., 2008; Weschler, 2000; Wisthaler and Weschler, 2010). However, we focus explicitly on gas-phase oxidation of VOCs. Reaction rates of O₃ and indoor-emitted terpenoids have been widely studied, for instance with d-limonene, α- and β-pinene, terpinolene, γ-terpinene, α-terpineol, linalool, and dihydromyrcenol, among others (e.g. Arey et al., 1990; Atkinson, 1990; Atkinson et al., 1990, 1992b; Forester et al., 2006; Grosjean and Grosjean, 1999; Wells, 2005).

The O₃ reacts with the alkene at the carbon double bond following the so-called Criegee mechanism, forming a primary ozonide that cleaves to yield a carbonyl and an excited Criegee intermediate (CI*), also known as a carbonyl oxide (Atkinson and Arey, 2003; Criegee, 1975). That CI* is either quenched to form a stabilized Criegee intermediate (SCI) that may react with water or an oxygenated organic (the ‘SCI channel’); or it can rearrange to form an excited hydroperoxide and then decompose to form an alkyl radical (R•) and OH (the ‘hydroperoxide channel’) (Atkinson and Aschmann, 1993; Atkinson et al., 1992a; Kroll and Seinfeld, 2008). These O₃/alkene reactions are considered the main driver of indoor OH concentrations; due to their short lifetimes, outdoor-to-indoor transport of OH radicals is not a strong indoor source (Carslaw, 2007; Sarwar et al., 2002; Weschler and Shields, 1996).

OH/VOC reactions lead to the formation of alkyl radicals, alkoxy radicals (RO•), peroxy radicals (RO₂•) and other species which transform by decomposition, isomerization, or hydrolysis, leading to the formation of oxygenated compounds, such as alcohols, carbonyls, carboxylic acids, and hydroxycarbonyls (Atkinson and Arey, 2003; Finlayson-Pitts and Pitts, 2000; Forester et al., 2007; Kroll and Seinfeld, 2008; Orlando and Tyndall, 2012; Orlando et al., 2003; Wells, 2005). Oxygenated organics formed by O₃ or OH reactions can be acute or chronic irritants, and they can sorb to surfaces, oxidize further, contribute to aerosol formation, or be removed by air exchange (Aalto-Korte et al., 2005; Anderson et al., 2007, 2012; Bein and Leikauf, 2011; Jakubowski and Czerczak, 2010; Jarvis et al., 2005; Kroll and Seinfeld, 2008; Weschler, 2011). The quantification of OH indoors is challenging, but OH has been predicted or measured at ~10⁻⁷–10⁻⁵ ppb (Carslaw, 2007; Sarwar et al., 2002; Weschler and Shields, 1996, 1997). OH-driven chemistry could play a minor role in terpenoid conversion indoors (Nazaroff and Weschler, 2004), however a recent investigation by Carslaw (2013) suggests that OH and O₃ contribute more or less equally to d-limonene oxidation.

NO₃ is also formed by O₃ reactions, but in this case from O₃ reacting with NO₂ to yield NO₃ and O₂ (Atkinson et al., 1992b; Nazaroff and Cass, 1986; Weschler et al., 1994). After formation, the NO₃ and remaining NO₂ are in equilibrium with dinitrogen pentoxide (N₂O₅), which can also react with water to form nitric acid (HNO₃) indoors (Weschler et al., 1994). NO₃/VOC reactions yield alkyl, alkoxy, and peroxy radicals, and stable carbonyls and oxygenated compounds that may contain organic nitrate groups (Ham, 2013; Harrison and Ham, 2010; Harrison and Wells, 2012; Jones and Ham, 2008). Organic nitrates are ‘under investigated’, but research on health effects and indoor NO_x cycles have emphasized the need for more research (Carslaw, 2007; Carslaw et al., 2012). Like OH, NO₃ is difficult to measure; however, modeling and inference experiments have estimated concentrations with an upper bound of ~10⁻³ ppb (Nojgaard, 2010; Weschler et al., 2006). An average NO₃/terpenoid reaction rate constant of ~10³ ppb⁻¹ h⁻¹ suggests that NO₃/terpenoid chemistry could impact indoor air (Flemmer and Ham, 2012; Ham, 2013; Harrison and Ham, 2010; Jones and Ham, 2008; Nazaroff and Weschler, 2004).

1.2. Recent advances on OH and NO₃ sources

Recent measurements by Alvarez et al. (2013) have identified photolysis of HONO, which is formed from combustion or NO₂ hydrolysis on indoor surfaces (Finlayson-Pitts et al., 2003; Girman et al., 1982; Spicer et al., 1993; Traynor et al., 1982), as a source of indoor OH. Previously, it was assumed that actinic light fluxes indoors attenuating through windows were not strong enough to photolyze HONO. However, to test for this source, OH, O₃, NO₂, NO and HONO concentrations, relative humidity, and the actinic light flux were monitored over time in a classroom setting (Alvarez et al., 2013). HONO photolyzes at wavelengths of ≤405 nm, and light in the range of 340–405 nm was measured. The authors demonstrated that larger calculated HONO photolysis rates corresponded to observed increases in OH. The Alvarez et al. (2013) experiments suggest the possibility of enhanced OH/VOC chemistry in settings with high concentrations of HONO and/or NO₂ and large indoor actinic fluxes, as also recently discussed by Gligorovski and Weschler (2013).

As discussed above, O₃/alkene reactions form stabilized Criegee intermediates (SCI). While the SCI has been an accepted species for nearly 40 years (Criegee, 1975), its indoor reactive chemistry is now being purposefully investigated. Lifetimes of tens of minutes are estimated for SCIs formed from ozonolysis of alkenes, which implies the possibility of CI*-driven chemistry being influential indoors beyond the ‘hydroperoxide channel’ OH formation pathway (Mauldin et al., 2012). The SCI has been shown to oxidize sulfur dioxide (SO₂) to sulfuric acid (H₂SO₄), an important species for outdoor particulate matter formation, and also to oxidize NO₂ to NO₃, which would represent a new source of this radical indoors (Mauldin et al., 2012; Ouyang et al., 2013; Taatjes et al., 2013; Welz et al., 2012). Consideration of these new sources of OH and NO₃ implies that NO₂ may play an even more important and central role in the oxidation of VOCs indoors than previously recognized.

2. Modeling methodology

This section uses the reaction information outlined previously to develop modeling to explore the magnitudes and source strengths of O₃, OH, and NO₃ in residential spaces, as well as the magnitudes and determinants of typical VOC conversion rates by those oxidants. Regarding the new sources discussed above, we include OH due to photolysis of HONO generated by deposition of NO₂ to indoor surfaces or from emissions of gas-fired appliances, as well as NO₃ formation due to SCI reactions. Since the focus of this paper is on gas-phase VOC conversion, we ignore the SCI reactions with indoor SO₂ to yield H₂SO₄, as well as products of surface reactions (with the exception of NO₂ deposition to yield HONO).

2.1. Time-averaged model

A time-averaged model was developed to predict the concentrations of O₃, OH, NO₃, NO, NO₂, HONO, N₂O₅, and SCI, based on the 20 reactions in Table 1. Time-averaged equations compute long-term average values and accommodate periodically cycling inputs that are considered as average values (El Orch et al., 2014; Nazaroff and Klepeis, 2003; Riley et al., 2002). Our model is admittedly a simplified representation of the true kinetics and is not explicit. Explicit or semi-explicit models are less appropriate for this type of many-case screening work due to their computational intensity and are better suited for deep investigation (e.g. Carslaw, 2007, 2013; Carslaw et al., 2012; Sarwar et al., 2002, 2003). Other researchers have used models of complexity similar to ours with good success. Weschler and Shields (1996) predicted a typical OH value at 6.7 × 10⁻⁶ ppb with a non-explicit model, while Sarwar et al. (2002) with their semi-explicit model predicted OH to be within 0.5% of the Weschler and Shields (1996) concentration for the same model inputs.

Table 1.

Reactions considered in the time-averaged model and their rate constants.

No.	Reaction	Rate constant	Source
1	O3 + alkenei → intermediates → OH + SCI + products	Table S1	1
2	OH + VOCi → products	Table S1	1
3	O3 + NO → NO2 + O2	kNO–O3 = 1.6 ppb–1 h–1	2
4	O3 + NO2 → NO3 + O2	kNO2–O3 = 0.0028 ppb–1 h–1	2
5	OH + NO + M → HONO + M	kNO–OH = 2800 ppb–1 h–1	2
6	OH + NO2 + M → HONO2 + M	kNO2–OH = 5300 ppb–1 h–1	2
7	OH + NO3 → HO2 + NO2	kNO3–OH = 2000 ppb–1 h–1	2
8	OH + OH → H2O + O	kOH–OH = 170 ppb–1 h–1	2
9	OH + O3 → HO2 + O2	kO3–OH = 6.0 ppb–1 h–1	2
10	NO3 + VOCi → products	Table S1	1
11	NO3 + NO → 2NO2	kNO–NO3 = 2300 ppb–1 h–1	2
12	NO3 + NO2 → N2O5	kNO2–NO3 = 180 ppb–1 h–1	2
13	N2O5 → NO3 + NO2	kN2O5(d) = 250 h–1	2
14	$2{\mathrm{NO}}_2\left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{aq}\right)\to \mathrm{HONO}\left(\mathrm{aq}\right)+{\mathrm{H}}^{+}+{\mathrm{NO}}_3^{-}$	Table 2 and kNO2·surf(HONO) = 0.055 h–1	3
15	${\mathrm{NO}}_2\left(\mathrm{g}\right)+\mathrm{HONO}\left(\mathrm{aq}\right)\to {\mathrm{H}}^{+}+{\mathrm{NO}}_3^{-}+\mathrm{NO}$	Table 2 and kNO2·surf(NO) = 0.055 h–1	3
16	HONO(aq) ↔ HONO(g)	Not considered in time-averaged model
17	HONO + hv → OH + NO	Table 2	4
18	OH + HONO → H2O + NO2	kHONO-OH = 430 ppb–1 h–1	2
19	SCI + NO2 → NO3 + products	kNO2–SCI = 600 ppb–1 h–1	5
20	SCI + H2O → products	kH2O–SCI = 0.0089 ppb–1 h–1	5

1. Oxidant/VOC reaction rates are from Atkinson and Arey (2003) and the Master Chemical Mechanism v3.2. See the Supplementary Information for specific information.

2. Atkinson et al., 1992b.

3. Spicer et al., 1993.

4. Alvarez et al., 2013.

5. Welz et al., 2012.

To predict O₃, OH, NO₃, NO, NO₂, HONO, N₂O₅, and SCI concentrations, eight time-averaged, mass balances for residences were written, which assume the indoor air is a single well-mixed control volume with air exchange due to a combination of infiltration and natural ventilation. Recirculation air exchange was not considered since we neglect losses within the mechanical system. Some studies have suggested that O₃ can be removed with efficiencies of <~10% by filters in mechanical air handling systems, but these were either conducted with airflow at very low face velocities in laboratory settings or exhibited low O₃ removal (mean removal of <2%) in field settings with single-stage filters (Hyttinen et al., 2003; Zhao et al., 2007). Sorption of VOCs to indoor surfaces is dynamic and not included.

For brevity, we only illustrate a general form of the mass balances used in this work. Time-averaged equations are similar to steady state equations (El Orch et al., 2014; Nazaroff and Klepeis, 2003; Riley et al., 2002), and they are the ratio of the pollutant sources and losses, as demonstrated for a generic pollutant concentration, C_i (ppb), in Equation (1):

$$C_i=\frac{p_i\lambda C_{i,o}+E_i∕\left(V{\Gamma }_i\right)+R_{\mathrm{S},i}}{\lambda +{\beta }_i+R_{\mathrm{L},i}}$$ (1)

where γ (h⁻¹) is the air exchange rate; p_i is the penetration factor of i through the building envelope; C_i,o (ppb) is the outdoor i concentration; E_i (μg/h) is the emission rate of i; V (m³) is the building volume; Γ_i is a conversion factor to change units from μg/m³ to ppb for i; β_i (h⁻¹) is the deposition rate of i; and R_S,i and R_L,i are source and loss chemical reactions for i, respectively. The reaction terms depend on the pollutant i but may include gas- or surface-phase reactions, photolysis, or dissociation (see Table 1).

Using the predicted concentrations of O₃, OH, or NO₃, which are C_O3, C_OH, and C_NO3 (ppb), respectively, the total conversion rate by each oxidant (ox) for all VOCs indoors can be determined by multiplying the respective oxidant concentration, C_ox (ppb), by the sum of the products of each VOC concentration j, C_j (ppb), and its reaction rate constant with that VOC, k_j·ox (ppb⁻¹ h⁻¹). That is:

$$\text{Total VOC conversion rate by each oxidant}=C_{\mathrm{ox}}\sum _j\left(k_{j\cdot \mathrm{ox}}{C}_j\right)$$ (2)

Equation (2) gives an indication of the total effect of an oxidant on indoor gas-phase VOC chemistry, rather than focusing on conversion of a few particular pollutants, such as terpenes alone.

2.2. Monte Carlo method and model input parameters

The model equations were used in four Monte Carlo operations, which run repeated cases of random sampling from probability distributions for input parameters to obtain output distributions, allowing the statistical influence of inputs on results to be quantified. The different Monte Carlo sets considered four residential spaces with different emission scenarios, called R1–R4, including:

• R1: stable indoor background VOCs and variable outdoor O₃ and NO_x concentrations

• R2: stable indoor background VOCs, variable outdoor O₃ and NO_x concentrations, and variable indoor d-limonene concentrations

• R3: stable indoor background VOCs, variable outdoor O₃ and NO_x concentrations, and variable indoor emissions of NO_x and HONO

• R4: stable indoor background VOCs, variable outdoor O₃ and NO_x concentrations, variable indoor d-limonene concentrations, and variable indoor emissions of NO_x and HONO.

We ran 10,000 unique cases for each of the four sets, for which the time-averaged equations were solved simultaneously with an in-house numerical solution program written in the statistical programming software Stata version 11 (StataCorp LP, College Station, TX, USA). Input parameters were best estimates from the literature. Depending on the input parameter type and/or its certainty, some were inputted as single values and some as probability distributions in the Monte Carlo operations.

For reaction rate constants, one value was used based on an indoor temperature of 25 °C (ASHRAE, 2013). Those rate constants are listed in Table 1 for all but the VOC reactions with O₃, OH, and NO₃. Gas-phase reaction rate constants involving oxidation of NO_x and HONO species except for SCI reactions (i.e., Reactions 3–9, 11–13, and 18) were from Atkinson et al. (1992b), while the deposition rate of NO₂ with indoor surfaces (Reactions 14 and 15) and the HONO photolysis rates were inputted as distributions (described below). NO₂ reacts on surfaces with water to produce HONO and NO, and surface production rates were from Spicer et al. (1993). That study reported a value for HONO, but not for NO, so we assumed the same value for NO as HONO production for NO₂ deposition. Gas-phase reactions and rates for SCIs were as in Welz et al. (2012). Due to uncertainty for SCIs from O₃/alkene reactions, we ignored SCI unimolecular decomposition, so the SCI results may be thought of as an upper bound.

Total VOC oxidation rates by O₃, OH, and NO₃ were determined by summing the products of reaction rate constants and median VOC concentrations for typical profiles in residences. The residential VOC concentrations are from Logue et al. (2011), who compiled 91 median concentrations from different studies, and those are listed in the Supplementary Information (SI) in Table S1. Also listed in Table S1 are the oxidant/VOC reaction rate constants, which are from Atkinson and Arey (2003) and the Master Chemical Mechanism v3.2 (Bloss et al., 2005; Jenkin et al., 1997, 2003; Saunders et al., 2003), and molar yields for OH from Weschler and Shields (1996). Additionally, the penetration of O₃ through the building envelope was modeled as constant, starting with the mean value from Stephens et al. (2012) of 0.8 but increasing it to 0.9 because some air exchange in residences is through open windows. The water vapor concentration was set for a relative humidity of 50% at 25 °C.

The Monte Carlo operations used input distributions for the residential air exchange rate and house volume, outdoor O₃ and NO_x concentrations, HONO photolysis rates, deposition rates of O₃ and NO₂ to surfaces, indoor emissions of NO, NO₂, and HONO, and indoor d-limonene concentrations. These parameter distributions were represented as lognormal. Table 2 lists their geometric means (GM) and geometric standard deviations (GSD) and 1st and 99th percentiles.

Table 2.

Lognormal parameters (GM = geometric mean; GSD = geometric standard deviation) for input distributions used in the Monte Carlo analysis, as well as their 1st and 99th percentiles.

Parameter	GM	GSD	1st percentile	99th percentile
λa (h–1)	0.75	2.1	0.128	4.17
CO3,outb (ppb)	25.5	2.31	3.74	142
CNOx,outb (ppb)	6.42	3.52	0.349	116
CNO2,out / CNOx,outb (ppb)	0.704	1.41	0.309	0.987
JHONOc (h–1)	0.2	2.5	0.0239	0.905
βO3d,e (h–1)	2.5	1.5	1.08	6.30
βNO2f (h–1)	1.18	1.5	0.513	2.94
Vg (m3)	387	1.5	153	967
Climh (ppb)	2.5	3.5	2.54	59.0

^aWeisel et al. (2005).

^bEPA (2013), monitoring data for 2012.

^cAlvarez et al. (2013).

^dLee et al. (1999).

^eMorrison et al. (2011).

^fSpicer et al. (1993).

^gUSBC (2011).

^hEstimated from Waring (2014), with distribution truncated for concentrations less than 2.5 ppb.

The air exchange rates, γ (h⁻¹), were fits to values from the Relationship of Indoor, Outdoor and Personal Air (RIOPA) study, which was conducted in the cities of Elizabeth, NJ, Houston, TX, and Los Angeles, CA (Weisel et al., 2005). For R2 and R4 cases, the d-limonene concentration, C_lim (ppb), distribution was estimated according to the ranges in the RIOPA study (Weisel et al., 2005), as used in Waring (2014), but truncated so the concentration was never less than the median background d-limonene concentration (2.5 ppb). For R3 and R4 cases, the residential house volume, V (m³), was estimated from the U.S. American Housing Survey (USBC, 2011) and used with emission rates for a gas-fired burner of NO (89.2 mg/h), NO₂ (136 mg/h) and HONO (3.50 mg/h) from Girman et al. (1982) to determine volume normalized emission rates (E_NO/V, E_NO2/V, and E_HONO/V), considering the burner was used for two hours per day.

The outdoor O₃ concentration (C_O3,out) distribution was the fit of O₃ data from all EPA monitoring stations across the U.S. for 2012 (EPA, 2013). The distributions for the outdoor NO_x concentrations were determined from EPA monitoring data for which there was concurrently available concentrations of NO₂, C_NO2,out (ppb), and NO_x, C_NOx,out (ppb). Using those concentrations, we calculated distributions for C_NOx,out and the ratio of outdoor NO₂ to NO_x, i.e., C_NO2,out/C_NOx,out. Then for each modeling case, the C_NO2,out was determined as C_NOx,out × (C_NO2,out/C_NOx,out), and the C_NO as (C_NOx,out – C_NO2,out).

The distribution for the O₃ deposition rate, β_O3 (h⁻¹), was from Lee et al. (1999) and Morrison et al. (2011), and the GM for the NO₂ deposition rate, β_NO2 (h⁻¹), was from Spicer et al. (1993) and assumed as having the same GSD as β_O3. Surface deposition rates of radicals OH, NO₃, and SCI were all assumed as having the OH base value of 7.06 h⁻¹ from Weschler and Shields (1996) and were varied correspondingly to the O₃ surface deposition rate distribution. The HONO photolysis rate, J_HONO (h⁻¹), was estimated from Alvarez et al. (2013), with the GM being the value observed during all times except for in cases of direct light and the 99th percentile being double their maximum observed value (to represent extremely lit rooms). We want to note that this distribution was taken from one study the literature, so there may be some uncertainty in its range; however, we chose this range to explore its potential impact fully.

3. Results and discussion

3.1. Oxidant concentrations and source strengths

Fig. 1a shows box plots of the log₁₀ of oxidant concentrations for the four Monte Carlo sets. The boxes show the 25th to 75th percentiles, the median is the line in the box middle, the whiskers are values within 1.5 multiplied by the range of the box, and outliers beyond this range are small circles. For O₃, R1 and R2 cases were similar, and concentrations were between 0.70 and 16 ppb for 10th and 90th percentiles; R3 and R4 were similar and that same range fell to 0.058–11 ppb. These O₃ concentrations are lower than in Lee et al. (2002), who measured a mean of 14.9 ppb, though their outdoor concentrations were much higher at an average of 56.5 ppb. Over all cases, the OH range for the same percentiles was between 4.8 × 10⁻⁷ and 8.0 × 10⁻⁶ ppb; for NO₃, the range was between 2.3 × 10⁻⁸ and 7.1 × 10⁻⁵ ppb. The O₃ and OH correspond well to those in previous measurements or modeling (Avol et al., 1998; Sarwar et al., 2002; Weschler, 2000; Weschler and Shields, 1996), but NO₃ is lower than has been suggested by Weschler et al. (2006) and Nojgaard (2010) and is more aligned with concentrations predicted by Carslaw (2007).

Fig. 1.

Box plots of (a) C_O3, C_OH, and C_NO3 for the different Monte Carlo sets R1–R4; (b) VOC oxidation rate by each oxidant for all cases within each set; (c) VOC oxidation rate by each oxidant for high outdoor O₃ and low outdoor NO_x cases only; (d) VOC oxidation rate by each oxidant for low outdoor O₃ and high outdoor NO_x cases only. See text for more details.

The stove emissions in R3 and R4 had a much larger influence on the O₃ concentrations than on the OH or the NO₃ concentrations. The R3 and R4 sets had the lowest average O₃ concentrations because the NO emitted by the gas-fired stove is a dominant O₃ sink. For R1 versus R2, the variable d-limonene concentration had little impact on O₃ overall, since the surface reaction and air exchange losses were more important. The OH concentrations were relatively stable across Monte Carlo sets, but showed a slight trend of R2 > R4, which were both greater than R1 and R3, since there were more O₃/d-limonene reactions in R2 and because OH was formed due to HONO photolysis in R4. The median NO₃ concentration was the greatest for R1, since there was more O₃ available to react with NO₂, though the upper range was higher for R3 for cases with concomitantly high outdoor O₃ and NO₂ emission.

To explore the relative impacts of the different OH and NO₃ formation mechanisms, we show box plots of the distributions of the fractional contribution of each source in Fig. 2. For OH, the sources are (i) alkene ozonolysis or (ii) HONO photolysis. For R1 and R2, the majority OH source was usually alkene ozonolysis, though HONO photolysis had a sizeable impact and sometimes dominated. The source strengths in R1 and R2 had similar distributions, with differences due to larger R2 d-limonene concentrations. However, for R3 and R4, HONO photolysis was the chief OH source due to the stove use that emitted HONO directly as well as emitted NO_x, which led to NO₂ surface deposition and additional HONO formation indoors. When interpreting this result, please keep in mind that some of our scenarios included values for J_HONO from high light fluxes. Regardless, this work shows that this source and its impacts on indoor chemistry deserve serious field investigation in residences with gas appliances.

Fig. 2.

Box plots of fractions contribution of various OH and NO₃ sources considered in the modeling, for the residential R1–R4 settings. For OH, source ‘O₃’ is O₃/alkene reactions; ‘J_HONO’ is HONO photolysis. For NO₃, source ‘O₃’ is O₃/NO₂ reactions; ‘Dis’ is dissociation of N₂O₅; ‘SCI’ is SCI/NO₂ reactions.

We also explored the relative source strengths of NO₃ formed by (i) O₃/NO₂ reactions, (ii) dissociation of N₂O₅ that was formed by NO₃/NO₂ reactions, or (iii) SCI/NO₂ reactions. For NO₃ in sets R1–R4, most all formation was due to O₃/NO₂ reactions. The N₂O₅ dissociation was sometimes important in all four sets as well, though it was the strongest in R3 because of high NO₂ due to stove use and subsequent high formation rates of N₂O₅, concurrent with the lowest O₃/VOC reaction rates. Due to the high d-limonene in R2 and R4 sets that led to more SCI formation, the source of NO₃ due to SCI reactions with NO₂ was important for a small number of cases in those sets alone, implying that the SCI source may not be that influential for NO₃ formation in many environments. Shallcross et al. (2014) predicted that high alkene concentrations in the 100 s ppb were necessary for the SCI source to approach the relative impact of the O₃/NO₂ source. Correspondingly, in R2 and R4, for SCI source to be responsible for ≥0.3 of the NO₃, the d-limonene concentration was always ≥108 ppb. d-Limonene concentrations such as these or higher can be reached during cleaning events (Singer et al., 2006).

3.2. Total VOC conversion rates

A good metric for an oxidant's influence on indoor chemistry is its total VOC oxidation rate (i.e., as in Equation (2)), and an oxidant's generic impact on concentrations can be first-order approximated by dividing the oxidation rate by the air exchange rate. That is, for an air exchange rate of 0.5 h⁻¹, a total VOC oxidation rate of 0.1 ppb/h would increase generic products by 0.2 ppb. Thus, VOC oxidation rates much lower than this will have little influence on product concentrations. We plotted the log₁₀ of the VOC oxidation rates for sets R1–R4 in Fig. 1b. Results illustrate that OH oxidation is as important as O₃ oxidation, and in R3 and R4 sets with NO_x emissions, the VOC conversion due to O₃ is actually lower than for OH since O₃ reacts strongly with NO. Both have ranges for 25th to 75th percentiles between ~0.01 and 1 ppb/h, and their top 25th percentiles are between ~1 and 100 ppb/h. The VOC oxidation rates by NO₃ are roughly an order of magnitude lower than those for O₃ or OH, suggesting that NO₃ reactions only influence indoor VOC conversion for a small subset of results.

Fig. 1b shows distributions for all 10,000 results for the Monte Carlo sets. However, due to the nature of the outdoor photochemical cycle, it is unlikely that high outdoor O₃ is concomitant with high outdoor NO and NO₂. Typically, in the morning high NO and NO₂ are coincident with low O₃, and in the afternoon this trend is reversed (Seinfeld and Pandis, 2006). To explore these parameter combinations, Fig. 1c and d plot high outdoor O₃/low outdoor NO_x cases and low outdoor O₃/high outdoor NO_x cases, respectively; i.e., cases where the distribution of the ratio of C_O3,out/C_NOx,out was >90th percentile or <10th percentile, respectively. The VOC oxidation by O₃, OH, and even NO₃ was higher in Fig. 1c over d, since indoor oxidative chemistry is driven by O₃. Moreover, when outdoor O₃ is low and NO_x is high, OH/VOC oxidation dominates. For NO₃, the highest rates of VOC conversion are for sets R3 and R4 with the large NO_x stove emissions for the high outdoor O₃/low outdoor NO_x cases.

Fig. 3 shows scatter plots of the VOC oxidation rates as functions of indoor concentrations of O₃, NO, and NO₂ for R2 and R4. These plots are useful to discern how the oxidative capacity of residences is affected by changes in O₃ and NO_x concentrations, which are highly variable. Only 100 cases for each Monte Carlo set are displayed so that trends are discernible. In Fig. 2a and d for both sets, VOC oxidation rates by O₃ and NO₃ are always positively correlated to C_O3; OH is strongly correlated to C_O3 for R2 but only weakly for R4, due to the source of OH from photolysis of the HONO in R4. In Fig. 2b and e, all VOC oxidation rates for R2 are uncorrelated to C_NO, yet for R4 those by O₃ and NO₃ oxidation are negatively correlated since NO in R4 is high and it is a large O₃ sink. The VOC oxidation by OH is mostly uncorrelated to C_NO for R4, which is logical since it was uncorrelated to C_O3. For Fig. 2c and f, the only correlations are between VOC oxidation rates by NO₃ with C_NO2 for R2, since there are higher concentrations of O₃ to react with NO₂ to yield NO₃.

Fig. 3.

Scatter plots of the VOC oxidation by O₃, OH, and NO₃ versus C_O3, C_NO, and C_NO2, over the R2 and R4 Monte Carlo sets (showing the first 100 cases only for plot clarity).

3.3. Determinants of oxidant concentrations and total VOC conversion rates

Figs. 1–3 were useful to discern general trends regarding the oxidant concentrations and VOC conversion rates in our results. To explore determinants of the results quantitatively, we conducted a sensitivity analysis. To do so, a multiple linear regression was applied to oxidant concentrations and VOC conversion results for each Monte Carlo set, after natural log-transforming the outcome and predictor variables, which yielded a better fit than regressing non-transformed variables. The predictor variables used in the regressions were {β, C_O3,out, β_O3, C_NO,out, C_NO2,out, β_NO2, J_HONO, C_lim, E_NOY/V}, where E_NOY/V (μg/m³ h) is the sum of E_NO/V, E_NO2/V, and E_HONO/V. The resulting coefficients of determination for all 24 regressions were R² = 0.72–0.95, with a mean (standard deviation) R² = 0.88 (0.070). We only present and discuss R2 and R4.

For our sensitivity analysis, Table 3 lists the standardized regression coefficients (SRC) for R2 and R4 regressions, and their actual regression coefficients are in Table S2 in the SI. The SRC is the actual coefficient normalized by the ratio of the sample standard deviations of the dependent to independent variables. SRCs range from −1 to +1, unless there is a high degree of multicollinearity among the predictor variables (Deegan, 1978), and are useful to compare the relative importance of model inputs on the outcome: a high |SRC| indicates a large influence on the outcome, while a |SRC| near zero indicates no influence, and an input with a −SRC changes the outcome negatively and a +SRC changes the outcome positively. The SRCs for any inputs can be compared, either within one or across different regressions, to quantitatively assess their relative impacts. To aid in the interpretation of SRC results, in Table 3 the SRCs over |0.1| (which are the most influential on the outcome variables) are bolded; also, the greatest positive and negative SRC for each regression is underlined.

Table 3.

Standardized regression coefficients (SRCs) of natural log-transformed inputs regressed against the natural log-transformed outcome variables for sets R2 and R4. The |SRCs| greater than 0.1 are in bold; the greatest positive and negative SRC for each outcome are underlined. See text for variable and set definitions.

Outcomea	Set	λ	C O3,out	β O3	C NO,out	C NO2,out	β NO2	J HONO	C lim	ENOY / V
Standardized regression coefficients for oxidant concentrations for R2 and R4
C O3	R2	0.47	0.76	–0.21	–0.19	–0.080	–0.00053	–0.0052	–0.037
	R4	0.68	0.65	–0.063	–0.088	–0.025	–0.0037	–0.0024	–0.0092	–0.19
C OH	R2	0.45	0.78	–0.23	–0.15	–0.013	0.034	0.075	0.17
	R4	0.25	0.67	–0.091	–0.084	–0.0081	0.12	0.42	–0.00051	–0.059
C NO3	R2	0.53	0.57	–0.15	–0.065	0.44	–0.12	–0.0054	–0.30
	R4	0.66	0.65	–0.061	–0.10	0.041	–0.084	–0.0028	–0.095	–0.15
Standardized regression coefficients for VOC oxidation rates by oxidant for R2 and R4
VOC-ox (O3)	R2	0.43	0.69	–0.19	–0.17	–0.073	–0.00090	–0.0045	0.45
	R4	0.65	0.63	–0.060	–0.085	–0.024	–0.0038	–0.0022	0.31	–0.18
VOC-ox (OH)	R2	0.40	0.69	–0.20	–0.13	–0.012	0.029	0.067	0.50
	R4	0.23	0.61	–0.082	–0.077	–0.0083	0.11	0.38	0.42	–0.055
VOC-ox (NO3)	R2	0.56	0.60	–0.16	–0.068	0.46	–0.13	–0.0055	0.027
	R4	0.66	0.65	–0.060	–0.10	0.041	–0.085	–0.0027	0.12	–0.15

^aConcentrations are units of ppb, oxidation rates in units of ppb/h.

We focus on SRCs for the VOC oxidation rates by O₃, OH, and NO₃. The largest +SRCs for VOC oxidation rates by O₃ or OH are for inputs of air exchange rate (λ) and outdoor O₃ (C_O3,out) and indoor d-limonene (C_lim) concentrations, since increases in λC_O3,out directly increase O₃ concentrations and the reactions of O₃/d-limonene increase O₃ oxidation rates while forming OH. However, VOC oxidation by NO₃ is increased by the sources of λC_O3,out and λC_NO2,out but much less by C_lim, since increasing d-limonene reduces indoor O₃ and NO₃ formation from ozonolysis of NO₂. The parameter J_HONO had a large positive influence for OH/VOC oxidation in R4, due to the photolysis of stove-emitted NO, NO₂, and HONO, though J_HONO is less meaningful in R2 without indoor emissions. The largest −SRCs for R2 are for O₃ deposition rates (β_O3), since this parameter reduces the O₃ that is a dominant component of the sources of all oxidants. For R4 for OH/VOC oxidation, the largest −SRC was also β_O3; however, for O₃/and NO₃/VOC oxidation, it was the stove emission (E_NOY/V) since the emitted NO reduces O₃.

3.4. VOCs most oxidized by O₃, OH, and NO₃ and subsequent products

To contextualize the influences of oxidant/VOC conversion rates on product formation, Table 4 lists for O₃, OH, and NO₃ the ten most oxidized VOCs for the background residential condition, as well as the percentage that each contributes to total VOC oxidation (determined by dividing oxidant-specific VOC reaction rates by the total of that for all VOCs, i.e., (k_j-oxC_j)/(Σ(k_j-oxC_j))). For instance, 68% of all O₃ reactions are with d-limonene. Generally, Table 4 demonstrates that d-limonene is the most oxidized VOC by all oxidants; that monoterpenes are largely responsible for O₃ and NO₃ reactions; and that OH reactions are more varied and favor the oxidation of a few monoterpenes, as well as alcohols, aldehydes, aromatics, and isoprene.

Table 4.

Ranking of the ten most important background VOCs for O₃, OH, and NO₃ loss in residences and the percentage of O₃, OH, and NO₃ loss for which those VOCs are responsible.

Rank	O3/VOCi	% O3 lossa	OH/VOCi	% OH lossb	NO3/VOCi	% NO3 lossc
1	d-Limonene	68%	d-Limonene	24%	d-Limonene	59%
2	α-Pinene	26%	Ethanol	16%	α-Pinene	26%
3	3-Carene	3.3%	Formaldehyde	9.7%	3-Carene	12%
4	Isoprene	1.2%	2-Butanol	9.1%	β-Pinene	1.0%
5	β-Pinene	0.44%	α-Pinene	6.5%	Isoprene	0.96%
6	Styrene	0.38%	Acetaldehyde	6.2%	Styrene	0.48%
7	2-Carene	0.17%	Isoprene	4.1%	Ethanol	0.33%
8	1,3-Butadiene	0.061%	Hexanal	3.4%	2-Carene	0.20%
9	Crotonaldehyde	0.033%	3-Carene	3.4%	2-Butanol	0.074%
10	Acrolein	0.014%	Toluene	1.6%	Acetaldehyde	0.037%

^aTotal loss rate for O₃ to VOCs was 6.6 × 10^–2 h^–1.

^bTotal loss rate for OH to VOCs was 1.5 × 10⁵ h^–1.

^cTotal loss rate for NO₃ to VOCs was 4.5 × 10³ h^–1.

Thus, O₃ almost solely reacts with terpenoids, accounting for an average of 99% of O₃ reactions in residences, again with 68% to D-limonene. Since previous analysis demonstrated that O₃/VOC conversion is important for many settings, the products of d-limonene and α-pinene ozonolysis are likely often elevated. These products include very reactive species such as CI*s and SCIs, as well as OH and hydrogen peroxide and other reactive oxygen species (Chen and Hopke, 2010; Li et al., 2002). Stable products include oxygenated organics such as formaldehyde, 4-acetyl-1-methylcyclohexene, limona ketone, and limonaldehyde (Grosjean et al., 1992; Rohr, 2013). Limonene ozonolysis strongly forms secondary organic aerosol (SOA) (Zhang et al., 2006; Waring et al., 2011; Youssefi and Waring, 2014), and Waring (2014) argued that SOA formation in residences could comprise a sizeable fraction of indoor aerosols when O₃ and d-limonene concentrations were high and air exchange rates were low.

Similarly, NO₃ reacts mostly with d-limonene at 59% and also with other monoterpenes. NO₃/terpene oxidation is dominated by NO₃ addition to the unsaturated C=C bond(s), which forms alkyl, alkoxy, and peroxy radicals before ultimately generating nitrated peroxides, carbonyls, and alcohols and SOA (Bolzacchini et al., 2001; Calogirou et al., 1999; Carslaw et al., 2012; Spittler et al., 2006). Jones and Ham (2008) identified those types of nitrated oxygenated products for NO₃/α-terpineol reactions, as well as identified acetone, glyoxal, methyl glyoxal, and others. However, according to the results in Fig. 1b–d, NO₃/VOC oxidation is about an order of magnitude less influential than for O₃ or OH (except for R3 and R4 with indoor NO_x and HONO emissions), so terpene oxidation and product formation will be typically more driven by O₃ or OH than NO₃ in most settings.

OH oxidizes a much richer suite of VOC types than either O₃ or NO₃ in the typical residence herein. OH/d-limonene reactions are still important, though less dominating than for O₃ or NO₃. The OH/terpene reactions generate formaldehyde, acetone, and other carbonyls, as well as larger oxygenated compounds that form SOA (Grosjean et al., 1992; Leungsakul et al., 2005; Wisthaler et al., 2001). Reactions with alcohols are also a dominant OH pathway, leading to carbonyls such as acetaldehyde and propanal or carboxyl acids such as acetic acid (Azad and Andino, 1999). Also, OH/aldehyde reactions yield hydroperoxyl and peroxyl radicals, as well as acylperoxy radicals, which in the presence of NO₂ can form peroxyacyl nitrates (PAN). OH reactions with toluene can yield peroxy and hydroperoxy radicals, as well as dicarbonyls, cresol, alcohols, and SOA (Bloss et al., 2005; Jang and Kamens, 2001; Jenkin et al., 1997, 2003; Saunders et al., 2003).

4. Conclusions

This study investigated the proportional contribution of VOC oxidation indoors by O₃, OH, and NO₃ within typical residences, by using a Monte Carlo-driven modeling effort with time-averaged equations. The model considered established oxidant sources, as well as newly recognized sources of OH and NO₃ indoors, including OH formation due to HONO photolysis and NO₃ formation due to SCI reactions with NO₂. Our model results demonstrated that OH formation due to photolysis could be important relative to alkene ozonolysis, and even be dominant in residences with stove use. The formation of NO₃ by SCI chemistry was not a substantial source for most indoor settings, with some exceptions occurring with high d-limonene concentrations. The VOC oxidation rates by O₃, OH, and NO₃ very generally increased with air exchange, outdoor O₃ and NO₂ concentrations, indoor d-limonene, and HONO photolysis; and they decreased with O₃ deposition and NO sources.

For our inputs, indoor VOC oxidations rates were dominated by O₃ and OH reactions for most settings, though high stove emissions reduced O₃ importance due to scavenging of O₃ by emitted NO. VOC oxidation by NO₃ was about an order of magnitude less influential than O₃ or OH. When outdoor O₃ was high and NO_x was low, VOC oxidation rates by O₃ and OH were very similar, but when outdoor O₃ was low and NO_x was high, OH/VOC oxidation was the stronger of the two. For O₃ and NO₃, reactions with d-limonene dominate the oxidation pathways; for OH, reactions with terpenes, alcohols, aldehydes, and aromatics were all common indoors. The products most likely to increase indoors due to VOC oxidation are from O₃ and OH reactions, and they are various radicals, reactive oxygen species, carbonyls, carboxylic acids, alcohols, and SOA species.

HIGHLIGHTS.

• Impacts of O₃, OH, and NO₃ on indoor residential VOC conversion were modeled.

• Time averaged equations were used in Monte Carlo modeling for four settings.

• New and established sources of radical oxidants were considered in the modeling.

• Total VOC conversion was dominated by ozonolysis and OH reactions, and not NO₃.

• Source of OH by HONO photolysis was strong, but NO₃ by NO₂ + SCI reactions was not.