The average closed-house AER (for EV1 to EV6) was measured to be 0.5 hour −1 , and v d is estimated to be 1 m hour −1 for a typical SVOC ( 2 , 31 ). Using a typical value of 3 m −1 for S/V ( 2 , 32 ), the expected value of τ, in this case, is estimated to be approximately 1000 s. Given the simplicity of the method and uncertainties in S/V and v d , this response time estimate is consistent with the values measured for small acids. For the conditions in this study, the τ values are predominantly determined by the product v d × S/V, with only minor dependence on AER. We note that there are considerable uncertainties in these assumed values, including the dependence of S/V on the degree of room furnishing and on room size. Uncertainty is also present in how v d varies with the physicochemical characteristics of both the gas and the surface to which uptake/desorption is occurring. During the experiments, the study site was more sparsely furnished than might be common; in addition, there was some instrumentation installed indoors that influenced surface abundance.

The fast response times for the small acids and phenol suggest that their airborne abundances are governed by rapid dynamic partitioning with a surface reservoir that does not have a significant mass transfer constraint. Given the similarity of the response times across a wide range of molecular weights, mass transfer through the air-side boundary layer is likely the rate-determining step in the replenishment process. Other species with considerably longer response times (e.g., ammonia, terpenes, isoprene, furfural, and D5 siloxane) may be more strongly sorbed to a surface or dissolved in a reservoir through which mass transfer is slower, e.g., the organic binder of a paint layer. It is plausible that the matrix may be sufficiently viscous and/or thick to impede the mass transfer rate to a value lower than the air-side mass transfer would yield. In addition, we cannot entirely rule out that relatively inaccessible air volumes slowly supply molecules, leading to their slower response times. However, this explanation for the slower response times seems unlikely, given the open design of the house and the very high internal mixing rates (see Materials and Methods). A response time of several hours was observed for SVOCs in a residence in California ( 8 ). The longer response time for the SVOCs may suggest that, for these SVOCs, gas-phase mass transfer is not rate limiting for air-surface exchange. Instead, diffusion in the indoor surface reservoirs may be the rate-limiting step, different from the behavior of many of the VOCs observed in the present study.

It is well recognized that organic molecules can partition to indoor surfaces ( 2 ), and past work using off-line measurements has illustrated a rebound effect for a variety of hydrocarbons and oxygenated VOCs after a period of EV in simulated and real residential environments ( 3 , 7 ). In the present study, volatile small acids (HONO, HNCO, and C1 to C9 monocarboxylic acids) and many small nonacidic species (ammonia, monoterpenes, isoprene, sesquiterpenes, D5 siloxane, furfural, phenol, and ethanol) all display rapid and repeatable rebounding, evidence of substantial dynamic partitioning of a diverse suite of species between indoor air and surfaces.

Direct evidence from analysis of surface nitrite on glass plates deployed during HOMEChem substantiates the hypothesis that indoor surfaces act as a reservoir for HONO (text S1), in agreement with similar measurements in a previous study ( 17 ). Other studies have also indirectly provided evidence for indoor surfaces being likely sources or reservoirs of carboxylic acids, e.g., elevated indoor carboxylic acid mixing ratios were observed in a university classroom when ventilation was off, likely due to off-gassing from indoor surfaces ( 21 ).

When ventilation is the controlling removal process for indoor air constituents emitted from a constant source, the indoor species should return to a steady-state mixing ratio after an EV period with a characteristic response time equal to the reciprocal of the AER.However, in this study, the establishment of steady-state indoor concentrations after EV occurs much more rapidly than 1/AER independent of the outdoor supply air fan operation status. This observation combines with the consistency of the response signals to demonstrate that there must be one or more large and responsive replenishment reservoirs in the studied indoor environment. Given the rapid response times, these reservoirs are almost certainly associated with either surface films or the outer layers of building materials and furnishings that are able to participate in rapid gas exchange. The repetitive behavior for each EV experiment indicates that the size of the reservoir is substantial, as it is not depleted after the house has been repetitively flushed.

Only the first six EV experiments (EV1 to EV6) are shown. Response times for EV7 are not shown due to the significant change of house conditions, i.e., dehumidification associated with air conditioner operation. The horizontal line and the cross symbol inside each box denote the median and the mean, respectively. The top and bottom boundaries of each box show the third and first quartiles. The top and bottom of the vertical line (i.e., the whisker) show the maximum and minimum data points, respectively. The acids were measured with CIMS (acetic acid measured with iodide CIMS and the others measured with acetate CIMS), and the nonacidic compounds were measured with the PTR-TOF-MS, except for NH 3 , which was measured by cavity ring-down spectroscopy. Data for D5 siloxane in EV1 and EV2 and for acetic acid in EV5 were excluded due to interferences.

The response time constants for all small acids and for phenol ( Fig. 2 ) were similar, on average, between 700 and 1000 s. Several other measured species exhibit a longer response time: NH 3 , sesquiterpenes, monoterpenes, isoprene, D5 siloxane, ethanol, and furfural have response times from 1600 to 2700 s. While the AC operation had some effects on trace gas mixing ratios as described above, the AC (on or off), including its effects on temperature and relative humidity, showed little influence on the response times of any of the gases after periods of EV (EV1 versus EV2 to EV6). For all species, there was no pronounced dependence of the response times on light levels (dark versus illuminated indoors) or the outdoor supply air fan operation (on or off).

Time constants for return to steady state. Until recently, indoor VOC and SVOC concentrations were largely made via off-line methods with limited time resolution. A key advantage of high time-resolution data from CIMS, PTR-TOF-MS, and on-line spectroscopic methods is the ability to quantify dynamic response times needed to reestablish steady-state conditions after ventilation perturbations. We have assessed response times by fitting exponential growth curves to mixing ratio data when the house was closed after periods of EV. Because of the temperature dependence of the observed indoor mixing ratios as the house warmed during the day, the original data were detrended to minimize the influence of temperature (see details in text S2 and fig. S2).

The operation of the outdoor supply air fan was intended to change the air exchange rate (AER) by either mechanical ventilation (fan on) or infiltration (fan off) (see Materials and Methods). With the outdoor supply air fan on for EV3 to EV6, there is only a slightly higher AER (on average 0.53 ± 0.06 hour −1 through mechanical ventilation) compared to EV1 and EV2 when the fan was off (on average 0.45 ± 0.02 hour −1 , due to infiltration) (table S2). The steady-state mixing ratio of measured species is not sensitive to the small difference in AER when outdoor supply air fan was on or off. Note also that the presence or absence of light in the house had no clear effect on the steady-state mixing ratios (compare EV1 to EV4 versus EV5 to EV7).

The steady-state mixing ratios for all species during the recovery period after each EV episode are similar across the course of the day, with small upward trends associated with and possibly attributable to increased house temperature with the air conditioning (AC) off. The increasing steady-state signal with increasing temperature, as reported previously for phthalates in the same test house ( 14 ), is likely due to a shift in partitioning between air and condensed-phase surface reservoirs. The nature of the surface reservoirs is discussed below. Note that the decrease of the steady-state concentrations for the small acids in Fig. 1 and fig. S1A after experiment EV7 is attributed to the operation of AC, i.e., through removal of water-soluble organic gases (WSOGs) by dissolution into condensing water during dehumidification. A similar decrease was observed for NH 3 and some neutral oxygenated species with relatively large water solubility, including phenol, ethanol, and furfural, and the effects were less pronounced for sparingly water-soluble species such as isoprene and monoterpenes (fig. S1B). These observations support the inference that AC can act as a sink for indoor WSOGs under humid conditions, as was demonstrated in another recent study ( 13 ).

A full list of compounds and their physicochemical properties is provided in table S1. Table S2 summarizes the average mixing ratios of individual species in indoor air during the EV and closed-house periods and in outdoor air. For example, the indoor mixing ratio of HONO at steady state after the first six EV periods (EV1 to EV6) was between 3.7 and 4.3 parts per billion (ppb), while the average outdoor mixing ratio was 0.57 ± 0.07 ppb. These abundances are similar to those previously reported ( 17 ). The mixing ratios of HONO during the EV period reflect the influence of outdoor air dilution on indoor HONO levels. In particular, indoor HONO decreased to ~1 ppb during the first EV period (EV1) and was slightly higher during subsequent experiments, especially in experiments EV4 to EV6. This observed increase in levels during EV is likely due to less indoor-outdoor air exchange during the last three experiments, arising from slower local wind speeds (table S2). Similarly, mixing ratios of other compounds during the EV periods in EV4 to EV6 were higher than those in EV1 to EV3. The steady-state indoor mixing ratio of HNCO varied between 0.09 and 0.11 ppb, larger than the average outdoor mixing ratio of 0.04 ± 0.01 ppb. These HNCO measurement results are similar to a median mixing ratio of 0.15 ppb reported in a Toronto residence ( 30 ). There is a relatively high indoor mixing ratio of formic acid (21 to 38 ppb) compared to a lower outdoor level (1.7 to 4.3 ppb).

The top panel shows the measured house temperature (T; left axis), relative humidity (RH; right axis), and absolute humidity (AH; second right axis). Temperature and RH were measured in the kitchen within 1 m of the CIMS inlet. The shaded areas indicate when doors and windows were open to increase the ventilation rate of the house. The hourly 2-min background measurement (measuring zero air) is shown with purple dots, followed by a 5-min outdoor measurement (orange dots). The average air exchange rate (AER) when the house is closed following each EV experiment is summarized in table S2. The color bars at the bottom of the plot show the state of outdoor air supply fan (on/off), window light (with/without), and air conditioning (AC) (on/off) during the experiment, with the green shaded periods showing when the fan, window light, and AC were off.

Indoor air mixing ratios. Time-of-flight (TOF) chemical ionization mass spectrometers (CIMSs) measured the mixing ratios of gas-phase acids during the HOMEChem campaign at the UTest house in Austin, Texas. A proton transfer reaction–TOF–MS (PTR-TOF-MS) measured nonacidic organic molecules; ammonia mixing ratios were determined by cavity ring-down spectroscopy (see Materials and Methods). The signals of each species decreased immediately upon enhancing the rate of ventilation by opening windows and doors and rapidly returned to the vicinity of their starting values upon shutting the windows and doors. Figure 1 illustrates this behavior for several acidic gases; other carboxylic acids, nonacidic species, and ammonia exhibit similar responses (fig. S1). Outdoor mixing ratios of all the measured species (the orange dots in Fig. 1 ) were lower than indoor levels, consistent with the observed decrease of indoor levels during EV. This evidence confirms that these chemicals are all emitted or formed indoors.

Increasing surface pH by ammonia spraying, attributable to uptake of elevated gas-phase NH 3 (fig. S5), had an opposite yet less pronounced effect on the air-surface partitioning, which may be due to the fact that many of the acids are already dissociated on the surface. In experiments AB2 and AB4, the ammonia cleaner was used immediately after vinegar mopping, and the effects of ammonia spraying were attenuated. In experiment AB3, the mixing ratios were influenced when the ammonia cleaner was applied before vinegar mopping as compared to the vinegar mopping case alone. We note that the observed rebound dynamics after EV periods are different on the cleaning day than on the EV day, potentially affected by the different nature of the surfaces, the role of AC, or the residual presence of cleaning agents.

After the first mopping experiment, HONO and HNCO increased substantially from 4.5 and 0.13 ppb (average for 15 min before mopping starts) to maxima of 15 and 0.48 ppb, respectively. The degree of increase became progressively smaller from experiment AB1 to AB4 for HONO and HNCO (fig. S4), although an increasing amount of vinegar was used and acetic acid mixing ratios in the air did not decrease (table S3 and fig. S5). It is possible that the surface pH and composition changed after mopping repetitively. Formic acid did not exhibit the same trend, possibly because it has a larger Henry’s law constant and is less volatile than HONO and HNCO (table S1). In addition, formic acid was influenced considerably by the AC system, for example, during the first mopping experiment, making it difficult to accurately quantify the influence of vinegar mopping separate from the influence of condensed water on the AC cooling coils.

The increase of gas-phase acids during vinegar mopping suggests that indoor surface reservoirs, specifically those with a substantial condensed water component, act as a transient source of these small acids. In particular, the data are consistent with an inference that acetic acid (pK a = 4.75) from the vinegar affects the pH of indoor surfaces by the uptake of gas-phase acetic acid (see fig. S5), resulting in acidified polar reservoirs. There may also be comparable effects arising directly from the application of acetic acid to the surface being mopped. The elevated HONO, HNCO, and HCOOH signals during vinegar mopping are consistent with their low pK a values (pK a < 4) as compared with the other acids (pK a > 4.8) (table S1). These stronger sorbed acids (HONO, HNCO, and HCOOH) are likely in the dissociated form before vinegar mopping. Decreasing surface pH leads to their protonation, shifting the air-surface partitioning toward the gas phase.

AB1 to AB4 represent four acid-base experiments. The shaded areas show when doors and windows were open to enhance house ventilation (blue). Times of mopping the floor with vinegar solution (green) and spraying ammonia on indoor surfaces (pink) are also indicated. Mixing ratios measured in outdoor air and for zero air are denoted by orange and purple dots. The top panel shows the RH and temperature measured in the kitchen. The AC system was turned off during the two ventilation periods.

On another day during the HOMEChem campaign (26 June 2018), the house floor was mopped with vinegar solutions four times (see Materials and Methods). This activity presumably alters indoor surface reservoir pH through the partitioning of enhanced levels of gas-phase acetic acid. The gas-phase mixing ratios of HONO, HNCO, and HCOOH increased during and following vinegar mopping; there was either only a small increase or no obvious change for weaker acids and for nonacidic species ( Fig. 3 and fig. S3). The ratios of the concentrations during mopping to the average steady-state concentrations during 15 min before mopping are shown in fig. S4. A ratio above 1.0 indicates an increase attributable to the mopping procedure. The increase of acid signals occurred during all four experiments when different amounts of vinegar were used (table S3).

Distribution of indoor volatile species between air and surface reservoirs

There are many surface reservoirs into which gas-phase compounds might partition. For example, organic films on indoor surfaces have been identified as temporary storage reservoirs for SVOCs (2, 10). For more water-soluble species, such as the small acids included in this work, a water-rich surface film would similarly enhance the uptake of water-soluble gases from indoor air. Situated below organic and water-rich surface films exist indoor finishing materials, such as paint, wallboard, flooring, and furnishings, which provide additional potential reservoirs. It is possible that bulk water, commonly present in the kitchen, bathroom, or AC system, could also participate as a sorptive substrate.

To display the distribution of chemicals in indoor environments and to assist in interpreting experimental observations, we apply two-dimensional chemical partitioning space plots, previously used to assess the phase distribution of organic compounds in the atmosphere (see text S3 for details) (18, 33). A few key assumptions are applied in the analysis. (i) We assume that polar and weakly polar partitioning media of variable volumes are present indoors; their geometry is irrelevant for the present purposes. We use liquid water and octanol as surrogates for these media, recognizing that this description simplifies a much more chemically complex system. Octanol is a surrogate for a weakly polar sorbing material, such as paint. Water is a surrogate for a more polar medium, such as hydrated gypsum in wallboard. (ii) Partitioning among indoor air, the polar reservoir and the weakly polar reservoir are assumed to be the only processes affecting gas-phase concentrations. We allow acid-base dissociation to occur in polar phase as in a liquid-water phase. (iii) The analysis assumes equilibrium partitioning between indoor air and surface reservoirs. The partitioning space plot is a useful graphical tool to display where a chemical resides under thermodynamic equilibrium conditions.

In Fig. 4, all chemical species are placed in the partitioning space plot based on their respective values of log K wa (water-air partitioning coefficient, i.e., Henry’s law constant) and log K oa (table S1). The dashed lines in each plot indicate boundaries for different fractions of compounds, with their location dependent on the relative volume of weakly polar, polar, and gas phases. Chemicals located on the boundary lines between two different color regions exist with equal abundance in the two phases. Chemicals located in the darkest pink, green, and blue regions of the plot have >99% abundance in one specific phase. Those areas more gently shaded pink, green, and blue have between 50 and 99% abundance in one specific phase, as indicated in the plot. The white central triangle shows the transition region where less than 50% is present in each of the three phases.

Fig. 4 Partitioning space plots. (A) An indoor environment with 1.5 × 10−7 m3 of weakly polar and polar reservoirs each per cubic meter of air, without acid and base dissociation; (B) same volume of polar and weakly polar reservoirs as in (A), but considering acid and base dissociation in the polar reservoir; (C) 7.5 × 10−6 m3 and 1.5 × 10−6 m3 of weakly polar and polar reservoir per cubic meter of air, respectively, with acid and base dissociation; and (D) a highly polluted outdoor environment with 100 mg m–3 each for liquid water and organic content in the ambient aerosol [phase separated into organic (represented by octanol) and water phase (51)], with acid and base dissociation. Names of the individual species are labeled in (A), with C1 to C9 representing monocarboxylic acids with one to nine carbons; their locations shift slightly in (B) and (C) relative to the boundaries, but the ordering does not change. The dashed lines in the space indicate boundaries for different fractions of compounds in each phase, and the blue text shows the fraction in gas versus polar phase for the dashed line below the blue label. The different symbols in (B) to (D) indicate the assumed pH of the polar phase, as indicated in the legend. Note that, in (D), the range of log K wa and log K oa is expanded to 13, as compared to 10 in (A) to (C).

The results in Fig. 4A predict that many species would be in the gas phase indoors under the assumed conditions, whereas the sequential EV perturbation experiments indicate instead that these molecules reside primarily in surface reservoirs. Whereas in Fig. 4A all molecules were assumed to be in their undissociated state, in both Fig. 4, B and C, we allow acids to dissociate at the specified pH of the polar reservoir and for ammonia to become protonated, according to the effective Henry’s law constant [K eff,wa = K wa (1 + 10pH-pKa) for acids, and K eff,wa = K wa (1 + 10pKa-pH) for bases, where pK a is for the protonated form of the base, e.g., NH 4 + ]. Figure 4C assumes much larger reservoir volumes than in Fig. 4 (A and B). Overall, the predictions in Fig. 4C are more consistent with the experimental observations as to whether a molecule is predicted to be in the gas phase or in a surface reservoir, with notable exceptions of isoprene and the monoterpenes.

The influence of acid dissociation on phase distribution is particularly large for the more acidic compounds with smaller values of K oa , i.e., those not predominantly in the weakly polar, organic phase. The overall effect is to move the location of the chemicals much closer to the polar phase portion of the plot, depending on the assumed pH of surface water. The effect is stronger for HONO, HNCO, and HCOOH than for the C3 to C9 acids, because they are located toward the left region of the partitioning space plots (in the polar phase component of the plot) and they have lower pK a values than the C3 to C9 acids (table S1). Trends displayed in the partitioning plots are consistent with findings from the vinegar mopping experiments, during which the largest changes in gas-phase concentration with mopping were observed for these lower pK a species. By contrast, the C3 to C9 acids are more likely partitioned to the weakly polar, organic reservoirs in the house and thus experience less change upon vinegar mopping. Including the effect of protonation for NH 3 shifts its distribution notably into the polar reservoir with pH between 4 and 7. Other polar phase interactions, such as hydration, hydrolysis, salt effects, and house conditions (e.g., temperature change), could also influence the air-surface partitioning (34–37).

If the polar reservoir consisted of uniformly thick liquid water films existing throughout the house (with an assumed S/V of 3 m−1), then they would be 50 nm thick in Fig. 4, A and B and 500 nm thick in Fig. 4C. The corresponding total volume is equivalent to 35 and 350 cm3 of aqueous water in the studied house (235 m3 volume), respectively. Aqueous surface films as thick as 50 and 500 nm are improbable. On the other hand, some water will certainly be sorbed to hygroscopic building materials such as gypsum wallboard, sorbed on furnishing fabrics, condensed in the AC system, and present in other forms of bulk water such as on sink surfaces and in sink drains. Regardless of its precise location, the results in Fig. 4 suggest that a large amount of condensed water (or other polar media) must exist in order for more water-soluble/polar molecules with low K oa values, such as NH 3 , HONO, HNCO, and HCOOH, to reside in a partitioning reservoir that exhibits rapid reversibility of the type exhibited in these experiments.

Similarly, if the weakly polar reservoir consisted entirely of a uniform organic film over all indoor surfaces, the film would be thick, specifically 2500 nm for the conditions in Fig. 4C. Current estimates for the thickness of deposited organic films on indoor surfaces are much smaller, on the order of a few tens of nanometers or less (10). Thus, under the assumptions of our model, there must be a larger organic reservoir prevalent indoors. This organic reservoir could be thicker organic films in the kitchen associated with cooking or it may be present in the building materials and surfaces that underlie condensed organic films (38, 39). A potential candidate is the painted walls and ceiling, ubiquitous in indoor environments, consisting of a viscous matrix of paint binder and pigment. Previous studies measured drywall paint thickness to be on the order of 30 to 50 μm (40), i.e., representing an organic reservoir volume much larger than assumed in modeling above. If only a fraction of that paint layer is available for rapidly reversible surface partitioning, then it could represent an important reservoir for compounds with low water solubility and large K oa values. Predictions for partitioning to a 50-μm-thick organic film demonstrate the maximum potential effect (see fig. S6), and in this case, most chemicals (except for NH 3 , HONO, HNCO, ethanol, β-pinene, and isoprene) would be predominantly present in the large organic, weakly polar reservoir.