PUF disks were purchased from Sibata Scientific Technology LTD (Saitama, Japan). n-Hexane (HPLC solvent grade) was purchased from Daejung Chemical & Metals Co. (Siheung, Korea). Naphthalene (≥99%) and naphthalene-d8 (≥98%) were purchased from Sigma-Aldrich (St Louis, MO, USA). Ball-shaped naphthalene deodorants were purchased from a local market in Seoul, Korea.

The rate of emission of naphthalene from a naphthalene ball (R_emission, mg h^-1 ball^-1) to the air in public toilets was estimated using a mass transfer equation:

where k_air is the mass transfer coefficient of naphthalene in air (m s^-1), A is surface area of a naphthalene ball (m²), Cairsurface is the atmospheric concentration at the surface of the ball (mmol m^-3), Cair∞ is atmospheric concentration of well-mixed air far from the ball (mmol m m^-3), and MW is the molecular weight of naphthalene (mg mmol^-1). Assuming that naphthalene is an ideal gas, equation (1) becomes

where R is the ideal gas constant (8.314 Pa m³ mol^-1 K^-1), T is the absolute temperature (K), ranging from 291 to 298 K, p° is the vapor pressure of naphthalene (Pa), and p^∞ is the partial pressure of naphthalene in bulk air, which was assumed to be close to zero.

The mass transfer coefficient (k_air) was estimated using the film diffusion theory for spherical coordinates:

where D_a is the diffusion coefficient of naphthalene (m² s^–1), r is the radius of a naphthalene ball (m), and δ is the thickness of the air boundary around the naphthalene ball (m). As D_a depends on the temperature, Cho et al. developed an equation to estimate D_a derived from 59 experimental data [20]:

where the coefficient of correlation between T and D_a is 0.981 in the temperature range 288–337 K. The value of δ was assumed to be on the order of a centimeter, i.e., 0.01–0.1 m, and uniformly distributed. From visual observations, the uniform range of r was assumed to be 0.005–0.04 m.

In earlier studies, the value of p° was measured at different temperatures, and equations correlating p° with temperature has been derived [21]. The equation by Macknick and Prausnitz was chosen for this study, because it has the least uncertainty (1.1% within the temperature range 280–304 K), and it covers a wide ambient temperature range [22]:

The parameters used in the modeling of R_emission are listed in Table 1.

The value of R_emission was also derived from triplicate measurements of the mass loss of a naphthalene ball in an experimental chamber over time. A custom-made acrylic chamber (inner volume: 125 L) with a mechanical fan and inlet and outlet ports for air flow was used. A naphthalene ball with a diameter of 0.04 m was placed on a polypropylene weighing boat on the floor of the chamber, and its mass was measured daily for three days. Air was pumped out by applying a negative pressure to the chamber using a vacuum pump. A flow meter was connected to measure the volumetric flow rates; the rate was adjusted to 20, 30, or 40 L min^–1 (corresponding air change rates of 10, 14.4, and 19.2 h^–1, respectively). The ambient temperature and relative humidity in the chamber were measured using a hygro-thermometer and ranged between 14 and 21.2°C and between 10% and 38%.

The steady-state atmospheric concentration of naphthalene in public toilets (C_in, mg m^–3) was estimated using a simple mass balance equation considering the production and elimination rates of naphthalene [23].

where C_out is the outdoor concentration (mg m^–3), which is so smaller than C_in as to be negligible, n_toilet is the number of naphthalene balls in one cubic meter of public toilet (balls m^–3), and k_e is the overall elimination rate constant (h^–1) [24]. For simplicity, it was assumed that air exchange was the dominant process for the elimination of naphthalene from toilet air. The volume of public toilets and total number of deodorant balls in the toilets were estimated by surveying 20 public toilets in Seoul, Korea. The calculated distribution of R_emission using equation 2 was used in the calculation of C_in (equation 6). The plausible range of k_e was assumed to be 7–15 h^–1 assuming a well-ventilated condition with completely opened windows and mechanical fans in the public toilets [25]. The parameters used in the modeling of C_in are also listed in Table 1.

The mass of the PUF-PAS disks was measured before their deployment in the toilets (3.11±0.18 g). A dark-colored plastic dome that served as a housing for the PUF-PAS was connected above each PUF-PAS disk with a fishing line to reduce potential environmental effects such as light, air flow, or coarse particles (Figure S1a, Supplementary Material) [26]. The open side of the housing enabled air to circulate around the PUF-PAS disk so as not to delay equilibrium. Nine public toilets where deodorant balls were deployed and frequently replenished were chosen for PUF-PAS monitoring. PUF-PAS with housings were deployed inside the toilets for seven days in triplicate (Figure S1b, c, Supplementary Material). The duration of seven days was chosen based on preliminary testing, in which chemical equilibrium between the air and PUF-PAS was reached in less than seven days (see Supplementary Material). The PUF-PAS was collected and immediately placed into an amber glass bottle containing 290 mL n-hexane without headspace. The bottles containing the PUF-PAS in n-hexane were extracted at 25°C and 150 rpm for ≥18 h. Naphthalene-d8 in n-hexane was added to the PUF-PAS extract as an internal standard before concentrating the extract. The combined extracts were concentrated to 2 mL using a rotary evaporator and a gentle N₂ gas stream.

The extracts were quantified using an Agilent 7890A gas chromatograph coupled with a 5975C series mass spectrometer (GC-MS; Santa Clara, CA, USA). An Agilent HP-5MS 5% phenyl methyl siloxane capillary column (30 m×0.25 mm ID×0.25 μm film thickness; Santa Clara, CA, USA) was used. Helium was used as the carrier gas at a flow rate of 3 mL min^–1. The injection volume of the sample was 2 μL, and the temperatures of the inlet and the detector were 250°C and 280°C, respectively. The oven temperature was initially held at 50°C, then ramped to 150°C at 10°C min^–1, further increased to 280°C at 20°C min^–1, and then held at 280°C for 6 min. The mass scan range was 35– 550 m/z, and data was extracted at 128 and 136 m/z for naphthalene and naphthalene-d8, respectively. The naphthalene concentrations in the n-hexane extracts were converted into the atmospheric concentration using the partition coefficient value (log K_PUF-air=4.4) measured by Parnis et al. [27].

To define the method detection limit (MDL) of PUF-PAS, seven PUF-PAS disks were spiked with 100 μL of a 14 mg L^-1 solution of naphthalene in n-hexane, and extracted using the same procedure as used for the real samples. The MDL of PUF-PAS for naphthalene (996 mg m_PUF^-3) was obtained from standard deviation of the spiked samples multiplied by 3.14 [28]. The corresponding value of C_in was 63 ng m^-3. Naphthalene was not detected above the MDL in blank PUF-PAS extracts. The extracts were calibrated using the internal standard naphthalene-d8. The external and internal standards covered the ranges 0.8–800 and 0.6–62 mg L_n-hexane^-1, respectively, and linear regression resulted in an R² value of greater than 0.99. For quality control, the sample with the third-highest external standard concentration among every five samples was analyzed as a control standard, and the coefficient of variance was less than 10%.

The main route of naphthalene intake by humans is the inhalation of atmospheric naphthalene. The exposure concentration (EC; mg m^–3) was calculated as:

where C_in is the concentration of naphthalene in toilet air (mg m^–3), ET is exposure time (h day^–1), EF is exposure frequency (d ^y–1), ED is exposure duration (year), and AT is averaging time (d) [29]. Details of the parameters used in the two exposure scenarios are shown in Table 2. Koreans’ average time in certain locations, and life expectancy were used for establishing the exposure scenarios [30,31]. Average values of time in locations and in activities related to dermal exposure to water were used to infer the average time spent in toilets, denoted by ET [30]. For the general population, the average EF and ET values in public toilets can be estimated as the average frequency and time spent on face washing. The life expectancy of Korean people estimated in 2016 by Statistics Korea was used for ED and AT [31]. When a representative value for a parameter was not available, assumed parameters were used for the development of the exposure scenarios. For public toilet cleaning staff, their exposure time can be assumed to be eight hours a day, five days a week.

The inhalation unit risk used in this study was established by the Office of Environmental Health Hazard Assessment (OEHHA) [32]. Briefly, studies of cancer related to naphthalene inhalation conducted by the NTP involved exposing male mice to up to 30 ppm naphthalene for 6 h per day, 5 days per week for 104 weeks. The human cancer potency of naphthalene was derived using a linearized multistage procedure based on the values of the increased incidences of nasal respiratory epithelial adenoma and nasal olfactory epithelial neuroblastoma in the mice. Then, OEHHA calculated the inhalation unit risk for naphthalene inhalation exposure as 3.4×10^–2 (mg m^–3)^–1. The excess inhalation cancer risk can be estimated by multiplying inhalation unit risk and EC.

The uncertainties in the estimation of R_emission, C_in, and the corresponding cancer risk were assessed by Monte Carlo simulation using R program [33]. Based on randomly selected values from the assumed distribution of each parameter, 50,000 iterations were conducted.

The distribution of R_emission was created using equation 1 and Monte-Carlo simulation (n = 50,000) (Figure 1). The mean and median values of R_emission were 5.3 and 2.4 mg h^–1 ball^–1, and the 90% confidence interval (CI) ranged from 0.18 to 19.48 mg h^–1 ball^–1. This distribution agreed well with the values of R_emission determined experimentally using a chamber study. The obtained experimental R_emission values were 5.96, 6.55, and 12.43 mg h^–1 ball^–1 at air change rates of 10, 14.4, and 19.2 h^–1, respectively. It was observed that R_emission increased with increasing air change rate. This could be explained by the increase in k_air in equation 2. Increasing the volume flow rate would reduce the thickness of the air boundary layer (δ), thus increasing k_air. The decrease in p^∞ would have a negligible effect on R_emission at such high air change rates. The measured R_emission also agreed well with that of Jo et al., who reported an emission rate of 5.3– 6.3 mg h^–1 at an air change rate of 0.5–2 h^–1 [6].

Based on the estimated distribution of R_emission, the distribution of C_in was also created using Monte-Carlo simulation (n = 50,000) (Figure 2a). The mean and median values of C_in were 0.18 and 0.07 mg m^–3 (90% CI: 0.0043–0.70).

The naphthalene concentration measured using PUF-PAS was above the MDL in seven of the nine toilets evaluated. In order to create a distribution of C_in based on field monitoring (Figure 2b), the C_in values below the MDL were assumed to be half the MDL (0.031 μg m^–3). The mean and median values were 0.0013 and 0.0076 mg m^-3, and the maximum value was 0.030 mg m^–3. It is noteworthy that the values of C_in measured using PUF-PAS were approximately two orders of magnitude lower than the range of values estimated in Section 3.1. The existence of other removal processes is supported by earlier studies, in which removal processes such as photolysis, oxidation, or sorption were suggested to be important [34,35]. Although the elimination of naphthalene via indirect photolysis might be possible, the photodegradation of naphthalene would be negligible because the photolysis rate constant with hydroxyl radical obtained using EPISuite^TM from the US Environmental Protection Agency (US EPA) under natural sunlight is only 0.12 h^–1 [36,37]. Sorption effects should be considered for the estimation of the lumped overall elimination rate constant (k_e). Singer et al. demonstrated the possibility of indoor atmospheric naphthalene removal by sorption to indoor walls, and suggested a removal coefficient of 1.64 h^–1 for this process [34]. Considering that public toilets contain many available sorption sites such as toilet paper, garments and other surfaces of visitors, and urinals, the removal coefficient due to the various sorption processes could be greater than that via air exchange.

Another possible reason for the difference in the estimated and measured C_in values could be the wetting of the naphthalene ball surfaces. A thin film of water on the surface of naphthalene ball would add additional mass transfer resistance. The modeling equations (equations 1 and 2) and our experimental R_emission conditions assumed that the surface of naphthalene was dry. However, the inclusion of a thin layer of water on the surface of the naphthalene ball would reduce R_emission, thus lowering the expected C_in.

Furthermore, the measurement data using PUF-PAS is hardly considered to reflect accurate C_in value and the method is even described as ‘semi-quantitative’ sampling [26]. Relatively high vapor pressure PAHs such as naphthalene, acenaphthylene and acenaphthene are not expected to be captured efficiently with PUF-PAS [38]. Since this study disregards the sampling efficiency of PUF-PAS and possibility of loss before extraction of PUF-PAS, the measured C_in is likely to be overestimated.

Cancer risks were calculated by multiplying the EC by the inhalation unit risk. The EC distributions were created in two different ways: from the C_in obtained from the indoor air model and from the C_in obtained using PUF-PAS monitoring. The resulting cancer risk distributions are depicted in Figure 3. As shown, the cancer risks estimated using the C_in value from the indoor air model were much higher than those obtained using C_in obtained from PUF-PAS monitoring under the same exposure scenarios (Figure 3a and c; Figure 3b and d). The 95th percentile of the cancer risk for cleaning staff was 1.6×10^–6, even when the monitored distribution of C_in was used (Figure 3c). According to the US EPA, a cancer risk between 10^–6 and 10^–4 implies a possible hazard [39]. The risk of workers who spend long periods of time in public toilets is at the verge of being possibly hazardous. Nevertheless, considering the uncertainty of PUF-PAS discussed in Section 3.2, measured C_in value can be regarded as the minimum limit of estimation. So, the risk of workers would be greater than 1.6×10^–6. In addition to this, indirect routes of exposure, such as the intake of dust particles and the desorption of sorbed naphthalene from clothes, as well as the ubiquitous presence of naphthalene in urban air, would increase their total exposure. For the general population, on the other hand, the 95th percentile cancer risk was 4.7×10^–9, even when C_in from the indoor air model was used (Figure 3b), implying that visiting public toilets is a negligible cancer risk factor.

In this study, the inhalation unit risk from the OEHHA was used for risk estimation, even though the uncertainty of this inhalation unit risk is still under debate. Several reports have described non-cancer health effects of the inhalation of naphthalene in humans [11,32]. The US EPA found that severe naphthalene-related human effects such as anemia, hematuria, coma, and death, which are generally related to the ingestion of naphthalene mothballs [4]. The working group of the US EPA found only two case studies involving human data, and declared that no inference could be made on the carC_inogenicity of naphthalene. They evaluated naphthalene as having inadequate evidence in humans in terms of its carcinogenicity. However, naphthalene was assessed by the US EPA to have sufficient evidence of carcinogenicity in experimental animals.

Naphthalene balls are still deployed in many public toilets, although their usage is decreasing because of the substitution of chlorinated organic chemicals such as 1,4-dichlorobenzene (1,4-DCB) [4]. The inhalation unit risk for inhalation exposure to 1,4-DCB established by OEHHA is 1.1×10^–2 (mg m^–3)^–1, which is similar to that of naphthalene by a factor of three [32]. Also, 1,4-DCB is also known to cause effects similar to those of naphthalene in humans via inhalation exposure. The inhalation exposure of mice to 1,4-DCB over two years resulted in liver tumors and bronchoalveolar adenomas [40]. In addition, the vapor pressure of 1,4-DCB (173 Pa at 20°C) is much higher than that of naphthalene (11 Pa at 25°C), which likely results in a higher C_in of 1,4-DCB [41]. Although the carcinogenic potential of 1,4-DCB is also still under debate, 1,4-DCB would not be a good alternative to naphthalene. Alternatives to naphthalene or 1,4-DCB are necessary for precaution. For example, the Ministry of Environment of Korea recommends the use of natural products such as wood charcoal, pieces of cedar wood, or aroma oils as an alternative to naphthalene sanitation balls [42]. In order to reduce risks, workers are recommended to be equipped with appropriate personal protection during their cleaning activities.