In previous studies, PFT dosers were often placed at one to three points in a room, such as near the air inlet or on the furniture, according to the predicted air pathways [8,13]. Indoor pollutants, however, are not emitted from the air inlet but rather from the surfaces of sources such as the walls, flooring, and furniture; these pollutants are also diluted by fresh air entering from outdoors. The modified method proposed in the present study can be used to determine the effective air exchange rates after taking into account the emission of pollutants from various sources; this can be achieved by placing the dosers of tracer gas at indoor locations that resemble emission sources. For example, placing the dosers at the four corners of a room can create flows that are similar to those generated during the emission and migration of actual pollutants from building materials. In addition, the systematic error due to the wind direction is possible to be avoided by this placing way [12].

In this study, four PFT dosers dispensing the same kind of PFT were placed at the four corners of a room at a height of 200 cm. The same was done in each of the other rooms but with other kinds of PFTs—a different kind in each room. More than 12 h after the placing the dosers, the air was passively sampled with a carbon molecular sieve cartridge (VOC-SD; Sigma-Aldrich Japan K.K., Japan), which can be used to simultaneously sample VOCs. The cartridges were hung from the ceiling at the center of each room at a height of 1.8 m for 24 h.

Consider a three-room house as shown in Figure 1. We assume steady-state conditions, perfect mixing in each room, and zero outdoor PFT concentration. Then the air exchange rates (three indoor-outdoor air infiltration rates, three indoor-outdoor air exhaust rates, and six inter-room air exchange rates) can be represented by nine mass-balance equations for the amount of PFTs and three mass-balance equations for the volume of air (Figure 1) [8].

In this study, the air flow rates were optimized by quasi-Newton’s method with the constraint Q > 0 to minimize the square sum of the differences between the left and right sides of the 12 mass-balance equations by using the solver function in Microsoft Excel 2003: (1) C A 2 × Q 21 + C A 3 × Q 31 − C A 1 × ( Q 10 + Q 12 + Q 13 ) = − M A C A 1 × Q 12 + C A 3 × Q 32 − C A 2 × ( Q 21 + Q 23 + Q 20 ) = 0 C A 1 × Q 13 + C A 2 × Q 23 − C A 3 × ( Q 31 + Q 32 + Q 30 ) = 0 C B 1 × Q 12 + C B 3 × Q 32 − C B 2 × ( Q 20 + Q 21 + Q 23 ) = − M B C B 2 × Q 21 + C B 3 × Q 31 − C B 1 × ( Q 12 + Q 13 + Q 10 ) = 0 C B 1 × Q 13 + C B 2 × Q 23 − C B 3 × ( Q 31 + Q 32 + Q 30 ) = 0 C C 1 × Q 13 + C C 2 × Q 23 − C C 3 × ( Q 30 + Q 31 + Q 32 ) = − M C C C 2 × Q 21 + C C 3 × Q 31 − C C 1 × ( Q 12 + Q 13 + Q 10 ) = 0 C C 1 × Q 12 + C C 3 × Q 32 − C C 2 × ( Q 21 + Q 23 + Q 20 ) = 0 Q 01 − Q 10 − Q 12 + Q 21 − Q 13 + Q 13 = 0 Q 02 − Q 20 − Q 21 + Q 12 − Q 23 + Q 32 = 0 Q 03 − Q 30 − Q 31 − Q 13 − Q 32 + Q 23 = 0 ( Q > 0 )

Five candidate PFTs were tested: perfluoromethylcyclohexane (PMCH; Alfa Aesar, USA), perfluoro-1,2-dimethylcyclohexane (PDCH; Fluorochem Ltd., USA), hexafluorobenzene (HxFBz; Wako Pure Chemical Industries, Ltd., Japan), octafluorotoluene (OFT; Wako Pure Chemical Industries, Ltd., Japan), and perfluoroallylbenzene (PFABz; Tokyo Chemical Industry Co., Ltd., Japan).

The PFTs captured in the cartridges were extracted with carbon disulfide (CS₂; Wako Pure Chemical Industries, Ltd., Japan) or hexane (Sigma-Aldrich, Inc., USA) by ultrasonication for 5 min. The extracted PFTs were analyzed on a gas chromatograph-mass spectrograph (GC-MS; HP6890-5973; Hewlett-Packard Co. Ltd., USA). Toluene-d₈ was used as an internal standard. The analytical conditions are listed in Table 1. Quantitative analysis was conducted in SIM mode and the monitored ions were as follows: HxFBz: 186, 117; OFT: 217, 236; PFABz: 217, 298; PMCH: 69, 131; PDCH: 69, 131. Calibration curves were linear between 0.01 and 100 μg·mL⁻¹ except for the solution of PDCH in CS₂.

The lower limit of detection (LOD) and lower limit of quantification (LOQ) of the analysis were defined as 3σ and 10σ of the absolute amount of the analyte (N = 5). In addition, detection and quantification limits for 24-h sampling with the passive sampler were calculated on the basis of the analytical LOD, LOQ, recovery efficiencies, and sampling rates.

To select the suitable PFTs and solvent, the recovery efficiencies of absorbed PFTs from the VOC-SD cartridges were evaluated. Aliquots with 10 μL of a methanol solution of PFTs (1.0 μg per aliquot) were used to spike the adsorbent (carbon molecular sieve) placed in a vessel with a microsyringe (N = 6). The vessels were covered with tight-fitting caps for 60 min. Then, the adsorbed PFTs were extracted with CS₂ or hexane and analyzed with the GC-MS.

To obtain the sampling rates of PFTs for the VOC-SD, the passive sampling cartridges were left in a thermostatic chamber in which the PFT gases were passed through at stable concentrations for 24 h (N = 3; Figure 2). The sampling rates were calculated by comparing the amounts of PFTs adsorbed by the cartridge (passive sampling) to the in-chamber concentration measured by active sampling. Although the surrounding air flows in an experimental chamber and actual residential environments are likely to be different, the wind speed has little effect on the sampling rate of PFC because the diffusion resistance of the sampling cartridge is much larger than that of the boundary layer on the surface of the tubes [14].

Figure 3 presents a photograph and schematic diagram of developed doser. To prevent leaks during transportation between the laboratory and measurement site, the device consists of two crimp-top glass vials with aluminum crimp seals and a rubber stopper. A needle (internal diameter: 0.61 mm) and polyethylene sintered filter maintain the dosing rate. The PFT liquid in the inner vial evaporates; diffuses through the needle, polyethylene sintered filter, and diffusion tube; and is emitted into the air. Due to the diffusion resistance, the indoor air flow is considered to have negligible effect on the dosing rate. To start dosing, the septa on both vials should be pierced with the needle. Expensive instruments such as a gas bottle, gas monitor, computer, and solenoid valve are not required for the method used to measure the air exchange rates in the present study. The PFT doser developed in this study consists of commercially available low-price glass vials and a needle. The doser also consists of a newly developed filter and a diffusion tube, which can be manufactured at low costs. An additional sampling cartridge is not required to be used because PFTs can be sampled in the same cartridge used for VOC sampling. One of the major advantages of this doser is that a constant dosing rate can be maintained despite disturbances during handling and transportation; another advantage is that this doser can be refilled with other tracer gases.

The dosing rate of the PFT doser was measured against time to confirm the stability. The decrease in weight of the doser was considered to be equal to the weight of PFT emitted. The dosing rates was measured by gravimetry every 48 h for 10 days in a thermostatic chamber (N = 10) at 5, 15, 25, 35, and 45 °C. To check leakage, the dosing rates from dosers with a no-hole needle were also measured over a period of 2 months.

To validate the developed PFT method, the results were compared with those of the CO₂ concentration decay method for a single room with a floor area of 17 m² and volume of 46 m³. The inlet flow was stabilized with an inverter controller and the room air was not mixed to match realistic conditions. PFT (HxFBz, OFT, and PFABz) dosers were placed at each of the four corners of the room at a height of 200 cm for more than 12 h. Following this, passive sampling cartridges were placed at three central points at 1-m intervals and a height of 180 cm for 8 h. The CO₂ concentration decay method was carried out in conformity with the JIS standard JIS A1406. CO₂ gas was released from a gas bomb room until the indoor concentration reached 2000 ppm. Then the CO₂ concentration was measured for 8 h with a Telaire 7001D (General Electric Company, USA). During the measurements, no one remained in the room.

The air exchange rates were measured everyday for six days during summer in three rooms of a residential apartment in the Tokyo metropolitan area, Japan. Two persons went about their daily life during the tests. The residence is on the third floor of a five-year-old, four-story reinforced concrete building and has three rooms: dining room & kitchen, 13.2 m² × 2.2 m; Japanese room, 10.7 m² × 2.2 m; and bedroom, 9.9 m² × 2.2 m (Figure 4). The volumes of the Japanese closet, bathroom and lavatory spaces were not included in the calculations of the air exchange rates because these spaces are not considered to be residential space. Because the frequency of opening and closing the Japanese closet was low (less than once a day) and the air flow due to the pressure difference between the room and closet seldom occurred, the closet space can be ignored in the calculations. If the volumes of the bathroom and lavatory spaces were included in the volume of the dining room & kitchen, the air exchange rates of the room could reduce by 30%.

The results of the tests are listed in Table 2. The mean recovery efficiencies and their standard deviations (SDs) from the 10-μg spiked cartridges extracted with CS₂ were 40% ± 3%, 72% ± 5%, 84% ± 6%, 2.7% ± 0.6%, and 24% ± 2% for HxFBz, OFT, PFABz, PMCH, and PDCH, respectively. The values obtained with hexane were <0.29%, 18% ± 2%, 54% ± 18%, and 84% ± 21% for HxFBz, OFT, PMCH, and PDCH, respectively. The precision was better for CS₂, regardless of the recovery efficiency. Hence, CS₂ was selected as the extraction liquid and HxFBz, OFT, and PFABz were selected as the tracer gases for three-zone air exchange measurement. The sampling rates of these three PFTs were 10.5 ± 1.1, 14.4 ± 1.4, and 12.2 ± 0.49 mL min⁻¹. The detection and quantification limits for 24-h sampling calculated using the analytical LOD and LOQ and the sampling rates were 0.20, 0.17, and 0.26 μg m⁻³ and 0.66, 0.58, and 0.85 μg m⁻³ for HxFBz, OFT, and PFABz, respectively.

The total amount of PFTs released from the doser was linearly related to the elapsed time for 240 h (Figure 5(a)). The dosing rates for HxFBz, OFT, and PFABz were calculated as 0.23 ± 0.009, 0.082 ± 0.006, and 0.015 ± 0.002 mg h⁻¹, respectively, at 25 °C, according to the slope of the correlation lines. The variance of the dosing rate was low for HxFBz and OFT among the 10 dosers (relative standard deviation (RSD) (= (SD/Mean) × 100): 2.6%–13% and 0.86%–13%, respectively). Although the variance for PFABz was low at 15–45 °C among the 10 dosers (RSD: 11%–16%), the dosing rate varied at 5 °C (RSD: 90%). In addition, the dosing rates exponentially increased with temperature (Figure 5(b)). Thus, to obtain more accurate air dosing rates, especially in winter, weight measurement of dosers before and after measurement of the air exchange rates is desirable. The PFT dose emitted from the device with the no-hole needle was 0.2 mg at 2 months, which is negligible.

The air exchange rates measured by the PFT method did not differ at three points in the room (RSD < 10%). The exchange rates measured using HxFBz and OFT (1.0 ± 0.02 h⁻¹, 0.95 ± 0.03 h⁻¹) are in agreement with the results obtained by the CO₂ concentration decay method (0.96 h⁻¹). However, the result obtained with PFABz (1.4 ± 0.12 h⁻¹) was 40% higher than that obtained by the CO₂ concentration decay method. This could be due to analytical and gravimetric error: the amount of PFABz collected in the sampling cartridge was close to the LOQ (16–20 ng per cartridge), and the total dose of PFABz during an 8-h period was small (1.6 mg) owing to the relatively low vapor pressure of PFABz. To reduce the gravimetric error, it is recommended that a longer dosing duration be used in the future surveys (e.g., 24 h). To reduce the analytical error, it is recommended that higher indoor PFABz levels be maintained by using a larger number of PFABz dosers in a room.

The 24-h average air exchange rates from outdoors to the dining room & kitchen, Japanese room, and bedroom (mean ± SD, N = 6) were 0.2 ± 0.3, 2.4 ± 1.6, and 2.6 ± 2.0 h⁻¹, respectively. The 24-h average air exchange rates from the other rooms to the dining room & kitchen, Japanese room, and bedroom (mean ± SD, N = 6) were 1.5 ± 0.6, 0.8 ± 0.7, and 2.0 ± 1.2 h⁻¹, respectively. The residents kept the windows open for 0–10 h per day. A comparison among the 24-h average air exchange rates for 6 days, revealed that the air exchange rates were high (4.3 and 3.6 h⁻¹) when the windows were kept open for 9.5 and 10 hour. This suggested that the human activity pattern (opening of windows) strongly influenced the air exchange rates. There were no windows in the dining room & kitchen. This could be the reason for the low air exchange rates (outdoor to indoor) in the dining room & kitchen.