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Environ. Sci. Technol. 2000, 34, 3101-3108

Diffusion and Sorption of Volatile Organic Compounds in Building Materials-Impact on Indoor Air Quality R . M E I N I N G H A U S , * ,†,‡ L. GUNNARSEN,§ AND H. N. KNUDSEN§ Centre Scientifique et Technique du Baˆtiment, 24 rue Joseph Fourier F-38400 Saint Martin D’Heres, France, Air Quality Unit, Environment Institute, Joint Research Centre, I-21020 Ispra, and Danish Building Research Institute, DK-2970 Hørsholm, Denmark

Volatile organic compounds (VOCs) are frequent indoor air pollutants. Indoor materials can act as buffers for VOCs, reducing peak concentrations but prolonging the presence of compounds in the air. The purpose of this paper is to present quantitative experimental results on diffusion and sorption of VOCs in indoor materials and to discuss the impact of these processes on indoor air quality. A twoflow system was chosen for the present study because this method allows mass flow across materials to be directly observed. For some materials, effective diffusion coefficients were only 1 order of magnitude below what is found in air. Two types of concrete showed a very high sorption capacity for ethyl acetate. Steady-state calculations were performed within a model room. By considering various wall materials, the influences of diffusion and of sorption on the air quality of the room are discussed. Regarding the case of gypsum board walls, it may be concluded that diffusion through the material can contribute to reducing the room air concentration, especially at low ventilation rates. The results indicate that sorption and diffusion processes can affect the ventilation requirements in such rooms.

Introduction Volatile organic compounds (VOCs) are frequent indoor air pollutants found at concentrations that are often higher indoors than outdoors (1-4). They can be emitted by materials such as carpets, paints, wallpapers, or PVC, they may enter a room from outdoors, or they are emitted or generated during human activities such as cooking or tobacco smoking (5-7). These compounds can have a negative effect on the occupant’s health, since they can act for example as irritants (8, 9). Moreover, many VOCs with low odor threshold values can provoke odor annoyance (10). A reduction of VOC concentration levels is desired and can be achieved by following one of several strategies: by source control; by filtering the indoor air; and by increased ventilation or improved ventilation efficiency. Diffusion across walls may also contribute to VOC transport in to and out of rooms. * Corresponding author present address: INERIS, Parc Technologique ALATA, B.P. No. 2, F-60550 Verneuil-en-Halatte; Phone: +33 44 55 61 99; fax: +33 44 55 63 02; e-mail: [email protected]. 476 762560; e-mail: [email protected]. † Centre Scientifique et Technique du Ba ˆ timent. ‡ Environment Institute, Joint Research Centre. § Danish Building Research Institute. 10.1021/es991291i CCC: $19.00 Published on Web 06/27/2000

 2000 American Chemical Society

In some situations the emission source cannot be identified or its removal is expensive. Increased or improved ventilation and/or the installation of filters seem to be straightforward solutions. But a process known as the sink effect can level out these measures: VOCs are sorbed by indoor surfaces and are emitted again lateron. Sink effects will lower peak concentrations, whereas a subsequent emission or desorption will prolong the presence of a compound in the indoor air. In other words, indoor materials can act as buffers for VOCs. The sink effect in the indoor environment has been the subject of numerous investigations (for example refs 1117). Molecular properties of the adsorbate as well as properties of the adsorbent material will determine to which extent the sink effect changes the indoor air concentration levels. For the description and prediction of the dynamic behavior of VOC indoor concentrations, several mathematical models were suggested (e.g. refs 15, 18, 19). Often, these models were not based on the underlying physical processes. Typically, they did not succeed in fitting experimental data satisfactorily. However, recently developed models, based on physical processes, appear to be more promising (20, 21). Ventilation consumes energy to condition and to distribute outdoor air, and hence should be kept as low as possible, while still sufficient to guarantee good indoor air quality. Mathematical models may be used as a tool for better adjustment of room ventilation to the actual needs. The purpose of the current paper is to present quantitative experimental results on diffusion and sorption of VOCs in indoor materials and to discuss the impact of these processes on indoor air quality. The results may be useful for the development of a new or the selection of an existing model based on physical processes, and they will give an estimate of the order of magnitude of the studied processes. Interactions of airborne chemicals and materials have been investigated with several different experimental techniques, which can be roughly divided into one-flow and twoflow approaches. In the first case, a material sample was placed in an environmental test chamber, where it was ventilated with VOC-containing air over a specified period of time. In indoor air science, this method has been frequently adopted. For the two-flow setup, the material sample was placed between two constantly ventilated chambers, and a compound was added to the supply air of one of the chambers (22-24). The VOC concentrations in the chamber air were measured in both cases. The two-flow system was chosen for the present study because the mass flow across the material can be observed. Diffusion coefficients may be calculated in a two-flow system from direct observations. Moreover, low VOC concentrations comparable or slightly higher than in many buildings can be established in the setup. The sorption and diffusion of two VOCs in eight materials were studied.

Experimental Method Experiments were performed using pairs of small-scale test chambers of Climpaq type (25). The experimental setup is illustrated in Figure 1, and a schematic view of the chamber is given in Figure 2. The test material was placed between two Climpaqs, in the following called primary chamber ((A) in Figure 1) and secondary chamber (B). Organic vapor of one single compound was constantly dosed with a VOC generator ((D) in Figure 1) (26) in a separate Climpaq (C) at constant ventilation rate with clean air. The air from chamber (C) was led to the five primary chambers (A). The secondary VOL. 34, NO. 15, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Schematic view of the experimental setup. Five pairs of Climpaqs were used simultaneously. Test samples separated the primary chambers (A), which were ventilated with VOC-containing air, from the secondary chambers (B), which were ventilated with clean air. Chamber (C) contained the VOC generator (D).

FIGURE 2. Schematic view of a Climpaq test chamber (top view). Air supply (W), damper (V), exhaust (U), main compartment (X), fan (Y), and metal grids (Z). chambers (B) were ventilated with clean air. Four experimental rounds were performed in order to study the combination of eight materials with two compounds. The concentrations in Climaq (C) (i.e. inlet concentrations for chambers (A)) were set at 11 mg/m3 and 15 mg/m3 for n-octane and 21 mg/m3 and 28 mg/m3 for ethyl acetate, respectively. These concentrations were chosen to comply with the sensitivity requirements of the detection instruments. They are higher than typical indoor concentrations (2-4) but are believed to be in the linear part of adsorption isotherms, since they are far below 1% of the saturation vapor pressure. The linearity assumption will be used throughout this publication and is a frequently accepted approach for the development/application of models. Air exchange rates in all chambers were set at 2 h-1 and quantified by SF6-decay measurements. A fan in each chamber ((Y)in Figure 2) ensured sufficient air mixing and kept air velocities around 0.08 m/s 10 cm from the material surface (in compartment (X) in Figure 2). Due to the particular geometry of the Climpaq, the air was recirculated at a high rate inside the chamber. The flow rate of supply air into the chamber was small compared with this internal recirculation. Consequently, the concentration gradients within the chamber were negligible. Since the chamber exhausts were open to the environment, the chambers were run almost at ambient pressure. Pressure differences between the two chambers would lead to additional viscous mass flow across the test specimen. A maximum overpressure of 1.6 Pa was observed close to the fan. Relative air humidity was held constant at 45 ( 3%, and temperature in the chambers was kept at 24 ( 0.5 °C. The whole setup was placed in the air quality laboratory at the Danish Building Research Institute (27) with the same climatic conditions as in the chambers. Ethyl acetate and n-octane were selected as model substances, representing polar and nonpolar compounds, respectively. Both compounds have comparatively low boiling points (126 °C for n-octane and 77 °C for ethyl acetate), which was an important selection criterion, because sink effects in the tubing system and in the Climpaqs will be minimized. Moreover, the diffusion transport should be faster for these 3102

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compounds, allowing for an observation of this process within a reasonable period of time. During the experiment, VOCcontaining air was introduced into the test chamber for 24 h (n-octane) and 48 h (ethyl acetate), respectively. This sorption phase was followed by a desorption phase, where clean air was introduced into the chambers. VOC concentrations in the Climpaqs (A), (B), and (C) were monitored every 15 min with an Innova 1312 or Bruel&Kjær 1302 photoacoustic detector (UA 0987 optical filter with a center wavenumber of 2950 cm-1) combined with a Valco VICI multiport valve and a Teflon tubing system. The 1312 instrument was span-calibrated for both target compounds at Innova, Nærum, Denmark, and the 1302 instrument was calibrated against the 1312 instrument. In general, the selected optical filter is more suitable for hydrocarbons. Detection limits were estimated (based on three times standard deviation of the background noise (28)) with 0.07 mg/m3 for n-octane and with 0.29 (0.65) mg/m3 for ethyl acetate; the figure in parentheses refers to the 1302 instrument. These values reflect the different sensitivities of the instruments. When measuring VOC concentrations, water vapor interferences were compensated for. Sorption effects in the sampling tubes were assessed before the experiments. Errors accounted for approximately 5% between two consecutive measurements for n-octane, when the concentration was increased in one step from background to maximum concentration, while no effect was found for ethyl acetate. Given that the time interval between two measurements was normally higher than under the chosen conditions and that concentrations in the chambers did not increase/ decrease stepwise, sorption effects in the tubes probably led to a very small underestimation of concentrations in the sorption phase and a slight overestimation in the desorption phase. Before the actual experiments were started, the precleansed Climpaqs with the preconditioned materials were ventilated for a purge phase of approximately 12 h, followed by the determination of Climpaq and material emissions. These concentrations were subtracted from concentrations obtained during the actual experiments. In almost all cases, Climpaq and material emissions were very close to the detection limits, being in the range of 0.04 mg/m3 for n-octane and 0.1-0.4 mg/m3 for ethyl acetate. For one material (brick wall), the background concentration was measured with approximately 3% of the inlet concentration of that experiment. As the materials were preconditioned for several weeks in the same atmosphere used in the Climpaqs, it appears reasonable to assume a constant material emission compared with the experimental time span. Cross-interferences from clean air components (in particular CH4) were compensated for by monitoring the same conditioned and filtered supply air in one empty Climpaq. Concentrations were afterward point-wise subtracted from the other chamber measurements. The sink effect of an empty chamber was measured, while the chamber was covered with a glass lid. This chamber was then run under identical experimental conditions as the other chambers. Finally, it was verified that concentration differences among the different chamber inlets were equal to or less than 1%. It should be emphasized that the combination of several compensation steps (i.e. compensation for water vapor interference, compensation for background fluctuations in the supply air, and compensation for material/Climpaq background emission, when required) allows for measuring the specific concentrations of respective compounds. The eight materials selected for this study are listed in Table 1. The selection was based on frequent use in Danish buildings.

TABLE 1. Characterization of the Investigated Materials

material

average thickness [mm]

mass/square meter [kg/m2]

PVC floor covering wallpaper with paste carpet acrylic paint on woodchip paper aerated concrete solid concrete brick wall gypsum board

1.6 0.2 8.5 0.5 21 15 25 12.5

2.08 0.26 2.51 0.23 16.82 34.47 42 9.68

solid PVC simple wallpaper, no PVC layer tufted PA nylon carpet with styrene-butadiene rubber backing H+H beton multiplate mix type 15 bricks (stoneclass 15, red) with mortar covered with cardboard paper

Materials’ edges were sealed to prevent leakage from the experimental setup. Aerated and solid concrete and gypsum board were sealed with aluminum tape. Brick wall and carpet were glued to metal frames with epoxy. The sealants were carefully applied to avoid mass flow around the material edges. Thin materials such as wallpaper and PVC floor covering were not sealed, because the material thickness was small compared to a test plate surface of ca. 0.25 m2. The materials were visually inspected for small cracks and were preconditioned at 24 °C and 45% RH for at least 3 weeks. To test for leaks into the test chambers, a constant SF6atmosphere was generated in the air surrounding the test chambers. Concentrations were then measured in Climpaqs (A), (B), and (C). In all cases, the leak rate was less than 1% of the ventilation. At steady-state, the sum of concentrations in the chambers (A) and (B) was very close to the concentration in the empty chamber, and to the concentration in chamber (C) (95-100%), giving additional proof that the setup was sufficiently tight to the environment and that the compensation procedures led to measurements of actual VOC concentrations.

Results Examples of concentration vs time curves are shown in Figure 3 a-h for several combinations of compounds and materials. Figure 3a shows the measured concentration in the empty Climpaq for n-octane. The curve obtained for the PVC floor covering (Figure 3b) exhibits a very similar shape, indicating that the sink effect on this material was small and that no measurable diffusion was observed. The mass flow across the wallpaper with paste (Figure 3c,d) was fast, being reflected by a rapid increase of concentration in the secondary chamber for both compounds. The sorption effect of this material was small, too. Brick wall showed a fast diffusion process for n-octane (Figure 3e), whereas a lag-phase was monitored in the secondary chamber for ethyl acetate (Figure 3f), which is due to the diffusive transport in combination with sorption. Aerated concrete showed a similar behavior, the lag-phase being even more pronounced (Figure 3g,h). Here, steady-state was not established in the chambers, indicating that the material was still sorbing a high amount of the compound at the end of the experiment. The same was found for the solid concrete (not shown). The following provides the theoretical background for the data evaluation. Effective diffusion coefficients at steady-state were calculated using Fick’s first law of diffusion (29)

m ˘ dx V˙ ∆x cB Deff ) )‚ A dc A cB - cA

description/annotation

(1)

where Deff is the effective diffusion coefficient (m2/h) and m ˘ is the mass flow through the material (mg/h), A the area of test specimen (m2). dx can be approximated with material thickness ∆x (m), and dc be approximated with ∆c ) cB -

cA where cA is concentration in the primary chamber (mg/ m3) and cB is the concentration in the secondary chamber (mg/m3). V˙ is the ventilation rate in the secondary chamber (m3/h). It is assumed that the concentration gradient in the material was linear and one-dimensional and that the diffusion coefficients were not depending on concentration. Note that Deff includes resistance to diffusion in the boundary layers of air at both sides of the material. However, this was small. Moreover, the boundary layer thickness will depend on the air velocity and on air flow characteristics (turbulent/laminar) within the Climpaq. Detailed information about these parameters in all parts of the chambers (for example close to the fan, or in the section close to the inlet and outlet) were not obtained, but it is reasonable to assume that the boundary layer was not of constant thickness. Hence, the effect of the boundary layer was not taken into mathematical consideration. Sorption capacities SA (mg m2/mg m-3) were calculated based on the difference between the mass flow into the primary chamber (m ˘ iC) and out of both primary (m ˘ iA) and secondary chamber (m ˘ iB). Numerical integration and normalization by averaged chamber concentration (cA+cB)/2 was used to calculate a sorption capacity according to eq 2. n

SA )

1 A

∑[m˘ i)1

iC

- (m ˘ iA + m ˘ iB)]‚∆ti

( )

(2)

cA + cB 2

∆ti stands for a time interval between single measurements. A normalization on averaged chamber concentration is based on the assumption that the concentration gradient in the material was linear. Given that no material was placed between the chambers, the actual concentration in the system would have been half of the concentration in chamber (C). The sorption properties of the empty Climpaq and of some of the thin materials were of the same order of magnitude as demonstrated in Figure 4. For that reason, the amount sorbed by the empty chamber was subtracted from the amount sorbed by the individual materials, resulting in corrected sorption capacities SA*. For the same reason, no sorption capacities were calculated for these thin materials. Sorption can be described by the partition coefficient K defined in eq 3

v ) K × ωeq

(3)

where v (kg/kg) is the sorbed mass divided by the mass of the sorbent at the equilibrium concentration. The concentration ωeq is the mass of compound in air per mass of air (kg/kg). K is deduced from the sorption capacity S*A by taking into account the test specimen mass per area (kg m-2) (Table 1) and an air density of 1.2 kg m-3. K expresses the ratio of VOL. 34, NO. 15, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Concentration vs time curves for (a) empty chamber with n-octane; (b) PVC with n-octane; (c) wallpaper with n-octane; (d) wallpaper with ethyl acetate; (e) brick wall with n-octane; (f) brick wall with ethyl acetate; (g) aerated concrete with n-octane; and (h) aerated concrete with ethyl acetate. 3104

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FIGURE 4. Sorbed mass of investigated materials and the empty chamber for both compounds, normalized on chamber concentrations (note axis break). sorbed mass of a compound per mass of material, divided by mass of a compound in air per mass of the air. K is characteristic of the compound/material combination and has the dimension 1. Equation 3 is only valid if the sorption isotherm is linear, which was assumed in the present calculations. Partition coefficients will be compared with literature values. Since also the desorption phase was monitored, information was available to the extent that the presence of a compound may be prolonged by previous sorption in the material. The dynamic character of the desorption process may for example be expressed by the time until the concentration has dropped down to one-fourth of its initial value, following considerations for instance given in ref 30. If the concentration within the chambers dropped according to a monoexponential function, this time t0.25 would besin analogy to the half-life periodscalculated as

t0.25 )

ln 4 k

(4)

where k is the air exchange rate of the chamber (h-1). The actual time until the concentration dropped to one-fourth of its initial value will be affected by the sink effect. It may be anticipated that the stronger the sink effect, the higher the deviation. The time, when one-fourth of the concentration was in fact reached, was calculated by adjacent data points. The higher a t0.25 value, the higher the potential of a material to prolong the presence of the compound in the air. Compared with the half-life period, a t0.25 value accentuates deviations from the monoexponential behavior more strongly. Clearly, different times until certain fractions of concentrations were reached could also have been considered. The calculated resultsseffective diffusion coefficients Deff, corrected sorption capacities SA*, partition coefficients K, and t0.25-valuessare given in Table 2.

Discussion Evaluation of the Experimental Results. The mass transport across the studied building materials is surprisingly fast. In some cases, effective diffusion coefficients were only 1 order of magnitude below those found in the air (31). Variations within each group of material may be high, due to the manufacturing process and the pretreatment of the sample. Still, differences between the different groups of materials appeared high enough to allow for a ranking. With respect to diffusion, the following ranking was found. Gypsum board showed the highest diffusion coefficient of all studied materials, followed by aerated concrete, carpet,

brick wall, solid concrete, wallpaper with paste, and acrylic paint on wallpaper. The studied PVC floor covering did not show measurable diffusivity under the selected experimental conditions. The diffusion properties of some of the materials were subsequently tested with a complementary method by other laboratories, and a good agreement of the results was obtained (32). A ranking of the investigated materials with respect to their sorption capacities SA* led to the following: Aerated concrete took up the highest amount of VOC, but also the solid concrete showed very high sorption capacities. The brick wall, the gypsum board, and the carpet followed these materials. Ranking based on t0.25-values led to the same ranking order. The carpet sorbed more n-octane compared with ethyl acetate, whereas the situation was opposite for gypsum board. Both types of concrete showed a very high sorption capacity for ethyl acetate. Steady-state concentrations during the experiments were not reached, even after 48 h. In particular for the studied concrete samples, large differences with respect to sorption capacities were observed for n-octane and ethyl acetate. This may be attributed to the ability to form hydrogen bonds (33), because ethyl acetate, in contrast to octane, can act as a hydrogen bond base via the oxygen of its ester group. Additionally, the presence of pores and capillaries could be an important parameter. At 45% RH, water condensation may take place in the pores. Henry’s law constants are a measure for the solubility of a species in water. For n-octane (3 × 10-4 M/atm) and ethyl acetate (5.97.4 M/atm) (34), these constants differ over several orders of magnitude. The solubility of a compound in capillarycondensed water in materials could therefore explain different sorption behaviors. A hydrolysis reaction of ethyl acetate in the basic concrete would also explain these differences. To test this, a sample of the aerated concrete was kept in an ethyl acetate atmosphere at saturation vapor pressure for 1 day (35). The material was afterward extracted with a methanol/water mixture. An aliquot of the extract was analyzed by gas chromatography. The amounts of free acetic acid (one of the hydrolysis products) were measured. Additionally, a blank was analyzed. The amounts of acetic acid in both extracts did not show considerable variation. It may therefore be concluded that the hydrolysis reaction does not contribute to the sink effect. There is little information about partition coefficients for VOC/material combinations found in the literature. As sorption is depending on both compound and material properties, a high variation of partition coefficients should be expected. Moreover, the sorption/desorption process will be strongly influenced by environmental parameters, such as humidity and temperature. For the combination of a cotton carpet with several chlorinated compounds, Borazzo (12) measured partition coefficients ranging from approximately 0.02 to 0.5 kgair/ kgmaterial at 25 °C. Tiffonet et al. (36) found a partition coefficient of 5.3 kgair/kgmaterial at 25 °C for the combination propanediol/paint. Kirchner et al. (16) reported partition coefficients for the combination 2-butoxyethanol and four different materials (wallpaper, gypsum board, acoustic tile, and carpet) to be in the range of 0.44-1.29 kgair/kgmaterial at 25 °C. The obtained partition coefficients of the present study were within the same order of magnitude. Moreover, as expected, polar compounds were more strongly sorbed by more porous materials. Practical Implications. The experimental results showed that VOC diffusion across building materials can be fast. Moreover, the materials that make up the envelope of a building have a high potential for taking up (and releasing) VOL. 34, NO. 15, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 2. Experimental Results: Effective Steady-State Diffusion Coefficients Deff; Corrected Sorption Capacities SA*; Partition Coefficients K; and t0.25-Valuesa material

Deff [10-6 m2/h]

SA* [mg m2/mg m3]

K [kgair/kgmaterial]

t0.25 [h]

Octane PVC floor covering wallpaper with paste carpet with SBR backing acrylic paint on woodchip paper aerated concrete solid concrete brick wall gypsum board

23 1261 32 2736 374 1170 3021

0.796

0.381

1.676 0.896 0.568 0.844

0.12 0.031 0.016 0.105

1.18 (0.35) 1.03 (0.35) 2.25 (0.37) 1.16 (0.37) 2.78 (0.36) 1.89 (0.36) 1.46 (0.36) 1.61 (0.36)

Ethyl Acetate PVC floor covering wallpaper with paste carpet with SBR backing acrylic paint on woodchip paper aerated concrete solid concrete brick wall gypsum board a

30 1626 41 >2038 >182 1705 4051

0.356

0.170

>36.652 >16.936 4.516 1.076

>2.614 >0.590 0.129 0.133

1.01 (0.35) 1.34 (0.35) 1.29 (0.37) 1.09 (0.37) 54.1 (0.36) 25.5 (0.36) 6.67 (0.36) 2.51 (0.36)

Theoretical values in parentheses.

VOCs. Therefore, it is interesting to assess the impact of these new experimental findings on the indoor air quality. In the following such an assessment of the practical implications of the results is performed by steady-state calculations of the consequences within a model room. The influences of diffusion and of sorption on the air quality of the room are discussed by considering various wall materials. Steady-state considerations do not necessarily reflect typical indoor situations, where transient conditions usually prevail. Moreover, the generalization (transfer) of experimental results obtained with only a few compounds and materials can be uncertain. But to illustrate the significance of the experimental results, the following discussions appear appropriate. The model room was defined with a size of 3 × 3 × 5 m3 (volume ) 45 m3, wall surface ) 48 m2). The air in the room was assumed to be perfectly mixed. Three different types of walls were considered for discussing the effects of sorption and diffusion. These assumptions were based on typical data for materials in Denmark (37). The three types of walls were selected to represent a very tight wall material; a medium permeable wall; and a highly permeable wall material. (1) Tight wall structures: All walls consisted of 10 cm thick concrete, and ceiling and floor were considered to be covered with diffusion-tight layers. (2) Medium permeable structures: All walls consisted of 11 cm thick brick walls, and ceiling and floor were covered with diffusion-tight material. (3) Highly permeable wall structures: All walls consisted of gypsum boards covered with wallpaper, i.e.: wallpaper with paste - two layers of gypsum board - interstitial space two layers of gypsum board - paste with wallpaper. The space between the walls, which are typically filled with glass wool, was considered to have negligible diffusion resistance, and its sorption capacity was not accounted for in the calculations. Ceiling and floor were considered to be diffusion-tight. The steady-state model is based on a simple dilution model where the emission rate is constant, see eq 5. At steady-state, the amount of a VOC emitted from a constant source into the room is removed by ventilation (first term on the right-hand-side in eq 5) and by transport due to diffusion through the walls (second term).

A SERu ) V˙ c + Dc x 3106

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(5)

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SERu is the unit specific emission rate of a constantly emitting source (mg/h), V˙ denotes the ventilation rate of the room (m3/h), c is the steady-state concentration (mg/m3), A is the total wall surface in the room (m2), x is the wall thickness (m), and D is the steady-state diffusion coefficient (m2/h). Concentrations of VOCs outside the model room were considered to be negligible. For a composite membrane of several layers, the concentration drop through the whole membrane is the sum of the drops through the individual layers (29). The mass flow is the same across each section. Therefore, the mass flow can be calculated as

m ˘ )-

A∆c x2 x1 + ... D1 D2

(6)

where x1 is the thickness of material 1 and D1 is the corresponding diffusion coefficient. This equation is valid for the composite system wallpaper/gypsum board. For discussing the influence of diffusion, the concentration drop of n-octane in the model room by mass transport across the walls was examined. A constant source with an emission rate of 50 µg/h was considered. Based on the simple steady-state mass balance given by eq 5, steady-state concentrations were calculated. Resulting concentrations are depicted in Figure 5. According to the Swedish housing stock study (38), approximately 86% of the investigated Swedish houses have ventilation rates below 0.35 L/s per m2 floor area, with most houses having ventilation rates around 0.2 L/s per m2 floor area, corresponding to 0.42 h-1 and 0.24 h-1 for the model room. For gypsum board walls, diffusion through the material reduced the room air concentration, especially at low ventilation rates, with a reduction of the steady-state concentration by about one-fourth. For the more diffusion tight materials and in rooms with higher ventilation rates, this effect became negligible. For instance in office buildings, where the ventilation rates are higher, the impact will therefore be small. Diffusion coefficients were obtained for only two compounds. Theoretically, the diffusion transport of a molecule is related to molecular properties such as molecular mass,

FIGURE 5. The resulting steady-state concentration of n-octane at different air exchange rates in the model room, when different wall structures are considered. Four different situations are shown: the highly permeable gypsum boards; the medium permeable brick walls; the tight concrete walls; and, as a comparison, the situation where no diffusion is taken into account.

phase was finished. Concentration measurements were stopped at this point of time, but obviously, the re-emission process still continued, with concentrations decreasing very slowly in the chambers. In other words, the materials reemitted the previously sorbed compound themselves for a longer period than diurnal changes as they occur, e.g. when ventilation rates vary. Similar behavior was found for other compound/material combinations, too (e.g. the aerated concrete gave off 80% of the previously sorbed n-octane after 48 h). The same effect can be illustrated by comparing measured t0.25-values with theoretical values. As can be seen in Table 2, high differences were observed. These above results indicate that sorption and diffusion processes may affect the ventilation requirements in certain rooms. The results were obtained under laboratory conditions at concentrations higher than typically found indoors and by considering steady-state situations. It should therefore be repeated that a direct transfer of the results to real building environments may not be straightforward.

Acknowledgments The project was supported by the European Commission through a grant from the EI-JRC, and the MATHIS project of the JOULE program, and the Danish Dr. Techn. A. N. Neergaards Foundation. Thanks are given to Innova, Nærum, Denmark, for providing the photoacoustic detector, and the Microdrop GmbH, Hamburg, Germany, for prompt support. R. Meininghaus wishes to express his thankfulness to Dr. H. Kno¨ppel of the Air Quality Unit of EI-JRC for making his stay at SBI possible and giving him the opportunity to work on this very interesting project.

Literature Cited

FIGURE 6. Sorption Capacities S*room in a model roomssee text for explanation. molecular size (volume or area), and volatility. Similar compounds may hence show similar diffusion characteristics. By diffusion through walls, VOCs may be spread more rapidly from one room to another. This may be an important and a not yet accounted-for aspect when selecting appropriate wall materials in workplaces where high concentrations of organic compounds can be expected. The use of diffusion barriers may be important to avoid contamination from one room to the other. The experimentally obtained results of sorption capacities SA* were used to calculate the sorption capacity for the model room S*room according to /

/

Sroom ) SA × Aroom ×

xroom xsample

(7)

where Aroom is the wall surface in the room, xroom is the wall thickness in a room, and xsample is the thickness of the studied test specimen. S*room is a measure of the buffer capacity of a material under normal use. Results for S*room are summarized in Figure 6. This buffer effect of the building envelope on the indoor air quality may be beneficial, since peak concentrations are reduced, and compounds may be stored in the masonry of a building. On the other hand, as exemplified in Figure 3, the sorbed compounds can be emitted afterward over an extended period of time. For the combination ethyl acetate/aerated concrete, approximately 50% of the compounds were re-emitted 72 h after the sorption

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Received for review November 16, 1999. Revised manuscript received March 21, 2000. Accepted April 25, 2000. ES991291I