Determination of partition and diffusion coefficients of formaldehyde in selected building materials and impact of relative humidity

Abstract

The partition and effective diffusion coefficients of formaldehyde were measured for three materials (conventional gypsum wallboard, “green” gypsum wallboard, and “green” carpet) under three relative humidity (RH) conditions (20%, 50%, and 70% RH). The “green” materials contained recycled materials and were friendly to environment. A dynamic dual-chamber test method was used. Results showed that a higher relative humidity led to a larger effective diffusion coefficient for two kinds of wallboards and carpet. The carpet was also found to be very permeable resulting in an effective diffusion coefficient at the same order of magnitude with the formaldehyde diffusion coefficient in air. The partition coefficient (K _ma) of formaldehyde in conventional wallboard was 1.52 times larger at 50% RH than at 20% RH, whereas it decreased slightly from 50% to 70% RH, presumably due to the combined effects of water solubility of formaldehyde and micro-pore blocking by condensed moisture at the high RH level. The partition coefficient of formaldehyde increased slightly with the increase of relative humidity in “green” wallboard and “green” carpet. At the same relative humidity level, the “green” wallboard had larger partition coefficient and effective diffusion coefficient than the conventional wallboard, presumably due to the micro-pore structure differences between the two materials. The data generated could be used to assess the sorption effects of formaldehyde on building materials and to evaluate its impact on the formaldehyde concentration in buildings.

Implications:

Based on the results of this study, the sink effects of these commonly used materials (conventional and “green” gypsum wallboards, “green” carpet) on indoor formaldehyde concentration could be estimated. The effects of relative humidity on the diffusion and partition coefficients of formaldehyde were found to differ for materials and for different humidity levels, indicating the need for further investigation of the mechanisms through which humidity effects take place.

Introduction

Formaldehyde has been of special concern as an indoor air pollutant and one of the key toxic pollutants because of its existence in a wide range of products and the adverse health effects associated with the exposure to this toxic air pollutant (Kim et al., 2001; Molhave, 1989; Salthammer et al., 2010; Weschler, 2009). Wall and floor finish materials such as painted gypsum wallboards and carpets represent a large amount of indoor surface materials. As new products that are labeled green based on the use of recycled raw materials for manufacturing become available, it is important to assess their potential impact on indoor air quality either as emission sources or sinks. This study focused on the sink effects and investigated how relative humidity influenced the effect because of the large range of humidity conditions in indoor spaces and the highly water-soluble nature of formaldehyde. The outcome of this study is also useful in further understanding of the effects of relative humidity (RH) variation on the formaldehyde emissions for indoor source control (Bouilly et al., 2006; Fang et al., 1999; Farajollah et al., 2009; Haghighat and Bellis, 1998; Huang et al., 2006; Wolkoff, 1998; Xu and Zhang, 2011; Zhang et al., 2002, 2003).

The capacity of and speed at which a material adsorbs a pollutant can be mechanistically characterized by the partition coefficient and effective diffusion coefficient, respectively (Zhang et al., 2002). Several methods have been established to determine the two coefficients, including static dual-chamber method (Bodalal et al., 2000, 2001), conventional small chamber sink test method (An et al., 1999), microbalance method (Cox et al., 2001, 2002), mercury intrusion porosimetry method (Blondeau et al., 2003; Xiong et al., 2008), and a dynamic dual-chamber method (Meininghaus et al., 2000; Xu et al., 2009). In this study, the dynamic dual-chamber method was selected.

Although experimental research of the impact of relative humidity on the transport and storage of formaldehyde and volatile organic compounds (VOCs) is important, very limited experimental research has been done on the effect of humidity on the effective diffusion coefficient and partition coefficient. Huang et al. (2006) tested the partition coefficient of five VOCs (cyclohexane, toluene, ethyl acetate, isopropyl alcohol, and methanol) in ceiling tile. They did not observe any influence of relative humidity except for methanol. The partition coefficient of methanol in ceiling tile decreased linearly with the increase of relative humidity. The authors attributed the phenomenon to the high polarity of methanol, which would result in strong attraction between water molecules and methanol molecules and hence weaken the interaction force between solid surface and the methanol molecule. In the study of Farajollah et al. (2009), five VOCs (octane, isopropanol, cyclohexane, ethyl acetate, and hexane) were measured for ceiling tile. Three relative humidity (RH) conditions (0%, 20%, and 40% RH) were investigated. Only minor humidity effect on the effective diffusion coefficient has been observed. Xu and Zhang (2011) studied the relative humidity effect on the diffusion and partition coefficients of formaldehyde in calcium silicate, and it was found that relative humidity had no significant influence on the effective diffusion coefficient on formaldehyde for the range of moisture conditions (25–80% RH) tested. For partition coefficient, between 25% and 50% RH, there was no significant difference. Relative humidity in 80% RH led to a higher partition coefficient for formaldehyde compared with 50% RH. The increase of partition coefficient of formaldehyde was likely due to formaldehyde absorption into the liquid water under the higher-humidity condition, but its impact was expected to be different from one RH range to another because of the nonlinear nature of the moisture retention curve. For water-soluble compounds such as methanol and formaldehyde, depending on the level of humidity and the pore size distribution of the material, an increase in relative humidity can have two opposing effects: water molecules can compete for the sorption site on one hand, but on the other hand absorb the VOCs in significant amount if the moisture content dramatically increases due to high relative humidity. The challenge is to determine at what levels of relative humidity either one of the two effects is significant.

The objective of this study is to (1) experimentally determine the partition and effective diffusion coefficients of formaldehyde for three materials (conventional gypsum wallboard, “green” wallboard, and “green” carpet) under three different relative humidity conditions (20%, 50%, and 70% RH); (2) determine the repeatability of the test by conducting an additional test of formaldehyde in conventional gypsum wallboard for one relative humidity condition (50% RH); and (3) improve the understanding of effects of humidity on VOC sorption.

Experiment Principle and Apparatus

Principle

A dual-chamber test system was used in this study in which two stainless steel chambers (dimensions of 0.35 m × 0.35 m × 0.15 m) were partitioned by a test specimen (Figure 1). Each chamber was supplied with inflow rate of 5 × 10⁻⁴ m³/min under controlled temperature and RH. Chamber A had a constant formaldehyde injection at 4080 μg/m³ in the inflow, whereas chamber B has no formaldehyde injection. Constant formaldehyde supply was provided by a Dynacalibrator (model 500; VICI Metronics Inc., Poulsbo, WA) containing a formaldehyde permeation tube (emission rate 2040 ng/min) heated at 90 °C. The pressure drop between two chambers was negligible as verified by pressure measurements, since the same amount of air flow rate was supplied to both chambers and the same piping configuration was used for both chambers. A mixing fan was mounted inside each chamber to ensure a good mixing condition. The formaldehyde concentration in the inflow of chamber A was set at constant, and the concentrations in chambers A and B (termed as C _A and C _B, respectively) were continuously monitored until it reached a steady state. The inlet concentration of chamber A was denoted as C _Ain, whereas the inlet concentration of chamber B was zero. Concentrations in the outlets of chambers A and B were monitored as C _Aout and C _Bout. Under well-mixed condition, C _A = C _Aout and C _B = C _Bout. At steady state, C _Aout and C _Bout became constant. The test measured concentrations were considered to reach the steady state when the moving average of C _Aout and C _Bout did not change more than 1% between two adjacent data points. One test result including measured formaldehyde concentrations in two chambers and supply concentration for conventional wallboard under 20% RH are shown in Figure 2. Formaldehyde concentration was measured by a proton transfer reaction mass spectrometry (PTRMS) (high-sensitivity PTRMS; Ionicon Analytik, Innsbruck, Austria), which was precalibrated under each RH condition by using high-performance liquid chromatography (HPLC) (model 230; Varian Analytical Instruments, Walnut Creek, CA) because PTRMS formaldehyde measurement was influenced by RH. The sampling flow rate by PTRMS was 8.56 × 10⁻⁵ m³/min. Only one PTRMS was employed in the test, so PTRMS sampling port was manually switched for measuring concentrations in chamber A's inlet air (C _Ain), chamber A's outlet air (C _Aout) and chamber B's outlet air (C _Bout) in the test period.

Figure 1. Schematic of dual chambers (Xu and Zhang, 2011).

Figure 2. Test concentrations for conventional gypsum wallboard under 20% RH.

Calculation of effective diffusion coefficient and partition coefficient

Effective diffusion coefficients

At steady state, based on the formaldehyde mass balance in the dual-chamber system, the diffusion flux through the specimen was described by

(1)

Hence, the effective diffusion coefficient, D _e, was obtained by

(2)

where D _e was effective diffusion coefficient in m²/sec; C _Ass and C _Bss were the formaldehyde concentrations in the air phase in chambers A and B in μg/m³ at steady state, respectively; L was the thickness of the material in m; A was the material area exposed to the air in m²; j was the mass flux in kg/m²·sec; and Q _B was the flow rate into chamber B in m³/sec. The effective diffusion coefficient obtained from dynamic dual chambers also included the effects of the convective mass transfer resistance through the air film on either surfaces of the material (i.e., the boundary layer resistances). The importance of boundary layer was described in the literature (Xu and Zhang, 2003). The error resulting from such assumption depended on the boundary layer flow conditions over the specimen surfaces and the magnitude of the internal diffusion resistance, and the detailed information was provided by Xu and Zhang (2011). For the materials studied, the error by neglecting the boundary layer resistance for conventional wallboards and “green” wallboards was calculated to be less than 1%, so it was assumed that the boundary layer resistances were negligible when compared with the in-material diffusion resistance for the materials tested for wallboards only. For tested carpets, the boundary layer resistance was considered in the results of effective diffusion coefficient because the boundary layer resistance was comparable to the in-material diffusion resistance.

Partition coefficient

The formaldehyde mass adsorbed by the material at the steady state was

(3)

where M was the total formaldehyde mass in the material in kg; t was the time range of each test in hr; t _end was the end time of the diffusion test in hr; Q _A and Q _B were the flow rates into chambers A and B in m³/sec, respectively; C _Ain was the inlet formaldehyde concentration of chamber A in μg/m³; and C _Aout and C _Bout were the formaldehyde concentrations in the outflow of chambers A and B in μg/m³, respectively. The partition coefficient was defined as (C _m was the formaldehyde concentration in the material in μg/m³; x was the depth in the direction of specimen thickness in m; L was the specimen thickness in m), considering eq 3 and linear concentration distribution in the material at steady state, partition coefficient was obtained by

(4)

where K _ma was dimensionless partition coefficient; V _mat was the volume of the test specimen in m³; and C _Ass and C _Bss were the formaldehyde concentrations in the air phase in chambers A and B in μg/m³ at steady state, respectively.

Sampling intervals

It took 11, 9, and 6 days for the diffusion tests of conventional wallboard, “green” wallboard, and “green” carpet, respectively, to complete. An air sample was taken at least every 8 hr for C _Aout and C _Bout.. For each of these data points, the PTRMS was used to take an air sample every 10 sec for total 5 min, and the average value was used to determine the concentration. In addition, the background concentrations of chambers A and B were taken before the injection of formaldehyde, and the constant injection rate was verified by measuring C _Ain daily.

Test specimen preparation

The materials were shipped in the size of 12 inches × 12 inches × 0.5 inches (0.30 m × 0.30 m × 0.013 m), which was also the size of the test specimen. Upon receipt, the materials were stored in a specimen storage room under 23 °C and 50% RH conditions. Prior to the test, the four edge sides of the material were sealed by formaldehyde-free tape and the material was placed in a specially designed specimen holder frame to prevent formaldehyde diffusion through the edges. The photographs of the sealed test specimens are presented in Figure 3.

Figure 3. Test specimens. (a) Conventional and “green” wallboard (note: the appearance of the two kinds of wallboards were the same, since the same paint was used). (b) “Green” carpet.

The difference in the composition of two wallboards

The conventional wallboard and “green” wallboard were painted with the same paint and air dried at the same time period. The conventional wallboard consisted primarily of gypsum, with a paper surfacing on the face, back, and long edges. The “green” wallboard was paperless and features fiberglass mats on both sides for superior moisture protection. The two kinds of wallboards were made by different companies.

Experimental design and test conditions

Four tests of conventional wallboard and three tests of green wallboard were performed. Three tests of “green” carpet were also completed. Each material was measured under three levels of relative humidity (20%, 50%, and 70%). Besides, for conventional wallboard, an additional test was conducted at 50% RH to investigate the repeatability of the test method. The temperature for 10 tests was all at 23 ± 1 °C. Relative humidity for all the wallboard tests and carpet test was controlled well within ±2% of the set points. The environmental conditions (temperature and relative humidity) of conventional wallboard and “green” wallboard were recorded continuously during the tests. In the tests of green wallboard, the temperature was slightly lower than the designated temperature (23 °C) by 2 °C, and had also larger standard deviation than desired likely, but the temperature was consistent among the three “green” wallboard tests, allowing direct comparison between these tests to identify the RH effect on the effective diffusion coefficient and partition coefficient for “green” wallboard.

During the test for carpet, the carpet was highly permeable, as shown in the air permeability measurement (Figure 4), and hence significant effort was added to upgrade the system for controlling and measuring the pressure difference across the test specimen so that the convective flux could be compensated in the calculation of effective diffusion coefficient. The permeability of the carpet specimen has been measured, which enabled calculation of the convective flux based on the online monitored minimal pressure difference across the test specimen (<2 Pa). Even a small pressure difference across the test specimen (in the order of 0.2 Pa) could result in significant convection flux, which needed to be corrected in the calculation of the effective diffusion coefficient.

Figure 4. Measured air flow rate versus pressure drop for determination of air permeability of the carpet specimen.

Assuming a constant pressure difference at the steady-state period, the associated convective formaldehyde flux and total formaldehyde flux can be calculated in the following equations:

Convective formaldehyde flux:

(5)

where δ was the permeability of the carpet in kg/m·sec·Pa; ΔP was the pressure drop between chamber A and chamber B in Pa; ρ_air was the air density at the test temperature in kg/m³, which was 1.192 kg/m³ at 23 °C; L was the thickness of the material in m; A was the material area exposed to the air in m²; C _Bout was the formaldehyde concentration in the outflow of chamber B in kg/m³; and j _convection was formaldehyde mass flux due to convection in kg/sec.

Total formaldehyde flux from chamber A to chamber B:

(6)

where j _total was formaldehyde mass flux due to both convection and diffusion in kg/sec; and Q _B was the flow rate into chamber B in m³/sec.

Hence the flux due to diffusion could be calculated as

(7)

where j _diffusion was formaldehyde mass flux due to diffusion in kg/sec. The above calculations provide an estimation of the effective diffusion coefficients based on the estimated pressure difference measured at the steady-state period of the test. The partition coefficient was calculated in the same way as for the other materials. In order to control and monitor the pressure difference across the test specimen for highly permeable materials such as the carpet, an Ashcroft differential pressure transmitter (model DXLdp; Stratford, CT, range −24.9∼24.9 Pa, accuracy 0.25%) was purchased and installed together with an online monitoring data acquisition system.

The measured pressure drop was corrected by subtracting the average of the noise signal (system error) from direct reading of the sensor in the test.

Results and Discussion

Conventional and “green” gypsum wallboards

Repeatability between duplicate tests at the same humidity condition

Table 1 shows that the repeatability for conventional wallboard at the same relative humidity was good. The relative difference between the two duplicate tests was 4.2% and 7.1% for effective diffusion coefficient and partition coefficient, respectively. These values were also used for the error bars in the other test results. The summarized results of each wallboard test are shown in Table 2, which includes five parameters: the supply formaldehyde concentrations into chamber A (C _Ain), the equilibrium concentrations at both chambers (C _Aout and C _Bout), and the effective diffusion coefficient (D _e) and partition coefficient (K _ma) at each test condition. The measured continuous formaldehyde concentrations in two chambers and supply concentrations are available in the U.S. Environmental Protection Agency (EPA) final report (EPA, 2010).

Table 1. Repeatability of conventional wallboard at 50% RH

	50% RH	50% RH (Repeat)	Difference	Average
D e (m^2/sec)	6.34 × 10^−8	6.61 × 10^−8	4.2%	6.48 × 10^−8
K ma	446	479	7.1%	463

Table 2. Summary of test results for wallboards

Materials	RH Condition (%)	C Ain (μg/m^3)	C Aout (μg/m^3)	C Bout (μg/m^3)	D e (m^2/sec)	K ma
Conventional wallboard	20	2662.8	2603.4	72.9	3.67 × 10^−8	304
	50	3106.0	2921.7	138.8	6.34 × 10^−8	446
	50 (repeat)	2665.9	2500.8	124.1	6.61 × 10^−8	479
	70	2443.2	2274.7	163.3	9.84 × 10^−8	404
“Green” wallboard	20	2649.5	2244.3	260.1	1.65 × 10^−7	1100
	50	2715.9	2178.8	330.2	2.24 × 10^−7	1205
	70	1591.2	1007.6	275.7	4.73 × 10^−7	1325

Effect of relative humidity

Figure 5 shows the derived effective diffusion coefficients and partition coefficients at three levels of relative humidity (20%, 50%, and 70% RH). Considering the uncertainty of 4.2% of the effective diffusion coefficient, a higher relative humidity led to a slightly larger effective diffusion coefficient for both conventional wallboard and green wallboard. The small increase is likely due to more frequent collisions between formaldehyde and water vapor molecules due to the increase in relative humidity. At a higher relative humidity, the amount of adsorbed moisture in the material would also be higher (Xu et al., 2009). If the surface diffusion plays a role in the moisture transport, it is then also plausible that the higher adsorbed moisture content at a higher RH value also contributed to the increase of the effective diffusion coefficient of formaldehyde due to its water solubility nature. These hypotheses need to be further investigated in future studies that also include detailed measurements of the moisture retention curve as well as the diffusion of mixture gases (formaldehyde and water vapor in this case). From 20% to 50% RH, the partition coefficient of formaldehyde in conventional wallboard increased by 52%. Again, the higher adsorbed moisture content in the material at a higher RH value was likely to be responsible for the increase of the high partition coefficient due to the water-soluble nature of formaldehyde (Xu and Zhang, 2011). However, considering the uncertainty of 7.1% for partition coefficient of the experimental method, from 50% to 70% RH, the partition coefficient of formaldehyde in conventional wallboard decreased slightly. However, the decrease was less than 3 times the experimental uncertainty. This phenomenon agreed with the findings of Pei and Zhang (2011). Three mechanisms between the interaction of moisture and formaldehyde pollutant determined the total adsorbed capacity of the porous media (Bouilly et al., 2006; Pei and Zhang, 2011). First, because of the water solubility of formaldehyde, a higher relative humidity could result in higher water content in the porous media, therefore, more formaldehyde could be dissolved in the adsorbed water. Second, more condensed water in higher relative humidity condition in the media could block micropores available for formaldehyde transport, and hence limited the diffusion into the media (however, this is unlikely in the current study, since the effective diffusion coefficient increased with the relative humidity). Third, corresponding higher content of water vapor in the higher relative humidity level competed for the available adsorption sites at the exposed surface with formaldehyde molecule, which reduced the adsorption ability of the media for formaldehyde. More detailed quantitative analysis based on the measurement of moisture retention curve and pore size distribution of gypsum is needed in the future to address the relative importance of each mechanism.

The partition coefficient of formaldehyde in green wallboard increased slightly with the increase of relative humidity in the test range of 20–70% RH (the increase was within 3 times the experimental uncertainty), probably due to the soluble nature of formaldehyde, which was absorbed more into the adsorbed moisture at a higher relative humidity.

Comparison of conventional and green wallboards

In Figure 5, the results of conventional and green wallboards were plotted together. By comparison, the effective diffusion coefficient of green wallboard at each level of relative humidity was significantly larger than the one of conventional wallboard. In other words, the diffusion resistance of green wallboard was smaller than the diffusion resistance of conventional wallboard. The partition coefficient of green wallboard at each level of relative humidity was also larger than conventional wallboard, indicating that the green wallboard had a larger storage capacity for formaldehyde. However, lower test temperature in the “green” wallboard test than in the conventional wallboard test (21 vs. 23 °C) may or may not account for all the increase in the partition coefficients. More quantitative analysis is needed in future studies.

Figure 5. Comparison of conventional and green wallboards.

Both the conventional and “green” wallboards had a water-based paint. As a result, the data represented above included the effects of RH on the formaldehyde transport and storage in the paint layer as well as the gypsum material. Separate tests would be needed to separate the effects on the two materials and determine the diffusion and partition coefficients for individual materials as well as the material systems (i.e., painted boards) as in the current study.

Comparison of effective diffusion coefficient with other literature values

In Table 3, the measured diffusion coefficient of gypsum wallboard is compared with the values reported by other literature. Attention should be given to the definition of diffusion coefficients. In this paper, only the effective diffusion coefficient is adopted. Some literature reported the apparent diffusion coefficient (D) instead of effective diffusion coefficient, and the relationship between D and D _e (Xu et al., 2009) was provided in the following equation:

Table 3. Comparison of effective diffusion coefficient with other literature values

Reference	Material	Compound	Efective DiffusionCoeffficient (m^2/sec)
This study	Conventional gypsum wallboard	Formaldehyde	6.34 × 10^−8
	“Green” gypsum wallboard	Formaldehyde	2.24 × 10^−7
Bodalal et al. (2000)	Plywood	Cyclohexane	5.39 × 10^−8
	Floor tile	Decane	2.73 × 10^−8
Zhang et al. (2002, 2003)	Painted drywall	Ethylbenzene	2.68 × 10^−8
	Painted drywall	Benzaldehyde	4.81 × 10^−8
	Ceiling tile	Benzaldehyde	2.61 × 10^−7
	Ceiling tile	Decane	9.62 × 10^−8
Farajollahi et al. (2009)	Ceiling tile	Hexane	1.97 × 10^−6
	Ceiling tile	Octane	1.79 × 10^−6
Meininghaus et al. (2000)	Gypsum	Octane	8.40 × 10^−7
Xu and Zhang (2011)	Calcium silicate	Formaldehyde	3.28 × 10^−6
Xiong et al. (2011)	Medium density fiberboard	Formaldehyde	8.15 × 10^−8

(8)

where K _ma was the partition coefficient of VOCs in the material. By comparison, it is seen that the tested effective diffusion coefficients are in the same order of magnitude with other reported values.

Carpet

The test results of carpet are summarized in Tables 4 and 5. Figure 6 provides the comparison of effective diffusion coefficients and partition coefficients of carpet at different RHs. Three tests were conducted for the carpet (20%, 50%, and 70% RH). The measured pressure drop was corrected by subtracting the average of the noise signal (system error) from direct reading of the sensor in the test. The noise reading of pressure sensor at 70% RH was relatively larger than the noises at 20% and 50% RH.

Table 4. Summary of calculated mass fluxes in carpet tests

Specimen	Designated RH (%)	Total Mass Flux(μg/sec)	Mass Flux Due to Convection* (μg/sec)	Mass Flux Due to Diffusion(μg/sec)
“Green” carpet	20	1.31 × 10^−8	−1.78 × 10^−8	3.09 × 10^−8
	50	1.25 × 10^−8	−1.85 × 10^−8	3.10 × 10^−8
	70	1.29 × 10^−8	−3.65 × 10^−8	4.94 × 10^−8
Note: *Negative sign means that the flux is from chamber B to chamber A.

Table 5. Summary of test results for carpet

Materials	RH Condition (%)	C Ain (μg/m^3)	C Aout (μg/m^3)	C Bout (μg/m^3)	D e (m^2/sec)	K ma
“Green” carpet	20	3346.71	1825.11	1530.71	2.30 × 10^−5	471
	50	3294.84	1721.42	1451.83	2.64 × 10^−5	661
	70	3388.96	1790.57	1491.51	5.00 × 10^−5	967

Figure 6. Effective diffusion coefficients and partition coefficients of carpet at different RHs.

The calculated effective diffusion coefficients at different RHs were at the same magnitude with the diffusion coefficient of formaldehyde in dry air (D _air) at 23 °C (1.49 × 10⁻⁵ m²/sec). The diffusion coefficient of formaldehyde in dry air at a specific temperature and pressure was obtained by eq 9 (Nelson, 1982):

(9)

where D _air was the diffusion coefficient of formaldehyde in m²/sec; m _A was the molecular weight of dry air in g/mol; m _B was the molecular weight of formaldehyde in g/mol; v _A was the molecular volume of dry air in mL/gmol; v _B was the molecular volume of formaldehyde in mL/gmol; T was the temperature in K; and P was the pressure in atm (1 atm = 1.01325 × 10⁵ Pa).

The effective diffusion coefficients at 20%, 50%, and 70% RH were at the same order of magnitude with the diffusion coefficient in air, but the values appeared to be larger (Figure 6), which could not be explained by diffusion theory for dilute systems. The larger diffusion coefficient was likely due to the relative larger signal noise observed during the experiment, especially pressure drop measurement. The second reason of this phenomenon might be method uncertainty in the measurement of porous carpet. The results implied that the dual-chamber method was not appropriate for the highly porous materials like carpet. Other published literature such as Little et al. (1994) provided the method to estimate the diffusion coefficient of VOCs in carpet.

The partition coefficient of formaldehyde in carpet increased slightly with the increase of relative humidity, likely due to the soluble nature of formaldehyde. A higher relative humidity led to a higher adsorbed moisture, which would increase the amount of formaldehyde absorbed.

Conclusions

A dynamic dual-chamber test system and method were used for the experiments. The objective of the study was to experimentally determine the partition and effective diffusion coefficients of formaldehyde for three materials (conventional gypsum wallboard, “green” wallboard, and “green” carpet) under three different relative humidity conditions (20%, 50%, and 70% RH). The data were intended for assessing the sorption effects of the materials for formaldehyde and the impact on the formaldehyde concentration in buildings, which was needed for exposure assessment. The following conclusions were drawn from the study:

1.	The test method had good repeatability, as verified by the duplicate tests for conventional wallboard at 50% RH.
2.	A higher relative humidity led to a larger effective diffusion coefficient for both conventional wallboard and green wallboard.
3.	Partition coefficient of formaldehyde in conventional wallboard became larger from 20% to 50% RH, but decreased slightly when the relative humidity was further increased from 50% to 70% RH. However, the decrease was less than 3 times the experimental uncertainty.
4.	The partition coefficient of formaldehyde in “green” wallboard and “green” carpet increased slightly with the increase of relative humidity (the increase was also within 3 times the experimental uncertainty), probably due to the soluble nature of formaldehyde, which was absorbed more into the adsorbed moisture at a higher relative humidity.
5.	The effective diffusion coefficient and partition coefficient of green wallboard at each level of relative humidity were significantly larger than the ones of conventional wallboard. The slightly lower temperature in the “green” wallboard than in the conventional wallboard tests (21 vs. 23 °C) may or may not be responsible for all of the difference, which required further investigation.
6.	The carpet specimen was highly permeable and the measured effective diffusion coefficients at 20%, 50%, and 70% RH were all at the same magnitude with the formaldehyde diffusion coefficient in dry air at 23 °C, but larger than diffusion coefficient in air. It indicated that the dual-chamber method was not appropriate for the measurement of highly porous material like carpet. The partition coefficient, however, increased slightly with the increase of RH level.

To better explain the data for the two kinds of gypsum boards, it is suggested that the pore size distributions of three layers of each type of board be measured in the future.

Nomenclature

A	=	specimen area, m2
C Ain	=	inflow VOC concentration for chamber A, μg/m3
C Bin	=	inflow VOC concentration for chamber B, μg/m3
C Aout	=	outflow VOC concentration for chamber A, μg/m3
C Bout	=	outflow VOC concentration for chamber B, μg/m3
C A	=	VOC concentration in chamber A, μg/m3
C Ass	=	VOCconcentration in chamber A at steady state, μg/m3
C B	=	VOC concentration in chamber B, μg/m3
C Bss	=	VOC concentration in chamber B at steady state, μg/m3
C m	=	the formaldehyde concentration in the material, μg/m3
D	=	apparent diffusion coefficient through material, m2/sec
D e	=	effective diffusion coefficient through material, m2/sec
D air	=	diffusion coefficient in air, m2/sec
j	=	mass flux across the specimen, kg/(m2s)
j total	=	formaldehyde mass flux due to both convection and diffusion in kg/sec
j diffusion	=	formaldehyde mass flux due to diffusion in kg/sec
j convection	=	formaldehyde mass flux due to convection in kg/sec
K ma	=	partition coefficient at equilibrium, = C m/C a, dimensionless
L	=	specimen thickness, m
M	=	total VOC mass in the material, kg
m A	=	molecular weight of dry air, g/mol
m B	=	molecular weight of formaldehyde, g/mol
P	=	pressure, Pa
Q A	=	supply air flow rate of chamber A, m3/sec
Q B	=	supply air flow rate of chamber B, m3/sec
RH	=	relative humidity, %
T	=	temperature, K
t end	=	end time of the diffusion test, hr
t	=	time, hr
V mat	=	volume of material, m3
v A	=	molecular volume of dry air, mL/gmol
v B	=	molecular volume of formaldehyde, mL/gmol;
x	=	depth in the direction of specimen thickness, m
ρair	=	air density at the test temperature in kg/m3
δ	=	permeability of the carpet in kg/m·sec·Pa

Acknowledgments

This study was financially supported by U.S. Environmental Protection Agency.