Building and Environment 93 (2015) 221e233
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Building and Environment journal homepage: www.elsevier.com/locate/buildenv
A prediction model of VOC partition coefficient in porous building materials based on adsorption potential theory Yanfeng Liu*, Xiaojun Zhou, Dengjia Wang, Cong Song, Jiaping Liu School of Environmental and Municipal Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 April 2015 Received in revised form 16 June 2015 Accepted 22 June 2015 Available online 25 June 2015
The partition coefficient (K) of the interface between air and building materials has a significant effect on the emission characteristics of volatile organic compounds (VOCs). Existing research on determining the partition coefficient is mostly performed experimentally. However, the experimental data only apply to a particular condition and are unable to reveal the functional mechanism of the primary controlling factors of K, such as temperature, VOC properties and building material parameters. This study deduced a dualscale calculation model of K respectively for micropores and macro-mesopores in porous materials based on the adsorption potential theory. The model considers a number of factors that affect the partition coefficient, such as pore scale, porosity, temperature, VOC properties and other parameters. Three types of medium density fiberboard (MDF) and one type of particleboard (PB) which were commonly used in interior decoration were chosen as the experimental objects in the mercury intrusion porosimetry (MIP) tests and the continuous temperature rising e variable volume loading (CTR-VVL) method. By fitting and comparing the experimental data and theoretical calculation values, the obtained equations of K exhibited high consistency with the experimental results, which provides a reliable approach to predict K. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Indoor air quality Porous building materials Volatile organic compounds (VOCs) Partition coefficient Adsorption potential theory
1. Introduction Volatile organic compounds (VOCs) released by modern building materials seriously affect the indoor air quality and can greatly harm the health of people [1e3]. Such compounds may cause sick building syndrome (SBS) with symptoms that include dizziness, giddiness, nausea, drowsiness, and inattentiveness [4e11]. To control and purify indoor VOCs, a full understanding of the VOC emission characteristics of the building materials is needed. The partition coefficient, K, is one of the key parameters of VOC emission, which is on the interface between the air and building materials [12], will directly affect the VOC emission rate and indoor VOC concentrations. Therefore, accurate calculation of the partition coefficient is critical in determining VOC emission characteristics and forecasting indoor VOC concentrations. Existing experimental methods of determining the K of building materials can be broadly divided into two categories. The first category, which includes the C-history method [13,14], the multi-
* Corresponding author. E-mail address:
[email protected] (Y. Liu). http://dx.doi.org/10.1016/j.buildenv.2015.06.025 0360-1323/© 2015 Elsevier Ltd. All rights reserved.
sorption equilibrium regression method [15,16], the multiemission/flush regression method [17,18] and the variable volume loading method [19], is to design a simple and easily controlled experiment based on the definition of the partition coefficient which is the ratio between the surface concentration of the adsorbed phase and the adsorbate concentration of the gas phase. The second category, which includes the straight-flow environmental chamber method [12], the CLIMPAQ method [20] and the two-chamber method [21], is to develop a mass transfer model for describing the VOC emission process in the experiment and to obtain the K by fitting the model to the experimental data. However, the values of K obtained by the above methods are specific values under fixed operating conditions, which can only represent a single working pair of material-VOC. The above methods fail to reveal the functional mechanism of the main controlling factors such as temperature, VOC properties and building material parameters. Thus, it is impossible to obtain the value of K for different material-VOC working pairs under uncertain environmental conditions by the above methods. Wang et al. [22] proposed a prediction formula of K, which established a correlation between K and the liquid molar volume of VOC. The value of K of some VOCs can be predicted or estimated
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Nomenclature
Symbols A emittable surface area of the material (m2) C VOC concentration in the gas phase (mg/m3) C0 initial VOC concentration of the mass transfer model in porous media (mg/m3) Ca equilibrium concentration of adsorbate in the gas phase (mol/m3) Cad VOC concentration in the adsorbed phase (mg/m3) Cequ,i equilibrium VOC concentrations in the chamber (mg/ m3) Cm equilibrium concentration of adsorbate at the adsorbent surface (mol/m3) Cm0 initial VOC concentration of the single-phase mass transfer model (mg/m3) Cw VOC concentration at the material-air contact surface (mg/m3) C∞(t) VOC concentration in the gas phase (mg/m3) d pore diameter (m) De effective diffusion coefficient (m2/s) Dg VOC diffusion coefficient in the gas phase (m2/s) Dad surface diffusion coefficient of VOC in the adsorbed phase (m2/s) g(y,t) time and space dependent VOC generation/elimination rate due to secondary source/sink behavior (mg/ m3$s1) h convective mass transfer coefficient on the material surface (m/s) K partition coefficient K1 partition coefficient on micropore surface K2 partition coefficient on macro and mesopore surface Ke effective partition coefficient Km partition coefficient at the building material surface of the single-phase mass transfer model Kn Knudsen number P intrusion pressure of the mercury (Pa)
from the available data of a few typical known species of VOCs in building materials. However, the precondition is that the predicted VOC molecular structure must be similar with the known VOCs, which means that the structures have the same chemical bonds and functional groups. This precondition limits the application range of the formula, and the prediction formula still fails to provide the influence of temperature and building material parameters on the partition coefficients. Zhang et al. [23] deduced the expression of K according to the Langmuir monolayer adsorption theory and established a functional relationship between K and temperature. However, the fundamental view of the Langmuir monolayer adsorption theory regards the solid surface as uniform, and no saturated atomic force field exists. Therefore, the adsorption mechanisms are the same on the solid surface; the gas will be adsorbed on the solid surface when it comes into contact with the surface. Once the surface is covered with a layer of gas molecules, the force field will be saturated and adsorption will no longer occur. Thus, the adsorption process is site-specific monolayer adsorption, and each adsorption site can only accommodate one adsorbate molecule; this process assumes that the adsorption heat is constant and there is no interaction between the adsorbed molecules. However, the nonuniformity of the solid surface will lead to the formation of
p p0 R T V V0 Va V Vm
balance pressure of the gas (Pa) saturated vapor pressure (Pa) universal gas constant (8.314 J/(mol$K)) thermodynamic temperature (K) adsorbed volume of per unit mass of adsorbent (m3/ mg) pore volume of per unit mass of adsorbent (m3/mg) volume of the airtight space (m3) liquid molar volume of adsorbate (m3/mol) adsorbent volume of per unit mass of adsorbent (m3/ mg)
Greek symbols a adsorption quantity of per unit mass of adsorbent (mol/mg) bi volumetric air/material phase ratio g surface tension of mercury (N/m) ε adsorption potential (J) r density of material (kg/m3) f total porosity f1 porosity of micropores f2 porosity of macro-mesopores f0 porosity of macropores f'' porosity of mesopores u contact angle between mercury and the material surface ( ) Abbreviations CTR-VVL continuous temperature rising e variable volume loading MDF medium density fiberboard MIP mercury intrusion porosimetry PB particleboard SBS sick building syndrome VOCs volatile organic compounds VVL variable volume loading
different types of active centers, which will show different affinities to the gas molecules. Additionally, a gas molecule may not only be absorbed by one activity center, but it is likely to be adsorbed at the adjacent location between two or more active centers on the solid surface [24,25]. In summary, the complexity of the microstructure of porous building materials and the variability of the environmental temperature cause diversity of the gas adsorption mechanism, which leads to difficulties in determining the gas emission characteristics. Therefore, it is important to establish the correlation between the partition coefficient and the main controlling factors. In this study, the adsorption characteristics of different pore scales were analyzed and a dual-scale calculation model of K was deduced. This model, which is verified experimentally, enables a reliable parameter calculation method for the study of VOC emission characteristics in porous building materials. 2. Theoretical analysis The adsorption potential theory considers that there is an adsorption potential energy field on the solid surface and gas molecules are adsorbed in this potential field. Polanyi [26] first quantitatively described this theory which states that at a constant
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temperature, the physical work attracts 1 mol of gas from the bulk phase to the adsorbed phase. If the adsorption temperature is much lower than the critical temperature of the gas, the gas is regarded as the ideal gas, and the adsorption potential can be expressed as
ε ¼ RT ln
p0 p
(1)
where R is the universal gas constant, 8.314 J/(mol$K); T is the thermodynamic temperature, K; p0 is the saturated vapor pressure under the experimental temperature, Pa; p is the balance pressure of the gas, Pa. Dubinin et al. [27] introduced the adsorption potential theory into the research on pore adsorption characteristics. They divided the pore structures into two categories, the micropore structure and the macro-mesopore structure. For micropore adsorption, they built the pore filling theory, which states that because the space is tiny in micropore whose size is in molecular scale, the adsorption potentials will be superimposed with each other. This effect causes the gas adsorption mechanism on microporous adsorbent completely different from that on a flat surface. As shown in Fig. 1(a), the superimposed Van der Waals dispersion forces from all pore wall directions cause the adsorption of molecules in the micropore. The gas adsorption behavior of the micropores is pore filling rather than the surface coverage form described by the monolayer adsorption theory shown in Fig. 1(b). Thus, the adsorption potential is much larger in the micropore than on the flat surface. For micropores, the Knudsen number is Kn 0:1, and the adsorption characteristic curve of the micropore structure can be described by the following formula [27]:
V ¼ V0 exp kε2
(2)
where V is the adsorbed volume of per unit mass of adsorbent, m3/ mg; V0 is the pore volume of per unit mass of adsorbent, m3/mg; k is a constant codetermined by the properties of the adsorbate and the adsorbent. The adsorption quantity of per unit mass of adsorbent, a, is defined as
a¼
V V
(3)
where V is the liquid molar volume of the adsorbate, m3/mol. By substituting Eqs. (1) and (2) into Eq. (3), the DubininRadushkevich adsorption equation can be obtained as the
223
following equation [28]:
a¼
" # V0 p 2 exp k RT ln 0 p V
(4)
For the ideal gas at low pressure, the relation between the adsorbate concentration and the pressure is
Ca ¼
a p ¼ V RT
(5)
where Ca is the equilibrium concentration of adsorbate in the gas phase, mol/m3. Considering the equilibrium concentration of the adsorbed phase and the gas phase are much lower than the saturation concentration, Henry's law describes this transient and reversible equilibrium relationship between the adsorption concentration on the pore surface and the adsorbate vapor concentration [29].
Cm ¼ KCa ¼
K p RT
(6)
where Cm is the equilibrium concentration of the adsorbate at the adsorbent surface, mol/m3. The adsorption quantity of per unit mass of adsorbent can also be expressed as
a ¼ Vm Cm ¼
KVm p RT
(7)
where Vm is the adsorbent volume of per unit mass of adsorbent, m3/mg. For micropores, the partition coefficient on the pore surface is defined as K1. Simultaneously solving Eqs. (4) and (7), the following is achieved:
" # V0 p 2 K Vm p exp k RT ln 0 ¼ 1 p RT V
(8)
Under constant temperature and volume conditions, according to the definition of the partition coefficient and the ideal gas state equation, K1 can be written as
K1 ¼
p0 p
K1 can be solved by substituting Eq. (9) into Eq. (8).
Fig. 1. Comparison between the two types of adsorption modes.
(9)
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"
1 VVm p0 K1 ¼ exp 0:5 ln0:5 V0 RT k RT
!# (10)
Cad ¼
K1 ¼ exp
1 k0:5 RT
ln0:5
Vp0 f1 RT
!#
Ke (11)
For the adsorbent with a large amounts of macro and mesopores, the Knudsen number of macropores is Kn 10; and the Knudsen number of mesopores is 0:1 < Kn < 10. The pore diameter is relatively large in these pores, so the dispersion force is not superimposed, and the adsorption potential decreases. The relationship between the adsorption potential and the adsorption volume in such an adsorbent structure is [27].
V ¼ V0 expð mεÞ
(12)
where m is a constant codetermined by the properties of the adsorbate and the adsorbent. The Freundlich adsorption isotherm [30] can be obtained by substituting Eqs. (1) and (12) into Eq. (3).
a¼
V0 V
p p0
V0 RT VVm p0
!
1 mRT
(14)
If the porosity of the macro-mesopores, f2, is already known, K2 can be expressed as
K2 ¼
f2 RT Vp0
(18)
where the effective diffusion coefficient De is defined as De ¼ fDg; the effective partition coefficient Ke is defined as 2 K2 Ke ¼ f þ ð1 fÞ f1 Kf1 þf . For material with only micropores or a þf 1
2
tiny porosity of macro-mesopores compared with micropores, Ke ¼ f þ ð1 fÞK1 ; conversely, for material with only macromesopores or a tiny porosity of micropores compared with macro-mesopores, Ke ¼ f þ ð1 fÞK2 . According to the experimental research of pore size distribution in porous building materials, the pores inside the vast majority of porous building materials are located within the macroscopic and mesoscopic scales; therefore, the ratio of micropores can be ignored. The convective mass transfer at the material-air contact surface can be described by the third boundary condition as follows:
vC ¼ h½Cw C∞ ðtÞ vy
(19)
(13)
Consistent with the above deduction of the partition coefficient in micropores, the partition coefficient in macro-mesopores is
K2 ¼
vC v2 C ¼ De 2 vt vy
De
mRT
(17)
Here, Eq. (16) can be converted as
If the porosity of the micropores f1 is already known, K1 can be expressed as
"
f1 K1 þ f2 K2 C f1 þ f2
where h is the convective mass transfer coefficient on the material surface, m/s; Cw is the VOC concentration at the material-air contact surface, mg/m3; C∞(t) is the VOC concentration in the gas phase, mg/ m3. If the building material is double-sided symmetrical in shape, there is no mass flux at the central section, so
vC ¼0 vy
(20)
Assuming that the distribution of the initial VOC concentration is homogeneous in the material:
!
1 mRT
(15) Cjt¼0 ¼ C0
Based on the above analysis, for any material, the partition coefficient can be predicted by the dual-scale calculation model as Eq. (11) or (15), if the pore size distribution is already known. To obtain the variational pattern of VOC concentration, the mass transfer model in porous media should be solved. The mass balance equation describing the internal gas diffusion in porous media is [31,32].
vC vC v2 C v2 Cad þ ð1 fÞ ad ¼ fDg 2 þ ð1 fÞDad f ± gðy; tÞ vt vt vy vy2 (16) where f is the total porosity; C is the VOC concentration in the gas phase, mg/m3; Cad is the VOC concentration in the adsorbed phase, mg/m3; Dg is the VOC diffusion coefficient in the gas phase, m2/s; Dad is the surface diffusion coefficient of VOC in the adsorbed phase, m2/s; gðy; tÞ is the time and space dependent VOC generation/ elimination rate due to secondary source/sink behavior, mg/m3$s1. Because the surface diffusion coefficient is several orders of magnitude smaller than the molecular diffusion coefficient and the Knudsen diffusion coefficient, the surface diffusion is negligible [33,34]. The secondary source/sink behavior is not considered here; therefore, gðy; tÞ can also be ignored. Based on Henry's law [29] and the dual-scale calculation model of K, Cad can be expressed as
(21)
For an airtight space, the equilibrium equation for the VOC concentration can be expressed as
dC∞ ðtÞ Va ¼ Ah½Cw C∞ ðtÞ dt
(22)
where Va is the volume of the airtight space, m3; A is the emittable surface area of the material, m2. The variational pattern of C∞ can be obtained by numerically solving Eqs. 18e22. Compared with the single-phase mass transfer model developed by Xu and Zhang [35], the relationship between the partition coefficient at the building material surface and the pore surface is
Km ¼ Ke
(23)
where Km is the partition coefficient at the building material surface of the single-phase mass transfer model. The initial VOC concentration of the single-phase mass transfer model is
Cm0 ¼ Ke C0
(24)
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3. Experiment This study focused on the VOC emission characteristics of indoor building materials that are mostly macroporous and mesoporous in structure [32,36]. The pore diameter measuring range of the mercury intrusion porosimetry (MIP) tests meets the measurement requirements for the porous structure of the building materials. The microstructural parameters obtained from the MIP tests are substituted into the macro-mesoscale calculation model of K to obtain the theoretical value. Then, the VOC emission experiments are conducted in an airtight environmental chamber using continuous temperature rising e variable volume loading (CTRVVL) method, by which the experimental data of K under different temperatures can be obtained. Through fitting and comparing the experimental data and the theoretically calculated values, the accuracy of the calculation model of K can be verified. 3.1. MIP tests The pore diameter is measured using MIP tests, wherein it is assumed that mercury cannot infiltrate solid surfaces; therefore, mercury can only be intruded into the pores of the material under a certain pressure to overcome the capillary resistance. The study on the pore structure of porous materials is associated with a certain pore geometry model. A relatively common and recognized cylindrical pore model is used in this study. Based on this model, the Washburn formula is used to establish the relationship between the intrusion pressure of the mercury and the pore diameter:
d ¼ 4g cos u=P
(25)
where d is the pore diameter, m; g is the surface tension of mercury, N/m; u is the contact angle between the mercury and the material surface, ; P is the intrusion pressure of the mercury, Pa. Eq. (25) shows that under the condition of the premises that g and u remain constant, mercury will be gradually intruded into the smaller pores under increasing pressure. If the pressure changes from P1 to P2, the corresponding pore diameter will vary from d1 to d2, and the intrusion volume of mercury will be measured between d1 and d2 per unit mass of material. For continuously increasing pressure, the pore size distribution can be obtained when measuring the corresponding intrusion volume of different pore diameters. The MIP tests use a PoreMaster GT-60 (Quantachrome, America) that has a pore diameter measuring range of 0.0036e950 mm. The device includes two low-pressure analysis stations and two highpressure analysis stations. The low-pressure sensor ranges from 1.5 to 350 kPa, the corresponding analysis pore diameter range is 400 to 4.26 mm, the accuracy is ±0.11% fso, and the resolution ratio is 5.26 Pa. Additionally, the high-pressure sensor ranges from 140 kPa to 420Mpa, the corresponding analysis of the pore diameter range is 10.66 to 0.0035 mm, the accuracy is ±0.05% fso, the lag is ±0.10% fso, and the resolution ratio is 6.32 kPa. The available instrument parameters show that the PoreMaster GT-60 can meet the measurement requirements for macro-mesoporous building materials. 3.2. CTR-VVL method The VVL method proposed by Xiong et al. [19] designates the volumetric air/material phase ratio as bi, and measures the corresponding equilibrium VOC concentrations, Cequ,i, in the airtight environmental chamber. By linearly fitting 1/Cequ,i and bi using the following equation
1 1 Km ¼ b þ Cequ;i Cm0 i Cm0
(26)
Cm0 and Km can be obtained according to the slope and intercept. In an airtight space, the equilibrium VOC concentrations of the same material are distinct under different temperatures. This study selected formaldehyde as the target VOC for concentration detection, which shows a faster emission rate and higher equilibrium concentration with the increase of temperature. Based on the emission characteristics of formaldehyde, for an identical piece of material and corresponding to a fixed bi, continuous measurements of the equilibrium concentrations of formaldehyde were made under low to high temperatures. The environmental chamber was not opened until all measurements of one bi were completed under multiple sets of temperatures. The measurements of another bi began when the background concentration fell below the limit. As described above, this experimental method is CTR-VVL method. The schematic diagram of the VVL and CTR-VVL method is shown in Fig. 2. There are several advantages compared with the VVL method, which is successively conducted on one material for a single temperature. (1) An identical piece of material is tested under multiple working conditions to avoid the inherent slight differences between different pieces of the material and to reduce the measuring error of the same bi. (2) The CTR-VVL method sets the previous equilibrium concentration as the initial environmental concentration of the following temperature condition, which accelerates the process to reach the equilibrium concentration. (3) The VVL method requires the environmental chamber to be cleaned after each temperature measurement, and the next measurement begins only when the background concentration is below the limit. In this study, the CTR-VVL method eliminates a series of preparatory work between each temperature condition, which speeds up the progress of the experiment. (4) An identical piece of material is tested in multiple working conditions rather than replacing a new material for each temperature, which reduces the material consumption. The experimental apparatus of the CTR-VVL method mainly includes the following: (1) an HJC1 environmental chamber, whose dimensions are 1.65 0.92 2.04 m (L W H), the volume inside the chamber is 1 m3, the accuracy range for the temperature measurements is ±0.5 C, and the accuracy range of the relative humidity measurements is ±5%. The inner wall material is manufactured by stainless steel, which is inert and non-adsorptive to the formaldehyde. Sealing strips that do not absorb formaldehyde seal the gaps on the chamber door. There is a fan at the top of the chamber to ensure that the VOC concentration is homogeneous in the chamber. The airflow direction is parallel to the surface of the test material, and the air velocity remains 0.1e0.3 m/s inside the chamber. The apparatus also contains (2) a Z300XP formaldemeter, whose measuring range for formaldehyde concentration is 0e30 ppm, the resolution ratio is 0.01 ppm, and the accuracy is ±5%. (3) A temperature and humidity recording system is also included and is composed of a K type thermocouple thermometer, which is used to record the inner wall temperature of the environmental chamber. The measurement range of the thermometer is 200 to þ1370 C, the resolution ratio is 0.1 C, and the accuracy is ±(1 C þ 0.3% rdg). Additionally, the wireless measurement device for the air temperature and relative humidity in the chamber, an iButtonDS1923, has a temperature measurement range of 20 to þ85 C with a resolution ratio of 0.5 C and an accuracy of ±0.5 C; its relative humidity measurement range is 0e100% with a resolution ratio of 0.6%. (4) Finally, the system includes an air velocity transducer SWEMA03, which is connected with the host SWEMA3000; its air velocity measurement range is 0.05e3.00 m/s,
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Fig. 2. Schematic diagram of the VVL and CTR-VVL method.
and it has an accuracy of ±0.04 m/s. A schematic diagram of the experimental apparatus is shown in Fig. 3. One month before beginning of the experiment, the building materials used in the environmental chamber experiment were cut into the required sizes. After being cut, aluminum foil tape was used to seal the edges of the building materials. Then, the building
materials were sealed into the black bags protected from light and kept in a dry place. The materials were only removed from the bags when the experiments began, which is make to ensure a uniform initial concentration in the building material. It was assumed that the default mass transfer process was only performed in the thickness direction, and there was no VOC leakage from the edges.
Fig. 3. Schematic diagram of the experimental apparatus.
Y. Liu et al. / Building and Environment 93 (2015) 221e233
4. Results and discussion
227
Table 1 Material properties based on the MIP tests.
4.1. The results of the MIP tests To obtain the theoretical calculation value of the partition coefficient of the porous building materials, the microstructure parameters of the materials should be tested first. The MIP tests selected three types of medium density fiberboard (MDF) and one type of particleboard (PB), which are widely used in interior decoration. The pore size distributions of the tested materials are shown in Fig. 4. As shown in Fig. 4, the pore size distributions of the four types of building materials were similar. The pore volumes decreased in the mesoscale range, and the values were close to 0 when the pore diameters approached 0.01 mm. The same rule can be found from the variation trends of the cumulative pore volume, which presented an obvious rising trend in the macroscale range; however, this trend gradually smoothed in the mesoscale range. The material parameters of the MIP tests are shown in Table 1. The porosity of macropores occupied a vast majority of the total porosity, and the porosity of mesopores was relatively small. The total porosity is the sum of the porosities of macropores and mesopores. Based on the above results of the MIP tests, the adsorption process of the four types of building materials can be described by the Freundlich adsorption equation as Eq. (13), and the corresponding theoretical values of the partition coefficient at the pore surface can be calculated by Eq. (15).
Material
f (%)a
f0 (%)b
f00 (%)c
V0 ( 109 m3/mg)
r (kg/m3)d
MDF 1 MDF 2 MDF 3 PB
55.92 47.16 55.42 43.22
49.83 42.33 48.68 36.69
6.09 4.83 6.74 6.53
0.706 0.634 0.754 0.650
790 743 735 665
a b c d
f is the total porosity. f0 is the porosity of macropores. f00 is the porosity of mesopores. r is the density of material.
4.2. The results of the environmental chamber experiments Experiments on the four types of selected building materials were conducted in the environmental chamber by the CTR-VVL method, and each type of material was cut into five different sizes corresponding with five different values of bi. The specific material parameters are shown in Table 2. The environmental chamber was in an airtight state when the measurements began; the relative humidity inside the chamber was controlled at 45 ± 5%. Each sample was tested the emission process of formaldehyde at the temperatures of 18 C, 23 C, 28 C and 33 C. Under each temperature condition, if the mean concentration of the formaldehyde in the chamber varied no more than 1% in 1 h, the formaldehyde was considered to reach the equilibrium concentration. At equilibrium, the temperature of the environmental chamber can be elevated to next higher condition. The
Fig. 4. Pore size distributions of the tested materials.
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Table 2 Material parameters in the environmental chamber experiments. Material
Length width height (mm mm mm)
MDF 1
710 710 355 200 155 710 710 355 200 155 710 710 355 200 155 710 710 355 200 155
MDF 2
MDF 3
PB
705 705 705 705 705 705 705 705 705 705 705 705 705 705 705 705 705 705 705 705
12 12 12 12 12 5 5 5 5 5 3 3 3 3 3 16 16 16 16 16
sample was not replaced for a new round of experiments until it was tested under each of the four temperature conditions. Linearly fitting 1/Cequ,i and bi by Eq. (26), the results are shown in Fig. 5. Cm,0 and Km are calculated using the slope and intercept after
Number of pieces
bi
2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1
82 165 332 590 762 199 400 798 1417 1829 332 665 1331 2363 3049 61 124 249 442 571
performing the linear fitting, and the results are shown in Table 3. With the temperature increase, the average kinetic energy of the molecules increased, and the adsorbates that were originally in fixed states crossed the potential barrier at the surface of
Fig. 5. Linear regression for the determination of Cm0 and Km.
Y. Liu et al. / Building and Environment 93 (2015) 221e233
229
Table 3 Cm0 and Km determined by CTR-VVL method. Material
Temperature ( C)
Cm0 ( 106 mg/m3)
Km
r2
MDF 1
18 23 28 33 18 23 28 33 18 23 28 33 18 23 28 33
17.81 20.91 25.45 32.86 8.780 9.184 10.09 12.43 4.800 5.090 5.968 7.027 38.95 42.69 46.06 56.13
3517 2681 2046 1718 5505 4461 3729 2795 4164 3170 2729 1909 6221 4901 3956 3328
0.9833 0.9475 0.9816 0.9797 0.9881 0.9543 0.9678 0.9663 0.9538 0.9739 0.9656 0.9730 0.9907 0.9838 0.9497 0.9674
MDF 2
MDF 3
PB
Fig. 7. The formaldehyde concentration distribution of MDF 1 at 18 C.
adsorbed phase, and finally converted to the desorption molecules. As a result, Cm,0 gradually increased while Km showed decreasing trend. This combined effect caused accelerated emission rates and higher equilibrium concentrations with the increasing temperature. Huang et al. [37] derived a theoretical correlation between Cm0 and temperature for formaldehyde emissions as follows:
a b Cm0 ¼ pffiffiffi exp T T
(27)
where a and b are constants. To verify the effectiveness of Cm0 measured by the CTR-VVL method, the experimental data of Cm0 were fitted with the
Fig. 6. Fitting results of the experimental Cm0 with the correlation in the literature.
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Y. Liu et al. / Building and Environment 93 (2015) 221e233
accurately reflect the equilibrium state and the error caused by it is negligible.
Table 4 The experimental K of different materials. Temperature ( C)
MDF 1
MDF 2
MDF 3
PB
18 23 28 33
7977 6081 4640 3896
10,417 8442 7056 5289
9339 7110 6120 4281
10,956 8631 6966 5860
theoretical correlation of Cm0 proposed by Huang et al. As shown in Fig. 6, the experimental data of Cm0 show a good consistency with the theoretical correlation, thus, the value of Cm0 measured by the CTR-VVL method is reliable. During the environmental chamber experiments, the concentration distribution in the material was constantly changing with the emission of formaldehyde. To analyze the effect of the nonuniform concentration distribution of the material acting on the equilibrium concentration, the emission process of MDF 1 at 18 C was calculated. After 15 h, the mean concentration of the formaldehyde in the chamber varied no more than 1% in 1 h, the formaldehyde was considered to reach the equilibrium concentration. The predicted concentration distribution of MDF 1 is shown in Fig. 7. After 15 h, the error is 5.62% comparing the maximum concentration and the lowest concentration. However, the difference of the equilibrium concentration induced by this error will not be more than 2.81%, which is less than the measuring error of the apparatus. The equilibrium criterion used in the experiment can
4.3. Verification The experimental Km can be converted to K by Eq. (23) when Km was measured by the CTR-VVL method and the porosity f was measured by MIP tests. The converted results are shown in Table 4. The unknown constant m can be obtained by fitting the experimental K listed in Table 4 with the theoretical model of K. Because the form of Eq. (15) cannot be used in fitting directly, the macromesoscale calculation model of K was firstly converted to the logarithmic form.
ln K ¼
1 fRT ln mRT VP0
(28)
As shown in Eq. (28), K is not only related with temperature but also with the material properties (e.g., f) and the adsorbate properties (e.g., V and P0). The liquid molar volume of formaldehyde, V, is 3.681 105 m3/mol. The saturated vapor pressure of formaldehyde, P0, can be calculated by the Antoine equation. In the temperature range of 0e70 C, the expression is
P0 ¼ 133:3 exp 17:29
2534 T 16:75
Fig. 8. Fitting results of the experimental K with the theoretical calculation model.
(29)
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Substituting Eq. (29) into Eq. (28), the following form is achieved:
ln K ¼
q 2534 ln T þ þ ln f 2:947 T T 16:75
4.4. Sensitivity analysis
where q ¼ it can be obtained by fitting the experimental K with the theoretical model. The fitting results of the different building materials are shown in Fig. 8. It can be observed from the fitting results that the experimental data and the theoretical values showed a high consistency; the predictive accuracy of the theoretical model can be accepted. The relational expressions of K varying with T are shown in Table 5, by which the K for formaldehyde of the four building materials at other temperatures can be predicted. To further verify the accuracy of the theoretical model, the partition coefficients of another four aldehyde compounds (acetaldehyde, propionaldehyde, valeraldehyde and heptaldehyde) were calculated. These four aldehydes and formaldehyde are homologues, which means they have similar molecular structure, the same chemical bonds and identical functional groups. So it was assumed that the constant q that was codetermined by the properties of the adsorbate and adsorbent is identical to the five aldehydes in one material. The values of P0 for the four aldehydes were calculated by their respective Antoine equations and then substituted in Eq. (28). The calculation formula of K are shown in Table 6. According to the values of q for the different materials listed in Table 5, and the calculation formula of K listed in Table 6, the values of K for the different aldehyde compounds in different materials can be calculated. Here, one temperature condition for each material was selected when the calculated K fit with the linear prediction formula ln K ¼ lV þ b, which was proposed by Wang et al. [16]; the results are shown in Fig. 9. For the four building materials, the natural logarithm of K presented a good linear relationship with V, and the values of the adjusted Rsquared all exceeded 0.98. The calculated K of this study
Table 5 The relational expressions of K and T for formaldehyde of the four building materials.
q
MDF 1
229.9
MDF 2
242.4
MDF 3
234.7
PB
245.5
Relational expressions of K and T 2534 3:528 K ¼ exp 229:9 ln T þ T16:75 T 2534 3:699 K ¼ exp 242:4 ln T þ T16:75 T 2534 3:537 K ¼ exp 234:7 ln T þ T16:75 T 2534 3:786 K ¼ exp 245:5 ln T þ T16:75 T
r2 0.9915 0.9451 0.9717 0.9192
Table 6 The calculation formula of K for the four aldehyde compounds. VOC Acetaldehyde Propionaldehyde Valeraldehyde Heptaldehyde
perfectly conformed to the prediction formula proposed by Wang et al. [16]; furthermore, additional research has been conducted on the functional mechanism of temperature and microstructure.
(30)
1 mR,
Material
231
Relational expressions of K and T 2284 þ ln f 1:760 K ¼ exp Tq ln T þ T43:15 2659 þ ln f 2:568 K ¼ exp Tq ln T þ T44:14 3030 þ ln f 2:880 K ¼ exp Tq ln T þ T58:15 1581 þ ln f þ 0:4391 K ¼ exp Tq ln T þ T161:3
To further analyze the influence of K on the VOC emission characteristics of building materials, a sensitivity analysis was used to study the variation law of VOC concentration with the change of K. The emission process of MDF 1 was selected as the analytic target at the temperature of 18 C; De was assigned a fixed value of 3.13 107 m2/s, C0 was 5065 mg/m3, while K was assigned a series value as 7977, 3989, 5983, 9971 and 11,966. The convective mass transfer coefficient (h) of air flowing over the material surface is 1.79 103 m/s. Then, the emission parameters were substituted into the mass transfer model of porous media, Eqs. 18e22. The solved VOC concentrations are shown in Fig. 10. With the decrease of K, the VOC emission rate and the equilibrium concentration increased, while the time was prolonged to reach the equilibrium concentration. Therefore, the value of K has a direct and significant effect on the VOC emission characteristics; the accurate calculation of K is of great importance to the study of VOC emission.
5. Conclusions The partition coefficient is a key parameter influencing the VOC emission characteristics of building materials. This paper dissected the adsorption principle of the microstructure in porous building materials. The pores in building materials were divided into two scales, microscale and macro-mesoscale. A dualscale calculation model of K was deduced based on the DubininRadushkevich and Freundlich adsorption isotherm, respectively corresponded with micropores and macro-mesopores. This model established the functional relationship between K and microstructure, VOC property and temperature; however, the functional mechanisms of some other influence factors such as material texture and relative humidity are not discussed here, and required more in-depth research. To verify the accuracy of the theoretical model of K, a CTR-VVL method was proposed to measure Cm0 and Km of building materials. This method can improve the experimental accuracy and efficiency as well as reduce the material consumption on the basis of VVL method. Four types of macro-mesoporous materials commonly used in indoor decoration were selected as the subjects of the formaldehyde emission experiments conducted by the CTR-VVL method. The experimental data of Cm0 of the four materials showed a good consistency with the theoretical correlation in the literature [37]. The relational expressions of K varying with temperature were obtained by fitting the experimental data of K with the theoretical calculation model, which can predict the K under different temperatures. Additionally, the partition coefficients of another four aldehyde homologues were also calculated; the results agreed well with the prediction formula proposed by Wang et al. For microporous materials, the theoretical model has not been varied by independent experiments, mainly because the main research objects in this paper are porous building materials, the vast majority of which are macromesoporous materials. The adsorption effect of micropores deserves further experimental research to be applied to microporous materials in other research fields. In terms of the present research results, the proposed prediction model of the partition
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Fig. 9. Linear regression of lnK and V.
coefficient provides a new way to study the VOC emission characteristics of porous building materials, which is the basis for determining indoor VOC control principles and management approaches.
Acknowledgments We wish to thank the Funds for Creative Research Groups of China (Grant No. 51221865) and the Key Scientific and Technological Innovation Team of Shaanxi province, China (Grant No. 2014KCT-01) for the funding support. References
Fig. 10. Sensitivity analysis of K in the VOC emission characteristics.
[1] J. Choi, C. Chun, Y. Sun, Y. Choi, S. Kwon, C.G. Bornehag, J. Sundell, Associations between building characteristics and children's allergic symptoms e a crosssectional study on child's health and home in Seoul, South Korea, Build. Environ. 75 (2014) 176e181. [2] W. Collinge, A.E. Landis, A.K. Jones, L.A. Schaefer, M.M. Bilec, Indoor environmental quality in a dynamic life cycle assessment framework for whole buildings: focus on human health chemical impacts, Build. Environ. 62 (4) (2013) 182e190. [3] J. Kolarik, J. Toftum, The impact of a photocatalytic paint on indoor air pollutants: Sensory assessments, Build. Environ. 57 (4) (2012) 396e402. [4] T. Salthammer, S. Mentese, R. Marutzky, Formaldehyde in the Indoor Environment, Chem. Rev. 110 (2010) 2536e2572. [5] M. Ongwandee, R. Moonrinta, S. Panyametheekul, C. Tangbanluekal, G. Morrison, Investigation of volatile organic compounds in office buildings in bangkok, thailand: concentrations, sources, and occupant symptoms, Build. Environ. 46 (7) (2011) 1512e1522. [6] C. Yu, D. Crump, A review of the emission of VOCs from polymeric materials used in buildings, Build. Environ. 33 (6) (1998) 357e374. [7] L.Z. Zhang, J.L. Niu, Modeling VOCs emissions in a room with a single-zone multi-component multi-layer technique, Build. Environ. 39 (5) (2004)
Y. Liu et al. / Building and Environment 93 (2015) 221e233 523e531. [8] V. Polizzi, A. Adams, A.M. Picco, E. Adriaens, J. Lenoir, C.V. Peteghem, S.D. Saeger, N.D. Kimpe, Influence of environmental conditions on production of volatiles by Trichoderma atroviride in relation with the sick building syndrome, Build. Environ. 46 (4) (2011) 945e954. [9] X. Wu, M.G. Apte, R. Maddalena, D.H. Bennett, Volatile organic compounds in small-and medium-sized commercial buildings in California, Environ. Sci. Technol. 45 (20) (2011) 9075e9083. [10] Y.M. Kim, S. Harrad, R.M. Harrison, Concentrations and sources of VOCs in urban domestic and public microenvironments, Environ. Sci. Technol. 35 (6) (2001) 997e1004. [11] C.J. Weschler, Changes in indoor pollutants since the 1950s, Atmos. Environ. 43 (1) (2009) 153e169. [12] J.C. Little, A.T. Hodgson, A.J. Gadgil, Modeling emissions of volatile organic compounds from new carpets, Atmos. Environ. 28 (2) (1994) 227e234. [13] J. Xiong, Y. Yao, Y. Zhang, C-history method: rapid measurement of the initial emittable concentration, diffusion and partition coefficients for formaldehyde and VOCs in building materials, Environ. Sci. Technol. 45 (8) (2011) 3584e3590. [14] Y. Yao, J. Xiong, W. Liu, J. Mo, Y. Zhang, Determination of the equivalent emission parameters of wood-based furniture by applying C-history method, Atmos. Environ. 45 (31) (2011) 5602e5611. [15] X. Wang, Y. Zhang, A new method for determining the initial mobile formaldehyde concentrations, partition coefficients, and diffusion coefficients of dry building materials, J. Air Waste Manag. Assoc. 59 (7) (2009) 819e825. [16] X. Wang, Y. Zhang, J. Xiong, Correlation between the solid/air partition coefficient and liquid molar volume for VOCs in building materials, Atmos. Environ. 42 (33) (2008) 7768e7774. [17] J. Xiong, W. Chen, J.F. Smith, Y. Zhang, J. Zhang, An improved extraction method to determine the initial emittable concentration and the partition coefficient of VOCs in dry building materials, Atmos. Environ. 43 (26) (2009) 4102e4107. [18] J. Xiong, Y. Zhang, Impact of temperature on the initial emittable concentration of formaldehyde in building materials: experimental observation, Indoor Air 20 (6) (2010) 523e529. [19] J. Xiong, W. Yan, Y. Zhang, Variable Volume Loading Method: a convenient and rapid method for measuring the initial emittable concentration and partition coefficient of formaldehyde and other aldehydes in building materials, Environ. Sci. Technol. 45 (23) (2011) 10111e10116. [20] R. Meininghaus, L. Gunnarsen, H.N. Knudsen, Diffusion and sorption of volatile organic compounds in building materials-impact on indoor air quality, Environ. Sci. Technol. 34 (15) (2000) 3101e3108.
233
[21] A. Bodalal, J.S. Zhang, E.G. Plett, A method for measuring internal diffusion and equilibrium partition coefficients of volatile organic compounds for building materials, Build. Environ. 35 (2) (2000) 101e110. [22] X. Wang, Y. Zhang, J. Xiong, Correlation between the solid/air partition coefficient and liquid molar volume for VOCs in building materials, Atmos. Environ. 42 (33) (2008) 7768e7774. [23] Y. Zhang, X. Luo, X. Wang, K. Qian, R. Zhao, Influence of temperature on formaldehyde emission parameters of dry building materials, Atmos. Environ. 41 (15) (2007) 3203e3216. [24] A.W. Adamson, Physical Chemistry, Higher Education Press, Beijing, 1982. [25] F. Daniels, Physical Chemistry, China Machine Press, Beijing, 1984. [26] M. Polanyi, The Potential Theory of Adsorption, Science 141 (3585) (1963) 1010. [27] M.M. Dubinin, E.D. Zaverina, Zhur. Fiz. Khim 23 (1949) 1129. [28] M.M. Dubinin, L.V. Radushkevich, On the characteristic curve equation for active carbons, Dokl. Akad. Nauk. SSSR, Ser. Khim 55 (1947) 331. [29] S.S. Cox, J.C. Little, A.T. Hodgson, Measuring concentrations of volatile organic compounds in vinyl flooring, J. Air Waste Manag. Assoc. 51 (8) (2001) 1195e1201. [30] Z.G. Zhao, Application Principle of Adsorption, Chemical Industry Press, Beijing, 2005. [31] C.S. Lee, F. Haghighat, W.S. Ghaly, A study on VOC source and sink behavior in porous building materials-analytical model development and assessment, Indoor Air 15 (3) (2005) 183e196. [32] J. Xiong, Y. Zhang, X. Wang, D. Chang, Macro-meso two-scale model for predicting the VOC diffusion coefficients and emission characteristics of porous building materials, Atmos. Environ. 42 (21) (2008) 5278e5290. [33] R.E. Treybal, Mass-transfer Operations, McGraw-Hill International Editions, Paris, 1981. [34] S. Murakami, S. Kato, K. Ito, A. Yamamoto, Analysis of chemical pollutants distribution based on coupled simulation of CFD and emission/sorption processes, Edinburgh, UK: Indoor Air 99 (1999). [35] Y. Xu, Y. Zhang, An improved mass transfer based model for analyzing VOC emissions from building materials, Atmos. Environ. 37 (18) (2003) 2497e2505. [36] P. Blondeau, A.L. Tiffonnet, A. Damian, O. Amiri, J.L. Molina, Assessment of contaminant diffusivities in building materials from porosimetry tests, Indoor Air 13 (3) (2003) 310e318. [37] S. Huang, J. Xiong, Y. Zhang, Impact of temperature on the ratio of initial emittable concentration to total concentration for formaldehyde in building materials: theoretical correlation and validation, Environ. Sci. Technol. 49 (2015) 1537e1544.
