Department of Building Science, Tsinghua University, Beijing , China

Transcription

1 Supporting Inforation A SPME based C a -history ethod for easuring SVOC diffusion coefficients in clothing aterial Jianping Cao 1,, Ningrui Liu 1,, Yinping Zhang 1,,* 1 Departent of Building Science, Tsinghua University, Beijing , China Beijing Key Laboratory of Indoor Air Quality Evaluation and Control, Beijing , China * Corresponding Author Address: Departent of Building Science, Tsinghua University, Beijing , China; Phone: ; Fax: ; E-ail: zhangyp@tsinghua.edu.cn. This supporting inforation (15 pages) includes 5 sections, 5 figures and 1 table. S1

2 Section S1. SVOC ass transfer odel in a coonly used chaber According to Figure (a) and assuptions explained in the ain text, the equation describing SVOC ass transfer in the clothing is 1-3 ( ) ( ) C x C x = D, 0< x< δ t x (S1) where C is SVOC concentration in the clothing (µg/ 3 ); t is tie (s); x is the distance to the botto of the clothing in direct contact with the botto of the chaber (); and δ is the thickness of clothing (). Because the chaber air is ventilated, i.e., air is oving, a convective ass transfer process occurs between the surface of clothing and the chaber air. Consequently, SVOC sorption rate of clothing, S (µg/( s)), is: ( ) ( ) C x C x S= D = h Ca, x= δ x K x= δ (S) where h is the convective ass transfer coefficient at the surface of clothing (/s). The SVOC sorption rate on the interior surface of chaber wall, S w (µg/( s)), is: 4, 5 S h C q dq w w w= w, a = Kw dt (S3) where h,w is the convective ass transfer coefficient at the interior surface of chaber wall (/s); q w is the SVOC concentration on the chaber wall surface (µg/ ); and K w is the partition coefficient of SVOC between the chaber wall surface and air (). The ass balance of SVOC in the chaber air is expressed as: dc dt a V QCa, inlet QCa SwAw SA = (S4) where V is the volue of air in the chaber ( 3 ); Q is the air flow rate ( 3 /s); C a,inlet is the SVOC concentration of the air flow (µg/ 3 ); A w is the sorption area of chaber wall surface ( ); A is the planar, projected area of clothing ( ). Before the clothing is placed in the chaber, the air flow contains SVOC that has been introduced into the chaber for a sufficiently long tie to coat the chaber S

3 wall, e.g., 1 days. 6-8 If the experiental tie begins when the clothing is placed into the chaber, the initial conditions are: a a,0 w w,0 ( ) ( ) C = C, q = q, C x = 0 t = 0, 0 < x< δ (S5) where C a,0 (µg/ 3 ) and q w,0 (µg/ ) are the SVOC concentrations in the chaber air and on the chaber wall surface, respectively, at the instant that clothing is placed into the chaber. In existing ethods, the SVOC sorption aount in clothing, M (µg), and C a are always onitored. 6, 8 C a can be calculated using equation (S4), and M can be calculated by: 0 ( ) d M = C x Adx (S6) Cobining equations (S1)-(S6), C a and M are of the following functional fors: ( ) 1 (,,,,,, ) C t = F h h K K D t (S7) a w w ( ) (, w,, w,,, ) M t = F h h K K D t (S8) Other paraeters, i.e., C a,inlet, C a,0, q w,0, δ, A, A w, V and Q, are not included in equations (S7) and (S8) because they can be easily easured. S3

4 Section S. Coparison of C a estiated by equations (8) and (10) Figure S1. Coparison of C a estiated by equations (8) and (10). Fo is the Fourier nuber for ass transfer (Fo = D t/δ ); C a * is the diensionless SVOC concentration in the chaber air (C a * = C a /y 0 ). Figure S1 shows that equation (8) estiates for gas-phase SVOC concentrations in the chaber air overlap estiations of equation (10) when the diensionless tie (i.e., Fourier nuber for ass transfer (Fo )) is larger than If Fo is larger than 0.17, the relative deviation between C a estiated by equation (8) and by equation (10) is less than 5%. Consequently, the applied condition of siplifying equation (8) to equation (10) is Fo 0.17, i.e., t 0.17δ /D. S4

5 Section S3. Variation of q 1 as a function of K δ/l Figure S. Variation of q 1 as a function of K δ/l. Figure S shows how the first positive root of equation (9), q 1, varies as a function of K δ/l, the ter on the right of equation (9). The ter q 1 is constant and equal to π/ when K δ/l is larger than 400. S5

6 Figure S3. Equation (8) and (11) estiates copared to experiental data for (a) DiBP, (b) DnBP, and (c) TCPP. (a) (b) S6

7 (c) S7

8 Section S4. Derivation and application condition of Equation (4) Firstly, we assue that there is a very thin air gap between clothing and source aterial. Under steady state, the ass transfer resistance within the air gap (R ag ) can be estiated as L ag /D a (where L ag is the thickness of air gap, D a is the SVOC diffusion coefficient in the air), and the ass transfer resistance within clothing (R c ) is δ/(k D ). 1, 9 If the air gap is sufficiently thin (e.g., thinner than icroeters), R ag will be far saller than R c (or R ag /R c << 1). Taking DnBP as an exaple, our calculation iplies that R ag will be saller than 0.4 s/ if L ag is thinner than 1 μ, while R c is about 1900 s/ (D a = /s 10, δ and D can be found in the ain text, and K was easured by Cao et al. 1 ), indicating that R ag /R c < (i.e., R ag /R c << 1). That is, R ag is negligible copared to R c, indicating that SVOC concentration can be treated as unifor within the air gap according to the principle of the luped paraeter ethod. 9 Consequently, we have: C = C = C (S9) a,source ap a,clothing where C a,source is SVOC gas-phase concentration adjacent to source aterial surface, C ap is SVOC concentration within the air gap, and C a,clothing is SVOC gas-phase concentration adjacent to the clothing aterial surface. According to the definition of partition coefficient: 11 K i1 concentration of i in phase 1 = (S10) concentration of i in phase we know that C a,source = C 0 /K e (where C 0 is SVOC concentration within the source aterial, K e is SVOC source/air partition coefficient), which is exactly y 0 defined by Xu and Little 1 ; and C a,clothing = C (x=0)/k. Consequently: C K 0 e ( y ) ( x= 0) = 0 = Cap = (S11) K which is equation (4) in the ain text. We can know fro the above analysis that Equation (4) is suitable if the clothing directly contacts with source aterial (since R ag = 0 in this case). However, if the S8 C

9 clothing does not directly contact the source aterial, the applied condition of Equation (4) is that R ag should be far less than R c (or R ag /R c < 0.1), i.e., the applied condition treats C ag as uniforly distributed in the air gap. 9 That is, the thickness of air gap (L ag ) should be less than 0.1D a δ/(k D ). Taking DnBP as an exaple, our calculation iplies that L ag should be less than It should be noted that a cirtical assuption is ade in Equation (4) of the ain text (as well as in the above analysis), i.e., y 0 can be treated as a constant. In the present case, the conditions for treating y 0 as a constant are: 1) the SVOC ass in the clothing is not significant copared to the ass in the source, and ) the SVOC ass transfer rate within the source aterial should be far greater than that within the clothing aterial. For condition 1), we have perfored a siple calculation. Assuing that SVOC ass transfer within the chaber has reached equilibriu (in this case, SVOC ass in the clothing reached its axiu), SVOC ass in the clothing (M c ) will be equal to δk C a_equ (C a_equ is the equilibriu SVOC concentration in the chaber air, which ay not equal y 0 if condition 1) is false), SVOC ass in the source aterial (M s ) will be equal to L s K e C a_equ. Therefore, the ratio of M c to M s is M M c δ K LK = (S1) s s e Taking DnBP as the exaple, we obtain that M c /M s 10-5, indicating that condition 1) is reasonable. For condition ), we have also perfored a siple calculation. The ass transfer resistance within the source aterial (R s ) = L s /(K e D s ) (L s is the thickness of source aterial, and D s is the SVOC diffusion coefficient within the source), R s was calculated to be about 10 s/ if L s equals 5 (thickness of PVC flooring used in this study), D s equals /s (easured by Xu and Little 1 for DEHP in PVC flooring, D s of DnBP should be greater than this value) and K e equals (according to the value of C 0 /y 0 easured by Liang et al. 13 for DnBP). The ass S9

10 transfer resistance within the clothing (R c ) is about s/ as we estiated above. Note that the ass transfer resistance is the inverse of the ass transfer rate at steady state. 9 Consequently, at steady state, the SVOC ass transfer rate within the source aterial is about 00 ties greater than that within the clothing aterial (because R s /R c 0.005, i.e., (1/R s )/(1/R c ) 00), indicating that condition ) is also reasonable. S10

11 Section S5. Evaluation of equations (5) and (6) assuptions With reference to ass transfer of gas-phase SVOCs in a chaber siilar to that described in Cao et al. 4 (which has no clothing aterial in the chaber), ass transfer of SVOCs in the present chaber is an unsteady diffusion process, in two diensions, altitude and radial. Cao et al. 4 have deonstrated that the effect of ass transfer in the radial direction on the concentration distribution of SVOC in the chaber air is insignificant for a siilar chaber shape. Therefore, the ass transfer of SVOCs in the present chaber can be regarded as a one-diensional unsteady diffusion process, in the altitude direction: ( ) ( ) C x C x = D,0< x< δ t x ( ) ( ) Ca x Ca x L = Da, δ < x< δ + t x (S13) (S14) ( 0) 0 C x= = K y (S15) D ( ) ( ) C x Ca x = Da x x x= δ x= δ (S16) C a ( x δ ) C ( x= δ ) = = (S17) K a ( δ ) C x= + L x = 0 (S18) ( δ) ( δ δ ) C 0 < x< = 0, C < x< + L = 0, t = 0 (S19) a where equations (S13) and (S14) are the control equations for SVOC diffusion in the clothing and chaber air, respectively; equation (S15) describes the boundary condition at the interface of clothing and source aterial (identical with equation (4)); equations (S16) and (S17) describe the boundary conditions at the interface of clothing and chaber air; equation (S18) describes the boundary condition in the iddle of the chaber; and equation (S19) describes the initial condition (identical S11

12 with equation (7)). Equations (S13)-(S19) were solved by nuerical calculation using MATLAB (R01b, MathWorks, Inc.), in which C a for any position at any instant can be obtained. Figure S4 shows how C a varies with tie in the iddle of the present chaber (i.e., x = δ + L/) and how C a varies with tie as estiated by equation (8) of the ain text. Equation (8) assues that SVOC is uniforly distributed in the chaber air. Figure S4. C a estiated by equations (S13)-(S19) copared with C a estiated by equation (8). Fo is the Fourier nuber for ass transfer (Fo = D t/δ ), C a * is the diensionless concentration of gas-phase SVOCs in the chaber air (C a * = C a /y 0 ). S1

13 Table S1. Paraeters used in odel siulations of deral exposure to gas-phase DnBP Paraeters Definition of paraeters Values h (/h) Convective ass transfer coefficient 3.1 a K (-) Clothing/air partition coefficient a K ssl (-) Skin surface lipids/air partition coefficient a K sc (-) Stratu corneu/air partition coefficient a K ve (-) Viable epideris/air partition coefficient a D ( /s) Diffusion coefficient in clothing (Case 1) b (Case ) a - (Case 3) D a ( /s) Diffusion coefficient in air a D ssl ( /s) Diffusion coefficient in skin surface lipids a D sc ( /s) Diffusion coefficient in stratu corneu a D ve ( /s) Diffusion coefficient in viable epideris a δ () Thickness of clothing 1.0 a L ag () Air gap between clothing and skin surface 5.0 c L ssl (µ) Thickness of skin surface lipids 1. a L sc (µ) Thickness of stratu corneu 3 a L ve (µ) Thickness of viable epideris 100 a C a,loading (µg/ 3 ) C a (µg/ 3 ) Gas-phase concentration during the tie clothes were exposed to gas-phase DnBP Gas-phase concentration during the tie participant was exposed to gas-phase DnBP 119 a 14 a a Values used by Morrison et al. ; b D easured in this study; c When L ag ~4-5, the estiated results of Morrison et al. fit experiental data well. Consequently, L ag is selected as 5.0 in this study. S13

14 Figure S5. Applicable sapling tie of the present ethod (according to equation (14)) for various D. S14

15 References 1. Cao, J.; Weschler, C. J.; Luo, J.; Zhang, Y. C-history ethod, a novel approach to siultaneously easure source and sink paraeters iportant for estiating indoor exposures to phthalates. Environ. Sci. Technol. 016, 50 (), Morrison, G. C.; Weschler, C. J.; Beko, G. Deral uptake of phthalates fro clothing: Coparison of odel to huan participant results. Indoor Air 017, 7 (3), Moholkar, V. S.; Waroeskerken, M. M. C. G. Investigations in ass transfer enhanceent in textiles with ultrasound. Che. Eng. Sci. 004, 59 (), Cao, J.; Zhang, X.; Little, J. C.; Zhang, Y. A SPME-based ethod for rapidly and accurately easuring the characteristic paraeter for DEHP eitted fro PVC floorings. Indoor Air 017, 7 (), Xu, Y.; Liu, Z.; Park, J.; Clausen, P. A.; Benning, J. L.; Little, J. C. Measuring and predicting the eission rate of phthalate plasticizer fro vinyl flooring in a specially-designed chaber. Environ. Sci. Technol. 01, 46 (), Liu, X.; Guo, Z.; Roache, N. F. Experiental ethod developent for estiating solid-phase diffusion coefficients and aterial/air partition coefficients of SVOCs. Atos. Environ. 014, 89, Morrison, G.; Shakila, N. V.; Parker, K. Accuulation of gas-phase ethaphetaine on clothing, toy fabrics, and skin oil. Indoor Air 015, 5 (4), Liu, X.; Allen, M. R.; Roache, N. F. Characterization of organophosphorus flae retardants sorption on building aterials and consuer products. Atos. Environ. 016, 140, Bergan, T. L.; Incropera, F. P.; DeWitt, D. P.; Lavine, A. S. Fundaentals of Heat and Mass Transfer; John Wiley & Sons: Hoboken, New Jersey, United States, Lugg, G. A. Diffusion coefficients of soe organic and other vapors in air. Anal. Che. 1968, 40 (7), Gschwend, P. M. Environental Organic Cheistry. John Wiley & Sons: Hoboken, New Jersey, United States, Xu, Y.; Little, J. C. Predicting eissions of SVOCs fro polyeric aterials and their interaction with airborne particles. Environ. Sci. Technol. 006, 40 (), Liang, Y.; Xu, Y. Iproved ethod for easuring and characterizing phthalate eissions fro building aterials and its application to exposure assessent. Environ. Sci. Technol. 014, 48 (8), S15