Supporting Information for:
Deposition vs. Photochemical Removal of PBDEs from Lake Superior Air
Jonathan D. Raff and Ronald A. Hites*
School of Public and Environmental Affairs
Indiana University
Bloomington, Indiana 47405
*Author to whom correspondence should be addressed at [email protected]
Contents: 19 pages that include 5 tables, 4 figures, and 20 references.
S1
TABLE S1: Polybrominated diphenyl ether congeners studied in this work.
2
6
4
2'
O
3
3'
6'
5
Compound
2-bromodiphenyl ether
IUPAC abbreviation
BDE-1
3-bromodiphenyl ether
BDE-2
4-bromodiphenyl ether
BDE-3
2,2'-dibromodiphenyl
ether
2,4-dibromodiphenyl
ether
3,3'-dibromodiphenyl
ether
4,4'-dibromodiphenyl
ether
2,2',4-tribromodiphenyl
ether
2,4,4'-tribromodiphenyl
ether
2,2',4,4'tetrabromodiphenyl
ether
3,3',4,4'tetrabromodiphenyl
ether
2,2',4,4',5pentabromodiphenyl
ether
2,2',4,4',6pentabromodiphenyl
ether
BDE-4
BDE-7
BDE-11
BDE-15
BDE-17
BDE-28
BDE-47
4'
5'
Compound
2,3,4,5,6-pentabromodiphenyl
ether
3,3',4,4',5-pentabromodiphenyl
ether
2,2'4,4',5,5'hexabromodiphenyl ether
2,2'4,4',5,6'hexabromodiphenyl ether
2,3,3',4,5,6hexabromodiphenyl ether
2,2',3,4,4',5,5'heptabromodiphenyl ether
2,2',3,4,4',5,6heptabromodiphenyl ether
2,2',3,3',4,4',5,6'octabromodiphenyl ether
2,2',3,3',4,4',6,6'octabromodiphenyl ether
2,2',3,3',4,4',5,5',6nonabromodiphenyl ether
IUPAC abbreviation
BDE-116
BDE-126
BDE-153
BDE-154
BDE-160
BDE-180
BDE-183
BDE-196
BDE-197
BDE-206
BDE-77
2,2',3,3',4,5,5',6,6'nonabromodiphenyl ether
BDE-208
BDE-99
2,2',3,3',4,4',5,5',6,6'decabromodiphenyl ether
BDE-209
BDE-100
S2
TABLE S2: Absorption cross sections, 10–18 cm2 molecule–1 (base e), as a function of
wavelength  for selected PBDE congeners measured at 298 K in isooctane.

280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
BDE-1
4.057
3.842
3.867
3.747
3.306
2.706
2.019
1.398
0.912
0.597
0.394
0.276
0.194
0.144
0.108
0.074
0.058
0.044
0.036
0.028
0.023
0.021
0.013
0.020
0.014
0.004
0.007
BDE-3
5.939
5.751
5.488
5.113
4.616
4.125
3.749
3.572
3.583
3.627
3.455
2.953
2.234
1.546
0.996
0.617
0.379
0.241
0.160
0.108
0.070
0.058
0.037
0.026
0.026
0.010
0.018
BDE-4
6.946
7.707
7.250
5.819
4.277
3.052
2.136
1.465
0.967
0.637
0.419
0.286
0.196
0.142
0.100
0.075
0.051
0.034
0.029
0.020
0.021
0.025
0.020
0.021
0.017
0.011
0.010
0.009
0.003
BDE-7
5.572
5.412
5.430
5.644
5.938
6.097
6.033
5.787
5.413
5.001
4.614
4.347
4.201
4.212
4.251
4.117
3.691
3.064
2.359
1.723
1.201
0.826
0.586
0.404
0.283
0.218
0.151
0.121
0.084
0.070
0.061
0.028
0.027
0.029
0.015
0.018
0.016
0.012
0.017
0.012
0.006
S3
BDE-11
7.187
8.004
8.703
8.466
7.393
5.936
4.361
2.994
1.959
1.279
0.862
0.605
0.441
0.341
0.270
0.217
0.179
0.146
0.126
0.100
0.091
0.082
0.063
0.044
0.029
0.022
0.019
0.009
BDE-15
7.624
7.713
7.645
7.272
6.797
6.299
5.946
5.852
5.984
6.156
6.013
5.402
4.476
3.477
2.515
1.726
1.129
0.734
0.476
0.315
0.217
0.164
0.127
0.099
0.075
0.065
0.052
0.046
0.028
0.026
0.022
0.007
0.009
BDE-17
7.468
7.737
7.735
7.607
7.415
7.073
6.520
5.889
5.289
4.851
4.623
4.627
4.743
4.694
4.225
3.461
2.659
1.978
1.425
1.011
0.732
0.528
0.394
0.285
0.231
0.172
0.138
0.112
0.096
0.079
0.070
0.053
0.052
0.060
0.050
0.043
0.036
0.037
0.021
0.022
BDE-28
7.728
7.478
7.256
7.174
7.208
7.276
7.307
7.262
6.993
6.385
5.590
4.874
4.325
3.983
3.737
3.435
3.033
2.530
1.992
1.481
1.062
0.739
0.523
0.366
0.265
0.185
0.141
0.101
0.072
0.036
0.020
TABLE S2 (cont.): Absorption cross sections, 10–18 cm2 molecule–1 (base e), as a function of wavelength  for selected PBDE congeners measured at 298 K in isooctane.

280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
BDE-47
8.684
8.799
9.151
9.620
9.889
9.711
9.143
8.430
7.735
7.233
7.030
7.152
7.365
7.252
6.467
5.285
4.094
3.096
2.290
1.667
1.223
0.861
0.622
0.432
0.317
0.231
0.181
0.146
0.115
0.101
0.081
0.084
0.065
0.057
0.050
0.046
0.046
0.047
0.032
0.031
0.021
0.028
0.022
0.019
BDE-49
10.325
10.300
10.286
10.366
10.254
9.868
9.454
9.332
9.229
8.720
7.792
6.885
6.124
5.359
4.432
3.446
2.568
1.860
1.308
0.895
0.609
0.395
0.266
0.165
0.117
0.067
0.049
0.024
0.025
0.022
0.025
0.018
0.012
BDE-77
9.256
9.379
9.685
10.061
10.228
10.075
9.644
9.100
8.598
8.238
8.185
8.492
8.901
8.971
8.451
7.394
6.045
4.631
3.355
2.346
1.600
1.094
0.759
0.555
0.410
0.328
0.246
0.211
0.189
0.160
0.135
0.116
0.095
0.081
0.091
0.082
0.063
0.042
0.039
0.042
0.028
BDE-99
8.570
8.960
9.514
10.049
10.317
10.230
9.943
9.695
9.554
9.536
9.590
9.717
9.775
9.512
8.818
8.009
7.426
7.202
7.027
6.597
5.762
4.685
3.687
2.790
2.076
1.494
1.048
0.712
0.470
0.312
0.206
0.138
0.093
0.065
0.057
0.032
0.017
0.018
0.008
S4
BDE-100 BDE-116 BDE-126 BDE-153
7.539
7.109
8.383
8.586
8.090
6.638
8.466
9.167
8.444
6.265
8.564
9.925
8.453
5.921
8.729
10.694
8.111
5.635
8.895
11.273
7.580
5.415
8.933
11.566
7.036
5.274
8.841
11.761
6.698
5.155
8.684
11.997
6.679
5.065
8.446
12.223
6.967
4.996
8.195
12.364
7.421
4.880
7.930
12.493
7.742
4.768
7.768
12.723
7.394
4.629
7.746
12.855
6.318
4.464
7.807
12.573
4.907
4.319
7.826
11.800
3.581
4.171
7.746
10.931
2.535
4.036
7.552
10.451
1.767
3.936
7.121
10.481
1.224
3.875
6.503
10.600
0.846
3.799
5.640
10.157
0.579
3.757
4.641
8.961
0.387
3.685
3.686
7.321
0.274
3.605
2.793
5.753
0.182
3.468
2.089
4.381
0.122
3.295
1.520
3.312
0.072
3.112
1.095
2.455
0.050
2.899
0.815
1.791
0.039
2.680
0.584
1.263
0.024
2.468
0.435
0.866
0.026
2.255
0.319
0.603
0.029
2.027
0.255
0.396
0.017
1.864
0.183
0.267
1.673
0.133
0.179
1.465
0.100
0.133
1.322
0.072
0.098
1.190
0.056
0.072
1.036
0.052
0.053
0.888
0.028
0.047
0.773
0.015
0.025
0.655
0.027
0.559
0.013
0.474
0.408
0.377
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
0.005
0.011
0.313
0.276
0.241
0.200
0.167
0.133
0.136
0.126
0.105
0.087
0.066
0.069
0.057
0.046
0.046
0.034
0.032
0.021
0.016
0.010
0.014
0.014
0.018
0.009
0.005
S5
TABLE S2 (cont.): Absorption cross sections, 10–18 cm2 molecule–1 (base e), as a function of wavelength  for selected PBDE congeners measured at 298 K in isooctane.

280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
BDE-154 BDE-160 BDE-180 BDE-183 BDE-196 BDE-197 BDE-206 BDE-208 BDE-209
6.986
10.993
6.569
8.737
8.059
12.462
10.743
18.270
43.437
7.234
9.450
6.475
8.764
7.810
11.998
10.346
17.589
32.943
7.386
7.712
6.307
8.857
7.554
11.597
9.899
16.858
26.544
7.479
6.368
6.103
9.028
7.424
11.340
9.520
16.189
22.164
7.609
5.456
5.934
9.275
7.359
11.071
9.170
15.427
19.139
7.881
4.869
5.878
9.665
7.448
10.828
8.970
14.674
16.924
8.420
4.510
6.012
10.290
7.659
10.542
8.933
13.946
15.275
9.167
4.270
6.313
10.939
7.915
10.131
9.006
13.238
14.057
9.818
4.118
6.742
11.362
8.150
9.666
9.160
12.590
13.083
9.997
3.983
7.102
11.323
8.359
9.225
9.328
12.047
12.312
9.690
3.868
7.211
10.918
8.380
8.809
9.343
11.513
11.745
9.169
3.721
7.042
10.415
8.238
8.593
9.271
11.151
11.333
8.533
3.591
6.711
9.886
8.043
8.596
9.065
10.840
11.038
7.870
3.433
6.349
9.415
7.920
8.779
8.830
10.523
10.789
7.394
3.319
6.046
9.207
7.833
8.966
8.570
10.262
10.561
7.455
3.200
5.935
9.562
8.021
9.041
8.484
9.990
10.310
8.157
3.091
5.995
10.423
8.285
8.760
8.463
9.706
10.039
8.982
3.016
6.255
11.173
8.588
8.226
8.610
9.414
9.752
9.039
2.971
6.700
11.020
8.885
7.506
8.912
9.105
9.500
8.007
2.900
7.110
9.756
9.152
6.836
9.260
8.791
9.244
6.388
2.888
7.388
7.955
9.131
6.192
9.402
8.451
9.062
4.714
2.833
7.288
6.173
8.765
5.671
9.257
8.123
8.976
3.361
2.777
6.891
4.686
8.131
5.338
8.851
7.801
8.915
2.331
2.649
6.204
3.519
7.287
5.058
8.204
7.594
8.927
1.622
2.529
5.479
2.635
6.390
4.905
7.501
7.328
9.022
1.105
2.384
4.716
1.984
5.484
4.762
6.731
7.065
9.080
0.759
2.231
4.042
1.488
4.649
4.619
6.009
6.822
9.016
0.500
2.045
3.414
1.119
3.954
4.469
5.359
6.599
9.004
0.332
1.876
2.902
0.829
3.345
4.261
4.725
6.261
8.807
0.214
1.728
2.433
0.616
2.776
4.071
4.147
5.940
8.525
0.132
1.563
2.048
0.458
2.326
3.849
3.641
5.599
8.204
0.079
1.422
1.742
0.327
1.935
3.600
3.154
5.238
7.833
0.047
1.268
1.455
0.249
1.602
3.369
2.756
4.894
7.484
0.037
1.105
1.199
0.200
1.359
3.152
2.412
4.533
7.023
0.019
0.997
1.016
0.154
1.129
2.938
2.103
4.232
6.622
0.015
0.909
0.862
0.126
0.913
2.739
1.810
3.930
6.263
0.013
0.779
0.708
0.099
0.767
2.514
1.546
3.625
5.884
0.015
0.676
0.564
0.083
0.634
2.308
1.336
3.351
5.481
0.006
0.615
0.479
0.046
0.545
2.117
1.169
3.080
5.056
0.523
0.380
0.028
0.447
1.942
0.991
2.837
4.660
0.468
0.330
0.008
0.389
1.755
0.849
2.599
4.272
0.403
0.264
0.017
0.310
1.580
0.698
2.352
3.948
0.347
0.218
0.034
0.243
1.387
0.604
2.154
3.563
0.308
0.182
0.191
1.240
0.519
1.957
3.217
S6
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
0.286
0.247
0.224
0.183
0.157
0.122
0.126
0.124
0.119
0.103
0.095
0.084
0.063
0.055
0.060
0.040
0.029
0.017
0.021
0.017
0.017
0.019
0.019
0.009
0.004
0.167
0.146
0.131
0.092
0.061
0.051
0.065
0.073
0.063
0.056
0.044
0.039
0.157
0.129
0.112
0.105
0.083
0.067
0.039
0.042
0.020
S7
1.119
0.975
0.842
0.741
0.649
0.537
0.477
0.412
0.331
0.272
0.250
0.213
0.181
0.130
0.103
0.098
0.092
0.080
0.061
0.047
0.036
0.026
0.026
0.020
0.017
0.014
0.461
0.369
0.354
0.308
0.279
0.202
0.171
0.152
0.120
0.106
0.118
0.105
0.089
0.088
0.076
0.074
0.058
0.039
0.017
0.016
0.015
1.788
1.576
1.443
1.316
1.160
1.024
0.874
0.808
0.680
0.598
0.522
0.496
0.458
0.383
0.324
0.284
0.252
0.220
0.186
0.155
0.136
0.125
0.123
0.117
0.100
0.089
0.072
0.058
0.052
0.053
0.041
0.030
0.016
0.020
0.023
0.023
0.018
2.909
2.601
2.284
2.083
1.780
1.532
1.369
1.178
1.008
0.914
0.768
0.647
0.551
0.463
0.377
0.358
0.339
0.297
0.255
0.225
0.200
0.184
0.168
0.151
0.119
0.093
0.091
0.094
0.092
0.097
0.078
0.072
0.060
0.041
0.041
0.046
0.043
0.039
0.028
0.047
0.037
0.043
0.029
0.032
0.027
0.021
FIGURE S1: UV-vis absorption spectra of PBDE congeners measured at 298 K in isooctane. Note that the shape and position of absorption bands are dependent on the bromine substitution pattern, suggesting that the two rings of the diphenyl ether act as independent chromophores [1].
6
5
4
Mono-BDEs
3
BDE-1
BDE-3
2
1
Absorption Cross Section (x10
18
2
-1
cm molecule , base e)
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
11
10
9
8
7
6
5
4
3
2
1
0
11
10
9
8
7
6
5
4
3
2
1
0
280
Di-BDEs
BDE-4
BDE-7
BDE-11
BDE-15
Tri-BDEs
BDE-17
BDE-28
Tetra-BDEs
BDE-47
BDE-49
BDE-77
Penta-BDEs
BDE-99
BDE-100
BDE-116
BDE-126
290
300
310
320
330
Wavelength (nm)
S8
340
350
360
2
-1
cm molecule , base e)
18
Absorption Cross Section (x10
13
12
11
10
9
8
7
6
5
4
3
2
1
0
12
11
10
9
8
7
6
5
4
3
2
1
0
12
11
10
9
8
7
6
5
4
3
2
1
0
12
11
10
9
8
7
6
5
4
3
2
1
0
12
11
10
9
8
7
6
5
4
3
2
1
0
280
Hexa-BDEs
BDE-153
BDE-154
BDE-160
Hepta-BDEs
BDE-180
BDE-183
Octa-BDEs
BDE-196
BDE-197
Nona-BDEs
BDE-206
BDE-208
Deca-BDE
290
300
310
320
330
Wavelength (nm)
S9
340
350
360
Quantum Yield Measurements.
Irradiations of mono- and dibromodiphenyl ethers and a chemical actinometer (Cl2) were
performed in a 160 cm3 quartz reaction chamber located in the oven of a Hewlett-Packard
5890 gas chromatograph (for temperature control) and interfaced to a Hewlett-Packard
5989A quadrupole mass spectrometer operated in the electron ionization (EI) mode [2].
Collimated light was provided by a 200 W Xe(Hg) arc lamp (Hamamatsu Corporation)
that was filtered by a dichroic mirror (Newport Corporation) to eliminate infrared radiation and an interference filter (Andover Corporation) to select light of 307  26 nm at
FWHM.
In a typical experiment, between 0.2–5 g of a selected PBDE dissolved in cyclohexane
was added to the reaction chamber containing helium at 323 K; cyclohexane acted as
both a solvent and a OH radical scavenger. The instrument responses for the most intense m/z values were monitored before and after irradiation of the reactor to establish the
background (dark) decay of the PBDE signal. Irradiations were carried out for 3–5
minutes and corrected for the average background decay before deriving the photolysis
rates. A few experiments with BDE-7 were performed in the presence of 1,3-butadiene
(~1  1014 molecules cm–3, kBr = 5.7  10-11 cm3 molecule–1 s-1 [3]), to scavenge Br atoms; no differences in photolysis rates were observed in the presence or absence of 1,3butadiene, indicating that reactions with Br atoms did not contribute to the observed
BDE-7 decays.
Chlorine gas (~1014 molecules cm–3) was used as an actinometer in separate experiments
at 298 K. Methanol (~2  1014 molecules cm–3) and oxygen (5 % in helium) were added
to the reactor during the actinometer experiments to prevent chlorine atom recombination
and scavenge alkyl radicals that would enhance Cl2 consumption [4]. The m/z values
monitored during the PBDE photolysis and actinometer experiments were as follows: diphenyl ether, 170 [M]+, monobromodiphenyl ethers 248 [M]+, dibromodiphenyl ethers,
328, [M + 2]+, chlorine, 70, [M]+. The reaction chamber was cleaned after each experiment by heating it to 150 ºC and flushing it with helium for 60 min.
S10
Applicability of Solution-Phase Spectra for Gas-Phase Photolysis Calculations.
In deriving the absorption cross-sections of PBDEs from solution spectra and using them
to estimate gas-phase photolysis frequencies, we assume that the position and intensity of
absorption bands is independent of phase (gas vs. solution). In reality, solvent effects
will result in a shift of the PBDE spectra relative to those measured in the gas phase.
Spectra of aromatic hydrocarbons recorded in perfluorinated hydrocarbon solvents show
negligible shifts compared to gas-phase spectra [5] and provide a surrogate for gas-phase
spectra. Although PBDEs are only slightly soluble in perfluorinated solvents, the spectra
of several PBDEs in perfluorohexane (C6F14) were recorded, indicating that the lowest
energy band of the congeners studied would likely result in a 1–2 nm red shift in isooctane compared to the gas-phase; see Figure S2. The intensity of absorption bands may also be different in the gas- vs. solution-phase; this effect is more difficult to assess, but aromatic compounds have been observed to have higher cross-sections (by up to 50%) in
hydrocarbon solutions compared to the gas-phase [6]. No corrections were applied to the
absorption spectra used to calculate the photolysis frequencies.
Solvent Shift, in nm
4
3
2
1
0
3
7
15
28
47
49
99
100
BDE Congener
FIGURE S2: Solvent shift  = (C8H18) – (C6F14) of the lowest energy absorption
band of several PBDE congeners in two different solvents: Isooctane (C 8H18) and perfluorohexane (C6F14) at 298 K. The average spectral shift ( = +1.7 nm) is indicated by
the dashed line.
S11
Photochemical Dibenzofuran Formation.
Evidence for the formation of brominated dibenzofurans was also obtained during irradiation of gas-phase PBDEs in the above experiments. As shown in Figure S3, the
broad-band photolysis ( > 260 nm) of BDE-1 for 14 min is accompanied by an increase
in the signal of m/z 168, the molecular ion of dibenzofuran. Similarly, 2-bromodibenzofuran, m/z 246 [M]+, is formed during the photolysis of BDE-7 at 307 nm; see
Figure S3. The low volatility of 2-bromodibenzofuran and its tendency to undergo subsequent photolysis prevents substantial amounts from accumulating in the reactor during
the experiment and explains the weak signal intensity observed. These products were
confirmed by gas chromatographic mass spectrometry (GC/MS) after they were extracted
from the reaction chamber walls with organic solvents using documented methods [2].
Dibenzofuran products were not observed when similar experiments were performed for
the photolysis of 4-bromodiphenyl ether (BDE-3) or 4,4-dibromodiphenyl ether (BDE15).
These results provide direct evidence that PBDEs containing bromines in an orthoposition form brominated dibenzofurans via dehydrodebromination when photolyzed in
the gas-phase. This observation corroborates previous reports of bromodibenzofurans
formed during the photolysis of PBDEs in solution [7,8,9]. The potential toxicity of
brominated dibenzofurans is of great concern due to their similarity to polychlorinated
dibenzo-p-dioxins and furans. Our results indicated that one possible source of brominated dibenzofurans observed in atmospheric samples [10] may be from the photolytic decomposition of PBDEs. However, bromodibenzofurans are more highly conjugated than
PBDEs due to their rigid structure, causing their absorption bands to extend further into
the solar actinic range [11,12]. Thus, the atmospheric lifetimes of gas-phase polybrominated dibenzofurans due to photolysis are expected to be shorter than those for PBDEs.
The yield of dibenzofurans from PBDE photolysis appears to be sensitive to the bath-gas
composition. For example, photolysis of BDE-1 at  > 260 nm in helium in the presence
of acetone showed enhanced production of dibenzofuran. It was also more difficult to
detect dibenzofuran from BDE-1 photolysis during experiments carried out in air compared to experiments conducted in helium. However, in this case it was unclear whether
this was from the reduced sensitivity of the mass spectrometer under these conditions or
if the yield of dibenzofuran was indeed lower due to quenching of the excited state by O2.
Additional investigations into PBDE photochemistry would be useful to help understand
the nature of the excited state (singlet or triplet) that produces dibenzofurans [13] and the
effect that oxygen and photosensitizers (e.g., acetone [14]) may have on dibenzofuran
yields.
S12
Br
Signal Intensity
O
O
(m/z 248)
(m/z 168)
0
2
4
6
8
Time (minutes)
10
12
14
Signal Intensity
Br
O
(m/z 328)
x10
Br
O
(m/z 246)
0
1
2
Time (minutes)
3
Br
4
FIGURE S3. (top) Decay of 2-bromodiphenyl ether (BDE-1) and formation of dibenzofuran during broad-band irradiation at  > 260 nm. (bottom) Loss of 2,4-dibromodiphenyl
ether (BDE-7) and formation of 2-bromodibenzofuran from irradiation centered at 307
nm; the signal for m/z 246 has been magnified by 10 for clarity. Both experiments were
carried out at 325 K in a bath gas of He at ~740 Torr.
S13
TABLE S3: Estimates of gas-phase photolysis rate constants (J), photolysis lifetimes
(photo), hydroxy radical rate constants (kOH), and hydroxyl radical lifetimes (OH) for
PBDEs.
Congener
#Br
Ja
10–5 s-1
BDE-1
BDE-3
BDE-4
BDE-7
BDE-11
BDE-15
BDE-17
BDE-28
BDE-47
BDE-49
BDE-77
BDE-99
BDE-100
BDE-116
BDE-126
BDE-153
BDE-154
BDE-160
BDE-180
BDE-183
BDE-196
BDE-197
BDE-206
BDE-208
BDE-209
1
1
2
2
2
2
3
3
4
4
4
5
5
5
5
6
6
6
7
7
8
8
9
9
10
0.024
0.081
0.043
1.7
0.082
0.36
2.0
0.93
3.1
0.52
3.8
7.4
0.52
72
6.8
13
5.8
60
57
13
62
184
118
305
470
kOHb
photo OH
–12
3
10 cm
h
h
molecule-1 s-1
5.1 1157
56
5.1
344
56
2.1
650
134
3.6
17
80
4.7
338
61
2.1
77
134
1.4
14
203
1.4
30
203
1.0
9
285
1.0
54
283
1.0
7
281
0.55
4
520
0.72
54
398
1.6
0.4
182
0.69
4
412
0.23
2 1236
0.37
5
773
0.99
0.5
288
0.16
0.5 1780
0.17
2 1722
0.11
0.4 2642
0.12
0.2 2437
0.066
0.2 4313
0.066 0.09 4313
0.034 0.06 8498
Calculated using modeled actinic flux and by assuming photo = 0.5; actinic flux was the sun intensity at
noon, averaged over 0–2.5 km at the solstices and equinoxes (see text). bThe values are for T = 298 K, as
calculated from structure activity relationships [15, 16].
a
S14
TABLE S4: The fraction (f) of PBDEs in the particle phase at 288 ± 1 K, as determined
from atmospheric samples collected with high volume air samplers at five different sites
in the east-central U.S. [17,18].
Congener
diphenyl ether
17
28
49
47
66
85
99
100
154
153
206–208
209
#Br
0
3
3
4
4
4
5
5
5
6
6
9
10
N
f
0
0.05
0.06
0.19
0.17
0.25
0.61
0.42
0.32
0.62
0.79
0.99999
0.99999
13
14
12
16
13
14
16
16
16
15
±2
0.04
0.04
0.12
0.09
0.12
0.16
0.12
0.11
0.15
0.13
#Br is the number of bromine substituents; N is the number of samples; 2 is the 95% confidence interval
of the mean. For the purposes of deriving an empirical expression to describe the partitioning of PBDEs to
the particle-phase, it is assumed that diphenyl ether is entirely in the gas-phase and that nona-BDEs and deca-BDE occur 99.999% in particles.
Fraction in the Particle Phase
FIGURE S4: The fraction (f) of PBDEs in the particle phase at 288 ± 1 K vs. the number of bromine substituents, as determined from atmospheric samples collected with high
volume air samplers at 5 different sites in the east-central U.S. [17,18]. The error bars are
the 95% confidence interval of the mean. The data, which also appear in Table S4 is fit to
the expression, f = 1.005 / [1 + e–(#Br – 5.207)/0.876], with R2 = 0.958.
1.0
O
0.8
Br n
0.6
0.4
0.2
0.0
0
1
2
3
4
5
6
7
Number of Bromines
S15
8
9
10
Uncertainties in Lifetime Estimates
The uncertainty associated with the terms used to construct the mass balance of PBDEs in
Lake Superior can be high, especially for variables derived from single measurements or
for those associated with meteorological parameters. Unfortunately, it is virtually impossible to quantitatively propagate these errors and to apply them to the final fluxes as given in Table 1 and in Figure 4. Part of the problem is that many of the errors associated
with the information used in the mass balance calculation are not quantitatively known,
and the distribution functions of these errors are often non-normal. For example, most
environmental concentration measurements are log-normally distributed [19,20]. While
it is possible to guess at the errors for many (but not all) of the terms used in the mass
balance calculation, propagation of these errors leads to unrealistically high errors for the
final result [21]. In fact, it may be more appropriate to base the error propagation on logarithmically transformed data. At the moment, our best estimate of the errors associated
with the fluxes is about a factor of 2.
S16
TABLE S5: List of Symbols Used and Their Meaning
A

Fem
F
Fdry
f
FOH
Fphoto
Fsed
Fvap
Fwet
H'
I
J
kBDE
k Cl 2
kdry
KL
kOH

kOH

k photo
kvap
kwet

p
[PBDE]
p

photo
tot
W
Z
surface area of Lake Superior
photolysis quantum yield
emission rate of a PBDE congener to the Lake Superior
airshed
solar actinic flux
removal rate due to particle dry deposition
fraction of a PBDE congener in the particle-phase
removal rate due to reactions with OH radical
removal rate due to photolysis
flow of a given PBDE congener to the sediment
removal rate due to vapor deposition (air-water exchange)
removal rate due to wet deposition
dimensionless Henry's Law constant
light intensity
photolysis frequency (the first order photolysis rate constant)
pseudo-first order photolysis decay rates of a given BDE
congener
pseudo-first order photolysis decay rates of Cl2
rate constant for removal by dry deposition
total liquid-phase mass transfer coefficient
room temperature OH rate constant
pseudo-first order removal rate constant with respect to
OH radical reactions, considering particle-partitioning
removal rate constant with respect to photolysis, considering particle-partitioning
gaseous dry deposition removal rate constant
rate constant for wet removal of PBDEs from the atmosphere
wavelength in nm
deposition velocity for the particle-bound PBDEs
concentration of PBDE in the specified phase
annual precipitation rate for Lake Superior
absorption cross section to the base e
photolysis lifetime
overall lifetime of PBDEs in the atmosphere
washout ratio of a specified PBDE congener
tropospheric mixing height
S17
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2.
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8.
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11.
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S18
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12.
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13.
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S19