quantitative structure-property relationships for vapor pressures of polybrominated diphenyl ethers
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Quantitative structure-property relationships for vaporpressures of polybrominated diphenyl ethersJ.W. Chen a , P. Yang a , S. Chen a , X. Quan a , X. Yuan c , K.-W. Schramm b & A. Kettrup aa School of Environmental Science and Technology , Dalian University of Technology , Dalian, 116023,People's Republic of Chinab Institute of Ecological Chemistry , GSF-National Research Center for Environment and Health ,Neuherberg, Munich, D-85764, Germanyc Department of Environmental Science , Northeast Normal University , Changchun, 130024, People'sRepublic of Chinad Lehrstuhl für Ökologische Chemie und Umweltanalytik , Technische Universität München , Freising-Weihenstephan, 85350, GermanyPublished online: 29 Oct 2010.
To cite this article: J.W. Chen , P. Yang , S. Chen , X. Quan , X. Yuan , K.-W. Schramm & A. Kettrup (2003) Quantitative structure-property relationships for vapor pressures of polybrominated diphenyl ethers, SAR and QSAR in Environmental Research, 14:2, 97-111,DOI: 10.1080/1062936031000073135
To link to this article: http://dx.doi.org/10.1080/1062936031000073135
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QUANTITATIVE STRUCTURE–PROPERTYRELATIONSHIPS FOR VAPOR PRESSURES OF
POLYBROMINATED DIPHENYL ETHERS
J.W. CHENa,b,*, P. YANGa,c, S. CHENa, X. QUANa, X. YUANc, K.-W. SCHRAMMb and
A. KETTRUPb,d
aSchool of Environmental Science and Technology, Dalian University of Technology, Dalian 116023,People’s Republic of China; bInstitute of Ecological Chemistry, GSF-National Research Center forEnvironment and Health, D-85764, Neuherberg, Munich, Germany; cDepartment of EnvironmentalScience, Northeast Normal University, Changchun 130024, People’s Republic of China; dLehrstuhl
fur Okologische Chemie und Umweltanalytik, Technische Universitat Munchen, 85350Freising-Weihenstephan, Germany
(Received 20 June 2002; In final form 12 September 2002)
Based on quantum chemical descriptors, by the use of partial least squares regression, quantitative structure–property relationship models for subcooled liquid vapor pressures (PL) of polybrominated diphenyl ether (PBDE)congeners were developed. The Q2
cum value of the optimal model obtained is as high as 0.993, indicating a goodpredictive ability and robustness of the model. Although disagreements were observed between the predicted log PL
values and log PL values of validation set, the model obtained can still be used for estimating PL of other PBDEcongeners, considering the fact that accurate PL values for compounds with low volatility are extremely difficult todetermine experimentally. Intermolecular dispersive interactions play a leading role in governing the values of PL,followed by electrostatic, dipole–dipole and dipole-induced dipole interactions. Intermolecular dispersiveinteractions also govern the values of enthalpies of vaporization.
Keywords: Vapor pressure; PBDE; QSPR; PLS; Theoretical molecular structural descriptors
INTRODUCTION
Polybrominated diphenyl ethers (PBDEs) are widely used as flame or fire retardants that are
added to products such as textiles, electronic equipment and insulation materials. The IUPAC
numbering scheme for polychlorinated biphenyl congeners is also used for PBDEs. PBDEs
are ubiquitous environmental pollutants and have been detected in biotic and abiotic matrixes
including fish, birds, sediments, air, marine mammals and human plasma and milk [1–5]. It
has been reported that the environmental levels of PBDEs have been increasing since the mid
ISSN 1062-936X print/ISSN 1029-046X online q 2003 Taylor & Francis Ltd
DOI: 10.1080/1062936031000073135
*Corresponding author. E-mail: [email protected]; [email protected]
SAR and QSAR in Environmental Research, 2003 Vol. 14 (2), pp. 97–111
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1970s [1,6–8]. It was found that PBDEs have a potential to induce/down-regulate liver
enzyme production, negatively influence the regulation of the thyroid hormone system and
induce immunotoxicity [6]. They also induce neurotoxicity when administered at a sensitive
period of brain growth [6]. Thus the pollution of PBDEs has become of increasing concern to
scientists in recent years. A special issue of Chemosphere (Volume 46, Issue 5) was
published recently to provide a state-of-the-science understanding of the occurrence,
analytical methods, environmental levels, environmental fate and sources and toxicology and
risk assessment. Among the special issue, de Wit [6] provided an extensive overview of
PBDEs and other brominated flame retardants.
Physicochemical parameters are indispensable to the fate assessment of persistent organic
pollutants. Of the 209 possible PBDE congeners, fewer than 40 have been synthesized [2,9].
Relatively few physical–chemical properties have been measured. The lack of generally
available pure congeners is a major impediment to chemical analysis and property
determination. It is thus important to develop predictive models for physicochemical
properties of PBDEs.
Vapor pressure is a key physicochemical property of chemicals that can be used to
assess the distribution of a chemical among air, air particles, water, soil and plant
[10–15]. In 2001, Wong et al. [16] determined the supercooled liquid vapor pressures
(PL) at 258C of 23 PBDE congeners with a gas chromatographic (GC) retention
technique. In the same year and using the same method, Tittlemier and Tomy [17]
determined PL values of six PBDEs at 258C. In 1997, based on a statistical analysis of
the data obtained with different methods and derived from 152 references, Delle Site
compared critically the various methods determining vapor pressure values and
concluded that the indirect determination based on GC retention times “can be
recommended as one of the most suitable methods for the determination of the vapor
pressure of low volatility compounds” [16,18].
Combining the data determined previously [16,17], there are totally 26 PBDE congeners
for which PL values have been determined. Wong et al. [16] proposed a PL estimation
method from relative retention times (RRT) on the CPSil-8 column of GC for additional
PBDE congeners. However, the method is limited because the RRT values are available for
only 31 PBDE congeners. Among the 31 congeners, PL values for 17 PBDEs were
determined previously [16,17]. Thus for most of the PBDE congeners, PL values are lacking.
Experimental determination of PL is time-consuming and expensive. Furthermore, because
of limited number of chemical standards for PBDEs, it seems impossible to measure PL
values for all the other PBDEs.
Quantitative structure–property relationship (QSPR) is an alternative approach for
estimating vapor pressure. The premise of QSPR is that physicochemical properties of
organic compounds are governed by the molecular structural characteristics (geometric and
electronic) expressed in terms of appropriate molecular descriptors [13]. This method
requires only the knowledge of the chemical structures. When significant QSPR models are
obtained, they may also provide insight into which aspect of the molecular structure
influences the property. Some previous studies [10–15,19] showed that it was indeed feasible
and successful to develop QSPR models for vapor pressure. Thus it is the purpose of this
study to develop QSPR models for PL of PBDEs, based on the experimental values.
Various molecular structural descriptors, like constitutional descriptors [12,15],
electrostatic descriptors [12,15], topological descriptors [12,13,15], geometrical descriptors
[12,15] and quantum chemical descriptors [11,12,14,19], have been used to develop QSPRs
for vapor pressure. As quantum chemical descriptors can be easily obtained by computation,
can clearly describe defined molecular properties, and are not restricted to closely related
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compounds, the development of QSPR models in which quantum chemical descriptors are
used is of great importance.
As partial least squares (PLS) regression can analyze data with strongly collinear, noisy
and numerous X variables [20], it was used for model development in the present study. PLS
finds the relationship between a matrix Y (containing dependent variables—often only one
for QSPR studies) and a matrix X (containing predictor variables) by reducing the dimension
of the matrix X while concurrently maximizing the correlation between them.
METHOD
All 209 PBDE congeners were included in the study. The 23 PBDEs for which PL values at
258C were determined by Wong et al. [16], were selected as training set. The six PBDEs for
which PL values at 258C were measured by Tittlemier and Tomy [17], were used as test set.
The log PL values for these congeners are listed in Table I.
It is known that intermolecular dispersive interactions, dipole–dipole interactions, dipole-
induced dipole interactions, hydrogen bonding and electrostatic interactions, may govern the
magnitude of log PL. Thus a total of 13 theoretical molecular structural descriptors were
selected to describe the intermolecular interactions. Among the 13 descriptors, 12 were
computed by quantum chemistry methods.
The computational time for semi-empirical molecular orbital methods is much shorter
than needed by ab initio methods. Recently, Seward et al. [21] studied the effect of precision
of molecular orbital descriptors on toxicity modeling of selected pyridines. They found
instances where calculated quantum chemical descriptors, for example, the energy of the
lowest unoccupied molecular orbital (ELUMO) and the energy of the highest occupied
molecular orbital (EHOMO), varied both between different Hamiltonian versions and other
similar software packages. However, there are strong correlations between the values
calculated from different Hamiltonians and software packages. Seward et al. [21] found the
variability in no way affects the statistical significance of QSAR models. For the current
study, PM3 Hamiltonian [22,23] contained in the quantum chemical computation software
MOPAC was applied to compute the quantum chemical descriptors.
MOPAC_2000 contained in the CS Chem3D Ultra (Ver. 6.0) was used to compute
quantum chemical descriptors. The molecular structures were optimized using eigenvector
following [24], a geometry optimization procedure within MOPAC 2000. The geometry
optimization criteria GNORM was set at 0.1. The 12 quantum chemical descriptors include:
average molecular polarizability (a), dipole moment (m), m 2, standard heat of formation
(DHf), total energy (TE), electronic energy (EE), core–core repulsion energy (CCR), EHOMO,
ELUMO, the largest negative net atomic charge on a carbon atom (q2C ), the most positive net
atomic charges on a hydrogen atom (qþH), and the most positive net atomic charges on a
bromine atom (qþBr). In addition, molecular weight (Mw) was also selected as a molecular
structural descriptor. The values for all the molecular structural descriptors are listed in an
appendix, which can be obtained from the corresponding author.
Simca (Simca-S Version 6.0, Umetri AB & Erisoft AB) software was used to perform the
PLS regression. The conditions for the computation were: cross validation rounds ¼ 7,
maximum iteration ¼ 200, missing data tolerance ¼ 50% and significance level
limit ¼ 0.05. All the variables were centered and scaled to unit variance. The criterion
used to determine the model dimensionality (the number of significant PLS components) is
cross validation. With cross validation, observations are kept out of the model development,
then the response values (Y) for the kept out observations are predicted by the model, and
compared with the actual values. This procedure is repeated several times until every
QSPR FOR VAPOR PRESSURES OF PBDES 99
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3.7
53
0.0
24
^0
.041
1.9
42
0.0
04
^0
.007
66
2,3
0 ,4
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23
.62
32
3.6
23
0.0
23
^0
.040
1.9
71
1.9
75
0.0
04
^0
.007
67
2,3
0 ,4
,5-
23
.624
0.0
22
^0
.038
1.9
67
0.0
03
^0
.005
68
2,3
0 ,4
,50 -
23
.621
0.0
22
^0
.038
1.9
69
0.0
03
^0
.005
69
2,3
0 ,4
,6-
23
.39
82
3.3
94
0.0
31
^0
.053
1.9
60
1.9
66
0.0
02
^0
.003
70
2,3
0 ,40 ,5
-2
3.7
48
0.0
25
^0
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1.9
66
0.0
03
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71
2,3
0 ,40 ,6
-2
3.2
30
0.0
23
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23
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71
.946
0.0
03
^0
.005
72
2,3
0 ,5
,50 -
23
.651
0.0
22
^0
.038
1.9
71
0.0
03
^0
.005
QSPR FOR VAPOR PRESSURES OF PBDES 101
Dow
nloa
ded
by [
Yor
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rsity
Lib
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es]
at 1
5:00
11
Nov
embe
r 20
14
TA
BL
EI
–co
nti
nued
Lo
gP
L(P
a)
logD
Hv
ap
(kJ/
mo
l)IU
PA
Cn
um
ber
No
men
cla
ture
Ob
s.P
red
.S
EC
IV.S
.R
RT
Ob
s.P
red.
SE
CI
73
2,3
0 ,50 ,6
-2
3.8
77
0.0
32
^0
.055
1.9
50
0.0
03
^0
.005
74
2,4
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-2
3.7
06
0.0
23
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1.9
71
0.0
03
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75
2,4
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-2
3.3
08
23
.382
0.0
28
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1.9
55
1.9
67
0.0
03
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76
2,3
0 ,40 ,50 -
23
.176
0.0
43
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1.9
49
0.0
03
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77
3,3
0 ,4
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23
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72
3.7
08
0.0
36
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1.9
79
1.9
72
0.0
04
^0
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78
3,3
0 ,4
,5-
23
.991
0.0
33
^0
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1.9
75
0.0
04
^0
.007
79
3,3
0 ,4
,50 -
24
.034
0.0
47
^0
.081
1.9
83
0.0
05
^0
.009
80
3,3
0 ,5
,50 -
24
.176
0.0
70
^0
.121
1.9
86
0.0
06
^0
.010
81
3,4
,40 ,5
-2
4.0
34
0.0
37
^0
.064
1.9
77
0.0
04
^0
.007
82
2,2
0 ,3
,30 ,4
-2
4.1
89
24
.321
0.0
29
^0
.050
1.9
96
1.9
99
0.0
03
^0
.005
83
2,2
0 ,3
,30 ,5
-2
4.5
01
0.0
31
^0
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2.0
01
0.0
03
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.005
84
2,2
0 ,3
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-2
4.3
57
0.0
30
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1.9
75
0.0
06
^0
.010
85
2,2
0 ,3
,4,4
0 -2
4.4
13
0.0
30
^0
.052
25
.54
24
.55
12
.007
0.0
03
^0
.005
86
2,2
0 ,3
,4,5
-2
4.1
19
0.0
35
^0
.060
1.9
92
0.0
04
^0
.007
87
2,2
0 ,3
,4,5
0 -2
4.5
15
0.0
31
^0
.053
1.9
99
0.0
03
^0
.005
88
2,2
0 ,3
,4,6
-2
4.4
06
0.0
30
^0
.052
1.9
79
0.0
06
^0
.010
89
2,2
0 ,3
,4,6
0 -2
4.3
43
0.0
37
^0
.064
1.9
64
0.0
08
^0
.014
90
2,2
0 ,3
,40 ,5
-2
4.5
53
0.0
32
^0
.055
2.0
09
0.0
04
^0
.007
91
2,2
0 ,3
,40 ,6
-2
4.3
39
0.0
30
^0
.052
1.9
84
0.0
05
^0
.009
92
2,2
0 ,3
,5,5
0 -2
4.6
88
0.0
34
^0
.059
2.0
00
0.0
03
^0
.005
93
2,2
0 ,3
,5,6
-2
4.3
67
0.0
30
^0
.052
1.9
76
0.0
06
^0
.010
94
2,2
0 ,3
,5,6
0 -2
4.4
76
0.0
36
^0
.062
1.9
71
0.0
07
^0
.012
95
2,2
0 ,3
,50 ,6
-2
4.6
45
0.0
34
^0
.059
1.9
76
0.0
06
^0
.010
96
2,2
0 ,3
,6,6
0 -2
4.8
58
0.0
38
^0
.066
1.9
35
0.0
14
^0
.024
97
2,2
0 ,3
,40 ,50 -
24
.366
0.0
32
^0
.055
1.9
90
0.0
04
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.007
98
2,2
0 ,3
,40 ,60 -
24
.353
0.0
38
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1.9
72
0.0
07
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99
2,2
0 ,4
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-2
4.1
66
24
.193
0.0
28
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24
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2.0
01
2.0
07
0.0
03
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.005
10
02
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-2
4.3
96
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30
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1.9
98
0.0
03
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10
12
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0 -2
4.1
50
0.0
27
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.047
2.0
02
0.0
03
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10
22
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0 -2
3.9
14
0.0
32
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1.9
79
0.0
06
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10
32
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,50 ,6
-2
4.2
92
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29
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1.9
92
0.0
04
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10
42
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0 -2
4.8
76
0.0
40
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.069
1.9
48
0.0
12
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.021
10
52
,3,3
0 ,4
,40 -
24
.441
0.0
32
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.055
2.0
11
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04
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10
62
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0 ,4
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24
.440
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36
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.062
2.0
04
0.0
03
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10
72
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-2
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43
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34
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11
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04
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10
82
,3,3
0 ,4
,50 -
24
.539
0.0
32
^0
.055
2.0
16
0.0
05
^0
.009
J.W. CHEN et al.102
Dow
nloa
ded
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Yor
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rsity
Lib
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es]
at 1
5:00
11
Nov
embe
r 20
14
TA
BL
EI
–co
nti
nued
Lo
gP
L(P
a)
logD
Hv
ap
(kJ/
mo
l)IU
PA
Cn
um
ber
No
men
cla
ture
Ob
s.P
red
.S
EC
IV.S
.R
RT
Ob
s.P
red.
SE
CI
10
92
,3,3
0 ,4
,6-
24
.581
0.0
34
^0
.059
1.9
92
0.0
04
^0
.007
11
02
,3,3
0 ,40 ,6
-2
4.4
01
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32
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1.9
84
0.0
04
^0
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11
12
,3,3
0 ,5
,50 -
24
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36
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.062
2.0
16
0.0
04
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11
22
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0 ,5
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24
.665
0.0
33
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1.9
92
0.0
04
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11
32
,3,3
0 ,50 ,6
-2
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13
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35
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1.9
89
0.0
04
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11
42
,3,4
,40 ,5
-2
4.5
62
0.0
34
^0
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2.0
08
0.0
04
^0
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11
52
,3,4
,40 ,6
-2
4.5
20
24
.563
0.0
32
^0
.055
2.0
08
1.9
94
0.0
03
^0
.005
11
62
,3,4
,5,6
-2
4.5
08
0.0
31
^0
.053
24
.30
21
.981
0.0
05
^0
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11
72
,3,4
0 ,5
,6-
24
.546
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32
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1.9
91
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04
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11
82
,30 ,4
,40 ,5
-2
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44
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25
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2.0
10
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04
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11
92
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,40 ,6
-2
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33
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33
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24
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32
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12
02
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52
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2.0
14
0.0
04
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12
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-2
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47
0.0
48
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.083
2.0
04
0.0
03
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12
22
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0 ,40 ,50 -
24
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0.0
34
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1.9
97
0.0
03
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12
32
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,40 ,50 -
24
.300
0.0
33
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2.0
04
0.0
03
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12
42
,30 ,40 ,5
,50 -
24
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0.0
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2.0
05
0.0
03
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12
52
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-2
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03
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83
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05
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12
63
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-2
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44
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50
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2.0
19
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12
73
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40
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57
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21
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82
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25
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39
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2.0
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92
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25
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36
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04
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13
02
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25
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2.0
41
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04
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13
12
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25
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0.0
41
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2.0
21
0.0
06
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13
22
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25
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0.0
44
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2.0
10
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08
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13
32
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25
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0.0
48
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2.0
43
0.0
04
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13
42
,20 ,3
,30 ,5
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25
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41
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2.0
18
0.0
07
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13
52
,20 ,3
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25
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16
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07
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13
62
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25
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41
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1.9
66
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16
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13
72
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63
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41
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2.0
46
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04
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82
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25
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0.0
40
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39
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04
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13
92
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-2
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11
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30
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02
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25
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12
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25
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42
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36
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22
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25
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40
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32
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25
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42
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-2
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12
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2.0
21
0.0
06
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.010
QSPR FOR VAPOR PRESSURES OF PBDES 103
Dow
nloa
ded
by [
Yor
k U
nive
rsity
Lib
rari
es]
at 1
5:00
11
Nov
embe
r 20
14
TA
BL
EI
–co
nti
nued
Lo
gP
L(P
a)
logD
Hv
ap
(kJ/
mo
l)IU
PA
Cn
um
ber
No
men
cla
ture
Ob
s.P
red
.S
EC
IV.S
.R
RT
Ob
s.P
red.
SE
CI
14
52
,20 ,3
,4,6
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25
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0.0
48
^0
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1.9
76
0.0
15
^0
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14
62
,20 ,3
,40 ,5
,50 -
25
.359
0.0
42
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2.0
41
0.0
04
^0
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14
72
,20 ,3
,40 ,5
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25
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40
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2.0
26
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06
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14
82
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44
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23
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06
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14
92
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,40 ,50 ,6
-2
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15
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15
02
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25
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54
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13
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15
12
,20 ,3
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0 ,6
-2
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51
0.0
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2.0
03
0.0
09
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15
22
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25
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0.0
44
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1.9
70
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15
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15
32
,20 ,4
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25
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42
5.0
48
0.0
38
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2.0
32
2.0
39
0.0
04
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42
,20 ,4
,40 ,5
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24
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38
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2.0
33
0.0
05
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.009
15
52
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25
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60
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99
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10
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15
62
,3,3
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-2
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15
0.0
42
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2.0
46
0.0
04
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15
72
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0 ,4
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25
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41
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51
0.0
05
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15
82
,3,3
0 ,4
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-2
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27
0.0
42
^0
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2.0
30
0.0
05
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.009
15
92
,3,3
0 ,4
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0 -2
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91
0.0
42
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2.0
50
0.0
05
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.009
16
02
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0 ,4
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-2
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49
0.0
46
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2.0
31
0.0
05
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16
12
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0 ,4
,50 ,6
-2
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25
0.0
46
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34
0.0
05
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16
22
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25
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04
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16
32
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25
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40
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29
0.0
05
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16
42
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0 ,40 ,50 ,6
-2
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12
0.0
41
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2.0
20
0.0
06
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16
52
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-2
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60
0.0
58
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2.0
31
0.0
05
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16
62
,3,4
,40 ,5
,6-
25
.434
0.0
46
^0
.079
2.0
30
0.0
05
^0
.009
16
72
,30 ,4
,40 ,5
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25
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0.0
41
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2.0
47
0.0
04
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16
82
,30 ,4
,40 ,50 ,6
-2
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32
0.0
43
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2.0
42
0.0
04
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16
93
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25
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65
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56
0.0
05
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17
02
,20 ,3
,30 ,4
,40 ,5
-2
6.0
37
0.0
52
^0
.090
2.0
77
0.0
06
^0
.010
17
12
,20 ,3
,30 ,4
,40 ,6
-2
6.0
40
0.0
52
^0
.090
2.0
60
0.0
08
^0
.014
17
22
,20 ,3
,30 ,4
,5,5
0 -2
6.2
93
0.0
58
^0
.100
2.0
78
0.0
06
^0
.010
17
32
,20 ,3
,30 ,4
,5,6
-2
6.1
17
0.0
52
^0
.090
2.0
55
0.0
08
^0
.014
17
42
,20 ,3
,30 ,4
,5,6
0 -2
6.1
14
0.0
54
^0
.093
2.0
48
0.0
10
^0
.017
17
52
,20 ,3
,30 ,4
,50 ,6
-2
6.4
08
0.0
61
^0
.105
2.0
62
0.0
07
^0
.012
17
62
,20 ,3
,30 ,4
,6,6
0 -2
6.5
87
0.0
67
^0
.116
2.0
13
0.0
16
^0
.028
17
72
,20 ,3
,30 ,4
,50 ,60 -
26
.112
0.0
57
^0
.098
2.0
38
0.0
11
^0
.019
17
82
,20 ,3
,30 ,5
,50 ,6
-2
6.3
97
0.0
59
^0
.102
2.0
58
0.0
08
^0
.014
17
92
,20 ,3
,30 ,5
,6,6
0 -2
6.0
96
0.0
56
^0
.097
2.0
00
0.0
18
^0
.031
18
02
,20 ,3
,4,4
0 ,5
,50 -
26
.080
0.0
52
^0
.090
2.0
76
0.0
06
^0
.010
J.W. CHEN et al.104
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TA
BL
EI
–co
nti
nued
Lo
gP
L(P
a)
logD
Hv
ap
(kJ/
mo
l)IU
PA
Cn
um
ber
No
men
cla
ture
Ob
s.P
red
.S
EC
IV.S
.R
RT
Ob
s.P
red.
SE
CI
18
12
,20 ,3
,4,4
0 ,5
,6-
26
.075
0.0
52
^0
.090
2.0
63
0.0
07
^0
.012
18
22
,20 ,3
,4,4
0 ,5
,60 -
26
.238
0.0
55
^0
.095
2.0
55
0.0
09
^0
.016
18
32
,20 ,3
,4,4
0 ,50 ,6
-2
6.1
29
0.0
53
^0
.091
2.0
60
0.0
08
^0
.014
18
42
,20 ,3
,4,4
0 ,6
,60 -
26
.694
0.0
67
^0
.116
2.0
26
0.0
14
^0
.024
18
52
,20 ,3
,4,5
,50 ,6
-2
6.3
11
0.0
57
^0
.098
2.0
53
0.0
09
^0
.016
18
62
,20 ,3
,4,5
,6,6
0 -2
6.3
99
0.0
57
^0
.098
2.0
07
0.0
17
^0
.029
18
72
,20 ,3
,40 ,5
,50 ,6
-2
6.0
74
0.0
52
^0
.090
2.0
56
0.0
08
^0
.014
18
82
,20 ,3
,40 ,5
,6,6
0 -2
6.3
57
0.0
62
^0
.107
2.0
19
0.0
14
^0
.024
18
92
,3,3
0 ,4
,40 ,5
,50 -
26
.136
0.0
53
^0
.091
2.0
83
0.0
06
^0
.010
19
02
,3,3
0 ,4
,40 ,5
,6-
26
.04
32
6.0
88
0.0
52
^0
.090
26
.63
2.0
64
2.0
67
0.0
07
^0
.012
19
12
,3,3
0 ,4
,40 ,50 ,6
-2
6.2
03
0.0
54
^0
.093
2.0
64
0.0
07
^0
.012
19
22
,3,3
0 ,4
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0 ,6
-2
6.6
89
0.0
71
^0
.122
2.0
68
0.0
07
^0
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19
32
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0 ,40 ,5
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5.9
06
0.0
56
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2.0
64
0.0
07
^0
.012
19
42
,20 ,3
,30 ,4
,40 ,5
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26
.890
0.0
65
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2.1
10
0.0
08
^0
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19
52
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,30 ,4
,40 ,5
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26
.825
0.0
63
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.109
2.0
93
0.0
10
^0
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19
62
,20 ,3
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,60 -
27
.089
0.0
71
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2.0
88
0.0
11
^0
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19
72
,20 ,3
,30 ,4
,40 ,6
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27
.491
0.0
87
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.150
2.0
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0.0
18
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19
82
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,30 ,4
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27
0.0
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^0
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2.0
94
0.0
10
^0
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19
92
,20 ,3
,30 ,4
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0 ,60 -
26
.934
0.0
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2.0
74
0.0
13
^0
.022
20
02
,20 ,3
,30 ,4
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27
.340
0.0
77
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.133
2.0
46
0.0
18
^0
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20
12
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,30 ,4
,50 ,6
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27
.361
0.0
78
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2.0
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0.0
17
^0
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20
22
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27
.414
0.0
77
^0
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2.0
46
0.0
19
^0
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20
32
,20 ,3
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0 ,5
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6.8
98
0.0
64
^0
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2.0
91
0.0
10
^0
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20
42
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0 ,5
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0 -2
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70
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76
^0
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2.0
56
0.0
17
^0
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20
52
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98
0.0
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2.0
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^0
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20
62
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-2
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77
0.0
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22
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^0
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20
72
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0 -2
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54
0.0
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^0
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2.0
80
0.0
21
^0
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20
82
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,30 ,4
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0 ,6
,60 -
28
.191
0.0
89
^0
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2.0
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0.0
22
^0
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20
92
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28
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2.1
32
0.0
21
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Ob
s.,O
bse
rved
val
ues
;P
red.,
Pre
dic
ted
val
ues
;SE
,S
tandar
der
rors
for
the
pre
dic
ted
val
ues
;C
I,95%
Confi
den
cein
terv
als;
V.S
.,V
alid
atio
nse
tof
PL
Sm
odel
(1);
RR
T,th
eco
rres
pondin
glo
gP
Lval
ues
wer
ees
tim
ated
from
rela
tive
rete
nti
on
tim
eson
the
CP
Sil
-8co
lum
nof
GC
[16].
QSPR FOR VAPOR PRESSURES OF PBDES 105
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observation has been kept out once and only once. The prediction error sum of squares
(PRESS) is the squared differences between observed Y and predicted values when the
observations were kept out, which is computed as:
PRESS ¼i
Xm
XðY im 2 Y imÞ
2
where Yim denotes the observed Y values, Y im denotes the predicted values, i stands for
different observations, and m stands for different dependent variables (m ¼ 1 for the current
study). Based on PRESS, Q 2 (the fraction of the total variation of the dependent variables
that can be predicted by a component) and Q2cum (cumulative Q 2) can be calculated as:
Q2 ¼ 1:0 2PRESS
SS
Q2cum ¼ 1:0 2
Y PRESS
SS
� �a
; ða ¼ 1; 2; . . .AÞ
where SS is the residual sum of squares of the previous dimension,Q
(PRESS/SS)a is the
product of PRESS/SS for each individual component a. When PRESS=SS # 0:952 or
Q2 $ ð1 2 0:952Þ ¼ 0:097; the tested PLS component is considered significant. It is obvious
that Q2cum is a good measure of the predictive power and robustness of the model. When Q2
cum
is larger than 0.5, the model is considered to have a good predictive ability. Besides Q2cum,
model adequacy was mainly measured as the number of PLS components (A), the correlation
coefficient between observed and fitted values (R), and the significance level ( p).
RESULTS AND DISCUSSION
Variable importance in the projection (VIP) is a parameter showing the importance of a
variable in a PLS model. According to the manual of Simca-S (Version 6.0), VIP is the sum
over all model dimensions of the contributions of variable influence (VIN). For a given PLS
dimension (a) and a given X term (k), VIN 2 is computed from the squared PLS weight of that
X term, multiplied by the percent explained SS by that PLS dimension. VIP value is
calculated from the accumulated value over all PLS dimensions,
VIPk ¼XA
a¼1
ðVINÞ2k
divided by the total percent explained SS by the PLS model and multiplied by the number of
terms in the model. Terms with large values of VIP are the most relevant for explaining
dependent variable.
According to the previous experience in QSPR studies [25], all the theoretical molecular
structural descriptors are not necessary to the QSPR modeling. To obtain an optimal QSPR
model using the subset of the molecular structural descriptors, the following procedures were
followed. First, PLS analysis with all the 13 theoretical molecular structural descriptors as
predictor variables was performed. Then the variable with the lowest VIP value was
eliminated and PLS analysis was performed once more. This procedure was repeated until
there were only two variables remained in the PLS model. As a result, 12 PLS models were
obtained. Comparing the Q2cum values of the 12 PLS models, it was found that exclusion one
of the variables, m, qþH , ELUMO and CCR in a previous model resulted in increase of the Q2
cum
value for the following PLS model. Thus a PLS regression analysis with the remaining nine
theoretical molecular descriptors as predictor variables was performed further, resulting in
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a new PLS model. The Q2cum value of the new PLS model was the highest among all the 13
PLS models obtained. Therefore, it can be concluded that the new PLS model, termed PLS
Model (1), is the optimal one. The model fitting results for Model (1) are listed in Table II.
In Table II, r2XðadjÞðcumÞ and r2
YðadjÞðcumÞ stand for cumulative variance of all the X0s and Y0s,
respectively, explained by all the extracted components. It can be concluded from Table II
that in Model (1), 2 PLS components were selected, which explained 79.0% of the variance
of the predictor variables and 99.5% of the variance of the dependent variable. Based on the
unscaled pseudo-regression coefficients of the predictor variables and a constant transformed
from PLS results of Model (1), a QSPR equation like those obtained from multiple regression
analysis was obtained, as follows:
log PL ¼ 3:911 £ 1024TE 2 1:709 £ 1023Mw 2 1:068 £ 1022aþ 7:053 £ 1025EE
2 3:052 £ 1023DHf þ 2:307EHOMO 2 4:531qþBr 2 6:923q2
C þ 6:048
£ 1022m2 þ 2:299 £ 10 ð1Þ
The Q2cum value of Model (1) is as high as 0.993, indicating a good predictive ability and
robustness of the model. The predicted log PL values together with their standard errors (SE)
are listed in Table I. According to the manual of Simca-S (Version 6.0), SE was calculated
from the variance of the prediction, VðYÞ, for a given response y at a point X0, which is
computed as:
VðYÞ ¼1
Nþ t0ðT
0TÞ21t0
0
� �s2
where N standards for the number of observations, T is the matrix of scores that summarize
the X variables, t0 stands for the scores t of observation X0 and s 2 is the y error variance
estimated from the sum of squares of the residuals of y divided by the degree of freedom for
PLS. Confidence intervals of the predicted log PL can be computed from SE by multiplying
by a t-distribution value with the appropriate degrees of freedom. In the present study, as all
the variables were centered and scaled to unit variance, the degree of freedom is Nð23Þ2
Að2Þ2 1 ¼ 20: At significance level p ¼ 0:05; the critical value of Student’s t value is 1.725.
As a result, the 95% confidence intervals (CI) of the predicted log PL values were calculated,
which are listed in Table I.
As shown by Fig. 1, for the compounds contained in the training set, the correlation
between observed and predicted log PL values are significant ðr ¼ 0:998; p , 0:0001Þ: The
predicted log PL values from Model (1) also consist with those values estimated from RRT
values [16], as indicated by Fig. 1 and Table I. For the 23 PBDE congeners, Wong et al. [16]
presented the linear relationships between log PL, molar volume and RRT, after dividing the
PBDE congeners into three groups, non-ortho PBDEs, mono-ortho PBDEs and di-ortho
PBDEs. Observing Fig. 1, it can be concluded for the present study, it is unnecessary to
divide the PBDE congeners, implying that the theoretical molecular descriptors contained in
Model (1) can sufficiently differentiate PBDE congeners.
TABLE II Model fitting results
Models N A r2X(adj)(cum) r2
Y(adj)(cum) Q2cum r p
1 23 2 0.790 0.995 0.993 0.998 , 0.00012 23 2 0.999 0.975 0.975 0.989 , 0.0001
QSPR FOR VAPOR PRESSURES OF PBDES 107
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For the six PBDE congeners in the validation set, linearity can also be observed between
the observed values and the predicted values from Model (1). However, it is evident that the
predicted values of Model (1) are higher than the empirical values determined by Tittlemier
and Tomy [17]. This is not surprising because the observed values determined by Wong et al.
[16] for PBDE-47, PBDE-99 and PBDE-190, were found to be larger than the PL values
determined by Tittlemier and Tomy [17] by a factor of ca. 7. Thus it can be concluded that
systematic errors exist between the two determinations. Again the great deviations are not
surprising because accurate vapor pressures of low volatility chemicals (such as PBDEs) are
very difficult to measure.
The VIP values and PLS weights (W*[1] and W*[2]) for the variables included in PLS
Model (1) are listed in Table III. From the PLS weights, it can be seen how much a single
variable contributes in each PLS component to the modeling of log PL. The first PLS
component is mainly related to the descriptors TE, Mw, a, EE, DHf, EHOMO and qþBr. The
absolute values of W*[1] for these descriptors are larger than 0.317 and larger than the
absolute values of W*[1] for the other two descriptors, which implies that these descriptors
FIGURE 1 Plot of observed and predicted log PL values at 258C.
TABLE III The VIP values and PLS weights (W*[1] and W*[2])
Variables VIP W*[1] W*[2]
TE 1.170 0.393 0.053Mw 1.170 2 0.393 2 0.053a 1.169 2 0.393 2 0.075EE 1.158 0.389 2 0.001DHf 1.147 2 0.385 0.044EHOMO 1.071 0.358 0.319qþBr 0.953 2 0.317 0.320q2C 0.341 0.050 2 0.804m 2 0.261 0.074 0.373
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are inter-correlated. Since TE, Mw, a, EE and DHf are relevant to molecular size, the first
PLS component may condense information on size of PBDE molecules. In addition, as
shown by the VIP values, the descriptors TE, Mw, a, EE and DHf are much more significant
than the other descriptors in explaining log PL. The values of TE and EE for the PBDE
molecules are negative, and decrease with the increase of Mw. It can thus be concluded from
the pseudo-regression coefficients that log PL decreases with the increase of molecular size.
As increasing molecular size leads to increasing a values, and intermolecular dispersive
interactions are in direct proportion to the product of a of two interacting molecule [25], in
general, the first PLS component describes intermolecular dispersive forces in governing the
values of log PL. The descriptor EHOMO characterizes the ability of a molecule to donate
electrons in intermolecular interactions. EHOMO also relates to the intermolecular dispersive
forces, because molecular ionization potentials (energy), which can be considered to be equal
to the negative values of EHOMO, determine the intermolecular dispersive forces too.
The second PLS component is loaded primarily on the descriptors EHOMO, qþBr, q2
C and m 2,
for which the absolute value of W*[2] is larger than 0.319, and much larger than the absolute
values of W*[2] for the other molecular structural descriptors. The descriptors qþBr and q2
C
may be relevant to the intermolecular electrostatic interactions. The descriptor m 2 relates
with the intermolecular dipole–dipole and dipole–induced dipole interactions. However,
these interactions are not as significant as the dispersive interactions because the second PLS
component contributes less than the first PLS component to Model (1).
It would be of interests to investigate the aspects of the molecular structure influencing the
enthalpies of vaporization (DHvap) reported by Wong et al. [16]. PLS regression using
logarithms of the absolute values of DHvap as dependent variable, and the 13 molecular
structural descriptors as predictor variables, was performed. Similarly the PLS analysis was
performed step by step with deleting the least significant descriptor indicated by the VIP
value. At last an optimal PLS model, termed Model (2), was selected with respect to the Q2cum
value. The modeling fitting results of Model (2) are listed in Table II.
Model (2) is robust as indicated by the Q2cum value. Based on Model (2), logDHvap values
and their 95% confidence intervals for all the PBDE congeners were also calculated, as listed
in Table I. The correlation between observed and predicted logDHvap values is shown by
FIGURE 2 Plot of observed and predicted logDHvap values at 258C.
QSPR FOR VAPOR PRESSURES OF PBDES 109
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Fig. 2. There are only four theoretical molecular structural descriptors involved in Model (2),
a, CCR, TE and Mw. The analytical form of Model (2) is
logDHvap ¼ 3:469 £ 1023a2 2:813 £ 1025CCR 2 5:660 £ 1025
TE þ 2:416 £ 1024Mw þ 1:511ð2Þ
It can be concluded from Model (2) that the absolute values DHvap increase with increasing
molecular size, and intermolecular dispersive interactions play an important role in
governing the values of DHvap.
CONCLUSIONS
It is successful to develop QSPR models for PL of PBDE congeners. The Q2cum value of the
model is as high as 0.993, indicating a good predictive ability and robustness of the model.
Although disagreements were observed between the predicted log PL values and log PL
values of the validation set, the model obtained can still used for estimating PL of other
PBDE congeners, considering the fact that accurate PL values for compounds with low
volatility are extremely difficult to determine experimentally. Intermolecular dispersive
interactions play a leading role in governing the values of PL, then comes electrostatic,
dipole–dipole and dipole-induced dipole interactions. Intermolecular dispersive interactions
also govern the values of enthalpies of vaporization.
Acknowledgements
The study was supported by Huo Ying-Dong Education Foundation, and Teaching and
Research Award Program for Outstanding Young Teachers in Higher Education Institutions
of MOE (TRAPOYT), P. R. China. The research results were attained with the assistance of
the Alexander von Humboldt Foundation.
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