Gas chromatographic peak identification for polybrominated diphenyl ethers under different temperature programs

Journal of Chromatography A, 1107 (2006) 248–256

Gas chromatographic peak identification for polybrominated diphenyl ethers under different temperature programs Hongxia Zhao, Xingya Xue, Qing Xu, Feifang Zhang, Xinmiao Liang ∗ Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China Received 10 October 2005; received in revised form 13 December 2005; accepted 19 December 2005 Available online 19 January 2006

Abstract A method has been developed for gas chromatographic peak recognition of polybrominated diphenyl ethers (PBDEs) under different temperature programs. On the basis of an identification database of retention parameters (A, B values) of gas chromatography and retention times of the selected internal standards, the retention times of BDEs can be accurately estimated. In comparison with the experimental retention values, the predicted retention times have been proved to be very accurate. In addition, owing to only a part of BDE analytical standards are available, using 40 BDEs as a training set, the quantitative relationship between retention parameters of BDEs and molecular connectivity indexes has been found. The correlation coefficients are greater than 0.997. The A, B values of all the remaining 169 BDE congeners have been predicted. © 2005 Elsevier B.V. All rights reserved. Keywords: Polybrominated diphenyl ethers; Prediction; Chromatographic retention parameters; Molecular connectivity indexes

1. Introduction Polybrominated diphenyl ethers have been widely used around the world as flame retardants to reduce the fire risk in plastics, carpets, electronic equipment, textiles and building materials [1,2]. They are structurally similar to other environmentally persistent aromatics, i.e. PCDD/Fs and polychlorinated biphenyls (PCBs). Therefore, there is a growing belief that this family may be the next environmental contaminant of concern. At present, BDEs have been found in a wide range of environmental and biological samples including birds, edible marine organisms, marine mammals and human beings [3–7]. Environmental monitoring for the past 20 years has shown that BDEs are persistent in sediment and bioaccumulate in tissues [8–10]. Levels in human milk are increasing [11,12], as are levels in organisms that inhabit in deep oceans [9,13]. BDE-47 is the most abundant congener in environmental tissues, followed by BDE-99, -100, -153, and -154. Production of commercial penta-BDE formulations, which contain predominantly BDE47 and -99, accounts for 10% of the BDE market, while the production of octa- and deca-BDE mixtures accounts for 15%

∗

Corresponding author. Tel.: +86 411 84379519; fax: +86 411 84379539. E-mail address: [email protected] (X. Liang).

0021-9673/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2005.12.065

and 75%, respectively. Commercial octa-BDE mixtures contain tetra-and pentabrominated diphenyl ethers only as minor contaminants. The predominance of lower brominated congeners in biota, therefore, may be due to preferential bioavailability and bioaccumulation of these BDEs, debromination of the higher brominated congeners, or factors such as transport and stability in the environment. Although the acute toxicity of BDEs is thought to be low relative to PCDD/Fs and non-ortho-substituted PCBs [14], the chronic effects may result in thyroid hormone disruption, neurobehavioral toxicity and, for some congeners, possibly cancer [15–19]. Thus, it is necessary to identify and monitor concentrations of BDE congeners in environmental matrices. The primary aim of this work was to develop a method to accurately predict gas chromatographic retention time of BDEs under different program temperature conditions. In addition, only a small number of the 209 possible BDE congeners standards are available, which further hinders comprehensive assessments of their environmental concentrations and patterns, as well as more complete toxicological investigations. Thus, the second objective of this study was to develop quantitatively predictive models to help identify the remaining BDE congeners for which analytical standards are currently unavailable, but yet their environmental data are needed.

H. Zhao et al. / J. Chromatogr. A 1107 (2006) 248–256

2. Theory

3. Experimental

According to the statistical thermodynamic treatment in chromatography, the chemical potentials in gas and liquid phases are equal at equilibrium. The linear relationship between the logarithm of retention factors and the reciprocal of the temperature of the column in isothermal HRGC has been found considerably applicable and reliable in practice as expressed by Eq. (1),

3.1. Materials

ln k = A +

B T

(1)

where k is the retention factor, k = (t − t0 )/t0 in which t and t0 are the retention time and the dead time at the column temperature T (K), respectively, and A, B are the intercept and the slope of the plot of ln k versus the reciprocal of temperature, respectively. The transport distance under isothermal conditions can be calculated by the following equation:
Liso i =

ti

L dt

ti−1 t0 [1 + k(T )]

=

L(ti − ti−1 ) t0 [1 + k(Ti )]

(2)

where L is the column length; ti − ti−1 , the running time for ith congener under isothermal conditions; t0 , the dead time of the whole system; k(Ti ), the retention factor at temperature Ti . On the other hand, the transport distance using linear temperature program is as follows: Llinear = i

L r




Ti

Ti−1

dT t0 [1 + k(T )]

(3)

where r is the rate of linear temperature program; Ti−1 , the initial temperature; and Ti , the end temperature. The corresponding transport time under linear temperature program is the retention linear = 1. time when L = Liso i + Li For every congener of BDEs, the relative index of the ith congener can be calculated according to the retention data of prior calculated prediction values as Pi =

ti,pre − tn,pre tn+1,pre − tn,pre

(4)

where Pi is the relative retention index of ith congener, which is a constant under a certain chromatographic condition; ti,pre , the retention time of the ith congener; tn,pre and tn+1,pre are the retention times of the nth and (n + 1)th selected internal standards of BDEs, respectively, which are near to the ith congener with tn,pre < ti,pre < tn+1,pre . The values for tn,pre , ti,pre and tn+1,pre are obtained from Eqs. (2) and (3) under a certain temperature program condition. The subscript pre denotes the predicted data. The calibrated retention time of ith congener in a sample can be obtained from Eq. (5), ti,cal = tn,exp + Pi (tn+1,exp − tn,exp )

(5)

where the subscripts cal and exp denote the calibrated and experimental data, respectively.

249

A total of 40 BDEs were used in this study; among them, 13 BDE congeners containing BDE1 (2-bromodiphenyl ether), BDE10 (2,6-dibromodiphenyl ether), BDE13 (3,4 -dibromodiphenyl ether), BDE30 (2,4,6-tribromodiphenyl ether), BDE32 (2,4 ,6-tribromodiphenyl ether), BDE35 (3,3 ,4-tribromodiphenyl ether), BDE37 (3,4,4 -tribromodiphenyl ether), BDE75 (2,4,4 ,6-tetrabromodiphenyl ether), BDE116 (2,3,4,5,6-pentabromodiphenyl ether), BDE155 (2,2 ,4,4 ,6,6 -hexabromodiphenyl ether), BDE166 (2,3,4,4 ,5,6-hexabromodiphenyl ether), BDE181 (2,2 ,3,4,4 ,5,6-heptabromodiphenyl ether) and BDE190 (2,3,3 ,4,4 ,5,6-heptabromodiphenyl ether) in nonane solution were obtained from Cambridge Isotope Laboratories, USA. BDE-MXE containing BDE3 (4bromodiphenyl ether), BDE7 (2,4-dibromodiphenyl ether), BDE15 (4,4 -dibromodiphenyl ether), BDE17 (2,2 ,4-tribromodiphenyl ether), BDE28 (2,4,4 -tribromodiphenyl ether), BDE47 (2,2 ,4,4 -tetrabromodi phenyl ether), BDE49 (2,2 ,4,5 tetrabromodiphenyl ether), BDE71 (2,3 ,4 ,6-tetrabromodiphenyl ether), BDE66 (2,3,4,4 -tetrabromodi phenyl ether), BDE99 (2,2 ,4,4 ,5-pentabromodiphenyl ether), BDE77 (3,3 ,4,4 -tetrabromodiphenyl ether), BDE85 (2,2 ,3,4,4 -pentabromodiphenyl ether), BDE100 (2,2 ,4,4 ,6-pentabromodiphenyl ether), BDE119 (2,3 ,4,4 ,6-penta bromodiphenyl ether), BDE126 (3,3 ,4,4 ,5-pentabromodiphenyl ether), BDE138 (2,2 ,3,4,4 ,5 hexabromodiphenyl ether), BDE153 (2,2 ,4,4 ,5,5 -hexa bromodiphenyl ether), BDE154 (2,2 ,4,4 ,5,6 -hexabromodiphenyl ether), BDE156 (2,3,3 ,4,4 ,5-hexabromodiphenyl ether), BDE183 (2,2 ,3,4,4 ,5 ,6-heptabromodiphenyl ether), BDE184 (2,2 ,3,4,4 ,6,6 -heptabromodiphenyl ether), BDE191(2,3,3 ,4,4 ,5 ,6-heptabromodiphenyl ether), BDE196 (2,2 ,3,3 ,4,4 ,5,6 octabromodiphenyl ether), BDE197 (2,2 ,3,3 ,4,4 ,6,6 -octabromo diphenyl ether), BDE206 (2,2 ,3,3 ,4,4 ,5,5 ,6-nonabromodiphenyl ether), BDE207 (2,2 ,3,3 ,4,4 ,5,6,6 -nona bromodiphenyl ether) and BDE209 (2,2 ,3,3 ,4,4 ,5,5 ,6,6 -decobromodiphenyl ether) in nonane solution was purchased from Wellington Laboratories, Ontario, Canada. The GC column was a narrow-bore model (0.25 mm I.D.) obtained from J&W Scientific. The stationary phase of capillary column with 30 m in length was (5% phenyl)methylpolysiloxane (0.25 um film thickness, DB-5). 3.2. Chromatographic analysis GC analysis was performed on an Agilent-6890N gas chromatograph in splitless mode. The injector was operated at 260 ◦ C. The electron-capture detection (ECD) system was kept at 300 ◦ C, while the makeup gas for ECD had a flow rate of 60 mL/min. N2 was used as carrier gas and makeup gas. The temperature program conditions are stated in (A)–(E): (A) 180 ◦ C (2.0 min), 1.2 ◦ C min−1 , 320 ◦ C (10.0 min); (B) 180 ◦ C (2.0 min), 1.4 ◦ C min−1 , 320 ◦ C (10.0 min);

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250

(C) 180 ◦ C (2.0 min), 1.6 ◦ C min−1 , 320 ◦ C (10.0 min); (D) 180 ◦ C (2.0 min), 1.8 ◦ C min−1 , 320 ◦ C (10.0 min); (E) 180 ◦ C (2.0 min), 2.0 ◦ C min−1 , 320 ◦ C (10.0 min). Chromatographic data were acquired with Agilent workstation system. The program for peak simulation and identificationComplex Sample Analysis Software System (CSASS), version 10.0 was compiled with Microsoft Visual C ++ 6.0 (Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China). Statistical analyses and correlations were performed using SPSS, version 10.0 for Windows. 3.3. Peak identification The peak assignment of BDE-MXE was achieved by comparison with the following data: (1) BDE-MXE HRGC/LRMS TIC on DB-5HT from Wellington Labs; (2) published retentiontime database of 126 BDE congeners and two Bromkal technical mixtures on seven capillary gas chromatographic columns [20]. 4. Results and discussion 4.1. Determination of A and B parameters A and B values of chemicals are two very important parameters to predict their retention times under different temperature programs. Here, the retention times of 40 BDE congeners under five temperature program conditions were determined so as to obtain their retention parameters (A, B values). The dead times were detected by the retention time of CH2 Cl2 . The A, B values were calculated through linear regression according to Eq. (1). Table 1 lists 40 pairs of A, B values determined, and all the

regression coefficients are higher than 0.9999. As a result, the retention times can be predicted from the A, B values with Eqs. (2) and (3) under any temperature program. 4.2. Calibration of the retention times When temperature program condition is too complex or the retention time of the chemical is too long, using A and B values to predict retention time may produce large error. This is probably due to actual pressure gradient present inside the column. However, this kind of error is systematic error and can be corrected by choosing similar compounds as internal standards. In order to accurately predict retention times of 40 BDEs in this work, eight BDE congeners (shown in Table 1) were selected as internal standards to calibrate the retention times on DB-5. As these internal standards can be separated very well with specific pattern, the corresponding peaks could be recognized very easily. The calibration method was achieved based on the calculated relative retention index Pi , and the experimental retention times of the internal standard congeners. Thus, the relevant retention times of the internal standard congeners acquired from a certain experiment were used in Eq. (5) to obtain the calibrated retention time of each BDE congener. One temperature program (F: 90 ◦ C (2.0 min), 30 ◦ C min−1 , 200 ◦ C, 1.5 ◦ C min−1 , 325 ◦ C (7.0 min)) was chosen to evaluate this calibration method of peak assignments. Table 2 shows calibrated results by A, B values under this temperature program. To clarify the suggested calibration method, an example for calculating the calibrated retention time of BDE15 under this temperature program is given as follows: the predicted retention times of BDE15 and its corresponding internal standards BDE1 and BDE35 are 10.740, 7.127 and 16.150, respectively. Then, the Pi value and the calibrated retention time of BDE15 were worked out according to Eqs. (4)

Table 1 A, B values of BDE congeners determined on DB-5 PBDE number

Br substitution

DB-5 A

1a 3 10 7 13 15 30 32 17 28 35a 37 75 49 71 47 66a 77 100 119 a

242,6 2,4 3,-4 4,-4 2,4,6 2,6-4 2,4-2 2,4-4 3,4-3 3,4-4 2,4,6-4 2,4-2,5 2,6-3,4 2,4-2,4 2,4-3,4 3,4-3,4 2,4,6-2,4 2,4,6-3,4

BDE internal standards used for calibration.

−13.38 −13.63 −14.35 −14.02 −14.55 −14.55 −15.00 −15.12 −14.73 −14.87 −15.27 −15.26 −15.64 −15.68 −15.71 −15.50 −15.47 −15.80 −16.05 −16.1

PBDE number

Br substitution

B 6475.90 6638.33 7380.64 7137.30 7547.31 7588.47 8136.62 8247.16 7855.84 8039.51 8349.10 8389.46 8883.58 8836.28 8967.91 8764.79 8703.58 9096.63 9597.14 9484.83

99a 116 85 126 155a 154 153 138 166a 156 184 183 191 197 181a 196 190 207 206 209a

2,4,5-2,4 2,3,4,5,62,3,4-2,4 3,4,5-3,4 2,4,6-2,4,6 2,4,5-2,4,6 2,4,5-2,4,5 2,3,4-2,4,5 2,3,4,5,6-4 2,3,4,5-3,4 2,3,4,6-2,4,6 2,3,4,6-2,4,5 2,3,4,6-3,4,5 2,3,4,6-2,3,4,6 2,3,4,5,6-2,4 2,3,4,5-2,3,4,6 2,3,4,5,6-3,4 2,3,4,5,6-2,3,4,5 2,3,4,5,6-2,3,4,6 2,3,4,5,6-2,3,4,5,6

DB-5 A

B

−15.93 −15.69 −15.99 −16.16 −16.44 −16.52 −16.35 −16.16 −16.48 −16.20 −16.54 −16.62 −16.33 −16.57 −16.63 −16.95 −16.66 −17.02 −17.28 −17.63

9310.06 9299.77 9363.85 9675.39 10134.29 10028.88 9830.15 9675.39 10211.85 10016.57 10530.78 10404.63 10202.78 10567.67 10556.51 11006.46 10592.75 11376.51 11589.25 12117.80

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Table 2 Comparison of predicted vs. measured retention values of BDEs, and those reported by Korytar under the same temperature programa PBDE number

tRexp (exp)

tRpre (min)

errpre (min)

tRcal (min)

errcal (min)

RRT (ref)

RRT (exp)

RRT (pre)

1 3 10 7 13 15 30 32 17 28 35 37 75 49 71 47 66 77 100 119 99 116 85 126 155 154 153 138 166 156 184 183 191 197 181 196 190 207 206 209

7.230 7.445 9.227 9.899 10.520 10.861 12.870 14.391 14.926 15.746 16.258 16.984 21.134 21.776 22.141 23.200 24.400 26.441 30.375 31.120 32.622 33.455 36.829 37.568 37.568 39.337 42.771 47.421 47.627 49.205 51.381 53.134 55.861 64.112 57.384 66.442 58.104 77.468 79.675 90.438

7.127 7.343 9.113 9.783 10.403 10.740 12.750 14.280 14.820 15.643 16.150 16.883 21.063 21.710 22.073 23.147 24.360 26.413 30.360 31.110 32.627 33.460 36.857 37.590 37.590 39.377 42.797 47.440 47.677 49.237 51.423 53.173 55.903 64.640 57.843 66.983 58.603 78.090 80.300 91.130

0.103 0.102 0.114 0.116 0.117 0.121 0.120 0.111 0.106 0.103 0.108 0.101 0.071 0.066 0.068 0.053 0.040 0.028 0.015 0.010 0.005 0.005 0.028 0.022 0.022 0.040 0.026 0.019 0.050 0.032 0.042 0.039 0.042 0.528 0.495 0.542 0.499 0.623 0.625 0.692

7.230 7.447 9.219 9.888 10.507 10.847 12.858 14.388 14.926 15.750 16.258 16.985 21.129 21.771 22.132 23.195 24.400 26.441 30.368 31.114 32.622 33.455 36.838 37.568 37.568 39.351 42.762 47.393 47.627 49.190 51.377 53.127 55.859 64.106 57.384 66.462 58.109 77.464 79.684 90.438

0.000 0.002 0.008 0.011 0.013 0.014 0.012 0.003 0.000 0.004 0.000 0.001 0.005 0.005 0.009 0.005 0.000 0.000 0.007 0.006 0.000 0.000 0.009 0.000 0.000 0.014 0.009 0.028 0.000 0.015 0.004 0.007 0.002 0.006 0.000 0.020 0.005 0.003 0.009 0.000

0.095 0.099 0.123 0.133 0.142 0.147 0.174 0.195 0.202 0.214 0.221 0.232 0.290 0.294 0.299 0.313 0.328 0.355 0.405 0.414 0.433 0.444 0.486 0.495 0.496 0.517 0.560 0.617 0.621 0.640 0.666 0.687 0.721 – 0.754 – 0.763 1.001 1.027 1.171

0.095 0.098 0.121 0.130 0.138 0.142 0.169 0.189 0.196 0.206 0.213 0.222 0.277 0.285 0.290 0.304 0.320 0.346 0.398 0.408 0.427 0.438 0.482 0.492 0.492 0.515 0.560 0.621 0.624 0.645 0.673 0.696 0.732 0.860 0.770 0.892 0.780 1.040 1.070 1.214

0.095 0.098 0.121 0.130 0.138 0.142 0.168 0.188 0.196 0.206 0.213 0.223 0.277 0.285 0.290 0.304 0.320 0.346 0.398 0.408 0.427 0.438 0.483 0.492 0.492 0.516 0.560 0.621 0.624 0.644 0.673 0.696 0.732 0.861 0.770 0.892 0.780 1.040 1.070 1.214

a

Temperature program: 90 ◦ C for 2 min, then up to 200 ◦ C at 30 ◦ C/min, then up to 325 ◦ C at 1.5 ◦ C/min for 7.5 min.

and (5), that is, Pi,15 = 0.4004 and tR(cal)15 = 10.847. It is obvious that the calibrated retention time tR(cal) = 10.847 is closer to the experimental retention time tR(exp)15 = 10.861 than to the predicted retention time tR(pre)15 = 10.740 calculated with Eqs. (2) and (3). The results for the calibrated retention times of 40 BDE congeners are also shown in Table 2. All errors of calculation are less than 7 s under this condition of temperature program. The maximum error of prediction was 0.028 min. However, the peak width at the bottom of the peak in the chromatogram was nearly 20 s. Therefore, the error of calibration is tolerable in the peak identification.

grams can be accurately simulated. Fig. 1 shows the simulated chromatograms under two temperature programs (G: 80 ◦ C, 25 ◦ C min−1 , 200 ◦ C, 1.8 ◦ C min−1 , 320 ◦ C (5.0 min) and H: 80 ◦ C, 20 ◦ C min−1 , 200 ◦ C, 1.6 ◦ C min−1 , 320 ◦ C (5.0 min)). From the simulated chromatograms under two conditions, we can clearly see elution order and co-elutions of BDEs. As shown in Fig. 1, one co-elution pairs (BDE126 and 155) cannot be separated under these conditions on DB-5.

4.3. Simulation of the chromatograms

Using relative retention times (RRTs) to identify chemicals under a certain temperature program condition is a common method. In order to test the reliability and accuracy of this method, we compared the predicted RRTs based on A and B values determined with the experimental RRTs under condition

Based on parameters A, B values and the retention time of internal standards, using the software CSASS, the chromatograms of BDE congeners under different temperature pro-

4.4. Comparison of the predicted RRTs and the experimental RRTs

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H. Zhao et al. / J. Chromatogr. A 1107 (2006) 248–256

Fig. 1. Peak recognition for BDE congeners: (a) simulated chromatogram of BDEs under condition G; (b) experimental chromatogram of BDEs under condition G; (c) simulated chromatogram of BDEs under condition H; (d) experimental chromatogram of BDEs under condition H.

F. RRTs for all peaks were obtained by dividing the retention time for the analyte of interest by the sum of the retention times of BDE47 and BDE183. Table 2 lists the experimental RRTs, and the predicted RRTs. From Table 2, we know that the predicted RRTs are fundmentally the same as the experimental RRTs and the biggest error is 0.001. Fig. 2 shows the correlation of the predicted RRTs and the experimental RRTs with the correlation coefficient (R) = 0.9999 and standard error (SE) = 6.13 × 10−5 . In addition, in Table 2, we also list the experimental RRTs under the same condition reported by Korytar et al. [20] in a recent article. The experimental RRTs in this study are compared with the cited experimental RRTs. The biggest error is 0.043, which

may be induced by the difference in the systems used. Fig. 3 shows the correlation of the experimental RRTs in this study and the cited experimental RRTs with the correlation coefficient (R2 ) = 0.9993 and standard error (SE) = 0.0077. 4.5. Prediction of the remaining retention parameter A and B values Similar to polychlorinated biphenyls, there are 209 possible BDE congeners. However, at present, standards are available for only a small number of the 209 congeners. Hence, it is impossible to directly determine parameter A, B values of all the

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253

Stepwise multiple linear regression analysis for A and B performed on thirty-eight molecular connectivity indexes resulted in Eqs. (6) and (7): APBDE = −1.469 − 6.5693 χc + 0.9735 χpc + 0.6367 χpc +2.4848 χpc + 1.2099 χpc + 4.41810 χpc −247.3019 χvp − 11.2983 χvc + 14.2906 χvpc −46.6168 χvpc

(6)

R2 = 0.995, SE = 0.074, F = 555.327, N = 40 BPBRE = −7961.004 − 726.583 χc − 798.325 χpc −181.9817 χpc − 3099.9928 χpc − 498.4859 χpc Fig. 2. Plot of the predicted RRTs (this study, RRTpre2005 ) vs. the experimental RRTs (this study, RRTexp2005 ) of BDEs.

−4046.73210 χpc + 277993.09 χvp + 34661.623 χvc −8901.1866 χvpc + 71997.568 χvpc

(7)

R2 = 0.996, SE = 92.79, F = 642.272, N = 40 The correlation coefficients of two models are higher than 0.995, which indicate that >99.5% of the total variation in the predicted A and B values of BDE congeners are explained by the fitted models. The standard errors for Eqs. (6) and (7) are 0.074 and 92.79, respectively. The corresponding coefficients of varia-

Fig. 3. Plot of the exprimental RRTs (this study, RRTexp2005 ) vs. the experimental RRTs determined by Korytar et al. (RRTexp2004 ) for BDE congeners.

209 BDE congeners. Thus, there is a need for predictive tools to help estimate the remaining BDE congeners for which A, B values are currently unavailable, but for which environmental data are needed. Based on the experimental A, B values of 40 BDE congeners, the correlation between A and B values and molecular connectivity indexes for the first time have been studied. As we know, molecular connectivity indexes have been found to be very successful in modeling retention data [21,22]. Thirty-eight molecular connectivity indexes of BDE congeners were calculated by a program written in Microsoft Visual C++, as shown in Table 3. Table 3 Type of molecular connectivity index in regression analysis 0χ

5χ

1χ 2χ 3χ

4χ

6χ

p p p

7χ 8χ 9χ

p

10 χ

p

c

p p p

3χ 4χ 5χ 6χ

p

pc

7χ 8χ 9χ

pc pc pc

pc

10 χ

pc

v

0χ

pc

1χ 2χ 3χ

4χ 5χ

v vp vp vp vp

6χ 7χ 8χ 9χ

vp vp vp

vp 10 χ vp

3χ 4χ 5χ 6χ 7χ

vc vpc vpc vpc vpc

8χ 9χ

vpc

vpc 10 χ vpc

Fig. 4. Comparison of retention parameters: (a) plot of Aexp vs. Apre ; (b) plot of Bexp vs. Bpre .

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Table 4 The A, B values of the remaining 169 BDEs predicted by their molecular connectivity indexes PBDE

A (pre)

B (pre)

PBDE

A (pre)

B (pre)

PBDE

A (pre)

B (pre)

2 4 5 6 8 9 11 12 14 16 18 19 20 21 22 23 24 25 26 27 29 31 33 34 36 38 39 40 41 42 43 44 45 46 48 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 67 68 69 70 72 73

−13.56 −14.13 −14.09 −14.23 −14.23 −14.15 −14.43 −14.37 −14.38 −14.72 −14.84 −14.55 −14.85 −14.84 −14.92 −14.83 −14.52 −15.03 −14.95 −14.72 −14.86 −14.98 −15.00 −15.02 −15.14 −15.01 −15.16 −15.29 −15.40 −15.42 −15.38 −15.35 −15.07 −15.12 −15.50 −15.27 −15.32 −15.45 −15.21 −14.88 −15.50 −15.52 −15.49 −15.52 −15.21 −15.53 −15.45 −15.23 −15.54 −15.33 −15.13 −15.59 −15.66 −15.38 −15.61 −15.57 −15.40

6541.89 7166.77 7325.50 7284.39 7284.39 7232.80 7408.22 7443.27 7381.65 7945.90 7935.23 7681.42 8101.79 8177.43 8218.64 8081.81 7818.12 8114.24 8033.51 7794.52 7986.00 8114.66 8177.86 8072.85 8149.79 8189.51 8201.47 8630.80 8741.15 8770.96 8693.50 8669.35 8418.39 8427.09 8662.69 8481.47 8465.70 8607.85 8367.12 8138.20 8866.90 8898.10 8760.86 8771.37 8525.31 8965.49 8890.82 8649.69 8850.96 8704.29 8542.19 8781.06 8768.59 8522.65 8825.22 8670.53 8502.30

74 76 78 79 80 81 82 83 84 86 87 88 89 90 91 92 93 94 95 96 97 98 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 117 118 120 121 122 123 124 125 127 128 129 130 131 132 133 134 135 136 137 139

−15.60 −15.59 −15.66 −15.73 −15.68 −15.67 −15.83 −15.87 −15.57 −15.90 −15.93 −15.69 −15.69 −16.00 −15.76 −15.92 −15.57 −15.67 −15.62 −15.43 −15.90 −15.72 −16.05 −15.81 −15.83 −15.54 −16.02 −15.98 −16.01 −15.78 −16.05 −15.83 −16.02 −15.70 −15.79 −16.00 −15.85 −15.78 −16.12 −16.08 −15.93 −16.04 −16.15 −16.08 −15.90 −16.11 −16.31 −16.24 −16.29 −16.05 −16.06 −16.32 −15.93 −16.01 −15.74 −16.40 −16.23

8855.68 8846.26 8867.64 8827.48 8699.35 8951.07 9302.42 9249.70 9042.05 9356.40 9353.70 9193.07 9141.09 9393.05 9195.42 9245.58 9078.20 9045.09 9007.52 8912.06 9276.04 9076.20 9270.49 9088.01 9085.23 8866.96 9554.90 9450.75 9411.21 9231.17 9468.56 9292.46 9329.99 9137.61 9154.44 9533.16 9354.42 9273.86 9475.61 9303.51 9117.95 9474.74 9535.68 9389.47 9255.97 9351.21 9971.85 9835.32 9846.44 9699.92 9654.13 9760.64 9599.14 9504.94 9316.79 10014.75 9827.21

140 141 142 143 144 145 146 147 148 149 150 151 152 157 158 159 160 161 162 163 164 165 167 168 169 170 171 172 173 174 175 176 177 178 179 180 182 185 186 187 188 189 192 193 194 195 198 199 200 201 202 203 204 205 208

−16.20 −16.34 −16.02 −16.11 −16.11 −15.88 −16.44 −16.12 −16.20 −16.17 −15.96 −16.08 −15.72 −16.45 −16.26 −16.37 −16.17 −16.22 −16.46 −16.19 −16.25 −16.13 −16.51 −16.39 −16.61 −16.62 −16.42 −16.61 −16.28 −16.40 −16.40 −16.14 −16.33 −16.28 −16.01 −16.73 −16.56 −16.44 −16.10 −16.44 −16.20 −16.71 −16.45 −16.52 −16.84 −16.57 −16.53 −16.55 −16.26 −16.32 −16.18 −16.68 −16.46 −16.73 −16.36

9803.27 9906.89 9762.02 9685.90 9660.20 9501.88 9939.30 9729.86 9681.21 9722.37 9503.97 9671.55 9377.33 10098.62 9885.14 9893.35 9876.54 9723.80 9999.06 9803.71 9835.56 9655.75 9970.94 9818.56 10083.52 10464.08 10254.69 10271.04 10190.35 10123.66 10099.60 9898.98 10166.71 9997.88 9788.56 10435.31 10263.71 10268.82 9988.13 10159.13 9957.09 10481.81 10171.77 10264.64 10778.50 10662.65 10489.91 10451.97 10313.62 10268.76 10129.93 10653.79 10475.98 10716.29 10575.44

tion are 0.473% and 1.019%, which are the relative percentage of errors at the mean of the A and B values, respectively. The F values for two models are 555 and 642, respectively, which greatly exceeds the critical F values 2.66 at α = 0.05. These results show

that the two models are highly significant. As can be seen in Fig. 4, the experimental A and B values of BDEs have good correlation with the predicted A and B values based on molecular connectivity indexes. Thus, the agreement between the predicted

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255

5. Conclusion A method has been developed to predict the gas chromatographic retention times of polybrominated diphenyl congeners under different temperature programs. The retention equations ln k = A + (B/T) for 40 BDEs in gas chromatography have been used to evaluate the properties of the regression coefficients A and B, which have been widely accepted as highly reliable chromatographic retention parameters. Moreover, using the A, B values of BDEs and the retention time of internal standards, the retention times can be accurately predicted at any temperature programming. The method offers the potential to assist in the identification of BDEs in environmental samples following an efficient clean-up preparation. In addition, the quantitative relationship between the retention parameters A, B values of BDEs and their molecular connectivity indexes has been reported. Two optimized equations are obtained from stepwise multiple linear regression analyses performed on the thirty-eight molecular connectivity indexes, with correlation coefficients greater than 0.997. Furthermore, the A, B values of the remaining 169 BDEs were predicted. Acknowledgements This study was partly supported by National Basic Research Program of China (No. 20235020). The authors are also grateful to Professor Lefeng Zhang for his help with the manuscript. References Fig. 5. Validation of the predicted retention values: (a) Plot of the predicted RRTs basing on the predicted A and B values (RRTpre2005 ) vs. RRTs obtained experimentally by Korytar et al. (RRTexp2004 ) for 86 BDE congeners; (b) Plot of the predicted RRTs basing on the predicted A and B values (RRTpre2005 ) vs. RRTs determined by Rayne and Ikonomou (RRTexp2003 ) for 46 BDE congeners.

and the experimental values should be satisfactory. By the Eqs. (6) and (7), A and B values of all the remaining BDEs were predicted by their molecular connectivity indexes, as shown in Table 4. According to these predicted A and B values, we can estimate retention times of the remaining BDE congeners under different temperature programs on DB-5. In order to test the accuracy of the retention times estimated based on the predicted A and B values, we compared the predicted RRTs under condition F with the RRTs obtained experimentally by Korytar et al. for 86 BDE congeners (Fig. 5a). From Fig. 5a, we can see that the predicted RRTs based on the predicted A, B values and the experimental RRTs have good linear fit with R2 = 0.995. In addition, the predicted RRTs under condition I (100 ◦ C (1.0 min), 2 ◦ C min−1 , 140 ◦ C, 4 ◦ C min−1 , 220 ◦ C, 8 ◦ C min−1 , 330 ◦ C (6.0 min)) in this study were also plotted against the RRTs obtained experimentally by Rayne and Ikonmomou [23] for 46 BDE congeners (Fig. 5b). The correlation also has a good linearity, with R2 = 0.993.

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