Chemosphere 93 (2013) 1742–1746

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Chemosphere

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A possible simplification of the Goss-modified Abraham solvationequation

0045-6535/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.chemosphere.2013.05.081

⇑ Address: Aquatic Ecology and Water Quality Management Group, WageningenUniversity, P.O. Box 47, 6700 AA Wageningen, The Netherlands. Tel.: +31(0)623879203; fax: +31 (0)88 3357775.

E-mail address: paul.vannoort@wur.nl

Paul C.M. van Noort ⇑Aquatic Ecology and Water Quality Management Group, Wageningen University, P.O. Box 47, 6700 AA Wageningen, The NetherlandsDeltares, P.O. Box 85467, 3508 AL Utrecht, The Netherlands

h i g h l i g h t s

� For air-organic solvent partitioning, using V is not needed in the Goss-modified solvation equation.� For water as one of the phases, leaving out V leads to only a small decrease in statistical quality.� The relatively large Gibbs energy for cavity formation possibly causes deviating behavior of water.

a r t i c l e i n f o

Article history:Received 10 April 2013Received in revised form 21 May 2013Accepted 25 May 2013Available online 21 June 2013

Keywords:PartitioningLFERSolvationHydrogen bondingPolymers

a b s t r a c t

Abraham solvation equations find widespread use in environmental chemistry and pharmaco-chemistry.Recently Goss proposed a modified Abraham solvation equation. For various partitioning processes, thepresent study investigates the consequences for the fit when the Abraham solvation parameter V is leftout of this modified solvation equation. For air-organic solvent partition, the Abraham solvation param-eter V can be omitted from the Goss-modified Abraham solvation equation without any loss of statisticalquality. For air–water partitioning, organic biphasic system partitioning, as well as water-organic solventpartitioning, omitting the V parameter from the Goss-modified Abraham solvation equation leads to onlya small deterioration of statistic quality.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Poly-parameter linear free energy relationships (pp-LFERs, Eqs.(1)–(3)) can be used to accurately predict coefficients for partition-ing (P) over environmental and biological phases. In these pp-LFERs, the logarithmic partition coefficient is calculated as thesum of free energy contributions to partitioning resulting fromcavity formation and various intermolecular interactions betweenthe solute and surrounding phase molecules.

Log P ¼ c þ eEþ sSþ aAþ bBþ vV ð1Þ

Log P ¼ c þ eEþ sSþ aAþ bBþ lL ð2Þ

Log P ¼ c þ lLþ sSþ aAþ bBþ vV ð3Þ

In Eqs. (1)–(3), the capital letters denote the solute descriptors.The values of the coefficients to the solute descriptors (given aslower case letters) depend on the phase system. V is the McGowancharacteristic volume [(dm3 mol�1)/100], calculated from atomincrements. L is the logarithm of the experimentally determinedgas to n-hexadecane partition coefficient at 298 K. Both solutedescriptors are some measure of the solute’s potential for vander Waals interactions and solvent cavity formation. E is the calcu-lated solute excess molar refractivity relative to an alkane with thesame V; S is the solute dipolarity/polarizability; A and B are the sol-ute overall hydrogen bond acidity and basicity. Values for S, A, andB are usually determined from experimental phase distributions orchromatographic retention data.

Eqs. (1)–(3) only slightly differ from each other. They differ inthe use of the solute descriptors E, V, and L. Some prefer to useEq. (1) for condensed systems, and to use Eq. (2) for gas–solventpartitioning. Goss (2005) showed that Eqs. (1) and (2) can be verywell replaced by Eq. (3) and may even lead to more accurate pre-dictions for some partitioning systems. His derivation of Eq. (3) isbased on the following notion. Eqs. (1) and (2) use the solventdescriptors E, V, and L to account for solvent cavity formation

P.C.M. van Noort / Chemosphere 93 (2013) 1742–1746 1743

and van der Waals interactions. The combination of the V and Ldescriptors also accounts for solvent cavity formation and vander Waals interactions. Therefore, Goss saw no need for the usethe solvent descriptor E in pp-LFERs and, therefore, suggested theuse of Eq. (3). He acknowledged that V and L are inter-correlatedto some extent, because L provides information on the cavity for-mation as well. Such an inter-correlation may possibly lead to aredundancy of the use of V in Eq. (3). In fact, some data in Goss(2005) seem to suggest that. Therefore, for partitioning coefficientsfor a large number of partitioning systems, the present study com-pares the fit to Eq. (3) with the fit to Eq. (4) in which the solutedescriptor V is not used.

Log P ¼ c þ lLþ sSþ aAþ bB ð4Þ

2. Results and discussion

2.1. Air-solvent partitioning

Coefficients for partitioning from air to N,N-dimethylformam-ide, methanol, olive oil, water, and for log k’ data on capillary col-umn DB-1 were taken from Goss (2005). Those for n-butanol, n-pentanol, n-hexanol, n-heptanol, n-nonanol, and n-decanol werefrom Abraham et al. (2008). Coefficients for partitioning to o-, m-,

Table 1Statistics and coefficients (standard error between parentheses) for pp-LFERs for air-solvenlists the data for Eq. (4).

Solvent r2 SE N F c

n-Butanol 0.995 0.28 78 3126 0.01(0.10.995 0.28 78 3855 �0.10(0

n-Pentanol 0.998 0.2 106 12604 �0.11(00.998 0.2 106 15912 �0.11(0

n-Hexanol 0.991 0.23 105 2101 �0.31(00.991 0.22 105 2652 �0.30(0

n-Heptanol 0.998 0.17 78 6386 �0.17(00.998 0.17 78 8090 �0.16(0

n-Nonanol 0.998 0.17 82 6098 �0.20(00.998 0.17 82 7708 �0.24(0

n-Decanol 0.994 0.18 54 1636 �0.28(00.994 0.18 54 2085 �0.31(0

N,N-dimethylformamide 0.971 0.16 49 371 �0.21(00.969 0.16 49 472 �0.09(0

Log k0 data for capillary column DB-1 0.991 0.09 53 1063 �1.93(00.990 0.10 53 1212 �1.83(0

Methanol 0.988 0.16 72 1129 �0.01(00.988 0.16 72 1363 0.11(0.0

Olive oil 0.970 0.16 84 504 �0.38(00.969 0.16 84 618 �0.25(0

o-Xylene 0.998 0.14 59 5913 0.08(0.10.998 0.14 59 7530 0.09(0.0

m-Xylene 0.999 0.16 79 10298 �0.26 (0.998 0.19 79 8763 0.06(0.0

p-Xylene 0.998 0.13 91 6975 0.01((0.0.997 0.14 91 7930 0.17(0.0

[HxomMIm]+[(Tf)2N]�a 0.994 0.06 34 954 �0.57(00.992 0.07 34 851 �0.44(0

[(Hxom)2Im]+[(Tf)2N]�b 0.991 0.07 34 650 �0.40(00.989 0.07 34 655 �0.28(0

Water 0.997 0.12 390 25028 �0.59(00.986 0.25 390 6638 �1.46(0

a 1-Hexyloxymethyl-3-methylimidazolium bis(trifluoromethylsulphonyl)imide.b 1,3-Dihexyloxymethylimidazoliumbis(trifluoromethylsulphonyl)imide.

and p-xylene were from Stephens et al. (2011). Those for two ionicliquids were from Sprunger et al. (2010). These data were fitted toEq. (3) as well as Eq. (4). The values of the fitted coefficients arelisted in Table 1 along with some statistical data. For 6 of 15 theorganic solvents, values for v form fitting to Eq. (3) in Table 1 arenot different from zero. For the other solvents, except m-xylene,values for v are with 2 to 3 standard errors not different from zero.Values for r2 and standard errors did not change on using Eq. (4)instead of Eq. (3). Values for F from fitting to Eq. (4) were slightlyhigher because of the reduction in the number of fitting variables.Even for m-xylene, for which v is far from zero, the standard errorincreases only slightly, from 0.16 to 0.19, on using Eq. (4). For gas-humic acid partitioning, Niederer et al. (2006) obtained a fitted va-lue of 0.08 ± 0.27 for v which is not different from zero. Further-more, Sprunger et al. (2008) determined the fit of gas-to-olive oilpartition coefficients to Eq. (4). Their fitted values for v are closeto zero as well. Together, all results for the organic solventsstrongly suggests that invoking the solute parameter V in Eq. (3)is not necessary and that, from a statistical point of view, Eq. (4)can be better used instead.

For water as a solvent, the fitted value for v from Eq. (3) is farfrom zero. On using Eq. (4), r2 decreases and the standard error in-creases. Note, however, that the standard error increases onlyslightly from 0.12 to 0.25. To further explore the possible deviating

t partitioning. For each solvent, the first line lists the data for Eq. (3), the second line

s a b l v

1) 1.34(0.13) 3.35(0.08) 2.61(0.10) 0.64(0.07) �0.40(0.28).08) 1.47(0.09) 3.39(0.08) 2.62(0.10) 0.55(0.02) –

.08) 1.18(0.10) 3.62(0.06) 1.67(0.07) 0.73(0.05) �0.02(0.24)

.04) 1.19(0.07) 3.62(0.06) 1.67(0.06) 0.72(0.02) –

.14) 0.88(0.13) 3.61(0.08) 1.79(0.11) 0.81(0.07) 0.03(0.32)

.09) 0.87(0.08) 3.61(0.07) 1.80(0.11) 0.82(0.02) –

.11) 0.84(0.11) 3.55(0.07) 1.43(0.07) 0.82(0.06) 0.04(0.28)

.06) 0.83(0.07) 3.54(0.06) 1.43(0.07) 0.83(0.02) –

.12) 0.68(0.11) 3.63(0.08) 1.29(0.06) 0.88(0.06) �0.11(0.28)

.05) 0.71(0.08) 3.64(0.07) 1.29(0.06) 0.86(0.02) –

.18) 0.74(0.25) 3.54(0.11) 1.12(0.14) 0.90(0.12) �0.11(0.52)

.10) 0.77(0.13) 3.55(0.09) 1.11(0.13) 0.88(0.03) –

.12) 2.33(0.13) 4.81(0.20) 0 0.64 (0.09) 0.53 (0.30)

.10) 2.15(0.08) 4.84(0.20) 0 0.78(0.03) –

.07) 0.28(0.07) 0.59(0.07) �0.10(0.07) 0.67(0.04) 0.35(0.15)

.05) 0.15(0.04) 0.57(0.07) �0.09(0.07) 0.75(0.01) –

.08) 1.19(0.11) 3.68(0.11) 1.49(0.10) 0.64(0.05) 0.36(0.20)5) 1.04(0.08) 3.68(0.11) 1.53(0.10) 0.72(0.02) –

.10) 1.01(0.12) 1.77(0.12) 0.01(0.10) 0.80(0.05) 0.35(0.22)

.07) 0.85(0.08) 1.70(0.12) 0.08(0.09) 0.88(0.02) –

2) 0.72(0.14) 0.69(0.08) 0.32(0.15) 0.96(0.07) 0.02(0.34)3) 0.72(0.09) 0.69(0.08) 0.33(0.13) 0.96(0.02) –

0.06) 1.22(0.12) 0.72(0.07) 0.05(0.08) 0.72(0.05) 1.09(0.18)3) 0.65(0.08) 0.52(0.08) 0.33(0.07) 1.00(0.01) –

06) 0.73(0.11) 0.73(0.07) 0.17(0.09) 0.88(0.04) 0.48(0.16)2) 0.44(0.05) 0.71(0.07) 0.24(0.09) 0.99(0.01) –

.06) 2.28(0.09) 2.43(0.10) 0.50(0.08) 0.65(0.04) 0.48(0.14)

.06) 2.03(0.07) 2.39(0.12) 0.60(0.09) 0.77(0.02) –

.07) 1.76(0.11) 2.37(0.11) 0.52(0.10) 0.71(0.04) 0.43(0.15)

.07) 1.53(0.07) 2.33(0.13) 0.61(0.10) 0.81(0.02) –

.03) 2.07(0.04) 3.67(0.03) 4.87(0.03) 0.48(0.02) �2.55(0.07)

.04) 3.25(0.05) 3.91(0.07) 4.45(0.06) �0.11(0.01) –

Table 2Statistics and coefficients (standard error between parentheses) for pp-LFERs for water-solvent partitioning. For each solvent, the first line gives the data for Eq. (3), the secondline gives the data for Eq. (4).

Solvent r2 SE N F c s a b l v

n-Butyl ether 0.933 0.31 83 318 0.79(0.23) �2.06(0.22) �0.97(0.13) �5.27(0.21) 0.50(0.11) 3.12(0.50)0.930 0.38 83 259 1.85(0.20) �2.96(0.21) �1.35(0.15) �4.93(0.25) 1.12(0.05) –

Trichloromethane 0.981 0.21 134 1346 0.58(0.09) �0.70(0.12) �3.39(0.08) �3.38(0.11) 0.21(0.06) 3.44(0.24)0.952 0.33 134 643 1.51(0.10) �2.07(0.12) �3.79(0.12) �2.59(0.14) 0.99(0.03) –

n-Octanol 0.988 0.15 314 4929 0.34(0.04) �1.41(0.05) �0.18(0.04) �3.45(0.05) 0.43(0.02) 2.41(0.10)0.962 0.25 314 1978 1.17(0.05) �2.44(0.06) �0.42(0.08) �3.02(0.07) 0.97(0.01) –

SDSa 0.937 0.28 135 381 1.37(0.13) �0.89(0.16) �0.23(0.11) �2.17(0.15) 0.24(0.07) 2.66(0.32)0.902 0.35 135 298 2.27(0.08) �1.96(0.13) �0.58(0.13) �1.57(0.16) 0.82(0.03) –

Diethyl ether 0.966 0.26 113 605 0.45 (0.14) �0.90 (0.16) �0.20(0.10) �4.95(0.15) 0.18 (0.09) 3.51 (0.36)0.935 0.35 113 391 1.32(0.14) �2.19(0.12) �0.75 (0.12) �4.28 (0.19) 1.00 (0.04) –

Hexadec-1-ene 0.999 0.11 105 20625 0.48(0.04) �1.85(0.06) �3.39(0.05) �4.88(0.08) 0.43(0.03) 2.81(0.12)0.994 0.28 105 3895 1.31(0.05) �2.84(0.11) �4.00(0.11) �4.52(0.20) 1.11(0.02) –

Deca-1,9-diene 0.992 0.23 58 1219 0.50(0.11) �2.03(0.12) �3.19(0.10) �4.41(0.18) 0.35(0.07) 3.35(0.31)0.973 0.41 58 472 1.46(0.12) �2.86(0.17) �3.75(0.15) �3.87(0.32) 1.05(0.05) –

Storage lipid 0.988 0.2 247 4073 0.55(0.06) �1.62(0.07) �1.93(0.10) �4.15(0.07) 0.58(0.03) 1.99(0.11)0.973 0.31 247 2220 1.44(0.05) �2.56(0.07) �2.27(0.14) �3.88(0.10) 1.01(0.01) –

o-Xylene 0.995 0.13 59 2284 0.51(0.11) �0.95(0.13) �3.12(0.08) �4.94(0.14) 0.37(0.06) 3.13(0.31)0.987 0.21 59 1007 1.55(0.04) �1.96(0.14) �3.42(0.12) �4.25(0.20) 0.97(0.03) –

m-Xylene 0.998 0.13 79 6614 0.44(0.05) �0.76(0.09) �3.15(0.06) �5.03(0.06) 0.27(0.04) 3.50(0.15)0.981 0.37 79 980 1.49(0.06) �2.58(0.15) �3.78(0.16) �4.11(0.14) 1.14(0.02) –

p-Xylene 0.997 0.14 91 6780 0.52(0.06) �1.00(0.11) �3.11(0.07) �4.94(0.09) 0.34(0.04) 3.26(0.17)0.986 0.33 91 1518 1.60(0.06) �2.90(0.13) �3.23(0.16) �4.49(0.21) 1.14(0.02) –

[HxomMIm]+[(Tf)2N]�b 0.996 0.11 34 1525 �0.21(0.12) 0.97(0.17) �1.38(0.19) �4.58(0.16) �0.28(0.07) 4.58(0.25)0.954 0.38 34 150 1.04(0.34) �1.48(0.38) �1.80(0.65) �3.64(0.52) 0.86(0.10) –

[(Hxom)2Im]+[(Tf)2N]�c 0.996 0.11 34 1543 �0.04(0.13) 0.45(0.18) �1.44(0.20) �4.56(0.17) �0.23(0.07) 4.53(0.27)0.959 0.37 34 171 1.19(0.34) �1.98(0.38) �1.86(0.65) �3.64(0.52) 0.91(0.10) –

a Sodium dodecylsulfate.b 1-Hexyloxymethyl-3-methylimidazolium bis(trifluoromethylsulphonyl)imide.c 1,3-Dihexyloxymethylimidazoliumbis(trifluoromethylsulphonyl)imide.

1744 P.C.M. van Noort / Chemosphere 93 (2013) 1742–1746

behavior of water as a solvent, fitting of water-solvent partitioningcoefficients to Eqs. (3) and (4) will be described in the next section.

2.2. Water-solvent partitioning

Coefficients for partitioning from water to n-butyl ether, tri-chloromethane, and n-octanol were taken from Goss (2005). Thosefor sodium dodecyl sulfate (SDS) were from Sprunger et al. (2007).Partition coefficients for diethyl ether were from Abraham et al.(2003). Those for hexadec-1-ene and deca-1,9-diene were fromAbraham and Acree (2012). Storage lipid-water partitioning coeffi-cients were from Geisler et al. (2012). Partition coefficients for xy-lenes were from Stephens et al. (2011). Those for two ionic liquidswere from Sprunger et al. (2010). The values of the fitted coeffi-cients are listed in Table 2 along with some statistical data. Forall solvents, values for v in Table 2 are distinctly different fromzero. This confirms the finding for the air–water partitioning inSection 2.1, that contributions from the McGowan characteristicvolume V may not be neglected, in case of water as a solvent.

To further investigate the origin of the peculiar behavior ofwater as a solvent compared to organic solvents, the enthalpyand entropy values of air-solvent partitioning at 298 K for somesolvents (including water) taken from van Noort (2012) were fittedto Eqs. (3) and (4). The values of the fitted coefficients are listed inTable 3 along with some statistical data. For water as a solvent, thevalue of v in the Eq. (3) pp-LFER for DH is substantially non-zero.For three out of the five organic solvents, the value of v is statisti-cally not different from zero. Similarly, for DS, the value of v is non-zero in case of water as a solvent while the value of v is statisticallynot different from zero for the same three organic solvents as for

DH. These findings do not clearly indicate if the need for waterbased pp-LFERs to includeg a V term is of either enthalpic or entro-pic origin.

It may well be that both enthalpic and entropic contributionsdetermine the peculiar behavior of water as compared to organicsolvents. In this respect it is interesting to note that, for the sol-vation thermodynamics of xenon in water, n-alkanes, and n-alco-hols, Graziano (2003) calculated the Gibbs free energy of cavityformation as well as the van der Waals interaction energy. Forwater, the Gibbs free energy of (xenon) cavity formation in wateris substantially larger than for the other solvents while the vander Waals interaction energy is not different from the othersolvents.

2.3. Organic biphasic systems

The results for air-organic solvent partitioning suggests that Eq.(4) can also better be used for organic solvent-organic solvent par-titioning because the ratio of two air-organic solvent partitioncoefficients equals the organic solvent-organic solvent partitioncoefficient. This is explored using two examples: experimental n-heptane–ethanolamine and isopentyl ether–ethanolamine parti-tioning data from Ariyasena and Poole (2013). For n-heptane–eth-anolamine partitioning, the data fitted to:

log Kp ¼ 0:185ð0:153Þ � 1:518ð0:150ÞS� 4:596ð0:096ÞA� 1:077ð0:136ÞBþ 0:045ð0:055ÞLþ 1:484ð0:255ÞV

r2 ¼ 0:991; SE ¼ 0:17; F ¼ 1146;N ¼ 60 ð5Þ

Table 3Statistics and coefficients (standard error between parentheses) for pp-LFERs for the enthalpy (DH) and entropy (DS) of air-solvent partitioning. The first line gives the data for Eq.(3), the second line gives the data for Eq. (4).

Solvent r2 SE N c s a b l v

n-Octanol DH 0.975 2.9 80 �7.11(1.76) �54.86(3.33) 5.29(2.47) �8.09(1.90) �9.72(0.99) 2.56(4.55)0.975 2.9 80 �6.19(0.65) �55.62(3.02) 4.21(1.54) �7.52(1.60) �9.18(0.27) –

DS 0.881 9.2 80 21.90(5.65) �24.75(7.91) 116.31(10.66) 9.06(6.08) 15.65(3.16) �10.92(14.56)0.880 9.2 80 17.97(2.09) �20.12(4.92) 119.59(9.69) 6.63(5.13) 13.37(0.85) –

N,N-Dimethylformamide DH 0.992 1.4 53 �1.33(0.94) �20.43(1.62) �47.57(2.41) �2.09(1.39) �5.18(0.66) �8.73(2.69)0.991 1.6 53 �4.02(0.50) �15.76(0.82) �45.61(2.56) �4.08(1.34) �7.30(0.15) –

DS 0.963 3.8 53 6.05(2.50) 26.25(4.28) 71.21(6.38) 4.34(3.62) 3.22(1.76) 23.34(7.11)0.950 4.2 53 13.22(1.33) 13.75(2.16) 65.98(6.78) 9.67(3.55) 8.87(0.40) �

Water DH 0.952 3.0 218 �10.61(0.92) 4.96(1.32) �39.20(1.46) �43.99(1.11) �1.54(0.60) �17.28(2.42)0.940 3.4 218 �15.50(0.69) 11.83(1.01) �36.59(1.57) �47.27(1.12) �5.53(0.24) �

DS 0.980 10.8 218 7.47(3.29) 24.75(4.72) 206.80(5.20) 241.64(3.95) 13.44(2.14) 12.05(8.63)0.980 10.8 218 10.88(2.22) 19.96(3.24) 204.98(5.05) 243.93(3.60) 16.23(0.78) �

Methanol DH 0.990 1.9 53 �5.35(1.24) �4.56(1.92) �46.11(2.44) �10.99(1.74) �7.37(0.80) �2.64(3.48)0.990 1.9 53 �6.23(0.44) �3.42(1.18) �45.45(2.26) �11.58(1.56) �7.96(0.18) �

DS 0.949 5.9 53 11.01(3.82) �2.17(5.92) 79.34(7.53) 8.09(5.38) 9.06(2.48) 13.27(10.75)0.947 5.9 53 15.42(1.37) �7.90(3.69) 76.00(7.07) 11.02(4.85) 12.04(0.56) �

Ethanol DH 0.988 2.1 42 �5.50(1.50) �1.90(2.54) �46.70(3.66) �10.51(2.12) �7.58(0.97) �3.70(4.13)0.988 2.1 42 �6.78(0.49) �0.04(1.47) �45.68(3.47) �11.13(2.00) �8.43(0.18) –

DS 0.941 6.3 42 14.23(4.60) �8.60(7.79) 76.13(11.21) 11.77(6.50) 9.68(2.98) 10.63(12.63)0.940 6.3 42 17.89(1.49) �13.94(4.49) 73.20(10.61) 13.55(6.13) 12.15(0.550 �

Trichloromethane DH 0.981 1.8 50 �2.45(1.49) �17.61(1.71) �5.86(1.67) �16.59(1.36) �2.36(0.81) �21.89(3.56)0.965 2.4 50 �10.12(1.11) �8.55(1.16) �1.19(2.00) �19.94(1.68) �7.12(0.31) –

DS 0.921 5.1 50 0.92(4.35) 31.71(4.96) 9.37(4.85) 32.73(3.95) �1.41(2.35) 43.12(10.37)0.891 6.0 50 16.02(2.79) 13.86(2.92) 0.16(5.04) 39.33(4.23) 7.97(0.79) –

P.C.M. van Noort / Chemosphere 93 (2013) 1742–1746 1745

and to:

log Kp ¼ 0:865ð0:126Þ � 2:272ð0:096ÞS� 4:848ð0:108ÞA� 0:653ð0:145ÞBþ 0:350ð0:023ÞL

r2 ¼ 0:985; SE ¼ 0:21; F ¼ 890;N ¼ 60 ð6Þ

For isopentyl ether–ethanolamine partitioning the fitting equa-tions are:

log Kp ¼ � 0:248ð0:163Þ � 0:535ð0:149ÞS� 3:134ð0:095ÞA� 0:714ð0:138ÞB� 0:173ð0:056ÞLþ 1:885ð0:272ÞV

r2 ¼ 0:983; SE ¼ 0:16; F ¼ 618;N ¼ 59 ð7Þ

and

log Kp ¼ 0:669ð0:129Þ � 1:440ð0:097ÞS� 3:487ð0:110ÞA� 0:172ð0:155ÞBþ 0:194ð0:024ÞL

r2 ¼ 0:97; SE ¼ 0:21; F ¼ 407;N ¼ 59

Comparison of Eq. (5) with Eq. (6), and of Eq. (7) with Eq. (8) af-fords that leaving out the V descriptor results in only a very smalldeterioration of statistical quality.

The present analysis for all biphasic systems shows that Eq. (4)instead of Eq. (3) can be used for air-organic solvent partitioningwithout loss of statistical accuracy. In fact, statistics improve whenusing Eq. (4). In case of water as a solvent, and in case of organicbiphasic systems, the use of Eq. (4) will result in a small increasein uncertainty (by 0.1 to 0.2 and 0.04 to 0.05 log units, respectively)which may be acceptable in some cases. The attractiveness of Eq.(4) is that no values for V are needed. This is especially importantfor branched compounds because the calculation of V from atomincrements may lead to inappropriate estimated values (van Noortet al., 2010, 2011). Still, the use of Eq. (4) requires experimentalvalues for L, because estimation of L may be problematic. Additivemodels for the estimation of Abraham’s molecular descriptor log Lhave been developed based on atom and functional group frag-ments (Platts et al., 1999). However, Bronner et al. (2010), evalu-ated the predictive performance of 3 software tools (ABSOLVE,which includes the estimation procedure of Platts et al., SPARC,

and COSMOtherm) for the log L value for 104 compounds including52 environmentally relevant pesticides, 6 hormones, 6 drugs and 4phthalates. None of the software tools reached the desired accu-racy, defined as root mean square error over all compared com-pounds, of ±0.3 log units. Therefore, there still is a need forfurther improvement of the Platts et al. estimation procedure for L.

3. Conclusions

For air-organic solvent partition, the Abraham solvation param-eter V can be omitted from the Goss-modified Abraham solvationequation without any loss of statistical quality. For air–water par-titioning, organic biphasic systems, as well as water-organic sol-vent partitioning, omitting the V parameter from the Goss-modified Abraham solvation equation leads to only a small deteri-oration of statistic quality.

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