- Email: [email protected]
Studies on the Cloud Points of Nonionic Surfactants with QSPR
CHEM. RES. CHINESE U.
Available online at www.sciencedirect.com
2007, 23(6), 715-719 Article ID 1005-904O(2007) -06-715-05
ScienceDirect
Studies on the Cloud Points of Nonionic Surfactants with QSPR* CHEN Mei-ling' , WANG Zheng-wu'g2' * , ZHANG Ge-xin' , GU Jin' , CUN Zhe' and TAO Fu-ming3 1. School of Chemistry and Materials Engineering, Southern Yangtze University, Wzui 214122, P. R. China; 2. Department of Food Science & Technology, School of Agriculture and Bwlogy , Shanghai Jiaotong University, Shanghai 201101 , P. R. China ; 3. Department of Chemistry and Biochemistry, C a l ~ o m i uState University, Fullerton CA 92834, USA Received Jan. 18, 2007 With quantum chemical parameters, topological indexes, and physical chemistry parameters aa descriptors, a quantitative structure-property relationship( QSPR) has been found for the cloud points of four series of nonionic surfactants( a total of 65 surfactants) . The best-regressed model includes six descripton , and the correlation coefficient of multiple determination is as high as 0.962. Keywords Nonionic surfactants; Cloud point ; Quantitative structure-property relationship
Introduction
new QSPR method in an attempt to significantly improve the above research. Semi-empirical molecular orbital and density functional methods were used to calculate the relevant molecular properties and further establish quantum chemical descriptors. In addition to several quantum chemical descripton, the topological indexes were also used to reflect information on molecule structure.
The cloud point ( CP) is an important property of nonionic surfactants and plays an important role in their application. A quantitative structure-property relationship( QSPR) for CP will allow us to sift and predict the CP of new compounds. Recently, prediction of the properties for surfactants with QSPR is increasingly becoming popular['-91. Several theoretical models on CP have been p r o p ~ s e d [ ~ - ~Some I. models[71 performed Cloud Point Data The majority of the CP data were taken from apparently well, but were restricted to certain varieties Rosen's text"'] , which were considered more reliable with a small number of surfactants, which limited their and consistent than others. Some of the updated data application. Moreover, the parameters included in these models could not fully reflect important molecular were, however, based on the recent l i t e r a t ~ r e [ ~ ' ~in '"] properties such as molecular structure, and hydrophilic which more accurate new measurement was made with the latest technology. Table 1 summarizes the data used and hydrophobic properties. On the other hand, other in the new QSPR model, where CnE,, CnPE, and model^[^*^] include a wide variety and a large number of surfactants, but the resulting correlation coefficient C,,E,P, represent surfactants C,H,+, ( OC,H, ),OH, is low. CnH2a+,C,H, ( OCZH, 1,OH and C12Hs ( OC2H4 1n The purpose of this study aims at investigating a ( OC,H6 ) ,OH respectively. Table 1 Values of descriptors, and the observed and the calculated CPs for 65 nonionic surfactants Surfactant
Linearalkyl ethoxylates
CdE, CsE, C6E3 C6E.j C6E5 C6E6
C,E, CBE3
X"
OJ
3.101 4.678 6.256 7.333 8.410 9.488 6.756 7.256 8.333
5.743 8.364 10.985 12.899 14.814 16.728 11.692 12.399 14.314
0.0169 0.0170 0.0164 0.0180 0.0186 0.0191 0.0161 0.0152 0.0163
RNOI~
RNO/KHo
KHO
KHAn
0.130 0.131 0.128 0.134 0.136 0.138 0.127 0. 124 0.128
0.00542 0.00445 0.00362 0.00396 0.00410 0.00421 0.00307 0.00256 0.00274
3.121 3.828 4.536 4.536 4.536 4.536 5.243 5.950 5.950
1.767 1.957 2.130 2.130 2.130 2.130 2.290 2.439 2.439
EHoM0/eV ELUMo/eV C P , -6.803 6.748 -6.748 6.748 - 6.748 6.776 6.748 6.748 6.748
-
-
-
1.823 1.714 1.687 1.633 1.633 1.605 1.687 1.687 1.633
46.6 36.0 37.0 63.8 75.0 83.0 27.6 7.0 39.5
CP, 48.5 38.8 29.5 62.1 74.0 89.2 24.5 11.8 40.2
Continued to next page.
* Supported by the National Natural Science Foundation of China( Nos. 20676051, 20573048) and Youth Foundation of Southern Yangtze University( No. 006283). * * To whom correspondence should be addressed. E-mail: zhengwuwang@hotmail. corn
Vol. 23
CHEM. RES. CHINESE U.
716 ~~~~~~~
~
X.
surtactant Linear alkyl
C~ES
ethoxylatea
C8E6
C8 E8 C8E9 C8EIZ c9 E4 c 9 Es c9 E6 c10E4
CIOES C10E6
ClOE, CIOEIO
CIIE, C11E5
E6
CI, E* c l Z E5 C12E6 C12E7
CIZE8 C12E9
ClZElO CI2Ell C13ES c13 E6
‘lJE8 C14ES
C14E7
C14E8
c15E6 CUE8 C16E6 C16E7 C16E8
c16 E9 C16E12
Alkyl phenol ethoxylates
CEPE7
cs PEIO c8pE13
c9 PEE c9 PE9 C9PE10
C9PEIZ c 9 m 3
CIZPE9 CIZPEll
c l Z pE15
Linear dodecyl po- CIZE3 p6 lyoxyethylene ply- CIZE4 Ps oxypmpylene ether C1z Es P4
Branched dkyl ethoxylates
IC6E6 IC10E6
TC~~
9.410 10.488 12.644 13.722 16.952 8.833 9.910 10.988 9.333 10.410 11.488 13.643 15.797 9.833 10.910 11.988 14.143 10.333 11.410 12.488 13.565 14.643 15.720 16.797 17.875 11.910 12.988 15.143 12.410 13.488 14.565 15. 643 13.988 16.143 14.488 15.565 16.643 17.720 20.954 13.655 16.888 20.123 15.233 16.310 17.388 19.543 20.620 17.810 19.965 10.410 18.720 18.220 17.720 9.419 11.419 E21.420 I~
~~
OJ
RNO
RNOIR
RNO/KH,
16.228 18.412
0.0171 0.0177 0.0186 0.0190 0.0197 0.0156 0.0165 0.0171 0.0149 0.0159 0.0166 0.0176 0.0184 0.0143
0.131 0.133
0.00288 0.00298 0.00313 0.00319 0.00332 0.00234 0.00247 0.00257 0.00203 0.00215 0.00225 0.00239 0.00249 0.00178 0.00189 0.00199 0.00213 0.00157 0.00168 0.00177 0.00184 0.00190 0:00195 0.00200 0.00204 0.00150 0.00159 0.00172 0.00135 0.00143 0.00150 0.00156 0.00130 0.00142 0.001 19 0.00125 0.00130 0.00135 0.00145 0.00168 0.00184 0.00194 0.00158 0.00164 0.00167 0.00174 0.00177 0.00126 0.00134 0.00215 0.00171 0.00174 0.00178 0. oO406 0.00346 0.00133
21.970 23.885 29.627 15.021 16.935 18.849 15.728 17.642 19.556 23.385 21.213 16.435
27.627 29.541 35.284 23.366 29.108 34.851 25.987 27.901 29.816 33.644 35.558 30.023 33.851 17.642 30.956 30.249 29.541 16.184 19.012
0.0153 0.0160 0.0172 0.0138 0.0148 0.0155 0.0162 0.0167 0.0172 0.0175 0.0179 0.0143 0.0151 0.0163 0.0138 0.0146 0.0153 0.0159 0.0142 0.0155 0.0138 0.0145 0.0151 0.0157 0.0169 0.0155 0.0170 0.0180 0.0157 0.0164 0.0166 0.0174 0.0177 0.0152 0.0162 0.0159 0.0150 0.0153 0.0157 0.0191 0.0260
35.663
0.0169
18. 349 20.263 24.092 17.142 19.056 20.970 22.885 24.799 26.713 28.627 30.541 19.763 21.678 25.506 20.470 22.385 24.299 26.213 23.092 26.920 23.779 25.713
0. 137 0.138 0.141 0.125 0.128 0.131 0.122 0.126 0. 129 0.133 0. 136 0.119 0.124 0.127 0.131 0.117 0. 122 0.125 0.127 0.129 0.131 0.133 0. 134 0.119 0.123 0.128 0.118 0.121 0. 124 0.126 0.119 0. 125 0.118 0.121 0.123 0.125 0.130 0.125 0.130 0.134 0.125 0.128 0.129 0.132 0.133 0.123 0.127 0.126 0. 122 0. 124 0.125 0.138 0.161 0.130
KH,
KHAn
5.950
2.439
5.950 5.950 5.950 5.950 6.657 6.657 6.657 7.364 7.364 7.364 7.364 7.364 8.071 8.071
2.439 2.439 2.439 2.439 2.580 2.580 2.580 2.714 2.714 2.714 2.714 2.714 2.841 2.841
8.071 8.071 8.778 8.778 8.778 8.778 8.778 8.778 8.778 8.778 9.485 9.485 9.485 10.192 10.192 10.192 10.192 10.899 10.899 11.607 11.607 11.607 11.607 11.607 9.259 9.259 9.259 9.966 9.966 9.966 9.966 9.966 12.088 12.088 7.364 8.778 8.778 8.778 4.699 7.527 12.692
2.841 2.841 2.963 2.963 2.963 2.963 2.963 2.963 2.963 2.963 3.080 3.080 3.080 3.193 3.193 3.193 3.193 3.301 3.301 3.407 3.407 3.407 3.407 3.407 3.043 3.043 3.043 3. 157 3. 157 3.157 3. 157 3.157 3.477 3.477 2.714 2.963 2.963 2.963 2.168 2.744 3.563
EHoMo/eV
ELuMo/eV
-6.748
1.605 1.605 1.605 1.605 1.605 1.633 1.633 1.605
- 6.748 -6.767 - 6.776 - 6.776 - 6.748 - 6.748 - 6.748 - 6.748 - 6.748 -6.748 - 6.748 - 6.748 - 6.748 6.748 - 6.748 - 6.748 -6.748 - 6.748 - 6.748 - 6.748 6.748 -6.748 - 6.748 - 6.748
-
-
- 6.748 - 6.748 - 6.748 - 6.748 - 6.748 - 6.748 - 6.748 -6.748 - 6.748 -6.748 - 6.748 - 6.748 - 6.748 - 6.748 -5.660 -5.660 -5.660
- 5.633 -5.660 -5.660 -5.660 -5.660 -5.660 -5.660 -5.660 -6.721 - 6.721 - 6.748 - 6.776 - 6.776 -6.476
1.633 1.633 1.605 1.605 1.605 1.633 1.633 1.605 1.605 1.660 1.633 1.605 1.605 1.605 1.605 1.578 1.578 1.660 1.605 1.605 1.660 1.605 1.605 1.605 1.605 1.605 1.605 1.605 1.605 1.605 1.578 0.082 0.082 0.082 0. 109 0.082 0.082 0.082 0.082 0.082 0.082 0.082 1.905 1.605 1.742 1.605 1.605 1.578
C P ,
CP,,
58.6 68.0 96.0 100.0 106.0 32.0 55.0 75.0 20.4 41.6 60.3 84.5 95.0 10.5
58.2 69.7 90.2 96.7 113.4 32.3 50.5 65.7 24.6 45. 3 62.1 82.2 96.5 16.4
37.0 57.5 82.0 6.0 31.5 51.0 64.7 77.9
39.6 58.2 80.4 5. 2 33.2 53.6 67.3 78. 1 87.0
87.8
95.5 96.9 100.3 103.6 25.0 23. 6 44.0 48.0 72.5 74.9 20.0 15.2 42.3 41.5 57.6 58.0 70.5 70. 8 37.5 33.9 66.0 65.7 32.0 25.2 53.0 44.6 65.0 59.6 75.5 71. 8 92.0 100.5 15.0 33.7 75.0 65.0 89.0 85.2 34.0 36.0 56.0 55. 1 75.0 62.4 84.0 77. 5 89.0 84.0 33.0 37.9 50.0 60.3 90.0 92.9 10.6 5. 1 84.5 82.2 29.8 41. 5 78.0 74.4 27.0 27.9 48.0 50.0
CHEN Mei-ling et
No. 6
Calculation of Descriptors 1 Calculation of Quantum Chemical Descriptors Gaussian 03 was used to calculate quantum chemistry descriptors. The initial molecular structure was built by HyperChem 7.0 and then optimized using the AM1 semi-empirical molecular orbital method. It was followed by the calculations of molecular frequencies at the AM1 level and single-point energy at the B3LYP16-31G level on the optimized molecular structure. The calculated quantum chemistry descriptors included the total molecular energy E ( eV ) , molecular volume V , the energies of the lowest unoccupied molecular orbital and the highest occupied molecular orbital EL",, ( eV) and EHOMO ( eV) , and the total dipole moment p and its components p - x , p - y and p
-2.
2 Calculation of Topological Index Descriptors The Kier & Hall index of zero-th order of the hydrophobic fragment of a compound, KH, , is defined as N Z; - Hi KH, = (Sr)-'", 6; = (1) zi - 2; - 1 i=l where the meanings of Zi, 22, Hiand N are interpreted on the basis of reference [ 121.
c
The zero-th and first order new structure information connectivity indices O J and 'J are respectively given as: OJ
=
c
C (ai x S ~ ) - " (~2 )
(Si)-ln and 'J =
where,
6i = (ni - l ) [ ( Z i - 2 ) / ( m i - 2 ) ] x N , ( 3 ) here, the meanings of ni, Zi , mi, N , , i ,j and k are interpreted on the basis of reference [ 131. The molecular connectivity index is defined as:
C ( P i x Qi)
calculated as the ratio of the number of oxygen atoms in the hydrophilic domain to the molecular weight of the surfactant.
Model Building Owing to the amphipathic structure and the large number of atoms in a surfactant molecule, only 19 descriptors were selected to describe the molecular structure of surfactants and the formation process of CP. Two additional descriptors, R N 0 l n and KHY , were introduced with the help of the method of the previous study"-31. There were a total of 21 descriptors, which were used as independent variables while CP was used as the dependent variable. A step-by-step partial correlation analysis was then carried out. The analysis resulted in nine variables with partial correlation coefficients larger than 0.3, as shown in Table 3. Finally, a stepwise multiple linear regression analysis was performed between the nine descriptors and the cloud points to search for the optimal correlation with the maximum squared correlation coefficient and the F-test. The squared correlation coefficient, R 2 , is a measure of the fit of the regression model. The correlation coefficient values closer to 1.0 represent the better fit of the model. The F-test reflects the ratio of the variation explained by the model and the variance owing to the error in the model. High values of the F-test indicate that the model is statistically significant. The standard error is measured by the error mean square, S2, which expresses the variation of the residuals on the regression line.
1 QSPRModel
(4)
-112
3 Calculation of Physical Chemistry Descriptor The relative number of oxygen atoms RNO can be
Results and Discussion
k
X" =
717
al.
i=l
Tables 2 and 3 present a summary of the regresHere, the meanings of Piand Qi are interpreted on the sion analysis and the resulting best general QSPR. basis of reference [ 141. Table 2 Best correlation models and their statistical characteristies for 65 nonionic sur€actants* Number of predictor parametera Constant RNO'" Constant RNO'" constant RNO'" constant RNO'" constant RNO'" Constant RNO'" Constant RNO'" Constant RNO'", Constant RNO'" Constant RNO'",
, RNO , RNO, KHA" , RNO, K H y , E,,,, , RNO, m;", E,,,, , E,,, , RNO, m;", E,,,, , E,,, , O J , RNO, E,,,, , EL,,,, , O J RNO, E,,,o, EL,,,,, '1, RNO/KH, , RNO, E,, , ELuro, O J , RNO/KH, , KHA"
RNO, EHOMO ELUMO, O J , RNO/KH, Constant RNO'" , RNO, EHOWJ, ELWO O J , RNOIKH, * Dependent variable: ,PC 9
9
9
9
a", xV a"X. KHo I
9
R2
F
SZ
0.300
26.989
0.414
0.614
49.385
0.308
0.748
60.236
0.251
0.812
64.702
0.185
0.907
114.857
0.131
0.925
119.327
0.119
0.924
144.426
0.118
0.931
131.314
0.114
0.941
128.731
0.107
0.952
138. 191
0.097
0.962
154.352
0.087
CHEM. RES. CHINESE U.
718
Table 3 Partial correlation coefHicient(r) between CP, RNO -0.813 0.OOO
r
SZ
RNOln
EHOMO
0.808 0.ooo
-0.663 0.006
RNo'KHO
0.576 0.OOO
The best QSPR model for cloud point results in: C P , , = -4191.055 + 35390.57 x RNO'" 132957 x RNO +481.398 x K H F 148.282 x E H O M O -79.719 xELUMO + 33.463 x O J +61990.83 x RNO/KH, 54.414 XX" -59.160 x KH, ( R2 = 0.962, S2= 0.0802, F = 154.352, n = 6 5 , P
Vol. 23
and each descriDtor for 65 nonionic surfactanta OJ
0.559 0.111
ELIJMO
my
- 0.542
- 0.524
0.066
0.009
0.518 0.006
X.
KHO - 0.474 0.036
scatter plot of some calculated CP,, values wrsm RNO (other calculated CP,, values have a similar relation with RNO). A linear correlation can be seen between the calculated cloud points and the RNO values, which is in good agreement with the experiment. Taking C,,E, ( n = 4-1 1 ) for example, the experiment data CP&, ( see Table 1 ) increases linearly ( from 6. 0100.3 ) with the number of oxyethylene units ( n ) . Since the RNO value increases with the number of oxyethylene units ( n ) , the experiment data CP,,, of CP (see Table 1 ) also increases linearly with the RNO value.
2 Physical Interpretations of Descriptors
Fig. 1 Scatter plot of the calculated CP, versus the observed CP, for 65 nonionic surfactants
As seen in Table 3 , each of the nine descriptors has a high correlation coefficient on the CP. Among all the descriptors, RNO has the highest correlation coefficient on the CP,,, ( r = - 0. 813). The hydrophilic group of a nonionic surfactant is mainly composed of oxyethylene units. H-bonds are easily formed between the ether oxygen atoms and water molecules. As a result, the number of oxyethylene units is indirectly correlated with the number of H-bonds. Fig. 2 shows a
Fig.2 Scatter plot of the calculated CP, vs. the RNO a.
C,E,,; b. C,E,; c. C,E,; d. C,,E,,; e. C,,E,;
f. CIZE,;
6. Cl,E,;
h. C,,E,; i. C,,E,; j . C,,E,.
The cloud points are fundamentally determined by the formation of H-bonds. When surfactants are dissolved in the aqueous solvent, the 0 atom in the EO chain, with one of its unshared pairs( the HOMO) , offers lone electron pair to the H atom of water molecule to form H-bond, and the water molecule offers its lone electron pair to the H atom in the OH group of alcohol (the LUMO) of nonionic surfactant to form H-bond. Thus, the E,,, and E,,, included in the QSPR model reflect the ability of forming H-bond between the surfactants and water molecules. It has been seen that for a particular hydrophobic group, the larger the percentage of oxyethylene in the surfactant molecule, the higher is the CP"51. The main reason is that ethylene oxide( EO) chain can form H-bonds with water molecules. The longer the EO chains, the larger are the number of H-bonds forming, and the higher is the energy required to break the H-bonds between water and surfactant polar groups. The RNO can reflect the influence of EO on the CP. A surfactant with a greater value of RNO should be more hydrophilic. According to the available experimental data"51 , the CP reflects the relationship between the hydrophilic and hydrophobic groups, and the ratio RNO/KH, represents the relative contributions of the hydrophilic and hydrophobic groups. It is reasonable that RNO/ KH, is included in the regression model. Branched-chain and benzene-containing nonionic surfactants were also included in the development of the QSPR model. The best-regressed model included new valance connectivity indices, O J and xu. xuwas used to distinguish unsaturated bonds from saturated
No.6
CHEN Mei-ling et al.
bonds. The number of valance electrons and the number of connected hydrogen atoms were used inXv calculation. The O J covered the total contribution from nonhydrogen atoms of the molecule. It distinguished the contributions of the 8 bonds from those of the IT bonds and also included other unique properties of the molecule. As a result, './ is strong in reflecting the unique characteristics of the molecule, and therefore, the descriptors './ andxu can fully reflect the influence of the surfactant structure and the surfactant chemical environment on the CP.
Conclusions This study has established a new QSPR model, Eq. ( 5 ) , with a high correlation coefficient ( RZ = 0.962). Three types of descriptors with specific physical origins are included: quantum chemical descriptors, topological indexes descriptors, and physical chemistry descriptors. The calculation of these descriptors is simple, and has proven useful for the prediction. The established QSPR model has significantly expanded the prediction of the cloud points for a large variety of nonionic surfactants. It can successively predict the cloud points of nonionic surfactants. The new QSPR model has involved the new valence connectivity indexes O./ and xV for the first time. The successful application of the method may
719
encourage future studies in this direction.
References Wang Z. W. , Li G. Z. , Mu J. H. , et al. , Chin. Chem. ku., 2002, 1 3 ( 4 ) , 363 Wang Z. W. , Feng J. L. , Wang H . J. , et al. , J. Dicp. Sci. Tech. , u)o5, 2 6 ( 4 ) , 441 Wang Z. W. , Feng J. L. , Wang Z. N. , et al, , J. DLp. Sci.
Tech. , 2006, 2 7 ( 1 ) , 11 Yuan S. L., Cai Z. T . , Xu G. Y. , et al. , A& Phys. Chin. Sin. , m3, 1 9 ( 4 ) , 334 L i Y . M . , Xu G. Y . , Luan Y. X., et al., J. DLp. Sci. Tech. , ZOOS, 2 6 ( 6 ) , 799 Huibera P. D. T . , Shah D. O . , KatritzLy A. R . , 1. CoUoid Interjkce Sci. , 1997, I 9 3 ( 1 ) , 132 Duarte L. J. N. , Canselier J. P. , Sw$adants & Detergents, m5,3,2 G U T . , GaleraG. P. A . , Colloidsurf. A . , 1999, 1 4 7 ( 3 ) , 365 Mo X. G . , Liu S. Y . , Chemistry, Mo1,64(8), 483 Roeen M. J. , Su&ctants and Zntefmial Phenomena, Wiley, New Yo&, 1987, 210 Mu J. H. , Li G . Z. , Chen W. J. , et al. , Chinese J. Chem. Phys. , u)ol, 1 4 ( 1 ) , 119 Steward J. J. P., J. Comput. Chem., 1989, 1 0 ( 2 ) , 209 Chen Y. , Journal of Nanjing Uniwrdy of Technology, u)o5,27 ( 4 ) , 41 Ni C. H. , Feng 2. Y. , Li L. C. , A& Chimica Sinica, 1998, 5 6 ( 4 ) , 359 Xia J. D. , Ni Y. Q. , Swjimtants and Detergent C h e m i a ~Pro~ cessing Technology, China Light Industry Press, Beijing, 1997, 371
Available online at www.sciencedirect.com
2007, 23(6), 715-719 Article ID 1005-904O(2007) -06-715-05
ScienceDirect
Studies on the Cloud Points of Nonionic Surfactants with QSPR* CHEN Mei-ling' , WANG Zheng-wu'g2' * , ZHANG Ge-xin' , GU Jin' , CUN Zhe' and TAO Fu-ming3 1. School of Chemistry and Materials Engineering, Southern Yangtze University, Wzui 214122, P. R. China; 2. Department of Food Science & Technology, School of Agriculture and Bwlogy , Shanghai Jiaotong University, Shanghai 201101 , P. R. China ; 3. Department of Chemistry and Biochemistry, C a l ~ o m i uState University, Fullerton CA 92834, USA Received Jan. 18, 2007 With quantum chemical parameters, topological indexes, and physical chemistry parameters aa descriptors, a quantitative structure-property relationship( QSPR) has been found for the cloud points of four series of nonionic surfactants( a total of 65 surfactants) . The best-regressed model includes six descripton , and the correlation coefficient of multiple determination is as high as 0.962. Keywords Nonionic surfactants; Cloud point ; Quantitative structure-property relationship
Introduction
new QSPR method in an attempt to significantly improve the above research. Semi-empirical molecular orbital and density functional methods were used to calculate the relevant molecular properties and further establish quantum chemical descriptors. In addition to several quantum chemical descripton, the topological indexes were also used to reflect information on molecule structure.
The cloud point ( CP) is an important property of nonionic surfactants and plays an important role in their application. A quantitative structure-property relationship( QSPR) for CP will allow us to sift and predict the CP of new compounds. Recently, prediction of the properties for surfactants with QSPR is increasingly becoming popular['-91. Several theoretical models on CP have been p r o p ~ s e d [ ~ - ~Some I. models[71 performed Cloud Point Data The majority of the CP data were taken from apparently well, but were restricted to certain varieties Rosen's text"'] , which were considered more reliable with a small number of surfactants, which limited their and consistent than others. Some of the updated data application. Moreover, the parameters included in these models could not fully reflect important molecular were, however, based on the recent l i t e r a t ~ r e [ ~ ' ~in '"] properties such as molecular structure, and hydrophilic which more accurate new measurement was made with the latest technology. Table 1 summarizes the data used and hydrophobic properties. On the other hand, other in the new QSPR model, where CnE,, CnPE, and model^[^*^] include a wide variety and a large number of surfactants, but the resulting correlation coefficient C,,E,P, represent surfactants C,H,+, ( OC,H, ),OH, is low. CnH2a+,C,H, ( OCZH, 1,OH and C12Hs ( OC2H4 1n The purpose of this study aims at investigating a ( OC,H6 ) ,OH respectively. Table 1 Values of descriptors, and the observed and the calculated CPs for 65 nonionic surfactants Surfactant
Linearalkyl ethoxylates
CdE, CsE, C6E3 C6E.j C6E5 C6E6
C,E, CBE3
X"
OJ
3.101 4.678 6.256 7.333 8.410 9.488 6.756 7.256 8.333
5.743 8.364 10.985 12.899 14.814 16.728 11.692 12.399 14.314
0.0169 0.0170 0.0164 0.0180 0.0186 0.0191 0.0161 0.0152 0.0163
RNOI~
RNO/KHo
KHO
KHAn
0.130 0.131 0.128 0.134 0.136 0.138 0.127 0. 124 0.128
0.00542 0.00445 0.00362 0.00396 0.00410 0.00421 0.00307 0.00256 0.00274
3.121 3.828 4.536 4.536 4.536 4.536 5.243 5.950 5.950
1.767 1.957 2.130 2.130 2.130 2.130 2.290 2.439 2.439
EHoM0/eV ELUMo/eV C P , -6.803 6.748 -6.748 6.748 - 6.748 6.776 6.748 6.748 6.748
-
-
-
1.823 1.714 1.687 1.633 1.633 1.605 1.687 1.687 1.633
46.6 36.0 37.0 63.8 75.0 83.0 27.6 7.0 39.5
CP, 48.5 38.8 29.5 62.1 74.0 89.2 24.5 11.8 40.2
Continued to next page.
* Supported by the National Natural Science Foundation of China( Nos. 20676051, 20573048) and Youth Foundation of Southern Yangtze University( No. 006283). * * To whom correspondence should be addressed. E-mail: zhengwuwang@hotmail. corn
Vol. 23
CHEM. RES. CHINESE U.
716 ~~~~~~~
~
X.
surtactant Linear alkyl
C~ES
ethoxylatea
C8E6
C8 E8 C8E9 C8EIZ c9 E4 c 9 Es c9 E6 c10E4
CIOES C10E6
ClOE, CIOEIO
CIIE, C11E5
E6
CI, E* c l Z E5 C12E6 C12E7
CIZE8 C12E9
ClZElO CI2Ell C13ES c13 E6
‘lJE8 C14ES
C14E7
C14E8
c15E6 CUE8 C16E6 C16E7 C16E8
c16 E9 C16E12
Alkyl phenol ethoxylates
CEPE7
cs PEIO c8pE13
c9 PEE c9 PE9 C9PE10
C9PEIZ c 9 m 3
CIZPE9 CIZPEll
c l Z pE15
Linear dodecyl po- CIZE3 p6 lyoxyethylene ply- CIZE4 Ps oxypmpylene ether C1z Es P4
Branched dkyl ethoxylates
IC6E6 IC10E6
TC~~
9.410 10.488 12.644 13.722 16.952 8.833 9.910 10.988 9.333 10.410 11.488 13.643 15.797 9.833 10.910 11.988 14.143 10.333 11.410 12.488 13.565 14.643 15.720 16.797 17.875 11.910 12.988 15.143 12.410 13.488 14.565 15. 643 13.988 16.143 14.488 15.565 16.643 17.720 20.954 13.655 16.888 20.123 15.233 16.310 17.388 19.543 20.620 17.810 19.965 10.410 18.720 18.220 17.720 9.419 11.419 E21.420 I~
~~
OJ
RNO
RNOIR
RNO/KH,
16.228 18.412
0.0171 0.0177 0.0186 0.0190 0.0197 0.0156 0.0165 0.0171 0.0149 0.0159 0.0166 0.0176 0.0184 0.0143
0.131 0.133
0.00288 0.00298 0.00313 0.00319 0.00332 0.00234 0.00247 0.00257 0.00203 0.00215 0.00225 0.00239 0.00249 0.00178 0.00189 0.00199 0.00213 0.00157 0.00168 0.00177 0.00184 0.00190 0:00195 0.00200 0.00204 0.00150 0.00159 0.00172 0.00135 0.00143 0.00150 0.00156 0.00130 0.00142 0.001 19 0.00125 0.00130 0.00135 0.00145 0.00168 0.00184 0.00194 0.00158 0.00164 0.00167 0.00174 0.00177 0.00126 0.00134 0.00215 0.00171 0.00174 0.00178 0. oO406 0.00346 0.00133
21.970 23.885 29.627 15.021 16.935 18.849 15.728 17.642 19.556 23.385 21.213 16.435
27.627 29.541 35.284 23.366 29.108 34.851 25.987 27.901 29.816 33.644 35.558 30.023 33.851 17.642 30.956 30.249 29.541 16.184 19.012
0.0153 0.0160 0.0172 0.0138 0.0148 0.0155 0.0162 0.0167 0.0172 0.0175 0.0179 0.0143 0.0151 0.0163 0.0138 0.0146 0.0153 0.0159 0.0142 0.0155 0.0138 0.0145 0.0151 0.0157 0.0169 0.0155 0.0170 0.0180 0.0157 0.0164 0.0166 0.0174 0.0177 0.0152 0.0162 0.0159 0.0150 0.0153 0.0157 0.0191 0.0260
35.663
0.0169
18. 349 20.263 24.092 17.142 19.056 20.970 22.885 24.799 26.713 28.627 30.541 19.763 21.678 25.506 20.470 22.385 24.299 26.213 23.092 26.920 23.779 25.713
0. 137 0.138 0.141 0.125 0.128 0.131 0.122 0.126 0. 129 0.133 0. 136 0.119 0.124 0.127 0.131 0.117 0. 122 0.125 0.127 0.129 0.131 0.133 0. 134 0.119 0.123 0.128 0.118 0.121 0. 124 0.126 0.119 0. 125 0.118 0.121 0.123 0.125 0.130 0.125 0.130 0.134 0.125 0.128 0.129 0.132 0.133 0.123 0.127 0.126 0. 122 0. 124 0.125 0.138 0.161 0.130
KH,
KHAn
5.950
2.439
5.950 5.950 5.950 5.950 6.657 6.657 6.657 7.364 7.364 7.364 7.364 7.364 8.071 8.071
2.439 2.439 2.439 2.439 2.580 2.580 2.580 2.714 2.714 2.714 2.714 2.714 2.841 2.841
8.071 8.071 8.778 8.778 8.778 8.778 8.778 8.778 8.778 8.778 9.485 9.485 9.485 10.192 10.192 10.192 10.192 10.899 10.899 11.607 11.607 11.607 11.607 11.607 9.259 9.259 9.259 9.966 9.966 9.966 9.966 9.966 12.088 12.088 7.364 8.778 8.778 8.778 4.699 7.527 12.692
2.841 2.841 2.963 2.963 2.963 2.963 2.963 2.963 2.963 2.963 3.080 3.080 3.080 3.193 3.193 3.193 3.193 3.301 3.301 3.407 3.407 3.407 3.407 3.407 3.043 3.043 3.043 3. 157 3. 157 3.157 3. 157 3.157 3.477 3.477 2.714 2.963 2.963 2.963 2.168 2.744 3.563
EHoMo/eV
ELuMo/eV
-6.748
1.605 1.605 1.605 1.605 1.605 1.633 1.633 1.605
- 6.748 -6.767 - 6.776 - 6.776 - 6.748 - 6.748 - 6.748 - 6.748 - 6.748 -6.748 - 6.748 - 6.748 - 6.748 6.748 - 6.748 - 6.748 -6.748 - 6.748 - 6.748 - 6.748 6.748 -6.748 - 6.748 - 6.748
-
-
- 6.748 - 6.748 - 6.748 - 6.748 - 6.748 - 6.748 - 6.748 -6.748 - 6.748 -6.748 - 6.748 - 6.748 - 6.748 - 6.748 -5.660 -5.660 -5.660
- 5.633 -5.660 -5.660 -5.660 -5.660 -5.660 -5.660 -5.660 -6.721 - 6.721 - 6.748 - 6.776 - 6.776 -6.476
1.633 1.633 1.605 1.605 1.605 1.633 1.633 1.605 1.605 1.660 1.633 1.605 1.605 1.605 1.605 1.578 1.578 1.660 1.605 1.605 1.660 1.605 1.605 1.605 1.605 1.605 1.605 1.605 1.605 1.605 1.578 0.082 0.082 0.082 0. 109 0.082 0.082 0.082 0.082 0.082 0.082 0.082 1.905 1.605 1.742 1.605 1.605 1.578
C P ,
CP,,
58.6 68.0 96.0 100.0 106.0 32.0 55.0 75.0 20.4 41.6 60.3 84.5 95.0 10.5
58.2 69.7 90.2 96.7 113.4 32.3 50.5 65.7 24.6 45. 3 62.1 82.2 96.5 16.4
37.0 57.5 82.0 6.0 31.5 51.0 64.7 77.9
39.6 58.2 80.4 5. 2 33.2 53.6 67.3 78. 1 87.0
87.8
95.5 96.9 100.3 103.6 25.0 23. 6 44.0 48.0 72.5 74.9 20.0 15.2 42.3 41.5 57.6 58.0 70.5 70. 8 37.5 33.9 66.0 65.7 32.0 25.2 53.0 44.6 65.0 59.6 75.5 71. 8 92.0 100.5 15.0 33.7 75.0 65.0 89.0 85.2 34.0 36.0 56.0 55. 1 75.0 62.4 84.0 77. 5 89.0 84.0 33.0 37.9 50.0 60.3 90.0 92.9 10.6 5. 1 84.5 82.2 29.8 41. 5 78.0 74.4 27.0 27.9 48.0 50.0
CHEN Mei-ling et
No. 6
Calculation of Descriptors 1 Calculation of Quantum Chemical Descriptors Gaussian 03 was used to calculate quantum chemistry descriptors. The initial molecular structure was built by HyperChem 7.0 and then optimized using the AM1 semi-empirical molecular orbital method. It was followed by the calculations of molecular frequencies at the AM1 level and single-point energy at the B3LYP16-31G level on the optimized molecular structure. The calculated quantum chemistry descriptors included the total molecular energy E ( eV ) , molecular volume V , the energies of the lowest unoccupied molecular orbital and the highest occupied molecular orbital EL",, ( eV) and EHOMO ( eV) , and the total dipole moment p and its components p - x , p - y and p
-2.
2 Calculation of Topological Index Descriptors The Kier & Hall index of zero-th order of the hydrophobic fragment of a compound, KH, , is defined as N Z; - Hi KH, = (Sr)-'", 6; = (1) zi - 2; - 1 i=l where the meanings of Zi, 22, Hiand N are interpreted on the basis of reference [ 121.
c
The zero-th and first order new structure information connectivity indices O J and 'J are respectively given as: OJ
=
c
C (ai x S ~ ) - " (~2 )
(Si)-ln and 'J =
where,
6i = (ni - l ) [ ( Z i - 2 ) / ( m i - 2 ) ] x N , ( 3 ) here, the meanings of ni, Zi , mi, N , , i ,j and k are interpreted on the basis of reference [ 131. The molecular connectivity index is defined as:
C ( P i x Qi)
calculated as the ratio of the number of oxygen atoms in the hydrophilic domain to the molecular weight of the surfactant.
Model Building Owing to the amphipathic structure and the large number of atoms in a surfactant molecule, only 19 descriptors were selected to describe the molecular structure of surfactants and the formation process of CP. Two additional descriptors, R N 0 l n and KHY , were introduced with the help of the method of the previous study"-31. There were a total of 21 descriptors, which were used as independent variables while CP was used as the dependent variable. A step-by-step partial correlation analysis was then carried out. The analysis resulted in nine variables with partial correlation coefficients larger than 0.3, as shown in Table 3. Finally, a stepwise multiple linear regression analysis was performed between the nine descriptors and the cloud points to search for the optimal correlation with the maximum squared correlation coefficient and the F-test. The squared correlation coefficient, R 2 , is a measure of the fit of the regression model. The correlation coefficient values closer to 1.0 represent the better fit of the model. The F-test reflects the ratio of the variation explained by the model and the variance owing to the error in the model. High values of the F-test indicate that the model is statistically significant. The standard error is measured by the error mean square, S2, which expresses the variation of the residuals on the regression line.
1 QSPRModel
(4)
-112
3 Calculation of Physical Chemistry Descriptor The relative number of oxygen atoms RNO can be
Results and Discussion
k
X" =
717
al.
i=l
Tables 2 and 3 present a summary of the regresHere, the meanings of Piand Qi are interpreted on the sion analysis and the resulting best general QSPR. basis of reference [ 141. Table 2 Best correlation models and their statistical characteristies for 65 nonionic sur€actants* Number of predictor parametera Constant RNO'" Constant RNO'" constant RNO'" constant RNO'" constant RNO'" Constant RNO'" Constant RNO'" Constant RNO'", Constant RNO'" Constant RNO'",
, RNO , RNO, KHA" , RNO, K H y , E,,,, , RNO, m;", E,,,, , E,,, , RNO, m;", E,,,, , E,,, , O J , RNO, E,,,, , EL,,,, , O J RNO, E,,,o, EL,,,,, '1, RNO/KH, , RNO, E,, , ELuro, O J , RNO/KH, , KHA"
RNO, EHOMO ELUMO, O J , RNO/KH, Constant RNO'" , RNO, EHOWJ, ELWO O J , RNOIKH, * Dependent variable: ,PC 9
9
9
9
a", xV a"X. KHo I
9
R2
F
SZ
0.300
26.989
0.414
0.614
49.385
0.308
0.748
60.236
0.251
0.812
64.702
0.185
0.907
114.857
0.131
0.925
119.327
0.119
0.924
144.426
0.118
0.931
131.314
0.114
0.941
128.731
0.107
0.952
138. 191
0.097
0.962
154.352
0.087
CHEM. RES. CHINESE U.
718
Table 3 Partial correlation coefHicient(r) between CP, RNO -0.813 0.OOO
r
SZ
RNOln
EHOMO
0.808 0.ooo
-0.663 0.006
RNo'KHO
0.576 0.OOO
The best QSPR model for cloud point results in: C P , , = -4191.055 + 35390.57 x RNO'" 132957 x RNO +481.398 x K H F 148.282 x E H O M O -79.719 xELUMO + 33.463 x O J +61990.83 x RNO/KH, 54.414 XX" -59.160 x KH, ( R2 = 0.962, S2= 0.0802, F = 154.352, n = 6 5 , P
Vol. 23
and each descriDtor for 65 nonionic surfactanta OJ
0.559 0.111
ELIJMO
my
- 0.542
- 0.524
0.066
0.009
0.518 0.006
X.
KHO - 0.474 0.036
scatter plot of some calculated CP,, values wrsm RNO (other calculated CP,, values have a similar relation with RNO). A linear correlation can be seen between the calculated cloud points and the RNO values, which is in good agreement with the experiment. Taking C,,E, ( n = 4-1 1 ) for example, the experiment data CP&, ( see Table 1 ) increases linearly ( from 6. 0100.3 ) with the number of oxyethylene units ( n ) . Since the RNO value increases with the number of oxyethylene units ( n ) , the experiment data CP,,, of CP (see Table 1 ) also increases linearly with the RNO value.
2 Physical Interpretations of Descriptors
Fig. 1 Scatter plot of the calculated CP, versus the observed CP, for 65 nonionic surfactants
As seen in Table 3 , each of the nine descriptors has a high correlation coefficient on the CP. Among all the descriptors, RNO has the highest correlation coefficient on the CP,,, ( r = - 0. 813). The hydrophilic group of a nonionic surfactant is mainly composed of oxyethylene units. H-bonds are easily formed between the ether oxygen atoms and water molecules. As a result, the number of oxyethylene units is indirectly correlated with the number of H-bonds. Fig. 2 shows a
Fig.2 Scatter plot of the calculated CP, vs. the RNO a.
C,E,,; b. C,E,; c. C,E,; d. C,,E,,; e. C,,E,;
f. CIZE,;
6. Cl,E,;
h. C,,E,; i. C,,E,; j . C,,E,.
The cloud points are fundamentally determined by the formation of H-bonds. When surfactants are dissolved in the aqueous solvent, the 0 atom in the EO chain, with one of its unshared pairs( the HOMO) , offers lone electron pair to the H atom of water molecule to form H-bond, and the water molecule offers its lone electron pair to the H atom in the OH group of alcohol (the LUMO) of nonionic surfactant to form H-bond. Thus, the E,,, and E,,, included in the QSPR model reflect the ability of forming H-bond between the surfactants and water molecules. It has been seen that for a particular hydrophobic group, the larger the percentage of oxyethylene in the surfactant molecule, the higher is the CP"51. The main reason is that ethylene oxide( EO) chain can form H-bonds with water molecules. The longer the EO chains, the larger are the number of H-bonds forming, and the higher is the energy required to break the H-bonds between water and surfactant polar groups. The RNO can reflect the influence of EO on the CP. A surfactant with a greater value of RNO should be more hydrophilic. According to the available experimental data"51 , the CP reflects the relationship between the hydrophilic and hydrophobic groups, and the ratio RNO/KH, represents the relative contributions of the hydrophilic and hydrophobic groups. It is reasonable that RNO/ KH, is included in the regression model. Branched-chain and benzene-containing nonionic surfactants were also included in the development of the QSPR model. The best-regressed model included new valance connectivity indices, O J and xu. xuwas used to distinguish unsaturated bonds from saturated
No.6
CHEN Mei-ling et al.
bonds. The number of valance electrons and the number of connected hydrogen atoms were used inXv calculation. The O J covered the total contribution from nonhydrogen atoms of the molecule. It distinguished the contributions of the 8 bonds from those of the IT bonds and also included other unique properties of the molecule. As a result, './ is strong in reflecting the unique characteristics of the molecule, and therefore, the descriptors './ andxu can fully reflect the influence of the surfactant structure and the surfactant chemical environment on the CP.
Conclusions This study has established a new QSPR model, Eq. ( 5 ) , with a high correlation coefficient ( RZ = 0.962). Three types of descriptors with specific physical origins are included: quantum chemical descriptors, topological indexes descriptors, and physical chemistry descriptors. The calculation of these descriptors is simple, and has proven useful for the prediction. The established QSPR model has significantly expanded the prediction of the cloud points for a large variety of nonionic surfactants. It can successively predict the cloud points of nonionic surfactants. The new QSPR model has involved the new valence connectivity indexes O./ and xV for the first time. The successful application of the method may
719
encourage future studies in this direction.
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