QSPR Study of Critical Micelle Concentrations of Nonionic

of new nonionic Gemini aldonamide-type surfactants J. Colloid Interface Sci. .... A. New family of nonionic Gemini surfactants, determination and ...
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Ind. Eng. Chem. Res. 2008, 47, 9687–9695

9687

QSPR Study of Critical Micelle Concentrations of Nonionic Surfactants Alan R. Katritzky,*,⊥ Liliana M. Pacureanu,⊥,‡ Svetoslav H. Slavov,⊥ Dimitar A. Dobchev,⊥,§,| and Mati Karelson§ Center for Heterocyclic Compounds, Department of Chemistry, UniVersity of Florida, GainesVille, Florida 32611, Institute of Chemistry of Romanian Academy, M. Viteazul 24, Timisoara 300223, Romania, Institute of Chemistry, Tallinn UniVersity of Technology, Ehitajate tee 5, Tallinn 19086, Estonia, and MolCode Ltd., Soola 8, Tartu 51013, Estonia

Linear and nonlinear predictive models are derived for a data set of 162 nonionic surfactants. The descriptors in the derived models relate to the molecular shape and size and to the presence of heteroatoms participating in donor-acceptor and dipole-dipole interactions. Steric hindrance in the hydrophobic area also plays an important role in micellization. The derived linear and nonlinear QSPR models could be useful to predict the CMCs of broad classes of nonionic surfactants. 1. Introduction and Interpretation of CMC Surfactants are amphiphilic molecules that contain at least one polar group and one hydrophobic nonpolar group, each of which may be composed from a variety of constituents that confer the hydrophobic and hydrophilic character. Surfactant systems are of special research interest due their wide applications in industrial and domestic area such as detergency, solubilizing agents, emulsifying agents, dispersing agents, coatings, and pharmaceutical adjuvants. When surfactants are in solution, above a certain concentration, called the critical micelle concentration (CMC), they tend to undergo spontaneous self-association into ordered structures called micelles. The CMC is influenced by many external factors including temperature, pressure, pH, ionic strength, volume of the solution, and also by the surfactant chemical structure such as the length of hydrophobic tail, headgroup area, etc. The influence of temperature on micellization is much studied: the hydrophilic and hydrophobic group’s interactions with water vary significantly with temperature. Usually the CMC of surfactants are determined by the measurement of physicochemical parameters of their aqueous solutions as function of surfactant concentration, especially conductometry, tensiometry, fluorescence emission spectroscopy, calorimetry, kinetic approaches, light scattering, NMR spectrometry, cyclic voltametry, etc.1-8 Surfactants are classified by their net charge into three main subclasses: cationic, anionic, and nonionic. Ionic surfactants and especially polymerizable anionic surfactants (and the corresponding polymers) are of most practical interest but are more complex to model. The nonionic surfactants are of particular interest for experimental and theoretical studies because of their good solubility and ease of synthesis. Zwitterionic (amphoteric) surfactants form a subclass of nonionic surfactants. Other classifications of surfactants invoke the structural nature of the hydrophobic tails, e.g., linear, branched, fluorinated, etc. The main varieties of nonionic surfactants are based on fatty alcohols, fatty acids and esters, ethoxylated alcohols and phenols, glycerol esters, alkyl polyglycosides, ethylene oxide/propylene oxide * Corresponding author. Phone: (352) 392-0554. Fax: (352) 3929199. ⊥ University of Florida. ‡ Institute of Chemistry of Romanian Academy. § Tallinn University of Technology. | MolCode, Ltd.

copolymers, polyalcohols and ethoxylated polyalcohols, sorbitol and sorbitan derivatives, alkanolamines and alkanolamides, thiols, etc. Much scientific effort has been devoted to the experimental studies and prediction of the CMC of nonionic surfactants by various theoretical and empirical methods.9-12 Thermodynamic studies led to the pseudophase theory of micellization as a phase separation phenomenon and to the mass-action theory of micelles as chemical aggregates of amphiphiles in multiple chemical equilibria.11 Theoretical approaches developed to understand micelle formation, growth, structure, size distribution, and critical micelle concentration include phenomenological, statistical-thermodynamic, and geometric-packing theories.11 Puvada and Blankschtein used a molecular model of micelization13 to predict properties of nonionic surfactants while the approach of van Lent and Scheutjens was based on selfconsistent field theory.14 2. Previous Correlations of CMC with Structure Various empirical and theoretical studies have been employed to correlate the CMC values and toxicity of the surfactants with their molecular structure.9-12,15 Our group first correlated CMC with molecular structure employing a general QSPR approach for a data set of 77 nonionic surfactants using CODESSA software and a heuristic algorithm.9 The regression equation of R2 ) 0.983 then reported9 (eq 1) included two topological descriptors for the hydrophobic fragment of the molecule: (i) the Kier and Hall index of zeroth order (c-KH0) and (ii) the average information content of second order (c-AIC-2), together with (iii) a constitutional descriptor s relative number of nitrogen and oxygen atoms (RNNO). log CMC ) -(0.567 ( 0.009)c-KH0 + (1.054 ( 0.048)c-AIC-2 + (7.5 ( 1.0)RNN - (1.80 ( 0.16) (1) According to eq 1, the CMC of nonionic surfactants depends largely on the hydrophobic fragment (decreasing with its size), but increasing with the size of the hydrophilic fragment. For the same data set of nonionic surfactants used to derive eq 1, Saunders and Platt18 applied (i) the LFER method (linear free energy relationship) that separates the solute-solvent interactions into five physicochemical descriptors, to obtain a

10.1021/ie800954k CCC: $40.75  2008 American Chemical Society Published on Web 10/29/2008

9688 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008

correlation coefficient of R2 ) 0.903, and (ii) a surface area QSPR approach which produced R2 ) 0.856.16 Chen correlated the CMC values for aqueous solutions of nonionic polyoxyethylene alcohol surfactants using a modified Aranovich and Donohue (AD) excess Gibbs energy model.12 The p-NRTL [segment-based-polymer-NRTL (nonrandom twoliquid)] model was used for the same types of surfactants to account for the nonideality of aqueous nonionic surfactants solutions.17 Li et al.11 have correlated the CMC points at 25 °C of nonionic surfactants using s-UNIQUAC (segment-based universal quasi-chemical model) and SAFT (statistical associating fluid theory) equations. Critical micelle concentrations were predicted accurately by Cheng et al. with the trend of hydrophobic chain and ethylene oxide group using the UNIFAC equation.18 Yuan and co-workers19 reported a highly significant correlation (R2 ) 0.998) for a data set of 37 structurally similar alkyl ethoxylates and octylphenol ethoxylates. The descriptors involved in their model were as follows: octanol/water partition coefficient, heat of formation, molecular volume, and LUMO energy. For the same classes of compounds Wang et al. proposed a model including Kier and Hall index of zeroth order, the total energy (or the heat of formation), and the molecular dipole moment with R2 ) 0.995.20 Temperature has a major influence on CMC.9 At constant temperature the CMC increases as the number of oxyethylene groups increase, and the reverse phenomena is observed when the number of carbon atoms from hydrophobic tail increases. The influence of the temperature on nonionic surfactants micellization is mainly due to the increase of hydrophobicity with respect to the increase of the temperature caused by the destruction of hydrogen bonds between water molecules and hydrophilic groups. Consequently, it determines the decrease of the CMC. Hence, an interpolation technique can be used to calculate log CMC at different temperatures using the plot of log CMC vs 1/T, which is approximately linear for nonionic surfactants.9 In the case of p,t-octylphenol ethoxylates a minimum on the CMC-temperature curve was observed to move toward higher temperatures as the number of ethoxy groups increases. Temperature dependence studies of n-dodecylpolyoxyethylene glycol monoether revealed that CMC initially decrease until the minimum is reached and after that increase as the temperature is increased further. The increase of CMC is supposed to be due to the loss of water structure surrounding the hydrophobic group as the temperature increases. As temperature increases, this effect became preponderant and lead to the increase of CMC.21 3. Present Work This paper attempts to develop the more general QSPR model for the micellization of nonionic surfactants using molecular and fragment descriptors by (i) extending the number and diversity of the surfactants treated, (ii) testing our previous QSPR model9 on the new data, (iii) searching for better models, and (iv) relating the descriptors involved in the new model to the micellization phenomenon. 4. Data Set Our present data set (Table 1) consists of 162 nonionic surfactants. In addition to the 77 CMC values previously studied,9 we included 85 newly available CMCs all measured at 25 °C in water containing no additional salts, cosurfactants, or other additives. The current data set contains several classes

of linear ethoxylated alcohols and octylphenols, a large number of carbohydrate derivatives, and dimeric surfactants gathered from references 4, 9, 11, 19, 20, and 22-34. As previously,9 a logarithmic transformation of CMC (given in molar units) was used in order to improve the normal distribution of the experimental data. All nonionic surfactants experimental data are collected in Table 2, which provides (i) the code of the nonionic surfactants (second column), (ii) the negative logarithm of critical micelle concentration determined experimentally (third column), and (iii) the predicted -log CMC values from the QSPR models of eq 1, Table 4, and ANN (columns four-six). 5. Methodology The geometry of each anionic surfactant molecule was preoptimized using the molecular mechanics force field (MM+) as implemented in HyperChem 7.5.35 Further refinement of molecular geometries was obtained using the AM1 (Austin Model-1) semiempirical method36 with a gradient norm limit of 0.1 kcal/(mol Å). The optimized geometries were then used to calculate up to 700 molecular and fragment descriptors classified into (i) constitutional 38, (ii) topological 38, (iii) geometrical 14, (iv) charge-related 313, and (v) semiemprical 316, which were calculated using CODESSA-PRO software.37 The hydrophobic parameter log P and the molar refractivity defined for the whole molecules and for the hydrophobic fragments were calculated using the EPI Suite38 package and uploaded into the CODESSA storage. CODESSA-PRO has previously been used to correlate and predicted many physical properties and biological activities, including boiling points39 partition coefficients (log D),40 solvent scales,41 correlation of liquid viscosity with molecular structure for organic compounds,42 the binding energies for 1:1 complexation systems between various organic guest molecules and β-cyclodextrin,43 the in vitro minimum inhibitory concentration (MIC) of 3-aryloxazolidin-2-one antibacterials to inhibit growth of Staphylococcus aureus,44 partition coefficients of drugs between human breast milk and plasma,45 HIV-1 protease inhibitory activity of substituted tetrahydropyrimidinone,46 toxicities of polychlorodibenzofurans, polychlorodibenzo-1,4dioxins, and polychlorobiphenyls.47 Molecular fragments have repeatedly been used successfully in structure-property studies.48-51 Although fragment-based QSPRs have been criticized for using a larger number of variables compared to whole molecular descriptor-based approaches,48 our previous correlations of critical micelle concentrations using appropriate fragment descriptors that account for structural diversity9,10 and produced physico-chemically meaningful correlations with improved statistical characteristics. Statistical theory demonstrates that QSPR correlations utilizing two or more variables which intercorrelate with R2 higher than 0.6 are not reliable. The best multilinear regression (BMLR) algorithm42 was used to generate reliable QSPR models from an initial pool of orthogonal descriptors preselected by the ABC approach (see the description of the method below). The BMLR selects the best two, three, etc., parameter regression equations, based on the highest R2 value in a stepwise regression procedure.51 During the BMLR procedure the descriptor scales are normalized and centered automatically, and the final result is given in natural scales. Thus, the models generated provide the optimum property representation from a given descriptor pool. Two validation techniques were applied: leave-one-out crossvalidation and Y-scrambling.53 The corresponding squared cross-

Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9689 Table 1. Code, Name, and Chemical Structures for Nonionic Surfactants

9690 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 Table 1. Continued

validated correlation coefficient (R2cv) for all selected models is calculated automatically by the validation module implemented in the CODESSA PRO package. Nonlinear Artificial Neural Network (ANN) Modeling. The artificial neural network (ANN) algorithm used in this work is multiperceptron feed-forward based with back-propagation of the error. A typical architecture of such network is shown in Figure 1. The ANN method is more computationally intensive than linear regression since the nonlinear coefficients (weights and biases) are changed iteratively, requiring repeated evaluation of the network outputs. However, the greater mathematical flexibility found in ANNs often leads to models superior to those of MLR. Adjusting the weights and biases to fit target values is known as “training the network”. The increased mathematical flexibility of ANNs and the large number of adjustable parameters can overtrain the neural network and result in apparently good fits by chance. To avoid this situation, the data set needs to be split into training and validation subsets. The weights and biases are adjusted based on the rms (root-mean-squared) error of the training set members, and the rms error of the validation set is calculated periodically throughout the training. Overtraining is considered to occur when the rms error of the validation set begins to rise. The training process stops when the validation error is at its minimum, to provide a network that may be used with reasonable confidence for future predictions. Training the network is simply an optimization problem. One of the simplest methods for optimization of the weights during the training period is the delta rule. It propagates back the changes of error with respect to the weights on each iteration (epoch) so that the ANN uses supervised learning based on the experimental CMC’s. Once the ANN is trained, it can be used for QSPR predictions and analysis of novel surfactants. Because of the mathematical complexity of the ANN models, their physicochemical interpretation is usually difficult or nontrivial.

6. Results and Discussion QSAR Model Development. The best multilinear regression method (BMLR) was used to correlate the descriptors to the negative logarithm of CMC. The square of the correlation coefficient (R2), the cross-validated squared correlation coefficient (R2cv), the external predictive squared correlation coefficient (R2ext), the Fisher criterion (F), and the squared standard deviation (s2) were used as criteria for stability and robustness of the models. A small difference between R2 and R2cv denotes high predictive ability of the QSPR model. The regression coefficients and their errors are represented by X and ∆X, respectively. The “breaking point” rule54 was used to determine the optimal number of descriptors in the model. It is based on the significant improvement of R2 with respect to the number of consecutive descriptors in the model. An Estimation of the Predictive Power of Eq 1. The limited domain of applicability of eq 1 is demonstrated by the moderate quality of the predictions when it is applied to the new structurally diverse set of 85 surfactants (R2 ) 0.555). However, eightsurfactants(Sorb-Ol-3,bis(C8GA),bis(C12GA),bis(C12GH), bis(C8LA), bis(C12LA), C16-OCO-Glu, C18-OCO-Glu), all characterized by complex hydrophilic and hydrophobic domains,23 are identified as extreme outliers. After the removal of these extreme outliers (see Figure 2) the quality of prediction based on eq 1 was increased significantly (R2 ) 0.873). New QSPR Modeling of the Full Set of 162 Nonionic Surfactants. A modified QSPR approach55 aimed (i) to propose a general QSPR model including all compounds while still keeping the traditional “training/test set” separation in use and (ii) to minimize the possibility of “correlations by chance” by limiting the initial set of descriptors. It is consisted of the following steps: 1. All 162 data points of the initial data set were ordered in descending order of their -log CMC values. 2. By selection of every third point from the original data set three new subsets (conventionally denoted as A, B, and C)

Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9691 Table 2. Experimental and Predicted by Eq 1, Model of Table 4, and ANN -log CMC Valuesa -log CMC

-log CMC

pred

no.

structure code

model of Table 4 ANNAB+C no.

-log CMCexp

eq 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

C6EO3 C6EO4 C6EO5 C8EO4 C8EO5 C9EO8 C10EO5 C10EO7 C12EO1 C12EO14 C14EO9 C16EO8 C16EO10 C8PhEO30 C8PhEO40 C9PhEO2 C9PhEO5 C9PhEO12 H4EO3 F4EO3 H6EO3 F6EO3 C12AmEO3 C12AmEO6 C12AmEO9 F4C3NCOEO2 F4C3NCOEO3 F6C3NCOEO2 F6C3NCOEO3 F8C3NCOEO2 F8C3NCOEO3 Gly4Ol-1 Gly4La-1 Gly4 St-1 Gly6Ol-1 Gly6La-1 Gly6 St-1 Gly10Ol-1 Gly10La-1 Sorb-La-1 Sorb-Ol-1 Sorb-Ol-3 C8-Lactose

0.959 [31] 1.032 [12] 1.017 [12] 2.063 [12] 1.959 [28] 2.520 [11] 3.100 [11] 3.015 [12] 4.638 [12] 4.260 [19] 5.046 [19] 5.921 [12] 5.699 [23] 3.959 [4] 4.119 [4] 3.377 [32] 3.328 [32] 3.301 [32] 2.097 [28] 2.699 [28] 3.523 [28] 4.097 [28] 3.292 [24] 3.187 [24] 3.125 [24] 2.009 [27] 2.854 [27] 3.824 [27] 4.046 [27] 4.620 [27] 4.959 [27] 4.484 [22] 4.402 [22] 4.650 [22] 4.562 [22] 4.446 [22] 4.553 [22] 4.676 [22] 4.549 [22] 4.440 [22] 4.578 [22] 4.944 [22] 2.580 [33]

0.997 0.946 0.908 2.033 1.989 2.420 3.025 2.955 4.299 3.804 4.842 5.798 5.747 3.522 3.493 3.823 3.64 3.454 1.448 1.800 3.203 3.506 3.564 3.446 3.374 1.661 1.670 3.357 3.351 5.055 5.037 5.057 3.245 6.119 4.947 3.150 6.008 4.817 3.045 3.384 5.214 19.151** 0.891

1.372 1.400 1.434 2.453 2.479 3.015 3.325 3.396 3.905 4.295 4.719 5.172 5.232 4.171 4.481 3.355 3.400 3.535 2.821 2.857 4.165 4.139 3.395 3.386 3.362 3.000 2.902 3.927 3.978 4.965 5.264 3.946 3.757 5.329 4.076 3.861 5.260 4.334 4.146 3.599 4.079 5.529 2.213

1.090 1.168 1.410 2.254 2.067 2.839 3.176 3.264 4.346 4.273 4.735 5.279 5.587 4.079* 4.320* 3.365 3.364 3.452* 2.753* 2.749 4.164 4.125 3.321 3.292 3.258* 2.474 2.874 3.491* 4.022 4.857 5.138 4.175 3.768 5.125 4.313* 4.188 4.934 4.432* 4.396* 4.020 4.440 5.484* 2.447

44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111

C4E1 C4E6 C6E3 C6E6 C9E1 C8E3 C8E6 C8E9 C10E3 C10E4 C10E6 C10E8 C10E9 C11E8 C12E2 C12E3 C12E4 C12E5 C12E6 C12E7 C12E8 C12E9 C12E12 C13E8 C14E6 C14E8

0.009 [9] 0.110 [9] 1.000 [9] 1.164 [9] 2.310 [9] 2.125 [9] 2.004 [9] 1.886 [9] 3.222 [9] 3.167 [9] 3.046 [9] 3.000 [9] 2.886 [9] 3.523 [9] 4.481 [9] 4.284 [9] 4.194 [9] 4.194 [9] 4.060 [9] 4.086 [9] 4.000 [9] 4.000 [9] 3.854 [9] 4.569 [9] 5.000 [9] 5.046 [9]

0.184 -0.055 0.997 0.878 2.274 2.090 1.954 1.881 3.131 3.072 2.987 2.928 2.905 3.426 4.200 4.125 4.065 4.017 3.977 3.943 3.915 3.89 3.832 4.395 4.933 4.869

0.241 0.404 1.372 1.467 2.368 2.428 2.524 2.606 3.268 3.297 3.368 3.423 3.443 3.788 3.933 3.954 3.982 4.01 4.054 4.067 4.117 4.146 4.23 4.417 4.624 4.683

0.196 0.344* 1.321 1.350* 2.351 2.405 2.324* 2.255 3.068* 3.247 3.192* 3.290 3.416* 3.695 4.266 4.204 4.052 4.051* 4.056 4.37* 4.039 4.098 4.121* 4.500 4.655 4.799

125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

pred

structure code

model of Table 4 ANNAB+C

-log CMCexp

eq 1

C8-Lactitol C12-Lactose C12-Lactitol C16-Lactose C16-Lactitol n-C12-Mpyr C4-OCO-Xyl C5-OCO-Xyl C6-OCO-Xyl C7-OCO-Xyl C8-OCO-Xyl C9-OCO-Xyl C4-O-Xyl C5-O-Xyl C6-O-Xyl C7-O-Xyl C8-O-Xyl C9-O-Xyl C10-O-Xyl C11-O-Xyl C4-S-Xyl C5-S-Xyl C6-S-Xyl C8-OCO-Glu C12-OCO-Glu C16-OCO-Glu C18-OCO-Glu C12-O-Malt C12H25CONH(C2H4O)4H C8TGlupyr bis(C8GA) bis(C12GA) bis(C12GH) bis(C8LA) bis(C12LA) Glupyr-1 Glupyr-2 Glupyr-3 Glupyr-4 Glupyr-5 Glupyr-6 Glupyr-7

2.561 [33] 3.370 [33] 3.370 [33] 5.020 [33] 5.120 [33] 3.740 [23] 0.921 [34] 1.237 [34] 2.000 [34] 1.745 [34] 2.357 [34] 2.745 [34] 1.237 [34] 1.420 [34] 2.027 [34] 2.036 [34] 2.174 [34] 2.678 [34] 3.092 [34] 3.523 [34] 0.745 [34] 1.337 [34] 1.796 [34] 2.796 [34] 3.638 [34] 3.854 [34] 3.699 [34] 3.482 [29] 3.301 [29] 2.071 [26] 4.174 [25] 5.420 [25] 5.284 [25] 3.886 [25] 5.051 [25] 2.143 [30] 1.883 [30] 2.699 [30] 2.509 [30] 1.801 [30] 0.959 [30] 1.886 [30]

1.020 3.035 3.141 5.007 5.098 3.606 -0.384 0.068 0.640 1.215 1.777 2.323 -0.237 0.208 0.774 1.343 1.899 2.44 2.965 3.478 -0.016 0.411 0.961 1.665 3.778 5.720** 6.650** 3.035 3.488 1.933 8.332** 11.942** 11.888** 8.123** 11.727** 1.323 1.370 1.323 1.370 1.385 -0.384 1.323

2.015 3.786 3.586 4.860 4.679 3.897 0.397 0.842 1.434 1.981 2.470 2.895 0.348 0.809 1.408 1.961 2.453 2.898 3.288 3.644 0.359 0.824 1.420 2.437 3.903 4.929 5.345 3.519 3.463 2.406 4.426 5.146 5.138 4.484 4.714 2.177 2.122 2.043 2.018 2.081 0.335 2.123

2.101 3.757 3.579* 4.816* 4.772 3.845 0.684 1.036 1.773 1.910 2.412 2.298* 0.386 0.941 1.847 1.756* 2.387* 2.877* 3.273 3.630* 0.511 1.120* 1.544 2.596 3.775* 4.599 4.309 3.508 3.365 2.394 4.375 5.184 5.175 4.262 4.839* 2.162 2.092 2.107 2.023* 2.037* 0.671* 2.050*

3.523 [9] 3.481 [9] 0.049 [9] 1.016 [9] 1.670 [9] 2.547 [9] 2.526 [9] 2.237 [9] 2.638 [9] 2.638 [9] 3.745 [9] 4.886 [9] 1.602 [9] 2.658 [9] 3.721 [9] 3.222 [9] 3.620 [9] 3.469 [9] 5.292 [9] 3.585 [9] 2.299 [9] 2.193 [9] 3.398 [9] 3.292 [9] 3.611 [9] 3.413 [9]

3.713 3.692 0.423 0.791 1.614 2.476 2.395 2.123 2.775 2.810 3.761 4.723 1.777 2.853 3.875 3.177 3.606 3.035 4.885 3.488 2.464 2.416 3.543 3.47 3.417 3.943

3.672 3.71 0.996 1.047 1.604 2.097 2.186 2.378 3.206 3.208 3.973 4.581 2.396 3.229 3.9 3.898 4.11 3.703 4.2 3.366 2.41 2.148 3.309 3.221 3.049 3.39

3.566 3.684* 0.938 1.333* 1.240* 2.131* 2.225 2.313 3.202* 3.139 3.931 4.701 2.262 3.027 3.372* 3.583 3.796 3.686 4.964* 3.444 2.337* 2.177 3.369 3.043* 3.113 3.014*

New Set

Old Set C8PHE9 C8PHE10 IC4E6 IC6E6 IC8E6 IC10E6 IC10E9 C8GLYCER C10DIOL C11DIOL C12DIOL C15DIOL C8GLUC C10GLUC C12GLUC C12DELAC C12MALT C12SUCR C18SUCR C11CONEO C9CONE3E C9CONE4E C11CONE2 C11CONE3 C11CONE4 C12ALAE4

9692 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 Table 2. Continued -log CMC no.

structure code

-log CMCexp

112 113 114 115 116 117 118 119 120 121 122 123 124

C15E8 C16E6 C16E7 C16E9 C16E12 C8PHE1 C8PHE2 C8PHE3 C8PHE4 C8PHE5 C8PHE6 C8PHE7 C8PHE8

5.456 [9] 5.780 [9] 5.770 [9] 5.678 [9] 5.638 [9] 4.305 [9] 4.116 [9] 4.013 [9] 3.886 [9] 3.824 [9] 3.678 [9] 3.602 [9] 3.553 [9]

a

-log CMC

pred

eq 1

model of Table 4

ANNAB+C

5.336 5.864 5.829 5.771 5.707 4.122 4.022 3.945 3.886 3.838 3.838 3.765 3.737

4.942 5.113 5.142 5.202 5.291 3.502 3.488 3.517 3.538 3.564 3.717 3.625 3.638

5.226 5.272 5.340* 5.439 5.305* 3.910* 3.708 3.882* 3.691 3.730 3.700 3.921* 3.634

no.

structure code

-log CMCexp

151 152 153 154 155 156 157 158 159 160 161 162

C12GLYE4 C12SARE4 CF6SE2 CF6SE3 CF6SE5 CF6SE7 CF6SESE2 CF6SE2SE CF6SE3SE CF6CONE3 CF8CONE3 CF10CONE

3.474 [9] 3.533 [9] 4.602 [9] 4.553 [9] 4.432 [9] 4.319 [9] 4.638 [9] 4.585 [9] 4.469 [9] 3.260 [9] 4.921 [9] 6.523 [9]

pred

eq 1

model of Table 4

ANNAB+C

3.915 3.943 4.649 4.573 4.465 4.395 4.634 4.574 4.486 3.330 5.002 6.630

3.614 3.589 4.316 4.317 4.328 4.361 4.258 4.304 4.269 3.693 4.818 5.616

3.575 3.752* 4.318 4.388 4.091* 4.349 4.269* 4.325* 4.190* 3.568 4.849 6.076*

Note! The ANN test set compounds are marked with an asterisk. The surfactants marked with a double asterisk are outliers.

Figure 1. Feed-forward back-propagation neural network.

Figure 2. Plot of predicted vs experimental -log CMC values for new set (eight outliers removed) nonionic surfactants using eq 1.

were constructed. Thus, for each of the subsets the data distribution of the investigated property values is similar. 3. The three binary sum combinations A + B, A + C, and B + C were used to form the training subsets. 4. The standard QSAR modeling procedure including best multiple linear regression method (BMLR) was applied to the subsets obtained in step 3. 5. The “breaking point” restriction rule was used to determine the optimal number of descriptors of the generated models.

Figure 3. Number of descriptors used in the submodels vs R2.

6. The complementary parts to each of these three subsets (C, B, and A, respectively) were used as external validation data sets by considering their consistency. 7. All the descriptors that appeared in the obtained models of step 5 were tested to obtain a general model including all 162 surfactants from the initial data set. 8. The general model was again validated using classical internal cross-validation and scrambling procedures. QSPR models involving up to seven descriptors for the A + B, A + C, and B + C subsets were generated (step 4). The application of the “breaking point” rule (Figure 3) suggested that models with four descriptors would be optimal (see Table 3). At the next stage (step 7) only those descriptors listed in Table 3 were used to derive a general model for the whole data set including 162 surfactants. As for the submodels, the “breaking point” rule was used again for identification of the optimal number of descriptors allowed to enter the model (see Figure 4), and once again, a four-descriptor model was indicated. This model and its statistical parameters are shown in Table 4 and Figure 5. To examine the sensitivity of the proposed QSPR model to chance correlations, a Y-scrambling procedure was applied; i.e., the model was fitted to randomly reordered activity values and then compared with the one obtained for the actual activities. Twenty such randomizations were performed, which produced R2 ranging from 0.211 to 0.265 (average R2 ) 0.237). The

Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9693 Table 3. Statistical Characteristics of the Four-Descriptors Models for the A + B, A + C, and B + C Subsets ID

∆X

X

t test

training set: A + B; test set: C; R ) 0.872; R 2

0 1 2 3 4

-5.814 1.640 0.1835 0.9222 -1.239

0.5164 0.06894 0.01153 0.08963 0.1927

descriptors 2

cv

-11.26 23.78 15.92 10.29 -6.430

) 0.861; R

2

ext

) 0.895; F ) 175.78; s2 ) 0.236

intercept average complementary information content (order 2)a number of F atoms maximum Coulombic interaction for a C-C bonda number of double bondsa

training set: A + C; test set: B; R2 ) 0.911; R2cv ) 0.901; R2ext ) 0.843; F ) 263.89; s2 ) 0.165 0 1 2 3 4

-5.429 2.371 -1.965 8.265 -0.01106

0.3890 0.08754 0.1433 0.7242 0.0013

-13.96 27.08 -13.71 11.41 -8.231

intercept average complementary information content (order 2)a FNSA-2 fractional PNSA (PNSA-2/TMSA) [Zefirov’s PC] average bonding information content (order 1)a YZ shadow

training set: B + C; test set: A; R2 ) 0.884; R2cv ) 0.873; R2ext ) 0.856; F ) 196.19; s2 ) 0.212 0 1 2 3 4 a

-13.38 1.843 2.220 -4.012 13.81

2.267 0.06969 0.3116 0.6652 2.654

-5.901 26.44 7.124 -6.031 5.202

intercept average complementary information content (order 2)a average information content (order 0)a FPSA-1 fractional PPSA (PPSA-1/TMSA) [Zefirov’s PC] min (>0.1) bond order of a C atomb

For hydrophobic fragment. b For hydrophilic fragment.

Table 4. Statistical Characteristics of the General QSPR Model (R2 ) 0.888; R2cv ) 0.879; F ) 309.95; s2 ) 0.203)

a

ID

X

∆X

t test

descriptors

0 1 2 3 4

-4.270 1.781 2.893 -1.336 -0.009777

0.2867 0.05469 0.2408 0.1620 0.001272

-14.89 32.56 12.02 -8.246 -7.688

intercept average complementary information content (order 2)a average information content (order 0)a FNSA-2 fractional PNSA (PNSA-2/TMSA) [Zefirov’s PC] YZ shadow

For hydrophobic fragment.

substantial difference between the actual R2 and the averaged R2 from the scrambling procedure supports the stability of the model. The model of Table 4 contains two fragment descriptors concerning the hydrophobic fragment: the “average complementary information content (order 2)” and the “average information content (order 0)”. Despite the similarity of their formulation, these descriptors are highly orthogonal (R ) -0.309). The t test criterion was used to determine the descriptors’ significance, which is as follows: average complementary information content (order 2) > average information content (order 0) > FNSA-2 fractional PNSA (PNSA-2/TMSA) [Zefirov’s PC] > YZ shadow. The most important descriptor, “average complementary information content (order 2)”, is defined as a sum taken over all the atomic layers in the coordination sphere of a given atom. k

CIC ) log2 n- kIC k

k

IC )

ni

∑ n log

2

i)1

ni n

(2)

(3)

where n is the total number of atoms, ni the number of atoms in the ith class, and k is the number of classes. The division of the atoms in classes is based on the coordination sphere defined for the molecule. For example, for the first-order index the atoms fall in the same class if they are of the same type and valence, while for the second order they need to have the same number of neighbors.52 The positive regression coefficient sign implies that surfactants characterized by large, complex hydrophobic fragments will likely possess low CMCs. The “average information content (order 0)” descriptor is defined for the hydrophobic fragment of the surfactant and can be calculated similarly to eq 3. The positive regression coef-

ficient implies that the bigger the descriptor value, the lower the CMC of nonionic surfactants. Its presence in the model might be related to the importance of the steric hindrance in the hydrophobic area in the micelle state. The “FNSA-2 fractional PNSA [Zefirov’s PC]” descriptor is defined by the ratio of the “total charge weighted partial negatively charged molecular surface area” to the “total molecular surface area” and reflects the negative charge redistribution within the molecule (a whole molecule descriptor). Its appearance in the model is probably connected to the presence of heteroatoms (in both the tails and the heads) and their possibility to participate in donor-acceptor or dipole-dipole interactions, thus effectively increasing the surfactant solubility (and CMC) in the aqueous phase. By the orientation of the molecule in the space along the axes of inertia the areas of the shadows of the molecule are projected on the XY, XZ, and YZ planes.56 The normalized shadow areas are calculated by applying 2D-square grid on the molecular projection and by summation of the areas of squares overlapped with a projection. It is usually stated that the “shadow area” type of descriptors are related to the molecular volume (bulk). The unexpected negative sign of the descriptor coefficient (leading to increased CMCs with the increase of YZ shadow descriptor) lead us to analyze the dependence between “YZ shadow” values and the molecular volume which, surprisingly, were found almost orthogonal (R2 ) 0.251). ANN Modeling. A sensitivity analysis performed by building 1-1-1 NN models was aimed to select a good starting set of descriptors related to the CMC. The descriptors characterized with lowest error at the output were selected for further examination. The visual inspection of the scatter plots showing the variability of the CMCs in respect to the descriptors lead to a combination of four descriptors: “average complementary information content (order 2)” and “average information content (order 1)”, both defined

9694 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008

2

Figure 4. Number of descriptors used in the submodels vs R .

Figure 6. Predicted vs experimental -log CMC values (A + B training set and C test set case is shown). Table 5. ANN Results for the Training and Test Subsets training set A+B A+C B+C average

R2tr

std dev

0.946 0.971 0.951 0.956

0.309 0.232 0.297 0.279

test set

R2ext

C B A

0.947 0.938 0.942 0.942

linear model is relatively easy to interpret from a physicochemical point of view revealing an insight regarding the micellization phenomenon, whereas the complexity of the ANN procedure does not allow a direct interpretation of the molecular descriptors. 7. Conclusions

Figure 5. Predicted vs experimental -log CMC values of the general model.

for the hydrophobic fragment, “FNSA-2 fractional PNSA (PNSA2/TMSA) [Zefirov’s PC]”, and “YZ shadow”. These descriptors were used as an input vectors for the ANN. To ensure a similar distribution of the data for the training and test subsets, the ABC separation method (as described above) was applied. The A + B, A + C, and B + C subsets defined above were used to train the network. To avoid overtraining, the rms of the respective validations sets was monitored during the training process. When the rms for the validation sets started to increase, it was taken as a stopping criterion for the training of the ANN at a given epoch. To define the ANN topology, we constructed several ANN architectures varying the number of the neurons in the hidden layer from 2 to 6. Thus, it was found that the 4-5-1 architecture (i.e., 4 neurons in the input layer, 5 neurons in the hidden layer, and 1 neuron in the output) generalizes the best and avoids overparameterization of the model. The ANN modeling results are shown in Table 5 and Figure 6 (“A + B” training set and “C” test set case is shown). A comparison between the descriptors in Table 4 and the ANN model shows that they are almost identical with the exception of the “average information content” descriptor, which in the ANN model is first order. A general comparison of the multilinear and nonlinear models shows that BMLR and ANN models provide results of similar quality. However, the multi-

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ReceiVed for reView June 17, 2008 ReVised manuscript receiVed August 26, 2008 Accepted September 10, 2008 IE800954K