Indian Journal of Chemistry Vol. 38A, February 1999, pp. J JJ-J 18

Papers

Correlation of critical micelle concentration of nonionic surfactants with molecular descriptors

Minati Kuanar, Saroj K Kuanar & Bijay K Mishra*

Centre of Studies in Surface Science and Technology, Department of Chemistry, Sambalpur University, Jyoti Vihar 768 019. Indi a

Received 13 January 1998; revised 25 September 1998

The critical micelle concentration (CMC) values of three sets. of fortysix nonionic surfactants with oxyethylene groups as the hydrophilic group have been subjected to quantitative structure-property relationships (QSPR) studies. The hydrophobic groups have varied number of carbon atoms with linear, octyl phenol and branched alkyl chain derivatives. Molecular descriptors derived from the chemical graphs have been used for the studies. A general regression model has been proposed to predict the CMC of non ionic surfactants. Plots related to principal components ofmoleclilar descriptors resulted in the ordination of non ionic surfactants.

Hydrophile-lipophile balance in a surfactant molecule plays an important role in micelle formation . The hydrophilic group of the amphiphile molecule favours water solubility while its hydrophobic group forces it to remain away from water. This stress in the amphiphilic molecule in aqueous medium leads to the formation of a thermodynamically stable aggregate . Hydrophobic groups are mostly aliphatic or aromatic hydrocarbon moieties while hydrophilic groups are ei ther ionic or polar. The balance in the hydrophobic and hydrophilic characteristics of these two groups determines the CMC at which the amphiphiles aggregate. CMC is the most important solution property of a surface-active compound. CMC determines the adsorption of surfactants at an interface . This adsorption phenomenon characteristically reduces the interfacial tension and, hence, is of great interest to technologists in many processes such as emulsification, foaming, wetting, solubilization, detergency, particle suspension and surface coatings. The importance of CMC has led to development of various methods for its measurement for a wide range of surfactants and under different solvent conditions .

Several attempts have been made to obtain quantitative structure-CMC relationship for prediction of CMC. A linear relationship has been found between the logarithin of CMC and the number of alkane carbon atoms for homologous series l

,

Log CMC=A-Bn ... (I)

where A and B are empirical regression coefficients. Ravey et al. 2 have found similar relationships between

the CMC and the number of ethylene oxide residues . Becher3 has found a very good relationship between log CMC and the carbon number, n, with the ethylene oxide number, m, for linear alkylethoxylate surfactants. Ravey et al. 2 have improved the correlation by including a nonlinear term in the form of the product of the alkane carbon number and the ethylene oxide number, n x m, Log CMC=A + Bn + Cm + Dnm . . . (2) However, some QSPR studies4.6 have been carried out on other surface phenomena. Stanton and Jurs4 have utilized the charged partial surface area (CPSA) descriptor to correlate surface tension of organic molecules . Employing CPSA descriptors, they have developed a six parameter model (R2=O.908, F=39) for a set of 31 organic molecules. Recently, Katritzky el aC have developed a general prediction methodology, coded into software (CODESSA: comprehensive descriptors for structural and statistical analysis), and successfully employed it for the prediction of a variety of physical properties of compounds. They have employed topological descriptors, which reflect structural topological characteristics of the molecule. In a recent paper Hubier et al. 8 have used the CODESSA program for the calculation of descriptors and have applied it for prediction of CMC of some non ionic surfactants. They have studied a diverse set of 77 non ionic surfactants using descriptors of hydrophilic and hydrophobic fragments of surfactants together with ad hoc molecular descriptors.

In the present paper we have utilized molecular connectivity parameters, information content para-

114 INDIAN J CHEM, SEC. A, FEBRUAR Y 1999

Table I--Observed log CMC values (25°C), ad hoc and graph theoret ica l molecular descriptors o f 46 nonionic surfactants

Surfactants Observed logCMC

C4EI C4E6 C6E3 C6E6

C8EI C8E3 C8E6 C8E9 C IOE3 C IOE4 ( IOE6

C IOE8 C IOE9 C II E8 C I2E2 C I2E3 C I2 E4 C I2 E5 C I2 E6 C I2E7 C I2E8 C I2E9 C I2E I2 C 13 E8 C I4 E6 C I4E8 C I5 E8 C I6E6 C I6E7 C 1 6 1 ~9

C I6E I2 C8PhEI C8PhE2 C8Ph E3

'8PhE4 C8 Ph E5 C8PhE6 C8PhE7 C8PhE8 C8PhE9 C8PhE I0 IC4E6 IC6E6 1(8126

IC IOE6 IC IOE9

- 0.009 - 0 .11 0 - 1.000 - 1.1 64 -2.3 10 - 2. 125 -2.004

- 1.886 -3.222

-3 .167 - 3.046 -3 .000 -2.886 - 3.523 - 4.48 1 - 4.284 - 4. 194

-4 . 194 - 4.060 - 4.086 - 4 .000 - 4.000 ·-3.854 -4.569 - 5.000 - 5.046 -5.456 -5 .780 -5.770 - 5.678

-5 .638 - 4.305 - 4.116 - 4.0 13 - 3.886 - 3.824 - 3.678 - 3.602 - 3.553 -3. 523 -3.481 -0.049 ':'1.01 6

- 1.670 -2.547 -2.526

n

4 4 6 6 8 8 8 8

10 10 10 10 10 II 12 12 12 12 12 12 12 12 12 13 14 14 15 16 16 16 16

8 8 8 8 8 8 8 8 8 8 4 6 8

10 10

m

I 6 3 6 I

3 6 9

3 4 6 8 9. 8 2 3 4 5 6 7 8 9

12 8 6 8 8 6 7 9

12

I 2 3 4 5 6 7 8 9

10 6 6 6 6 9

I o o o o o o o o o o o o o o o

meters and ad hoc descriptors for fortysix nonionic surfactants for the prediction of criti cal micelle concentration.

Materials and Methods Dala Base

The CMC values have been obtained for three

o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o

I o o o o o

3.9 14 3. 101 11 .4 1 8.487 7.9 14 6.255

12.4 1 9.487 5.9 14 5.10 1 8.964 7.255

13.41 10.49 17.9 1 13.72 9.9 14 8.255

11 .-1 1 9.333 14 .41 11 .49 17.4 1 13.64 18 .9 1 14.72 17.9 1 14. 14 18.4 1 14 .64 10.9 1 9.255 12.4 1 10.33 13 .9 1 11.41 15.4 1 12.49 16.9 1 13.56 18.4 1 14.64 19.9 1 15.72 24.4 1 18.95 18.91 15.1 4 16.4 1 13.49 19.41 15 .64 19.9 1 16.14 17.4 1 14.49 18.9 1 15 .56 21.91 17.72 26.4 1 20.95

8.152 6.588 9 .744 7.665

11.24 8.742 l2. 74 9 .820 14 .24 10.90 15 .74 11.97 17.24 13.05 18.74 14 .13 20.24 15.2 1 21.74 16.28 11 .27 8.343 12.27 9.343 13.27 10.34 14.27 11.34 18.77 14 .58

IC S IC

1.996 0.4408 1.76 1 0 .3020 1.856 0.3443 1.78 1 0 .2980 1.778 0.3469 1.8 18 0 .3256

1.52 1 0 .2490 1.733 0 .2669 1.776 0 .3086 1.779 0 .2999 1.765 0.2834 1.745 0.2694 1.734 0 .2633 1.74 1 0.2669 1.733 0 .2632 I. 734 0 .2935 1.747 0 .2879 1.750 0 .28 18 1.748 0.2757 1.743 0 .2698 1.736 0 .2643 1.729 0.259 1 1.705 0 2456 1.73 1 0.26 17 1.753 0.2798 1. 725 0 .2590 l. 7 18 0 .2564 l. 736 0.2655 1.710 0 .2575 1.710 0 .2502 1.699 0.240 I 2.284 0.4 184 2.290 0.4037 2.266 0 .3868 2.232 0 .3707 2. 196 0 .3560 2. 16 1 0 .3428 2. 128 0 .3 311 2.096 0.3206 2.067 0 .3 111 2.040 0.3026 1.76 1 0 .3020 1.844 0 .3086 1.858 0.3042 1.852 0.2973 1.80 I 0. 2736

C IC

2.494 4072 3.536 4. 196

3.309 3 .767 3 .702 4 .759 3.979 4. 152 4.463 4.73 1 4.85 1 4.782 4.783 4. 173 4.3 19 4.460 4.592 4.7 16 4.833 4.943 5.237 4.884 5.327 4.933 4.982 4 .521 4.933 5.123 5.377 3. 175 3.382 3.592 3.790 3.974 4. 143 4.299 4 .443 4.577 4.701 4.072 4. 133 4.250 4. 377 4.784

different sets of amphiphiles from literatureS and these are given in Table I. The reported CMC values are in aqueous medium and at 25°C.

Elhoxylaled linear alcohols

CnEm : CnH2n+IO-(C2 H40)m- H Example :

"

.,.

,

KUANAR e/ aL CORRELATION OF CMC WITH MOLECULAR DESCRIPTORS 115

C4E I: Butyl ethylene oxide : C4H90-{C2~O)-H

Ethoxylated octyl phenols

C8PhEm : CSHI70- (C6H40 )-(C2H40 )m- H

Example:

C9PhE I: p-t-Octyl phenyl ethylene oxide:

CsH 1 70-(P.)C6~O-(C2~O)!-H

Ethoxylated branched alcohols

ICnEm : (CH3)2 CH-(CH2)n-O-(C2~O)m-H

Example:

IC4E6: Propyl 2-methyl hexaethoxylate: (CH3)2CH-CH2-0-(C2H40)6-H The molecular descriptors considered in the present analysis are of two types, ad hoc molecular descriptors (number of carbon atoms in the hydrophobic dpmain, n, and number of oxyethylene group in the hydrophilic domain, m) and structural descriptors (graph theoretical parameters).

Graph theoretical parameters Grapb theoretical parameters (which encode

information ahout the molecular structure) are obta~ned from the s imple chemical graph of a molecule. We have considered two types of graph .heoretical molecular descriptors having generic differences.

Molecular connectivity indices (IX and IX v) The first-order connectivity index, IX,9 and the

first-order connectivity index, lXV, 10 are obtained by using Eqs (3) and (4) respectively.

IX = I (5;5)-112 . . . (3)

. . . (4)

where 8; and ~ represent the count of non-hydrogen a-bond electrons contributed by atoms. i and j and,

8' ~ and 5 j represent the count of all non-hydrogen

valence electrons contriDuted by atoms i and j in the molecular graph.

. . . (5)

z ~ represents the number of valence electrons; h;

denotes the number of hydrogen atoms attached to the particular atom.

Information theoretic topological indices (IC< SIC and CIC)

To obtain these parameters a total molecular graph (where hydrogen is not suppressed) is initially constructed for the molecule. For each vertex (atom), partition coordinates are assigned according to the va lence and bonding characteristics of atom with its immediate neighbourhood . The co':ordinates bear the information of types of bonds between the concerned atom and the adjacent atom. The co-ordinates are then, classified according to their partition co­ordinates . From the probabi lity of the class and the number of atoms in the molecular graph, IC is calculated by using Shannon ' s formula ," ,12

... (6)

where p;=n;ln is the probability of class i, n, is the number of members in class i, n is the number of atoms in the molecule. Structural information content (S IC) and complementary information content (C IC) are obtained by using Eqs (7) and (8), 12

SIC=IC/log2n , . . (7)

, .. (8)

Ad hoc descriptors, sLlch as number of carbon atoms, ' n', 'number of oxyethylene units , om ' , and their derivatives 'n x m' , have been used in the quantitative structure-property relationship. Three dummy descriptors have been used to differentiate three classes of surfactants. One or zero value is assi gned fo r the presence or absence of a particular class of hydrophobic group in the structure. Hb" Hb2 or Hb] is one for the presence of normal alkyl or octyl phenol or isoalkyl grollp respectively. Otherwi se, the value is zero. The indices obtained for fortysix surfactant molecules are listed in Table I.

Principal component analysis

Principal component analysis (PCA) IS a multivariate statistical analysis for estimating the inherent dimensionality of a set of orthogonal principal components from the linear combination of the existing variables. Orthogonal parameters have found successful applications in quantitative structure-property relationships. Every principal component is a linear combination of the starting variables. The new set is built in order to explain the maximum amount of variance. The first principal component accounts for maximum amount of variance in the data; and the second principal component accounts for a maximum amount of the

116 INDIAN J CHEM, SEC. A, FEBRUARY 1999

Table 2---Cross correlation matrix of log CMC and the molecu lar descriptors

Log n m nm Hb l Hb2 HbJ IX IXV IC SIC CIC CMC

Log 1.00 CMC n -0.87 1.00 m -0.24 0.38 1.00 nm - 0.60 0.76 0.86 1.00 Hbl -0. 15 0.46 0.06 0.31 1.00 Hb2 -0. 15 -0.33 -0. 12 -0.26 - 0.76 Hb3 -0.43 -0.26 0.06 - 0. 11 -0.50 IX -0.57 0.63 0.90 0.90 0.09 IXV -0.62 0.70 0.87 0.94 0.15 IC -0.00 -0.44 -0.34 -0.44 -0.78 SIC -0.33 -0.64 - 0.70 -0.74 -0.52 CIC -0.54 0.71 0.82 0.86 0.29

0 B u 0

::;: - 1 00 U 0 CI

.2 -2 ,po

" 0 0 .,

-3 ~8 ;;; :;

<b/ 0 -4 .. U

-5 '0

-6 .B0

-6 -5 -4 -3 -2 - 1 a Obsenled log CMC

Fig. I-Scatter plot of the calculated versus observed log CMC of fortysix non ionic surfactants

remaining variance in the data . The cross correlation matrix of all the molecular descriptors used to derive the principal com ponent is given in Table 2.

Method of optimization In the present study six ad hoc molecular

descriptors and five graph theoretical molecular descriptors have been used to generate the basic regression modeL By using multipl e regress ion analysis (MRA) the multiple correlation coefficient (R\ F value, and the residual mean square (RMS) va lues are obtained for the regress ion modeL The increase in R2 and F va lues and decrea:>e in RMS va lues are the indicators of optimized regress ion modeL T he ' t ' values obtai ned for each variable in a regression mode l is an indicator of the appropriateness of incorporation of the variable in the regression modeL High ' t' value suggests goodness of fit of the variable in the regress ion model. In the present work a successive exclusion of variable (SEV) technique has been suggested where, from the basic

1.00 -0.18 -0.05 -0.09

0.92 0.61

-0.31

1.00 -0.09 -0. 112 -0.05 -0.04 -0.04

c '" c o c.

3

g 0 u

~ - 1 U -= 0. -2

" c 8 -3 .. VI

-4

1.00 0.99

-0.27 - 0.72

0.90

o

-6

1.00 -0.32 1.00 -0.76 0.82 1.00

0.92 -0.50 -0.87 1.00

o 0 o 0

o o

o

o o

-3 o 3 6

F irs! Principal Com ponen! (PC ,)

Fig. 2-Plot of first principal component aga inst the seco nd principal componen t

regression model , successive regress ion models have been derived by exclusion of variab le having the mll11mUm ' t ' va lue_ The resultant stati stica l parameters like R2, F and RMS have been ana lysed. The regression model with max imum F and minimum RMS va lue is considered for the optimi zed regress ion model. For the statistical calculations, SAS software package was used.

Results and Discussion

As the micell ization process is mostly due to hydrophob ic interaction, the parameter, re lated to structura l variation due to change in the number of carbon atoms in the alkyl chain has a re latively good correlation with the critical mi ce ll e concentration. An analysis of the cross corre lation matrix (Tab le 2) reveal s a high corre lation of ' n' with CMC values (r =

0.8746) . T he other variables wi th correlation coefficient values more than 0_5 are ' nm ', IX,IX", and

..

-,

•

KUANAR et al. : CORRELATION OF CMC WITH MOLECULAR DESCRIPTORS 117

Tabfe 3----Optimization of regression model for predicting critical micellar concentration (CMC) of 46 nonionic surfactants

Basic regression model Explanatory variable: Ten molecular descriptors R2=0.995, F=698.6, RIvIS=0.0145 Successive Exclusion ofYariables

tmin Excluded R2 F RMS variable

-0.67 Hbl 0.9950 788.3 0.01428

-0.84 IC 0.9949 894.0 0.1416

-1.20 nm 0.9947 1010 0.01433 1.26 SIC 0.9944 1160 0.01454 2.62 n 0.9934 1208 0.0 1674

-2.08 CIC 0.9927 1396 0.0 1810 4.10 m 0.9897 1349 0.02491

C IC. When all variables are taken together for multiple regression analysis a correlation coefficient value of 0.9950 with F value 698 .6 is obtained. In the process of anaJysis, out of three dummy descriptors, Hb, is automatically excluded due to multicoli­nearityl 3. Analyzing the 't' values, subsequent regression models were derived by exclud ing variables with minimum 't' value. Table 3 shows a stepwise exclusion of variables for deriving subsequent regression model for the prediction of CMC for fortysix non ionic surfactants. With excluding variables, the F value went on increasing and after a maximum the value started decreasing. The equation with maximum F value is considered as the optimized regression model (9) for calculating the CMC values. Interestingly, in the optimized regression model, the variable 'n' is not included, though it has recorded maximum ' r ' value whi le correlating with log CMC (Table 3).

Log CMC=(0.09368±0.02286)m-(2 .29300 ± 0.07082)Hb2+(2.43280±0.0718) IX-(3.42670 ±O.08163) IXV+(O.71088±O.07276) .... (9)

R2=0.9927, F= 1396 and RMS=0.OI81

The ' m' value refers to the hydrophilicity of the surfactant. With increasing m value, the hydrophilicity increases and solubi lity of the surfactant in water increases which leads to increase in CMC. Thi'S proposition gets support from the positive coefficient of the descriptor "m' in Eq. (9). Similarly, IX has also a positive contribution to the CMC, i.e., with increasing IX value, the CMC value Increases. The IX value has been calculated considering the total molecular graph (both hydrophobic and hydrophilic) and thus it contributes to the size of the molecule as a whole. The negative

coefficient for Hb2 parameter indicates the decrease in CMC due to presence of branching in the hydrophobic group. Similarly IXV also experiences a negative coefficient and thus makes a negative contribution to the CMC.

The plot of calculated log CMC values using Eq. (9) against observed log CMC values is shown in Fig. I , which reflects the applicability of regression model for predicting CMC values of non ionic surfactants.

Orthogonal parameters, derived from the basi s set of variab les have been app lied successfully to explain quantitative structure-property relationship of amino acids l4. With a view to getting better regression model, the principal components of all the variables have been derived by using principa l component ana lysis . The resultant cumulative variance reveals that, the initial five principal components (PCs) can explain 98 .8% of the total variance. However, when a ll the five PCs were used to generate an optimized regression model , the corresponding stati stical parameters were found to be less significant than those in the original basic regression model.

Kuanar and Mishra have used princ ipal components in classifying organic solvents and am ino acids I5.16

• In the present study the first principal components were plotted against the second principal components of all the fortysix surfactants. When the plot (Fig. 2) is analysed, three di stinct linear plots are obtained separating the three c lasses of surfactants. The C4E I is found to lie c lose to the two different classes, i.e. , CnEm and ICnEm .

Generally, principal components are mathematical constructs and do not embody any direct phys ical meaning l7. However, the first and second princi pal components have been successfully used for ordi nation of the surfactants. The graph theoretical parameters of the surfactants are found to have major contribution in predicting CMC of the surfactants .

Acknowledgement One of the authors (MK) thanks the CS iR, New

Delhi, for the award of a Senior Research Fellowship. The authors thank Prof. G.B. Behera for hi s critical suggestions during the preparation of the manuscript.

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