Prediction of critical micelle concentration of cationic surfactants using connectivity indices

Anna Mozrzymas Bozenna Rzycka-Roszak Relationship for predicting Logcmc for cationic surfactants having chloride as counterion from only molecular connectivity indices was found. It is suggested that the index 0 includes some information about hydrophobicity while indices 4 pc and 4 pc include some information about hydrophilicity of the cationic surfactants studied. The structures of 23 compounds used for the correlation are quite diverse. 1 Introduction cmc (mM) [Ref.] 61 [13], 21 [14], 4.5 [13], 1.4, 0.35 [15] 220 [18] 12,4 [18] 2 Data Table 1 Experimental values of cmc of compounds study Name of Compound N -alkyl-N , N , N -trimethylammonium chlorides (n = 10, 12, 14, 16, 18) N -dodecyl-N , N -dimethylammonium chloride dodecylamine hydrochlorides (n = 8, 10, 12) betaine chloride alkyl esters (n = 10, 12, 14, 16) N -dodecyl-N -methylpiperidinium chloride N -dodecyl-N -methylmorpholinium chloride N -alkyl-pyridinium chlorides (n = 12, 16, 18) N -alkoxycarbonylmethyl-N alkyl-piperidinium chlorides (n = 8, 10, 12) N -octylnicotinamide chloride N -dodecylnicotinamide chloride The data set was chosen to contain only cationic surfactants, especially quaternary ammonium chloride salts. Literature data for cmc are given in Table 1. All values of cmc were measured in pure water at 25C. The chemical structures of the surfactants taken into consideration and their abbreviations are shown in Fig. 1. 3 Method j =1 i=1 Fig. 1 Chemical structures of the investigated surfactants and their abbreviations. j=1 i=1 4 Results and discussions In the process of searching for the relationships between cmc and topological descriptors we used, just as in the previous paper [12], ten indices: five connectivity indices (from zeroth to fourth order) and five valence connectivity indices (from zeroth to fourth order). These indices were calculated for the compounds studied using Eqs. 13. The calculated connectivity indices are listed in Table 2. Using a stepwise method we have obtained three models. In each model we start our correlation procedure with one index, i.e. the first step is common for each model and it is presented in Table 3. We see that the best correlations in the first step are for the relationships containing the first-order valence connectivity index 1 and the zeroth-order valence connectivity index 0 . These indices define first steps for Model 1 and Models 2 and 3, respectively. In the first model the search for the best equation consists of three steps including the first step described above. The result of all correlations is presented in Table 4. The best correlation in the first step in Model 1 is for the relationship containing the index 1 , and we get the following formula: Logcmc = 1.339 0.402 1 3.2 Correlation formula Table 2 The connectivity indices and the experimental Logcmc values 9.268 7.303 0.927 1.436 13.814 9.268 7.303 0.927 1.436 13.515 8.454 7.487 1.849 0.961 12.887 9.454 8.194 1.849 0.961 14.301 10.454 8.901 1.849 0.961 15.715 11.454 9.608 1.849 0.961 17.129 8.932 6.475 0.204 0.433 12.165 10.932 7.889 0.204 0.433 14.993 11.932 8.596 0.204 0.433 16.407 6.561 5.786 1.561 0.75 10.864 7.561 6.493 1.561 0.75 12.278 8.561 7.200 1.561 0.75 13.692 9.561 7.907 1.561 0.75 15.106 10.561 8.614 1.561 0.75 16.521 9.162 7.591 1.215 1.696 13.009 10.162 8.298 1.215 1.696 14.423 11.162 9.005 1.215 1.696 15.837 7.270 5.364 0.408 0.289 11.355 4.414 2.768 0 0 6.9498 5.414 3.475 0 0 8.364 6.414 4.182 0 0 9.778 8.236 6.593 0.704 1.425 10.745 10.236 8.007 0.704 1.425 13.573 9.268 7.303 0.927 1.436 1.699 8.845 6.855 0.927 1.436 1.678 7.611 6.433 1.620 0.601 1.745 8.611 7.140 1.620 0.601 2.260 9.611 7.847 1.620 0.601 2.721 10.611 8.554 1.620 0.601 3.481 7.971 5.417 0.118 0.219 1.824 9.971 6.831 0.118 0.219 3.046 10.971 7.538 0.118 0.219 3.620 6.561 5.786 1.561 0.75 1.215 7.561 6.493 1.561 0.75 1.678 8.561 7.200 1.561 0.75 2.347 9.561 7.907 1.561 0.75 2.854 10.561 8.614 1.561 0.75 3.461 8.318 6.536 0.986 1.367 0.928 9.318 7.243 0.986 1.367 1.678 10.318 7.950 0.986 1.367 2.260 7.270 5.364 0.408 0.289 1.801 4.414 2.768 0 0 0.699 5.414 3.475 0 0 1.319 6.414 4.182 0 0 1.870 6.625 4.582 0.26 0.45 0.658 8.625 5.996 0.26 0.45 1.906 Table 3 The values of the correlation coefficients for first step Connectivity index Table 4 The values of the correlation coefficients for each step in the Model 1 Connectivity index Calculated Logcmc In the third step the 0 index (zeroth-order valence connectivity index) was added (see Table 4) and the corresponding equation is the following: At this step the process of searching for the best relationship was ended because the further additions of other indices did not change the correlation coefficient significantly. The process of selecting the best relationship for Model 1 is illustrated in Figs. 2, 3, 4. When we choose in the first step the zeroth-order valence connectivity index 0 , we will obtain Model 2 and Model 3. The second step in these models is common and it is presented in Table 5. Now we can see that the best correlations in the second step are for the relationships containing the fourth-order connectivity index 4 pc (Model 2) and the second-order connectivity index 2 or fourth-order valence connectivity index 4 pc (Model 3). In second model the search for the best equation consists of two steps including the steps presented in Tables 3 and 5. The result of these correlations is presented in Table 6. The obtained formula for the first step in Model 2 is: Logcmc = 1.427 0.262 0 = 0.974, Calculated Logcmc Calculated Logcmc Fig. 4 Scatter plot of the calculated Logcmc versus the experimental Logcmc (r F = 818.46, s = 0.137). Step 3 (final) Connectivity index Correlation coefficient Table 6 The values of the correlation coefficients for the steps in the Model 2 Connectivity index 0 STEP 1 STEP 2 0.118 0.812 0.815 0.987 0.817 Calculated Logcmc Fig. 5 Scatter plot of the calculated Logcmc versus the experimental Logcmc (r F = 787.82, s = 0.14). Step 2 (final) Table 7 The values of the correlation coefficients for each step in the Model 3 0.744 0.731 0.654 0.255 0.118 0.812 0.815 0.736 0.286 0.068 0.856 0.826 0.941 0.842 0.987 0.817 0.833 0.826 0.942 0.990 0.965 0.993 0.943 0.988 0.948 0.956 0.943 Calculated Logcmc The best correlation in third step in Model 3 is for the relationship which, in addition to the previous one, contains the index 2 (second-order connectivity index) and the formula for Logcmc becomes: The process of selecting the best relationship for Model 3 is illustrated in Figs. 6, 7 8. It is worth noting that Model 2 and Model 3 show the best correlations among all the formulae containing two and three indices respectively. The specification of all models is listed in Table 8. The calculated logarithm of cmc values using the Models 13 and experimental Logcmc for the surfractants studied are listed in Table 9. From the previous calculation and from Table 9 it follows that Model 3 is t (...truncated)