6626
Langmuir 1997, 13, 6626-6632
Effects of Cationic Micelles on Rate of Intramolecular General Base-Catalyzed Ethanediolysis of Ionized Phenyl Salicylate (PS-) M. Niyaz Khan* and Zainudin Arifin Department of Chemistry, Universiti Malaya, 50603 Kuala Lumpur, Malaysia Received January 31, 1997. In Final Form: September 10, 1997X The plot of pseudo-first-order rate constants (kobs) for ethanediolysis of ionized phenyl salicylate (PS-) in the absence of cetyltrimethylammonium bromide (CTABr) vs percent (v/v) ethanediol shows a continuous decrease in slope with the increase in ethanediol content from 15 to 80% (v/v). However, the presence of 0.03 M CTABr causes a continuous increase in the slope of the plot of kobs versus % (v/v) ethanediol within the ethanediol content range 15-80% (v/v). At constant temperature and [HOCH2CH2OH]T (total concentration of ethanediol), pseudo-first-order rate constants (kobs) reveal a monotonic decrease with the increase in [CTABr]T (total concentration of CTABr). These results are explained in terms of the pseudophase model of micelles. Pseudo-first-order rate constants (kMROH) for ethanediolysis of PS- in the micellar pseudophase show a continuous increase in the slope of the plot of kMROH versus % (v/v) ethanediol [range 15-50% (v/v)] at 30 °C. Similar results are obtained at different temperatures ranging from 25 to 45 °C.
Introduction Monohydric alcohols generally disrupt the formation of normal micelles.1 Complete destruction of cetyltrimethylammonium bromide (CTABr) micelles was observed in mixed aqueous-organic solvents containing 10-15% (v/ v) alkanols (such as methanol, ethanol, n-propanol, and 2-propanol) as organic cosolvents.2 Polyhydric alcohols, on the other hand, allow the formation of micelles over the entire range of aqueous solutions and also in the pure liquid, but the cmc values are significantly larger in these organic solvents than that in pure water for a particular surfactant.2,3 In a recent study on the effects of CTABr micelles on methanolysis of ionized phenyl salicylate (PS-), the existence of micelles could be kinetically detected in CH3OH-H2O solvents containing 2% (v/v) CH3CN, 2 × 10-4 M PS-, and a methanol content < 60% (v/v) at 30 °C.4 The formation of micelles in glycerol and ethanediol has been studied by a few investigators partly because of the biological importance of these polyhydric alcohols.1-3 The presence of CTABr micelles was observed in mixed ethanediol-water solvents containing even up to 99% (w/ w) ethanediol.1 Systematic kinetic studies on the effects of micelles on rates of organic reactions in aqueousalkanol solvents have been carried out by a few investigators.1,5 Although a large amount of kinetic work on the effects of micelles on rates of intermolecular organic reactions has been carried out during the last three to four decades,6 very few kinetic studies on the effects of micelles on rates of intramolecular reactions appear to have been carried out.7 The effects of anionic micelles on intramolecular general base (IGB) catalysis in hydrolysis,8 X Abstract published in Advance ACS Abstracts, November 1, 1997.
(1) Bunton, C. A.; Gan, L.-H.; Hamed, F. H.; Moffatt, J. R. J. Phys. Chem. 1983, 87, 336 and references cited therein. (2) Ionescu, L. G.; Romanesco, L. S.; Nome, F. Sarmisegetuza Research Group. In Surfactants in Solution; Mittal, K. L., Lindaman, B., Eds.; Plenum Press: New York, 1984; Vol 2, p 789. (3) Ionescu, L. G.; Fung, D. S. J. Chem. Soc., Faraday Trans. 1 1981, 77, 2907. (4) Khan, M. N.; Arifin, Z. Langmuir 1996, 12, 261. (5) Bertoncini, C. R. A.; Nome, F. J. Phys. Chem. 1990, 94, 5875. Rubio, D. A. R.; Zanette, D.; Nome, F.; Bunton, C. A. Langmuir 1994, 10, 1151, 1155. (6) Bunton, C. A.; Savelli, C. Adv. Phys. Org. Chem. 1986, 22, 213. (7) Cerichelli, G.; Mancini, G.; Luchetti, L.; Savelli, G.; Bunton, C. A. J. Phys. Org. Chem. 1991, 4, 71. Cerichelli, G.; Luchetti, L.; Mancini, G.; Savelli, G.; Bunton, C. A. J. Colloid Interface Sci. 1993, 160, 85.
S0743-7463(97)00097-8 CCC: $14.00
alkanolysis,9 and aminolysis10 of PS- have been studied in aqueous solvents containing e2% (v/v) CH3CN. Ethanediol is known to allow micelle formation while methanol inhibits it.1 The present study was carried out with the following aims: (i) to determine the effects of CTABr micelles on rates of ethanediolysis of PS-, (ii) to determine the kinetic cmc (critical micelle concentration) of CTABr at different contents of ethanediol in the mixed ethanediol-water solvents, (iii) to study the structural behavior of ethanediol in the presence of CTABr micelles, and (iv) to compare the kinetic data with those reported for methanolysis of PS- under essentially similar experimental conditions.4 The observed results and the probable explanations are described in this paper. Experimental Section Materials. Reagent grade chemicals such as ethanediol, phenyl salicylate, cetyltrimethylammonium bromide (CTABr), and acetonitrile were obtained from BDH, Fluka, and Aldrich. All other chemicals used were also of reagent grade. The stock solutions of phenyl salicylate were prepared in acetonitrile. Kinetic Measurements. The rates of cleavage of ionized phenyl salicylate (PS-), in mixed solvents containing 0.01 M NaOH, 2% (v/v) CH3CN, and varying contents of ethanediol and water, were studied spectrophotometrically by monitoring the appearance of product, the phenolate ion, at 290 nm. The details of the kinetic procedure are described elsewhere.11 The absorbance versus time data obeyed a first-order rate law under the experimental conditions of the entire kinetic runs. This showed that the rate of hydrolysis of 2-hydroxyethyl salicylate was negligible compared to the rate of ethanediolysis of PS-. The details of the data analysis are the same as described elsewhere.11 The observed values of the molar extinction coefficients of reaction mixtures containing products as well as authentic ionized alkyl salicylate, AlS- (such as ionized methyl salicylate), phenolate ion, and salicylate ion revealed the presence of nearly 85% 2-hydroxyethyl salicylate, 15% salicylate ion, and 100% phenolate ion.
Results (a) Cleavage of PS- in HOCH2CH2OH-H2O Solvents in the Absence and Presence of a Constant (8) Khan, M. N.; Na’aliya, J.; Dahiru, M. J. Chem. Res., Synop. 1988, 116; J. Chem. Res., Miniprint 1988, 1168. Khan, M. N. J. Chem. Soc., Perkin Trans. 2 1990, 445. (9) Khan, M. N. Int. J. Chem. Kinet. 1991, 23, 837. (10) Khan, M. N.; Dahiru, M.; Na’aliya, J. J. Chem. Soc., Perkin Trans. 2 1989, 623. (11) Khan, M. N. J. Chem. Soc., Perkin Trans. 2 1989, 199.
© 1997 American Chemical Society
Ethanediolysis of Ionized Phenyl Salicylate
Langmuir, Vol. 13, No. 25, 1997 6627
Figure 1. Effect of ethanediol (ROH) content on the pseudofirst-order rate constants (kobs) for ethanediolysis of ionized phenyl salicylate (PS-) at 0.0 M CTABr (O), 0.03 M CTABr (0), and 0.09 M CTABr (×).
Concentration of CTABr. In order to discover the effect of the presence of a constant concentration of CTABr on the kobs versus % (v/v) HOCH2CH2OH profile, several kinetic runs were carried out in the absence and presence of 0.03 and 0.09 M CTABr at 30 °C in mixed HOCH2CH2OH-H2O solvents containing 0.01 M NaOH and 2% (v/v) CH3CN. The ethanediol content ranges covered in these reactions were 15-90% (v/v) at [CTABr] ) 0, 1580% (v/v) at [CTABr] ) 0.03 M, and 15-60% (v/v) at [CTABr] ) 0.09 M. Pseudo-first-order rate constants (kobs) are shown graphically in Figure 1. (b) Effects of [CTABr] on the Rate of Cleavage of PS- at a Constant Content of HOCH2CH2OH in Mixed HOCH2CH2OH-H2O Solvents. The rates of cleavage of PS- were studied at different [CTABr] in mixed HOCH2CH2OH-H2O solvents containing a constant content of ethanediol, 0.01 M NaOH, and 2% (v/v) CH3CN at a constant temperature. These observations were obtained at various contents of ethanediol [15-50% (v/v)] and at different temperatures (25-45 °C). Pseudo-firstorder rate constants (kobs) for some of these observations are shown in Figure 2.
Figure 2. Plots showing the dependence of the pseudo-firstorder rate constants (kobs) for the reaction of ROH (where ROH ) HOCH2CH2OH) with PS- at 15% (v/v) ROH and 30 °C (O), 20% (v/v) ROH and 30 °C (4), 20% (v/v) ROH and 35 °C (3), 20% (v/v) ROH and 40 °C (0), and 30% (v/v) ROH and 40 °C (]). Solid lines are drawn through the calculated points using eq 2 and the parameters kMROH and K1 as listed in Tables 1 and 2.
a region in the pH-rate profiles where rates are independent of pH. Under such conditions, it has been shown that the rate of alkanolysis or hydrolysis of phenyl salicylate involves alkanol (ROH) or H2O and ionized phenyl salicylate (PS-) as the reactants. The rates of hydrolysis13 and alkanolysis14 of PS-, under such conditions, have been shown to increase by nearly 106-fold due to the occurrence of intramolecular general base (IGB) catalysis through an intramolecular intimate ion-pair intermediate (T).13,15 Thus, under the present experimental conditions, the reactants are HOCH2CH2OH and PS- in the ethanediolysis of phenyl salicylate and the rates of the reactions between HOCH2CH2O- and PSand between, HO- and PS- are negligible.
Discussion The values of the molar extinction coefficients at 290 nm (290) of PS- and PSH (nonionized phenyl salicylate) are nearly 800 and 1700 M-1 cm-1, respectively. The values of the initial absorbance (Aobs°, i.e. absorbance at the reaction time t ) 0) of the reaction mixtures containing 2 × 10-4 M phenyl salicylate, 0.01 M NaOH, and 2% (v/v) CH3CN were found to be unchanged with the change in the contents of ethanediol from 15 to 90% (v/v) in mixed aqueous solvents. These absorbance values were also unaffected due to the presence of e0.09 M CTABr. These results show the presence of nearly 100% ionized form of phenyl salicylate in the reaction mixtures of the entire kinetic runs carried out in this study. As described elsewhere,12 the rates of alkanolysis and hydrolysis of phenyl salicylate at 0.01 M NaOH constitute (12) Khan, M. N. Int. J. Chem. Kinet. 1987, 19, 757.
(a) Analysis of Observed Data: kobs versus % (v/v) HOCH2CH2OH in the Absence and Presence of a Constant [CTABr]. Pseudo-first-order rate constants (kobs), obtained in the absence of CTABr, appear to increase (13) Khan, M. N.; Gambo, S. K. Int. J. Chem. Kinet. 1985, 17, 419. (14) Khan, M. N.; Audu, A. A. J. Phys. Org. Chem. 1992, 5, 129. (15) Khan, M. N. J. Phys. Chem. 1988, 92, 6273.
6628 Langmuir, Vol. 13, No. 25, 1997
Khan and Arifin
sharply with the increase in [HOCH2CH2OH]T (where [HOCH2CH2OH]T represents the total concentration of ethanediol) in the water-rich region and become almost independent of [HOCH2CH2OH]T in the ethanediol-rich region of the mixed aqueous solvents (Figure 1). These observations can be easily explained in terms of selfassociation of ethanediol molecules as described in detail elsewhere.4 This approach leads to eq 1
kobs )
k[HOCH2CH2OH]T 1 + 2KA[HOCH2CH2OH]T
(1)
where k represents the second-order rate constant for the reaction of HOCH2CH2OH with PS- and KA is the association constant for dimerization of ethanediol, i.e. KA ) [(HOCH2CH2OH)2]/[HOCH2CH2OH].2 It may be worthwhile to mention that the change in the content of ethanediol in the mixed aqueous solvents changes both [HOCH2CH2OH]T and the dielectric constant () of the medium simultaneously. The change in may be argued to affect both k and KA in eq 1. But reasonably good fitting of the observed data to eq 1 indicates that both k and KA are kinetically insensitive to the change in within the ethanediol content range of the present study. If the change in medium properties has a significant effect on k and KA, then it is highly unlikely for the observed data (kobs versus [HOCH2CH2OH]T) to fit to eq 1. Pseudo-first-order rate constants (kobs), obtained in the absence of CTABr, were found to fit to eq 1 reasonably well, and the nonlinear least-squares calculated values of k and KA are (1.74 ( 0.06) × 10-3 and (37.5 ( 3.0) × 10-3 M-1, respectively. The value of k for HOCH2CH2OH is only slightly smaller than k ()2.12 × 10-3 s-1) for CH3OH and slightly more than 2.5-fold larger than k ()6.3 × 10-4 M-1 s-1) for ethanol12 while the value of KA for HOCH2CH2OH is slightly more than 2-fold larger than KA () 15.6 × 10-3 M-1) for CH3OH4 and nearly 2-fold smaller than KA ()75.5 × 10-3 M-1) for ethanol12 under similar experimental conditions. Ethanediol is known to form both intra- and intermolecular hydrogen bonds16 whereas methanol and ethanol molecules cannot form intramolecular hydrogen bonds. The formation of intramolecular hydrogen bonds would reduce KA.17 In terms of the statistical factor (2 for ethanediol and 1 for ethanol), KA for ethanediol should be higher than that for ethanol. Thus, the lower value of KA for ethanediol than that for ethanol may partly be attributed to the possible existence of intramolecular hydrogen bonding in ethanediol in mixed aqueous solvents. Since the cleavage of PS- in aqueous-ethanediol solvents occurs via parallel reactions involving hydrolysis and ethanediolysis, kobs ) k1 + k2, where k1 and k2 represent the pseudo-first-order rate constants for ethanediolysis and hydrolysis of PS-, respectively. However, under the experimental conditions of the present study, k1/k2 g5, and hence k2 may be neglected compared with k1. It may be noted that the increase in the contents of ethanediol in mixed aqueous solvents must increase k1 (due to an increase in [HOCH2CH2OH]) and decrease k2 {due to decrease in [H2O] and in the dielectric constant () of the reaction medium, ) 78.4 at 25 °C for water18 and ) 37.7 at 25 °C for ethanediol19 }. A reasonably good fit of kobs to eq 1, as evident from the plot of Figure 1, where the (16) Ueda, M.; Urahata, T.; Katyam, A.; Kuroki, N. Sen’i Gakkaishi 1977, 32, 301. Beaudoin, J. L. J. Chim. Phys. 1977, 74, 268. (17) We thank one of the reviewers for drawing our attention toward this point. (18) Akhter, M. S. Colloids Surf. A 1997, 121, 103. (19) Weast, R. C. Handbook of Chemistry and Physics, 63rd ed.; CRC Press, Inc.: Boca Raton, FL, 1982; p E-52.
Scheme 1
solid line is drawn through the calculated rate constants (kcalcd), and from the maximum residual error [)100(kobs - kcalcd)/kobs] of 4%, obtained at 50% (v/v) HOCH2CH2OH, supports the conclusion that k2 is negligible compared with k1, resulting in kobs ≈ k1. Pseudo-first-order rate constants (kobs), obtained in the presence of 0.03 and 0.09 M CTABr, did not fit eq 1 (Figure 1). A linear increase in kobs with the increase in percent (v/v) HOCH2CH2OH may be seen until nearly 25% (v/v) ethanediol (Figure 1). An increase in ethanediol content beyond 25% (v/v) caused a sharp nonlinear increase in kobs until the ethanediol content became nearly 70% (v/v). Similar observations were obtained in the methanolysis of PS- under essentially identical experimental conditions.4 The values of kobs, obtained at 80% (v/v) ethanediol, were almost the same in the absence and presence of 0.03 M CTABr. The rate constants (kobs) for methanolysis of PS- were found to be unaffected due to the presence of 0.03 M CTABr at methanol contents > 65% (v/v).4 The lower values of kobs at ethanediol content’s of < 80% (v/v) in the presence of 0.03 and 0.09 M CTABr compared to those in the absence of CTABr are the consequence of the presence of micelles. It may be concluded that probably either there were no more micelles or there was no more micellar incorporation of PS- in the solvents containing 2 × 10-4 M PS-, 0.03 M CTABr, 0.01 M NaOH, 2% (v/v) CH3CN, and >80% (v/v) ethanediol in mixed aqueous solvents at 30 °C. The values of kobs, obtained within 15-25% (v/v) ethanediol at 0.03 and 0.09 M CTABr, gave the value of the apparent second-order rate constant (k) as (2.60 ( 0.07) × 10-4 M-1 s-1. The ratio k (at [CTABr] ) 0)/k(at [CTABr] ) 0.03 and 0.09 M) turned out to be 6.7, which is significantly larger than the corresponding value of 4.5 for methanolysis of PS- at 30 °C.4 This shows that the rate-decreasing effect of CTABr micelles is larger in ethanediolysis than in methanolysis of PS-. (b) Analysis of Observed Data: kobs versus [CTABr]T at a Constant Percent (v/v) HOCH2CH2OH. The increase in [CTABr]T (total CTABr concentration) from 0.0 to 0.09 M decreased kobs by many fold at different contents of ethanediol and temperatures. As discussed elsewhere,4 the inhibitory effects of [CTABr]T on kobs are due to CTABr micellar incorporation of PS-. The rate of ethanediolysis of PS- at a constant temperature and content of ethanediol in mixed aqueous solvents may be explained in terms of the pseudophase model of the micelle,20 as described by Scheme 1. The subscripts NM and M in Scheme 1 represent the nonmicellar pseudophase and the micellar pseudophase, respectively. In Scheme 1, PS-M represents micelle bound PS-, K1 is the binding constant for PS-NM (free anionic ester) and Dn (CTABr micelle), ROH represents ethanediol, and kNMROH and kMROH stand for the pseudo-first-order rate constants for ethanediolysis of PS- in the nonmicellar pseudophase and micellar pseudophase, respectively. The reaction steps for the hydrolysis of PS-NM and PS-M are not included in Scheme 1 because the rate constants (20) Menger, F. M.; Portnoy, C. A. J. Am. Chem. Soc. 1967, 89, 4698.
Ethanediolysis of Ionized Phenyl Salicylate
Langmuir, Vol. 13, No. 25, 1997 6629
Table 1. Effect of Ethanediol on Pseudo-First-Order Rate Constants (kMROH) for Ethanediolysis of PS- in the Micellar Pseudophase, Binding Constants (K1), and the Critical Micelle Concentration (cmc) of CTABr in Mixed H2O-HOCH2CH2OH Solvents at 30 °Ca ROH,b % (v/v)
104 cmc,c M
104kMROH,d s-1
K1,d M-1
Re
no. of runs
15 20 25 30 40 50
1.7 (1.6)f 2.4 (2.4) 2.8 (2.7) 4.6 (4.3) 13.0 (13.1) 35.0 (34.0)
6.36 ( 0.28g 7.95 ( 0.83 9.38 ( 2.28 12.6 ( 2.7 20.6 ( 1.7 28.4 ( 1.0
7450 ( 600g 6960 ( 730 3540 ( 810 2480 ( 520 1740 ( 230 1150 ( 100
5.8 6.1 6.1 5.6 3.9 3.4
17 13 13 14 13 13
[phenyl salicylate]0 ) 2 × 10-4 M; [NaOH] ) 0.01 M; λ ) 290 nm; the reaction mixture for each kinetic run contained 2% (v/v) CH3CN, and the total concentration of CTABr ranged from 0.0 to 0.09 M. b ROH ) HOCH2CH2OH. c Best kinetic cmc obtained as described in the text. d Calculated from eq 2. e R ) kNMROH/kMROH. f Parenthesized values were obtained by the graphical procedure of Broxton. g Error limits are standard deviations.
Table 2. Effect of Temperature on Pseudo-First-Order Rate Constants (kMROH) for Ethanediolysis of PS- in the Micellar Pseudophase, Binding Constants (K1), and the Critical Micelle Concentration (cmc) of CTABr at Constant Content of HOCH2CH2OH in Mixed H2O-HOCH2CH2OH Solventsa ROH,b temp, % (v/v) °C 104cmcc, M 20
30
a
for these reactions are negligible compared to the corresponding rate constants kNMROH and kMROH. A sceptic might argue that the actual concentration of hydroxide ions in the micellar pseudophase ([-OHM]) may be significantly higher than that in the nonmicellar pseudophase ([-OHNM]) due to competition between hydroxide ions and counterions (Br-) for micellar incorporation. Although ion exchange between -OHNM and Br-M cannot be ruled out, the concentration of -OHM in the micellar region where PS-M molecules exist could not be sufficient to make the reaction between -OHM and PS-M or -OHCH2CH2OHM and PS-M significant compared with that between HOCH2CH2OHM and PS-M. This conclusion is based upon the fact that the pseudo-first-order rate constants for hydrolysis of ionized phenyl salicylate were found to be unchanged with the increase in [NaOH] from 0.01 to 0.04 M in aqueous solvent containing 2% (v/v) CH3CN and 0.0015 M CTABr (under such conditions, the fraction of micellized PS- molecules is 0.90).21 Similarly, the pseudo-first-order rate constants for methanolysis of PS- were found to be independent of [NaOH] within the range 0.005-0.050 M at several [CTABr]T values ranging from 0.0 to 0.01 M.22 The observed rate law {rate ) kobs[PS-]T (where [PS-]T ) [PS-NM] + [PS-M])} and Scheme 1 can lead to eq 2, where the concentration of micelles [Dn] ) [CTABr]T cmc (critical micelle concentration). ROH
kobs )
kNM
+ kM
ROH
K1[Dn]
1 + K1[Dn]
(2)
In order to calculate the unknown parameters, kMROH and K1, from eq 2, the value of the cmc under specific kinetic conditions is required. The values of the kinetic cmc under different kinetic conditions as determined by both the iterative technique4 and the graphical technique of Broxton23 are summarized in Tables 1 and 2. The cmc values, obtained by these two techniques, are not significantly different from each other. The generally accepted value of the cmc of aqueous CTABr is 9 × 10-4 M in the absence of any added solute at 30 °C.6 The presence of (1-5) × 10-5 M p-nitrophenyl diphenyl phosphate (pNPDPP) in aqueous CTABr produced the cmc as (2-3) × 10-4 M at 0.05 M -OH.1 Similar observations have been reported by many investigators.24-27 The value of the cmc of CTABr (21) Khan, M. N.; Arifin, Z. J. Colloid Interface Sci. 1996, 180, 9. (22) Unpublished observations. (23) Broxton, T. J.; Christie, J. R.; Dole, A. J. J. Phys. Org. Chem. 1994, 7, 437 and references therein.
40
25 30 35 40 45 25 30 35 40 45 25 30 35 40 45h
2.3 (2.1)f 2.4 (2.4) 2.7 (2.8) 3.8 (3.7) 4.8 (4.5) 4.1 (4.0) 4.6 (4.3) 5.9 (6.0) 8.0 (8.4) 12.0 (11.0) 13.6 (12.6) 13.5 (13.1) 18.8 (18.0) 24.0 (24.0) 26.0 (26.4)
104kMROHd s-1
K1,d M-1
no. of runs
Re
5.82 ( 0.4g 7140 ( 480g 5.8 7.95 ( 0.83 6960 ( 730 6.1 11.7 ( 2.5 4180 ( 630 5.9 17.8 ( 2.7 3510 ( 420 5.1 26.9 ( 5.6 3060 ( 570 4.6 7.76 ( 1.36 4330 ( 560 6.1 12.6 ( 2.7 2480 ( 520 5.6 18.2 ( 3.6 2180 ( 350 5.1 26.8 ( 5.0 1920 ( 340 5.0 43.7 ( 4.8 2210 ( 300 3.9 13.3 ( 0.3 3270 ( 100 4.3 20.6 ( 1.7 1740 ( 230 3.9 29.6 ( 3.0 1420 ( 190 4.0 42.7 ( 7.4 1020 ( 200 3.8 58.8 ( 6.4 671 ( 75 3.8
a -gNotations have the same meanings as in Table 1. concentration of CTABr range: 0.0-0.075 M.
13 13 13 15 12 13 14 13 12 12 13 13 13 14 14 h
Total
turned out to be 8 × 10-5 M at 30 °C in aqueous solvent containing 2% (v/v) CH3CN, 2 × 10-4 M PS-, and 0.01 M NaOH.21 The value of the cmc ()3.5 × 10-3 M) at 50% (v/v) ethanediol (Table 1) may be compared with the cmc ()6.0 × 10-3 M) obtained at 25 °C in mixed waterethanediol solvent containing 50% (v/v) ethanediol, 0.01 M NaOH, and (1-5) × 10-5 M pNPDPP.1 The larger value of the cmc ()6.0 × 10-3 M) in the presence of (1-5) × 10-5 M pNPDPP compared with the cmc ()3.5 × 10-3 M) in the presence of 2 × 10-4 M PS- may be attributed to both the amount and nature of the solutes (pNPDPP and PS-). The plot of ln(cmc) versus % (v/v) ROH (where R ) HOCH2CH2 and CH3) as shown in Figure 3 shows that the stability of the micelle in pure and mixed H2O-ROH solvents varies in the order H2O > HOCH2CH2OH > CH3OH. The plots in Figure 3 appear to be linear within the ROH content range of 10 or 15 to 40 or 50% (v/v). Attempts were made to fit the observed data to the empirical equation (eq 3). The linear least squares technique was
ln(cmc) ) ln(cmc)0 + Ψ ROH
(3)
used to calculate the empirical parameters, ln(cmc)0 and Ψ, from eq 3, and the results obtained are shown in Table 3. The values of (cmc)0 at different temperatures in mixed aqueous solvents containing methanol or ethanediol as organic cosolvent are slightly lower than the corresponding cmc values obtained in the absence of ROH (cmc ) 8 × 10-5 M at 37 °C21). This shows that eq 3 is not obeyed by the values of cmc obtained at
