Water−N,N-Dimethylformamide Alkyltrimethylammonium Bromide

Mar 15, 2005 - (MBS) and bromide ions was studied in water-DMF .... quently, the micellar ionization degree is calculated from the ratios of the slope...
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Langmuir 2005, 21, 3303-3310

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Water-N,N-Dimethylformamide Alkyltrimethylammonium Bromide Micellar Solutions: Thermodynamic, Structural, and Kinetic Studies Marı´a del Mar Graciani, Marı´a Mun˜oz, Amalia Rodrı´guez, and Maria Luisa Moya´* Departamento de Quı´mica Fı´sica, Universidad de Sevilla, C/ Profesor Garcı´a Gonza´ lez s/n, 41012 Sevilla, Spain Received December 21, 2004. In Final Form: February 3, 2005 Various amounts of N,N-dimethylformamide (DMF) with the weight percentage of DMF varying within the range 0-20, were added to aqueous micellar solutions of hexadecyl-, tetradecyl-, and dodecyltrimethylammonium bromides (CTAB, TTAB, and DTAB, respectively). Information about changes in the critical micelle concentrations, in the micellar ionization degrees, in the aggregation numbers, and in the polarity of the interfacial region of micelles upon changing the weight percent of DMF was obtained through conductivity and fluorescence measurements. Surface tension measurements permitted the estimation of the Gordon parameter of the water-DMF mixtures. The thermodynamic and structural changes provoked by the addition of DMF to the cationic micellar solutions were evidenced through the micellar kinetic effects observed in the reaction methyl 4-nitrobenzenesulfonate + Br-, investigated in the water-DMF cationic micellar solutions. The pseudophase kinetic model was adequate to quantitatively rationalize the dependence of the observed rate constant on surfactant concentration as well as on the weight percent of DMF.

Introduction Surfactants are widely used in both industry and everyday life, and the properties of surfactant aqueous solutions have received considerable attention. Recently, the aggregation phenomenon of amphiphiles in nonaqueous media has been the scope of many researchers due to the increasing use of these materials in applications which require water-free or water-poor media.1 The solvents used in these studies are strongly polar with water resembling properties, such as ethylene glycol, formamide, or glycerol.2-9 Most of the investigations carried out focused mainly on two aspects: the requirement from a solvent for amphiphilic assembly and what the structural properties of the aggregates formed in these media are. To obtain the answers, a frequent approach used is the gradual replacement of water with other polar solvents, as this allows one to explore a wide range of polarities. Several studies of surfactant aggregation have been carried out using this method.10-20 In relation to the physical properties of the solvent needed for the amphiphilic aggregation * To whom correspondence should be addressed. E-mail: moya@ us.es. Homepage: www.us.es/coloides. (1) (a) Holmberg, K.; Laughlin, R. Curr. Opin. Colloid Interface Sci. 1997, 2, 453. (b) Wa¨rheim, T. Curr. Opin. Colloid Interface Sci. 1997, 2, 472. (2) Ionescu, L. G.; Fung, D. S. J. Chem. Soc., Faraday Trans. 1 1981, 77, 2907. (3) Wa¨rheim, T.; Jo¨nsson, A. J. Colloid Interface Sci. 1988, 125, 627. (4) Jonstro¨ner, M.; Sjo¨ber, M.; Wa¨rnheim, T. J. Phys. Chem. 1990, 94, 7549. (5) Gharibi, H.; Palepu, R. Bloor, D. M.; May, D. G.; Wyn-Jones, E. Langmuir 1992, 8, 782. (6) Sjo¨ber, M.; Silveston, R.; Kronberg, B. Langmuir 1993, 9, 973. (7) Ceglie, A.; Colafemmina, G., Della Monica, M.; Olsson, U.; Jonson, B. Langmuir 1993, 9, 1449. (8) Nagarajan, R.; Wang, C.-C. J. Colloid Interface Sci. 1996, 178, 471. (9) Ylihautala, M.; Vaara, J.; Ingman, P.; Diehl, P. J. Phys. Chem. B 1997, 101, 32. (10) Backlund, S.; Bergenstahl, B.; Molander, O.; Wa¨rheim, T. J. Colloid Interface Sci. 1989, 131, 393. (11) Sjo¨berg, M.; Heriksson, U.; Wa¨rheim, T. Langmuir 1990, 6, 1205.

to occur, all of these solvents have high cohesive energies and dielectric constants and considerable hydrogen bonding ability.11 Evans et al.21 have suggested that the hydrogen bonding ability is a prerequisite for micellization to happen. In the present work, the micellization of alkyltrimethylammonium bromides in mixtures of water-N,N-dimethylformamide has been studied, with the surfactants being dodecyl-, tetradecyl-, and hexadecyltrimethylammonium bromides. The ability of N,N-dimethylformamide (DMF) to bring about the self-association of conventional amphiphiles can be characterized by its Gordon parameter,22 G ) γ/V h 1/3, where γ is the solvent surface tension and V h its molar volume. For DMF, the Gordon parameter is equal to 0.83 J m-3. Since G values above 1.0-1.2 J m-3 seem to be required for self-association of the micellar type, micellization is not expected to occur in pure DMF. However, in this work, the water-DMF mixtures investigated are water rich, with the weight percentage of DMF ranging from 0 to 20, and the values of the Gordon (12) Palepu, R.; Gharibi, H.; Bloor, D. M.; Wyn-Jones, E. Langmuir 1993, 9, 110. (13) Callagham, A.; Doyle, R.; Alexander, E.; Palepu, R. Langmuir 1993, 9, 3422. (14) Gracie, A.; Turner, D.; Palepu, R. Can. J. Chem. 1996, 74, 1616. (15) Penfold, J.; Staples, E.; Tucker, I.; Cummins, P. J. Colloid Interface Sci. 1997, 185, 424. (16) (a) Carnero Ruiz, C. Colloid Polym. Sci. 1999, 277, 701. (b) Carnero Ruiz, C. J. Colloid Interface Sci. 2000, 221, 262. (c) Carnero Ruiz, C.; Molina-Bolı´var, J. A.; Aguiar, J.; MacIsaac, G.; Moroze, S.; Palepu, R. Langmuir 2001, 17, 6831. (17) Hazra, P.; Chakrabarty, D.; Sarkar, N. Langmuir 2002, 18, 7872. (18) Rodrı´guez, A.; Graciani, M. M.; Mun˜oz, M.; Moya´, M. L. Langmuir 2003, 19, 7206. (19) Graciani, M. M.; Rodrı´guez, A.; Mun˜oz, M.; Moya´, M. L. Langmuir 2003, 19, 8685. (20) Rodrı´guez, A.; Mun˜oz, M.; Graciani, M. M.; Ferna´ndez Pacho´n, S.; Moya´, M. L. Langmuir 2004, 20, 9945. (21) Evans, D. F.; Miller, D. D. In Organised Solutions. Surfactants in Science and Technology; Friberg, S. E., Lindman, B, Eds.; Dekker: New York, 1992; p 33. (22) Ramadan, M.; Evans, D. F.; Lumry, R.; Philson, S. J. Phys. Chem. 1985, 89, 3405.

10.1021/la046833a CCC: $30.25 © 2005 American Chemical Society Published on Web 03/15/2005

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parameter corresponding to these mixtures are well above 1.2 J m-3 (see below). Therefore, the formation of the cationic micellar aggregates occurs in these mixtures and thermodynamic and structural information about the water-DMF micellar solutions can be obtained by using various experimental techniques. The critical micelle concentrations (cmc’s) and the micellar ionization degrees, R, of the water-DMF cationic surfactant solutions were estimated through conductivity measurements. The II/IIII pyrene ratio23 was used to get information on the polarity of the interfacial region. Fluorescence quenching of pyrene by N-hexadecylpyridinium chloride allows us to estimate the aggregation numbers of the micelles present in the water-DMF micellar solutions studied.23 Solvent surface tensions corresponding to the homogeneous water-DMF mixtures were measured in order to estimate the Gordon parameter of these mixtures. The structural and thermodynamic changes provoked by the increase in the amount of DMF in the mixture could be evidenced through variations in the reaction rates of appropriate micelle-modified processes taking place in the water-DMF micellar solutions when the surfactant concentration changes. With this in mind, the substitution (SN2) reaction between methyl 4-nitrobenzenesulfonate (MBS) and bromide ions was studied in water-DMF dodecyltrimethylammonium bromide (DTAB), tetradecyltrimethylammonium bromide (TTAB), and hexadecyltrimethylammonium bromide (CTAB) micellar solutions. The mechanism of this reaction is well-known,24 and it is not necessary to add bromide ions to the micellar reaction media, since the bromide counterions of the surfactant molecules react with the organic substrate. This means that no changes in the characteristics of the micellar pseudophase are expected due to the presence of the reactants (the organic substrate concentration is low). Therefore, sctructural information obtained for the waterDMF micellar solutions can be used with confidence in the rationalization of the kinetic micellar effects. It is worth noting that kinetic studies in water-organic solvent micellar solutions are few.18-20,25 All experiments were made at 298.2 K. Experimental Section Materials. Methyl 4-nitrobenzenesulfonate was from Fluka. DTAB, TTAB, and CTAB were from Fluka and used as received. N,N-Dimethylformamide was from Fluka and used without further purification. Pyrene was obtained from Aldrich and was purified before use. Hexadecylpyridinium chloride was from Fluka. Conductivity Measurements. Conductivity was measured with a Crison microCM 2201 conductimeter connected to a waterflow thermostat maintained at 298.2 ( 0.1 K. The conductimeter was calibrated with KCl solutions of the appropriate concentration range. Surface Tension Measurements. The solvent surface tensions were measured with a du Nou¨y tensiometer (KSV 703, Finland). The tensiometer was connected to a water-flow cryostat maintained at 298.2 ( 0.1 K. Prior to each measurement, the ring was heated briefly by holding it above a Bunsen burner until glowing. The vessel was cleaned by using chromic sulfuric acid, boiled in distilled water, and then flamed with a Bunsen burner before use. The precision in the measurements was (1 mN m-1. (23) Kalyanasundaram, K. Photochemistry in Microheterogeneous Systems; Academic Press: New York, 1987. (24) (a) Ingold, C. K. Structure and Mechanisms in Organic Chemistry, 2nd ed; Cornell University Press: Ithaca, NY, 1969. (b) Lowry, T. H.; Richardon, K. S. Mechanism and Theory in Organic Chemistry, 3rd ed.; Harper and Row: New York, 1987. (c) Reichardt, C. Solvents and Solvent Effects in Organic Chemistry, 2nd ed.; VCH: Weinheim, Germany, 1988. (25) Ionescu, L. G.; Trinadle, V. L.; de Souza, E. F. Langmuir 2000, 16, 988.

del Mar Graciani et al. Fluorescence Measurements. Fluorescence measurements were made by using a Hitachi F-2500 fluorescence spectrophotometer. The temperature was kept at 298.2 ( 0.1 K by a waterflow thermostat connected to the cell compartment. Solutions of pyrene (1 × 10-6 mol dm-3) in the different waterDMF micellar solutions were prepared as in ref 26. In all cases, a surfactant concentration well above the cmc was used. Pyrene was excited at 334 nm, and its emission was recorded at 373 and 384 nm, which correspond to the first and third vibrational peaks, respectively, with the use of excitation and emission slits of 10 and 5 nm, respectively. A scan speed of 240 nm/min was used. A value of II/IIII equal to 1.36 was found in CTAB aqueous micellar solutions, with [CTAB] ) 0.02 M, in agreement with the literature data.27 A study of the fluorescence quenching of pyrene by Nhexadecylpyridinium chloride (CePyCl) was carried out. The introduction of pyrene in the water-DMF micellar solutions was done as in ref 28. The pair pyrene/CePyCl ensures that the residence time of the quencher in the micelles is much longer than the fluorescence lifetime of the probe.29 The probe concentration was kept low enough (2 × 10-6 mol dm-3) to avoid excimer formation, and the quencher concentration was varied from 5 × 10-5 to 25 × 10-5 mol dm-3. These values give [pyrene]/[micelles] and [quencher]/[micelles] ratios low enough to ensure a Poisson distribution.30 The aggregation number obtained for the DTAB micellar aggregates in aqueous solutions is in agreement with literature data.31 Kinetics. The reaction between methyl 4-nitrobenzenesulfonate + Br- was recorded at 280 nm in a Unicam UV-2 spectrophotometer as described in ref 19. The kinetics were followed for more than five half-lives in all of the water-DMF micellar media. The observed rate constants were obatained from the slopes of the ln(A∞ - At) against time plots, with At and A∞ being the absorbances at time t and at the end of the reaction, respectively. Each experiment was repeated at least twice, and the observed rate constants were reproducible within a precision better than 5%. The temperature was maintained at 298.2 ( 0.1 K using a water-jacketed cell compartment connected to a water-flow thermostat.

Results Table 1 shows the values of the critical micelle concentrations (cmc’s) and of the micellar ionization degrees, R, of the different water-DMF micellar solutions. These magnitudes were obtained through conductivity measurements by using the Williams method.32 The cmc values were determined from inflections in plots of conductivity, κ, against the surfactant concentration. The data points above and below the inflection are fitted to two equations of the form κ ) A[surfactant] + B, and by solving the two equations simultaneously, the point of intersection is obtained. Least-squares analysis is employed. Subsequently, the micellar ionization degree is calculated from the ratios of the slopes of the plots of κ versus [surfactant] above and below the cmc. Figure 1 shows the dependence of the specific conductivity, κ, of water-DMF CTAB solutions on surfactant concentration. One can see in Figure 1 that an increase in the percentage by weight of DMF results in a less abrupt change in conductivity in going from the premicellar surfactant concentration range to the postmicellar surfactant concentration range, as (26) Domı´nguez, A.; Ferna´ndez, A.; Gonza´lez, N.; Iglesias, E.; Montenegro, L. J. Chem. Educ. 1997, 74, 1227. (27) Garcı´a Sa´nchez, F.; Carnero Ruiz, C. J. Lumin. 1996, 69, 179. (28) Velazquez, M. M.; Costa, M. B. J. Chem. Soc., Faraday Trans. 1990, 86, 4043. (29) Malliaris, A.; Lang, J.; Zana, R. J. Colloid Interface Sci. 1986, 110, 237. (30) (a) Infelta, P.; Gratzel, M. J. Chem. Phys. 1979, 70, 179. (b) Infelta, P. P. Chem. Phys. Lett. 1980, 61, 88. (c) Hunter, T. F. Chem. Phys. Lett. 1980, 75, 152. (31) Del Burgo, P.; Junquera, E.; Aicart, E. Langmuir 2004, 20, 1587. (32) Phillips, J. N. Trans. Faraday Soc. 1955, 51, 561.

Water-DMF Alkyltrimethylammonium Bromide Solutions

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Table 1. Cmc, Micellar Ionization Degree, r, II/IIII Intensity Ratio of the 1:3 Pyrene Vibronic Bands, Aggregation Number, Nagg, Standard Free Energy of Micelle Formation, ∆G°M, and Free Energy of Transfer, ∆G°trans Values for Water-DMF Alkyltrimethylammonium Bromide Micellar Solutions (T ) 298.2 K) -∆G°M ∆G°trans II/IIII Nagg a (kJ mol-1) (kJ mol-1)

wt % DMF

cmc/ mol dm-3

R

0 5 10 20

9.25 × 10-4 14.6 × 10-4 19.7 × 10-4 37.4 × 10-4

0.22 0.26 0.28 0.31

CTAB 1.36 59 1.36 54 1.37 46 1.38 41

30.5 28.1 26.6 23.4

2.4 3.9 7.1

0 5 10 20

3.62 × 10-3 4.94 × 10-3 6.42 × 10-3 11.0 × 10-3

0.23 0.26 0.28 0.32

TTAB 1.37 58 1.38 46 1.38 38 1.41 28

24.6 22.9 21.5 18.8

1.7 3.1 5.8

0 5 10 20

1.45 × 10-2 1.87 × 10-2 2.50 × 10-2 3.35 × 10-2

0.25 0.29 0.32 0.36

DTAB 1.40 56 1.41 43 1.41 36 1.44 25

18.3 16.9 15.3 13.8

1.4 3.0 4.5

a The aggregation numbers given in this table are approximate (see the text).

Figure 1. Dependence of the specific conductivity, κ, in µS cm-1, on surfactant concentration for water-DMF CTAB micellar solutions. The inset of this figure shows the application of the Phillips (dotted line) and Williams (solid line) methods to the water-DMF CTAB solutions with 20 wt % DMF. The arrows indicate the cmc’s obtained. T ) 298.2 K.

compared to that in pure water, introducing some uncertainties in the evaluation of the cmc values corresponding to the high weight percentage of DMF by using the Williams method. To investigate this point, the Phillips method33 was used to estimate the cmc’s, the latter applied through an integration by the Runge-Kutta method and a least-squares Levenberg-Maquardt fitting, as described in ref 34. The inset in Figure 1 shows an example of the Williams and Phillips methods applied to conductivity data. The two values are in good agreement. The same result was obtained in all of the water-DMF micellar solutions investigated, which means that the cmc’s obtained through the Williams method, shown in Table (33) Mosquera, V.; Garcı´a, M.; Varela, L. M. In Handbook of Surfaces and Interfaces of Materials; Nalwa, H. S., Ed.; Academic Press: New York, 2001; Vol. 3, p 401. (34) Van Os, N. M.; Haak, J. R.; Rupert, L. A. Physicochemical Properties of Selected Anionic, Cationic and Nonionic Surfactants; Elsevier: New York, 1993.

Figure 2. Influence of the quencher (N-hexadecylpyridinium chloride) concentration on the intensity of pyrene fluorescence in water-DMF TTAB solutions with 10 wt % DMF. T ) 298.2 K.

1, are reliable. It also gives reliability to the R values shown in this table. Table 1 summarizes the values of the intensity ratio of the vibronic bands 1:3, II/IIII, of pyrene for the waterDMF cationic micellar solutions studied. This table also shows the aggregation numbers, Nagg, of the micelles present in the water-DMF cationic micellar solutions obtained by studying the fluorescence quenching of pyrene by N-hexadecylpyridinium chloride. The influence of the quencher concentration on the intensity of pyrene fluorescence in water-DMF TTAB, with 10 wt % DMF micellar solutions, is shown in Figure 2. The Nagg value found for DTAB is in good agreement with the literature.31 Despite this, the aggregation numbers obtained for TTAB and CTAB in aqueous solutions are too small.34 An explanation for these low values was given in ref 35 by considering that the quenching process with CePyC is not very effective. For such a bulky quencher in large CTAB and TTAB micelles, the diffusion toward an excited probe molecule is too slow to ensure complete quenching in all micelles containing both an excited probe and a quencher molecule. There is another point that could also be responsible for the low Nagg values obtained. As indicated by Gratzel and Thomas,36 alkyltrimethylammonium bromide micelles contain a large fraction of adsorbed bromide ions that can quench the pyrene excited state. Nonetheless, despite the method rendering aggregation numbers too low, it is clear that Nagg decreases as the amount of DMF in the mixture increases. Table 2 shows the solvent surface tension, γ, the molar volume, V h , and the Gordon parameter, G ) γ/V h 1/3, for the water-DMF mixtures used as the bulk phase in the cationic micellar solutions investigated. The molar volumes of the mixtures were estimated from V h )V h DMFXDMF +V h water(1 - XDMF). Figure 3 shows the influence of changes in the surfactant concentration on the observed rate constant, kobs/s-1, for the reaction methyl 4-nitrobenzenesulfonate (MBS) + Brin some water-DMF alkyltrimethylammonium bromide micellar solutions, with the surfactants being CTAB, TTAB, and DTAB. Table 3 summarizes the second-order rate constant, k2,bulk/dm3 mol-1 s-1, for the same process in water-DMF mixtures in the absence of surfactant. The (35) Stam, J.; Depaemelaere, S.; De Schryver, F. C. J. Chem. Educ. 1998, 75, 93. (36) Gra¨tzel, M.; Thomas, J. K. J. Am. Chem. Soc. 1973, 95, 6885.

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del Mar Graciani et al.

Table 2. Solvent Surface Tension, γ, Solvent Molar Volume, V h , and Gordon Parameter, G, for Some Water-DMF Mixtures (T ) 298.2 K)a wt % DMF

γ (mN m-1)

V hb (dm3 mol-1)

G ) γ/ V h 1/3 (J m-3)

0 5 10 20 100

71.8 62.0 57.7 50.4 35.2

18.07 18.83 19.64 21.50 77.4

2.74 2.33 2.14 1.81 0.83

a The data corresponding to the pure solvents were taken from ref 37. b Estimated considering V h )V h DMFXDMF + V h water(1 - XDMF).

Table 3. Dependence of the Second-Order Rate Constant, k2,bulk/dm3 mol-1 s-1, for the Reaction Methyl 4-Nitrobenzenesulfonate + Br- on the Amount of DMF Present in Water-DMF Mixtures (T ) 298.2 K) wt % DMF 104k2,bulk (dm3 mol-1 s-1)

0 4.5

5 4.8

10 5.5

20 6.1

Discussion Table 1 shows that, for the three surfactants studied, an increase in the amount of DMF present in the solution results in an increase in the critical micelle concentration as well as in the micellar ionization degree. To quantify this effect, the Gibbs free energy of micellization, ∆G°M, can be calculated by using eq 1:39,40

∆G°M ) (2 - R)RT ln cmc

(1)

where R is the micellar ionization degree. Table 1 summarizes the ∆G°M values obtained for the different surfactant solutions investigated. It is worth noting that eq 1 is applicable when the aggregation number is large. Since the aggregation number decreases with an increase in the weight percentage of DMF, the ∆G°M values listed in Table 1 for the higher percentages of DMF, particularly in the case of DTAB, have to be considered as being approximate. From Table 1, one can see that micellization becomes less spontaneous upon an increase in the amount of DMF in the mixture for the three surfactants studied. Besides, the micellar ionization degree increases and the aggregation number decreases (see Table 1) by increasing the weight percent of DMF. To explain these results, the following solvent-dependent contributions to the free energy of micellization can be considered: (i) the surfactant tail transfer free energy, which accounts for the solvophobic effect; (ii) the aggregate-core solvent interfacial free energy; and (iii) the headgroup interaction free energy. The increase in the cmc originates mainly from the small magnitude of the tail transfer free energy from DMF compared to that from water. This effect can be quantified in the water-DMF micellar solutions investigated through the estimation of the free energy ∆G°CH2 for the transfer of one methylene CH2 group from the bulk phase (bulk meaning the water-DMF mixture) to the micellar pseudophase by using eq 2:5

(2 - R) ln cmc ) const + m

Figure 3. Influence of the surfactant concentration on the observed rate constant, kobs/s-1, for the reaction methyl 4-nitrobenzenesulfonate + Br- in (a) water-DMF CTAB micellar solutions, (b) water-DMF TTAB micellar solutions, and (c) water-DMF DTAB micellar solutions. T ) 298.2 K.

k2,bulk value corresponding to pure water is in agreement with literature data.38 (37) Marcus, Y. Ion Solvation; Wiley: London, 1985.

[

]

∆G°CH2 RT

(2)

in which the plot of (2 - R) ln cmc against m, the number of carbon atoms in the surfactant chain, is plotted for a homologous series of surfactants and ∆G°CH2 can be estimated from the slope. Good straight lines were found for pure water and for the three water-DMF mixtures studied, despite having only three points in each plot. Table 4 summarizes the ∆G°CH2 values obtained by using eq 2. The value obtained in water is in agreement with the literature.5 The dielectric constant of DMF is much smaller than that of water (36.71 compared to 78.39 at 298.2 K37); however, the decrease in the dielectric constant for the weight percent of DMF ranging from 0 to 20 goes from 78.39 to 74.86 at 298.2 K.37 This small decrease in the dielectric constant would result in a small increase in the ionic interactions at the micellar surface; nonetheless, (38) Brinchi, L.; Di Profio, P.; Germani, R.; Savelli, G.; Spretti, N.; Bunton, C. A. Eur. J. Org. Chem. 2000, 3849. (39) Evans, D. F.; Wennestro¨m, H. The Colloidal Domain: Where Physics, Chemistry and Biology Meets; VCH: New York, 1994. (40) Desnoyers, J. E.; Perron, G. Langmuir 1996, 12, 4044.

Water-DMF Alkyltrimethylammonium Bromide Solutions Table 4. Values of the Free Energy, ∆G°CH2, for the Transfer of One Methylene CH2 Group from the Bulk Phase to the Micellar Pseudophase in the Water-DMF Alkyltrimethylammonium Bromide Micellar Solutions Investigated (T ) 298.2 K) wt % DMF ∆G°CH2a (kJ mol-1) a

0 3.0

5 2.8

10 2.5

20 2.3

Values estimated by using eq 2.

these interactions decrease rather than increase upon increasing the weight percent of DMF because of the increase in the ionic strength due to the increase in the monomer concentration provoked by the increase in the cmc. As a result, the micellar ionization degree increases upon increasing the weight percent of DMF (see Table 1). Despite the weaker ionic headgroup repulsions, the equilibrium aggregation numbers decrease when the amount of DMF in the solution increases (see Table 1) because of the dominating influence of the interfacial energy contribution (the DMF-hydrocarbon interfacial tension decreases as the percentage by weight of DMF in the mixtures increases). The effect of DMF on the micellization process can be estimated by means of the so-called free energy of tranfer, ∆G°trans, which can be written as40

∆G°trans ) (∆G°M)water-DMF - (∆G°M)water

(3)

The values of ∆G°trans estimated by using eq 3 are listed in Table 1. One can see in this table that the presence of DMF in the bulk phase affects the micellization process more the longer the hydrocarbon chain of the surfactant is. This is a reasonable result if variations in the surfactant tail transfer free energy are the main factor controlling the cmc. The positive values of ∆G°trans can be understood on the basis of a reduction in the solvophobic interactions caused by the improved solvation, which leads to an increase in the solubility of the hydrocarbon tails in the presence of DMF and consequently in an increase in the cmc. It is interesting to note that the ability of a solvent to bring about the self-association of conventional amphiphiles can be related to its cohesive energy density,22 which can be characterized by the Gordon parameter, G ) γ/V h 1/3, where γ is the solvent surface tension and V h its molar volume. Table 2 shows the values of the Gordon parameter for the different mixtures used as bulk phases in the micellar solutions. The G values show that the presence of DMF in the solvent induces a decrease in the solvent cohesiviness, thereby increasing the solubility of the hydrocarbon tails and decreasing the solvophobic effect. Table 1 shows the II/IIII intensity ratio of the 1:3 pyrene monomer vibronic bands. These intensities show a strong dependence on the solvent environment, with both the solvent dipole and the dielectric constant being important in this effect. The relative intensities of the first and third vibronic peaks are directly related to the dielectric constant where the probe is housed. The II/IIII values corresponding to the aqueous cationic micellar solutions indicate that the pyrene is located close to the micellar surface.41 Table 1 shows that the micellar surface of DTAB micelles is somewhat more polar than those of CTAB and TTAB micelles in aqueous solutions. This is also true when DMF is added to the solution. It shows that the II/IIII ratio increases slightly upon increasing the weight percent of DMF in the mixtures. That is, the bulk-micelle interface (41) (a) Zana, R.; Strazielle, C.; Lianos, P. J. Colloid Interface Sci. 1981, 80, 208. (b) Lianos, P.; Zana, R. J. Colloid Interface Sci. 1981, 84, 100.

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region becomes more polar when the weight percent of DMF increases from 0 to 20. The same dependence of the polarity of the bulk-micelle interface region on the weight percent of organic solvent was found for water-ethylene glycol CTAB, TTAB, and DTAB micellar solutions18 as well as for water-ethylene glycol SDS, Brij35, and SB3-14 micellar solutions.20 This increase in polarity could be related to the decrease in the aggregation number of the micellar aggregates when the amount of organic solvent present in the solution increases. A decrease in Nagg would mean a less-packed micelle, thus making the penetration of the solvent molecules, DMF as well as water, in the palisade layer easier and resulting in a more polar environment of the polarity probe. The structural and thermodynamic changes provoked in the cationic micellar solutions by the increase in the amount of DMF present in the solution could be evidenced through the variations of appropriate micelle-modified processes. If pseudophase kinetic models are considered, the observed rate of reaction between a substrate (S) and a nucleophile (N) is assume to be equal to the sum of the reaction occurring in the bulk phase and in the micellar pseudophase. The differential rate expression is

d[ST] ) kobs[ST] ) k2,bulk[Sbulk][Nbulk] + k2m[Sm][N]m dt (4) Here, square brackets indicate concentrations expressed in moles per liter of solution volume. The subscripts and superscripts T, bulk, and m refer to the total, the waterDMF phase, and the micellar pseudophase, respectively. The observed rate of the reaction depends on the solution concentrations of the substrate and the nucleophile. However, the rate of the reaction in the micellar pseudophase depends on the concentration of N within the micelle in moles per liter of the reaction volume of N, [N]m, and not on its solution concentration, [Nm].42 The relation between these concentrations is [N]m ) [Nm]/ (Vm[surfactant]), where Vm is the molar reaction volume in units of liters per mole. Chemical reactions in micellar solutions are generally run under pseudo-first-order conditions in which the total concentration of N is substantially greater than that of S and the observed rate constant, kobs/s-1, can be written as42d

kobs )

k2,bulk + (k2m/Vm)[Nm]Km 1 + Km[surfactantm]

(5)

In this equation, (k2m/Vm) ) k2m (s-1) is the second-order rate constant in the micellar pseudophase written with concentrations as a molar ratio, [Nm]/[surfactantm]. Km is the equilibrium binding constant which describes the distribution of the organic substrate (S) molecules between the bulk and micellar pseudophases. [Surfactantm] is the micellized surfactant concentration, equal to the total surfactant concentration minus the cmc. The substitution (SN2) reaction between methyl 4-nitrobenzenesulfonate and Br- seems to be an adequate choice to make evident the thermodynamic and structural changes originating in the cationic micellar solutions due to the increase of DMF in the bulk phase. This reaction takes place in the (42) (a) Berezin, I. V.; Martinek, K.; Yatsimirskii, A. K. Russ. Chem. Rev. 1973, 42, 787. (b) Romsted, L. S. In Surfactants in Solution; Mital, K. L., Lindman, B., Eds.; Plenum Press: New York, 1984; Vol. 2, p 1015. (c) Bunton, C. A.; Nome, F.; Quina, F.; Romsted, L. S. Acc. Chem. Res. 1991, 24, 357. (d) Bunton, C. A.; Yao, J.; Romsted, L. S. Curr. Opin. Colloid Interface Sci. 1996, 65, 125.

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bulk phase as well as in the micellar pseudophase in cationic micellar solutions,19,43 and its rate will be modified in micellar solutions through concentration micellar effects as well as through micellar medium effects. Variations in the micellar ionization degree will play a central role by determining the bromide ion concentration at the micellar surface, with this being the reaction site when the process occurs in the micellar pseudophase. Changes in the cmc will also affect the bromide ion concentration in the bulk phase and in the micellar pseudophase, for a given total surfactant concentration. The organic substrate distribution between the two pseudophases is determined by the equilibrium binding constant, Km, and this magnitude is expected to depend strongly on the bulk phase composition. Therefore, the contributions of the reaction taking place in each of the pseudophases will depend on the amount of DMF present in the solution, and kobs will also depend on it. Finally, changes in the characteristics of the micellar and bulk pseudophases, such as variations in polarity, will affect the values of the second-order rate constants in the two pseudophases through micellar medium effects and thus kobs values. Before considering the experimental kinetic data shown in Figure 3, it is necessary to take into account that the reaction of methyl 4-nitrobenzenesulfonate with water can make a contribution to the MBS + Br- process under study.43a Besides, the reaction MBS + H2O is affected by the presence of micelles43b and by the composition of the water-DMF solution.44 Brinchi et al.43b found that the rate of the spontaneous hydrolysis of methyl 4-nitrobenzenesulfonate decreases by increasing the surfactant concentration in hexadecyltrimethylammonium mesylate (CTAOMs) micellar solutions. These authors considered that the micellar kinetic effects were similar for CTAOMs and other hexadecyltrimethylammonium surfactants with different counterions. With regard to the DMF effects on the hydrolysis of MBS molecules, the reaction was investigated in water and in water-DMF homogeneous solutions. Experimental results showed that an increase in the weight percent of DMF in the mixture from 0 to 20 results in a decrease in the observed rate constant for the process MBS + H2O from 5.8 × 10-5 to 4.8 × 10-5 s-1, with the kinetic effects of the addition of this amount of DMF to pure water being small. The authors assumed that the influence of changes in the surfactant concentration on the spontaneous hydrolysis of methyl 4-nitrobenzenesulfonate found in CTAOMs micellar solutions is similar to that found in CTAB, TTAB, and DTAB micellar solutions in the presence as well as in the absence of DMF. The spontaneous hydrolysis is much slower than the MBS + Br- process. Nonetheless, the kinetic data in Figure 3 have been corrected when necessary, from the spontaneous hydrolysis contribution. Figure 3 shows that an increase in the surfactant concentration results in an increase in the reaction rate in all of the water-DMF cationic micellar solutions investigated, until kobs reaches a plateau. This is an expected result, since an increase in surfactant concentration causes a further incorporation of the methyl 4-nitrobenzenesulfonate molecules into the micellar pseudophase, where a high bromide ion concentration is present. Besides, for a given surfactant concentration, an (43) (a) Bonan, C.; Germani, R.; Ponti, P. P.; Savelli, G.; Bunton, C. A. J. Phys. Chem. 1990, 94, 533. (b) Brinchi, L.; Di Profio, P.; Germani, R.; Savelli, G.; Bunton, C. A. Langmuir 1997, 13, 4528. (c) Mun˜oz, M.; Graciani, M. M.; Rodrı´guez, M. L. J. Colloid Interface Sci. 2003, 266, 208. (d) Graciani, M. M.; Rodrı´guez, A.; Mun˜oz, M.; Moya´, M. L. Langmuir 2002, 18, 346. (44) Brinchi, L.; Di Profio, P.; Germani, R.; Savelli, G.; Gillitt, N. D.; Bunton, C. A. J. Colloid Interface Sci. 2001, 236, 85.

del Mar Graciani et al.

increase in the weight percent of DMF present in the bulk phase provokes a decrease in the observed rate constant. To explain the experimental results, eq 5 will be considered. The distribution of bromide ions between the bulk and micellar pseudophases was assumed to follow eq 6:45

KBr- )

[Br-m] [Br-bulk]([surfactantm] - [Br-m])

(6)

Considering eq 6 and the mass balance, one can write

KBr-[Br-m]2 - (KBr-[surfactantm] + KBr-[Br-T] + 1) + KBr-[surfactantm][Br-T] ) 0 (7) For a given KBr- value, eq 7 permits one to calculate the bromide ion concentration in the micellar pseudophase as a function of the total surfactant concentration and of the total bromide ion concentration. Afterward, by using eq 6, the bromide ion concentration in the bulk phase can be obtained. The authors considered a KBr- value of 1000 dm3 mol-1 in the CTAB aqueous micellar solution.19 For the rest of the micellar solutions where the reaction was investigated, KBr- was estimated by considering the relation between this equilibrium constant and the micellar ionization degree. To take the relation between KBr- and R into account, the equilibrium constant can be expressed as

KBr- )

1-R R2[surfactantm]

(8)

which indicates that a high micellar ionization degree corresponds to a low binding parameter. The change in KBr- when the micellar ionization degree changes can be written as

KBr-(R) KBr-(R0)

)

(1 - R)R02 (1 - R0)R2

(9)

where R0 is the micellar ionization degree of the aqueous CTAB micelles and R is the micellar ionization degree of any of the other water-DMF micellar solutions used as reaction media. That is, the KBr- values corresponding to the different micellar reaction media were calculated by using the micellar ionization degrees listed in Table 1 and eq 9. By using these binding parameter values and the cmc’s listed in Table 1 and considering eqs 6 an 7, the bromide ion concentrations in the bulk and micellar pseudophases were calculated for the different waterDMF micellar reaction media. The k2,bulk values were obtained experimentally and are shown in Table 3. One can see that an increase in the amount of DMF present in the mixture results in an increase in the second-order rate constant of the reaction MBS + Br-. This is in agreement with our expectations, since an increase in the weight percent of DMF in the solution causes a diminution of the polarity of the mixture, as was mentioned above, and this would favor reactions in which charge is dispersed in the transition state, as is the case of the reaction under study.43b The solid lines in Figure 3 are the fittings of the experimental data by using eq 5. One can see that the agreement between the theoretical and experimental data was good in all cases. Values of the two adjustable (45) (a) Bacaloglu, R.; Bunton, C. A.; Cerichelli, G.; Ortega, F. J. Phys. Chem. 1990, 94, 5068. (b) Bunton, C. A.; Moffatt, J. R. J. Phys. Chem. 1988, 92, 2896.

Water-DMF Alkyltrimethylammonium Bromide Solutions Table 5. Fitting Parameters For the Reaction Methyl 4-Nitrobenzenesulfonate + Br- in Water-DMF Alkyltrimethylammonium Bromide Micellar Solutions at 298.2 K 103(k2m/Vm) ) k2m (s-1)

wt % DMF

Km (dm3 mol-1)

0 5 10 20

76 55 45 21

0 5 10 20

73 47 31 14

4.13 4.07 4.17 4.4

0 5 10 20

DTAB 39 27 18 8

3.92 3.63 3.72 3.9

CTAB 5.87 5.24 5.07 4.9 TTAB

parameters obtained, (k2m/Vm) and Km, are listed in Table 5. With regard to the fittings, it is interesting to note that the use of experimental cmc, R, and k2,bulk data has reduced as much as possible the number of adjustable parameters. It was possible for the authors to use a value of KBr- in CTAB different from 1000 M-1, since one can find in the literature several values for this magnitude. However, as in previous works, the authors have checked the influence of using one or another KBr- on the adjustable parameter values obtained from the fittings, finding that (k2m/Vm) and Km are similar in all cases. On the other hand, in respect to the lack of meaning of kinetic constants estimated from fittings of kinetic data pointed out by some authors,46 it is important to say that only one set of (k2m/Vm) and Km values gave the best fitting for each of the micellar solutions investigated. For this to happen, the reaction was studied in a wide surfactant concentration range, depending on the cmc of the surfactant solution. Nonetheless, taking the simplicity of the model used for explaining the kinetic data into account, only substantial changes in the adjustable parameter values are worth discussing. Figure 3 shows that the pseudophase model used is adequate to rationalize the micellar effects observed in the water-DMF micellar solutions investigated. The Km values listed in Table 5 are small (in agreement with previous results43b,d), and they show the trend Km(CTAB) > Km(TTAB) > Km(DTAB) for all of the water-DMF micellar reaction media. Besides, an increase in the weight percent of DMF present in the solution results in a decrease in the equilibrium binding constant for the three cationic surfactants studied. Methyl 4-nitrobenzenesulfonate molecules are expected to be located at the micellar surface.47 The equilibrium binding constant of this organic substrate to the cationic micelles would depend on changes in the polarity of the two pseudophases in which it distributes. With regard to the micellar pseudophase, the II/IIII values listed in Table 1 indicate that the polarity of the micellar surface region is slightly smaller for CTAB than for TTAB, with DTAB having the highest value. On the other hand, an increase in the amount of DMF present in the bulk phase results in a small increase in the polarity of the micellar surface region of the cationic micelles. Conse(46) (a) Brinchi, L.; Di Profio, P.; Germani, R.; Savelli, G.; Gillitt, N. D.; Bunton, C. A. J. Colloid Interface Sci. 2001, 236, 85. (b) Khan, N. M.; Ismail, E. J. Chem. Soc., Perkin Trans. 2 2001, 1346. (47) Bacaloglu, R.; Bunton, C. A.; Cerichelli, G.; Ortega, F. J. Phys. Chem. 1989, 93, 1490.

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quently, the affinity of the MBS molecules for the micellar pseudophase is expected to follow the trend CTAB > TTAB > DTAB, with this affinity being weaker with the higher the amount of DMF present in the mixture. The presence of DMF in the bulk phase provokes a diminution in the polarity of the solution, as is shown through a decrease in the dielectric constant, in the π* polarity index and in the Reichardt parameter.37 The Gordon parameter corresponding to the water-DMF solutions also decreases upon increasing the weight percent of DMF in the mixture, as shown in Table 1. All of this indicated that the bulk phase is a better solvent for the organic substrate as the amount of DMF increases. From the above reasons, Km is expected to decrease upon increasing the weight percentage of DMF, as was found. Table 5 shows that (k2m/Vm) values follow the trend CTAB > TTAB > DTAB in the absence as well as in the presence of DMF. To compare the reactivity in water and in micelles, the second-order rate constants, k2m, have to be calculated. With this in mind, and from the data in ref 48, the molar reaction volumes were estimated to be equal to 0.37, 0.33, and 0.30 dm3 mol-1 for CTAB, TTAB, and DTAB in aqueous micellar solutions, respectively. The k2m values calculated for the reaction MBS + Br- were 2.17 × 10-3, 1.36 × 10-3, and 1.17 × 10-3 dm3 mol-1 s-1 for CTAB, TTAB, and DTAB, respectively, to be compared to k2,w ) 4.5 × 10-4 dm3 mol-1 s-1. The k2m values in waterDMF micellar solutions could not be estimated because the corresponding Vm values are not known. In the case of water-ethylene glycol Triton X-100 micellar solutions, it was found that an increase in the weight percent of organic solvent present in the solution provoked a decrease in the aggregation number and in the hydrodinamic radius of the micelles, with this resulting in a small decrease in Vm. Taking into account the decrease in the aggregation number found in the micellar solutions investigated by increasing the weight percent of DMF in the solutions, a reasonable assumption would be that Vm decreases upon increasing the amount of DMF or, at least, a substantial increase in the molar reaction volume is not expected by increasing the weight percent of DMF. Therefore, taking the k2,bulk and (k2m/Vm) values in Tables 3 and 5 into account, one can conclude that the reaction MBS + Bris faster in the micellar pseudophase than in the bulk phase in the water-DMF micellar solutions studied. The main factors involved in this acceleration would be the electrophilic interaction of the ammonium headgroups and the forming nitrobenzenesulfonate ion and disruption of the hydration shell of the bromide ion.49 The dependence of k2m on the surfactant nature could be related to the different polarities of the bulk-micellar interface regions of CTAB, TTAB, and DTAB micelles, with the reaction being faster the lower the polarity of the interfacial region is. However, the differences are not large and to discuss them would be rather speculative. The same can be said with respect to the observed variations in k2m by changing the weight percent of DMF in the solution, and therefore, no discussion will be done. Summarizing, the addition of N,N-dimethylformamide, up to a percentage by weight of 20, to hexadecyl-, tetradecyl-, and dodecyltrimethylammonium bromide aqueous micellar solutions results in an increase in the (48) Imae, T.; Ikeda, S. J. Phys. Chem. 1986, 90, 5216. (49) (a) Bohme, K. D.; Young, L. B. J. Am. Chem. Soc. 1970, 92, 7354. (b) Bohme, K. D.; Mackay, G. I.; Pay, J. D. J. Am. Chem. Soc. 1974, 96, 4027. (c) Tanaka, K.; Mackay, G. I.; Payzant, J. D.; Bohme, D. K. Can. J. Chem. 1976, 74, 1643. (d) Olmsted, W. E.; Braumen, J. I. J. Am. Chem. Soc. 1977, 99, 4219. (e) Henchman, M.; Paulson, J. F.; Hiel, P. M. J. Am. Chem. Soc. 1983, 105, 5509. (f) Dewar, M. J.; Storch, D. M. J. Chem. Soc., Chem. Commun. 1985, 94.

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critical micelle concentration and in the micellar ionization degree, whereas the micellar aggregation number decreases. The polarity of the interfacial region increases slightly upon increasing the weight percent of DMF. These thermodynamic and structural changes control the micellar effects observed in the reaction methyl 4-nitrobenzenesulfonate + Br- taking place in the water-DMF CTAB, TTAB, and DTAB cationic micellar solutions. The slowdown of the reaction originating from the addition of DMF is mainly the result of two factors: (i) the decrease in the bromide ion concentration at the micellar surface, where the reaction takes place, due to an increase in the micellar ionization degree, and (ii) the decrease in the equilibrium binding constant due to the water-DMF mixtures being a better solvent for the organic substrate molecules than pure water and to the interfacial region of the cationic micelles becoming more polar by increasing the amount of DMF present in the solution. Nevertheless,

del Mar Graciani et al.

the second-order rate constant in the micellar pseudophase in any of the water-DMF micellar solutions studied is faster than that in the bulk phase, although it shows a weak dependence on changes in the weight percent of DMF. Acknowledgment. This work was financed by the DGCYT (grant BQU2002-00691) and Consejerı´a de Educacio´n y Ciencia de la Junta de Andalucı´a (FQM-274). The authors thank Profesor Victor Mosquera, from the University of Santiago de Compostela, Spain, for helping us in the application of the Phillips method for obtaining the cmc values. The authors also thank Professor Ana Troncoso, from the University of Seville, Spain, for helping us in the fluorescence measurements. LA046833A