Study on Molecular Aggregates of N-(1,1-Dihydroperfluoroalkyl)-N,N

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Study on Molecular Aggregates of N-(1,1-Dihydroperfluoroalkyl)-N,N,N-trimethylammonium Chloride Kaori Kubo, Yoshikiyo Moroi,* Kazuo Nomura, Yutaka Abe,† and Toshio Takahashi† Graduate School of Sciences, Kyushu University, Fukuoka 810-8560, Japan, and Material Science Research Center, Lion Corporation, Tokyo 132-0035, Japan Received April 15, 2002. In Final Form: July 23, 2002 Dissolution into water of solid fluorinated cationic amphiphiles was investigated in detail for four amphiphiles with different alkyl chain lengths: N-(1,1-dihydroperfluorooctyl)-, N-(1,1-dihydroperfluorodecyl)-, N-(1,1-dihydroperfluorododecyl)-, and N-(1,1-dihydroperfluorotetradecyl)-N,N,N-trimethylammonium chloride. The dissolution seemed quite fast just from appearance, but it took a very long time to reach thermodynamic dissolution equilibrium, where a specific conductance of the solution steadily increased with time even after the solid particles perfectly disappeared from the solution. Change in sizes of molecular aggregates with time was confirmed by dynamic light scattering, and the distribution of sizes decreased with time and with increasing temperature. The critical micelle concentrations (cmc’s) were determined from the specific conductivity change against concentration, after the dissolution equilibrium was reached. The cmc of the latter two amphiphiles monotonically increased with temperature, and the Gibbs energy contribution per CF2 group to micellization was 1.54 times as large as that per CH2 group from the slope of the plots of ln(cmc) against the carbon number of the alkyl chain. The rate of dissociation of micellar aggregates to monomers was traced by electric conductivity on an oscilloscope screen, and the activation energy obtained from its temperature dependence was found to decrease with increasing alkyl chain length. Taking all experimental results into consideration, the processes from the solid state to aggregates in the dissolved state in thermodynamic equilibrium were proposed.

Introduction Fluorinated amphiphiles are more surface active than their corresponding hydrogenated amphiphiles in such respects as critical micelle concentration (cmc) and interfacial tension. Thus, their solution and interfacial properties have long been a matter of interest from both theoretical and practical viewpoints.1 Recently, their functions have been made clear from the practical point of view, and the compounds are widely used in daily life as cosmetics, toothpaste, and so on. Above all, fluorinated surfactants show high biocompatibility and have been investigated pharmaceutically as carriers of oxygen and drugs in intravascular systems.2-4 Such interesting properties as above result from a fluorocarbon chain with a stiff structure which leads to the formation of molecular aggregates with lower curvature.5 Because of such molecular structure, fluorinated surfactants show higher hydrophobicity and start to aggregate at a relatively lower concentration than hydrogenated ones.6-12 In addition, * To whom correspondence should be addressed. Tel: 81-92726-4742. Fax: 81-92-726-4842. E-mail: [email protected]. † Lion Corp. (1) Kissa, E. Fluorinated Surfactants; Marcel Dekker: New York, 1993. (2) Riess, J. G. New J. Chem. 1995, 19, 891. (3) Riess, J. G.; Krafft, M. P. Chem. Phys. Lipids 1995, 75, 1. (4) Greenspan, J. S.; Wolfson, M. R.; Shaffer, T. H. Biomed. Instrum. Technol. 1999, 33, 253. (5) Rossi, S.; Karlsson, G.; Ristori, S.; Martini, G.; Edwards, K. Langmuir 2001, 17, 2340. (6) Kunieda, H.; Shinoda, K. J. Phys. Chem. 1976, 80, 2468. (7) Guittard, F.; Taffin de Givenchy, E.; Cambon, A. J. Colloid Interface Sci. 1996, 177, 101. (8) Mukerjee, P.; Handa, T. J. Phys. Chem. 1981, 85, 2298. (9) Mukerjee, P.; Korematsu, K.; Okawauchi, M.; Sugihara, G. J. Phys. Chem. 1985, 89, 5308.

these fluorocarbon properties can make it possible even for single-chain amphiphiles to form vesicles in an aqueous solution, although it is usually unfavorable for singlechain hydrocarbon amphiphiles.13,14 However, scientific reports on fluorinated surfactants are much less in number compared with those of conventional hydrogenated surfactants as for dilute aqueous solutions. This is partly because the small gradient of refractive index with concentration peculiar to fluorinated compounds greatly limits the utility of light-scattering methods, which are most useful for size determination of their aggregates. Moreover, the low cmc value for surfactants with longer fluorinated chains causes the operational difficulties of dealing with very dilute solutions without experimental errors.15 What makes matters worse is low reproducibility of solution properties for longer fluorinated surfactants,16 where most surfactants investigated have been anionic ones with fewer than 11 carbon atoms. Therefore, longer tailed fluorinated surfactants have not been much investigated, and in addition, the investigation on cationic ones was quite scarce because of difficulty in their synthesis.17 Although a fluorinated surfactant could be regarded apparently as a substitution product of a (10) Tomasic, V.; Chittofrati, A.; Kallay, N. Colloids Surf., A 1995, 104, 95. (11) Mukerjee, P.; Gumkowski, M. J.; Chan, C. C.; Sharma, R. J. Phys. Chem. 1990, 94, 8832. (12) Sua´rez, J. M.; Lo´pez-Fonta´n, L. J.; Sarmiento, F.; Mosquera, V. Langmuir 1999, 15, 5265. (13) Krafft, M. P.; Giulieri, F.; Riess, J. G. Colloids Surf., A 1994, 84, 113. (14) Giulieri, F.; Krafft, M. P. Colloids Surf., A 1994, 84, 121. (15) Moroi, Y.; Take’uchi, M.; Yoshida, N.; Yamauchi, A. J. Colloid Interface Sci. 1998, 197, 221. (16) Furuya, H.; Moroi, Y.; Kaibara, K. J. Phys. Chem. 1996, 100, 17249. (17) Yamabe, T.; Moroi, Y.; Abe, Y.; Takahashi, T. Langmuir 2000, 16, 9754.

10.1021/la020350u CCC: $22.00 © 2002 American Chemical Society Published on Web 10/19/2002

Molecular Aggregates of Fluorinated Amphiphiles

hydrocarbon surfactant, the actual synthetic route of fluorinated surfactants is far different from that of hydrogenated ones.1 In this study, four cationic homologues of fluorinated surfactants were newly synthesized: N-(1,1dihydroperfluorooctyl)-N,N,N-trimethylammonium chloride (C8-TAC), N-(1,1-dihydroperfluorodecyl)-N,N,N-trimethylammonium chloride (C10-TAC), N-(1,1-dihydroperfluorododecyl)-N,N,N-trimethylammonium chloride (C12-TAC), and N-(1,1-dihydroperfluorotetradecyl)-N,N,Ntrimethylammonium chloride (C14-TAC). These compounds are expected to form layered large aggregates because of the shape of these molecules whose packing parameter is almost unity by the Corey-Pauling-Koltun (CPK) atomic model. Indeed, very large particles were observed by the quasi-elastic light scattering method even for the shortest surfactant C8-TAC. In addition, it took a very long time for these aggregate systems to reach a thermodynamic equilibrium, especially for C12-TAC and C14-TAC. For C12-TAC, for example, drift of electric conductivity continued for more than 10 days. This study is aimed, therefore, to make clear the reason it takes such a long time to reach thermodynamic equilibrium and to find the final molecular aggregates at the equilibrium. The observed results must contribute much to further study on solution properties of fluorinated amphiphiles. Experimental Section Materials. The preparation of C12-TAC was mentioned in the previous paper.17 The other two were synthesized as follows: Methyl perfluorooctanoate (Daikin Chemicals), methyl perfluorodecanoate and methyl perfluorotetradecanoate (Exfluor Res.), dimethylamine (2.0 M) solution in methanol (Aldrich), and other reagents (Kanto Chemicals) were used without further purification. 1H NMR spectra were obtained with a JEOL 300 MHz spectrometer for a purity check of the amphiphiles. N-(1,1-Dihydroperfluorooctyl)-N,N,N-trimethylammonium Chloride (1). N-(1,1-Dihydroperfluorooctyl)-N,N,N-trimethylammonium iodide18 (35 g) was dissolved into 100 mL of methanol and eluted through 200 g of Amberlyst A-26 in a column of 3 cm diameter which was substituted with chloride ion by 10% LiCl methanol solution. The solution was dried by evaporation of the solvent, and then the white crystalline solid was purified by recrystallization from ethanol/acetone (1/9 (v/v)) solution to afford 27.8 g of 1 (82%). 1H NMR (CD3OD) δ: 4.80 (CH2, 2H, t, J ) 16 Hz), 3.61 (CH3, 9H, s). N-(1,1-Dihydroperfluorodecyl)-N,N-dimethylamine (2). Dimethylamine methanol solution (30%, 100 mL) was titrated to methyl perfluorodecanoate (50 g, 95.9 mmol) dispersed in 100 mL of methanol and was stirred for 1 day. The solution was dried by vacuum evaporation to produce a yellow solid. The solid dissolved in diethyl ether was titrated into LiAlH4 (25.0 g, 606 mmol) dispersed in diethyl ether at -10 °C. After 3 days of stirring at room temperature, water (25 mL), 15% NaOH aqueous solution (25 mL), and water (75 mL) were added slowly and stepwise to the diethyl solution cooled by iced water. The white solid was filtered and washed with fresh diethyl ether. The diethyl ether solution was dried with anhydrous MgSO4 and then evaporated. The yellow solid thus obtained was distilled (100 °C, 0.5 mmHg) to afford 23.3 g of 2 (42%). 1H NMR (CD3OD) δ: 3.00 (CH2, 2H, t, J ) 16 Hz), 2.30 (CH3, 6H, s). N-(1,1-Dihydroperfluorodecyl)-N,N,N-trimethylammonium Chloride (3). Methyl iodide (32.7 g, 231 mmol) was titrated to 2 (21.0 g, 39.8 mmol), dissolved in ethanol (150 mL) at room temperature, and refluxed in an oil bath for 4 h. After cooling to room temperature, the solution was poured into 200 mL of diethyl ether. The solution with a white solid was stored at -20 °C for 1 night, and the solid was filtered. After drying in a vacuum, the solid was dissolved in 100 mL of methanol, eluted through the ion-exchange resin, and recrystallized as described for 1, to (18) Matsui, K.; Kikuchi, Y.; Sugimoto, K.; Suzuki, N. Tokkyo Koho; Japan Patent Office, Tokyo, JP61-207362, 1986; pp 207-362.

Langmuir, Vol. 18, No. 23, 2002 8771 afford 15.2 g (26.3 mmol) of 3 (64%). 1H NMR (CD3OD) δ: 4.67 (CH2, 2H, t, J ) 16 Hz), 3.47 (CH3, 9H, s). N-(1,1-Dihydroperfluorotetradecyl)-N,N-dimethylamine (4). Methyl perfluorotetradecanoate (20.0 g, 27.5 mmol) was treated with 50 mL of 30% dimethylamine methanol solution and then LiAlH4 (6.0 g, 145 mmol) in diethyl ether as described for 2. Compound 4 (3.0 g, 4.1 mmol) was yielded at 15%. 1H NMR (CDCl3) δ: 3.10 (CH2, 2H, t, J ) 16 Hz), 2.42 (CH3, 6H, s). N-(1,1-Dihydroperfluorotetradecyl)-N,N,N-trimethylammonium Chloride (5). Methyl chloride was introduced into N-(1,1dihydroperfluorotetradecyl)-N,N-dimethylamine, 4 (5.0 g, 6.9 mmol), dissolved in acetonitril (50 mL), and stirred with NaHCO3 (100 mg) in an autoclave at 3 kg/cm2. After 4 days of stirring, the solution was dried by evaporation of the solvent. The white crystalline solid was purified by recrystallization from ethanol/ acetone solution to afford 1.9 g of 5 (35%). 1H NMR (CD3OD) δ: 4.65 (CH2, 2H, t, J ) 16 Hz), 3.45 (CH3, 9H, s). The surfactants were further purified by repeated recrystallizations from mixed solvents: ethanol-acetone for C8-TAC, ethanol-cyclohexane for C10-TAC, methanol-acetone for C12TAC, and ethanol-ether for C14-TAC. Purity was checked by elemental analysis and NMR measurement. The observed and calculated values (in parentheses) for elemental analysis were in satisfactory agreement by weight percentage: C 27.43 (27.66), H 2.32 (2.34), N 2.89 (2.93) for C8-TAC; C 26.78 (27.03), H 1.96 (1.92), N 2.35 (2.42) for C10-TAC; C 26.68 (26.59), H 1.64 (1.64) N 1.95 (2.07) for C12-TAC; C 26.35 (26.26), H 1.43 (1.43), N 1.72 (1.80) for C14-TAC. In the NMR measurements, there was no peak for impurities. The water used for preparation of all the aqueous solutions was distilled twice from an alkali permanganate solution. Static Light Scattering (SLS). Details of the measurement are given in the previous study.19 As for C8-TAC in the aqueous solution, the Debye plots were made at 298.2 K for the molecular weight of the aggregates, and the angle dependence of the scattered-light intensity was checked for the shape of the aggregates by an SLS600 (Otsuka Electronics). Quasi-Elastic Light Scattering (QELS). A DLS-7000 (Otsuka Electronics) was used to measure the size distribution of the aggregates, where the light source was an argon laser. The time-dependent correlation function of the scattered-light intensity was measured at a scattering angle of 90°. The measurement was made for C8-TAC and C10-TAC at various temperatures. The solutions of 3 × cmc prepared at room temperature were filtered through a filter of 0.1 µm pore size before the measurement. After the scattered-light intensity became stable, the size distribution of the aggregates was measured. Hysteresis of Electric Conductivity against Temperature. This observation is to see the reason it takes such a long time for the electric conductivity of the aqueous solution of the present amphiphiles to reach an equilibrium value after the conductivity drift, even though the solution is filtered through a filter of 0.1 µm pore size. After a certain amount of solid amphiphile and 20 mL of water were put together into a closed conductivity cell and this system reached a thermal equilibrium in a thermostat, the electric conductivity of the system was traced with time, where the system was agitated all the time in the cell. The conductivity value was recorded every 10 min for 40 min at a definite temperature for both cases of increasing and decreasing temperature. The conductivity was traced first with increasing temperature (from 278.2 to 348.2 K) and then with decreasing temperature (from 338.2 to 278.2 K) after the system was kept above 338 K for more than 10 h. Finally, the conductivity was traced back by increasing temperature. This set of consecutive operations was done for the systems whose amphiphile concentrations were cmc, 2 × cmc, and 3 × cmc. Determination of Critical Micelle Concentration. The cmc’s were determined by electric conductivity of the solutions at different concentrations below and above the cmc. Before the measurement, an estimation of the cmc’s was made using the previous cmc data for CnF2n+1COOLi (n ) 5-11) at 298.2 K,15,20 (19) Morisue, T.; Moroi, Y.; Shibata, O. J. Phys. Chem. 1994, 98, 12995. (20) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems; NSRDS-NBS 36; National Bureau of Standards, U.S. Government Printing Office: Washington, DC, 1971.

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Figure 2. Shift of the size distribution with time for the C8TAC solution: concentration ) 39.5 mmol dm-3. Figure 1. The Debye plots for the C8-TAC solution at 298.2 K. assuming that the slopes of ln(cmc) against the carbon number (Cn) of the alkyl chain would not be much different among the surfactants whose headgroups are nevertheless different. Before the measurement, the concentrated amphiphile solution was kept at 335 K all night long. The temperature of the system was controlled within (0.01 K by a thermostat. After the system reached a thermal equilibrium, the solution was diluted stepwise by adding a certain volume of distilled water with a syringe after the same volume of the solution was withdrawn from the cell. The measurements were carried out over the temperature range from 288.2 to 328.2 K. Dissociation of Aggregates to Monomers. As for the three surfactants except C14-TAC, the aqueous solutions above their cmc’s were diluted below the cmc in order to obtain the rate constant for dissociation of molecular aggregates to monomers. Surfactant solution (400 µL) of 5 × cmc was poured into 4 mL of double-distilled water in a test tube with a microsyringe, where the solution was stirred constantly. An LCR meter traced the time dependence of the solution conductivity during the dilution process, outputting the electric resistance of the aqueous solution as voltage on an oscilloscope screen (TDS430A, Tektronix).

Figure 3. Change of aggregate diameter with temperature for C8-TAC: concentration ) 4.30 mmol dm-3.

Results and Discussion Static Light Scattering (C8-TAC). The mean molecular weight of the aggregates was determined first by the Debye plots for the C8-TAC solution at 298.2 K using the reduced scattered-light intensity at 90°, and then the mean aggregation number was calculated to be 285 (Figure 1). Such a large number means the existence of very large aggregates that are not spherical. In other words, it is less possible to form spherical aggregates for the fluorinated surfactant which has a rigid hydrophobic chain with almost the same cross-sectional area as the headgroup. Then, the angle dependence of the reduced scattered-light intensity was checked over the angle range from 45° to 135° at 298.2 K in order to confirm the nonspherical shape of the aggregates. The result showed an obvious angle dependence, which indicates that the aggregates formed in the solution are not spherical. Judging from the molecular structure whose packing parameter is almost equal to 1, the molecular aggregates are more lamellar than spherical in shape. Quasi-Elastic Light Scattering (C8-TAC, C10TAC). The time dependence of the size distribution of the aggregates was examined using the solutions of 3 × cmc prepared at room temperature. By naked eye observation, the solutions set in the QELS apparatus kept at 298.2 K dimly glimmered sometimes and at some places in the dark, when the particles scattered an incident beam. This

indicates the presence of large particles, and the twinkle from the solution was different from that of dust flashed by the incident light. In fact, the experimental results of QELS showed the presence of plural size distributions in solutions for both C8-TAC and C10-TAC, and their distribution maxima decreased with time. In addition, the aggregates are quite larger than expected (Figure 2). Such large aggregate formation is observed in the case of long fluorocarbon amphiphiles.16 Molecular aggregates change their size among themselves through transfer of monomeric species in the bulk. Therefore, it should take a very long time to reach thermodynamic equilibrium for such aggregate systems in which the chemical potential of monomer in equilibrium with one aggregate is nearly equal to that in equilibrium with the other aggregate of a different size. At the same time, the change of the size distribution with temperature could be examined by naked eye observation. The scattered light became sharp and strong with increasing temperature from room temperature up to 333.2 K. Changes in the size distribution with temperature were also confirmed by QELS as shown in Figure 3. It was not possible to carry out the QELS measurement for C12-TAC and C14-TAC due to their quite dilute concentration and small refractive index, but a similar intensity histogram from QELS can be easily expected, judging from the poor reproducibility and the


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Figure 4. Hysteresis of electric conductivity against temperature for C8-TAC.




time dependence of the electric conductivity of the solutions prepared at room temperature. Hysteresis of Electric Conductivity against Temperature. Figures 4-7 show the hysteresis of electric conductivity against temperature for C8-, C10-, C12-, and C14-TAC, respectively. The conductivity measurement is composed of the following four processes: (i) electric conductivity was traced with increasing temperature from 278.2 to 348.2 K (up 1), (ii) the system was left at a temperature around 338 K all night (for more than 10 h), (iii) the same measurement as in process i was made with decreasing temperature from 338.2 to 278.2 K (down), and finally, (iv) the conductivity was traced back the downprocess again by increasing temperature (up 2). This set of consecutive operations was carried out for the solutions whose concentrations were cmc, 2 × cmc, and 3 × cmc for every surfactant. In all the processes, the conductivity values were recorded at every 10 min for 40 min at a certain temperature. As shown in Figures 4-7, processes iii and iv are almost reversible, although the κ values of these two processes are quite different from those of

process i, especially at lower temperatures. In addition, the conductivity kept increasing at any temperature over the whole temperature range examined during process i, which was profound especially for C12-TAC and C14-TAC. For processes iii and iv, however, it took less than 10 min to reach a stable conductivity for all the systems studied. As for process i, an increase in the conductivity with time might result from polydispersity in the size of quite large aggregates and from destruction of large aggregates of lamellar structure to smaller ones through monomers in a bulk phase. Especially when the chemical potential of the monomer in a bulk phase is almost equal to that in equilibrium of the aggregates of different sizes, it should take a very long time to reach thermodynamic equilibrium of the system. By keeping the solution at the highest temperature (process ii), the system reaches the final state of smaller aggregates, and therefore, the aggregates easily transform to become the equilibrium state, even when the temperature is changed. Dependence of the hysteresis on concentration being compared for the same surfactant, it turned out that the more concentrated the solution, the

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Figure 8. Changes of specific conductivity with total surfactant concentration for C12-TAC.

more the aggregates are structuralized or in lamellar form at lower temperatures. At the same time, the longer the hydrophobic chain, the more structuralized the aggregates become at lower temperatures, as is clear from the differences among the four amphiphiles. Change of Critical Micelle Concentration with Temperature (C12-TAC and C14-TAC). Figure 8 illustrates changes of the electric conductivity with concentration for C12-TAC at various temperatures from 288.2 to 328.2 K. Although the conductivity of the solution at a certain concentration prepared at room temperature had continued to increase for a very long time, the solution treated once at high temperature showed good reproducibility for the conductivity. This means that the system itself needs quite a long time to reach the stable aggregate state when prepared at room temperature, while the solution once heated above 338.2 K all night long easily becomes an equilibrium state within a relatively short period of time, as is seen in the above section. Therefore, heated solutions were used for all measurements. The cmc is usually determined as the concentration at an intersection between two straight lines of the conductivity below and above it, but the present amphiphiles do not have a clear intersection, because change in the gradient of the conductivity against concentration is very slow around the cmc. This indicates that the aggregation number of micelles is relatively small. Indeed, the micellar size became much smaller at higher temperatures and for longer hydrophobic chains. This tendency could be equally observed for the four present surfactants including C8-TAC and C10-TAC. Therefore, the cmc’s were determined as the concentration corresponding to the maximum change in the gradient. That is, the first derivatives of the conductivity with respect to concentration were plotted against the concentration, and an inflection point of the derivative curve was regarded as the cmc.21 The cmc of C12-TAC increased monotonically with temperature (Figure 9). For C14-TAC, the first derivative did not have a clear inflection point, and therefore, the concentration where the conductivity started to stray downward from a straight line on the conductivities at lower concentrations was determined as the cmc. The indistinctness of the inflection point indicates that smaller aggregates than (21) Phillips, J. N. Trans. Faraday Soc. 1955, 51, 561.

Kubo et al.

Figure 9. Change of cmc with temperature for C12-TAC and C14-TAC. Table 1. Critical Micelle Concentrations of C12-TAC and C14-TAC at Different Temperatures surfactant

temperature/K

cmc/mmol dm-3

C12-TAC

288.2 298.2 308.2 318.2 322.8 288.1 298.2 308.1 318.0 328.2

0.25 0.25 0.28 0.34 0.35 0.023 0.029 0.032 0.034 0.036

C14-TAC

those of C12-TAC are formed and that the C14-TAC aggregates grow in their size little by little with the concentration above the cmc, once heated above 328.2 K. The cmc’s at various temperatures are summarized in Table 1 and are plotted against temperature in Figure 9. The monotonic increase in the cmc’s with temperature for both C12-TAC and C14-TAC indicates that the micellizations are enthalpy driven. The change of the logarithm of the cmc’s against the carbon number of the alkyl chain is shown in Figure 10, in which the change for the corresponding hydrogenated surfactants with identical headgroups is also given using their cmc.20 If the degree of counterion binding to micelles is known, it is possible to discuss the Gibbs energy contribution per carbon atom to micelle formation (∆GCH20 or ∆GCF20) from the slopes of both surfactant series. Roughly speaking, a fluorocarbon chain is more hydrophobic than a hydrocarbon chain by 1.54-fold just from the slopes above, the same degree being assumed. Kinetics for Dissociation of Aggregates into Monomers (C8-, C10-, C12-TAC). The present purpose is to evaluate the rate constants for the process of the system from the state where surfactant molecules partly exist as aggregates to the state where all the surfactant molecules exist as monomers. The measurement was carried out as follows: immediately after the concentrated solution was diluted below the cmc, the conductivity change of the system was followed for about 1 min with an oscilloscope. The constant value was not obtained even 1 min later from an injection of the concentrated solution into water, but it took more than 30 min to reach a constant value on a LCR meter, although the voltage drifted slightly.


Langmuir, Vol. 18, No. 23, 2002 8775 k

A 98 M

(1)

where A, M, and k are the aggregates, the monomers, and the dissociation rate constant, respectively. The rate equation is given by

d[AM] ) -k[AM] dt

(2)

where [AM] is an equivalent concentration of ionic amphiphile in the aggregates to dissociate to monomers. When [AM0] is the concentration of [AM] at t ) 0, eq 2 gives rise to

[AM] ) [AM0]e-kt

Figure 10. 10. Dependence of ln(cmc) on the carbon number for alkyltrimethylammonium chloride at 298.2 K.

(3)

If the total equivalent concentration of the amphiphile is [St], the concentration of monomers, [M], is expressed by eq 4 from eq 3:

[M] ) [St] - [AM0]e-kt

(4)

On the other hand, the conductivity κ is given by the following relation:

κ ) λA[A] + λM[M]

(5)

where λA and λM are the molar conductivity of aggregate and monomer, respectively. Since the size of the aggregates is much larger than that of monomer, λA ≈ 0 or λM . λA as for the conductivity. Neglecting the micellar term in eq 5 and substituting eq 4 into eq 5, κ can be expressed as eq 6:

κ ) λM[St]{1 - ([AM0]/[St])e-kt}

Figure 11. Change of conductivity with time for dissociation of aggregates into monomers for C12-TAC.

Judging from the results in the preceding sections, it seems better to use the solution above the cmc once heated above 338 K for kinetics for dissociation of the aggregates into monomers. If single decay is observed, the aggregate system once heated might be monodisperse. However, it was quite hard to obtain reproducible rate constants by using the solution once heated, but the reason was not clear. Therefore, the solution prepared at room temperature was employed for this study after standing for a few days. For every surfactant, the solution conductivity κ increases rapidly at first and then gradually with some steps during the dissociation process (Figure 11). The first rapid increase of κ is due to dispersion of the monomeric ions into bulk water caused by their recent addition into water, and some latter nonmonotonic steps mean a few size distributions of the aggregates and their stepwise dissociation into monomers. The last step of the dissociations was used for calculation of the rate constant and the activation energy, because the last half of the decay was traced with relatively high accuracy and because the last decay seemed to be the main decay. Dissociation of the aggregates to the monomers is expressed by

(6)

When the time is taken to be sufficiently long and all aggregates are dissociated to monomers, the conductivity value κ becomes κ∞() λM[St]). Then, eq 6 is rewritten as follows:

ln(1 - κ/κ∞) ) -kt + ln([AM0]/[St])

(7)

The slope for the plots of ln(1 - κ/κ∞) against t then gives the dissociation rate constant. The time dependence of the electric conductivity at several temperatures was analyzed according to eq 7 (Table 2), and the activation energy for the present dissociation process was determined from the Arrhenius plots (Figure 12). The activation energies for the present surfactants are given in Table 3, where other reference values16,22,23 are also given for comparison with the present values. It is quite interesting that the aggregates with longer fluorocarbons have a lower activation energy for their dissociation into monomers. This is quite reasonable, however, judging from the smaller aggregation number of micelles for longer amphiphiles, as was mentioned in the section on cmc change. Usually, the formation and dissociation of hydrocarbon aggregates are very rapid, and the lifetime is 10-2-10-9 s. In the case of the present fluorocarbon surfactants, the process of dissociation could be traced in the order of seconds by the (22) Aniansson, E. A. G.; Wall, S. N.; Almgren, M.; Hoffmann, H.; Kielmann, I.; Ulbricht, W.; Zana, R.; Lang, J.; Tondre, C. J. Phys. Chem. 1976, 80, 905. (23) Baumuller, W.; Hoffman, H.; Ulbricht, W.; Tondre, C.; Zana, R. J. Colloid Interface Sci. 1978, 64, 418.

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Kubo et al. Table 3. Activation Energy for Dissociation of Aggregates to Monomers

a

surfactant

Ea/kJ mol-1

C8-TAC C10-TAC C12-TAC C4H9NH3+C11F23COONi2+(C12H25SO4-)2 Na+C14H29SO4-

59 34 25 76a 67b 144c

Reference 16. b Reference 21. c Reference 22.

Figure 12. 12. The Arrhenius plots for the dissociation processes. Table 2. Rate Constants for Dissociation of Aggregates to Monomers at Different Temperatures surfactant

temperature/K

k/s-1

C8-TAC

283 288 298 308 283 288 298 308 283 288 298 308

0.63 0.67 2.4 3.8 0.13 0.14 0.27 0.39 0.011 0.012 0.018 0.024

C10-TAC

C12-TAC

specific conductivity, and the rate of the dissociation is relatively slow. Therefore, it can be concluded that the exchange between monomers and aggregates takes place very slowly and that the aggregates take a long time to reach the thermodynamic equilibrium state when fluorocarbon surfactant molecules form the aggregates at lower temperatures. In addition, another possible reason for the present aggregate systems to take a very long time to reach thermodynamic equilibrium is that the chemical potential of monomer in equilibrium with one aggregate is nearly equal to that in equilibrium with the other aggregate of different size.

Figure 13. Illustration for dissolution of the fluorocarbon amphiphiles from solid to aqueous solution.

Judging from all experimental results above, the dissolution of the present fluorocarbon amphiphiles from a solid state to a solution state can be illustrated as follows: (i) intrusion of water molecules into the hydrophilic layer of headgroups, (ii) peeling-off of lamellar layers from the solid, and (iii) decrease in size from larger lamellar aggregates to smaller aggregates through monomers in the bulk (Figure 13). Acknowledgment. This work was supported by Grant-in-Aid for Scientific Research No. 10554040 from the Ministry of Education, Science, and Culture of Japan, which is gratefully acknowledged. LA020350U

Study on Molecular Aggregates of N-(1,1-Dihydroperfluoroalkyl)-N,N

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