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Equilibrium and Dynamic Surface Tension Properties of Partially Fluorinated Quaternary Ammonium Salt Gemini Surfactants Tomokazu Yoshimura,*,† Akiko Ohno, and Kunio Esumi Department of Applied Chemistry, Faculty of Science, Tokyo UniVersity of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan ReceiVed December 19, 2005. In Final Form: March 3, 2006 The equilibrium and dynamic surface tension properties of a partially fluorinated quaternary ammonium salt gemini surfactant 1,2-bis[dimethyl-(3-perfluoroalkyl-2-hydroxypropyl)ammonium]ethane bromide (CnFC3-2-C3CnF, where n represents fluorocarbon chain lengths of 4, 6, and 8) were investigated, and the effects of the fluorocarbon chain length and the number of chains on them were discussed. The plot of the logarithm of the critical micelle concentration (cmc) against the fluorocarbon chain length for CnFC3-2-C3CnF showed a linear decrease with an increase in chain length. On the basis of the slope of this plot, it was found that the variation in cmc with respect to the chain length is large for fluorinated gemini surfactants. The surface tension at the cmc decreased significantly; this surface tension value is lower than that of conventional fluorinated monomeric surfactants. In particular, the lowest value was 13.7 mN m-1 for n ) 8. Furthermore, it was confirmed that the kinetics of adsorption at the interface decrease with an increase in the fluorocarbon chain length and the concentration.
Introduction Fluorinated surfactants with a fluorocarbon chain as the hydrophobic group exhibit thermal and chemical stability, high gas-dissolving capacities, low solubility in water, and excellent surface activities such as a remarkably low critical micelle concentration (cmc) and a high efficiency in reducing the surface tension.1-4 These properties are characterized by strong intramolecular bonds and weak intermolecular interactions. Fluorinated surfactants are used in paints, inks, waxes, additives for etching, plating baths, fire extinguishing agents for oil fires, and so on. Recently, a gemini surfactant that possesses two hydrophobic and two hydrophilic parts was very actively investigated by many researchers.5-8 Most gemini surfactants have two hydrocarbon chains in the hydrophobic parts. Oda et al.9 synthesized a partially fluorinated quaternary ammonium salt gemini surfactant 1,2bis[dimethyl-(4-perfluorooctylbutyl)ammonium]ethane bromide in five-step reactions. Its aggregation properties were investigated by cryogenic transmission electron microscopy (cryo-TEM), revealing the formation of unilamellar vesicles with diameters of 15-200 nm. To the best of our knowledge,10-15 there are very * Corresponding author. E-mail:
[email protected]. † Nara Women’s University, Nara 630-8506, Japan. (1) Kissa, E. In Fluorinated Surfactants and Repellents, 2nd ed.; Marcel Dekker: New York, 2001; p 103. (2) Shinoda, K.; Hato, M.; Hayashi, T. J. Phys. Chem. 1972, 76, 909. (3) Krafft, M. P.; Riess, J. G. Biochimie 1998, 80, 489. (4) Riess, J. G. Tetrahedron 2002, 58, 4113. (5) Zana, R.; Xia, J. In Gemini Surfactants: Synthesis, Interfacial and SolutionPhase BehaVior, and Applications; Marcel Dekker: New York, 2003. (6) Zana, R. In Structure-Performance Relationships in Surfactants, 2nd ed.; Esumi, K., Ueno, M., Eds.; Marcel Dekker: New York, 2003; Chapter 7, p 341. (7) Rosen, M. J. CHEMTECH 1993, 23, 30. (8) Menger, F. M.; Littau, C. A. J. Am. Chem. Soc. 1993, 115, 10083. (9) Oda, R.; Huc, I.; Danino, D.; Talmon, Y. Langmuir 2000, 16, 9759. (10) Nishida, J.; Brizard, A.; Desbat, B.; Oda, R. J. Colloid Interface Sci. 2005, 284, 298. (11) Massi, L.; Guittard, F.; Ge´ribaldi, S. Prog. Colloid Polym. Sci. 2004, 126, 190. (12) Li, Y.; Li, P.; Wang, J.; Wang, Y.; Yan, H.; Dong, C.; Thomas, R. K. J. Colloid Interface Sci. 2005, 287, 333. (13) Marty, F.; Bollens, E.; Rouvier, E.; Cambon, A. J. Fluorine Chem. 1990, 48, 239. (14) Gaysinski, M.; Joncheray, L.; Guittard, F.; Cambon, A.; Chang, P. J. Fluorine Chem. 1995, 74, 131.
few reports with regard to fluorinated gemini surfactants. None of these reports have investigated surface tension. Recently, a cationic gemini surfactant with partially fluorinated spacers was synthesized, and its aggregation behavior in solution was studied.16 In this article, we describe physicochemical properties such as equilibrium and the dynamic surface tension of a partially fluorinated quaternary ammonium salt gemini surfactant 1,2bis[dimethyl-(3-perfluoroalkyl-2-hydroxypropyl)ammonium]ethane bromide (CnFC3-2-C3CnF, where n represents fluorocarbon chain lengths of 4, 6, and 8). Scheme 1 shows the synthesis route of the fluorinated quaternary ammonium salt gemini surfactant CnFC3-2-C3CnF. The fluorinated gemini surfactant used in this study contains two 3-perfluoroalkyl-2-hydroxypropyl chains in the hydrophobic part; the fluorocarbon chain length and the hydrocarbon chain part of these chains are different as compared to the 4-perfluorooctylbutyl chains of fluorinated gemini surfactant C8FC4-2-C4C8F, as reported by Oda et al.9 Furthermore, we performed the synthesis of a fluorinated gemini surfactant using two-step reactions and ion exchange. Experimental and Methods Materials. 3-Perfluorobutyl-1,2-epoxypropane, 3-perfluorohexyl1,2-epoxypropane, and 3-perfluorooctyl-1,2-epoxypropane were purchased from Daikin Ind., Ltd. (Osaka, Japan). N,N′-Dimethylethylenediamine from Aldrich and iodomethane from Tokyo Kasei Co., Ltd. (Tokyo, Japan) were used without further purification. Acetone, diethyl ether, ethyl acetate, hexane, magnesium sulfate, methanol, and sodium hydroxide were purchased from Kanto Chemicals Co., Inc. (Tokyo, Japan). Synthesis of N,N′-Dimethyl-N,N′-di(3-perfluoroalkyl-2-hydroxypropyl)ethylenediamine Hydrochloride. 3-Perfluoroalkyl1,2-epoxypropane (0.0454 mol) [alkyl ) butyl (n ) 4), hexyl (n ) 6), and octyl (n ) 8)] was added to a stirred solution of N,N′dimethylethylenediamine (0.0227 mol, 2 g) in methanol containing NaOH. The mixture was refluxed for over 40 h under alkaline conditions by adding NaOH. After the solvent was evaporated under reduced pressure, the residue was washed three times with water and dissolved in hexane (in hot ethyl acetate for n ) 8). Hydrochloric (15) Guittard, F.; Geribaldi, S. J. Fluorine Chem. 2001, 107, 363. (16) Li, Y.; Li, P.; Dong, C.; Wang, J.; Wang, Y.; Yan, H.; Thomas, R. K. Langmuir 2005, 21, 6703.
10.1021/la0534266 CCC: $33.50 © 2006 American Chemical Society Published on Web 04/04/2006
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acid gas was injected into the hexane solution for 30-40 min, and the precipitate obtained was collected by filtration. The product was washed twice with ethyl acetate, recrystallized from mixtures of acetone and methanol (washed several times with hot methanol for n ) 8), and dried under reduced pressure to yield N,N′-dimethylN,N′-di(3-perfluoroalkyl-2-hydroxypropyl)ethylenediamine hydrochloride in the form of white solids. The yields were 61, 45, and 23% for n ) 4, 6, and 8, respectively. Synthesis of 1,2-Bis[dimethyl-(3-perfluoroalkyl-2-hydroxypropyl)ammonium]ethane Iodides (CnFC3-2-C3CnF 2I-). A solution of N,N′-dimethyl-N,N′-di(3-perfluoroalkyl-2-hydroxypropyl)ethylenediamine hydrochloride in 1 N NaOH was stirred while heating for 30 min. After it was cooled to room temperature, the separated oily material was extracted with diethyl ether. The diethyl ether solution was dried over anhydrous magnesium sulfate, and the ether was removed to give N,N′-dimethyl-N,N′-di(3-perfluoroalkyl-2hydroxypropyl)ethylenediamine. Mixtures of N,N′-dimethyl-N,N′-di(3-perfluoroalkyl-2-hydroxypropyl)ethylenediamine and an excess amount of iodomethane were refluxed in acetone at 64 °C for over 50 h under a nitrogen atmosphere. After acetone and iodomethane were removed by evaporation, the residue was washed with hexane, recrystallized several times from mixtures of ethanol and hexane, and dried under reduced pressure to give CnFC3-2-C3CnF 2I- (n ) 4, 6, and 8) in the form of white solids. The yields were 96, 98, and 99% for C4FC3-2-C3C4F 2I-, C6FC3-2-C3C6F 2I-, and C8FC3-2-C3C8F 2I-, respectively. Ion Exchange. CnFC3-2-C3CnF 2I- was dissolved in methanol and passed through a column of Dowex 1-X8 anion-exchange resin (Br form, 50-100 mesh). After the eluted solution was evaporated under reduced pressure, the residue was recrystallized from mixtures of acetone and methanol and dried under reduced pressure, yielding 1,2-bis[dimethyl-(3-perfluoroalkyl-2-hydroxypropyl)ammonium]ethane bromides (CnFC3-2-C3CnF, n ) 4, 6, and 8) in the form of white solids. Measurements. The surface tensions of the aqueous solutions of the fluorinated gemini surfactant were measured with a Kru¨ss K100 tensiometer by the Wilhelmy plate technique. The conditions for the measurement have been described elsewhere.17 The dynamic surface tension was measured using a Kru¨ss BP2 bubble-pressure tensiometer, a method that involves the measurement of the maximum pressure necessary to blow a bubble in a liquid from the tip of a capillary. The measurements were conducted with effective surface ages ranging from 5 ms to 30 s. Furthermore, the scattering intensity was measured by using dynamic light scattering (DLS) (DLS-7000 spectrophotometer, Otsuka Electronics Co., Ltd.), and the electrical conductivity measurements were performed using a CM-20E TOA electrical conductivity meter. All of the surfactant solutions were prepared using Milli-Q Plus water (resistivity ) 18.2 MΩ cm), and all of the measurements were performed at 25 °C. 19F NMR (JEOL JNM-EX 500 MHz, CD OD, CF COOH): n ) 3 3 4 δ -82.73 (t, 3F), -114.21 (q, 2F), -125.67 (s, 2F), -127.18 (s, 2F); C4FC3-2-C3C4F 2I- δ -82.70 (t, 3F), -113.15 to -114.95 (q, 2F), -125.63 (s, 2F), -127.14 (s, 2F); C4FC3-2-C3C4F δ -82.70 (t, 3F), -113.16 to -114.94 (q, 2F), -125.64 (s, 2F), -127.15 (s, 2F). C6FC3-2-C3C6F δ -82.50 (t, 3F), -112.94 to -114.71 (q, 2F), -122.83 (s, 2F), -123.97 (s, 2F), -124.67 (s, 2F), -127.41 (s, 2F). C8FC3-2-C3C8F δ -82.43 (t, 3F), -112.91 to -114.66 (q, 2F), (17) Yoshimura, T.; Nyuta, K.; Esumi, K. Langmuir 2005, 21, 2682.
-122.58 (s, 2F), -122.95 (s, 4F), -123.81 (s, 2F), -124.58 (s, 2F), -127.36 (s, 2F). 1H NMR: C FC -2-C C F(CD OD, TMS) δ 2.46-2.55 (m, 4H), 4 3 3 4 3 3.35 (s, 6H), 3.43 (s, 6H), 3.55 (m, 2H), 3.75 (m, 2H), 4.17 (m, 2H), 4.30 (m, 2H). Elemental analysis (Perkin-Elmer 2400II CHNS/O): n ) 4. Calcd for C18H24N2F18O2Cl2: C, 30.31; H, 3.39; N, 3.93. Found: C, 30.48; H, 3.31; N, 3.83. n ) 6. Calcd for C22H24N2F26O2Cl2: C, 28.93; H, 2.65; N, 3.07. Found: C, 28.78; H, 2.61; N, 3.07. n ) 8. Calcd for C26H24N2F34O2Cl2: C, 28.05; H, 2.17; N, 2.52. Found: C, 28.20; H, 2.05; N, 2.42. C4FC3-2-C3C4F 2I-. Calcd for C20H28N2F18I2O2: C, 25.99; H, 3.05; N, 3.03. Found: C, 25.65; H, 2.93; N, 2.97. C6FC3-2-C3C6F 2I-. Calcd for C24H28N2F26I2O2: C, 25.64; H, 2.51; N, 2.49. Found: C, 25.34; H, 2.45; N, 2.44. C8FC3-2-C3C8F 2I-. Calcd for C28H28N2F34I2O2: C, 25.40; H, 2.13; N, 2.12. Found: C, 25.34; H, 2.04; N, 2.12. C4FC3-2-C3C4F. Calcd for C20H28N2Br2F18O2: C, 28.93; H, 3.40; N, 3.37. Found: C, 28.42; H, 3.26; N, 3.39. C6FC3-2-C3C6F. Calcd for C24H28N2Br2F26O2: C, 27.98; H, 2.74; N, 2.72. Found: C, 27.98; H, 2.80; N, 2.62. C8FC3-2-C3C8F. Calcd for C28H28N2Br2F34O2: C, 27.34; H, 2.29; N, 2.28. Found: C, 27.14; H, 2.18; N, 2.32.
Results and Discussion Equilibrium Surface Tension. The partially fluorinated quaternary ammonium salt gemini surfactants CnFC3-2-C3CnF show a good water solubility at 25 °C. Figure 1 shows the curve of surface tension as a function of the concentration of CnFC32-C3CnF for n ) 4, 6, and 8. The cmc and surface tension values at the cmc (γcmc) are summarized in Table 1. The values of the cmc obtained by the surface tension curves are consistent with the concentrations of break points obtained from the scattering intensity by the DLS method, as shown in Figure 2. In general, when aggregates are formed, the scattering intensity begins to increase dramatically with concentration. Furthermore, it continues to increase when the size or number of aggregates increases. Therefore, the scattering intensities of fluorinated gemini surfactants begin to increase sharply with the concentration; the
Figure 1. Variation in the surface tension with the surfactant concentration for CnFC3-2-C3CnF at 25 °C: 1, n ) 4; 0, n ) 6; and b, n ) 8.
Properties of Ammonium Salt Gemini Surfactants
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Table 1. Parameters Obtained by the Surface Tension Plots of Partially Fluorinated Gemini Surfactants CnFC3-2-C3CnF
a
surfactant
cmc (mmol dm-3)
γcmc (mN m-1)
106Γcmca (mol m-2)
Acmca (nm2/molecule)
∆G0mic (kJ mol-1)
∆G0ads (kJ mol-1)
C4FC3-2-C3C4F C6FC3-2-C3C6F C8FC3-2-C3C8F
11.3 0.172 0.00593
20.3 19.8 13.7
1.49 (2.24) 1.27 (1.91) 1.21 (1.82)
1.11 (0.74) 1.31 (0.87) 1.37 (0.91)
-7.5 -13.5 -21.1
-42.2 -54.6 -69.3
The values in parentheses are calculated for n ) 2.
Figure 2. Variation in the scattering intensity obtained from DLS with the surfactant concentration for CnFC3-2-C3CnF: 1, n ) 4; 0, n ) 6; and b, n ) 8.
Figure 3. Relationship between the cmc and the fluorocarbon chain length for CnFC3-2-C3CnF.
break points in the curves correspond to the cmc. The fluorinated gemini surfactants exhibit smaller γcmc values than the quaternary ammonium salt hydrocarbon gemini surfactant 1,2-bis(alkyldimethylammonium)ethane bromide [10-2-10 for alkyl ) decyl (γcmc ) 32 mN m-1) and 12-2-12 for dodecyl (γcmc ) 40 mN m-1)].18 It is noteworthy that the cmc for n ) 6 is lower than for 12-2-12 (cmc ) 1.1 mmol dm-3), as would be expected from the equivalence of 1 CF2 to 1.5 CH2 units.19 Similar to hydrocarbon monomeric surfactants, the cmc of the fluorinated gemini surfactants decreases with an increase in the fluorocarbon chain length. Figure 3 shows the plot of the number of carbon atoms in the fluorocarbon chain against the logarithm of the cmc of the fluorinated gemini surfactants. In general, an empirical equation (18) Dam, Th.; Engberts, J. B. F. N.; Kartha¨user, J.; Karaborni, S.; van Os, N. M. Colloids Surf., A 1996, 118, 41. (19) Fisicaro, E.; Pelizzetti, E.; Viscardi, G.; Quagliotto, P. L.; Trossarelli, L. Colloids Surf., A 1994, 84, 59.
that relates the cmc to the various surfactant structures can be expressed in the following form: log cmc ) A - BN, where A is a constant for a particular ionic head at a given temperature, B is a constant, and N is the number of carbon atoms in the hydrophobic chains.20 Although there are few data, we discuss this equation with three points. When this equation is based on the assumption that the N value is equal to the sum of chain lengths of 1.5-fold carbons in the fluorocarbon chain plus 3 carbon lengths in the 2-hydroxypropyl chain, the B value of the fluorinated gemini surfactant is 0.55. This value is greater than that for anionic and cationic monomeric surfactants (B ) 0.3) and the corresponding quaternary ammonium salt hydrocarbon gemini surfactant (B ) 0.41).21 This indicates that the cmc variation with the fluorocarbon chain length is relatively large for the fluorinated gemini surfactant. Furthermore, it was found that the cmc value of this surfactant is approximately equal to that of the corresponding hydrocarbon gemini surfactant with a hydrocarbon chain that is 1.7-1.8 times longer than the fluorocarbon chain. This value is greater than those reported for fluorinated monomeric surfactants (1.5-1.7 times),2,22,23 indicating that the hydrophobic interaction between fluorocarbon chains in a molecule is relatively strong. The effectiveness of reducing the surface tension for the fluorinated gemini surfactants is significantly greater than that for the hydrocarbon gemini surfactants; this is attributed to the presence of two fluorocarbon chains in a molecule, which makes a positive contribution to the adsorption at the air/water interface. The surface tension at concentrations above the cmc also decreases with an increase in the fluorocarbon chain length. The efficiency of the fluorinated gemini surfactant in terms of surface tension reduction increases with chain length. Shinoda et al. reported that the surface tensions of fluorinated monomeric surfactants are as low as 15-20 mN m-1 or even lower.2,24,25 It was suggested that the higher hydrophobicity of the fluorocarbon chain enhances the amphiphilic character of the surfactant and increases the surface activity. The adsorbed amount of a surfactant (Γ) can be calculated according to the Gibbs adsorption equation, Γ ) -(1/iRT)(dγ/d ln C).26 Here, γ denotes the surface tension, R is the gas constant (8.31 J mol-1 K-1), T is the absolute temperature, and C is the surfactant concentration. The value of i for the fluorinated gemini surfactants in this study is considered to be 2 and 3 in order to take into consideration the number of molecular species possibly involved, namely, one surfactant molecule and one (i ) 2) and two (i ) 3) counterions.27 Then, the area occupied per surfactant molecule (Acmc) at the air/water interface is obtained from the value of saturation adsorption at the cmc (Γcmc) by using the (20) Klevens, H. B. J. Phys. Colloid Chem. 1948, 52, 130. (21) Zana, R.; Le´vy, H. Colloids Surf., A 1997, 127, 229. (22) Selve, C.; Ravey, J. C.; Moudjahid, C. El; Moumni, E. M.; Delpuech, J. J. Tetrahedron 1991, 47, 411. (23) Ravey, J. C.; Gherbi, A.; Stebe, M. J. Prog. Colloid Polym. Sci. 1981, 259, 761. (24) Kunieda, H.; Shinoda, K. J. Phys. Chem. 1976, 80, 2468. (25) Schuierer, E. Tenside 1976, 13, 1. (26) Rosen, M. J. Surfactants and Interfacial Phenomena, 3rd ed.; John Wiley and Sons: New York, 2004; p 60. (27) Alami, E.; Beinert, G.; Marie, P.; Zana, R. Langmuir 1993, 9, 1465.
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Figure 4. Variation in the electrical conductivity with the surfactant concentration for CnFC3-2-C3CnF at 25 °C: (a) n ) 4, (b) n ) 6, and (c) n ) 8.
following expression: Acmc ) 1/NΓcmc, where N is Avogadro’s number. The greater the effectiveness of adsorption, the smaller the area occupied by a surfactant molecule. Furthermore, the Γcmc and Acmc values of the fluorinated gemini surfactants are listed in Table 1. The Acmc values increase with increasing fluorocarbon chain length, indicating that the adsorption and orientation of fluorinated gemini surfactants change with chain length. The Acmc values for the fluorinated gemini surfactants obtained with i ) 2 are close to the values for twice the molecular area of the fluorinated monomeric surfactants (0.41-0.55 × 2 nm2/molecule).2 In addition, the Acmc values of the fluorinated gemini surfactants are also close to those of the corresponding quaternary ammonium salt hydrocarbon gemini surfactants with two dodecyl chains and a spacer chain of 3-6 (1.05-1.43 nm2/ molecule for i ) 2),27 indicating that the adsorption at the air/ water interface is independent of the nature of hydrophobic chains. The standard free energy of the micellization and adsorption (∆G0mic and ∆G0ads, respectively) of fluorinated gemini surfactants can be obtained from the following equations:28,29
∆G0mic ) RT
cmc (21 + β) ln(55.3 ) - (RT2 ) ln 2
∆G0ads ) ∆G0mic -
πcmc Γ
(1) (2)
where πcmc denotes the surface pressure at the cmc (πcmc ) γ0 - γcmc, where γ0 and γcmc are the surface tensions of water and the surfactant solution at the cmc, respectively). Furthermore, β is the apparent degree of counterion binding at the micelle/solution interface, calculated from β ) 1 - R (R is the degree of micelle ionization). Here, R is taken as the ratio of the values of dκ/dC (κ denotes the conductivity) above and below the cmc obtained from the electrical conductivity measurements. Figure 4 shows the variations in conductivity with concentration. The break points obtained in these measurements are consistent with the cmc obtained using the surface tension measurements. The R values of the fluorinated gemini surfactants are found to be 0.90, 0.91, and 0.82 for n ) 4, 6, and 8, respectively. The R values for n (28) Zana, R. Langmuir 1996, 12, 1208. (29) Rosen, M. J.; Aronson, S. Colloids Surf., A 1981, 3, 201.
) 4 and 6 are larger than that for n ) 8, suggesting that fluorinated gemini surfactants with shorter chain lengths form micelles with a relatively small aggregation number. The ∆G0mic and ∆G0ads values of the fluorinated gemini surfactants are also summarized in Table 1. The absolute values of ∆G0ads are significantly greater than those of ∆G0mic for all the fluorocarbon chain lengths, suggesting that in comparison to micellization the adsorption of fluorinated gemini surfactants is higher. Furthermore, both of the absolute values increase with the fluorocarbon chain length. This implies that the interaction between the fluorocarbon chains is strengthened as the chain length increases. These results are also supported by the pC20 value and the cmc/C20 ratio, which are obtained from the method proposed by Rosen.26 The pC20 values are 3.28, 5.31, and 7.13, and the cmc/C20 ratios are 21.3, 35.0, and 80.8 for n ) 4, 6, and 8, respectively. The pC20 values of fluorinated gemini surfactants are greater than those of fluorinated monomeric surfactants (2.50-3.56).1 In general, the cmc/C20 ratios of conventional hydrocarbon monomeric surfactants are low, 3 or less, and the larger the ratios, the greater the tendency of the surfactant to adsorb at the air/water interface relative to the micelle formation. The cmc/C20 ratios of the fluorinated gemini surfactants are very large and increase with the fluorocarbon chain length. From these results, it was suggested that in comparison with the micellization in solution the adsorption at the air/water interface for the fluorinated gemini surfactants is higher. Dynamic Surface Tension. To investigate the kinetics of adsorption for the fluorinated gemini surfactants, dynamic surface tension measurements were performed by the maximum bubblepressure technique. These dynamic methods can measure the surface tension in a few milliseconds and are highly suitable for investigating the kinetics of surfactant adsorption. The variation of the dynamic surface tension as a function of the surface age for n ) 4 and 6 is shown in Figure 5. The dynamic surface tension for n ) 8 is close to that of water, even for the longest measurement time (not shown). The time required to attain the equilibrium surface tension increases with the fluorocarbon chain length, indicating the difficulty of adsorption at the air/water interface from the interior of the solution because of the steric hindrance caused by the long chains. This implies that fluorinated gemini surfactants with shorter fluorocarbon chains diffuse faster
Properties of Ammonium Salt Gemini Surfactants
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Figure 5. Dynamic surface tension with surface age for CnFC32-C3CnF at 25 °C: (a) n ) 4; 0, cmc × 0.086; 2, cmc × 0.43; O, cmc × 1.7; 9, cmc × 3.4 and (b) n ) 6; b, cmc × 0.49; 0, cmc × 0.98; 2, cmc × 2.9; O, cmc × 4.9; 9, cmc × 13.
and adsorb more effectively at the air/water interface. This trend is also observed for some hydrocarbon gemini surfactants.17,30,31 The dynamic surface tensions after 30 s for n ) 4 are close to the equilibrium surface tension values, whereas the dynamic surface tensions for n ) 6 are significantly greater than the equilibrium values. Furthermore, the time required to attain surface tension equilibrium increases with decreasing surfactant concentration; the equilibration is more rapid above the cmc than below it. Another way of analyzing the dynamic surface tension is by using the diffusion-controlled adsorption model. The Ward and Tordai model is most commonly used.32 The process can be analyzed quantitatively using the following integral equation
Γ(t) )
(4Dπ )
1/2
(C0t1/2 +
∫0tCs(τ) dxt - τ)
(3)
where t is the time, Γ(t) is the surface concentration, D is the monomer diffusion coefficient, C0 is the bulk concentration, Cs(t) is the concentration at the subsurface, and τ is a dummy timedelay variable. Values of D at short times, which are based on the short-time approximation (eq 3), can be obtained by the (30) Yoshimura, T.; Ishihara, K.; Esumi, K. Langmuir 2005, 21, 10409. (31) Yoshimura, T.; Ichinokawa, T.; Kaji, M.; Esumi, K. Colloids Surf., A 2006, 273, 208.
Figure 6. Dynamic surface tension as a function of t1/2 for CnFC32-C3CnF: (a) n ) 4 and (b) n ) 6. Symbols are the same as those in Figure 5.
following equation using dynamic short-time surface tension data33
γ - γ0 ) -2C0RT
(Dtπ )
1/2
(4)
where γ0 denotes the surface tension of the solvent. Furthermore, apparent diffusion coefficients can be calculated from long-time dynamic surface tension data by using the equation by Hansen and Joos34,35
γt - γe )
RTΓ2 C0(π/4Dt)1/2
(5)
where γe is the equilibrium surface tension at infinite time and Γ is the surface excess concentration, which can be obtained from the equilibrium surface tension measurements. At a constant surfactant concentration C0, the plots of γ versus t1/2 based on eq 4 and γt versus t-1/2 based on eq 5 should be linear if the adsorption is diffusion-controlled, allowing the evaluation of D from the slope of each plot. Figures 6 and 7 show the plots of dynamic surface tension versus t1/2 and t-1/2 for n ) 4 and 6, respectively. These plots exhibit linear behavior over the shorter (32) Ward, A. F. H.; Tordai, L. J. Phys. Chem. 1946, 14, 453. (33) Bendure, R. L. J. Colloid Interface Sci. 1971, 35, 238. (34) Hansen, R. S. J. Phys. Chem. 1960, 64, 637. (35) Rillaerts, E.; Joos, P. J. Phys. Chem. 1982, 86, 3471.
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Table 2. Parameters Calculated from the Dynamic Surface Tension for CnFC3-2-C3CnF n)4
n)6
concentration (mmol dm-3)
gradient (mN m-1 s1/2)
D (m2 s-1)
concentration (mmol dm-3)
gradient (mN m-1 s1/2)
D (m2 s-1)
0.969 (cmc × 0.086) 4.85 (cmc × 0.43) 19.4 (cmc × 1.7) 38.8 (cmc × 3.4)
16.3 3.54 0.898 0.645
9.54 × 10-14 8.05 × 10-14 7.83 × 10-14 3.80 × 10-14
0.0840 (cmc × 0.49) 0.168 (cmc × 0.98) 0.504 (cmc × 2.9) 0.840 (cmc × 4.9) 2.27 (cmc × 13)
20.8 70.3 39.4 24.7 16.0
4.11 × 10-12 8.97 × 10-14 3.18 × 10-14 2.91 × 10-14 9.47 × 10-15
time scales (t1/2) and longer time scales (t-1/2). In the case of plots with a short time scale, when t equals zero, the values of the intercept should be close to the surface tension value of water, approximately 72 mN m-1. The values of the intercept for n ) 6 are close to the surface tension value of water, whereas for n ) 4 they are less than that of water. Measurements on a shorter time scale (
