9576
J. Phys. Chem. B 2001, 105, 9576-9580
Thermodynamics of Molecular Self-Assembly of Two Series of Double-Chain Singly Charged Cationic Surfactants Guangyue Bai,† Jinben Wang,† Haike Yan,*,† Zhixin Li,‡ and Robert. K. Thomas‡ Center for Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Beijing, 100080, P. R. China, and Physical and Theoretical Chemistry Laboratory, Oxford UniVersity, South Parks Road, Oxford OX1 3QZ, U.K. ReceiVed: March 15, 2001; In Final Form: June 18, 2001
Microcalorimetric measurements have been made as a function of temperature on the series of double-chain cationic surfactants consisting of a dimethylammonium headgroup attached to alkyl chains of different lengths, CM and CN, giving the formula CMH2M+1CNH2N+1N(CH3)2Br. We have studied compounds with two values of M, 12 and 14, and values of N equal to 1, 2, 4, 6, 8, 10, etc., which we designate by the simpler formula CMCNDAB. In both series, the magnitudes of the values of ∆Hmic pass through a negative minimum at N ) 4-6. At room temperature, this results in the compounds with M ) 12 and N ) 4 and 6 having endothermic enthalpies of micellization. All the other values measured were exothermic. This minimum in ∆Hmic at N ) 4-6 is more than compensated by the behavior of the entropy of micellization, to the extent that no abnormal variation of cmc down the series is observed. Thus, as found for the geminis, simple measurements of ∆Gmic via the cmc conceal more interesting variations in ∆Hmic and ∆Smic. The values of ∆CP,m for both series were first reported in this work, and they were all found to be negative. The results show that the values of ∆CP,m for the C14CNDAB series have a marked minimum but those for the C12CNDAB just have a weak minimum with N.
Introduction There have been few systematic studies of series of surfactants where the main thermodynamic functions have been accurately determined. Several authors have used microcalorimetry to determine values of enthalpy (∆Hmic) and entropy (∆Smic), which can give more insight into the process of micellization than the simple determination of Gibbs free energy (∆Gmic) from the critical micelle concentration (cmc).1-11 It is also worth noting that the values of ∆Hmic obtained by microcalorimetry are direct measurements and can often be made more accurately than the indirect determination of ∆Gmic from the cmc. In recent years, Kresheck et al.12-15 reported microcalorimetric results of the thermodynamics of micellization of the long-chain alkyldimethylphosphine oxides in H2O and D2O solution. This promoted assuredly the development in the field of thermodynamics of micellization.15 In a previous paper,16 we have found that the study of a relatively long series of similar compounds reveals interesting trends in the variation of ∆Hmic and ∆Smic, which are not apparent in the behavior of either the cmc or ∆Gmic. Furthermore, we found that the variation of ∆Hmic and ∆Smic with the temperature was large, and we were able to follow the behavior of the heat capacity of micellization (∆CP,m), which may also be a useful thermodynamic function for understanding the process of micellization.1-4,15 In the present paper, we present microcalorimetric measurements on two series of double-chain cationic surfactants. These consist of a dimethylammonium headgroup attached to alkyl chains of different length, CM and CN, giving the formula CMH2M+1CNH2N+1N* Corresponding author. Fax: 86-010-62559373. Tel: 86-010-62562821. E-mail:
[email protected]. † Institute of Chemistry, the Chinese Academy of Sciences. ‡ Physical and Theoretical Chemistry Laboratory, Oxford University.
(CH3)2Br. We have studied compounds with two values of M, 12 and 14, and values of N equal to 1, 2, 4, 6, 8, 10, etc. We designate these compounds by the simpler formula CMCNDAB. As far as we can ascertain, comparable thermodynamic measurements have only been made on compounds with N ) 14,5,9, or on related versions of the symmetrical double-chain compounds, for example, on the double-chain chlorides by Ro´zyckaRoszak et al.17 Several of the compounds in these two series also do not seem to have been studied previously by any method. The normal difficulty in studying a series of compounds with varying chain length is that the Krafft temperature intervenes at some point in the series and only a small run of compounds can be studied. In the present series of compounds, the disorder introduced by the mismatch of the two chains seems to circumvent this difficulty. A further point of interest about these double-chain compounds is that the symmetrical versions have been widely used because of their readiness to form vesicles.18-21 However, the longer-chain symmetrical compounds often have quite high Krafft points. The introduction of asymmetry gives the possibility of lowering the Krafft point and hence of generating compounds of greater utility than the currently available symmetrical ones. Experimental Section Materials. The CMCNDAB series of surfactants were synthesized and purified as follows. The alkyldimethylamine of one chain was reacted with excess of the other chain alkyl bromide in methanol or acetone at 40 °C for 2 weeks. The solvent was removed by evaporation and the excess bromide removed by washing with ether. The CMCNDAB was then recrystallized three times from either acetone or an acetone/ ether mixture, depending on the chain length. The compounds where one chain has about half the length of the other were
10.1021/jp010975l CCC: $20.00 © 2001 American Chemical Society Published on Web 09/07/2001
Double-Chain Singly Charged Cationic Surfactants
Figure 1. Variation of the observed enthalpies (∆Hobs) with concentration (C) of the C12CNDAB in the microcalorimetry dilution experiment at 298.15, 303.15, and 308.15 K. (a) C12C2DAB (initial concentration, 80 mM); (b) C12C6DAB (initial concentration, 10-20 mM).
particularly difficult to purify because they were found to be soluble in most solvents. A crucial precaution in all the preparations was to ensure that there was no water present. The alkyldimethylamines were purchased, where available, from Aldrich. Where they were not available, they were prepared as follows. The alkyl bromide was mixed with excess dimethylamine in methanol solution and kept at 40 °C for 2 weeks. The methanol and excess dimethylamine were removed by evaporation, and any unreacted alkyl bromide was removed by washing with ether. The remaining alkyldimethylammonium bromide was dissolved in water and made basic with sodium hydroxide, and the alkyldimethylamine was extracted into ether. The final product was purified on a silica flash column. Elemental analysis of investigated compounds gave satisfactory results (C (0.5%, H (0.29%, N (0.11%, and Br (0.37%). Surface tension measurements were used further to establish the surface purity. In every case, the variation of surface tension with the logarithm of the concentration showed no evidence of a minimum, indicating that all the surfactants were pure with respect to their surface chemistry. All the surfactant solutions were prepared using doubly distilled water. Microcalorimetry Measurement. An improved LKB-2107 isothermal titration microcalorimeter with a 1 mL sample cell was used for the measurements. The experimental procedures have been described in a previous paper.22 It has a precision of electrical calibration better than (1%, and its accuracy was tested by measuring the dilution enthalpy (-0.643 ( 0.015 kJ/ mol) of a concentrated sucrose solution, giving results in good agreement with the literature values (-0.653 kJ/mol).23 For the experiments on the surfactants, the sample cell and the reference cell of calorimeter were initially respectively loaded with 0.5 and 0.7 mL pure water. A concentrated solution of surfactant
J. Phys. Chem. B, Vol. 105, No. 39, 2001 9577
Figure 2. Variation of the observed enthalpies (∆Hobs) with concentration (C) of the C14CNDAB in the microcalorimetry dilution experiment at 298.15, 303.15, and 308.15 K. (a) C14C4DAB (initial concentration, 10 mM); (b) C14C6DAB (initial concentration, 5-20 mM).
was injected to the stirred sample cell via a 500 µL Hamilton syringe controlled by a Braun 871182 pump. A series of injections, each 10-20 µL, was made until the desired range of dilution had been covered. The error limit is the standard deviation of the mean estimated from three-five times experiments. The experiments were performed at temperatures of 298.15, 303.15, and 308.15 ( 0.02 K. Results The titration processes were found to be endothermic for the majority of the measurements, and these correspond to negative enthalpies of micelle formation for these surfactants. The one series of measurements showing endothermic enthalpies of micelle formation were the C12CNDAB at 298.15 K with secondary chain lengths N ) 4 and 6. The typical calorimetric curves of the variation of the observed enthalpies of dilution (∆Hobs) with concentration (C) for the two series of surfactants, C12CNDAB and C14CNDAB were shown in Figures 1 and 2, respectively. Values of the cmc and the enthalpy of micellization, ∆Hmic, were determined from the curves according to literature methods.6,10,26 On each plot, a clear break corresponding to micelle formation was observed, allowing identification of the cmc by using an extrapolation;6,26 meanwhile, the enthalpy of micellization, ∆Hmic, is obtained from the difference between the observed enthalpies of the two linear segments of the plot,10 as shown in Figure 3. When the overall concentration is in the premicellar range, the added micelles from the concentrated solution dissociate into monomers, and the monomers are diluted. However, when the overall concentration reaches the cmc and above, the added micelles merely become diluted without any dissociation. We found that the ∆Hobs values bellow the cmc increase with temperature in Figure 1 and 2; hence,
9578 J. Phys. Chem. B, Vol. 105, No. 39, 2001
Bai et al. TABLE 2: Enthalpies and Heat Capacities of Micellization for C12CNDAB Series in Water at 298.15, 303.15, and 308.15 K ∆Hmic (kJ/mol) n
298.15 K
a
n
298.15 K
303.15 K
308.15 K
298.15 K 16.10 -13.9 5.11 1.88 0.69 0.25
0.76 0.72 0.56 0.47 0.38 0.26 0.14
1 15.90 ( 0.30 15.90 ( 0.40 16.00 ( 0.41 2 14.80 ( 0.30 14.96 ( 0.29 14.50 ( 0.30 4 8.20 ( 0.15 7.96 ( 0.22 8.88 ( 0.27 6 3.80 ( 0.07 3.29 ( 0.09 3.30 ( 0.10 8 1.50 ( 0.03 1.08 ( 0.03 0.91 ( 0.03 10 0.65 ( 0.01 0.58 ( 0.02 0.51 ( 0.02 12 0.30 ( 0.01 0.20 ( 0.02 0.11 ( 0.04 a
From ref 16.
n
298.15K
303.15K
308.15K
1 2 4 6 8 12
3.32 ( 0.05 3.06 ( 0.05 2.45 ( 0.05 1.12 ( 0.02 0.84 ( 0.03 0.098 ( 0.014a
3.33 ( 0.05 3.06 ( 0.05 2.59 ( 0.06 0.96 ( 0.02 0.69 ( 0.04 0.11 ( 0.01
3.43 ( 0.05 3.07 ( 0.05 2.10 ( 0.07 0.81 ( 0.03 0.52 ( 0.04 0.098 ( 0.014
a
At 313.15 K.
TABLE 4: Enthalpies of Micelle Formation for C14CNDAB Series in Water at 298.15, 303.15, and 308.15 K
This work. b The data are calculated using eq 2. c From ref 25.
the corresponding ∆Hmic values increase with temperature, suggesting that the hydrophobic interactions become weaker at relatively high temperatures.7 The Gibbs free energy of micellization (∆Gmic), namely, the free energy change for the transfer of one surfactant from the aqueous phase to the micellar pseudophase, is calculated using an expression in the literature:24
∆Gmic ) (1 + β) RT ln(cmc)
(1)
where the cmc is expressed in the molarity of surfactant (mol/ L) and β stands for the degree of dissociation of the micelle. The β values for C12CNDAB series are available from the literature,25 listed in Table 1. We note that the β error introduces some uncertainty into the value of ∆Gmic, an uncertainty that is not present in the determination of ∆Hmic. The entropy of micellization, ∆Smic, can then be derived using the values of ∆Hmic and ∆Gmic. The mean value of ∆CP,m over the whole temperature range was derived from the variation of ∆Hmic with temperature. The complete sets of calorimetric results are given in Tables 1-4. The cmc values of the C12CNDAB are available at 298.15 K, as shown in Table 1, mainly from noncalorimetric method.25 There is reasonable agreement at N ) 1 and N > 8, but there is a larger deviation at N ) 4 and 6. The log cmc versus N curves obey the following linear equation:
log cmc ) -aN + b
(2)
With N > 2, a ) 0.1830 for calorimetric method; with N > 3, a ) 0.217 for non-calorimetric method.25 It is clearly seen that the cmc values from our experiments are lower than the ones from noncalorimetric method. In a previous paper,27 we once obtained the cmc of sodium dodecyl sulfate (SDS) according to Andersson and Olofsson’s method,6 but it is not identical to the cmc obtained from surface tension measurement. This
-0.346 ( 0.022 -0.332 ( 0.043 -0.351 ( 0.054 -0.464 ( 0.023 -0.436 ( 0.036 -0.541 ( 0.032 -0.920 ( 0.061
CMC (mM)
noncalorimetryb βc
(kJ mol-1 K-1
TABLE 3: CMCs (mM) for C14CNDAB Series in Water at 298.15, 303.15, and 308.15 K
TABLE 1: CMCs (mM) for C12CNDAB Series in Water at 298.15, 303.15, and 308.15 K microcalorimetrya
∆Cp,m 308.15 K
-1.63 ( 0.03 -3.54 ( 0.05 -5.09 ( 0.07 -0.43 ( 0.01 -1.72 ( 0.03 -3.75 ( 0.06 1.52 ( 0.03 -0.70 ( 0.02 -1.99 ( 0.03 1.80 ( 0.04 -0.72 ( 0.02 -2.36 ( 0.04 -1.49 ( 0.03 -3.35 ( 0.10 -5.85 ( 0.12 -2.48 ( 0.05 -4.91 ( 0.17 -7.89 ( 0.16 -6.61 ( 0.13 -11.74 ( 0.29 -15.81 ( 0.3
1 2 4 6 8 10 12
Figure 3. Example of determining the cmc and ∆Hmic from the microcalorimetric curve.
303.15 K
∆Hmic (kJ/mol) n
298.15K
303.15K
∆Cp,m 308.15K
1 -4.55 ( 0.07 -6.79 ( 0.10 -9.24 ( 0.14 2 -2.90 ( 0.04 -5.29 ( 0.08 -6.99 ( 0.10 4 -1.15 ( 0.02 -2.88 ( 0.08 -5.09 ( 0.09 6 -0.92 ( 0.02 -3.04 ( 0.06 -5.60 ( 0.11 8 -3.22 ( 0.06 -5.53 ( 014 -7.90 ( 0.20 12 -24.88 ( 0.45a -16.08 ( 0.48 -20.85 ( 0.53 a
(kJ/ mol K) -0.469 ( 0.012 -0.409 ( 0.039 -0.394 ( 0.027 -0.469 ( 0.025 -0.476 ( 0.008 -0.998 ( 0.075
At 313.15 K.
mainly depends on the methods of determining the cmc of surfactant from different calorimetric curves.28 The values of ∆Hmic as a function of secondary chain length N are shown for the two series in Figure 4. Values of the first member of each series (N ) 1) have previously been obtained by several authors3,4,8,9 and again agree with our values. The temperature sensitivity of the enthalpies of micellization leads to the derived values of ∆CP,m listed in Tables 2 and 4. In all cases, ∆CP,m is negative, with magnitudes in the range 0.31.0 kJ mol-1 K-1. Woolley et al.4 also found comparable negative values for ∆CP,m in this temperature range for the N ) 1 compounds, although at lower temperatures (such as at 10 °C), the enthalpies of micellization are positive for CMTAB (M ) 10, 12, 14). Discussion Woolley et al., 4 and Mosquera et al.9 have discussed the variation of ∆Hmic for the single-chain cationic surfactants with N ) 1, i.e., the series (CMTAB). Their enthalpies of micelle formation changed linearly with M from a small positive value to become increasingly negative as M increased. Thus, the enthalpies of micelle formation were found to be positive when M e 10. For the present series of double-chain surfactants, -∆Hmic shows a definite minimum as the secondary chain length N increases for both M ) 12 and 14, as shown in Figure 4. The effect of this minimum actually changes the sign of ∆Hmic for the C12CNDAB at 298.15 K when N ) 4 and 6. This pattern
Double-Chain Singly Charged Cationic Surfactants
J. Phys. Chem. B, Vol. 105, No. 39, 2001 9579
Figure 5. Variation of ln(cmc) (mol/L) for the C12CNDAB with the secondary chain length (N) at 298.15, 303.15, and 308.15 K.
Figure 4. Variation of the enthalpy of micellization, ∆Hmic, for the two series of surfactants with the secondary chain length (N) at 298.15, 303.15, and 308.15 K. (a) C12CNDAB; (b) C14CNDAB.
of behaviour is quite different from that of the single-chain surfactants but is very similar to the gemini surfactants.16 There are three contributions to the thermodynamic functions that need to be considered: the van der Waals interaction between the chains, the headgroup repulsion, and the hydrophobic interaction. The van der Waals and hydrophobic interactions will always tend to make ∆Hmic negative. These would be expected to increase with the total number of carbon atoms in the surfactant. The surface areas per headgroup increase steadily with secondary chain length N,25 and so, the headgroup repulsion and the van der Waals interaction between the primary chains (i.e., the C12 or C14 chains) will decrease with N. The former will make a negative contribution to ∆Hmic, while the latter will lead to a reduction in the magnitude of a negative ∆Hmic. A contribution that may also make ∆Hmic less negative with increasing N for N < 6 if the short side chains remain partly immersed in the water and therefore are unable to take advantage either of the hydrophobic or the van der Waals interactions.25 This would mean that the addition of the first few methylene groups to the secondary chain would not contribute at all to the exothermicity. If the changes in ∆Hmic were a result of the increase in area per molecule at the cmc, we would expect ∆Hmic to become less negative over the whole range of increasing N. This is not what happens. We therefore conclude that it is the secondary chain contribution that causes the minimum. Thus, short secondary chains remain partly immersed in the water, but as their length increases, they behave more and more like normal hydrophobic chains, and the enthalpy starts to become more negative at large N. This effect is exactly paralleled in the closely related gemini surfactants. As mentioned above, the values of ∆Hmic increase with the temperature, but it is worth noting that the differences of the ∆Hmic between two temperatures become larger as increasing N, as shown in Figure 4. We cannot exactly interpret the reason; nevertheless, it can be ascertained that hydrophobic interaction is stronger with larger N than with smaller N, so the effect of temperature on the ∆Hmic is obvious when N is larger.
Figure 6. Variation of the thermodynamic parameters of micellization for the C12CNDAB with the secondary chain length (N) at 298.15 (24), 303.15 (Bn), and 308.15 K(09). Solid symbols, ∆Gmic; open symbols, -T∆Smic
Figure 7. Heat capacity of micellization, ∆Cp,m, for the two series of surfactants against the secondary chain length (N). (a) C12CNDAB; (b) C14CNDAB. The solid lines are the polynomial fiting lines.
A consequence of the minimum in ∆Hmic for the gemini surfactants is that there is a weak maximum in the cmc with varying spacer length. The maximum is much less marked than for ∆Hmic because it is largely offset by a corresponding
9580 J. Phys. Chem. B, Vol. 105, No. 39, 2001 maximum in ∆Smic. Here, although there is a minimum in -∆Hmic, there is no corresponding maximum in the value of the cmc. The cmc variation with N for the C12CNDAB appears to be quite normal, i.e., ln(cmc) varies almost linearly with N (N > 2), as shown in Figure 5. This must mean that the entropy variation with N not only passes through a maximum but also the magnitude of the maximum is such that it exactly compensates for the ∆Hmic variation. This behavior, shown in Figure 6, therefore provides a very striking example of how values of the cmc, and ∆Gmic from the cmc, can give a misleading impression of the behavior of the system. The values of ∆CP,m for the C14CNDAB series show a marked minimum, but those for the C12CNDAB just show a weak minimum with N, shown in Figure 7. There have been few such measurements and little or no theoretical interpretation to date for the two series of surfactants, so in recent work, we only report the actual values of ∆CP,m. One should expect that such information should become increasingly valuable as people explore the process of micellization and establish a reasonable theoretical model in greater depth than has hitherto been possible. Acknowledgment. We are grateful for financial support from the Royal Society, the Chinese Academy of Sciences, and the National Natural Science Foundation of China(20073055). References and Notes (1) Kresheck, G. C.; Hargraves, W. A. J. Colloid Interface Sci. 1974, 48 (3), 481-493. (2) Sharma, V. K.; Bhat, R.; Ahluwalia, J. C. J. Colloid Interface Sci. 1986, 112, 195-199. (3) De Lisi, R.; Fisicaro, E.; Milioto, S. J. Solution chem. 1988, 17 (11), 1015-1041. (4) Bashford, M. T.; Woolley, E. M. J. Phys. Chem. 1985, 89, 31733179.
Bai et al. (5) Woolley, E. M.; Bashford, M. T. J. Phys. Chem. 1986, 90, 30383046. (6) Andersson, B.; Olofsson, G. J. Chem. Soc., Faraday Trans. 1 1988, 84 (11), 4087-4095. (7) Johnson, I.; Olofsson, G.; Jo¨nnson, B. J. Chem. Soc., Faraday Trans. 1 1987, 83 (11), 3331-3344. (8) Bergstro¨m, S.; Olofsson, G. Thermochim. Acta, 1986, 109, 155164. (9) Mosquera, V.; Manuel del Rı´o, J.; Attwood, D.; Garcı´a, M.; Jones, M. N.; Prieto, G.; Suarez, M. J.; Sarmiento, F. J. Colloid Interface Sci. 1998, 206, 66-76. (10) Van Os, N. M.; Daane, G. J.; Haandrikman, G. J. Colloid Interface Sci. 1991, 141 (1), 199-217. (11) Muller, N. Langmuir 1993, 9, 96-100. (12) Kresheck, G. C.; Vitello, L. B.; Erman, J. E. Biochemistry 1995, 34, 8398. (13) Kresheck, G. C. J. Colloid Interface Sci. 1997, 187, 542. (14) Kresheck, G. C. J. Phys. Chem. B 1998, 102, 6596. (15) Kresheck, G. C. J. Am. Chem. Soc. 1998, 120, 10964-10969. (16) Bai, G. Y.; Wang, J. B.; Yan, H. K.; Li, Z. X. Thomas, R. K. J. Phys. Chem. B 2001, 105, 3105-3108. (17) RO Ä Øycka-Roszak, B.; Witek, S.; Przestalski, S. J. Colloid Interface Sci. 1989, 131 (1), 181-185. (18) Kunitake, T.; Okahata, Y. J. A.m. Chem. Soc. 1977, 9, 3860-3861. (19) Kondo, Y.; Uchiyama, H.; Yoshino, N.; Nishiyama, K.; Abe, M. Langmuir 1995, 11, 2380-2384. (20) Marques, E. F.; Regev, O.; Khan, A.; Miguel, M. Da G.; Lindman, B. J. Phys. Chem. B 1998, 102, 6746-6785. (21) Marques, E. F.; Regev, O.; Khan, A.; Miguel, M. Da G.; Lindman, B. J. Phys. Chem. B 1999, 103, 8353-8363. (22) Bai, G. Y.; Wang, Y. J.; Wang, J. B.; Yang, G. Y.; Yan, H. K. Sci. Chin, Ser. B: Chem. 2000, 43 (6), 617-624. (23) Gucker, F. T., Jr; Pickerd, H. B.; Planck, R. W. J. Am. Chem. Soc., 1939, 61, 459-471. (24) Zana, R. Langmuir 1996, 12, 1208-1211. (25) Zana, R. J. Colloid Interface Sci. 1980, 78 (2), 330-337. (26) Olofsson, G.; Wang, G. In Polymer-Surfactant Systems; Kwak, J. C. T., Ed.; Surfactant Science Series 77; Marcel Dekker: New York, 1998; pp 318-356. (27) Wang, Y.; Han, B.; Yan, H.; Kwak,J. C. T. Langmuir 1997, 13, 3119-3123. (28) Tam, K. C.; Seng, W. P.; Jenkins, R. D.; Bassett, D. R. J. Polym. Sci., Part B: Polym. Phys. 2000, 38, 2019-2032.
