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Heat Evolution of Micelle Formation, Dependence of Enthalpy, and Heat Capacity on the Surfactant Chain Length and Head Group
Journal of Colloid and Interface Science 246, 380–386 (2002) doi:10.1006/jcis.2001.8050, available online at http://www.idealibrary.com on
Heat Evolution of Micelle Formation, Dependence of Enthalpy, and Heat Capacity on the Surfactant Chain Length and Head Group Ella Opatowski,1 Michael M. Kozlov, Ilya Pinchuk, and Dov Lichtenberg2 Department of Physiology and Pharmacology, Tel Aviv University, Sackler Faculty of Medicine, Tel Aviv 69978, Israel Received October 17, 2001; accepted October 22, 2001
Micelle formation by many surfactants is endothermic at low temperatures but exothermic at high temperatures. In this respect, dissociation of micelles (demicellization) is similar to dissolving hydrocarbons in water. However, a remarkable difference between the two processes is that dissolving hydrocarbons is isocaloric at about 25◦ C, almost independently of the hydrocarbon chain length, whereas the temperature (T ∗ ) at which demicellization of different surfactants is athermal varies over a relatively large range. We have investigated the temperature dependence of the heat of demicellization of three alkylglucosides with hydrocarbon chains of 7, 8, and 9 carbon atoms. At about 25◦ C, the heat of demicellization of the three studied alkylglucosides varied within a relatively small range (1H = −7.8 ± 0.4 kJ/mol). The temperature dependence of 1Hdemic indicates that within the studied temperature range the heat capacity of demicellization (1CP,demic ) is about constant. The value of 1CP,demic exhibited an apparently linear dependence on the surfactant’s chain length (1CP,demic /nCH2 = 47 ± 7 kJ/mol K). Our interpretation of these results is that (i) the transfer of the head groups from micelles to water is exothermic and (ii) the temperature dependence of the heat associated with water-hydrocarbon interactions is only slightly affected by the head group. This implies that the deviation of the value of T ∗ from 25◦ C results from the contribution of the polar head to the overall heat of demicellization. Calorimetric studies of other series of amphiphiles will have to be conducted to test whether the latter conclusion is general. °C 2002 Elsevier Science (USA) Key Words: surfactants; detergents; alkylglucosides; micelles; demicellization; enthalpy; isothermal titration calorimetry; heat capacity.
INTRODUCTION
Although the theoretical basis of micelle formation is not fully established, it is commonly regarded as an entropy-driven process (1–7). The heat associated with micellization, as observed for many surfactants, changes from being positive at low temperatures to being negative at high temperatures (8–12). In other words, dissociation of micelles (demicellization) is characterized by a positive and high heat capacity, 1C P , and is exothermic 1 This work constitutes part of Ella Opatowski’s Ph.D. thesis, approved by the Senate of Tel-Aviv University. 2 To whom correspondence should be addressed. Fax: 972-3-6409113. E-mail: [email protected].
0021-9797/02 $35.00
° C 2002 Elsevier Science (USA)
All rights reserved.
at low temperatures but endothermic at high temperatures (8). Hence, at a specific temperature, T ∗ , demicellization is athermal (13). In this respect, demicellization is similar to other processes that relate to the hydrophobic effect, including the process of dissolving hydrocarbons in water (14–18). However, demicellization differs from dissolving hydrocarbons in water in several respects, one of which is that the heat capacity associated with demicellization is always smaller than that expected from the empirical correlation obtained for hydrocarbons 1C P = 33 · n H J · mol−1 · K−1 (19), where n H is the number of hydrogen atoms of the chain. The heat capacity change associated with the transfer of a hydrocarbon into an aqueous solution is about 66 J · mol−1 · K−1 for each added CH2 group, whereas the changes observed for surfactants are smaller (49.2 J mol−1 · K−1 for each added CH2 group of the nonionic polyoxyethyleneglycol ethers (20) and about 50 J · mol−1 · K−1 for most of the studied ionic surfactants (10, 15)). Furthermore, a recent study devoted to demicellization of alkyldimethylphosphine oxides (11) raised doubts regarding the assumption of a constant value for the contribution of methylene groups to the enthalpy of micelle formation (i.e., the assumption of group additivity). In relating to the low heat capacities of demicellization, in comparison to the transfer of hydrocarbons into water, it has been proposed that micellization removes only part rather than the entire hydrocarbon chain from contact with water (10, 15–17, 19, 21, 22). Accordingly, demicellization involves exposure of only part of the CH2 groups to water. In the context of this interpretation, the total value of 1C P = 450 J · mol−1 · K−1 obtained for octylglucoside at 298 K (i.e., 56 J · mol−1 · K−1 per CH2 group) has been interpreted in terms of the established reduced hydrophobicity of the first methylene moieties attached to the head group, to mean that on the average 2–3 methylene groups of this surfactant are exposed to water in the micellar state (8, 21, 22). Another important difference between demicellization and dissolving hydrocarbons in water is that the latter process is athermal at about T ∗ = 25◦ C, almost independent of the chain length of the hydrocarbon (18), whereas the value of T ∗ of the different surfactants studied thus far varies over a relatively broad range (13–60◦ C), depending on the surfactant’s head group and hydrocarbon chain length (e.g., 11, 12, 23–32).
380
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Recently, it has been hypothesized that head group-head group interactions make temperature-independent exothermic contribution to the heat of dissociation of micelles (13). The present study was undertaken to test whether this contribution can explain the dependence of T ∗ on the surfactant chain length. NOMENCLATURE
cmc ITC 1Q Dt D tit Dmtit Dwtit n CH2 nH T∗ Tc∗ 1Hchain 1 H˜ demic (1Hdemic )0 1Hdilution 1Hhead 1CP,demic 1CP,chain 1CP,head
critical micellar concentration isothermal titration calorimeter heat evolution as measured by ITC total detergent concentration in the calorimeter’s cell total detergent concentration in the titrant micellar detergent concentration in the titrant monomer concentration in the titrant number of carbon atoms in the alkyl chain number of hydrogen atoms in the alkyl chain temperature at which demicellization of a given surfactant is athermal temperature at which demicellization of the chains is isocaloric 1Hdemic enthalpy of demicellization enthalpy associated with the transfer of the hydrocarbon chain from micelles to water experimentally obtained value of 1Hdemic at Tc∗ enthalpy associated with demicellization of at 0◦ K enthalpy of dilution enthalpy associated with the transfer of the head group from micelles to water heat capacity associated with demicellization heat capacity associated with transfer of polar head from micelles to water heat capacity associated with demicellization of head groups MATERIALS AND METHODS
Preparation of Mixed Micelles A solution of PC in chloroform was dried under a stream of nitrogen and solubilized by a concentrate solution of an alkylglucoside (NG, OG, or HG) of the appropriate concentration in buffer A. Calorimetric Measurements All the calorimetric experiments were carried out using Microcal’s OMEGA isothermal titration calorimeter (ITC), as described in our recent publications (33, 34). In this study we used two different protocols: (i) Infinite dilution: titration of small volumes (10–25 µL) containing solutions of pure alkylglucoside, or alkylglucoside/PC mixtures into a buffered solution, pH 7.4 (respective to protocol III in our previous publications (34)). (ii) Infinitesimal dilution: titration of small volumes (10– 25 µL) of a buffer solution into solutions of either pure alkylglucoside or alkylglucoside/PC mixtures (respective to protocol I in our previous publications (34)). Each experiment was accompanied by the appropriate control experiment. Specifically, the heat associated with each titration of a buffered surfactant solution into a buffered solution was corrected by substracting the (very small) heat associated with titrating a buffered solution into a buffered solution. Evaluation of 1Hdemic and 1CP,demic 1Hdemic was evaluated as previously proposed by Paula et al. (8). 1CP,demic was evaluated from the temperature dependence of 1Hdemic , assuming that this dependence is linear, namely that for the studied temperature range 1CP,demic is temperature independent. Although the latter assumption is, in principle, incorrect (see below), it has been adopted in many of the recent publications regarding the temperature dependence of the heat of demicellization (10, 18). Furthermore, given the precision of experimental data, its use can be justified for evaluation of 1CP,demic over a relatively small temperature range (18).
Materials Egg PC was purchased from Sigma Chemical Co. (St. Louis, MO). All the studied alkylglucosides, namely heptylglucoside (HG; C7 -Glu), octylglucoside (OG; C8 -Glu), and nonylglucoside (NG; C9 -Glu) were purchased from Calbiochem (La Jolla, CA). Tris buffer was purchased from Fluka (Buchs, Switzerland). NaCl and EDTA (analytical grade) were purchased from Merck (Darmstadt, Germany). Preparation of Pure Micelles Surfactant solutions were freshly prepared by dissolving the weighted amount of surfactant in the required volume of buffer A (140 mM NaCl, 0.5 mM EDTA, 0.02% NaN3 , and 10 mM Tris, pH 7.4).
RESULTS
The temperature dependencies of 1Hdemic obtained for three alkylglucosides with hydrocarbon chain lengths of 7, 8, and 9 are depicted in Fig. 1. Each of these dependencies is apparently linear within the studied range of temperature. Accordingly, the dependence of 1Hdemic on T can be characterized by two factors: the slope of the temperature dependence (1CP,demic ) and either the temperature, T ∗ , at which micelle formation is athermal (1Hdemic = 0), or the value of 1Hdemic extrapolated to zero temperature (1Hdemic )0 . As obvious from the inset to Fig. 1, increasing the chain length, n CH2 , results in larger slopes of the apparently linear dependence of 1Hdemic on temperature (i.e., higher values of 1CP,demic ) lower values of (1Hdemic )0 , and lower
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FIG. 1. Enthalpy of demicellization as a function of temperature for three different alkylglucosides (Cn –Glu, where n = 7, 8, and 9). Most calorimetric titrations were conducted according to the infinite dilution protocol (33, 34). At room temperature 1Hdemic was also determined from infinitesimal dilution experiments in which 10- to 25-µL aliquots of Buffer A were titrated into the alkylglucoside solution of a concentration of 40–100 mM. The inset presents both the enthalpy at 0 K and the heat capacity of the three surfactants as functions of the alkyl chain length.
values of T ∗ . To a first approximation, the value of 1CP,demic appears to depend linearly on the chain length (Fig. 1, inset; 1CP,demic /n CH2 = 47 ± 7J · mol−1 · K−1 ). The latter value is in agreement with the results obtained for other hydrophobic systems upon varying chain lengths (35). Notably, the lines describing the dependencies of 1Hdemic on T for the three alkylglucosides intersect each other at about 20– 30◦ C. We think that the fact that the three lines do not intersect each other at exactly the same temperature can be attributed to
experimental errors (see discussion). Accordingly, we assume that the lines do intersect each other at one common point and define the temperature of intersection as Tc∗ . To interpret Tc∗ , it is important to recall that T ∗ , the temperature at which demicellization is athermal, depends on the surfactant’s chain length, whereas the value of Tc∗ is independent of chain length. In this respect, Tc∗ is similar to the chain length-independent temperature ∗ ), at which dissolving hydrocarbons of about 25◦ C (Thydrocarbon in water is athermal.
HEAT CAPACITY OF SURFACTANTS
383
FIG. 2. Schematic description of the temperature dependence of the enthalpy of demicellization for three different surfactants of a common head group and different chain lengths (n − 1, n, and n + 1). Panel A depicts the theoretical dependencies expected according to our model, based on the assumption that at a given temperature the lines describing the dependende of 1Hdemic on T intersect each other (i.e., that at Tc∗ , 1Hdemic = 1Hhead ). Panel B depicts a more realistic case where the three lines do not intersect each other at exactly the same temperature. Assuming that this deviation is due to experimental errors, the value of Tc∗ for all the surfactants with the same head group can be evaluated from that temperature at which the sum of deviations of 1Hdemic from the common value (1Hdemic )Tc∗ is minimal. Specifically, when T = Tc∗ (to be detected), (1 H˜ demic ) = (1Hdemic )0 + Tc∗ 1C P . The latter value, obtained experimentally from the dependence of 1Hdemic on T for a given surfactant, differs from the predicted value of 1Hdemic (=1Hhead ) as evaluated from the data on several surfactants. The difference (panel C) is given by (1Hhead ) − 1 H˜ demic = (1Hdemic )Tc∗ − 1C P · Tc∗ − (1Hdemic )0 . The sum of square values of the distances of 1 H˜ demic obtained for n surfactants of a common head from the value (1Hhead ) common to these surfactants is given by 12 =
n P
[(1Hdemic )Tc∗ − 1C P,i · Tc∗ − (1Hdemic,0 )i ]2 .
i=1
Minimization of the value of 12 yields Tc∗ and (1Hdemic )Tc∗ .
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TABLE 1 Temperature of Isocaloric Transfer of Alkylglucosides from Aggregates to Water
We base the interpretation of our results on two assumptions: 1. The heat associated with demicellization (1Hdemic ) is a sum of two contributions 1Hdemic = 1Hchain + 1Hhead ,
T∗
[1]
n
Pure micelles
Mixed micelles
Mixed vesicles
where 1Hchain is associated with the transfer of the hydrocarbon chains from micelles (where they reside in a lipidic environment) to the aqueous solution and 1Hhead is the contribution associated with the transfer of the headgroups from micelles (where they interact with each other) to the aqueous solution. 2. The latter contributor (1Hhead ) is independent of the chain length.
7 8 9
326 319 321
332 320 313
336 321 311
Under these assumptions, at a certain temperature Tc∗ , 1Hdemic can be expected to be independent of the chain length (being equal for all the surfactants of the same head group). This temperature can be defined empirically as that temperature where the 1Hdemic values obtained for all the surfactants of a given head group are closest. The detailed procedure used for determination of Tc∗ is described in Fig. 2. The result of this procedure is that for the studied alkylglucosides Tc∗ = 297 K and the heat of demicellization at this temperature is 1Hhead = −7.8 kJ/mol. The latter value of Tc∗ is close to the value of T ∗ observed for dissolving hydrocarbons in water (18), indicating that, as observed for demicellization of the various surfactants, the difference between Tc∗ and T ∗ results from the contribution of head group interactions to the heat of formation of micelles. These interactions can be expected to depend upon the distance between neighboring glucose molecules. The distance between sugar head groups in both mixed micelles and mixed vesicles composed of surfactant and phosphatidylcholine (PC) is supposedly larger than that in pure surfactant micelles. Accordingly, we have expected that in mixed aggregates 1Hhead will make a smaller contribution to 1Hdemic , namely that at any temperature extraction of alkylglucoside monomers from the mixed aggregates would be less exothermic than dissociation of pure micelles. Under the assumptions that 1CP,demic is a linear function of the chain length and is only slightly dependent on both the head group interactions and the exact properties of the lipidic environment in the aggregates, we also expected that in the mixed aggregates T ∗ will be closer to Tc∗ because we expected 1Hhead to be smaller. Experiments conducted with mixed micelles containing the lowest possible OG/PC ratio (Re = 3; (36)) and with mixed vesicles containing the highest possible OG/PC ratio (Re = 1.3) revealed that, in contrast to our expectations, T ∗ is almost independent of the composition of the aggregates (Table 1). These rather unexpected results may be either due to (i) lateral phase separation of surfactant molecules on the surface of the PC-alkylglucoside mixed micelles, which leads to similar head group interactions in mixed aggregates and simple micelles or/and due to (ii) similar interactions between two adjacent glu-
coside head groups, on one hand, and glucoside-choline head group, on the other. Future research will have to be conducted to address this question. DISCUSSION
Evaluation of the Heat Capacity of Demicellization The heat capacity of demicellization, at any given temperature, is given by the derivative of 1Hdemic with respect to temperature 1CP,demic =
d1Hdemic . dT
[2]
As noted by Paula et al. (8), 1CP,demic is temperature dependent and may be a nonlinear function of temperature. Hence, 1Hdemic can be expected to exhibit a third (or higher) order polynomial dependence on T. However, the precision of the calorimetric data may be insufficient for treating these data in this fashion (19). Furthermore, over the relatively narrow range of temperature used in this and many other studies, 1Hdemic exhibits apparently linear dependence on T; i.e., 1CP,demic is apparently constant. This is true for the solubility of hydrocarbons in water for the temperature range of 15–35◦ C (18) and is also true for demicellization of many surfactants (see below). In other words, although the general tendency is that for both these processes, 1CP,demic decreases with temperature, the precision of the data is insufficient to quantitate this dependence for the studied temperature range (10, 19, 37). In fact, the data of Paula et al. on the demicellization of OG micelles at different temperatures (8) exhibited an apparently linear dependence (r 2 = 0.992), which could have been described in terms of a concentration-independent 1CP,demic (1CP,demic = 383 J · mol−1 · K−1 ). By comparison, description of the same dependence in terms of a second order polynom (8), which yielded a somewhat better fit (r 2 = 0.998), implied that 1CP,demic varies considerably with temperature (from 470 J · mol−1 · K−1 at 13◦ C to 290 J · mol−1 · K−1 at 70◦ C). In our experiments, the fit of the data points obtained for OG (over the temperature range of 7–60◦ C) to a linear dependence of 1Hdemic on T was almost the same as that obtained for a second order polynom (r 2 = 0.9972, as compared to r 2 = 0.9975, respectively). Given this reasonable fit of experimental data to a
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HEAT CAPACITY OF SURFACTANTS
linear dependence, we think that the precision of the experiments is insufficient for description of 1CP,demic as being temperature dependent. Accordingly, we relate to 1CP,demic as being constant throughout the studied temperature range. Temperature of Athermal Demicellization (T ∗ ), Theoretical Considerations The major objective of the present study is to explain the variation of T ∗ and its dependence on the surfactant’s chain length. The basic assumption we use for approaching this issue is the additivity of the heat. Specifically, we assume that the value of 1Hdemic is a sum of two enthalpies [1], where 1Hchain is the heat associated with transferring the hydrocarbon chain from the core of the micelle to the water, and 1Hhead is the heat associated with transferring the polar head group from micelles to water. We also assume that 1Hchain exhibits a linear dependence on temperature. At the temperature Tc∗ , all the lines describing 1Hdemic as a function of temperature for surfactants of different chain lengths but the same head group intersect each other. This means that at Tc∗ , 1Hdemic is independent of the chain length, namely that at Tc∗ the chain length-dependent heat associated with dissolving the hydrocarbon chains in water is zero. Hence, at any temperature other than Tc∗ 1Hchain = 1CP, chain (T − Tc∗ ).
[3]
If, in addition to the above assumptions, we assume, as a first approximation, that 1Hhead is independent of both the chain length and the temperature, it follows that 1Hdemic = 1Hhead + 1CP, chain (T − Tc∗ ).
[4]
This means that under our simplifying assumptions: (i) For any given series of surfactants with a chain length-independent 1Hhead , Tc∗ should be equal to the (chain length-independent) value of T ∗ observed for hydrocarbons, and (ii) at T = Tc∗ , 1Hdemic = 1Hhead . Accordingly, demicellization of all the surfactants of a given polar head group but different chain length involves the same heat 1Hhead at Tc∗ and since they differ with respect to their 1CP, chain , they cross the line where 1Hdemic = 0 at different temperatures, as schematically described in Fig. 2A. The actual value of T ∗ is then given by
Significance of Determination of Tc∗ Tc∗ is simply that temperature at which the dilution of a micellar solution is equal to zero (1Q = 0; i.e., 1H = 0 as well). Hence, Tc∗ is the most unambigously attainable calorimetric parameter because its measurement does not require any assumptions or computations. In all other cases, regardless of whether the calorimetric titration involves infinite or infinitesimal dilution, the experimentally observed 1Q can be used to compute 1Hdemic and 1Cp,demic only under limiting assumptions. As a consequence, unlike the value of T ∗ , the value of Tc∗ is subject to relatively large experimental errors. The results of our experiments (Fig. 1) are consistent within these errors with the proposed simple model. The enthalpy of demicellization at Tc∗ (−7.8 kJ/mol for alkylglucosides), which we attribute to interactions of the surfactant’s head groups (1Hhead ) may be due to cleavage of hydrogen bonds between adjacent sugar moieties in the micelles. However, this possibility has yet to be tested. What can be concluded at the present time is that the difference between 1CP,demic and 1C P of dissolving hydrocarbons in water is relatively small. Accordingly, the major contributor of 1Cp,demic must be the hydrophobic effect whereas the head group-associated interactions make only a minor contribution. In an attempt to evaluate the generality of our interpretation of the temperature dependence of 1Hdemic , we have reanalyzed the published data regarding the dependence of 1Hdemic on temperature for a few series of surfactants of a common head group and varying chain length (11, 23–27). Unfortunately, much of these data are of limited precision due to limitations of experimental tools available until recently (37, 38). This lack of precision may explain the apparent disagreement between some of the published data and the theoretically expected behavior, including the finding that in several cases (e.g., 23–25) common points of intersection (Tc∗ ) cannot be defined on the basis of the published results. Nonetheless, despite of these limitations, it appears that for those cases where Tc∗ can be defined, it is in the range of 20–25◦ C and that the value of T ∗ depends on the surfactant chain length because Tc∗ is chain length-independent whereas the heat capacity (1CP,demic ) is an increasing function of the chain length. More precise data will be required to test the generality of our hypothesis and to evaluate in detail the contribution of the polar head groups to the overall heat of demicellization and its temperature dependence. ACKNOWLEDGMENT
T ∗ = Tc∗ − 1Hhead /1CP, chain .
[5]
This explains the chain length dependence of T ∗ of a group of surfactants (e.g., those given in Fig. 1) of a common head group (and 1Hhead ) as being due to the chain length dependence of 1CP, chain .
We thank the Israel Science Foundation, founded by the Israel Academy of Science and Humanities-Centers of Excellence Program, for financial support.
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2. Israelachvili, J. N., “Intermolecular and Surface Forces.” Academic Press, London 1995. 3. Karplus, M., J. Chem. Phys. 105, 4294 (1996). 4. del Rio, J. M., and Jones, M. N., J. Phys. Chem. B 105, 1200 (2001). 5. Chernik, G. G., Curr. Opin. Colloid Interface Sci. 4, 381 (1999). 6. Blokzijl, W., and Engberts, J. B. F. N., Angew. Chem. 32, 1545 (1993). 7. Graziano, G., Phys. Chem. Chem. Phys. 1, 3567 (1999). 8. Paula, S., Sues, W., Tuchtenhagen, J., and Blume, A., J. Phys. Chem. 99, 11742 (1995). 9. Kameyama, K., and Toshio, T., J. Colloid Interface Sci. 137, 1 (1990). 10. Muller, N., Langmuir 9, 96 (1993). 11. Kresheck, G. C., J. Am. Chem. Soc. 120, 10964 (1998). 12. Kresheck, G. C., J. Phys. Chem. B 102, 6596 (1998). 13. Pestman, J. M., Kevelam, J., Blandamer, M. J., van Doren, H. A., Kellogg, R. M., and Engberts, J. B. F. N., Langmuir 15, 2009 (1999). 14. Madau, B., and Lee, B., Biophys. Chem. 51, 271 (1994). 15. Jolicoeur, C., and Philip, P. R., Can. J. Chem. 52, 1834 (1974). 16. Shinoda, K., J. Phys. Chem. 81, 1300 (1997). 17. Gill, S. J., Dec, S. F., Olofsson, G., and Wadsoe, I., J. Phys. Chem. 89, 3758 (1985). 18. Gill, S. J., Nichols, N. F., and Wadsoe, I., J. Chem. Thermodyn. 8, 445 (1976). 19. Gill, S. J., and Wadsoe, I., Proc. Natl. Acad. Sci. USA 73, 2955 (1976). 20. Andersson, B., and Olofsson, G., J. Chem. Soc., Faraday Trans. 1 84, 4087 (1988). 21. Streefland, L., Blandamer, M. J., and Engberts, J. B. F. N., J. Am. Chem. Soc. 118, 9539 (1996).
22. Noordman, W. H., Blokzijl, and Engberts, J. B. F. N., J. Org. Chem. 58, 7111 (1993). 23. Corkill, J. M., Goodman, J. F., and Tate, J. R., Trans. Faraday Soc. 60, 996 (1964). 24. Olofsson, G., J. Phys. Chem. 89, 1473 (1985). 25. Flockhart, B. D., J. Colloid Sci. 16, 484 (1961). 26. Adderson, J. E., and Taylor, H., J. Pharm. Pharmacol. 23, 312 (1971). 27. Adderson, J. E., and Taylor, H., J. Pharm. Pharmacol. 22, 523 (1970). 28. Aratono, M., Ohta, A., Ikeda, N., Motomura, K., and Takiue, T., J. Phys. Chem. B 101, 3535 (1997). 29. Endoh, K., Suga, H., and Fukada, H., J. Therm. Anal. Calorimetry 57, 669 (1999). 30. Musbally, G. M., Perron, G., and Desnoyers, J. E., J. Colloid Interface Sci. 129, 175 (1989). 31. Zielinski, R., Ikeda, S., Nomura, H., and Kato, S., J. Colloid Interface Sci. 129, 175 (1989). 32. Bashford, M. T., and Wookey, E. M., J. Phys. Chem. 89, 3173 (1985). 33. Opatowski, E., Kozlov, M. M., and Lichtenberg, D., Biophys. J. 73, 1448 (1997). 34. Opatowski, E., Lichtenberg, D., and Kozlov, M. M., Biophys. J. 73, 1458 (1997). 35. Okawauchi, M., Hagio, M., Ikawa, Y., Sugihara, G., Murata, M., and Tanaka, M., Bull. Chem. Soc. Jpn. 60, 2718 (1987). 36. Almog, S., Litman, B. J., Winley, W., Cohen, J., Wachtel, E. J., Barenholz, Y., Ben-Shaul, A., and Lichtenberg, D., Biochemistry 29, 4582 (1990). 37. Desnoyers, J., E., and Gerald, P., Langmuir 12, 4044 (1996). 38. Blandamer, M. J., Cullis, P. M., and Engberts, J. B. F. N., J. Chem. Soc., Faraday Transact. 94, 2261 (1998).
Heat Evolution of Micelle Formation, Dependence of Enthalpy, and Heat Capacity on the Surfactant Chain Length and Head Group Ella Opatowski,1 Michael M. Kozlov, Ilya Pinchuk, and Dov Lichtenberg2 Department of Physiology and Pharmacology, Tel Aviv University, Sackler Faculty of Medicine, Tel Aviv 69978, Israel Received October 17, 2001; accepted October 22, 2001
Micelle formation by many surfactants is endothermic at low temperatures but exothermic at high temperatures. In this respect, dissociation of micelles (demicellization) is similar to dissolving hydrocarbons in water. However, a remarkable difference between the two processes is that dissolving hydrocarbons is isocaloric at about 25◦ C, almost independently of the hydrocarbon chain length, whereas the temperature (T ∗ ) at which demicellization of different surfactants is athermal varies over a relatively large range. We have investigated the temperature dependence of the heat of demicellization of three alkylglucosides with hydrocarbon chains of 7, 8, and 9 carbon atoms. At about 25◦ C, the heat of demicellization of the three studied alkylglucosides varied within a relatively small range (1H = −7.8 ± 0.4 kJ/mol). The temperature dependence of 1Hdemic indicates that within the studied temperature range the heat capacity of demicellization (1CP,demic ) is about constant. The value of 1CP,demic exhibited an apparently linear dependence on the surfactant’s chain length (1CP,demic /nCH2 = 47 ± 7 kJ/mol K). Our interpretation of these results is that (i) the transfer of the head groups from micelles to water is exothermic and (ii) the temperature dependence of the heat associated with water-hydrocarbon interactions is only slightly affected by the head group. This implies that the deviation of the value of T ∗ from 25◦ C results from the contribution of the polar head to the overall heat of demicellization. Calorimetric studies of other series of amphiphiles will have to be conducted to test whether the latter conclusion is general. °C 2002 Elsevier Science (USA) Key Words: surfactants; detergents; alkylglucosides; micelles; demicellization; enthalpy; isothermal titration calorimetry; heat capacity.
INTRODUCTION
Although the theoretical basis of micelle formation is not fully established, it is commonly regarded as an entropy-driven process (1–7). The heat associated with micellization, as observed for many surfactants, changes from being positive at low temperatures to being negative at high temperatures (8–12). In other words, dissociation of micelles (demicellization) is characterized by a positive and high heat capacity, 1C P , and is exothermic 1 This work constitutes part of Ella Opatowski’s Ph.D. thesis, approved by the Senate of Tel-Aviv University. 2 To whom correspondence should be addressed. Fax: 972-3-6409113. E-mail: [email protected].
0021-9797/02 $35.00
° C 2002 Elsevier Science (USA)
All rights reserved.
at low temperatures but endothermic at high temperatures (8). Hence, at a specific temperature, T ∗ , demicellization is athermal (13). In this respect, demicellization is similar to other processes that relate to the hydrophobic effect, including the process of dissolving hydrocarbons in water (14–18). However, demicellization differs from dissolving hydrocarbons in water in several respects, one of which is that the heat capacity associated with demicellization is always smaller than that expected from the empirical correlation obtained for hydrocarbons 1C P = 33 · n H J · mol−1 · K−1 (19), where n H is the number of hydrogen atoms of the chain. The heat capacity change associated with the transfer of a hydrocarbon into an aqueous solution is about 66 J · mol−1 · K−1 for each added CH2 group, whereas the changes observed for surfactants are smaller (49.2 J mol−1 · K−1 for each added CH2 group of the nonionic polyoxyethyleneglycol ethers (20) and about 50 J · mol−1 · K−1 for most of the studied ionic surfactants (10, 15)). Furthermore, a recent study devoted to demicellization of alkyldimethylphosphine oxides (11) raised doubts regarding the assumption of a constant value for the contribution of methylene groups to the enthalpy of micelle formation (i.e., the assumption of group additivity). In relating to the low heat capacities of demicellization, in comparison to the transfer of hydrocarbons into water, it has been proposed that micellization removes only part rather than the entire hydrocarbon chain from contact with water (10, 15–17, 19, 21, 22). Accordingly, demicellization involves exposure of only part of the CH2 groups to water. In the context of this interpretation, the total value of 1C P = 450 J · mol−1 · K−1 obtained for octylglucoside at 298 K (i.e., 56 J · mol−1 · K−1 per CH2 group) has been interpreted in terms of the established reduced hydrophobicity of the first methylene moieties attached to the head group, to mean that on the average 2–3 methylene groups of this surfactant are exposed to water in the micellar state (8, 21, 22). Another important difference between demicellization and dissolving hydrocarbons in water is that the latter process is athermal at about T ∗ = 25◦ C, almost independent of the chain length of the hydrocarbon (18), whereas the value of T ∗ of the different surfactants studied thus far varies over a relatively broad range (13–60◦ C), depending on the surfactant’s head group and hydrocarbon chain length (e.g., 11, 12, 23–32).
380
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Recently, it has been hypothesized that head group-head group interactions make temperature-independent exothermic contribution to the heat of dissociation of micelles (13). The present study was undertaken to test whether this contribution can explain the dependence of T ∗ on the surfactant chain length. NOMENCLATURE
cmc ITC 1Q Dt D tit Dmtit Dwtit n CH2 nH T∗ Tc∗ 1Hchain 1 H˜ demic (1Hdemic )0 1Hdilution 1Hhead 1CP,demic 1CP,chain 1CP,head
critical micellar concentration isothermal titration calorimeter heat evolution as measured by ITC total detergent concentration in the calorimeter’s cell total detergent concentration in the titrant micellar detergent concentration in the titrant monomer concentration in the titrant number of carbon atoms in the alkyl chain number of hydrogen atoms in the alkyl chain temperature at which demicellization of a given surfactant is athermal temperature at which demicellization of the chains is isocaloric 1Hdemic enthalpy of demicellization enthalpy associated with the transfer of the hydrocarbon chain from micelles to water experimentally obtained value of 1Hdemic at Tc∗ enthalpy associated with demicellization of at 0◦ K enthalpy of dilution enthalpy associated with the transfer of the head group from micelles to water heat capacity associated with demicellization heat capacity associated with transfer of polar head from micelles to water heat capacity associated with demicellization of head groups MATERIALS AND METHODS
Preparation of Mixed Micelles A solution of PC in chloroform was dried under a stream of nitrogen and solubilized by a concentrate solution of an alkylglucoside (NG, OG, or HG) of the appropriate concentration in buffer A. Calorimetric Measurements All the calorimetric experiments were carried out using Microcal’s OMEGA isothermal titration calorimeter (ITC), as described in our recent publications (33, 34). In this study we used two different protocols: (i) Infinite dilution: titration of small volumes (10–25 µL) containing solutions of pure alkylglucoside, or alkylglucoside/PC mixtures into a buffered solution, pH 7.4 (respective to protocol III in our previous publications (34)). (ii) Infinitesimal dilution: titration of small volumes (10– 25 µL) of a buffer solution into solutions of either pure alkylglucoside or alkylglucoside/PC mixtures (respective to protocol I in our previous publications (34)). Each experiment was accompanied by the appropriate control experiment. Specifically, the heat associated with each titration of a buffered surfactant solution into a buffered solution was corrected by substracting the (very small) heat associated with titrating a buffered solution into a buffered solution. Evaluation of 1Hdemic and 1CP,demic 1Hdemic was evaluated as previously proposed by Paula et al. (8). 1CP,demic was evaluated from the temperature dependence of 1Hdemic , assuming that this dependence is linear, namely that for the studied temperature range 1CP,demic is temperature independent. Although the latter assumption is, in principle, incorrect (see below), it has been adopted in many of the recent publications regarding the temperature dependence of the heat of demicellization (10, 18). Furthermore, given the precision of experimental data, its use can be justified for evaluation of 1CP,demic over a relatively small temperature range (18).
Materials Egg PC was purchased from Sigma Chemical Co. (St. Louis, MO). All the studied alkylglucosides, namely heptylglucoside (HG; C7 -Glu), octylglucoside (OG; C8 -Glu), and nonylglucoside (NG; C9 -Glu) were purchased from Calbiochem (La Jolla, CA). Tris buffer was purchased from Fluka (Buchs, Switzerland). NaCl and EDTA (analytical grade) were purchased from Merck (Darmstadt, Germany). Preparation of Pure Micelles Surfactant solutions were freshly prepared by dissolving the weighted amount of surfactant in the required volume of buffer A (140 mM NaCl, 0.5 mM EDTA, 0.02% NaN3 , and 10 mM Tris, pH 7.4).
RESULTS
The temperature dependencies of 1Hdemic obtained for three alkylglucosides with hydrocarbon chain lengths of 7, 8, and 9 are depicted in Fig. 1. Each of these dependencies is apparently linear within the studied range of temperature. Accordingly, the dependence of 1Hdemic on T can be characterized by two factors: the slope of the temperature dependence (1CP,demic ) and either the temperature, T ∗ , at which micelle formation is athermal (1Hdemic = 0), or the value of 1Hdemic extrapolated to zero temperature (1Hdemic )0 . As obvious from the inset to Fig. 1, increasing the chain length, n CH2 , results in larger slopes of the apparently linear dependence of 1Hdemic on temperature (i.e., higher values of 1CP,demic ) lower values of (1Hdemic )0 , and lower
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FIG. 1. Enthalpy of demicellization as a function of temperature for three different alkylglucosides (Cn –Glu, where n = 7, 8, and 9). Most calorimetric titrations were conducted according to the infinite dilution protocol (33, 34). At room temperature 1Hdemic was also determined from infinitesimal dilution experiments in which 10- to 25-µL aliquots of Buffer A were titrated into the alkylglucoside solution of a concentration of 40–100 mM. The inset presents both the enthalpy at 0 K and the heat capacity of the three surfactants as functions of the alkyl chain length.
values of T ∗ . To a first approximation, the value of 1CP,demic appears to depend linearly on the chain length (Fig. 1, inset; 1CP,demic /n CH2 = 47 ± 7J · mol−1 · K−1 ). The latter value is in agreement with the results obtained for other hydrophobic systems upon varying chain lengths (35). Notably, the lines describing the dependencies of 1Hdemic on T for the three alkylglucosides intersect each other at about 20– 30◦ C. We think that the fact that the three lines do not intersect each other at exactly the same temperature can be attributed to
experimental errors (see discussion). Accordingly, we assume that the lines do intersect each other at one common point and define the temperature of intersection as Tc∗ . To interpret Tc∗ , it is important to recall that T ∗ , the temperature at which demicellization is athermal, depends on the surfactant’s chain length, whereas the value of Tc∗ is independent of chain length. In this respect, Tc∗ is similar to the chain length-independent temperature ∗ ), at which dissolving hydrocarbons of about 25◦ C (Thydrocarbon in water is athermal.
HEAT CAPACITY OF SURFACTANTS
383
FIG. 2. Schematic description of the temperature dependence of the enthalpy of demicellization for three different surfactants of a common head group and different chain lengths (n − 1, n, and n + 1). Panel A depicts the theoretical dependencies expected according to our model, based on the assumption that at a given temperature the lines describing the dependende of 1Hdemic on T intersect each other (i.e., that at Tc∗ , 1Hdemic = 1Hhead ). Panel B depicts a more realistic case where the three lines do not intersect each other at exactly the same temperature. Assuming that this deviation is due to experimental errors, the value of Tc∗ for all the surfactants with the same head group can be evaluated from that temperature at which the sum of deviations of 1Hdemic from the common value (1Hdemic )Tc∗ is minimal. Specifically, when T = Tc∗ (to be detected), (1 H˜ demic ) = (1Hdemic )0 + Tc∗ 1C P . The latter value, obtained experimentally from the dependence of 1Hdemic on T for a given surfactant, differs from the predicted value of 1Hdemic (=1Hhead ) as evaluated from the data on several surfactants. The difference (panel C) is given by (1Hhead ) − 1 H˜ demic = (1Hdemic )Tc∗ − 1C P · Tc∗ − (1Hdemic )0 . The sum of square values of the distances of 1 H˜ demic obtained for n surfactants of a common head from the value (1Hhead ) common to these surfactants is given by 12 =
n P
[(1Hdemic )Tc∗ − 1C P,i · Tc∗ − (1Hdemic,0 )i ]2 .
i=1
Minimization of the value of 12 yields Tc∗ and (1Hdemic )Tc∗ .
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TABLE 1 Temperature of Isocaloric Transfer of Alkylglucosides from Aggregates to Water
We base the interpretation of our results on two assumptions: 1. The heat associated with demicellization (1Hdemic ) is a sum of two contributions 1Hdemic = 1Hchain + 1Hhead ,
T∗
[1]
n
Pure micelles
Mixed micelles
Mixed vesicles
where 1Hchain is associated with the transfer of the hydrocarbon chains from micelles (where they reside in a lipidic environment) to the aqueous solution and 1Hhead is the contribution associated with the transfer of the headgroups from micelles (where they interact with each other) to the aqueous solution. 2. The latter contributor (1Hhead ) is independent of the chain length.
7 8 9
326 319 321
332 320 313
336 321 311
Under these assumptions, at a certain temperature Tc∗ , 1Hdemic can be expected to be independent of the chain length (being equal for all the surfactants of the same head group). This temperature can be defined empirically as that temperature where the 1Hdemic values obtained for all the surfactants of a given head group are closest. The detailed procedure used for determination of Tc∗ is described in Fig. 2. The result of this procedure is that for the studied alkylglucosides Tc∗ = 297 K and the heat of demicellization at this temperature is 1Hhead = −7.8 kJ/mol. The latter value of Tc∗ is close to the value of T ∗ observed for dissolving hydrocarbons in water (18), indicating that, as observed for demicellization of the various surfactants, the difference between Tc∗ and T ∗ results from the contribution of head group interactions to the heat of formation of micelles. These interactions can be expected to depend upon the distance between neighboring glucose molecules. The distance between sugar head groups in both mixed micelles and mixed vesicles composed of surfactant and phosphatidylcholine (PC) is supposedly larger than that in pure surfactant micelles. Accordingly, we have expected that in mixed aggregates 1Hhead will make a smaller contribution to 1Hdemic , namely that at any temperature extraction of alkylglucoside monomers from the mixed aggregates would be less exothermic than dissociation of pure micelles. Under the assumptions that 1CP,demic is a linear function of the chain length and is only slightly dependent on both the head group interactions and the exact properties of the lipidic environment in the aggregates, we also expected that in the mixed aggregates T ∗ will be closer to Tc∗ because we expected 1Hhead to be smaller. Experiments conducted with mixed micelles containing the lowest possible OG/PC ratio (Re = 3; (36)) and with mixed vesicles containing the highest possible OG/PC ratio (Re = 1.3) revealed that, in contrast to our expectations, T ∗ is almost independent of the composition of the aggregates (Table 1). These rather unexpected results may be either due to (i) lateral phase separation of surfactant molecules on the surface of the PC-alkylglucoside mixed micelles, which leads to similar head group interactions in mixed aggregates and simple micelles or/and due to (ii) similar interactions between two adjacent glu-
coside head groups, on one hand, and glucoside-choline head group, on the other. Future research will have to be conducted to address this question. DISCUSSION
Evaluation of the Heat Capacity of Demicellization The heat capacity of demicellization, at any given temperature, is given by the derivative of 1Hdemic with respect to temperature 1CP,demic =
d1Hdemic . dT
[2]
As noted by Paula et al. (8), 1CP,demic is temperature dependent and may be a nonlinear function of temperature. Hence, 1Hdemic can be expected to exhibit a third (or higher) order polynomial dependence on T. However, the precision of the calorimetric data may be insufficient for treating these data in this fashion (19). Furthermore, over the relatively narrow range of temperature used in this and many other studies, 1Hdemic exhibits apparently linear dependence on T; i.e., 1CP,demic is apparently constant. This is true for the solubility of hydrocarbons in water for the temperature range of 15–35◦ C (18) and is also true for demicellization of many surfactants (see below). In other words, although the general tendency is that for both these processes, 1CP,demic decreases with temperature, the precision of the data is insufficient to quantitate this dependence for the studied temperature range (10, 19, 37). In fact, the data of Paula et al. on the demicellization of OG micelles at different temperatures (8) exhibited an apparently linear dependence (r 2 = 0.992), which could have been described in terms of a concentration-independent 1CP,demic (1CP,demic = 383 J · mol−1 · K−1 ). By comparison, description of the same dependence in terms of a second order polynom (8), which yielded a somewhat better fit (r 2 = 0.998), implied that 1CP,demic varies considerably with temperature (from 470 J · mol−1 · K−1 at 13◦ C to 290 J · mol−1 · K−1 at 70◦ C). In our experiments, the fit of the data points obtained for OG (over the temperature range of 7–60◦ C) to a linear dependence of 1Hdemic on T was almost the same as that obtained for a second order polynom (r 2 = 0.9972, as compared to r 2 = 0.9975, respectively). Given this reasonable fit of experimental data to a
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linear dependence, we think that the precision of the experiments is insufficient for description of 1CP,demic as being temperature dependent. Accordingly, we relate to 1CP,demic as being constant throughout the studied temperature range. Temperature of Athermal Demicellization (T ∗ ), Theoretical Considerations The major objective of the present study is to explain the variation of T ∗ and its dependence on the surfactant’s chain length. The basic assumption we use for approaching this issue is the additivity of the heat. Specifically, we assume that the value of 1Hdemic is a sum of two enthalpies [1], where 1Hchain is the heat associated with transferring the hydrocarbon chain from the core of the micelle to the water, and 1Hhead is the heat associated with transferring the polar head group from micelles to water. We also assume that 1Hchain exhibits a linear dependence on temperature. At the temperature Tc∗ , all the lines describing 1Hdemic as a function of temperature for surfactants of different chain lengths but the same head group intersect each other. This means that at Tc∗ , 1Hdemic is independent of the chain length, namely that at Tc∗ the chain length-dependent heat associated with dissolving the hydrocarbon chains in water is zero. Hence, at any temperature other than Tc∗ 1Hchain = 1CP, chain (T − Tc∗ ).
[3]
If, in addition to the above assumptions, we assume, as a first approximation, that 1Hhead is independent of both the chain length and the temperature, it follows that 1Hdemic = 1Hhead + 1CP, chain (T − Tc∗ ).
[4]
This means that under our simplifying assumptions: (i) For any given series of surfactants with a chain length-independent 1Hhead , Tc∗ should be equal to the (chain length-independent) value of T ∗ observed for hydrocarbons, and (ii) at T = Tc∗ , 1Hdemic = 1Hhead . Accordingly, demicellization of all the surfactants of a given polar head group but different chain length involves the same heat 1Hhead at Tc∗ and since they differ with respect to their 1CP, chain , they cross the line where 1Hdemic = 0 at different temperatures, as schematically described in Fig. 2A. The actual value of T ∗ is then given by
Significance of Determination of Tc∗ Tc∗ is simply that temperature at which the dilution of a micellar solution is equal to zero (1Q = 0; i.e., 1H = 0 as well). Hence, Tc∗ is the most unambigously attainable calorimetric parameter because its measurement does not require any assumptions or computations. In all other cases, regardless of whether the calorimetric titration involves infinite or infinitesimal dilution, the experimentally observed 1Q can be used to compute 1Hdemic and 1Cp,demic only under limiting assumptions. As a consequence, unlike the value of T ∗ , the value of Tc∗ is subject to relatively large experimental errors. The results of our experiments (Fig. 1) are consistent within these errors with the proposed simple model. The enthalpy of demicellization at Tc∗ (−7.8 kJ/mol for alkylglucosides), which we attribute to interactions of the surfactant’s head groups (1Hhead ) may be due to cleavage of hydrogen bonds between adjacent sugar moieties in the micelles. However, this possibility has yet to be tested. What can be concluded at the present time is that the difference between 1CP,demic and 1C P of dissolving hydrocarbons in water is relatively small. Accordingly, the major contributor of 1Cp,demic must be the hydrophobic effect whereas the head group-associated interactions make only a minor contribution. In an attempt to evaluate the generality of our interpretation of the temperature dependence of 1Hdemic , we have reanalyzed the published data regarding the dependence of 1Hdemic on temperature for a few series of surfactants of a common head group and varying chain length (11, 23–27). Unfortunately, much of these data are of limited precision due to limitations of experimental tools available until recently (37, 38). This lack of precision may explain the apparent disagreement between some of the published data and the theoretically expected behavior, including the finding that in several cases (e.g., 23–25) common points of intersection (Tc∗ ) cannot be defined on the basis of the published results. Nonetheless, despite of these limitations, it appears that for those cases where Tc∗ can be defined, it is in the range of 20–25◦ C and that the value of T ∗ depends on the surfactant chain length because Tc∗ is chain length-independent whereas the heat capacity (1CP,demic ) is an increasing function of the chain length. More precise data will be required to test the generality of our hypothesis and to evaluate in detail the contribution of the polar head groups to the overall heat of demicellization and its temperature dependence. ACKNOWLEDGMENT
T ∗ = Tc∗ − 1Hhead /1CP, chain .
[5]
This explains the chain length dependence of T ∗ of a group of surfactants (e.g., those given in Fig. 1) of a common head group (and 1Hhead ) as being due to the chain length dependence of 1CP, chain .
We thank the Israel Science Foundation, founded by the Israel Academy of Science and Humanities-Centers of Excellence Program, for financial support.
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