Modeling the Micellization Behavior of Mixed and Pure n-Alkyl

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Modeling the Micellization Behavior of Mixed and Pure n-Alkyl-Maltosides Alekos D. Tsamaloukas,*,† Andreas Beck,‡ and Heiko Heerklotz*,† †

Leslie Dan Faculty of Pharmacy, University of Toronto, Toronto ON, M5S 3M2, Canada and ‡Department of Biophysical Chemistry, Biocenter of the University of Basel, Basel, Switzerland Received October 13, 2008. Revised Manuscript Received January 26, 2009 The micellization behavior of a series of n-alkyl-maltosides in aqueous solution was studied by isothermal titration calorimetry (ITC) and dynamic light scattering (DLS) at 25 °C. Demicellization experiments were conducted with single component micelles of octyl (OM), nonyl (NM), decyl (DM), undecyl (UM), and dodecyl (lauryl, LM) maltoside and binary mixtures of LM with OM, NM, DM and UM, respectively. A model was derived on the basis of the pseudophase approximation to fit the complete demicellization curves. It yielded good global fits of the curves obtained at different mixing ratios and ranging over >3 orders of magnitude in concentrations. It provides a quantitative explanation for the two-range coassociation behavior of the surfactant mixtures also in the absence of second critical micelle concentration (CMC) phenomena. The hydrodynamic radius, RH, of the mixed micelles was the average of that of the pure components as seen by noninvasive backscattering (NIBS) DLS. Methylene group contributions were constant for octyl through myristyl chains, amounting to -3.1 kJ/mol for the standard free energy and -1.8 kJ/mol for the enthalpy of micellization. RH increased by 0.25 nm per methylene.

1. Introduction Surfactants are versatile agents for accomplishing tasks as different as washing dishes, solubilizing integral proteins from their native membranes,1-4 dispersing poorly water-soluble substances (e.g., for drug delivery5-7), or exerting sterilizing or spermicidal8 properties in ointments and cosmetics. As a consequence, a large body of literature exists on pure and mixed surfactants.9-11 This includes graphical12,13 and analytical14 determinations of the aqueous and micellar concentrations of mixed alkyl sulfates12,13 and sulfoxides,14 respectively. This information will be derived here for alkyl maltosides by a new approach and provide a new view of the principal association behavior of mixed surfactants. Owing to the pioneering works of Kresheck, Olofsson, Blume, *Authors to whom correspondence should be addressed. E-mail: [email protected] and [email protected]. (1) Helenius, A.; Simons, K. Biochim. Biophys. Acta 1975, 415(1), 29–79. (2) Tanford, C.; Reynolds, J. A. Biochim. Biophys. Acta 1976, 457(2), 133–70. (3) Lichtenberg, D.; Robson, R. J.; Dennis, E. A. Biochim. Biophys. Acta 1983, 737(2), 285–304. (4) le Maire, M.; Champeil, P.; Moller, J. V. Biochim. Biophys. Acta 2000, 1508(1-2), 86–111. (5) Alkan-Onyuksel, H.; Ramakrishnan, S.; Chai, H. B.; Pezzuto, J. M. Pharm. Res. 1994, 11(2), 206–12. (6) Zhang, X.; Burt, H. M.; Von Hoff, D.; Dexter, D.; Mangold, G.; Degen, D.; Oktaba, A. M.; Hunter, W. L. Cancer Chemother. Pharmacol. 1997, 40(1), 81–6. (7) Das, G. S.; Rao, G. H. R.; Wilson, R. F.; Chandy, T. J. Biomed. Mater. Res. 2001, 55(1), 96–103. (8) Apel-Paz, M.; Doncel, G. F.; Vanderlick, T. K. Langmuir 2005, 21(22), 9843–9849. (9) Scamehorn, J. F., Ed. Phenomena in Mixed Surfactant Systems; ACS Symposium Series 311; American Chemical Society: Washington, DC, 1986. (10) Holland, P. M., Rubingh, D. N., Eds. Mixed Surfactant Systems; ACS Symposium Series 501; American Chemical Society: Washington, DC, 1992. (11) Ogino, K., Abe, M., Eds. Mixed Surfactant Systems; Surfactant Science Series 46; Marcel Dekker: New York, 1993. (12) Mysels, K. J.; Otter, R. J. J. Colloid Sci. 1961, 16, 462–473. (13) Shedlovsky, L.; Jakob, C. W.; Epstein, M. B. J. Phys. Chem. 1963, 67, 2075–2078. (14) Clint, J. H. J. Chem. Soc., Faraday Trans. 1975, 71, 1327–1334.

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and others,15-17 isothermal titration calorimetry (ITC) became a key tool for characterizing surfactant self-association in detail already decades ago. A single run provides a complete, precise dissociation curve and direct measurement of the , without the need for enthalpy of micellization, ΔHaqfm S choosing a specific model or fitting the data. The dissociation curve provides more information than just a single critical micelle concentration (CMC) value; it shows for most systems that the onset of micelle formation is not a sharp transition but occurs over a substantial concentration range from the appearance of first hydrophobic aggregates to the concentration where micelles have reached their characteristic size and the monomer concentration remains essentially constant. Much less straightforward is the recording and interpretation of ITC demicellization curves for mixed surfactant systems, and only few groups have presented such material so far. Blume and co-workers studied mixtures of bile salts with sodium oleate. Moulik and co-workers provided a wealth of ITC (and other) data on surfactant mixtures such as different alkyltrimethylammonium bromides (CnTABs),18 the nonionic MEGA 10 with CnTABs,19 different alkyl triphenyl phosphonium bromides,20 C14TAB with tetradecyltriphenylphosphonium bromide (C14TPB) and tetradecylpyridinium bromide (C14PB),20 and others. They interpreted the complex curves in terms of a first and second CMC (CMC1 and CMC2) analogously to the concentration-dependent association of single surfactants forming small micelles at CMC1 but large (e.g., rod-like) micelles at a higher CMC2. This is quite (15) Kresheck, G. C.; Hargraves, W. A. J. Colloid Interface Sci. 1974, 48, 481–493. (16) Olofsson, G. J. Phys. Chem. 1985, 89, 1473–1477. :: (17) Paula, S.; Sus, W.; Tuchtenhagen, J.; Blume, A. J. Phys. Chem. 1995, 99, 11742–11751. (18) Hildebrand, A.; Garidel, P.; Neubert, R.; Blume, A. Langmuir 2004, 20(2), 320–8. (19) Prasad, M.; Moulik, S. P.; Palepu, R. J. Colloid Interface Sci. 2005, 284(2), 658–666. (20) Basu Ray, G.; Chakraborty, I.; Ghosh, S.; Moulik, S. P.; Holgate, C.; Glenn, K.; Palepu, R. M. J. Phys. Chem. B 2007, 111(33), 9828–9837.

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convincing for mixtures of surfactants preferring different types and topologies of micelles. However, it becomes rather empirical for surfactants forming similar micelles individually, yet showing, nevertheless, a calorimetric demicellization curve with two cooperative association phenomena.19 Whereas the mixed CMC1 is to a good approximation obtained in terms of Lange’s equation21,22 (eq 1), the definition seem less clear. and interpretation of CMC2 and ΔHaqfm S Another previously unsolved problem is the deconvolution of the contributions of the two surfactants to the overall heat measured, which is a prerequisite for deriving the monomeric and micellar concentrations of the surfactants during and after the association process. A temperature- and concentration-dependent sphereto-rod transition was described for tridecyl and tetradecyl maltoside chains,23 but for the mixtures of alkyl maltosides studied here, a second-CMC concept is not warranted. Instead, micelles are initially formed mainly by the lowCMC compound, and these micelles show a cooperative binding of the higher-CMC compound at higher concentration without a substantial change in their size and shape. We have therefore developed a first model for a complete global fit of calorimetric demicellization curves obtained for surfactant mixtures and applied it to globally fit series of up to nine ITC demicellization curves recorded at different mixing ratios and concentrations. The model is based on the pseudophase separation model24-26 and shows some analogy to Clint’s model for surface tension data of mixed surfactant systems.14 Similarities in the ITC data and concepts are also observed with the coassociation behavior of polymers and surfactants.27,28 Dynamic light scattering (DLS) was used to characterize the effects of chain length and composition in the hydrodynamic radius and to check for composition-dependent changes in micellar topology that would account for a “second CMC”. In addition to the new approach to characterize the coassociation of surfactants, we have obtained valuable insight into the interpretation of thermodynamic micellization parameters from comparing the results for the homologous series of alkyl maltosides.

2. Materials and Methods 2.1. Surfactants. The sugar-based, nonionic surfactants n-octyl-β-D-maltopyranoside (abbreviated octyl maltoside, OM), n-nonyl-β-D-maltopyranoside (nonyl maltoside, NM), n-decyl-β-D-maltopyranoside (decyl maltoside, DM), n-undecyl-β-D-maltopyranoside (undecyl maltoside, UM), and n-dodecyl-β-D-maltopyranoside (lauryl maltoside, LM), were obtained from Anatrace, Inc. (Maumee, OH). Note that other authors use the symbol DDM (dodecyl maltoside) instead of LM. All surfactants were 99% pure as specified by the Anagrade label of Anatrace29 and used without further purification. The required amounts of the respective surfactants to achieve (21) Lange, H.; Beck, K.-H. Kolloid Z. Z. Polym. 1973, 251, 424–431. (22) Lange, H. Kolloid Z. Z. Polym. 1953, 131, 96–103. (23) Heerklotz, H.; Tsamaloukas, A.; Kita-Tokarczyk, K.; Strunz, P.; Gutberlet, T. J. Am. Chem. Soc. 2004, 126(50), 16544–52. (24) Elworthy, P. H.; Mysels, K. J. J. Colloid Interface Sci. 1966, 21, 331–347. (25) Stainsby, G.; Alexander, A. E. Trans. Faraday Soc. 1949, 45, 585–597. (26) Stainsby, G.; Alexander, A. E. Trans. Faraday Soc. 1950, 46, 587–597. (27) Diab, C.; Tribet, C.; Gohon, Y.; Popot, J. L.; Winnik, F. M. Biochim. Biophys. Acta 2007, 1768(11), 2737–2747. (28) Wang, G.; Olofsson, G. J. Phys. Chem. B 1998, 102(46), 9276–9283. (29) Anatrace Catalog; Anatrace: Maumee, OH, 2007.

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specific concentrations (or mole fractions) in both single and binary surfactant systems were dissolved in 18 MΩ cm water obtained from a NANOpure A filtration system. For DLS measurements, water was passed consecutively through syringe filters with pore diameters of 450 and 200 nm, respectively, prior to dissolving the surfactants. 2.2. Isothermal Titration Calorimetry. ITC experiments were performed on VP-ITC and OMEGA microcalorimeters from Microcal (Northampton, MA).30,31 Surfactant solutions were degassed before filling, and all experiments were performed at 25 °C. The ITC demicellization assay has been widely used.15-17,32-34 A dispersion of the surfactant or surfactant mixture with a concentration of approximately 25 times the estimated CMC is titrated from the 300 μL-syringe into the calorimeter cell (V∼1.4 mL) filled with water. Mixed micelles were obtained by mixing appropriate aliquots of aqueous stock solutions of the two compounds to reach the desired final concentrations. To investigate the demicellization behavior of mixtures containing surfactants with very different individual CMCi values, we have usually performed two separate titrations. The behavior in the low concentration regime was resolved using a surfactant concentration in the syringe, Csyr S , of about 15-20 times the CMC of the mixture as given by eq 1. The high concentration regime was resolved using a surfactant mixture in the syringe with a Csyr S of about 40-50 times the CMC of the mixture. A typical injection protocol is based on gradually increasing aliquots of ΔV = 1-15 μL injected from the step-motor-driven injection syringe into the calorimeter cell. Two consecutive injections are usually spaced apart by ∼10 min to ensure proper re-equilibration of the system. The first 1 μL injection is not considered in the data evaluation for technical reasons, as explained in detail elsewhere.35 2.3. Dynamic Light Scattering. Mixtures of LM with OM or NM with varying mole fraction of LM, XLM, at total surfactant concentrations of 200 and 100 mM, respectively, were prepared in filtered water (see above) and studied by DLS at 25 °C. Similarly, stock solutions of single surfactant systems were prepared and serially diluted for concentrationdependent measurements. All surfactant solutions were sonicated before being transferred into the cuvette, a 45 μL :: low-volume quartz batch cuvette from Hellma, Mullheim, Germany, to avoid possible scattering artifacts from air bubbles. The measurements were carried out on a Zetasizer Nano ZS from Malvern (Malvern Instruments Ltd., Worcestershire, UK), which utilizes noninvasive backscattering (NIBS). The beam of a 4 mW He-Ne laser (operating at a wavelength of 633 nm) is focused into the cuvette containing the surfactant solution. The intensity of scattered light is recorded in backscattering geometry at an angle of 173°. The software operating the instrument automatically performs a mathematical analysis of the correlation curve. This procedure yields a value for the intensity weighted average of the hydrodynamic diameter, 2  RH, and the polydispersity index (PDI).

3.

Theory

21,22

Lange showed that the CMC of an ideal mixture of i surfactants depends on their mole fractions, Xi (mole number of surfactant i over mole number of all surfactants, but not (30) Chellani, M. Am. Biotechnol. Lab. 1999, 17(1), 14–18. (31) Wiseman, T.; Williston, S.; Brandts, J. F.; Lin, L.-N. Anal. Biochem. 1989, 179, 131–137. (32) Bach, J.; Blandamer, M. J.; Burgess, J.; Cullis, P. M.; Soldi, L. G.; Bijma, K.; Engberts, J. B. F. N.; Kooreman, P. A.; Kacperska, A.; Chowdoji Rao, K.; Subha, M. C. S. J. Chem. Soc., Faraday Trans. 1995, 71, 1229–1235. (33) Heerklotz, H.; Seelig, J. Biophys. J. 2000, 78(5), 2435–40. (34) Kresheck, G. C. J. Am. Chem. Soc. 1998, 120, 10964–10969. (35) Heerklotz, H.; Seelig, J. Biochim. Biophys. Acta 2000, 1508(1-2), 69–85.

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water) and their individual CMC values, CMCi, as X Xi 1 ¼ CMC CMCi i

ð1Þ

3.1. Phase Separation Model. Our model describing ITC demicellization experiments was derived on the basis of the formalism of Clint14 (derived to model γ(log C) curves, i.e., surface tension as a function of surfactant concentration) for binary surfactant mixtures. This formalism is based on the assumption that micelles and the aqueous surfactant solution can be treated as two different phases. We briefly summarize here the key equations for a binary surfactant system (multicomponent systems can be treated analogously). The concentrations of monomers of surfactant 1 (having a mole fraction X1 in the surfactant mixture), Caq S1, and surfactant 2, Caq S2, are given by the following expressions for a total surfactant concentration CS smaller than the mixed CMC (as defined by eq 1) CS < CMC

w

aq CS1 ¼ X1 CS aq CS2

¼ ð1 -X1 ÞCS

ð2Þ

For the case CS g CMC, Clint14 has derived on the basis of the equality of the chemical potentials in all coexisting phases

aq CS1 ¼

-ðCS -ΔCMCÞ (

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðCS -ΔCMCÞ2 þ 4X1 CS ΔCMC   2 2 CMC CMC1 -1

ð3Þ and aq CS2

¼

! aq CS1 CMC2 1CMC1

ð4Þ

where ΔCMC  CMC2 - CMC1 was introduced as a symbol for the difference of the two CMC values. Choosing surfactant S2 to be the one with the smaller CMC (CMC2 < CMC1), only the positive square root in eq 3 yields meaningful solutions for Caq S1. Note that this approach inherently contains a case distinction, i.e., CS < CMC, and CS g CMC that is computationally treated with the help of an if/else construct. 3.2. Modeling of ITC Curves. The heats observed per mole injected in an ITC demicellization assay, Qobs, are modeled in a stepwise mode using eq 5: Qobs ¼ Qdil þ

aq aq ðΔCS1 Þdemic ðΔCS2 Þdemic mfaq mfaq ΔHS1 þ ΔHS2 ΔCS ΔCS ð5Þ

denotes the molar heat of transfer of where, e.g., ΔHmfaq S1 surfactant S1 from a micelle into water (note that the sign has to be reversed for the process of micellization, i.e., ΔHmfaq S = -ΔHaqfm ). The constant term Qdil in eq 5 is introduced to S summarize heats of dilution (micelle and monomer dilution heats17,18), as well as all other unwanted heat effects that are due to imperfections of the experimental setup used (for a general discussion of Qdil, see refs 17 and 18). The expressions (ΔCaq Si )demic denote the mole number of surfactant that is Langmuir 2009, 25(8), 4393–4401

released from micelles disintegrating after injection into the cell (given per cell volume). This release (or, with a negative sign, uptake) upon re-equilibration is the actual origin of the demicellization heat measured. All together, there are three contributions to the change in the aqueous concentration after an injection, (i) the heat-producing contribution from (de)micellization, (ΔCaq Si )demic, (ii) the increase caused by aqueous monomers that were injected from the syringe, and (iii) the monomers included in the small yet significant part of the sample that is displaced by the injected volume and flows over from the totally filled calorimeter cell. The last term in eq 6 quantifies the calorimetrically inactive contributions (ii) and (iii) to (ΔCaq Si )demic so that the monomer concentration change arising from (heat-producing or -consuming) demicellization after the kth injection is given by36 aq aq aq ðΔCSi Þdemic ðkÞ ¼ CSi ðkÞ -CSi ðk -1Þ -

ΔVk aq, syr aq aq ½CSi -0:5ðCSi ðkÞ þ CSi ðk -1ÞÞ V

ð6Þ

For a given experiment with a binary mixture, eq 5 with eqs 2 and 6 (or with eqs 3, 4, and 6) is a model function with five , and Qdil). To allow for parameters (2  CMC, 2  ΔHmfaq S such a large set of adjustable parameters, we have performed global fits of at least five traces obtained in titrations of mixtures with different compositions. We are willing to share the Excel spreadsheet used for these global fits; interested colleagues are welcome to contact us for a free copy and instructions.

4.

Results

4.1. ITC Demicellization Experiments for Single Surfactant Systems. A representative ITC demicellization experiment for a single surfactant system is shown in panel A of Figure 1. A micellar solution of UM at a concentration of 7 mM was titrated in a series of consecutive 10 μL injections into the calorimeter cell filled with water at 25 °C. Each injection gives rise to a deflection of the compensation heater signal (denoted Dp) from its baseline value. Integration of the power peaks from a manually adjusted baseline yields heats of reaction as explained in detail elsewhere.35 These are normalized to the total mole number of surfactant injected (i.e., for injection k divided by the term Csyr S ΔVk) to yield Qobs as described in eq 5. We should note that the measurements with OM involve large concentrations and, hence, large absolute heats that may exceed the dynamic range of the VP ITC (at least for standard settings); the data presented here were obtained on an OMEGA ITC. In panel B of Figure 1, experimental Qobs values (open symbols) for all the single surfactant systems investigated in this study are plotted as a function of the total surfactant concentration in the cell, CS (note the logarithmic scale used for the x-axis). The values used for CS correspond to the arithmetic mean of the surfactant concentration in the cell before and after the kth injection.37 The traces show the typical, quasi-sigmoidal behavior. As long as the surfactant concentration in the cell (abscissa) is below the CMC, the injected micelles dissolve to monomers. This gives rise to a release of heat that is reflected by the negative (exothermic) . value of the demicellization enthalpy, ΔHmfaq S (36) Tsamaloukas, A. D.; Keller, S.; Heerklotz, H. Nat. Protoc. 2007, 2(3), 695–704. (37) Heerklotz, H.; Epand, R. M. Biophys. J. 2001, 80(1), 271–9.

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Tsamaloukas et al. Table 1. Thermodynamic Parameters of Micelle Formation of Pure Alkyl Maltosides at 25°C in Watera surfactant

ΔHaqfm (kJ/mol) S

CMC (mM)

LM 0.9 0.17 [0.17] UM 2.9 0.64 [0.59] DM 4.9 2.1 [1.8] NM 5.6 7.6 [6.0] OM 8.4 23.3 [19.5] a The enthalpy of micelle formation, ΔHaqfm , is obtained by sign S values measured. Estimated maximum errors are reversal of the ΔHmfaq S aqfm . Values in square (20% for the CMC and (0.2 kJ/mol for ΔHS brackets are reference data from the Anatrace catalog.29

often symmetric, and the point of inflection agrees well with the concentration where 50% of the total heat of demicellization is measured. , in the Definitions of the heat of demicellization, ΔHmfaq S literature differ in referring to monomers in dilute solution or to monomers at the CMC. Here we follow the procedure of Blume and co-workers17 and use aq ΔHSaqfm  ðQm obs ðCMCÞ -Qobs ðCMCÞÞ3

Figure 1. Results of ITC demicellization experiment for singlesurfactant systems. (A) Experimental raw data of an ITC demicellization experiment injecting 7 mM UM into water at 25 °C. Shown is the compensation heater power Dp as a function of time, t, for an injection protocol consisting of one 1 μL and 28  10 μL injections. Integration of the peaks shown in panel A and normalization with respect to the moles of titrant injected yields heats of reaction, Qobs. These are plotted in panel B for all the alkyl maltosides investigated as a function of the total surfactant concentration, CS (note the logarithmic scale). Concentrations of the surfactants in the syringe, Csyr S , were chosen as follows: 3.5 mM (LM, ]), 7 mM (UM, r), 25 mM (DM, Δ), 100 mM (NM, O), and 185 mM (OM, 0). aq The arrow in the DM curve represents Qm obs(CMC) - Qobs(CMC) as used in eq 7. For the single surfactant systems shown here, the curves turn rather steeply toward a value close to zero (heat of dilution) at the CMC, since the injected micelles no longer dissolve in a solution above the CMC, and thus no heat of demicellization is detected. The step between complete dissolution of the injected micelles and the case where the injected micelles no longer disintegrate is, however, not instantaneous as predicted by the phase separation model.24-26 Micelles fulfill the requirements for a thermodynamic phase only to a relatively poor approximation, and hence the transition we observe occurs over a certain concentration range. This causes some ambiguity in the definition of the CMC. From a thermodynamic point of view, the best representation of the critical concentration is the point of inflection of the quasi-sigmoidal transition, i.e., the maximum of the first derivative of the Qobs(CS) curve.17 For pure surfactants, as shown in panel A of Figure 1, the transition is 4396

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CSsyr

CSsyr ð7Þ -CMC

m where Qaq obs(CMC) and Qobs(CMC) are estimated by a linear extrapolation of the heat curves below and above the sigmoidal transition, respectively, to its midpoint (the CMC) (see arrow for DM in Figure 1B). The term Csyr S / CMC) corrects the heat from the normalization “per (Csyr S mole of surfactant added” as used in the plot to “per mole of micellar surfactant added” (monomers in the syringe amounts to between 5 and 14% of the titrant and do not contribute to the heat of demicellization measured). The thermodynamic parameters are, together with the reference CMC data from the Anatrace catalog,29 summarized in Table 1. 4.2. Demicellization Curves of Binary Surfactant Mixtures. Figure 2 shows experimental data (symbols) as well as fit curves (lines) based on the phase separation model for the demicellization of binary surfactant mixtures of LM with UM and LM with DM, respectively, in water at 25 °C. In contrast to the single surfactant systems, the traces obtained for the mixtures are no longer symmetric sigmoidal curves. Instead, a sudden, albeit small decrease of the absolute heats measured indicates the onset of association, i.e., the CMC of the mixed system as described by eq 1. Then, the micellar fraction of the surfactants grows gradually with increasing concentration as indicated by gradually decreasing absolute heats in the course of the titration. Using the model derived above, we have respectively fitted these five (or seven) curves in the two panels of Figure 2 globally by optimizing 9 (or 11) parameters: CMCLM, aqfm aqfm CMCUM (CMCDM), ΔHaqfm LM , ΔHUM (ΔHDM ), and five (or seven) individual values for the constant heat of dilution, Qdil, of each titrant. It has been known that the phase separation model fits demicellization curves of most nonionic surfactants only very poorly; also here, the curves for the pure systems deviate substantially from the data. It is therefore rather surprising that the mixed systems are fitted much better. Given the complexity of these curves being modeled by less than two free parameters per curve, we may stress a not only empirical but physically meaningful approximation of the data by the simple model.

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Figure 2. Experimental data (symbols) and fit curves (lines, see eq 5) of demicellization experiments with mixtures of LM/UM (top) and LM/DM (bottom); see plot for compositions. The heat per mole of surfactant injected, Qobs, is shown as a function of the total surfactant concentration in the sample cell, CS. The curves in each panel were fitted globally in terms of shared values of ΔHaqfm and Si CMCi for the pure components (listed in Table 2) and individual, small heats of dilution. For the mixtures of surfactants differing in 2-4 methylenes per chain, it may need two experiments with different titrant concentrations to cover the required concentration range of more than 3 orders of magnitude at sufficient resolution. The shapes of the demicellization curves obtained by different titrant concentrations (i.e., the fit curves in the top and bottom panels of Figure 3) differ from each other because the titrant contains (i) different relative amounts of aqueous surfactant (larger for lower concentration) and (ii) different intermicellar interactions (stronger for higher concentration). The former (i) are explicitly considered in the model, and in the latter (ii), constant heat contribution is covered by allowing for individual heats of dilution. For the sake of illustrating the shape of the association curve, the model lines are plotted over the whole abscissa range in the lower panels of Figure 3; the information regarding the position and shape in the low concentration range arises from the globally fitted, upper panels. As in Figure 2, we obtain surprisingly good fits of virtually all mixtures in spite of the very limited number of free parameters per curve, even for LM-OM with its extreme difference in CMC resulting in larger errors. The slightly | for LM in mixtures with DM and OM lower |ΔHmfaq S compared to pure LM might be another consequence of the limited ability of the model to fit curves for pure substances. It might also result from a small excess enthalpy Langmuir 2009, 25(8), 4393–4401

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of the mixture, but this would be too small to warrant a detailed quantitative discussion. We conclude that the model provides a good fit of the association curves of the mixtures, its assumptions are approximately fulfilled, and the parameters are meaningful. A summary of the parameters obtained in the global fit for all the surfactant mixtures shown in Figures 2 and 3 are provided in Table 2. A detailed explanation of the phenomena governing the demicellization curve is given in section 5.1. 4.3. Micelle Sizes of Pure Surfactants and Binary Surfactant Mixtures. DLS measurements of pure and mixed alkyl maltoside micelles performed here yielded monomodal size distributions with polydispersity indices below 0.25. We have plotted the intensity-weighted, average hydrodynamic radius, RH, in Figure 4. Note that, for Rayleigh scattering as performed here, the scattered light intensity increases proportionally to the sixth power of the particle size so that the intensity-weighted average represents a value close to the upper limit of the size distribution. Figure 4B shows the results for pure alkyl maltoside micelles of the different species and at different concentrations, respectively. As one might expect because of the growing length of the molecules, RH increases with increasing alkyl chain length. Furthermore, there is a slight increase of RH for OM, NM, DM, and UM with increasing concentration by ∼0.3 A˚/mM, which could result from intermicellar interactions. LM shows a more significant increase by 0.5 A˚/mM, suggesting additional effects that tend to increase RH with increasing concentration, such as a micellar growth. A measurement of 100 mM LM in buffer (10 mM Tris, 100 mM NaCl, pH 7.4) yielded the same RH, PDI, and count rate as reported above for 100 mM LM in pure water (data not shown). This suggests that the size of the micelles is not affected by any electrostatic interactions. Figure 4C,D shows RH and the scattered light intensity of mixed micelles as a function of their composition, specified in terms of the mole fraction of LM, XLM. In contrast to mixtures of ionic/nonionic surfactants,38,39 the RH and intensity values obtained here for the mixtures agree within error with the weighted averages of those obtained for the pure components (indicated by the solid linear regression lines). This suggests that all micelles share the same principal topology.

5.

Discussion

5.1. The Coassociation of Mixed Surfactants. Let us consider the demicellization curves of surfactant mixtures as shown in Figures 2 and 3. Instead of smooth sigmoidal curves, we obtained curves with two steep transition regions. Similar curves have been described in terms of two different aggregate topologies being formed at different characteristic concentrations (first and second CMC). However, in contrast to classical “second CMC” phenomena, Figure 4 shows clearly that all surfactants and their mixtures form (at least at CS < 100 mM) small micelles with sizes differing only slightly due to different chain lengths. That means the systems studied here do not show a second CMC in the classic sense. (38) Bucci, S.; Fagotti, C. Langmuir 1991, 7, 824–826. (39) Shaw, D.; Dubin, P., Characterisation of mixed micelles. In Malvern Application Note; http://www.malvern.co.uk/common/downloads/campaign/ MRK506-01.pdf.

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Figure 3. Demicellization curves for mixtures of LM/NM (left panels) and LM/OM (right panels) analogous to those shown in Figure 2. The mixtures considered here, however, exhibit such large differences in the individual CMCs that experiments with low (15-20  CMC, top panels) and high (40-50  CMC, bottom panels) surfactant concentration in the syringe had to be considered in the global fit. The model curves in the lower panel also represent information about primary association obtained from the upper panel. Table 2. Summary of the Fit Parameters Obtained for the Surfactants (Rows) in Various Binary Surfactant Mixtures (Boxes with Two Rows Each) in the Global Fitting Procedurea ΔHaqfm (kJ/mol) S

CMC (mM)

LM UM

1.1 3.1

0.15 0.64

LM DM

0.6 4.7

0.16 2.3

LM NM

0.9 5.5

0.17 7.8

mixture

LM 0.5 0.15 OM 8.1 23.0 a The corresponding experiments, as shown in Figures 2 and 3, were conducted at 25°C in water. Heats of dilution, Qdil, obtained in the global fits ranged from -0.5 to 0.5 kJ/mol for individual traces.

As explained in the results section, the global fits of a few adjustable parameters to the complex and extensive data sets in Figures 2 and 3 have provided strong evidence for the applicability of our simple model based on the pseudophase approximation. Let us now discuss how the model explains the coassociation behavior and its resemblance of a second CMC. Figure 5A illustrates the aqueous and micellar concentrations of LM as a function of LM concentration, both in the absence (thin dotted lines) and presence (bold solid lines) of DM (XLM = 0.5) calculated using the pseudophase model. On the first glance, the addition of the highCMC compound, DM, has only relatively little effect on LM association. The principal differences are (i) that association starts already at a LM concentration slightly below the CMC of individual LM and (ii) that, upon micelle formation, the monomer concentration decreases with 4398

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increasing total concentration. The latter is due to the increasing incorporation of DM into the micelles, which adds entropy of mixing and, thus, promotes also the further uptake of LM monomers. A completely different picture is obtained for the highCMC component, DM (Figure 5B). When first micelles form at the CMC of the mixed system, they contain less than 10% of DM (see Figure 5C). At higher concentration, DM partitions between micelles and aqueous phase, as described by a constant mole fraction partition coefficient, KDM: KDM ¼

m CDM 355:5 M m m ÞC aq ðCDM þ CLM DM

ð8Þ

In spite of a constant KDM, there is an apparent cooperativity observed in the association curve. Uptake of DM monomers into the micelles increases their entropy of mixing, thus promoting further uptake. The resulting nonlinear increase of the micellar fraction with increasing concentration shows some resemblance to a “second CMC”. The monomer concentration of DM tends, at very high concentration, toward XDMCMCDM . The coassociation curve of DM shows no breakpoint or specific feature at the CMC of pure DM. Above, we have stated that the fits of the ITC curves shown in Figures 2 and 3 are actually better for mixtures than for the pure components. This could be explained in terms of small primary or premicellar aggregates occurring for pure surfactant systems. Whereas primary aggregation and subsequent growth is allowed for in the pseudophase model for mixtures, it is not for individual surfactants. 5.2. Ideal versus Nonideal Mixing. Lange’s equation for the CMC of a surfactant mixture (eq 1) holds true for surfactants mixing without any significant excess free energy Langmuir 2009, 25(8), 4393–4401

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Figure 4. DLS data. (A) Intensity-weighted size (= 2  RH) distributions of micelles of NM (red, left), NM-LM (XLM = 0.5, blue, middle) and LM (green, right); all 100 mM. Panels B and C display the intensity-weighted, hydrodynamic radius, RH for pure alkyl maltosides as a function of concentration (panel B), and as a function of the mole fraction of LM, XLM (panel C), for various binary mixtures of LM with OM (O), and LM with NM (0) in water at 25 °C. Panel D shows the back-scattered intensities (derived count rates) corresponding to the measurements shown in panel C. Note that the values for XLM = 1 in panels C and D do not agree with each other because they refer to different absolute LM concentrations. The standard deviation of at least 8 measurements is smaller than the size of the symbols, but minor additional errors may apply so that the deviations from linearity are not considered significant.

(as is a prerequisite for ideal mixing). It predicts that the reciprocal CMC of a mixture is linear on the mole fraction scale. Figure 6 shows the reciprocal CMCs as identified by the first sudden decrease of the absolute heats of the experimental titration curves for all mixtures investigated (see Figures 2 and 3) as a function of the mole fraction of LM. Virtually all data lie on straight lines, indicating that they are in accord with Lange’s rule for ideal mixtures (eq 1). That means, for the systems studied here, it is not warranted to consider activity coefficient-based corrections to the formula for the mixture CMC as put forward and experimentally Langmuir 2009, 25(8), 4393–4401

Figure 5. Concentration-dependent association of LM (A) and DM (B) as a function of their individual concentration in 1:1 mixtures of the two (XLM = 0.5, bold solid lines) and for dispersions of the single component (thin dotted lines), respectively. The partial concentration of LM and DM localized in micelles is denoted Cm LM and Cm DM, respectively, and shown in red. The aqueous concentrations are aq denoted Caq LM and CDM, respectively, and shown in blue. Panel C displays the mole fraction of LM in mixed micelles (Xm LM, bold line) and the total mole fraction of LM in the sample (XLM, dotted line). validated by Holland and Rubingh40 and also experimentally tested by others18,41-43 for mixtures of ionic/nonionic and ionic/ionic surfactants. Truly ideal mixing also requires vanishing excess enthalpy and entropy of mixing, a fact that cannot be concluded from the CMCs since enthalpy and entropy changes often compensate each other so that they do not affect the free energy. We can, however, also rule out substantial excess enthalpy or entropy because the fits shown in Figures 2 and 3 were obtained assuming that the enthalpy of micellization (40) Holland, P; Rubingh, D. J. Phys. Chem. 1983, 87, 1984–1990. (41) Chakraborty, T.; Ghosh, S.; Moulik, S. P. J. Phys. Chem. B 2005, 109, 14813–14823. (42) Couderc, S.; Li, Y.; Bloor, D. M.; Holzwarth, J. F.; Wyn-Jones, E. Langmuir 2001, 17, 4818–4824. (43) Ghosh, S.; Moulik, S. P. J. Colloid Interface Sci. 1998, 208, 357–366.

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Figure 6. Plots of the reciprocal CMC of binary surfactant mixtures of UM, DM, NM, and OM, respectively (see plot), with LM as a function of the mole fraction of LM, XLM, at 25 °C in water. of both components, respectively, is the same for entering of the a pure or mixed micelle. The values of ΔHaqfm S surfactants obtained in global fits including mixed micelles (Figures 2 and 3, Table 2) correspond reasonably well with those for pure micelles (Figure 1, Table 1). The ideal mixing observed in the thermodynamic characterization of the mixtures is paralleled by an absence of transitions or thresholds in micelle structure. Instead, the hydrodynamic radius of the mixed micelles changes linearly with composition as illustrated by Figure 4B. 5.3. The Effect of Chain Length on Micelle Properties. The hydrodynamic radius, RH, is the radius of a sphere that would diffuse with the same speed as the micelle studied. It is not surprising that RH is found to be larger than the maximum length of the molecule, lmax (estimated from Tanford’s value for the length of alkyl chains and a maltoside headgroup size of ∼10 A˚, see Figure 7A) because it includes bound water and contributions from fluctuations and deviations from a spherical shape. Because of the intensityweighted averaging, RH becomes particularly sensitive to the presence of some slower moving micelles. It is interesting to note that hydration and so forth does not give rise to a constant difference between RH and lmax. Instead, the difference increases with increasing chain length, and the slope of RH(nC), 2.5 A˚/CH2, is significantly larger than dlmax/dnC = 1.265 A˚.44 Generally, this could reflect (i) an increasing tendency for deviations from spherical shape, (ii) a starting, geometric radius smaller than lmax (44) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; Wiley: New York, 1980.

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Figure 7. Micellization parameters of homologous series at 25 °C. Hydrodynamic radius, RH and maximum length of a stretched molecule, lmax (see text) (A), enthalpy of micelle formation, ΔHaqfm S (B), and CMC (C) are shown as a function of the number of carbons in the alkyl chain, nC. In addition to the data on alkyl maltosides (M, red solid spheres) obtained here and for nC = 13, 14 in ref 23, literature data are shown for lysolipids37 (lysoPC, open blue circles), alkyldimethylphosphine oxides34 (DPO, green up triangles), alkyltriphenylphosphonium bromides19 (TPB, black down triangles), and alkyltrimethylammonium bromides32 (TAB, magenta diamonds). Solid symbols in panel A refer to 100 mM, and open symbols refer to LM at 200 and 400 mM (for details, see Figure 4). due to packing constraints, and (iii) increasing hydration/ roughness of the headgroup region. A detailed elucidation of this phenomenon could greatly benefit from small-angle neutron scattering (SANS) measurements but is outside the scope of this paper. The function of DLS in this study was to decide whether the two-step association behavior could be explained by the surfactants forming micelles of different principal topologies, giving rise to second-CMC phenomena. This could clearly be ruled out for the systems and conditions investigated here. The effect of chain length on the enthalpy of micelle , is illustrated by panel B of Figure 7. formation, ΔHaqfm S The solid red spheres represent the results obtained here and published values for TM and MM.23 The figure shows that decreases linearly with increasing chain length ΔHaqfm S (parameters listed in Table 3) and changes its sign from Langmuir 2009, 25(8), 4393–4401

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Table 3. Parameters of Linear Fits of the Effect of Chain Length of Alkyl Maltosides on a Number of Experimental Parameters Characterizing Micelle Formationa property Y

slope (dY/dnC)

RH

A˚

lmax

A˚

ΔHaqfm S

kJ/mol

-1.8

Δμ0,aqfm S

kJ/mol

-3.2

2.5

intercept [Y(nC f 0)] 5.5

44

1.265

∼15 23 7.0

-TΔS0,aqfm S a

kJ/mol -1.4 -15 The slope can formally be interpreted as a methylene group contribution. For a detailed, critical interpretation, see text.

endothermic to exothermic between LM and TM, i.e., nC = 12 and 13. The linearity suggests that aggregates of the same principal structure are formed; the formation of rod-like micelles by TM and MM at higher concentration and/or temperature23 is not reflected here. Chain length-dependent changes in the structure of soap fibers were, for example, shown to induce an offset in their otherwise linear dependence of the dissolution enthalpy versus chain length.23 It is interesting to note that ΔHaqfm of alkyl maltosides is S quite close to the values obtained for lysolipids37 and even those of the cationic alkyl-TABs32 and -TPBs19 (except for nC = 16) with the corresponding chain lengths (see Figure 7B). In particular, all four series show approximately the same methylene group contribution, as indicated by the almost identical slopes of the linear regressions. Ethylene glycol alkyl ethers (CmEOn) show much larger absolute heats of micellization but a similar methylene group contribution.33,45 A somewhat smaller but also negative group contribution was measured for alkyl-DPOs.34 A logarithmic plot of the CMC as a function of nC (Figure 7C) showing a linear behavior implies a constant group contribution of methylenes to the standard chemical , according to33 potential change of micellization, Δμ0,aqfm S Δμ0S, aqfm ¼ RT ln

CMC 55:5 M

ð9Þ

where the molar concentration of water and dilute solutions, 55.5 M, converts the CMC from molar to mole fraction units. The fit parameters for the data measured here (nC= 8-12) and in ref 23 (for nC = 13, 14) for alkyl maltosides are given in Table 3. Figure 7C compares the results obtained here with literature data. Using

, we have calculated the entropic enthalpy changes, ΔH0,aqfm S contributions to the standard free energy of micelle forma, as included in Table 3. tion, -TΔS0,aqfm S It is interesting to note that hydrocarbon association/ solution shows virtually no enthalpy change at room temperature so that the standard free energy change of about -3 kJ/mol is exclusively due to a gain in entropy.44,46 A possible explanation for the gain in enthalpy upon micelle formation, approximately -2 kJ/mol per methylene at 25 °C, arises from the fact that the hydrocarbon chains in a micelle are partially aligned, which should improve their packing and intermolecular interactions (enthalpically favorable) but reduces their conformational and motional freedom (entropically unfavorable).37

Conclusions 1.

The model derived here on the basis of the pseudophase separation concept provides good, meaningful fits of the complex demicellization curves of binary mixtures of alkyl maltosides. This establishes ITC as an excellent tool for the detailed characterization also of mixed micellar aggregation.

2.

The model provides a quantitative explanation for the fact that the progress in coassociation involves two characteristic ranges; this does not require any concentration-dependent changes in micellar structure that are the basis of “second CMC” phenomena in the classic sense. Alkyl maltosides with octyl through undecyl chains mix virtually ideally with LM as detected not only in terms of free energy but also regarding enthalpy and entropy of mixing. The hydrodynamic radii of micelles of the homologous series, OM through LM, grow twice as much as the alkyl chain length. A group contribution of about -2 kJ/mol per methylene to the enthalpy of micellization appears to be characteristic for surfactants. This is at variance with the isenthalpic nature of the aqueous dissolution or aggregation of hydrocarbons, suggesting a lower enthalpy to be associated with the partial alignment and ordering of the chains in a micelle. This phenomenon has, however, no effect on the free energy since favorable enthalpy change is fully compensated by a loss in entropy.

3.

4.

5.

and taking into account that the measured enthalpy changes, , should approximately agree with standard ΔHaqfm S

Acknowledgment. We thank Sandro Keller (Leibnitz Institute for Molecular Pharmacology, Berlin) for important comments on the manuscript. Funding from NSERC (# 341920-07) and the Canadian Research Chairs Programme is gratefully acknowledged.

(45) Chen, L.-J.; Lin, S.-Y.; Huang, C.-C.; Chen, E.-M. Colloids Surf., A 1998, 135, 175–181.

:: (46) Gill, S. J.; Wadso, I. Proc. Natl. Acad. Sci. U.S.A. 1976, 73(9), 2955–2958.

0, aqfm 0, aqfm 0, aqfm ¼ ΔHS -TΔSS ΔμS

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ð10Þ

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