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Model-Free Analysis of Critical Micellar Concentrations for Detecting Demixing in Surfactant Mixtures Erik Frotscher, Jonas Höring, Grégory Durand, Carolyn Vargas, and Sandro Keller Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b00339 • Publication Date (Web): 07 Mar 2017 Downloaded from http://pubs.acs.org on March 9, 2017

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Analytical Chemistry

Model-Free Analysis of Critical Micellar Concentrations for Detecting Demixing in Surfactant Mixtures

Erik Frotscher,† Jonas Höring,† Grégory Durand,‡,§ Carolyn Vargas,† and Sandro Keller*,†

†

‡

§

Molecular Biophysics, University of Kaiserslautern, Erwin-Schrödinger-Str. 13, 67663 Kaiserslautern, Germany

Equipe Chimie Bioorganique et Systèmes Amphiphiles, Université d’Avignon et des Pays de Vaucluse, 33 rue Louis Pasteur, 84000 Avignon, France

Institut des Biomolécules Max Mousseron, UMR 5247 CNRS-UM-ENSCM, 15 avenue Charles Flahault, 34093 Montpellier Cedex 05, France

*

Corresponding author. E-mail: [email protected]

1 ACS Paragon Plus Environment


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ABSTRACT Aqueous mixtures of two or more surfactants are often employed for research or industrial purposes because such mixtures offer advantages over single-surfactant systems. This is particularly true for mixtures of fluorocarbon (FC) and hydrocarbon (HC) surfactants, which display a broad range of mutual miscibilities in mixed micelles. Unfortunately, the prediction and even the experimental elucidation of the micellar mixing behavior of surfactant mixtures remain challenging, as evidenced by conflicting results and conclusions derived from diverse, and often complex, mixing models. One of the most intriguing questions is whether certain combinations of FC and HC surfactants form only one type of mixed micelle or rather demix into two micelle populations—namely, FC-rich and HC-rich ones. Here, we demonstrate a novel approach to the model-free analysis of critical micellar concentrations (CMCs) of surfactant mixtures that is based on a fit of the experimental data with cubic splines using a stringent thermodynamic criterion for mixing. As a proof of principle, we analyze CMC values determined by isothermal titration calorimetry and confirm the conclusions with the aid of combined 1H- and 19F-NMR spectroscopy. Specifically, we show that aqueous mixtures of an FC maltoside and an HC maltoside conform with the assumption of only one type of micelle regardless of the mixing ratio, whereas combining the same FC surfactant with an HC surfactant carrying a zwitterionic phosphocholine headgroup gives rise to two coexisting micelle populations at high mole fractions of the FC maltoside.


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INTRODUCTION The mixed micellization of surfactants is an important phenomenon to study because it is relevant to diverse scientific and industrial applications such as the formation of oil repellents,1 the solubilization of hydrophobic compounds from soil,2 and the solubilization and stabilization of membrane proteins.3,4 Of particular interest are pseudobinary aqueous mixtures of surfactants comprising either a hydrogenated carbon chain or a (partially) fluorinated carbon chain.5 Such surfactant mixtures combine different advantageous properties of both surfactant types, but the often poor mutual miscibility of hydrocarbon (HC) and fluorocarbon (FC) moieties6,7 can hamper the formation of homogeneously mixed micelles.8 Numerous studies on FC/HC surfactant mixtures have revealed that their mixing behavior is not only hard to predict but even difficult to ascertain experimentally, as vastly diverging (de)mixing scenarios have been observed and proposed for various surfactant mixtures.5 These scenarios include mixing within one type of micelle,9–11 segregation—that is, demixing—leading to the coexistence of two micelle populations,12–15 or both, depending on the mixing ratio of the two.16–18 Moreover, data interpretation is often complex and ambiguous, and approaches that furnish robust results tend to be labor-intensive and require sophisticated instrumentation such as nuclear magnetic resonance (NMR),10,12,15,17,19 small-angle neutron scattering (SANS),20 and cryo-transmission electron microscopy (cryo-TEM).12 These difficulties arise chiefly because micellar (de)mixing is often so complex that it evades reasonably simple thermodynamic models.5,20 Here, we present an approach for identifying micellar demixing in surfactant mixtures on the basis of critical micellar concentrations (CMCs), that is, on values that are straightforward to obtain from a broad range of methods. We determined CMCs by isothermal titration calorimetry (ITC) demicellization experiments21–23 and tested an established non-ideal mixing model based on regular solution theory.24 We then analyzed the experimental CMC values in a model-free manner by constrained cubic-spline regression. The validity of the conclusions thus derived was confirmed by 1Hand

19

F-NMR. Experiments were performed on the FC surfactant 3,3,4,4,5,5,6,6,7,7,8,8,8-trideca-

fluoro-n-octyl-β-d-maltopyranoside (F6OM; Figure S1), a mild fluorinated detergent that has proven useful for membrane-protein studies.25 F6OM was mixed with two HC surfactants, namely, either n-decyl-β-d-maltopyranoside (DM; Figure S1), which bears the same nonionic headgroup as F6OM, or zwitterionic n-dodecylphosphocholine (DPC; Figure S1) to shed light on the effects of headgroup chemistry on the mixing behavior.



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EXPERIMENTAL SECTION Materials All chemicals were purchased in the highest purity available. F6OM was obtained from Anatrace (Maumee, USA), DM and n-dodecylphosphocholine (DPC) were from Glycon Biochemicals (Luckenwalde, Germany), monobasic and dibasic sodium phosphate were from Carl Roth (Karlsruhe, Germany), NaCl (AnalaR Normapur) was from VWR (Darmstadt, Germany), D2O was from Deutero (Kastellaun, Germany), and sodium trifluoroacetate and 4,4-dimethyl-4-silapentane-1-sulfonic acid (DSS) were from Sigma–Aldrich (Steinheim, Germany). Surfactant powders were weighed on a highprecision XP205 Delta Range microbalance (Mettler Toledo, Greifensee, Switzerland) and dissolved in triple-distilled water or phosphate buffer (10 mM phosphate, 150 mM NaCl, pH 7.4) for experiments with nonionic DM or zwitterionic DPC, respectively. Isothermal titration calorimetry ITC was performed at 25°C on a VP-ITC (Malvern, Worcestershire, UK). A surfactant solution at a concentration 10–15 times the CMC was loaded into the injection syringe, and the reference and sample cells were filled with triple-distilled water or buffer. Experimental settings included an injection volume of 3–10 µL, time spacings sufficient to allow the signal to return to the baseline, a stirring speed of 310 rpm, a reference power of 58.6–83.7 µJ/s, and a filter period of 2 s. Samples were measured at least twice. Automated baseline adjustment, peak integration, and normalization of reaction heats with respect to the molar amount of surfactant injected were done with NITPIC.26 Integrated heats were fitted to a sigmoidal function to determine the CMC as the total surfactant concentration at the inflection point of the isotherm.22,23 Data were fitted by nonlinear least-squares regression in Excel (Microsoft, Redmond, USA) using the Solver add-in (Frontline Systems, Incline Village, USA).27 NMR spectroscopy F6OM/DM mixtures were prepared by mixing and diluting stock solutions in D2O to reach final total surfactant concentrations of 1–10 mM, thereby maintaining an F6OM bulk mole fraction of 0.25. F6OM/DPC mixtures were prepared by combining and diluting stock solutions in phosphate buffer and adding 5% (v/v) D2O for locking to arrive at final total surfactant concentrations of 0.5–2 mM at an F6OM bulk mole fraction of 0.75. Measurements were performed at 25°C. 1H-NMR spectra of F6OM/DM and F6OM/DPC samples were recorded on, respectively, Avance 400 and Avance 600 spectrometers (Bruker Biospin, Rheinstetten, Germany) using DSS in D2O as external reference (δ = 0 ppm). 19F-NMR spectra were recorded on an Avance 400 spectrometer (Bruker Biospin) using sodium trifluoroacetate as external standard (δ = −76.55 ppm).


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RESULTS AND DISCUSSION The representative thermogram in Figure 1a was obtained from an ITC demicellization experiment using a surfactant mixture containing F6OM and DM as FC and HC components, respectively. The concentrations of F6OM and DM were 7 mM each, corresponding to an F6OM bulk mole fraction (XF6 OM ) of 0.5. At the beginning of the titration, dilution of micelles to total surfactant concentrations below the CMC of the mixture led to micelle disintegration, which gave rise to exothermic enthalpy changes. The signal sharply decreased in magnitude as the total surfactant concentration in the calorimeter cell reached the “mixed CMC”. Integration of the injection peaks yielded a sigmoidal isotherm (Figure 1b), which was fitted with a generic sigmoidal function to derive the CMC as the total surfactant concentration at the inflection point.22,23 The isotherms of both kinds of mixtures studied here—that is, F6OM/DM (Figure 1c) and F6OM/DPC (Figure 1d)—displayed only one distinct transition irrespective of the mixing ratio. Importantly, however, the absence of a second steep transition does not preclude the possibility that a second type of micelle is formed at higher surfactant concentrations (see below). In fact, two separate transitions in demicellization isotherms are observed in only a few fortunate cases28–31 in which both transitions lie within the dynamic concentration range of one ITC experiment and are characterized by significantly different demicellization enthalpies. The mixed CMCs thus derived for surfactant mixtures at various XF6 OM values (Figure 2a,b) reveal a pronounced deviation from ideal mixing towards higher CMC values, as expected for the net unfavorable effect of replacing FC/FC and HC/HC by FC/HC contacts (cf. Supporting Information eq S1).32,33 Regular solution theory is a simple yet powerful approach that is frequently used for fitting and parameterizing such non-ideal mixed micellization.24 Thereby, a so-called net interaction parameter (β) is introduced (eqs S2–S9) to account for synergistic mixing (β < 0), ideal mixing (β = 0), or net repulsion (β > 0) of the two surfactants. The latter case includes a critical value (β = 2), above which demixing into two coexisting micelle populations is expected, since such pseudophase separation becomes more favorable than mixing in one type of micelle.34 Hence, in the range defined by 0 < β < 2, mixing within only one micellar phase takes place because the net repulsive effect of FC/HC contacts is overcompensated by the entropy of mixing. In the present cases, the best-fit values of β amounted to 1.6 and 1.2 for F6OM/DM and F6OM/DPC, respectively, thus suggesting no demixing for both surfactant mixtures at first glance. However, closer inspection of the data clearly shows that this mixing model can describe the experimental data well across the entire range of XF6 OM only in the case of F6OM/DM (Figure 2a), whereas a strong, systematic deviation is obvious for F6OM/DPC at high XF6 OM (Figure 2b). Traditionally, more complicated mixing scenarios have been dealt with by adding higher-order terms,35 but this often results in over-parameterization and, in the current case, did not allow for a satisfactory fit of the mixed CMC values of F6OM/DM (data not shown).



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To analyze the above mixed CMCs without the necessity of assuming a particular model and with a minimum number of adjustable parameters, we determined the composition of the mixed micelles from the first derivative of the mixed CMC with respect to XF6 OM (eq S10).36 Numerical differentiation of experimental data often suffers from pronounced susceptibility to noise, which is accentuated by the relatively small number of data points (i.e., CMC values at different XF6 OM ) typically available. To circumvent this issue and allow for maximum flexibility of our model-free approach, we fitted the experimental CMC values using cubic-spline regression (eqs S10–S14). Furthermore, we defined a thermodynamic—that is, model-free—constraint imposed by the assumption of homogeneous micellar mixing; in the presence of only two pseudophases (namely, an aqueous phase containing surfactant monomers as well as one kind of micellar phase), the mole fraction of each of the two surfactants in the mixed micelles (Xmm i ) has to increase when the bulk mole fraction of the same surfactant (Xi ) increases: ∂Xmm i >0 ∂Xi

(1)

Using this rigorous, thermodynamic constraint, we could adequately fit the CMCs of F6OM/DM, thus corroborating the above conclusion from regular solution theory that the experimental data conform with the presence of only one type of micelles. By contrast, the experimental F6OM/DPC data could not be reasonably approximated at high XF6 OM , which excludes the possibility that only one type of micelles is formed across the entire mixing range. Conversely, this means that the data can be quantitatively rationalized only if micellar demixing is considered. The micellar compositions derived from different mixing scenarios are shown in Figure 2c,d. In the case of F6OM/DPC, cubic-spline regression without the thermodynamic constraint of eq 1 would allow for a close fit with the data (Figure 2b) but would yield compositions that are physically meaningless at high XF6 OM , as (i) Xmm i decreases with increasing Xi and (ii) Xmm assumes values that are greater than unity or negative for i F6OM and DPC, respectively (Figure 2d). Thus, we conclude that our F6OM/DM data agree with mixing of these FC and HC surfactants within one population of mixed micelles independent of the mixing ratio, whereas the F6OM/DPC data can be explained only in terms of micellar demixing at high XF6 OM , irrespective of the detailed mixing model used. To validate the conclusions drawn on the basis of thermodynamic arguments, we performed NMR measurements on F6OM/DM and F6OM/DPC mixtures at the mixing ratios in question. For FC/HC mixtures, combined

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F- and

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H-NMR spectroscopy provides information on the chemical

environment and, thereby, the micellization of each surfactant individually.10,11,15 The chemical shifts of atoms in the surfactant chains change when micelles form with increasing surfactant concentration, as exemplified for F6OM/DM at XF6 OM = 0.25 (Figure 3a,b). Plotting the chemical shift change against the reciprocal surfactant concentration10,15,17 yielded breakpoints indicating the onset of micellization. For F6OM/DM, we observed only one coinciding breakpoint for the 19F and 1H signals (Figure 3c). For F6OM/DPC at XF6 OM = 0.75, by contrast, two breakpoints were found (Figure 3d), thus confirming the 6 ACS Paragon Plus Environment

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appearance of a second population of mixed micelles. Comparison of the different linear ranges reveals a much steeper slope after the first breakpoint than after second breakpoint for the 19F signal, while the opposite is true for the 1H signal. This indicates that the first breakpoint corresponds to the formation of F6OM-rich micelles and the second one to the appearance of DPC-rich micelles. Taken together, NMR spectroscopy corroborated the above conclusion that F6OM and DM mix homogenously within one micelle population, whereas F6OM and DPC demix into two coexisting types of mixed micelles at high XF6 OM .



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CONCLUSION We demonstrate how mixed micellization can be evaluated with the aid of a model-free approach based on constrained cubic-spline regression of CMC values to identify micellar demixing. This approach does not require sophisticated instrumentation but solely a method that is capable of determining reasonably accurate CMC values, such as, for instance, ITC,21–23 surface tensiometry,32,37,38 conductometry,39,40 or fluorescence spectroscopy.41 An earlier approach to the model-independent evaluation of mixed micellization relies on a synergy parameter that is calculated from experimental CMC values.42 Although this parameter is useful for quantifying nonideal mixing, it does not provide a quantitative criterion for identifying micellar demixing. Our ITC data show that the fluorinated octyl maltoside surfactant F6OM forms a single population of mixed micelles with the hydrogenated decyl maltoside surfactant DM, whereas mixing it with the hydrogenated phosphocholine surfactant DPC results in micellar demixing at high mole fractions of F6OM. On a broader note, this observation demonstrates that the generally poor miscibility of fluorocarbon and hydrocarbon chains does not necessarily lead to micellar demixing, as headgroup interactions can make decisive contributions.


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ASSOCIATED CONTENT Supporting Information Chemical structures of surfactants (Figure S1) and theoretical background of non-ideal mixing (eqs S1–S9) and model-free analysis of CMC values by cubic-spline regression (eqs S10–S14). (PDF)

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT We thank Dr. Harald Kelm and Christiane Müller (University of Kaiserslautern) for access to NMR and the Deutsche Forschungsgemeinschaft (DFG) for grant KE 1478/7 1 to S.K.



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REFERENCES (1) Shinoda, K.; Nomura, T. J. Phys. Chem. 1980, 84, 365–369. (2) Shi, Z.; Chen, J.; Yin, X. J. Air Waste Manage. 2013, 63, 694–701. (3) Sehgal, P.; Mogensen, J. E.; Otzen, D. E. BBA-Biomembranes 2005, 1716, 59–68. (4) Oliver, R. C.; Lipfert, J.; Fox, D. A.; Lo, R. H.; Kim, J. J.; Doniach, S.; Columbus, L. Langmuir 2014, 30, 13353–13361. (5) Peyre, V. Curr. Opin. Colloid. In. 2009, 14, 305–314. (6) Powell, R. J.; Swinton, F. L. J. Chem. Thermodyn. 1970, 2, 87–93. (7) Andrews, A.; Morcom, K.; Duncan, W.; Swinton, F.; Pollock, J. J. Chem. Thermodyn. 1970, 2, 95–103. (8) Mukerjee, P.; Yang, A. Y. S. J. Phys. Chem. 1976, 80, 1388–1390. (9) Peyre, V.; Patil, S.; Durand, G.; Pucci, B. Langmuir 2007, 23, 11465–11474. (10) Nordstierna, L.; Furo, I.; Stilbs, P. J. Am. Chem. Soc. 2006, 128, 6704–6712. (11) Amato, M. E.; Caponetti, E.; Martino, D. C.; Pedone, L. J. Phys. Chem. B 2003, 107, 10048– 10056. (12) Kadi, M.; Hansson, P.; Almgren, M.; Furó, I. Langmuir 2002, 18, 9243–9249. (13) Funasaki, N.; Hada, S. J. Phys. Chem. 1980, 84, 736–744. (14) Asakawa, T.; Miyagishi, S.; Nishida, M. Langmuir 1987, 3, 821–827. (15) Dong, S.; Xu, G.; Hoffmann, H. J. Phys. Chem. B 2008, 112, 9371–9378. (16) Nakano, T. Y.; Sugihara, G.; Nakashima, T.; Yu, S. C. Langmuir 2002, 18, 8777–8785. (17) Barthelemy, P.; Tomao, V.; Selb, J.; Chaudier, Y.; Pucci, B. Langmuir 2002, 18, 2557–2563. (18) Aratono, M.; Ikeguchi, M.; Takiue, T.; Ikeda, N.; Motomura, K. J. Colloid Interf. Sci. 1995, 174, 156–161. (19) Carlfors, J.; Stilbs, P. J. Phys. Chem. 1984, 88, 4410–4414. (20) Kadi, M.; Hansson, P.; Almgren, M.; Bergström, M.; Garamus, V. M. Langmuir 2004, 20, 3933– 3939. (21) Paula, S.; Sus, W.; Tuchtenhagen, J.; Blume, A. J. Phys. Chem. 1995, 99, 11742–11751. (22) Broecker, J.; Keller, S. Langmuir 2013, 29, 8502–8510. (23) Textor, M.; Keller, S. Anal. Biochem. 2015, 485, 119–121. (24) Holland, P. M.; Rubingh, D. N. J. Phys. Chem. 1983, 87, 1984–1990. (25) Frotscher, E.; Danielczak, B.; Vargas, C.; Meister, A.; Durand, G.; Keller, S. Angew. Chem. Int. Edit. 2015, 54, 5069–5073. (26) Keller, S.; Vargas, C.; Zhao, H.; Piszczek, G.; Brautigam, C. A.; Schuck, P. Anal. Chem. 2012, 84, 5066–5073. (27) Kemmer, G.; Keller, S. Nat. Protoc. 2010, 5, 267–281. (28) Du, C.; Cai, D.; Qin, M.; Zheng, P.; Hao, Z.; Yin, T.; Zhao, J.; Shen, W. J. Phys. Chem. B 2014, 118, 1168–1179. 10 ACS Paragon Plus Environment

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(29) Prasad, M.; Moulik, S. P.; MacDonald, A.; Palepu, R. J. Phys. Chem. B 2004, 108, 355–362. (30) Prasad, M.; Moulik, S. P.; Palepu, R. J. Colloid Interf. Sci. 2005, 284, 658–666. (31) Ray, G. B.; Chakraborty, I.; Ghosh, S.; Moulik, S. P.; Palepu, R. Langmuir 2005, 21, 10958– 10967. (32) Lange, H.; Beck, K. H. Kolloid Z. Z. Polym. 1973, 251, 424–431. (33) Clint, J. H. J. Chem. Soc. Faraday T. 1 1975, 71, 1327. (34) Kamrath, R. F.; Franses, E. I. Ind. Eng. Chem. Fund. 1983, 22, 230–239. (35) Gokcen, N. A. J. Phase Equilib. 1996, 17, 50–51. (36) Motomura, K.; Yamanaka, M.; Aratono, M. Colloid Polym. Sci. 1984, 262, 948–955. (37) Funasaki, N.; Hada, S. J. Phys. Chem. 1979, 83, 2471–2475. (38) Breyton, C.; Gabel, F.; Abla, M.; Pierre, Y.; Lebaupain, F.; Durand, G.; Popot, J. L.; Ebel, C.; Pucci, B. Biophys. J. 2009, 97, 1077–1086. (39) Kumar, D.; Rub, M. A. J. Phys. Org. Chem. 2016, 29, 394–405. (40) Mysels, K. J.; Otter, R. J. J. Colloid Sci. 1961, 16, 462–473. (41) Jumpertz, T.; Tschapek, B.; Infed, N.; Smits, S. H.; Ernst, R.; Schmitt, L. Anal. Biochem. 2011, 408, 64–70. (42) Bergström, M.; Jonsson, P.; Persson, M.; Eriksson, J. C. Langmuir 2003, 19, 10719–10725.



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FIGURE CAPTIONS Figure 1. ITC demicellization with binary surfactant mixtures. (a) Representative thermogram depicting differential heating power (∆p) as a function of time (t). A mixture of F6OM and DM at a total surfactant concentration of 14 mM and XF6 OM = 0.5 was titrated into water at 25°C. (b) Corresponding integrated heats (Q) against total surfactant concentration in the calorimeter cell (cS) showing experimental values (circles) and a sigmoidal fit (red line). The CMC was taken as the total surfactant concentration at the inflection point (dashed line). (c) Isotherms for F6OM/DM mixtures at different bulk mole fractions of F6OM (XF6 OM ) as indicated by the color code. (d) Isotherms for F6OM/DPC mixtures.

Figure 2. Analysis of mixed micellization. (a) Mixed CMC values (CMCmix) against bulk mole fraction of F6OM (XF6 OM ) for F6OM/DM mixtures, showing experimental values (circles) and best fits (lines) based on (i) ideal mixing, (ii) non-ideal mixing according to regular solution theory with the best-fit value of the net interaction parameter (β), and (iii) model-free cubic-spline regression with the constraint according to eq 1. (b) Same for F6OM/DPC mixtures with additional constraint-free spline ) against XF6 OM for F6OM/DM regression. (c) Mole fraction of F6OM in mixed micelles (XFmm 6 OM mixtures as derived from the different analyses summarized in panel a. (d) Same for F6OM/DPC mixtures.

Figure 3. NMR at 25°C. (a) 19F spectra focusing on the CF3 peak of F6OM in F6OM/DM mixtures at XF6 OM = 0.25 and total surfactant concentrations indicated in the legend. (b) 1H spectra focusing on the second CH2 group of DM for the same samples. (c) Chemical shift changes (∆δ) of peaks in panel a (red) and panel b (blue) plotted against reciprocal total surfactant concentration (cS–1), showing experimental data (circles), linear regressions (lines), and breakpoints separating ranges with different slopes (dashed line). (d) Same for the CF3 group of F6OM (blue) and the CH3 group of DPC (red) for F6OM/DPC mixtures at XF6 OM = 0.75.


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