Two-Step Micellization Model: The Case of Long-Chain Carboxylates

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Two-step micellization model: The case of long-chain carboxylates in water Ziga Medos, and Marija Bester-Rogac Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b01700 • Publication Date (Web): 14 Jul 2017 Downloaded from http://pubs.acs.org on July 15, 2017

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Two-step micellization model: The case of long-chain carboxylates in water Žiga Medoš Marija Bešter-Rogač*

Faculty of Chemistry and Chemical Technology, Večna pot 113, University of Ljubljana, SI1000 Ljubljana, Slovenia

*Corresponding author: Prof. Dr. Marija Bešter-Rogač Faculty of Chemistry and Chemical Technology, Večna pot 113, 1000 Ljubljana, SI Slovenia Tel: +386 1 4798 537 E-mail address: [email protected]

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ABSTRACT The micellization behaviour of the long-chain carboxylates: sodium and potassium octanoate (NaC8, KC8), sodium decanoate (NaC10), potassium decanoate (KC10), caesium decanoate (CsC10), choline decanoate (ChC10) and sodium dodecanoate (NaC12) in aqueous solutions were studied using isothermal titration calorimetry (ITC) in the temperature range between 288.15 and 328.15 K. Experimental data were analysed by help of improved model treating the micellization process as a two-step process. Furthermore, consideration of the state of the stock and titrated solutions during the experiment, allowed the elimination of all usually used empirical parameters. The proposed approach represents thus an essential improvement of the thermodynamic analysis of micellization process and turned out as (only) effective for the description of the micellization at carboxylates with moderate alkyl chain length (C8, C10). By fitting the model equation to the experimental data all thermodynamic parameters of micellization for both steps were estimated. It was found that first step is endothermic and thus solely entropy driven processes in the studied temperature range for all investigated systems. The same goes also to the second step, except for KC10, Cs10 and NaC12 where at temperatures above ~ 320 K the micellization was detected as exothermic process. The delicate balance between entropy and enthalpy results in weak temperature dependence of (negative) Gibbs free energy which turned out as the counter-ion almost independent quantity. The carboxylic groups are namely able to form H-bonds with water molecules and it is quite likely that they remain strongly hydrated even upon micellization. Thus the interactions with counter-ions are less expressed in comparison to those observed by other ionic surfactants (alkyl sulfates, cationic surfactants), where the micellization process was found to be an exothermic process even below ~300 K.

Key words: isothermal titration calorimetry; thermodynamics of micelle formation; longchain carboxylates; two-step micellization model


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INTRODUCTION Cationic surfactants, especially quaternary ammonium salts, have been widely studied, whereas less attention has been devoted to anionic surfactants,1 despite the fact that the alkyl sulfates belong to the most studied surfactants.2 However, long chain carboxylates were rarely the subject of systematic investigations, 3 even though the salts of fatty acid carboxylates were the first surface-active agents (»soaps«) made by mankind and are still widely used ingredient in commercial surfactants.4 However, the aggregation of sodium hexanoate (NaC6) and sodium octanoate (NaC8) in water was studied intensively by Persson et al. by concentration dependence of the 13C NMR chemical shifts.5 They found out, that the mean aggregation number for NaC6 is small (5 or even less) whereas for NaC8 first the formation of small aggregates (4-5 monomers) and then formation of larger ones (10-11 monomers) is reported. Recently, NaC86 and sodium decanoate (NaC10)7 were the subjects of intense molecular dynamic simulations (MD) studies, providing interesting insides into the structures of the aggregates. De Moura and Freitas6 reported that at NaC8 free monomers are not stable but tend to associate into micelles or small, short-lived clusters, which then break up or associate to form micelles. This finding is in excellent agreement with the behaviour of NaC8 determined by 13C NMR experiment.5 Long et al.7 observed that about 20 % of the surfactant methylene groups remaining in contact with water within micelle thus the surfactant tails remain significantly hydrated upon micellization. Similar was observed by Baar and co-workers8 for octyltrimethylammonium bromide (OTAB) by dielectric relaxation spectroscopy (DRS). Hence there should be no distinctive difference between anionic and cationic surfactants.

Thermodynamics of aggregation of NaC8 in water was studied by MD simulation by Bernardino and de Moura recently. 9 The well-known fact, that the hydrophobic effect has the main contribution to the micelle formation and that the overall process is largely entropydriven, was confirmed. But beside the expected favourable entropic contribution arising from the nonpolar alkyl chain they surprisingly observed also the favourable entropic contribution arising from the polar head. Even more, they concluded, that there is no stable aggregates without this contribution from the polar head to the Gibbs free energy of aggregation. The process was found as strongly endothermic, what was ascribed to the dehydration of the surfactant tail and polar head and to the electrostatic repulsion between the surfactant heads at the micellar surface. The results of these MD simulations also confirmed, that sodium 3 ACS Paragon Plus Environment

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counter-ions may partially screen the electrostatic repulsion between the negatively charged heads, but most counter-ions should remain in solution.

This conclusion was partially confirmed by our previous thermodynamic study of the micellization process of carboxylates using electric conductivity measurements applying pseudo-phase separation model and van’t Hoff enthalpy of micellization, ΔMH.3 For NaC8 it was found that the process is endothermic up to ~320 K and then it becomes exothermic. The entropy is positive in the whole investigated temperature range (278.15 K - 328.15 K), but it is not possible to split the contributions to the surfactant tail and polar head. From the estimated degree of micelle ionization (0.60  0.05) it can be concluded that upon micellization there is really a substantial part of sodium counter-ions in the solution.

Even a short comparison of anionic and cationic surfactants shows that there is an evident difference in energetics of micellization, despite the fact, that critical micelle concentrations, cmc, are mainly influenced on the length of hydrophobic tail. 3,10,11,12 In general, micellization is an endothermic process at low and exothermic at high temperatures. The temperature, at which ΔMH = 0 at cationic surfactants lies usually near the room temperature (298  5 K), but can be also influenced by counter-ion.13 Similar was found also for alkali decyl and alkali dodecyl sulfates,2 whereas at carboxylates the temperature with ΔMH = 0 is distinctly shifted towards higher values.3 However, for any reliable conclusion the direct determination of ΔMH is needed.

In present work the micellization behaviour of the long-chain carboxylates in water was investigated by isothermal titration calorimetry (ITC), as one of the most powerful techniques for thermodynamic characterization of aggregation processes. By selection of sodium octanoate (NaC8), potassium octanoate (KC8), sodium decanoate (NaC10), potassium decanoate (KC10), caesium decanoate (CsC10), choline decanoate (ChC10) and sodium dodecanoate (NaC12) as matter of research, the influence of the alkyl chain length and counter-ions on the micellization process was investigated. The experiments were carried out in the temperature range between 288.15 K and 328.15 K.


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Obtained experimental data were analysed by the improved (mass action) model, considering the micellization as a two-steps process, as proposed by De Moura and Freitas from MD simulations.6 In order to eliminate all empirical constants, used in the usually used models,14,15 the state of the solution in the syringe as well as the state of the solution in the titration cell was taken into account. By fitting of the model equation to the experimental data the corresponding standard thermodynamic parameters of micellization (for XC8 and XC10 for both steps: enthalpy, ΔM,1H, ΔM,2H; Gibbs free energy, ΔM,1G, ΔM,2G; entropy, ΔM,1S, ΔM,2S; heat capacity change, ΔM,1cp, ΔM,2cp ) were estimated and discussed in terms of the side alkyl chain length and the effect of counter-ions. In addition, ΔMcp was further correlated to the changes in solvent accessible surface upon micelle formation. Obtained results were correlated with those reported for other ionic surfactants and discussed in terms of differences in hydration of carboxylate and other head groups.

EXPERIMENTAL SECTION

Materials Commercially available reagents and solvents were used as received from Sigma Aldrich unless otherwise specified. Doubly-distilled deionized water was obtained from a Millipore Milli-Q water purification system (Millipore, USA). 1H spectra were recorded on a Bruker 500 MHz NMR spectrometer. Synthetic procedures Synthesis of alkali carboxylates Carboxylic acid was neutralized with corresponding alkali hydroxide and remaining water was removed by lyophilisation. Product was recrystallized from ethanol with addition of acetone. Recrystallization was repeated with acetone or ethyl acetate and product was dried at 120 °C. Products were characterized by IR spectroscopy, CHN elemental analysis and TGA.


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Synthesis of choline decanoate Chloroethanol was mixed with 33 % trimethylamine (TMA) solution in ethanol in autoclave in molar ratio 1:2. Mixture was stirred in an oil bath at 80 °C for 3 days. Excess TMA and solvents were removed under reduced pressure. Obtained product choline chloride (ChCl) was washed with ethanol and with diethyl ether. The adequate mixture of ChCl and decanoic acid was prepared by mass and dissolved in ethanol. Most of the required KOH for neutralization was added by mass in form of solid pallets, but the final amount was added in form of KOH solution in ethanol up to the inflexion point detected by measured potential of glass electrode. Most of the ethanol was removed by heating and solution was filtered to remove KCl then placed in a vacuum chamber at 60-70 °C with a liquid nitrogen trap for 1-2 days to remove all of the ethanol. 1H NMR (500 MHz, CDCl3) δ 4.08 (m, 2H), 3.70 (t, 2H), 3.35 (s, 9H), 2.12 (t, 2H), 1.55 (dd, J = 14.7, 7.3 Hz, 2H), 1.36 – 1.15 (m, 12H), 0.87 (t, J = 7.0 Hz, 3H).

Density measurements To enable the conversion between concentration scales, the density of some solutions were measured at pressure of 0.1 MPa and 298.15 K using a vibrating tube densimeter, Anton Paar DMA5000 with a declared reproducibility of 110-3 kgm-3. The results are given in Figure S1 and Table S1 in Supporting Information. The concentration dependence of densities in the concentration range of the concentration in the titration cell can be represented in form of polynomial  (T ) = a m2  b m  H2O (T ) , with coefficients listed in Table S2 in Supporting Information. Densities at other temperatures were estimated by help of known densities of water at investigated temperatures (Table S3 in Supporting Information) and the assumption that coefficients a and b are temperature independent.

Due to the minimal difference in densities of water and stock solutions of ChC10 and NaC12 (Table S1 in Supporting Information) here the density was taken to be approximately equal that of water in the whole concentration range of measurements.


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pH measurements Investigated long chain carboxylates are conjugate bases and therefore in aqueous solutions also carboxylic acid and hydroxide anion are presented in part. To check the extent of this process and estimate its influence on micellization, pH of solutions before and after cmc was measured at pressure of 0.1 MPa and 298.15 K using a pH-meter Iskra MA 5740 coupled by combined glass electrode (Mettler-Toledo InLab®423 Combination pH Micro Electrode). Before each experiment electrode was calibrated with phosphate (pH = 6.865) and borate (pH = 9.180) buffer solutions. Stock solution of surfactant was titrated into water to reproduce the conditions during ITC experiments. Obtained dependence of pH on concentration for all investigated systems is presented on Figure S2 in Supporting Information.

Isothermal titration calorimetry In a typical demicellization experiments, where the heat effects resulting from mixing aliquots of titrant solution injected by a motor-driven syringe with the solution (solvent) in the titration cell, were carried out by TAM 2277 calorimeter (Thermometric, Stockholm, Sweden). The titration cell was filled with one millilitre of triple-distilled water. The surfactant solution (515 times the value of cmc) was placed in a 250 µL syringe and the titration was carried out. If needed, the syringe was refilled and titration was continued do get the cover the whole range below, near and above cmc. For each system, experiments at five temperatures between 288.15 and 328.15 K were carried out. Stock solution of NaC12 formed a gel at lower temperature therefore measurement at 288.15 K was not carried out. Before each experiment, the instrument was calibrated by help of a known electric pulse. The area under the peak following each injection of the surfactant solution, obtained by integration of the raw signal (an example on Figure 1), is proportional to the heat effect expressed per mole of added surfactant per injection. By integration of all peaks the experimental heat of dilution, ΔH, as a function of surfactant concentration (enthalpograms) were obtained (Figures 2 and 3, S3 in Supporting Information). From known starting mass of the water in cell, concentration and density of stock solution in the syringe, the concentration after each addition was calculated first in mole of surfactant per


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kg of solution (applied in thermodynamic analysis) and then converted to molar concentration (used in diagrams) by help of known concentration dependence of density.

20 0 -20 -40

q/W

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-60 -80

-100 -120 0

10

20

30

40

50

60

70

80

90

100

110

t/h

Figure 1. Raw signal with subtracted baseline from TAM calorimeter for KC10 at 288.15 K.

Thermodynamics of micellization

Micellization is a well-known and often investigated process, where monomers form spherical structures due to polar duality of molecules or ions which form monomers. In fact, micellization should be regarded as a multi-step process or stepwise association with a series of equilibra with aggregation number starting from 2 to infinity16 and each with its own thermodynamic parameters. But first, most of formations are unfavourable and therefore irrelevant for thermodynamic studies and second, defining thermodynamic parameters for every aggregation number is highly impractical due to requirement of too many parameters at fitting the experimental data. Process of micellization is therefore often simplistically represented as equilibria between monomers and micelles with an average aggregation number. Usually, this way of modelling the micellization is good enough to calculate the thermodynamic parameters which fit well the experimental data if large aggregates at relatively low cmc are formed.


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However, when micellization is less favourable and occurs at higher concentrations forming primarily or partly aggregates with less than 20 monomers the one-step equilibrium model fails to fit data well over a wide temperature range and at higher concentrations. This observation can be ascribed to the fact, that aggregation number is dependent on concentration and temperature. This dependence could be taken into account by empirical relations but then the question arose, whether the Gibbs-Helmholtz equation is still valid. Except for micellization of NaC12, one-step model did not fit ITC experimental data well for any system investigated in this work. Therefore we developed a two-step micellization model, where no additional empirical constants are needed because the composition of titrated solution of surfactant is taken into account. The proposed micellization model can be represented with the equilibria, as shown in Scheme 1. However, it should be noted that the proposed two states cannot be considered as strict separated processes, but there is no strong border between them. Therefore we do not propose the existence of two well defined aggregation numbers but the dependence of the actual aggregation number with temperature and total surfactant concentration is taken into account, which will be discussed in detail later.

K M,2 / K M,1

K M,1

Scheme 1. The presentation of the two-step micellization process applied in the model.

Two-step micellization model for anionic surfactant can be represented with two equilibra

 n1C+ + n1 A-

 n2C+ + n2 A-

KM,1

KM,2

C n1 An1 (1- )n1 -

(1)

C n2 An2 (1- ) n2 -

(2)

where C+ are free cations or counter-ions, A– free anions or monomers of surfactant; Cβn1An1(1-β)n1– stands for smaller and Cβn2An2(1-β)n2– for larger micelles. It turned out tha the 9 ACS Paragon Plus Environment

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values of the degree of counter-ion binding, β, does not have a big impact on the calculated curve, therefore it is taken to be the same in both steps, while aggregation numbers, n1 and n2, are different. From standard Gibbs free energies for each step, ΔM,1G and ΔM,2G,

Δ M,1G θ = -

RT RT ln K M,1; Δ M,2G θ = ln K M,2 n1 n2

(3)

by using corresponding equilibrium constants, KM,1 and KM,2, K M,1 =

xM,1  n1

n1 A

xC x

; K M,2 =

xM,2

(4)

 n2

xC xAn2

and applying the approximation of the activities being equal to molar fraction of species the amounts of free counter-ions, nC, free monomers, nA, smaller micelles, nM,1 and larger micelles nM,2 can be calculated having the information on concentration and density of solution, total mass and molar masses of solvent and surfactant (see Supporting Information, p. S2). From known amounts of species in added titrant and cell before and after its addition theoretical enthalpy change can be calculated as follows. The enthalpy of solution can be written in two ways: a) by help of the enthalpies of ions

H = nsol H sol + nC H C + nA H A + nM,1 H M,1 + nM,2 H M,2

(5)

or b) with the enthalpies of ion pairs

H = nsol H sol + nS H S + nM,1 H CM,1 + nM,2 H CM,2

(6)

where indexes “sol”, “S” and “CM” represents solvent, free surfactant and micelles counterion pairs, respectively. For ion pairs the simplified Guggenheim approximation was applied to calculate standard enthalpies by θ

H S = H S + 2 RT 2 BS' bS

(7)


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' H CM,1 = H CM,1 + 1+ (1-  )n1  RT 2 BCM,1 bCM,1 θ

(8)

' H CM,2 = H CM,2 + 1+ (1-  )n2  RT 2 BCM,2 bCM,2 θ

(9)

where BS', BCM,1', and BCM,2' are the temperature dependent temperature derivates of Guggenheim’s coefficients BS, BCM,1, and BCM,2.17 Coefficients for micelle counter-ion interactions were taken to be the same for both steps. By introducing standard enthalpies of micellization, Δ M,1H and Δ M,2H,

Δ M,1H θ =

θ 1 θ H CM,1 - H S n1

(10)

Δ M,2 H θ =

θ 1 θ H CM,2 - H S n2

(11)

and combination of eqs 6-9, the enthalpy of solution can be written as θ

H = nsol H sol + nS H S + n1nM,1Δ M,1H θ + n2 nM,2 Δ M,2 H θ  2RT 2 BS' bS  ' ' RT 2 1+ (1-  )n1  BCM,1 bCM,1 + 1+ (1-  )n2  BCM,2 bCM,2 

(12)

which applies to any experimental method. By ITC experiment the measured heat changes ΔH =

q nCA,stock

=

H - H 0 - H stock nCA,stock

(13)

are the result of three contributions divided by total surfactant amount added, nCA,stock: enthalpy of stock solution, Hstock, and enthalpies of solution in cell before, H0, and after addition, H. By defining the change in amount of micelles, ΔnM,1/Δn and ΔnM,2/Δn,

ΔnM,1 Δn ΔnM,2 Δn

= n1

= n2

nM,1 - nM,1,0 - nM,1,stock

(14)

nCA,stock nM,2 - nM,2,0 - nM,2,stock

(15)

nCA,stock

and combining eqs 12 and 13, the final form of model equation is given as 11 ACS Paragon Plus Environment

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2 2  nS2 nS,0 nS,stock ΔH = Δ M,1 H + Δ M,2 H  2B  m Δn Δn nCA,stock  sol msol,0 msol,stock  n2 n2  n2 RT 2 ' BCM,1 1+ (1-  )n1   M,1 - M,1,0 - M,1,stock  + nCA,stock  msol msol,0 msol,stock  2 2 2  nM,2  nM,2,0 nM,2,stock RT 2 ' BCM,2 1+ (1 ) n   2  m nCA,stock  sol msol,0 msol,stock 

ΔnM,1

θ

ΔnM,2

θ

RT 2

' S

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   

(16)

The enthalpy change in eq 16 is depended on amounts of micelles and free surfactant before and after addition of stock solution, amounts in stock solution itself and mass of solvent in all three. A detailed derivation is given in Supporting Information, p. S3. The value of cmc for each of investigated system at given temperature was estimated numerically from the inflection point of the line representing the dependence of ΔnM,2/Δn on concentration. Despite all adjustable parameters having a thermodynamic meaning the two-step micellization model (at given temperature) has a significant number of parameters which results in strong correlations among some of them. However, a global fitting of the model equation to the corresponding experimental curves at all the examined temperatures by introducing their temperature dependence (see Supporting Information, p. S4) reduces their correlations significantly. Nevertheless, some parameters (n1, n2, β, ΔM,1G, ΔM,2G, BS'', BCM'') tend to have grater error than others because they are determined by the shape of the enthalpograms (derivatives) and not by absolute values of H.

RESULTS AND DISCUSSION The dependence of experimental heat of dilution, ΔH, on surfactant concentration (enthalpogram) for titration of KC10 in water in the investigated temperature range is shown in Figure 2. Similar enthalpy patterns were also obtained for other investigated systems at the same temperatures (Figure S3 in the Supporting Information). The comparison of enthalpograms at 298.15 K for all investigated surfactants is presented in Figure 3.


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5

H/kJmol

-1

0 T/K 288.15 298.15 308.15 318.15 328.15 1-step 2-step

-5

-10

-15 0.00

0.05

0.10 0.15 -1 c/molL

0.20

0.25

Figure 2. Temperature dependent enthalpograms for potassium decanoate, KC10, in water: , 288.15 K; , 298.15 K; , 308.15 K; , 318.15 K; , 328.15 K. Blue thin lines represent the fits of one-step model and red thick lines the fits of two-step model according to eq 16.

4

b)

2

2

0

0 -2

-1

-2

H/kJmol

-1

a) 4

H/kJmol

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298.15 K NaC8 NaC10 NaC12

-4 -6

-6

-8

-8

-10

-10

-12 0.0

0.1

0.2

0.3 0.4 -1 c/molL

0.5

0.6

0.7

298.15 K NaC10 KC10 CsC10 ChC10

-4

-12 0.00

0.05

0.10 0.15 -1 c/molL

0.20

0.25

Figure 3. The enthalpograms for a) sodium carboxylates, NaCX and b) decanoates, XC10, at 298.15 K. Solid lines represent the fits of two-step model according to eq 16.

From Figures 3 and S3 in Supporting Information is evident, that in some cases (NaC8, NaC10 and CsC10 at lower temperatures) an unusual peak near the inflection point can be observed, indicating probably the “competition” of another unknown and unexpected processes. Similar behavior has been observed recently by intense study of the thermodynamics of complexation between poly(diallyldimethylammonium chloride) and poly(sodium acrylate) by ITC, where the polyelectrolyte complex formation and coacervation 13 ACS Paragon Plus Environment

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turned out as sequential processes.18 It was assumed, that the coacervation is kinetically activated and starts only after the formation of the polyelectrolyte complex. The thermodynamic parameters for both processes were obtained from the adjustment of the experimental ITC curves with the model, which considers the total enthalpy change during titration as a sum of two separated contributions. In our work, the unusual peaks could be ascribed to some possible processes: more complex mechanisms of aggregation, interactions between cations (Na+, Cs+) and water molecules or additional changes due to formation of carboxylic acid in the system. From Figure S2 in Supporting Information it is evident namely, that pH values increase significantly at roughly the same concentrations (near cmc) and after that they do not change significantly. However, according to measured pH values, the amount of carboxylic acid, present in the solution, should never exceed 0.1 % for NaC8, NaC10 and CsC10. Therefore, by an assumption that these effects are negligible at other experimental points, the experimental points forming the peaks were not included in the fitting procedures. All mentioned possible processes should namely have different optimal Gibbs free energy making even a two-step model inadequate to reproduce experimental data. In addition, pKa values of approximately 4.8 for most short-chain carboxylic acids reported by Kanicky and Shah19 indicate that beyond 4 C atoms in the alkyl chain the effect of intramolecular interactions (i.e. the electronic effects on the carboxylic acid moiety by the rest of the molecule) are practically negligible. With increase in chain length of the molecule of long-chain fatty acids pKa values rise significantly and can be as high as about 8.8 for 16 C atoms in the chain.20 However, it was found that the values of pKa increase significantly already in micelle solutions of carboxylic acids starting with chain length of 8 C atoms.19 It was proposed that at micelle formation the fatty acid molecules get closer together and thus the proximity of other carboxyl groups serves to stabilize the acid proton, making it more difficult to remove it by the free hydroxide ions in the bulk solution. This statement supports well our results, presented on Figure S2 in Supporting Information: significant increase in pH at about cmc can be thus explained that here bigger fraction of protonated carboxylate group is present in the micelles than in form of free monomers of surfactant. Oppositely to octanoates and decanoates, it turned out that the micellization process of NaC12 can be well represented by an assumption of only one-step process in the model. Therefore


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here some of the equations in the fitting procedure are simplified but the principles remain the same. All results obtained by the fitting procedure are listed in Tables S4 and S5 in Supporting Information, where also comparison with some already reported data are made. Figure 4 presents the thermodynamic parameters of micellization for investigated systems in water at 298.15 K of both steps (ΔM,1H, ΔM,2H, ΔM,1G, ΔM,2G, TΔM,1S, TΔM,2S) for all investigated systems except for NaC12, where only one-step micellization process was assumed and thus only one set of thermodynamic data is shown in Figure 4 and Table S4 in Supporting Information. From Figure 4 and Table S4 in Supporting Information it is evident, that at 298.15 K the micellization process is endothermic (for both steps) accompanying with an increase in entropy resulting thus in the negative value of Gibbs free energy. ΔM,1H and ΔM,2H are decreasing with the temperature (Table S4 in Supporting Information) but the process become exothermic only at KC10, CsC10 and NaC12 at temperatures above ~320 K. Obtained thermodynamic data differ significantly from previous reported values, obtained by help of pseudo-phase separation model and van’t Hoff method for the enthalpy of micellization, despite the fact, that cmc values, determined in this work are in good agreement with reported ones, obtained from conductivity measurements3 (Table S4, Supporting Information). Even more, there is also a reasonable agreement between Δ MG as obtained from phase separation model ( ΔMGθ  (2   )RT ln xcmc ) in our previous work3 and values of ΔM,1G and ΔM,2G estimated here for both steps (Table S4 in Supporting Information).


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NaC12 ChC10



M,1G



M,2G

CsC10 KC10 NaC10

M,1H



M,2H



TM,1S



TM,2S



KC8 NaC8 -30

-20

-10

0 10 -1 kJmol

20

30

40

50

Figure 4. Thermodynamic parameters of micellization for investigated systems in water at 298.15 K: standard enthalpy, ΔM,1H, ΔM,2H, Gibbs free energy, ΔM,1G, ΔM,2G, and entropy contributions, TΔM,1S, TΔM,2S, for micellization for investigated systems in water as obtained by the fitting procedure with two-step model (except for NaC12, where one-step model was applied). Subscripts 1 and 2 refer to first and second step of the process, according to eqs 1 and 2.

Otherwise, the non-agreement between the van’t Hoff and calorimetric ΔMH is a long known issue but not well explained in the literature.21,22 However, in our previous work on micellization of alkyltrimethylammonium chlorides in aqueous solution a reasonable agreement between van’t Hoff and calorimetric ΔMH was found,11,12 so the reason for the here observed discrepancy cannot be ascribed to the experimental uncertainty. Thus, the difference between the van’t Hoff and calorimetric Δ MH here seems to be quite surprising. But one have to be aware, that van’t Hoff Δ MH is derived by help of GibbsHelmholtz relation over the temperature derivative of cmc =f (T), where usually this function is obtained by fitting the experimental data by a polynomial. In general, temperature 16 ACS Paragon Plus Environment

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dependence of cmc should be U-shaped, reaching a minimum near temperature where also ΔMH = 0. This temperature here is shifted distinctly toward higher values, the minima are less expressed, thus the polynomial representing cmc =f (T) and consequently all values obtained from their derivative are less reliable. Similar, but less expressed behaviour was observed also at decyltrimethylammonium chloride in our previous work.12

In addition, there is an immense difference between here estimated and reported values of the degree of counter-ion binding,  ,. This parameter seems to be quite model and method dependent. Values of  from the two-step micellizaton model for all studied systems except CsC10 ( = 0.47) are above 0.6 and appear to be almost independent of alkyl chain length and counter-ion. Caesium ion in water solution strongly binds water which agrees with our finding of lower counter-ion binding to micelles. Surprisingly,  values for NaC10, obtained from completely independent conductivity experiment, are in excellent agreement (0.45 3, 0.4423), however in the present work from the applied two-step model distinctly bigger value of  = 0.72 was estimated as for all other studied systems (Table S5 in Supporting Information). On the other hand, model value suits perfectly to  = 0.73, determined by Caponetti et al. from small-angle neutron scattering (SANS) experiment.24 It seems that the degree of counter-ion binding estimated from conductivity measurements is too low for all investigated systems. According to Danov and co-workers,25 the interpretation of the degree of binding of counterions to the micelle from the ratio of slopes above and below cmc in the conductivity vs. concentration plot is uncertain and was critically reconsidered in their recent work. As mentioned already before, there is no sharp border between the two equilibria (Scheme 1), therefore we can calculate fraction of surfactant in micelle form, α, and the actual average aggregation number, navg, which are both dependent on temperature and total surfactant concentration, as it is presented on Figure 5 for KC10 and S4 in Supporting Information for all investigated systems. Thus, the aggregation numbers n1 and n2, given in Figure 6 a) and Table S5 in Supporting Information, should in general be considered as the values of two limits. Each step has its own Gibbs free energy and after fitting procedure is finished eq 4 can be used to calculate amounts of micelles, nM,1 and nM,2, with size n1 and n2 at any temperature and total surfactant concentration which is used further to estimate navg, according to relation

navg 

n1nM,1 + n2 nM,2

(17)

nM,1 + nM,2 17 ACS Paragon Plus Environment

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as well as α = 1 – cA/c. At concentrations bellow cmc, the concentration of micelles is negligible therefore the accuracy of calculated average (eq 17) does not matter but as we approach cmc it is evident, that there are already smaller aggregates present in the solution which gradually increase in size with concentration. With increasing temperature fraction of micelles increases while their average size decreases.

a)

1.0 0.8



0.6

T/K 288.15 298.15 308.15 318.15 328.15

0.4 0.2 0.0

b)

15 14

navg

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13 12 11 10 9 0.00

0.05

0.10

0.15

0.20

0.25

-1

c/molL

Figure 5. Concentration dependence of a) molar fraction of surfactant in micelle form and b) average aggregation number for KC10 at investigated temperatures as estimated from eqs 4 and 17.

In case of octanoates the results of fitting the two-step micellization model in the first step indicates formation of smaller aggregates (n1 = 3  1) which is in agreement with results from 13

C NMR experiment5 and MD simulations 6 for NaC8. The estimated aggregation number of

NaC8 for the second step (n2 = 11  3) is in excellent agreement with reported 10-11 monomers in the aggregates, as obtained by 13C NMR experiment,5 as well as with 13  1, estimated by SANS experiment using roughened two-shell model.26 Caponetti et al.24 examined the concentration dependence of aggregation numbers for NaC12 by SANS experiment. Their value of n = 22  2, as extrapolated to the cmc, agrees well with our n = 21 18 ACS Paragon Plus Environment

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 5 obtained from one-step model. Unfortunately, due to the lack of data in the literature no further comparisons are possible. a)

40

n1

35

n2

30

n

25 20 15 10 5

b)

0

-1

-100 -200



-1

Mcp /Jmol K

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-300 -400 -500

first step second step

-600

NaC8

KC8 NaC10 KC10 CsC10 ChC10 NaC12

Figure 6. a) The aggregation numbers n1 and n2 and b) heat capacities of micellization for both steps for investigated octanoates and decanoates and for one-step model for NaC12.

Thus, the applied two-step model turned out to be very useful at the description of micellization process. First, the model curves fit well the experimental ITC data and second, the estimated parameters are – where applicable – in excellent agreement with the data obtained by SANS or/and MD simulations and 13C NMR experiment. Having a look on Table S4 in Supporting Information, the first step of micellization process is endothermic in the whole investigated temperature range for all octanoates and decanoates – thus the formation of smaller micelles is solely entropy driven process in all cases. The process in the second step is endothermic in the whole investigated temperature range for NaC8, KC8, NaC10 and ChC10, whereas at KC10, CsC10 and NaC12 it becomes exothermic above ~ 320 K. Thus, for all investigated systems the micellization process can be regarded as mainly entropy driven process, as for NaC8 it has been confirmed also by MD simulations.6,9 An inspection of data in Table S4 in the Supporting Information reveals the delicate balance between the 19 ACS Paragon Plus Environment

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enthalpy and entropy in the micellization process, resulting in moderate decrease in the Gibbs free energy. In part, this enthalpy/entropy compensation can be explained in terms of classical interpretation of the hydrophobic effect.27 The non-polar alkyl chains of the surfactant monomers are surrounded by ordered clathrate-like water structures (“hydrophobic hydration”). Upon micelle formation the alkyl chains are removed from the contact with water, these structures are destroyed and the structured hydration water is released into the bulk. This process is endothermic accompanied with positive entropy change. Additionally, it is assumed that the hydration water of the head groups upon incorporation in the micelles is also rearranged according to the surface charge density as a consequence of monomer association and counter-ions condensation. This process can be regarded as endothermic too,28 whereas the transfer of the hydrocarbon chains into the micelles and restoring the hydrogen bonding structure of the water around the micelles are assumed to be exothermic.29 There are also contributions for the partially dehydration (endothermic) of counter-ions at approaching and binding (exothermic) to the micelles surface.30 With increasing temperature, the structure of hydration water is less expressed and, consequently, the role of hydrophobic and other dehydration becomes weaker because less energy is required to break up the three-dimension water structure. Thus the process becomes more exothermic,31 and at a certain (usually approximately room temperature) the contribution of the ΔMH to the Gibbs free energy is neglected (ΔMH = 0) compared to the entropy term. As already mentioned, for studied carboxylates the micellization process is entropy driven practically in the whole investigated temperature range for both steps and only for some systems (KC10, CsC10, NaC12) ΔMH becomes negative at higher temperature (~ 320 K) as it is usual for ionic surfactants. The reason for this behaviour can be found probably in the interactions between studied carboxylates and water molecules which somehow should be different as at alkyl sulfates or cationic surfactants. Recently, the difference in the preferential binding of choline and sodium ions to carboxylate or sulfate headgroups was investigated by dielectric relaxation spectroscopy (DRS).32 It revealed that choline ions – condensed at the surface of carboxylate micelles – do not penetrate into the micellar core but remain separated from the carboxylate groups by a water layer. Furthermore, small size of sodium compared to choline also increases the possibility of water penetration into NaC12 micelle, whereas the surface of micelle is only partly covered 20 ACS Paragon Plus Environment

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by the hydration water. Similarly, more extensive hydration of NaC12 compared to sodium dodecylsulfate (SDS) micelles33 could be explained on the basis of relative sizes of carboxylate and sulfate headgroups as already revealed by the NMR studies on sodium dodecylsulfate and sodium dodecanoate where it was observed that compared to sulfates there is more space available for water molecules to penetrate between the headgroups of carboxylate micelles.34 Strange interactions between carboxylate group and sodium ion was observed also by DRS and supported by structural results from 1D-RISM and 3D-RISM calculations at ectoine recently.35 It was found namely, that Na+ and the carboxylate moiety of ectoine form waterseparated Na+ /ectoine aggregates. Nevertheless, the main driving force for the formation of micelles is still the apparent disaffinity of water and the nonpolar (interacting) surfaces known as hydrophobic effect. The parameter that illustrates this effect is the heat capacity of micellization, ΔMcp, which is highly negative for both steps (Figure 6 b), Table S4 in Supporting Information), what can be ascribed to the removal of water molecules from contact with nonpolar surface area upon micelle formation.36,37 Evidently for octanoates and decanoates, where the two-step model was applied, the values of heat capacity of micellization for the first step, ΔM,1cp, are less negative from that for the second step, ΔM,2cp. By modelling the micellization processes as a transfer of surfactant molecules into the micellar phase, the “theoretical” heat capacity, ΔMcp(th), can be expressed in terms of the change of water accessible nonpolar and polar surface areas, derived by Spolar et al.38 from protein folding

M cpθ (th)/J  K-1  mol-1  1.34(0.33)  ΔAnp /Å2  0.59(0.17)  ΔAp /Å2 







where Ap stands for the loss of water accessible polar and Ap for nonpolar surface area upon protein folding. Because the hydrophilic head groups of surfactants remain still hydrated upon micelle formation, the “theoretical” contribution of water accessible nonpolar surface area change to the heat capacity change upon micelle formation, ΔMcp(thnp), can be assumed to reflect only the change in exposure of the hydrophobic tails to water, by reducing eq 18 to


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M cpθ (th np )/J  K -1  mol-1  1.34(0.33)  ΔAnp /Å2  

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









This approach turned out as useful for a series of non-ionic surfactants.39,40  According to Richards,41,42,43 values of 30 Å2 and 88 Å2 as water accessible surface area for methylene and methyl group, respectively, can be taken into account. Thus the values of Anp for the hydrophobic tails of the surfactants investigated in this study can be assessed to 298, 358 and 418 Å2 for the C8, C10 and C12 alkyl chain, respectively. By using eq 19 then the values of ΔMcp(thnp) = -39998, -479118 and -560138 J K-1mol-1 for the C8, C10 and C12 alkyl chain, respectively, are obtained. Comparison of ΔMcp(thnp) with ΔM,1cp and ΔM,2cp (Figure 6 b), Table S5 Supporting Information) may lead to an assumption that in the smaller aggregates, formed in first step, the nonpolar alkyl chains in the micelle core are in stronger contact with water than those in larger micelles from the second step.   Interestingly, ΔMcp(thnp) and ΔM,2cp for KC10, CsC10 and ChC10 are in reasonable agreement leading to the conclusion that here the alkyl chains are completely removed from the contact with water, what obviously is not true for NaC10 and NaC12. This finding confirms also the observed difference results from DRS for ChC12 and NaC12, mentioned above.32 Choline ions are condensed at the surface of carboxylate micelles and do not penetrate into the micellar core. They were assumed to remain separated from the carboxylate groups by a water layer which obviously also prevent water molecules to penetrate deeper in the micelle. On the contrary, due to the small size of Na+ compared to choline cation, the water molecules are more likely to penetrate into NaC12 micelle, resulting here in less negative value of ΔMcp in comparison with ΔMcp(thnp). The same behaviour as for choline cations can be ascribed thus also to K+ and Cs+ because they are distinctly bigger than Na + (although weakly hydrated).

Finally, recent results on the hydration structure around the carboxyl group in the acetate aqueous solutions44 clearly indicate, that water molecules within the first hydration shell of the carboxyl group form hydrogen bonds with a geometry where one of the hydrogen atoms within a water molecule faces toward the carboxyl-oxygen atom of the acetate ion. This finding is in agreement with the results from DRS on decanoates leading to the assumption that the strong hydration of carboxylate group could be the main reason for the observed 22 ACS Paragon Plus Environment

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discrepancies in the micellization behaviour of studied carboxylates and other ionic surfactants. CONCLUSIONS The influence of alkyl chain length on the thermodynamics of micelization at long-chain carboxylates was investigated on sodium octanoate (NaC8), decanoate (NaC10) and dodecanoate (NaC12), whereas the counter-ion effect was studied on potassium octanoate (KC8) and decanoate (KC10) together with caesium (Cs10) and choline decanoates (ChC10). The process was followed by isothermal titration calorimetry (ITC) as well established method for this purpose. Experimental data were analysed by an improved model, describing the micellization process as a two-step process, as suggested by 13C NMR experiment5 and MD simluations.6 This approach turned out as only effective for the description of the micellization at carboxylates with moderate alkyl chain length (C8, C10), whereas micellization of NaC12 was successfully represented by one-step process. It was found that in the first step small aggregates (aggregation numbers from ~3 to ~10) are formed and the process turned out as endothermic for all investigated systems in the whole temperature range (288.15 K to 328.15 K). The second step of micellization process is endothermic in the whole temperature range for NaC8, KC8, NaC10 and ChC10, while at KC10, CsC10 and NaC12 it converted to the exothermic at ~320 K. Here, micelles are bigger with aggregation numbers from ~11 to ~30, what is in good agreement with available literature data obtained from SANS experiment (NaC8,26 NaC1224) and concentration dependence of the 13C NMR chemical shifts.5 On the whole, the micellization process is entropy driven because the favourable enthalpic contribution in the investigated temperature range is obviously extremely small. The reason for this behaviour must be in peculiar interactions between monomers, counterions and water, which obviously at carboxylates are different as at other ionic surfactants. It could be ascribed to the ability of carboxylic group to form H-bond with water molecules leading to the assumption that they remain strongly hydrated even upon micellization, as it has been already confirmed by DRS experiment recently.32 Consequently, the counter-ion binding plays less important role at micelle formation. This conclusion is well confirmed by cmc values which turned out as almost independent on counter-ions at the same chain length.


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ASSOCIATED CONTENT Notes: The authors declare no competing financial interests SUPPORTING INFORMATION Thermodynamics of micellization Densities of investigated systems at 298.15 K Figure S1. Densities of investigated systems at 298.15 K. Lines represent fits according to eq xxxiii using the corresponding coefficients from Table S2. Table S1. Molar masses, M, of investigated systems, concentrations, m, and densities, ρ, of stock solutions. Table S2. Coefficients a and b in eq xxxiii of NaC8, KC8, NaC10, KC10, CsC10 used to convert concentration scale. Table S3. Densities of water at different temperatures pH of investigated systems at 298.15 K Figure S2. pH of investigated systems at 298.15 K. Enthalpograms and results of thermodynamic analysis Figure S3. Enthalpograms of investigated long-chain carboxylates in water. Solid lines represent the fit according to the two-step micellization model (eq xxiii) for NaC8, KC8, NaC10, KC10, CsC10, ChC10 and simplified one-step micellization model for NaC12. Figure S4. Concentration dependence of a) molar fraction of surfactant in micelle form and b) average aggregation number for all systems at investigated temperatures as estimated from eqs viii and ix. Table S4: Thermodynamic parameters of micellization for investigated long-chain carboxylates in water at all the investigated temperatures for both steps: Gibbs free energies, ΔM,1G and ΔM,2G, enthalpies, ΔM,1H and ΔM,2H, entropies, ΔM,1S and ΔM,2S, of micellization, coefficients BS' and BCM' (eqs xii-xiv) and critical micelle concentration, cmc, in water as obtained for the second step by the fitting procedure. Values of cmc and Δ MG from the literature are given for comparisons. Table S5. Degree of counter-ion binding, , aggregation numbers, n1 and n2, heat capacities of micellization, ΔM,1cp and ΔM,2cp, for both steps and second temperature derivatives, BS'' and BCM'', (eqs xxviii and xxix) for investigated systems in water as obtained by the fitting procedure. The comparison with reported values  and ΔMcp (298.15 K) is presented also. The Supporting Information is available free of charge at http://pubs.acs.org.


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ACKNOWLEDGEMENTS The financial support by the Slovenian Research Agency through Grant No. P1-0201 is gratefully acknowledged. Ž.M. is grateful to Slovenian Research Agency for the position of young researcher enabling him the doctoral study.

REFERENCES

(1) Kroflič,A.; Šarac, B.; Bešter-Rogač, M. Thermodynamics and Specific Ion Effects in Connection with Micellization of Ionic Surfactants. In Colloid and Interface Chemistry for Nanotechnology; Kralchevsky, P.; Miller., R; Ravery, F., Eds.; CRC Press Taylor&Francis Group, Boca Raton, London, 2014; pp 475–502. (2) Ropers, M. H.; Czichocki, G.; Brezesinski, G. Counterion Effect on the Thermodynamics of Micellization of Alkyl Sulfates. J. Phys. Chem. B 2003, 107, 5281–5288. (3) Medoš, Ž; Bešter-Rogač, M. Thermodynamics of the micellization process of carboxylates: A conductivity study. J. Chem. Thermodynamics 2015, 83, 117–122. (4) Wolfrum, S.; Marcus, J.; Touraud, D.; Kunz, W. A renaissance of soaps? – How to make clear and stable solutions at neutral pH and room temperature. Adv. Colloid Interface Sci. 2016, 236, 28–42. (5) Persson, B.-O.; Drakenberg, T.; Lindman, B. Carbon-13 NMR of Micellar Solutions. Micellar Aggregation Number from the Concentration Dependence of the Carbon-13 Chemical Shifts. J. Phys. Chem. 1979, 83, 3011–3015. (6) De Moura, A. F.; Freitas, L. C. G. Molecular dynamics simulation of the sodium octanoate micelle in aqueous solution. Chem. Phys. Lett. 2005, 411, 464-478. (7) Long, J. A.; Rankin, B. M.; Ben-Amotz, D. Micelle Structure and Hydrophobic Hydration. J. Am. Chem. Soc. 2015, 137, 10809–10815. (8) Baar, C.; Buchner, R.; Kunz, W. Dielectric Relaxation of Cationic Surfactants in Aqueous Solution. 1. Solvent Relaxation. J. Phys. Chem. B 2001, 105, 2906–2913. 25 ACS Paragon Plus Environment

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(9) Bernardino, K.; Andr F.; de Moura, A. F. Aggregation Thermodynamics of Sodium Octanoate Micelles Studied by Means of Molecular Dynamics Simulations. J. Phys. Chem. B 2013, 117, 7324−7334. (10) Milioto, S.; Causi, S.; Crisantino, R.; De Lisi, R. Thermodynamic studies of octyltrimethylammonium chloride in water. J. Therm. Anal. 1992, 38, 2693–2705. (11) Šarac, B.; Bešter-Rogač, M. Temperature and salt-induced micellization of dodecyltrimethylammoniumchloride in aqueous solution: A thermodynamic study. J. Colloid Interface Sci. 2009, 338, 216–221. (12) Kroflič, A.; Šarac, B.; Bešter-Rogač, M. Influence of the alkyl chain length, temperature, and added salt on the thermodynamics of micellization: Alkyltrimethylammonium chlorides in NaCl aqueous solutions. J. Chem. Thermodyn. 2011, 43, 1557–1563. (13) Šarac, B.; Medoš, Ž.; Cognigni, A.; Bica, K.; Chen, L.-J.; Bešter-Rogač, M. Thermodynamic Study for Micellization of Imidazolium Based Surface Active Ionic Liquids in Water: Effect of Alkyl Chain Length and Anions. Colloids Surf. A: Physicochem. Eng. Aspects 2017, http://dx.doi.org/10.1016/j.colsurfa.2017.01.062 . (14) Kroflič, A.; Šarac, B.; Bešter-Rogač, M. Thermodynamic Characterization of CHAPS Micellization Using Isothermal Titration Calorimetry: Temperature, Salt, and pH Dependence. Langmuir 2012, 28, 10363–10371. (15) Šarac, B.; Meriguet, G.; Bernard, A.; Bešter-Rogač, M. Salicylate Isomer-Specific Effect on the Micellization of Dodecyltrimethylammonium Chloride: Large Effects from Small Changes. Langmuir 2013, 29, 4460–4469. (16) Schreier, S.; Malheiros, S. V. P.; de Paula, E. Surface active drugs: self-association and interaction with membranes and surfactants. Physicochemical and biological aspects. Biochim. Biophys. Acta 2000, 1508, 210–234. (17) Woolley, E. M.; Burchfield, T. E. Model for Thermodynamics of Ionic Surfactant Solutions. 2. Enthalpies, Heat Capacities, and Volumes. J. Phys. Chem 1984, 88, 2155–2163. (18) Vitorazi, L.; Ould-Moussa, N.; Sekar, S.; Fresnais, J.; W. Loh, W.; Chapel, J.-P.; Berret, J.-F. Evidence of a two-step process and pathway dependency in the thermodynamics


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TABLE OF CONTENTS/ABSTRACT GRAPHIC


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Two-Step Micellization Model: The Case of Long-Chain Carboxylates

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