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Micellization and partition equilibria in mixed nonionic/ ionic micellar systems: Predictions with molecular models Denitsa Yordanova, Eric Ritter, Irina Smirnova, and Sven Jakobtorweihen Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02813 • Publication Date (Web): 02 Oct 2017 Downloaded from http://pubs.acs.org on October 4, 2017

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Micellization and partition equilibria in mixed nonionic/ionic micellar systems: Predictions with molecular models D. Yordanova, E. Ritter, I. Smirnova, and S. Jakobtorweihen∗ Hamburg University of Technology, Institute of Thermal Separation Processes, Eissendorfer Str. 38, 21073 Hamburg, Germany E-mail: [email protected]

Abstract In practical applications, surfactant solutions are mostly used in mixtures of nonionic and ionic surfactants, because they have improved characteristics compared to single surfactant solutions. By adjusting the composition of the micelles and the pH value, the solubilization of solutes can be enhanced. Nevertheless, the partitioning of solutes between nonionic/ionic mixed micelles and the aqueous phase is studied to a much lesser extent than for single surfactant solutions. Theoretical methods to predict partition equilibria in mixed micelles are of interest for screening studies. For those the composition of the mixed micelle has to be known. Here we investigate mixtures of TX-114 (Triton X-114), Brij35 (C12E23), SDS (sodium dodecyl sulfate), and CTAB (cetyltrimethylammonium bromide). First, to investigate the surfactant compositions in the micelles molecular dynamics (MD) self-assembly simulations were applied. Thereafter, the predictive COSMO-RS model, which applies the pseudo phase approach, and its extension for anisotropic systems termed COSMOmic were compared for the prediction of partition equilibria in mixed micelles, where various molar ratios

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of the surfactants were considered. It could be demonstrated that both methods are applicable and lead to reasonable prediction for neutral molecules. However, taking into account the three-dimensional structure of the micelle is beneficial, as the calculations with COSMOmic are in better agreement with experimental results. As, the partition behavior of ionizable molecules in mixed micelles is of particular interest, the partitioning of ionized isovanillin in mixed Brij35/CTAB micelles at different micelle compositions was calculated with COSMOmic. Using a thermodynamic cycle, the position dependent pKa of isovanillin within the micelle is calculated based on COSMOmic free energy profiles. As a result, the protolytic equilibrium of isovanillin within the micelles can be taken into account, which is crucial for the reliable prediction of partition coefficients.

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Introduction

Surfactants are amphiphilic molecules, which consist of hydrophilic head groups and hydrophobic tail groups. They are classified by the charge of their head groups: nonionic, zwitterionic, anionic and cationic. In aqueous solutions at concentrations higher than their critical micelle concentration (CMC) surfactants form micelles. The water solubility of compounds can be enhanced in micellar solutions due to their favorable partitioning in the micelles compared to water. 1–3 This property is highly influenced by the charge of the surfactant head group. Due to this solubilization effect, surfactant based systems find applications in cosmetics, detergents and extraction processes. 4–11 The partition equilibria of a solubilized molecule (solute), defined as partition coefficient (Ki = cmicelle /cwater ), is a decisive factor i i regarding the efficiency of extraction processes. In practical applications, mostly mixtures of surfactants are used, because they have improved characteristics compared to single surfactants solutions. 12–14 For example, mixed micelles from block copolymers are promising vehicles for drug delivery due to improved physical stability and enhanced loading capacities compared to conventional polymeric micelles for drug delivery. 15 In separation processes, the 2


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extraction efficiency can be enhanced due to synergetic effects when mixtures of nonionic and ionic surfactants are used. 16,17 Despite their frequent usage in applications, only a few studies investigate the solubilization and partitioning in mixed surfactant systems. 5,6,18–22 For a better understanding and for the design of new processes, theoretical methods for the prediction of partition equilibria are desirable. The studies on modelling of partition behavior in micellar systems available in the literature mostly investigate single surfactant systems. The partitioning of solutes between mixed micelles and the aqueous phase is studied to a much lesser extent. In our previous studies, 21,22 the predictive thermodynamic model COSMO-RS 23,24 and its extension for anisotropic systems COSMOmic 25 were applied for the prediction of partition behavior of neutral molecules in mixed micellar systems. However, for the prediction of partition equilibria with molecular models such as COSMOmic the composition of the mixed micelle has to be defined. Therefore, the understanding of the micellization mechanism as well as the knowledge of the micellar composition are important. Thermodynamic theories for surfactant mixtures have focused on the CMCs of mixtures as well as on the micelle compositions. Most theories employ the pseudo phase separation approximation in combination with regular solution theory to model the intermicellar interactions responsible for the nonidealities in mixed micellar solutions. 26 The theoretical studies of mixed surfactant solutions available in the literature are mostly based on Rubingh’s approach, because it includes a specific molecular interaction parameter β, defined as an interaction energy difference between equal and nonequal surfactant molecules. 27 Micellization in mixed surfactant solutions has been studied using a variety of experimental techniques (e.g., static and dynamic light scattering, 28 neutron scattering, 29–31 NMR 32 ). However, mostly equimolar solutions were considered. Fang et al. 33 used the Fourier transform pulsed-field gradient (FT-PGSE) NMR technique to measure self-diffusion coefficients of TX-100 and CTAB surfactants in mixed aqueous solutions at different molar ratios. Some important micellization parameters, such as CMCs of the mixtures, compositions of the mixed micelles and the interaction parameter β have been obtained. It was demonstrated that at

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low surfactant concentrations deviations in the composition of the mixed micelles from the composition in the mixed solution occur. However, with an increase of the total surfactant concentration, the compositions of the mixed micelles approach the mole fraction of the mixed solution. The FT-PGSE NMR approach was also applied to study the micellization properties of Brij35/CTAB mixtures. 34 It has been shown that the mechanism of micelle formation is different from that of the TX-100/CTAB system. At any composition of the mixed solution, Brij35 molecules have a tendency to form pure Brij35 micelles first and the CTAB molecules enter them with increasing total surfactant concentration. Nevertheless, in both systems at total surfactant concentration higher than ∼1 mM the composition of the mixed micelles approaches the composition of the solution. In pharmaceutical applications the solubilization of ionizable compounds in mixed micelles is of particular interest to mimic physiological processes. 35–37 The partition equilibria of ionizable solutes is of importance in extraction processes as well. By adjusting the pH value, the surfactant types and the micelle compositions, the partition behavior of solutes can be tailored for the desired application. However, the partition behavior of ionized solutes in mixed micelles is less investigated than of neutral solutes. Mehling et al. 21 applied micellar liquid chromatography (MLC) to determine partition coefficients in mixed Brij35/CTAB micelles at different molar ratios. It could be demonstrated that partition coefficients of both the neutral and dissociated form increase with increasing CTAB content due to enhanced electrostatic interactions. In case of dissociated solutes, the evaluation with MLC is difficult due to very strong binding at higher CTAB content, designated as overbinding. 21,38,39 The prediction of partition equilibria of charged molecules in micellar systems is also challenging. There is a lack of theoretical methods to predict the partition behavior of ionized solutes in mixed micelles. Moreover, it is known that when both the neutral and the charged form of a solute bind to a lipid membrane, the pKa of the solute in the membrane differs from that in the aqueous solution. 40,41 Shifts of ionization constants were observed in micellar systems as well. 38,42

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Ionizations constants, interfacial electrostatic potential and protolytic equilibrium of acidbase indicators in various micellar pseudo phases are discussed in detail in ref 43. Since the partition behavior strongly depends on the ionization state of the molecule, the protolytic equilibrium in the micellar phase has to be taken into account. 44 The change of the ionization constant when a molecule passes through different environments can be estimated using experimental techniques and molecular models. 45 Thermodynamic cycles and free energy profiles from molecular dynamics (MD) simulations were combined to calculate the pKa of amino acids and adamantanes as function of depth in the lipid bilayer. 46–49 If free energy profiles in micelles are accessible, the same approach can be applied to micelles to calculate the favorable ionization state within the micelle. These profiles can be calculated with MD simulations, but also with the predictive model COSMOmic, 25 which is computationally more efficient. In this work, MD simulations and the model COSMOmic were combined to calculate partition coefficients in mixed nonionic ionic micelles. In our previous works, 50–52 this approach was successfully applied to predict partition equilibria in various single surfactant micellar systems and to predict CMCs of nonionic surfactants. 53 The three-dimensional micellar structure in atomic resolution is needed for a COSMOmic calculation. These structures can be taken from two kinds of MD simulations: self-assembly simulations and simulations of preassembled micelles. The simulations of pre-assembled micelles have the advantage that they are computationally more efficient, but the size and the composition of the mixed micelles have to be known. Here, we apply self-assembly MD simulations to obtain the compositions of TX-114/SDS and TX-114/CTAB mixed micelles. The most probable micelles occurring during these simulations were used for the prediction of partition coefficients with COSMOmic and the results are compared to COSMO-RS calculations by applying the pseudo phase assumption, which does not take into account the anisotropy of the micelles. To evaluate the prediction quality, partition coefficients of neutral solutes in equimolar TX-114/SDS and TX-114/CTAB solutions were experimentally determined using MLC. Furthermore, mixed

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Brij35/CTAB micelles are studied, where partition coefficients of neutral molecules in these mixed micelles at different molar ratios are calculated with COSMOmic and COSMO-RS. The micelle structures are obtained from MD simulations of pre-assembled micelles and the experimental data is taken from the literature. 21 Moreover, partition coefficients of isovanillin in its dissociated state were calculated with COSMOmic and compared to the available experimental data. A thermodynamic cycle based on COSMOmic free energy profiles was used to estimate the pKa and therefore the ionization state of isovanillin in the mixed micelles. It could be demonstrated, that the consideration of the protolytic equilibrium within the micelles is crucial for a reasonable prediction with COSMOmic.

2 2.1 2.1.1

Materials and methods Experiments Materials

The surfactants TX-114 and SDS were provided by Sigma-Aldrich and CTAB was purchased from Serva Electrophoresis. The pH was adjusted with HCl from Th. Geyer. All chemicals were used without further purification. 2.1.2

Micellar liquid chromatography

Partition coefficients in mixed surfactant systems (equimolar solution of TX-114/SDS and TX-114/CTAB, respectively) were determined using micellar liquid chromatography. In our previous studies, 21,39,52 the MLC technique was successfully applied for the determination of partition coefficients in various micelles. The chromatographic analysis was performed with an Agilent 1200 Series HPLC. The HPLC system included a quaternary pump, a tempered autosampler, a degasser, a diode array detector, and a column thermostat. A Nucleodur C18 Gravity column (Macherey Nagel, 4 x 125 mm, 5 µm, 100 ˚ A) with the corresponding pre-column was used and kept at 298 K. The pH of the mobile phase was adjusted with HCl 6


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to pH 2. The mobile phase flow rate was set to 0.5 mL/min. The column was equilibrated with the surfactant solution until a constant pressure and constant UV signals have been reached. The column was loaded with surfactant until the adsorption equilibrium and a breakthrough curve was recorded. The retention of the solutes was determined for five different surfactant concentrations in the mobile phase (0.1-0.5 wt.%), whereas the injection volume was 20 µL for all solutes. The partition coefficients were calculated according to the model of Armstrong and Nome. 54

2.2

Computational details

All MD simulations were performed with the GROMACS package version 4.6.7 55 using the CHARMM36 force field 56,57 and the CHARMM TIP3P water model. 58 Parameters for the bromide ions were taken from Joung and Cheatham 59 . The surfactant TX-114 was modeled with the force field parameters optimized in our previous work 51 according to the CHARMM general force field procedure. 57 A real space cutoff of 1.0 nm was applied for the Coulomb interactions, in addition the particle mesh Ewald method 60,61 was used. The Lennard-Jones interactions were cut off at 1.2 nm and switched from 0.8 nm on. The bonds to hydrogens were constrained with the LINCS algorithm, 62 where for constrains in water molecules the SETTLE algorithm was used. 63 2.2.1

Self-assembly simulations

Initial configurations for the self-assembly simulations of TX-114/SDS and TX-114/CTAB were prepared with PACKMOL 64 containing 200 randomly placed surfactant monomers. A concentration of 0.13 M was adjusted by adding a specific amount of water molecules. Counter ions were added explicitly to obtain charge neutrality. An energy minimization was performed with the steepest descent method. First, a 600 ps equilibration step was carried out in the NVT ensemble with a time step of 1 fs. Afterwards, a simulation in the NPT ensemble with the Berendsen barostat 65 was performed for 200 ps. Finally, the systems were 7


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simulated for 200 ns in the NPT ensemble with the Parinello-Rahman barostat 66 (isotropic coupling constant τp = 2 ps) with a time step of 2 fs. The temperature was fixed in all simulations at 283 K using the Nosé-Hoover thermostat 67 (coupling constant τt = 1 ps). 2.2.2

Pre assembled micelles

For the Brij35 CTAB mixed micelles, pre-assembled micelles were used as starting structures. They were generated with PACKMOL, 64 whereas water molecules were added such that the system had a surfactant concentration of 0.08 M. An aggregation number (Nagg ) of 40 was chosen for all micelles according to our previous investigations. 52 After an energy minimization with the steepest descent method, two equilibration steps were performed: a 600 ps simulation in the NVT ensemble, followed by a 200 ps simulation in the NPT ensemble with the Berendsen barostat 65 (see also section 2.2.1). The NPT simulations for sampling were carried out for 40 ns with the Parinello-Rahman barostat 66 (isotropic coupling constant τp = 2 ps) and the Nosé-Hoover thermostat 67 (τt = 1 ps). The temperature was fixed at 298 K and a time step of 2 fs was used. 2.2.3

Definition of micelles

In order to identify micelles from the self-assembly simulations and to proof the stability of the pre-assembled micelles, the method proposed by Sammalkorpi et al. 68 was applied. In this procedure, usually three distances between surfactant monomers are defined, where two surfactant monomers are being part of the same micelle if (1) one of the three defined distances is shorter than r1cut , or (2) two out of three distances are shorter than r2cut , or (3) all three distances are shorter than r3cut . The distances and the cutoffs are chosen according to the specific system after detailed visualization of the configurations to verify a reliable definition of micelles. Further details about the micelle definition criteria are described in our previous work. 50–52 In the case of mixed micelles, two carbon atoms (one from each surfactant type) were grouped to calculate distances between them. The distances and cutoffs used in

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this work are given in table 1. In figure 1 the structures of the surfactants are shown, where all atoms used for the definitions are highlighted. Table 1: Distances between carbon atoms and cutoffs used for the definition of micelles. The atoms of the nonionic surfactant are given first (e.g., in row one, column two C5 of TX-114 and C12 of SDS).

Surfactant system TX-114/SDS TX-114/CTAB Brij35/CTAB

distances C5 + C12 C5 + C19 C12 + C19

C4 + C11 C4 + C14 C6 + C18

C2 + C10 C1D + C6 C1 + C16

r1cut 0.58 0.58 0.68

cutoffs r2cut 0.78 0.78 0.68

r3cut 0.88 1.00 1.20

Figure 1: Structures of the surfactants: CTAB (cationic), SDS (anionic), TX-114 (nonionic) and Brij35 (nonionic). TX-114 has n = 7-8, here we simulated molecules with n = 7 only. The carbon atoms used for the micelle definition are highlighted.

2.3

COSMO-RS and COSMOmic

The conductor-like screening model for real solvation (COSMO-RS) 23,24 is a molecular model based on quantum chemistry and statistical thermodynamics. For micellar systems the pseudo phase approach is applied, where the micelle is treated as a homogeneous macroscopic surfactant phase in equilibrium with the aqueous bulk phase. The activity coefficients of the 9


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solutes at infinite dilution are calculated in the surfactant and aqueous phases, whereas both phases are assumed to be pure. 69 The partition coefficient Ki [Lwater /kgsurfactant ] is calculated as follows Ki =

γiwater v water γisurf v surf,mix

(1)

where γiwater and γisurf are the activity coefficients of the solute in water and in bulk surfactant phase, respectively. v water denotes the molar volume of water and v surf,mix the molar volume of the surfactant mixture. As the COSMO-RS approach assumes that the surfactant phase is homogeneous, an extension of COSMO-RS called COSMOmic 25 for anisotropic systems such as micelles and membranes was developed. In the COSMOmic calculation, the three-dimensional micelle structure is radially divided into spherical shells (in the following also named layers), whereas the composition within each layer is assumed to be homogeneous with a certain atomic composition of surfactant, water and ions. The micelle structure is calculated as average atomic distribution from MD simulations. The advantages to use average atomic distributions are explained in more details in our previous publications. 51,70 The probability of the solute to be located in each layer is calculated, whereby different orientations are taken into account. 25 Therefore, free energy profiles are obtained with COSMOmic; it was shown that these profiles are in agreement with profiles obtained from MD simulations. 71–73 For the systems TX-114/SDS and TX-114/CTAB micelle structures are obtained from the self-assembly simulations described in section 2.2.1. In both cases the most probable micelles which occur during the simulation are chosen, which are Nagg = 50 for the TX-114/SDS system and Nagg = 64 for TX-114/CTAB, respectively. The COSMO-RS and COSMOmic calculations require at least one conformer for each molecule type in the system. As the conformation of amphiphilic molecules is dependent on the environment, surfactant monomers were taken from MD simulations to obtain conformers present in micelles. Representative surfactant monomers were selected with respect to the solvent accessible surface. 70 The required surfactant DFT/COSMO calculations were 10


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performed with a single point calculation with Turbomole 6.6. 74 Conformers for the solute molecules were created with COSMOconf version 3.0 75 and the corresponding DFT/COSMO calculations were performed with Turbomole 6.6. 74 In this work, the COSMOtherm 76,77 (version C3.0 Release 15.01) implementation of COSMO-RS and COSMOmic with the BP TZVP C30 1501 parametrization was used. For further details about the models COSMO-RS and COSMOmic, please refer to the corresponding publications by Klamt et al. 23–25,78 and our research group. 52,69–71

2.4

Thermodynamic cycle and position dependent pKa

Partition coefficients of ionized isovanillin in Brij35/CTAB mixed micelles at different micelle compositions were calculated according to the procedure described below. It is known that when both the charged and the uncharged forms of a drug bind to a membrane with different binding constants, the pKa for the drug in the membrane should differ from that in the aqueous phase. 40 This change of the pKa in the micellar phase compared to the bulk aqueous phase has to be taken into account. 44,79 The position dependent pKa as function of the distance from the micelle center can be estimated based on the free energy profiles of both the charged and neutral form of the molecule. The thermodynamic cycle which allows this calculation is given in figure 2. In this case, ∆GAH and ∆GA− are the free energy profiles of the neutral and dissociated molecule, in this work they were calculated with COSMOmic. The free energy of dissociation in water ∆GAHw at a given pH can be calculated with

∆GAHw = 2.303RT(pKa − pH)

(2)

The pKa of isovanillin in water has a value of 8.89. 80 From these three terms the fourth term can be calculated, the free energy of dissociation in the micelle ∆GAHm and therefore the pKa in the micelle. In this calculation, the protolytic equilibrium of the hydronium ion between the micelle and water is neglected. 81 In order to distinguish between the micellar and

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water phase, the phase boundary between them has to be defined. The free energy profiles of neutral isovanillin obtained with COSMOmic were used to define a border between both phases: the water phase begins where the free energy has reached a value near zero (maximal deviation < 0.40 kJ/mol). Thereby, the interface positions are obtained, which are 2.65 nm for pure CTAB micelle, 2.75 nm for α = 0.8, 3.35 nm for α = 0.5 and 4.05 nm for α = 0.2, respectively.

Figure 2: Thermodynamic cycle to calculate the pKa as function of distance from the micelle center. This pKa is related to the free energy of dissociation in the micelle ∆GAHm . ∆GAH and ∆GA− are the free energies for the transfer from the water to the micelle phase for the neutral and dissociated solute. ∆GAHw is the free energy of dissociation in the water phase (see equation 2).

To calculate partition coefficients of ionizable solutes both the protonated (AH) and dissociated (A− ) form of the molecules have to be considered. 44 Each form is distributed between the micelle and the aqueous phases according to their specific partition coefficients (KAH and KA− ). The total partition coefficient that accounts for the partitioning of both forms KT can be expressed as the weighted average of KAH and KA− according to 40

KT = xAH KAH + xA− KA−

(3)

where xAH and xA− are the mole fractions of the protonated and dissociated form in the micelles, respectively. xAH and xA− are calculated as average over the micelle layers, whereas the mole fractions at different positions (layers) in the micelle are calculated at pH = 10.5 12


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(to be in accordance with the experimental determination 21 ) from the position dependent pKa with the Henderson-Hasselbalch equation

pH = pKa + log

x

A−

xAH

(4)

KAH is the partition coefficient of the neutral form at the given Brij35/CTAB micelle composition calculated with COSMOmic. It is assumed that the partitioning of dissociated solutes in the nonionic surfactant can be neglected. 21,82 Hence, KA− is the partition coefficient of the dissociated form in pure CTAB micelle calculated with COSMOmic. The experimentally determined partition coefficients of isovanillin at pH = 10.5 in mixed Brij35/CTAB micelles at different compositions are taken from ref 21. In the case of experiments using MLC, the ionization state of the solutes is calculated according to the adjusted pH of the mobile phase. As the determination of partition coefficients with MLC is based on retention models, it is not possible to distinguish between different ionization states of the same molecule. Therefore, this procedure does not allow the determination of KAH and KA− separately and it is assumed that the partition coefficient KT that accounts for the partitioning of both neutral and dissociated forms of the solute is measured. Hence, the partition coefficients of isovanillin at pH = 10.5 are used from ref 21 unmodified (further referred as ionizedexp ) and compared to the partition coefficients calculated with equation 3 (further referred as ionizedcalc ).

3 3.1

Results and Discussion Formation of TX-114/SDS and TX-114/CTAB mixed micelles

In this section, self-assembly MD simulations of mixed nonionic/ionic surfactant systems were performed to investigate the aggregation process at different surfactant ratios, as well as the composition of the mixed micelles. Moreover, micelle structures taken from these

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simulations are used for calculation of partition equilibria in section 3.2. Please note that pre-assembled micelles can also be used. In our previous study 52 , the prediction quality of COSMOmic using self-assembled and pre-assembled micelles was compared. It could be demonstrated that self-assembled and pre-assembled micelles with similar aggregation numbers and atomic distributions lead to similar predictions with COSMOmic. Therefore, the focus of the self-assembly simulations is not to obtain micelle structures, but either to investigate the aggregation behavior in mixed surfactant systems. Self-assembly simulations of TX-114/SDS mixtures at three molar ratios (α = 0.1, α = 0.5 and α = 0.9) and TX-114/CTAB (α = 0.5) were performed. In figure 3 the progress of the maximum aggregation numbers over the simulation time is shown. It can be seen that micelles become more stable when the content of the ionic surfactant increases, whereas more fluctuations in the aggregation number are obtained in the system with higher TX114 content. Moreover, the aggregation numbers decrease with increasing content of ionic surfactant. This behavior could be explained with the micelle size distributions in micellar solutions. It is known that all micellar systems exhibit some degree of polydispersity with respect to micelle aggregation numbers. 83 This is characteristic especially for solutions of nonionic surfactants. 84–86 However, in case of mixed nonionic/ionic micelles monodisperse solutions are observed. Kamayama and Takagi 87 reported monodisperse C12 E8 /SDS mixed micelles obtained from electrophoretic light scattering. Furthermore, Tokiwa and Aigami 88 investigated the micelle sizes of mixed SDS with dodecyl polyoxyethylene ether and determined decreasing micelle sizes with increasing SDS content. The same trend was observed for TX-100/SDS mixtures at low ionic strength, 89 which is in agreement with the trend from our self-assembly simulations. In contrast, Komaromy-Hiller et al. 90 reported no significant influence on the aggregation number of TX-114 when SDS and CTAB surfactants are added. Nevertheless, this can be attributed to the concentrations of the ionic surfactants in their study, which are very low (below their CMCs). Furthermore, at different nonionic/ionic surfactant ratios the obtained aggregation num-

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bers differ significantly, as expected. The aggregation number of TX-114/SDS micelles is 24 for αSDS = 0.9 and 200 for αSDS = 0.1, respectively. Both are in the range of aggregation numbers, obtained from self-assembly MD simulations in our previous studies: 20-38 50 for pure SDS and 183-216 51 for pure TX-114. The aggregation numbers in the equimolar TX114/SDS and TX-114/CTAB systems are 50 and 79, respectively. Both are higher than those of pure SDS and CTAB micelles (20-38 50 and 23 50 , respectively), which can be attributed to the TX-114 content. Therefore, the expected trend could be observed.

αSDS = 0.1 αSDS = 0.5 αCTAB = 0.5 αSDS = 0.9

200 max Nagg [-]

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150 100 50 0 0

50

100

150

200

simulation time [ns] Figure 3: Maximum aggregation number over time from self-assembly simulations of TX-114/SDS and TX-114/CTAB systems at different compositions α.

It has been demonstrated that the composition in the mixed micelles is a crucial parameter for the prediction of partition equilibria in mixed micelles. 21 In all self-assembly simulations in this work, the composition in the mixed micelles approaches the composition in the system, where the compositions in the micelles were calculated from the micelles formed at the end of the 200 ns simulations (data not shown). This is in agreement with the experimental observations for TX-100/CTAB mixtures at concentrations higher than ∼2 mM, where the composition of the mixed micelles is equal to the composition in the solution. 33 15


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The same behavior was observed for Brij35/CTAB, where the composition of the mixed micelles is equal to the composition in the solution at concentrations higher than ∼1 mM. 34 Please note that this is valid at concentrations higher than the CMCs of the surfactants. At concentrations below their CMCs, the composition of the mixed micelles differs from the surfactant ratios in the solution. 33,34 As the relevant concentrations in both simulations and experiments are higher than the CMCs of the mixed micellar solutions, for the prediction of partition equilibria in this work the composition in the mixed micelles is assumed to be equal to the composition in the initial mixed surfactant solution.

3.2

Partition equilibria in TX-114/SDS and TX-114/CTAB mixed micelles

Partition coefficients of neutral solutes in mixed TX-114/SDS and TX-114/CTAB micelles were experimentally determined using MLC and predicted with the COSMO-RS model and its extension for anisotropic systems COSMOmic. For both systems equimolar solutions are used in the experiments and therefore also in the calculations. The deviation between the experimental and calculated values is estimated using the root mean square error (RMSE). In this work, all partition coefficients were measured only once. However, the MLC technique has been established for the determination of partition coefficients of neutral molecules and we used the same method and retention model as described in our previous publications. 21,39 Therefore, the maximum error is assumed to be ∆logKi = ±0.25 in accordance with our previous experiments. The experimentally obtained and calculated partition coefficients in the system TX-114/SDS are shown in table 2. It can be seen that the predictions with COSMOmic are in very good agreement with the experimental data (RMSE = 0.25). The COSMO-RS model shows higher deviations with an overall RMSE = 0.55. The same relation is obtained for the system TX-114/CTAB, where the RMSE for the COSMOmic calculation is 0.37 and 0.64 for COSMO-RS, respectively (see table 3). Where for the system TX-114/SDS no trend is observed, all COSMOmic calculations for TX-114/CTAB with one exception (416


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hydroxybenzoic acid), show an overprediction. However, if this is a general behavior for TX-114/CTAB system, cannot be elucidated here as the number of solutes is too small. When comparing the two systems TX-114/SDS and TX-114/CTAB, it can be noticed that both COSMOmic and COSMO-RS have slightly higher deviations in the TX-114/CTAB micelles compared to TX-114/SDS. Since with a few exceptions the same set of solutes is considered, the higher deviation can be attributed to the CTAB surfactant. In our previous study, the COSMOmic model has been evaluated for the prediction of partition equlibria in various micellar systems. 52 It was observed that the predictions for CTAB micelles are more sensitive to the micelle structures and show generally higher deviations from experimental data than nonionic surfactants and SDS. Table 2: Calculated partition coefficients of neutral solutes in TX-114/SDS mixed micelles (equimolar composition) in comparison with experimental data.

logK calc

Solute 4-Hydroxybenzaldehyd 4-Hydroxybenzoic acid Coumaric acid Coumarin Ferulic acid Isovanillin Syringic acid Vanillic acid Vanillin RMSE a

logK exp

COSMOmica 1.63 2.24 2.30 1.56 2.63 1.70 2.34 2.42 1.86

COSMO-RS 1.27 2.46 2.60 0.88 2.84 1.26 2.60 2.64 1.51

0.25

0.55

1.84 1.97 2.25 1.68 2.25 1.76 1.97 2.09 1.72

The micelle structure used for the COSMOmic calculation was taken from a 200 ns self-assembly simulation, Nagg = 50.

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Table 3: Calculated partition coefficients of neutral solutes in TX-114/CTAB mixed micelles (equimolar composition) in comparison with experimental data.

logK calc

Solute 4-Hydroxybenzaldehyd 4-Hydroxybenzoic acid Acetophenone Coumarin Ethylvanillin Ferulic acid Isovanillin Orthovanillin Phenol Resorcin Vanillic acid Vanillin RMSE a

logK exp

COSMOmica 1.61 2.10 2.00 1.89 2.37 2.80 2.00 2.23 2.14 1.95 2.47 2.07

COSMO-RS 2.87 1.55 1.14 1.06 2.03 3.28 1.53 1.62 2.26 2.78 3.05 1.77

0.37

0.64

1.82 1.93 1.54 1.63 1.92 2.38 1.63 1.67 1.81 1.86 1.92 1.84

The micelle structure used for the COSMOmic calculation was taken from a 200 ns self-assembly simulation, Nagg = 64.

It could be concluded that the COSMO-RS pseudo phase approach partition coefficient calculations are in reasonable agreement to the experimental data for mixed micelles. Nevertheless, the usage of the COSMOmic model is beneficial, as the overall RMSEs in both systems are ∼0.3 log units lower than with COSMO-RS. Hence, taking into account the anisotropy of the micelles, which is neglected in the pseudo phase approach, is of importance for the prediction quality of partition equilibria in mixed micellar systems.

3.3

Partition coefficients of neutral solutes in Brij35/CTAB mixed micelles

For mixed micellar systems not only equimolar mixture are important, rather different compositions are relevant for the design of new processes. In order to evaluate COSMO-RS and COSMOmic for the prediction of partition equilibria in mixed micelles, the consideration of

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micelles with different compositions is of importance. In this work, partition coefficients of neutral solutes in Brij35/CTAB mixed micelles at different molar ratio of CTAB are calculated, as experimental data is available in ref 21. Micelle structures for the COSMOmic calculations are obtained from MD simulations of pre-assembled micelles (see section 2.2.2), whereas it is assumed that the molar ratio of CTAB in the mixed micelle is equal to the molar ratio of CTAB in the surfactant solution used in the experiments (see also discussion in section 3.1). The predicted partition coefficients in comparison to experimental data are shown in figure 4 and listed in table 4. It is known that usually higher partition coefficients are obtained for CTAB than for nonionic surfactants due to enhanced electrostatic interactions between the solutes and the cationic head group of CTAB. However, the partition coefficients do not increase linear with increasing CTAB content, which can be seen from the experimental data in figure 4. In general, it can be observed that the trend predicted by COSMOmic is qualitatively in agreement with the experiments. For some solutes (coumarin, ferulic acid, isovanillin) the predictions of COSMOmic partition coefficients are also quantitatively in good agreement to the experimental values at low CTAB content (α ≤ 0.5). Higher deviations are obtained at higher CTAB content, where the predicted partition coefficients overestimate the experimental values. In another study it was also found that predictions for CTAB micelles show higher deviations than predictions for Brij35 micelles. 52 An increase in the partition coefficients in CTAB compared to those in Brij35 is predicted by COSMO-RS as well. However, in the COSMO-RS calculations the partition coefficients increase linear with increasing CTAB content, which is not in accordance with the experimental data. The obtained linear trend can be attributed to the pseudo phase approach (micelle structure not taken into account) in COSMO-RS, whereas the trend predicted by COSMOmic is more precise.

19


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Table 4: Calculated and experimentally determined partition coefficients of neutral solutes in Brij35/CTAB mixed micelles at different micelle composition, where α is the mole fraction of CTAB, logK mic is the partition coefficient calculated with COSMOmic and logK RS with COSMO-RS, respectively. The experimental data was taken from ref 21. α = 0.0

logK mic

logK RS

Coumarin Ferulic acid Isovanillin Phenol Syringic acid Vanillic acid

1.44 2.60 1.60 2.10 2.38 2.40

0.87 2.83 1.22 2.01 2.59 2.01

RMSE

0.35

0.56

α = 0.2

logK exp 1.55 2.37 1.54 1.68 1.89 1.89

± ± ± ± ± ±

0.13 0.10 0.06 0.11 0.12 0.09

logK mic

logK RS

1.53 2.55 1.66 2.02 2.32 2.30

0.89 2.92 1.27 2.05 2.67 2.70

0.26

0.59

α = 0.5

logK exp 1.59 2.45 1.60 1.75 1.86 1.97

(a) coumarin 3.5

coumarin

COSMOmic

coumarin

COSMO-RS

coumarin

exp

0.09 0.04 0.04 0.01 0.02 0.02

logK RS

1.81 2.79 1.97 2.14 2.54 2.46

0.93 3.07 1.36 2.12 2.81 2.84

0.37

0.64

logK exp 1.69 2.37 1.65 1.77 1.95 2.05

± ± ± ± ± ±

0.14 0.04 0.04 0.01 0.02 0.02

logK mic

logK RS

2.39 3.15 2.57 2.23 2.88 2.64

0.96 3.21 1.44 2.18 2.94 2.98

0.59

0.70

0.5

3.0

1.0

3.0

0.4 0.6 αCTAB

4.0

COSMOmic

0.8

exp

syringic acid

logK [l/kg]

logK [l/kg]

3.5

3.0 2.5

0.4 0.6 αCTAB

0.8

1.0

0.8

1.0

vanillic acid

COSMOmic

vanillic acid

COSMO-RS

vanillic acid

exp

3.0 2.5 2.0

1.5 0.2

0.4 0.6 αCTAB

4.0

2.0

1.5

0.2

(f) vanillic acid

COSMO-RS

2.0

0.0

0.0

syringic acid

3.5

exp

0.08 0.10 0.19 0.25 0.04 0.02

2.0

syringic acid

COSMO-RS

phenol

0.73

± ± ± ± ± ±

2.5

1.0

COSMOmic

phenol

2.5

0.2

(e) syringic acid

phenol

0.90

2.18 2.91 2.36 2.40 2.34 2.49

1.0 0.0

(d) phenol

0.96 3.27 1.48 2.20 3.01 3.06

1.5

2.0 0.8

3.25 3.68 3.42 2.47 3.58 3.17

logK exp

exp

3.0

ferulic acid

3.5

0.03 0.05 0.04 0.01 0.02 0.02

logK RS

isovanillin COSMOmic isovanillin COSMO-RS isovanillin

COSMO-RS

2.5

1.0

± ± ± ± ± ±

3.5

COSMOmic

exp

1.5

0.4 0.6 αCTAB

1.85 2.67 1.86 2.06 1.98 2.13

logK mic

(c) isovanillin

ferulic acid

2.0

0.2

logK exp

ferulic acid

4.0

2.5

0.0

α = 1.0

(b) ferulic acid

logK [l/kg]

logK [l/kg]

3.0

± ± ± ± ± ±

logK mic

α = 0.8

logK [l/kg]

Solute

logK [l/kg]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1.5 0.0

0.2

0.4 0.6 αCTAB

0.8

1.0

0.0

0.2

0.4 0.6 αCTAB

0.8

1.0

Figure 4: Partition coefficients of 6 neutral solutes in Brij35/CTAB mixed micelles at different micelle compositions. The experimental data was taken from ref 21. Lines are added as guide to the eye.

It can be noticed that the deviations between the COSMO-RS calculations and experimentally determined partition coefficients increase with increasing CTAB content as well. The overall RMSE of COSMOmic and COSMO-RS in dependence of the CTAB content is shown in figure 5. The RMSE of COSMO-RS increases from 0.56 in pure Brij35 micelle to 0.73 in pure CTAB, whereas the difference is more pronounced for COSMOmic (from 0.35 to 0.90, respectively). Still, for α ≤ 0.8 COSMOmic provides quantitatively better predictions than COSMO-RS. This is not the case in pure CTAB, where the overall RMSE

20


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of COSMO-RS is 0.17 log units lower than for COSMOmic. However, it has to be noted that the sensitivity of the COSMOmic calculations on the used micelle structure and size (aggregation number) increases with increasing CTAB content. 52 In another study 73 we have investigated the influence of the CTAB micelle size on the COSMOmic calculations in detail. One finding was that the CTAB micelle size has especially for charged solutes an influence. 1.0 RMSE neutral solutes

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.8

COSMOmic COSMO-RS

0.6 0.4 0.2 0.0

0.2

0.4 0.6 αCTAB

0.8

1.0

Figure 5: RMSE of COSMOmic and COSMO-RS calculated partition coefficients of 6 neutral solutes in Brij35/CTAB mixed micelles at different surfactant compositions. Dotted lines are added as guide to the eye.

In summary, although the COSMO-RS predictions are reasonable, the predictions with COSMOmic, where the anisotropic environment within the micelle is accounted for, can be considered as more precise and are quantitatively in better agreement with experimental results. Hence, it is important to take into account the three dimensional structure of the micelles.

3.4

Partition coefficients of an ionized solute in Brij35/CTAB mixed micelles

It is known that the partition behavior in mixed nonionic/ionic micelles can be influenced by adjusting the pH of the surfactant solution. A partition coefficient increase in Brij35/CTAB mixed micelles is obtained when the acidic solute is dissociated. This effect is due to attractive forces between the negatively charged solute and the positively charged head group 21


Langmuir

of CTAB. Therefore, it is expected that the partition coefficient increases with increasing CTAB content in the mixed micelle for acidic solutes. Experimentally determined partition coefficients of ionized isovanillin in Brij35/CTAB mixed micelles at different molar ratios of CTAB are available in the literature 21 and calculated in this work using the COSMOmic model. For these calculations the protolytic equilibria not only in water, but also in the anisotropic micelle based on free energy profiles calculated with COSMOmic are taken into account. This is possible by applying a thermodynamic cycle, where the procedure is described in details in section 2.4. As an example, free energy profiles of isovanillin (neutral and charged) in a pure CTAB micelle and the estimated position dependent pKa are shown in figure 6. (a) free energy profiles 100 80

(b) position dependent pKa 25

Neutral Charged

20

60 40

pKa

free energy [kJ/mol]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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15

20 0

10

-20 0.0

1.0 2.0 3.0 distance from micelle center [nm]

5 0.0

4.0

1.0 2.0 3.0 distance from micelle center [nm]

4.0

Figure 6: (a) Free energy profiles of neutral and charged isovanillin in a CTAB micelle calculated with COSMOmic. (b) Calculated position dependent pKa of isovanillin in a CTAB micelle. The dotted line represents the experimental pKa of isovanillin in water. 80

The calculated and experimental partition coefficients of ionized isovanillin in Brij35/CTAB mixed micelles are given in table 5. Please note that the direct calculation of ionized molecules in mixed micelles with COSMOmic or COSMO-RS without taking into account the protolytic equilibrium within the micelle leads to very high deviations from the experimental values (up to some orders of magnitude), especially in micelles with high nonionic surfactant content. The calculated and experimentally determined partition coefficients for the protonated form of isovanillin are shown for comparison in figure 7. It can be seen that the 22


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calculated trends are in qualitative agreement with the experimental ones. For the dissociated state the absolute deviation from the experimental values is within ∼1 log unit at all molar ratios of CTAB, which is comparable to the deviation of the neutral form for α ≥ 0.8. It has to be noted that the partition coefficient of dissociated isovanillin in pure CTAB has an absolute deviation of 0.69 log units, which is in the range of the experimental error. Since this value is used for the calculation of the partition coefficients at α = 0.2, α = 0.5 and α = 0.8, its error contributes to the error of all calculated partition coefficients. If using a partition coefficient for pure CTAB, which is closer to the experimental value, the deviations at the other molar ratios would decrease as well. If using the experimental value in pure CTAB instead of the predicted one for the calculations at the other three molar ratios, the overall RMSE for the four compositions decreases from 0.81 to 0.51, respectively. Moreover, the difference between the calculated and experimental partition coefficient of neutral isovanillin in pure CTAB micelles is ∼1 log unit as well. Hence, the higher deviations in this system can be attributed to the interactions between isovanillin and CTAB in general rather than to the charge of the solute. 4.5

protonatedexp protonatedcalc ionizedexp ionizedcalc

4.0 logK [l/kg]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3.5 3.0 2.5 2.0 1.5 0.0

0.2

0.4 0.6 αCTAB

0.8

1.0

Figure 7: Partition coefficients of isovanillin in Brij35/CTAB mixed micelles at different micelle compositions. The experimental data was taken from ref 21. Lines are added as guide to the eye.

It was demonstrated that it is crucial to take into account the protolytic equilibrium within the micelle for the calculation of partition equilibria of ionized solutes with COSMO23


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 5: Calculated and experimentally determined partition coefficients of ionized isovanillin in Brij35/CTAB mixed micelles at different micelle compositions, where α is the mole fraction of CTAB, ionizedcalc is the partition coefficient calculated with COSMOmic using the procedure described in section 2.4. The experimental data was taken from ref 21.

α 0.2 0.5 0.8 1.0

logK ionized ionizedexp 3.13 2.36 ± 0.07 3.30 2.59 ± 0.08 3.56 2.54 ± 0.08 4.18 3.49 ± 0.96 calc

mic. By applying a thermodynamic cycle based on transfer free energies calculated with COSMOmic, the estimated partition coefficients are in qualitative agreement with the experimental data and have an absolute deviation within ∼1 log unit. Still, this method has to be evaluated using a larger set of partition coefficients of dissociated solutes in mixed micelles. However, for comparison, the direct calculation with COSMOmic considering only the dissociated form of isovanillin can lead to absolute deviations up to ∼15 log units for the micelles with high content of nonionic surfactant. It is known that COSMOmic was originally introduced for neutral molecules. Bittermann et al. 78 proposed an approach to improve the prediction quality for charged molecules in membranes by implementing an internal membrane dipole potential, which was empirically optimized to match experimental partition coefficients. The introduction of an internal potential for micelles analog to lipid membranes is only possible if a large set of experimentally determined partition coefficients for ionized solutes in a specific micelle type is available. The electrostatic potential should be optimized for each surfactant type explicitly. Unfortunately, experimental data for charged molecules, especially in mixed micelles is scarce in the literature. Therefore, the implementation of an electrostatic potential proposed by Bittermann et al. 78 is not applicable for mixed micelles due to lack of experimental data.

24


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4

Conclusions

In this work, the micellization process and partition equilibria in mixed nonionic/ionic micelles were investigated with molecular models. The aggregation behavior and the composition of mixed TX-114/SDS and TX-114/CTAB micelles were estimated from self-assembly MD simulations. In all cases, the composition in the micelles approaches the composition in the initial configuration, which is in accordance with experimental data in the relevant surfactant concentration range. 33,34 Therefore, for the predictions of partition coefficients it was assumed that the composition in the mixed micelle is equal to the composition in the mixed surfactant solution. The predictive models COSMO-RS and its extension for anisotropic systems COSMOmic 25 were applied for the calculation of partition coefficients of neutral solutes in various mixed micelles. It can be summarized, that both COSMO-RS and COSMOmic provide qualitatively correct predictions in the investigated systems. Nevertheless, the usage of COSMOmic shows advantages over the COSMO-RS pseudo phase approach, as the predictions are generally in better agreement with experimental data. Furthermore, partition behavior of dissociated isovanillin in mixed Brij35/CTAB at different molar ratios of CTAB was investigated. A thermodynamic cycle based on transfer free energies was applied (see figure 2) to obtain the position dependent pKa of isovanillin in the micelles. This allows the estimation of the protolytic equilibrium not only in water but also in the micelle. It could be concluded that taking into account the protolytic equilibrium within the micelle is crucial for a reasonable description of partition equilibria of ionized solutes in mixed micelles with COSMOmic. If considering only the ionized form of the solutes, the COSMOmic calculations in mixed micelles lead to much higher deviations from experimental data compared to neutral solutes. In summary, we conclude that COSMOmic can at least qualitatively predict the influence of surfactant mixtures on partition behavior of solutes. In many cases these calculations result also in good quantitative agreement (e.g., see table 2). However, a first condition is that the partition coefficients should be correctly predicted for the pure micelles of the involved surfactants. If this is not the case, micelles with a high content of 25


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the inaccurately described surfactant cannot be correctly described (e.g., see figure 4a).

Acknowledgement The authors appreciate financial support of the German Academic Exchange Service (DAAD). Computational resources have been provided by The North-German Supercomputing Alliance (HLRN).

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mond, P. T.; Yang, Y.-Y. Mixed micelles self-assembled from block copolymers for drug delivery. Curr. Opin. Colloid Interface Sci. 2011, 16, 182–194. (16) Gharibi, H.; Razavizadeh, B.; Hashemianzaheh, M. New approach for the studies of physicochemical parameters of interaction of Triton X-100 with cationic surfactants. Colloids Surf. A 2000, 174, 375–386. (17) Szymczyk, K.; Zdziennicka, A.; Krawczyk, J.; Jaczuk, B. Behaviour of cetyltrimethylammonium bromide, Triton X-100 and Triton X-114 in mixed monolayer at the (waterair) interface. J. Chem. Thermodyn. 2014, 69, 85–92. (18) Zhou, W. Solubilization of pyrene by anionic-nonionic mixed surfactants. J. Hazard. Mater. 2004, 109, 213–220. (19) Dar, A. A.; Rather, G. M.; Das, A. R. Mixed Micelle Formation and Solubilization Behavior toward Polycyclic Aromatic Hydrocarbons of Binary and Ternary CationicNonionic Surfactant Mixtures. J. Phys. Chem. B 2007, 111, 3122–3132. (20) Mehta, S.; Chaudhary, S. Micropartioning and solubilization enhancement of 1,2bis(bis(4-chlorophenyl) methyl)diselane in mixed micelles of binary and ternary cationic–nonionic surfactant mixtures. Colloids Surf., B 2011, 83, 139–147. (21) Mehling, T.; Kloss, L.; Ingram, T.; Smirnova, I. Partition Coefficients of Ionizable Solutes in Mixed Nonionic/Ionic Micellar Systems. Langmuir 2013, 29, 1035–1044. (22) Storm, S.; Jakobtorweihen, S.; Smirnova, I. Solubilization in Mixed Micelles Studied by Molecular Dynamics Simulations and COSMOmic. J. Phys. Chem. B 2014, 118, 3593–3604. (23) Klamt, A. Conductor-like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena. J. Phys. Chem. 1995, 99, 2224– 2235. 28


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gregation Number upon Clouding of a Nonionic Detergent: Effect of Ionic Surfactants and Sodium Chloride. Langmuir 1996, 12, 916–920.

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Ionic Micellar

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