Solubilization in Mixed Micelles Studied by Molecular Dynamics

Article pubs.acs.org/JPCB

Solubilization in Mixed Micelles Studied by Molecular Dynamics Simulations and COSMOmic Sandra Storm,* Sven Jakobtorweihen, and Irina Smirnova Hamburg University of Technology, Institute of Thermal Separation Processes, 21073 Hamburg, Germany

ABSTRACT: Up to now, micelles composed of different surfactants (mixed micelles) are rarely studied with molecular methods. This is in contrast to their importance for pharmaceutical or industrial applications, where it is of great interest to predict the partition behavior for a large set of solutes (screening) within mixed micelles. This work is focused on molecular simulations of phase equilibria in mixed surfactant systems, because mixtures of different types of surfactants (nonionic or ionic) in aqueous solution can change the partition behavior of solutes tremendously. The extension of COSMO-RS for anisotropic phases, named COSMOmic, is computationally efficient and can be used as a screening tool for finding adequate surfactant systems for a specific extraction task. However, it needs micellar structures as an input. Therefore, molecular dynamics (MD) simulations of the self-assembly of pure Brij35 (polyethylene glycol dodecyl ether) and mixtures either with CTAB (cetyltrimethyl ammonium bromide) or SDS (sodium dodecyl sulfate) at different concentrations are performed. The micelles from the self-assembly MD simulations are used to predict the partition behavior of various solutes between micelle and bulk water with COSMOmic. In this way, various micelles of different size and composition are investigated and structural influences on partition equilibria of solute molecules like ephedrine, acetone, toluene, coumarin, isovanillin, ferulic acid, vanillic acid, syringic acid, and phenol are analyzed. For the first time, the self-assembly of pure Brij35 and the mixtures of Brij35/CTAB and Brij35/SDS is studied on an atomistic scale. Significant influences of atomic structure and composition of mixed micelles on partition equilibria are elucidated. The findings of this detailed analysis are in good agreement with experimental data and likely to improve the knowledge and understanding of mixed micellar extraction processes and can pave the way for more practical applications in the future.

1. INTRODUCTION Surfactants are amphiphilic molecules, which consist of polar parts (head groups) and nonpolar parts (tail groups). The head groups may differ with respect to charge, which influences the solubilization process tremendously. In this article, the commercially available surfactants Brij35 (nonionic), CTAB (cationic), and SDS (anionic) have been investigated. Micelles formed by these surfactants can be used for extraction processes, as they can solubilize different components (solutes). Therefore, the formation of micelles, especially of mixed micelles, is of great importance for multiple technical applications.1−6 The self-assembly process takes place on a microscopic scale and is rather expensive to study via experiments. However, computer simulations provide an alternative to calculate micellar properties and to gain a deeper insight into the process of micelle formation.7−12 There are several simulation approaches available, which have different © 2014 American Chemical Society

advantages. The most detailed modeling approach and thus the computationally most demanding is based on all-atom molecular dynamics (MD) simulations.7,8 Due to the fact that most publications on mixed micelles are mainly based on experiments,4,5,13−16 approaches for simulations and predictions of these systems are rare. Especially, when new processes are developed, a fast screening of optimal surfactant systems is desired. Therefore, this article presents the self-assembly of mixed micelles by all-atom MD simulation. Afterward, the micelles have been analyzed according to their size and composition and the influence on solute partition behavior has been investigated by COSMOmic. In this work, the self-assembly of pure Brij35 and mixtures of Brij35 either Received: October 28, 2013 Revised: February 14, 2014 Published: February 17, 2014 3593

dx.doi.org/10.1021/jp410636w | J. Phys. Chem. B 2014, 118, 3593−3604

The Journal of Physical Chemistry B

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Table 1. Chemical Structures of Brij35, SDS, and CTAB

COSMOmic. The fundamentals and analysis methods of the models are described briefly in the following sections. 2.1. Molecular Dynamics Simulations. For all MD simulations, the open-source molecular dynamic package GROMACS 4.5.318,19 was used. The CHARMM36 force field20 was chosen due to its good parametrization of amphiphilic molecules like lipids.21,22 The surfactant SDS is already parametrized in the force field CHARMM36 and was used without any changes. The surfactant CTAB is not directly included in the force field, but all parameters were available (e.g., compare to the lipids DSPE and LPPC, which are included). The parameters for the surfactant Brij35 have been taken from the CHARMM general force field23 version 2b7 and were collected with the ParamChem program version 0.9.6 beta.24,25 This program assigns force field parameters by analogy, and a “penalty score” is returned to assess the quality of the parameters. All charges have a zero penalty, and among the bonded parameters, only the dihedral angle between the terminal oxygen atom (OH group), the next two carbons, and the first ether oxygen (see also Table 1) has a penalty. As this penalty is only 5 and thus a fair analogy is detected, it can be used without any further optimization.25 In the case of SDS and CTAB, the counterions sodium and bromide have been added to the system for reaching charge neutrality. Since bromide is not included in CHARMM36, the parametrization has been taken from Horinek et al.,26 who used the CHARMM general force field. Water was modeled with the CHARMM TIP3P force field.27,28 The structures of all surfactants and the corresponding counterions are displayed in Table 1. To set up a MD simulation, a specific amount of surfactant monomers was placed into a cubic box and filled with water to match a predetermined concentration by using the tool genbox of GROMACS. The energies of the initial configurations were minimized by the steepest descent method. After the energy minimization, a short simulation in the NVT ensemble was conducted for 600 ps, using the Nosé−Hoover thermostat29 with the coupling time constant of 1 ps and T = 298 K. All further simulations were performed in the NPT ensemble at p = 1 bar and T = 298 K using the Nosé−Hoover thermostat and the Parrinello−Rahman barostat30,31 (isotropic, coupling constant τp = 2 ps). The temperatures of all molecules were controlled independently with a coupling constant of 1 ps.

with CTAB or SDS in aqueous solution are studied by MD starting from a nonaggregated configuration at different concentrations. In this way, different sizes and compositions (in the case of mixtures) of micelles, which are realistic in comparison to experiments, are retrieved. The simulations were performed for at least 100 ns to ensure a sufficient amount of micelles for the analysis (at least 100 micelles per size were selected to overcome the influence of outliers as recommended previously).12 To the best of our knowledge, this is the first time that the self-assembly of these mixed micelle systems has been investigated with all-atom MD simulation. The micelles obtained by MD simulations were analyzed concerning their size (aggregation number) and atomic composition. On the basis of the structure of the micelles received by MD simulations, partition coefficients of a number of solutes were predicted using the model COSMOmic.17 COSMOmic is an extension of the model COSMO-RS (the conductor-like screening model for realistic solvation), developed by Klamt et al.,17 which takes anisotropy into account when predicting partition equilibria. COSMOmic predicts the free energy profile of solutes along the micelle, which can be used for the calculation of partition coefficients in aqueous micellar systems (see section 2.2). Therefore, the atomic distribution of the three-dimensional structure of a micelle is necessary and MD simulations on detailed all-atom scale are indispensable. In this way, detailed all-atom MD simulations have been combined with COSMOmic. Gaining whole free energy profiles of solutes in micellar systems with MD is computationally demanding. The benefit of the combination of MD with COSMOmic lies in the fact that micelles once simulated with MD can afterward be used within COSMOmic to retrieve partition equilibria for various solutes. The applicability of the new approach (combination of MD and COSMOmic) is first demonstrated for mixed surfactant systems.

2. MODELS AND METHODS MD simulations were conducted to study the self-assembly of pure Brij35 and the mixtures Brij35/CTAB and Brij35/SDS, each in aqueous solution. The most probable micelle structures were used for partition behavior predictions with the model 3594



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Table 2. System Configurations for MD Simulations of Pure Brij35, Brij35/SDS, and Brij35/CTAB in Aqueous Solutions at Different Surfactant Concentrations and Ratios no. of molecules surfactant system

nonionic surfactants

ionic surfactants/ions

water

cSurfactant,nonionic (mol/L)

αSurfactant,ionic

Brij35 Brij35 Brij35/SDS Brij35/SDS Brij35/SDS Brij35/CTAB Brij35/CTAB Brij35/CTAB

64 128 50 50 100 50 50 100

0 0 10 50 100 10 50 100

53010 106020 60000 60000 60000 60000 60000 60000

0.062 0.062 0.044 0.043 0.082 0.044 0.043 0.081

0 0 0.17 0.50 0.50 0.17 0.50 0.50

data or from simulation. Although the program COSMOtherm44 (which includes the COSMOmic package, version C30 release 13.01) can distinguish between different micelle shapes, in this work, only spherical micelles are taken into account, as all micelles obtained from the MD simulations are best characterized by this shape. In all COSMOmic calculations, micelle structures from our MD simulations are used to take the anisotropy of the system into account. COSMOmic also requires DFT/COSMO files for all components of the system and all solutes of interest. These DFT/COSMO files were obtained with Turbomole 5.1045 on the BP-TZVP46−48 level and the RI (resolution of the identity) approximation.49 They contain the histogram of the molecular surface area with respect to the screening charge density, which are called σ-profile in the COSMO-RS theory. A conformer analysis of all solute molecules has been performed with HyperChem 8.0.50 Furthermore, a representative surfactant monomer has to be selected for the assignment of the surface charges to the composition matrix of the micelle/water system. In a previous work,51 we demonstrated for lipid bilayers that the selection can be done with respect to the solvent accessible surface. For the sodium ion, which acts as a counterion for SDS, the optimized radii for COSMO-RS were taken from ref 52. Molecular interactions are expressed in the model COSMORS as pairwise surface interactions based on the polarization densities σ and σ′ of the surfaces.17 By statistical thermodynamics, the free energies and chemical potentials according to the interaction of the surface segments are obtained. The chemical potential of a solute X at a fixed position and orientation in a micellar system M can be written as17

For the NPT simulations, a time step of 0.002 ps has been used. The Lennard-Jones interactions were cut off at 1.2 nm and switched from 0.8 nm on. For the Coulomb interactions, a real space cutoff of 1.0 nm was applied besides the Particle Mesh Ewald method32,33 for long-ranged electrostatic interactions was selected. All bonds to hydrogen were constrained with the SETTLE34 and LINCS algorithms35 for water and other molecules, respectively. A summary of all MD simulations used within this work is provided in Table 2. The MD simulations were performed at different surfactant concentrations and ratios of nonionic to ionic surfactant, as presented in Table 2. The parameter αSurfactant,ionic describes the fraction of ionic surfactant with respect to the overall amount of surfactant and is defined in eq 1 xSurfactant,ionic ∝Surfactant,ionic = xSurfactant,ionic + xSurfactant,nonionic (1) with the mole fractions xSurfactant,ionic and xSurfactant, nonionic of ionic and nonionic surfactant in the aqueous solution. The fraction α = 0.5 was chosen, since the strongest deviations compared to the simulations of either pure nonionic or ionic surfactant are expected. In the literature, it is indicated that an equal mixture of surfactants might not necessarily lead to an equally distributed composition within a micelle, and the concentration of ionic surfactant might be much smaller compared to the nonionic surfactant.14,16,36 Therefore, also the ratio α = 0.17 has been chosen for comparison of the self-assembly as well as to study the effects on the partition equilibria. At α = 0.5, two independent simulations at different box sizes have been performed to study the size effect and prove the robustness of the simulation. 2.2. The Model COSMOmic. For the calculation of the partition behavior of solutes in micellar systems, the model COSMO-RS and the extension COSMOmic are applicable. The models are based on statistical thermodynamics and quantum chemical calculations and can be applied to predict thermodynamic properties of fluids and liquid mixtures. To use COSMO-RS, the micellar phase and the water phase are considered as separate phases, between which solute molecules can partition. In this approach, the micellar phase is considered as a “pseudo-phase”.37 The model COSMOmic17 is an extension of COSMO-RS38−43 that takes explicitly the threedimensional structure of a micelle into account. The micelle is radially divided into thin layers, such that each layer has a specific atomic composition with respect to the surfactants, ions, and water molecules. The composition within a layer is assumed to be homogeneous. The atomic distribution in the micelle/water system has to be known either from experimental

X X μMX (r X , dX) = μM,CRS (r X , dX) + μM,comb (r X , d X )

(2)

The radial coordinate of X is denoted as rX and its orientation within a layer by a unit vector dX. In all COSMOmic calculations, an infinite dilution of the solute is assumed. That is, no interactions between solute molecules are taken into account. The μXM,CRS term of the chemical potential is calculated from the surface segment pairing and is usually the dominating part, especially for polar compounds. The combinatorial part μXM,comb takes into account the size and shape of the solute and solvent molecules.17 Klamt et al.17 tested two other terms (for elastic deformation and a zeta-potential for charged solutes) and observed that they are at least for neutral compounds negligible. The total chemical potential, calculated with eq 2, can be used to calculate the partition function of a solute X with 3595



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Figure 1. Self-assembly of Brij35 at cBrij35 = 0.062 mol/L and 64 Brij35 monomers (pictures generated with VMD54): (a) micelles colored as identified via cutoff distances; (b) only the tail groups of the micelles are highlighted.

respect to all n layers (center positions) and all m orientations within one layer as follows:17 n

Z MX =

X ⎧ (r , d j) ⎫ ⎪ −μ ⎪ M i ⎬ ⎨ exp ∑∑ ⎪ ⎪ kT ⎩ ⎭ i=1 j=1 n

∑ Z MX(ri) = i=1

COSMOmic, please refer to the corresponding publications of Klamt et al.17,38−43 2.3. Analysis Methods. In order to distinguish between several micelles, a definition method for the micelle boundary is required. One efficient approach uses definitions via distances between atoms or center of masses of surfactant monomers. Aggregates of surfactants are considered as micelles, if at least one of the distances is smaller than the first and smallest cutoff rc1 or if two distances are smaller than the second cutoff rc2, and so on. This procedure was developed and validated by Sammalkorpi et al.7 and applied for the surfactants CTAB and SDS in our previous publication.12 To find optimal values for the cutoff radii, we presented the cmc (critical micelle concentration) as an optimization criterion.12 In this process, the cut-offs are chosen such that the cmc is reached in the bulk solution. This technique needs a small modification for nonionic surfactant Brij35. Due to the fact that Brij35 has a larger headgroup compared to its tail group, smaller micelles tend to be in close vicinity before they aggregate into larger micelles. To take this effect into account, distances between the C12 (terminal C atom), C6, and C1 atoms of all surfactants are considered but not the center of mass of the monomers. The cutoffs have been defined as rc1 = 0.55 nm and rc2 = rc3 = 0.68 nm, which is in the range of other published distances.7,12

m

(3)

In eq 3, k denotes the Boltzmann constant and T the temperature. The probability to find solute X in layer i is given by pMX (ri) =

Z MX(ri) Z MX

(4)

The free energy profile of the solute in the micellar system in relation to the bulk water phase can be calculated from the probability accordingly: GMX(ri) = −kT ln pMX (ri)

(5)

In this work, the whole free energy profile along the micelle was taken into account for the calculation of the partition coefficient of the solutes. The system size dependent partition coefficient KXM (molSurfactant/molwater) can be calculated as follows:17,53

KMX =

⎛ n (r ) ⎞⎞ n ⎛ ∑i = 1 ⎜V (ri)pMX (ri) − V (rn)pMX (rn)⎜ nw i ⎟⎟ ⎝ w(rn) ⎠⎠ ⎝ V (rn) n

ngw w (rn)

pMX (rn)

3. RESULTS AND DISCUSSION 3.1. Self-Assembly of Pure Brij35 in Aqueous Solution. Before studying the mixtures of Brij35 with CTAB or SDS, MD simulations of the pure Brij35 surfactant have been performed. Therefore, the sizes and structures of the micelles without any additives were retrieved and can be compared to those of the mixtures. Additionally, the pure Brij35 micelles can be used for the predictions with COSMOmic, to evaluate the influence of ionic surfactants on partition equilibria. The Brij35 molecules are large (composed of 200 atoms) in comparison to SDS (42 atoms) or CTAB (62 atoms). Compared to the ionic surfactants, Brij35 has a significantly larger headgroup in relation to the tail group. In consequence, it is very likely that the large head groups shield the tail groups and therefore the aggregation process may be hindered. Hence, at the beginning of the simulation, smaller micelles in close proximity were observed (see Figure 1). Occasionally, the tail

(6)

whereby V(ri) denotes the volume of layer i, nw(ri) is the amount of water molecules in layer i, and nwg represents the total amount of water molecules in the system. The partition coefficient KXM describes the ratio between the probabilities of a solute to be located in the micellar phase or the water phase. The system size dependent coefficient can be transferred into a system size independent partition coefficient PMW (Lwater/ kgSurfactant) that can be directly compared to experimental data: P MW =

NAV (rn) N ∑k =Surfactant nk Mk 1

·

ngw n w (rn)

·KMX (7)

NA is the Avogadro constant, nk is the amount of surfactant molecules of type k of the micelle, and Mk is the molecular mass of a surfactant k. The total amount of surfactants is given by NSurfactant. For further details about the models COSMO-RS and 3596



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smaller amount of surfactants needed to form micelles, as well as the increase in solubilization capacity. These effects have experimentally been observed by different groups.2,4−6,13−16,36 In general, it is difficult to obtain the cmc in all-atom MD simulations; therefore, we investigate the structures and compositions of the micelles. During the MD simulations, the aggregation process of free monomers, to small micelles, also called oligomers (1 mmol/L αSurfactant,ionic = 0.5 yields to xSurfactant,ionic = 0.5 and αSurfactant,ionic = 0.25 yields to xSurfactant,ionic = 0.25.14 It was also demonstrated that, at surfactant concentrations ≤1 mmol/L, large deviations of the micelle composition (x) from the composition in the solution (α) occur.14 However, it is important to note that the micelle composition was not measured directly; it was rather retrieved from different indirect techniques.14,16 Since our aim is the predictions of partition equilibria of different solutes at rather small surfactant concentrations of 1.0−1.2 wt %,16 the micelles obtained at α = 0.17 are compared with those obtained at α = 0.5. In this way, it can be investigated if the quality of prediction is enhanced for micelles with a lower ionic surfactant

Figure 4. Aggregation numbers (Nagg) of Brij35/CTAB (a) and Brij35/SDS (b) at different surfactant concentrations and compositions.

selection of micelles for the predictions with COSMOmic. The self-assembly at c3,Brij35/CTAB for the mixtures with CTAB differ most significantly, and a high amount of large micelles are formed with Nagg = 59−69. The profiles of the simulations at c1,Brij35/CTAB and c2,Brij35/CTAB are comparable (see Figure 4a). In the case of mixtures with SDS, as mentioned above, simulations at c2,Brij35/SDS and c3,Brij35/SDS lead to similar aggregation numbers. However, the simulation at c1,Brij35/SDS results in a pronounced peak around Nagg = 27−29 for Brij35/SDS (see Figure 4b). In order to select representative micelles for the 3598



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concentration, as indicated also by Mehling et al.16 The influence of the micelle composition with respect to the effects on the partition coefficients of various solutes is further analyzed in the following sections. 3.3. Prediction of Partition Equilibria in Mixed Micelles of Brij35/CTAB. Regarding the mixtures of Brij35/ CTAB, different groups of micelles (Brij35/CTAB: Nagg = 67 (α = 0.5), Nagg = 47 (α = 0.5), Nagg= 35 (α = 0.5), and Nagg = 38 (α = 0.17)) were analyzed with COSMOmic. The normalized radial distributions of the tail and head groups over the 30 layers of the micelles are presented in Figure 6. The

more or less similar; therefore, the effects on the partition coefficient are expected to be moderate. In Table 3, partition coefficients of different solutes in different systems (αCTAB and Nagg) experimentally determined Table 3. Micellar Partition Coefficients log PMW of Brij35/ CTAB for Neutral Solutesa

a All COSMOmic results are averaged over all micelles of the specific size and composition, and experimental data is taken from Mehling et al.16 with max RMSE ≤ 0.18. bExperiments measured at αCTAB = 0.5.

Figure 6. Normalized radial atomic distribution of the tail and head groups of mixed micelles of Brij35/CTAB, which are averaged over all micelles of each size and composition taken from the whole trajectories of the MD simulations from parts a to d as indicated in the graphs.

by MEUF (micellar enhanced ultrafiltration) or MLC (micellar liquid chromatography) by Mehling et al.16 are presented in comparison to the predictions with COSMOmic. The RMSE (root-mean-square error) of the predicted values is displayed to evaluate the prediction quality (see eq 8). It is defined as the deviation from the experimental results.

layer with index 0 is in the geometrical center of the micelle, whereas the last layer is pure bulk water. These distributions are the input parameters for the COSMOmic predictions. As expected, the tail groups of Brij35 and CTAB are in the center of the micelles and the head groups are pointing in the direction of the bulk aqueous phase. Due to the similar size and chemical structure of the tail groups, these groups of both surfactants are well mixed in the center, which is in accordance with the literature.13,14 On the contrary, the head groups of CTAB are much smaller than the head groups of Brij35; this is reflected by the rather sharp peak of the CTAB head groups and the broad distribution of the Brij35 head groups. The highest densities of the CTAB head groups at c1,Brij35/CTAB are shifted slightly toward the center and are not at the same position with the highest density for Brij35 as for c2,Brij35/CTAB and c3,Brij35/CTAB. Although over 100 micelles per profile were averaged, this might not be sufficient in order to achieve smooth profiles. However, all profiles of selected micelles are

RMSE =

1 n

n

∑ (log P MW,COSMOmic − log P MW,exp)2 i=1

(8)

Single error bars are not displayed, but the RMSE as well gives an estimate of the margin of deviation for each solute. The partition coefficients of pure Brij35 are in good agreement with experimental data, since all RMSE ≤0.41. The partition coefficients are increasing with increasing CTAB and the log PMW,COSMOmic at αCTAB = 0.17 are close to the experimental values (RMSE ≤ 0.36). The micelles at αCTAB = 0.5 (with Nagg = 35, 47, 67) give higher log PMW,COSMOmic compared to the log PMW,COSMOmic predicted for Nagg = 38 at αCTAB = 0.17, and the log PMW,COSMOmic increases with increasing micelle size at αCTAB = 0.5. The results of Table 3 indicate that the composition of micelles mixed with Brij35 and CTAB influences the partition behavior of neutral solutes, leading to higher partition 3599



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Table 4. Micellar Partition Coefficients log PMW of Brij35/ SDS of Neutral Solutesa

coefficients and thus a higher amount of solubilized solute in the micelles with a higher amount of ionic surfactant. The predictions for micelles simulated at αCTAB = 0.17 are close to the experimental values, measured at αCTAB = 0.5. This can be explained by the fact that, although nonionic and ionic surfactants are equally mixed in the experiments, at low surfactant concentrations, the micelle composition is xCTAB = 0.15.14,16 For this reason, our findings support the experimental results. Since the composition of each single micelle differs as well, Figure 7 presents a more detailed graph of the log PMW,COSMOmic per micelle composition for Nagg = 35 and αCTAB = 0.5, where various different compositions of micelles occurred.

a

All COSMOmic results are averaged over all micelles of the specific size and composition, and experimental data is taken from Mehling et al.16 with max RMSE ≤ 0.53. bExperiments measured at αSDS = 0.5.

for coumarin, but in the case of isovanillin, the log PMW,COSMOmic values are closer to the experimental values for smaller ionic surfactant concentrations, since the partitioning of isovanillin is generally overestimated (see Figure 7). 3.4. Prediction of Partition Equilibria in Mixed Micelles of Brij35/SDS. In comparison to CTAB, SDS is known to have a less pronounced effect on partition equilibria of hydrophobic solutes, when added to Brij35.16 The results of the log PMW of Brij35/SDS micelles are presented in Table 4 along with the system parameters and the experimental data. Table 4 shows that the partition behavior of strong hydrophobic solutes is overestimated for all micellar systems displayed here, but the partitioning is underestimated for more polar solutes (acetone). All solutes are considered in their neutral state. However, in the case of acetone, the experimental error is rather large with 0.53,16 so no reliable conclusion on the effect of SDS on Brij35 micelles can be drawn in this case. Overall, small solute molecules like acetone and phenol allow for the best prediction quality in the range of RMSE = 0.23− 0.62 compared to the other solutes investigated. Larger solutes are less accurately predicted in the micellar systems comprised of Brij35 and SDS. This might be due to the fact that structural effects and deformations of the micelles by the incorporation of solutes are neglected in the model COSMOmic, which was not observed for Brij35/CTAB. Another possibility could be that the model parameters for SDS/Brij35 micelles are not as precise as the parameters of CTAB/Brij35. However, the trend of the increase of log PMW with increasing ionic surfactant is obtained (except for acetone). Additionally, the micelles with Nagg = 38 and Nagg = 46 at αSDS = 0.5 show similar results. It was demonstrated15,16,36 that at low surfactant concentration and at αSDS = 0.5 the micellar composition is most likely in the

Figure 7. Composition effects of Brij35/CTAB at αCTAB = 0.5 and c2,Brij35/CTAB with Nagg = 35 on log PMW,COSMOmic of (a) coumarin and (b) isovanillin.

Even small changes in the micellar composition may lead to changes in the partition behavior for the solutes coumarin and isovanillin. Figure 7 presents the results of different micelles obtained by MD, so that each data point corresponds to one specific micelle. For coumarin, the log PMW,COSMOmic changes from ca. 1.5 to ca. 1.72 (on average), when xCTAB is increased from ca. 0.37 to ca. 0.52 (see Figure 7a). A similar trend is observable for isovanillin (see Figure 7b). Micelles with a low CTAB concentration are less probable compared to micelles with more equally distributed compositions of Brij35 and CTAB, which is in line with Figure 5. Both graphs presented in Figure 7 show a higher variance of the log PMW,COSMOmic for xCTAB = 0.43−0.52. This is probably due to the higher amount of analyzed micelles having a higher ionic surfactant content. The predicted log PMW,COSMOmic values at higher ionic surfactant concentration are closer to the experimental value 3600



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Figure 8. RMSE of log PMW,COSMOmic for Brij35/SDS (c2,Brij35/SDS = 0.043 mol/L, αSDS = 0.5). Calculations are done for all micelles with Nagg = 46. The x-axis presents the index of the micelles that corresponds to the time of occurrence during the simulation.

Figure 9. Normalized atomic distribution of Brij35/SDS micelles: (light colored) obtained from an averaged matrix of Nagg = 46 (c2,αSDS = 0.5); (dark colored) obtained from a single micelle at t = 83.4 ns.

range of xSDS = 0.12−0.20; also, the COSMOmic predictions are closer to the experimental values when micelles retrieved from MD at αSDS = 0.17 were used, compared to micelles from simulations with αSDS = 0.5. In Figure 8, the RMSE for all micelles with Nagg = 46 (at c2,Brij35/SDS = 0.043 mol/L and αSDS = 0.5) is presented. As indicated as lines in the graph, also an averaged atomic distribution matrix was calculated and used as input for COSMOmic, as suggested previously for bilayers.51 The averaged matrices give results close to the average log PMW,COSMOmic and RMSE. This leads to the conclusion that it is possible not only to use multiple micelles as an input for COSMOmic and make multiple simulations of the partition behavior but also take averaged matrices. This results in a reduced simulation time, since only one prediction based on the averaged atomic distribution is performed. For lipid bilayers, it was already demonstrated that using averaged distributions from MD simulations for COSMOmic calculations are advantageous.51 Physically, this approach is close to the experimentally determined partition coefficient, which also corresponds to an average over all micelles.

Figure 10. Brij35/SDS micelle with Nagg = 46 (c2,Brij35/SDS, αSDS = 0.5) at t = 83.4 ns with a large gap in water (pictures generated with VMD,54 atoms of surfactants with standard atomic coloring, water displayed as blue lines).

However, Figure 8 shows some outliers around t = 83.4 ns (index of micelle = 79). Since all predictions were performed with exactly the same input conditions (rmax of the micelle, number of layers = 30, etc.), only deviations in the micelle structure or water shell could be responsible for this outlier. By analyzing the averaged normalized atomic distribution, presented in Figure 9 for Nagg = 46 (c2,Brij35/SDS, αSDS = 0.5), no significant changes of the micellar structure in comparison to the micelle at t = 83.4 ns can be observed. Therefore, the water shell around the micelle at t = 83.4 ns is analyzed. The micelle with Nagg = 46 (c2,Brij35/SDS, αSDS = 0.5) at t = 83.4 ns and its water shell is presented in Figure 10. In the left top corner, the large gap in the water shell, resulting from another micelle in close proximity, can be observed. Besides, a large part 3601



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Notes

of one surfactant is reaching out into the water phase. However, when the original water shell distribution was exchanged against the water shell distribution from the averaged atomic distribution matrix, the predicted partition coefficients turned to be corrected and are in line with the coefficients obtained from other micelles. Thus, the incomplete water layer is responsible for the outlier at t = 83.4 ns, and it leads to the conclusion that the water shell has a significant influence. For this reason, gaps, which result from free surfactant monomers or other micelles close by, have to be avoided if possible. Therefore, the use of averaged matrices is recommended, as gaps in some snapshots can be compensated. Of course, this only holds when a small fraction of micelles show these gaps in their water shells.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors appreciate the financial support of the DFG (Project SM 82/4-2) and from Hamburg University of Technology research center “Integrated Biotechnology and Process Engineering”. Computational resources have been provided by the North-German Supercomputing Alliance (HLRN).

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4. CONCLUSIONS In this work, we presented a detailed analysis of the selfassembly of Brij35 and different mixtures of Brij35/CTAB and Brij35/SDS. This includes the evaluation of the growth of micelles and the different sizes and compositions within the micelles (in the case of mixed micelles). The assembly process of pure Brij35 was slower, probably due to the shielding effects of the large head groups. The micelle sizes obtained are in good agreement with the literature.36,55−58 In the case of mixed micelles, if a simulation is performed at a specific ratio of ionic to nonionic surfactant (αSurfactant,ionic), also the micelles possess nearly the same composition (xSurfactant,ionic) in the concentration ranges investigated. No pure nonionic or ionic micelles have been observed within our MD simulation, when different surfactants were mixed. The influence of size and composition on partition coefficients of various neutral solutes has been demonstrated. The composition of the micelles has a stronger influence than the size of the micelles in the investigated range. All results in terms of partition coefficients and mixed micellar composition are in good agreement with the literature.14−16,36 Additionally, we demonstrated the advantage of using averaged atomic distribution matrices to overcome the effects of outliers and speed up the simulation time, similar to findings for lipid bilayers.51 An interesting finding was that the water shell surrounding each micelle has a significant influence on the COSMOmic prediction quality of micelle/water partition coefficients. Micelles having free surfactants or other micelles close to it, leading to an incomplete water shell, should not be used for COSMOmic calculations. Finally, this work reveals significant new insights for mixed micellar processes of Brij35/CTAB and Brij35/SDS, which is important for future industrial applications. However, even more pronounced effects of the synergism of nonionic and ionic surfactant micelles are expected, when dealing with ionized solutes. Unfortunately, partition coefficients of ionized solutes can up to now not be predicted reliably with COSMOmic and further improvements on the model COSMOmic (and COSMO-RS) are needed by, for example, taking the ζ-potential into account, which is the focus of ongoing studies in our group.

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Solubilization in Mixed Micelles Studied by Molecular Dynamics

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