Article pubs.acs.org/Langmuir
Character of Localization and Microenvironment of Solvatochromic Reichardt’s Betaine Dye in Sodium n‑Dodecyl Sulfate and Cetyltrimethylammonium Bromide Micelles: Molecular Dynamics Simulation Study Vladimir S. Farafonov, Alexander V. Lebed,* and Nikolay O. Mchedlov-Petrossyan Department of Physical Chemistry, V. N. Karazin Kharkiv National University, 61022, Kharkiv, Ukraine S Supporting Information *
ABSTRACT: The problem of using surfactant micellar aqueous solutions as reaction media centers on estimating the polarity of the micellar pseudophase. The most popular approach is the utilization of solvatochromic dyes. Among the last, the strongest ones are the dipolar pyridinium N-phenolate dyes. The complication of such approach, however, consists in the nonuniform character of the environment of the indicator fixed in the micellar pseudophase. The aim of this study is to reveal the character of localization and orientation of the standard solvatochromic pyridinium N-phenolate dye, 4-(2,4,6-triphenylpyridinium-1-yl)-2,6-diphenylphenolate, the so-called Reichardt’s dye, within the micellar pseudophase of an anionic (sodium n-dodecyl sulfate, SDS) and cationic (cetyltrimethylammonium bromide, CTAB) surfactants using MD simulations. The locus and hydration of the dye are found to be dependent on the surfactant nature. New approaches are proposed to quantitatively describe the state of the dye within the pseudophase. The results confirm the experimental data, which indicate the higher polarity of the interfacial region in the case of the SDS micelles. Because this dye is also used as an interfacial acid−base probe, the corresponding study is simultaneously performed for its protonated, i.e., cationic form. The neutral and protonated forms of the dye are found to be localized and hydrated in a different way in both SDS and CTAB micelles. This should be taken into account when using the Reichardt’s dye as an acid−base indicator for estimating the electrical surface potential of micelles. The presented approach may be recommended to shed light upon the locus of other solvatochromic and acid−base indicators in micelles and micellar-like aggregates.
1. INTRODUCTION Presently, surfactant micellar solutions, microemulsions, and other organized solutions are widely used for carrying out various reactions and physicochemical processes.1−3 The reason is significant change in spectral and thermodynamic properties of compounds and reactions rates, which often take place in organized solutions. The main cause is adsorption of reactants in surface regions of micelles, also called Stern layers in the case of ionic micelles. The Stern layer is actually a mixture of hydrocarbon, electrolyte, and water having unique properties, rather different from that of a bulk solvent. Therefore, the totality of surface regions of micelles is called “pseudophase” and appears to play a role of (reaction) medium. Consequently, attempts have been made to characterize Stern layers of various micelles by parameters used for solvents. Here we focus on one of the most common parameters, namely, polarity. According to the accepted IUPAC definition (which is, at the same time, quite general), polarity is the overall solvation capability (solvation power) for solutes.4 Evidently, the latter is a complex resultant of contributions of individual solvent properties, such as relative permittivity, molecules’ dipole moment, hydrogen bonds donating and accepting abilities, etc. Therefore, a number of empirical parameters were introduced for characterizing © 2017 American Chemical Society
polarity. Probably, the most popular approach to quantitatively estimate it is the utilization of solvatochromic dyes, the strongest tools being the pyridinium N-phenolate dyes (Scheme 1).5,6 In this approach, the polarity parameter is the energy of the charge transfer absorption band, ET, of the dye dissolved in the examined medium. It is calculated from the wavelength of the maximum in the visible spectrum, λmax: E T = hcvmax ̃ NA = 2.8591 × 10−3vmax ̃ = 28591/λmax
(1)
Scheme 1. Molecular Structure of Pyridinium N-Phenolate Solvatochromic Dyes
Received: May 26, 2017 Revised: June 30, 2017 Published: July 19, 2017 8342
DOI: 10.1021/acs.langmuir.7b01737 Langmuir 2017, 33, 8342−8352
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Langmuir Here ET is the polarity parameter in kcal mol1, h, c, and NA are fundamental constants, and ṽmax and λmax are the wavenumber of the band maximum in cm1 its wavelength in nm, respectively. The value obtained with the so-called standard Reichardt’s dye (R1 = R2 = R3 = C6H5), which is abbreviated as RD further in the text, is called ET(30), in accordance with the number 30 of this dye within the set of compounds synthesized in the initial paper.5 Nowadays, the dimensionless normalized parameter, ENT , is usually used: E TN = [E T(30) − 30.7]/32.4
micellar media provides rather limited information about their own properties. Several experimental investigations have been performed in order to reveal the locus of the dye on micelle surfaces. Zachariasse et al.10 have shown via the 1H NMR spectroscopy in 0.05 M CTAB aqueous solution with the surfactant:dye ratio of 20:1 that the standard RD, when bound by micelles, exerts the largest influence on the methyl groups in headgroups and α-CH2 and β-CH2 protons. Hence, the dye is located in the micellar surface region. Plieninger and Baumgärtel23 deduced from the 1 H NMR data that the dye without ortho-substituents in the phenolate moiety (R1 = R2 = C6H5; R3 = H) is located in anionic SDS micelles in such a manner that the pyridinium center is in the plane of the O−SO3 group. At that, the phenolate group is introduced into the neighboring water layers. Furthermore, in cationic micelles the same authors expect that the anionic center of the same dye is among the trimethylammonium groups, whereas the cationic pyridinium portion is immersed into water.23 By contrast, Tada et al.20 also used the 1H NMR spectoscopy and stated that the dichloroderivative (R1 = R2 = C6H5; R3 = Cl) is rather deeply penetrated into the cationic micelles. As it can be seen, the available experimental data are fragmentary and somewhat contradictory. As a result, the problem of proper treatment of the ET values of micellar solutions is still not resolved. Therefore, the main aim of the present paper is to reveal the localization and orientation of the RD molecule in micelles of SDS and CTAB by means of MD simulations. The second aim is to compare obtained characteristics that will allow estimating the role of the localization factor in the difference between ET(30) parameters of SDS and CTAB micellar solutions. The MD simulation method has already been applied to the standard Reichardt’s dye in the environment of nonionic block copolymers.29 Other examples of MD modeling of dyes in surfactant environment are the sudies of rhodamine-labeled phospholipid incorporated into a lipid bilayer30 or sulforhodamine in SDS layers on water−air interfaces.31 Next, the considered problem is closely related to one more issue. The examining surfactant micelles, vesicles, and phospholipid liposomes was extended by using the standard Reichardt’s dye as an acid−base indicator, additionally to its solvatochromic properties (Scheme 2).11
(2)
ENT
The constants are chosen in such a way that, for water, equals to unity, and for tetramethylsilane, it equals zero.5 The λmax value of the RD molecule depends on the relative permittivity and hydrogen bond donating ability of the dye molecule microenvironment. The whole dye molecule as an electric dipole senses the former property, while the latter property is sensed by the O atom solely because it is the single hydrogen bond acceptor in the RD molecule. Therefore, the microenvironment of the oxygen atom of the dye is of particular importance.5,28 An illustrative example is the ENT values of 2-propanol and acetone, which equal 0.546 and 0.355, respectively.5 These solvents have similar relative permittivities, compositions and molecular geometries, and the difference in polarities is caused almost solely by the ability of 2-propanol to form a hydrogen bond with the dye O atom. Another example is methanol and acetonitrile, whose relative permittivity are similar but ENT values drastically differ (0.762 and 0.460, correspondingly).5 The numerous ET(30) and ENT values for pure and mixed solvents have been published presently.5−9 Further, the ET(30) and ENT values have been reported for a number of surfactant micellar solutions and related systems,6,10,11 including dendrimers.12 In this laboratory, the ENT values of the RD were determined for 36 surfactant systems.13 The RD was used for examining catanionic vesicles,14 cationic gemini surfactants,15 their mixtures with cetyltrimethylammonium bromide (CTAB),16 and CTAB mixtures with a double-tailed cationic surfactant.17 Afterward, a new indicator of the same series (R1 = R2 = C6H5; R3 = Cl) was proposed and used for the same purposes,18−20 whereas the standard dye was used to study zwitterionic surfactants of betaine type.21 In these and some other papers,20,22−27 the absorption spectra and ET values were determined at different concentrations of surfactants. The ET values of micelles of cationic and nonionic surfactants, estimated in such a way, are similar, whereas the polarities of micelles of anionic ones show the stronger hydration of the latter type of micelles, which is in line with some other independent approaches.13 For instance, for the micelles of CTAB and sodium dodecyl sulfate (SDS), the ENT values are found to be 0.688 and 0.827 respectively.10 Further study was carried out with a different dye (R1 = R2 = C6H5; R3 = H)22 and a set of other pyridinium N-phenolates.23 However, while in pure solvents the treatment of the measured polarity parameters is straightforward, this is not the case for colloid solutions. In microheterogeneous media, where the composition changes across the system, the composition of the dye molecule microenvironment depends also on its localization and orientation. Therefore, the following question is often put: Is the difference between measured ET(30) values of micellar solutions of different surfactants (e.g., SDS and CTAB) caused solely by different polarities and compositions of the surface layers of corresponding micelles, or is an additional reason the somewhat different locus of the RD molecule on micelle surfaces? If the second option is actual, then comparing ET(30) values of these
Scheme 2. Protolytic Equilibrium of the Standard Reichardt’s Dye
The protonated cationic form is colorless. This equilibrium allows estimating the surface electrostatic potential of micelles, Ψ, by means of the so-called apparent ionization constants, Kapp a , of the betaine dye.11,13,18 8343
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pK aapp = pK aw + log
w
γ +mD−
γ +mDH
−
ΨF RT ln 10
with detail ranging from all-atom to united-atom and even coarsegrained. We decided to employ all-atom models for the surfactants and the dye, and to keep tails charged because the interactions between studied species are quite weak and vanishing dipole moments of CHn groups could distort the subtle interactions balance in the solution, affecting simulation results. Further, models for all particles in the system should be mutually consistent, i.e., belong to the same force field (FF) and be parametrized in the same way. Particularly, this is important when a comparison of properties of two analogous compounds is performed because otherwise the observed difference in properties would partially be caused by differences in parametrization methodologies of potential models. Surfactants. We used a set of surfactant models, recently developed by us32,33 in the framework of OPLS-AA force field34 with rigorous following of the original force field parametrization methodology. They reproduce micelle size, shape, and degree of counterion binding with good accuracy. An additional advantage, which is relevant to this study, is using improved parameters for C−CC−C and H−CC−H dihedral angles. The original OPLS-AA parameters were shown to poorly reproduce properties (especially, density) of long hydrocarbons and their derivatives at room temperature because the artificial ordering of molecules appears.35,36 Therefore, several modifications of OPLS-AA parameters have recently been proposed for long hydrocarbons and lipids, which bring their calculated properties to the experimental values.35,36 In our models, the modification provided by Murzyn et al.36 was employed. The dye molecule can immerse into the micelle core, thus the accurate description of the latter is important. Water was described by the SPC model; for Na+ and Br ions, Aquist’s37 and Lybrand’s38 models were used. Betaine Dye. Because the RD molecule itself is a large conjugated zwitter-ionic system, we decided to calculate the charges ab initio rather than use the built-in OPLS-AA ones. The standard OPLS-AA methodology was followed: the dye molecule was optimized using the HF/6-31G(d) level of theory, and then the electrostatic potential distribution obtained was fitted by means of the CHELPG algorithm.39 Because charges obtained by fitting are known to be quite sensitive to the orientation of a molecule in space and, thus, poorly reproducible, we employed the RED Server, which was developed specially to facilitate calculation of atomic charges.40 The server performs all algorithm steps automatically for several random molecule orientations, which allows obtaining reliable charges. The Gaussian 09 software package was used.41 This approach was employed for both neutral and protonated forms of the dye. Special attention was devoted to the bonds between phenyl rings. OPLS-AA force field does not contain parameters for the PhPh bond, therefore, we used parameters developed by Dahlgren et al.42 As a counterion for the protonated form, we chose Cl; the standard model from the force field was used for it. The initial draft topology file was prepared using the TPPMKTOP server.43 The described potential model for CTAB33 and the prepared potential models for the RD are provided in the Supporting Information in GROMACS format. 2.2. Simulation Protocol. All simulations have been carried using the GROMACS 5 software package44 with following parameters: standard conditions (T = 298 K and p = 1 bar) maintained using Berendsen couplings with τT = 1 ps and τp = 1.5 ps, correspondingly, periodic boundary conditions, cutoff radius for van der Waals interactions of 1 nm, and particle mesh Ewald electrostatics. All bonds were constrained with the LINCS algorithm. The time step was 2 fs for the SDS simulations and 1.6 fs for the CTAB ones. It was found necessary to employ the smaller value for CTAB because constraining errors appeared during simulation with Δt = 2 fs. They were probably caused by long hydrocarbon chains. We chose to make the dye solubilized in micelles in the initial configurations because this approach significantly saves computational time. Actually, the relocation of the dye from bulk water to the micelle surface usually needs several tens of nanoseconds of time. Hereafter, solubilization means the location of a molecule inside the micellar core. To prepare such configurations, we used the following three-stage protocol.
(3)
Here Kwa is the thermodynamic ionization constant of the w m indicator in water, wγm + − and γ+ D DH are transfer activity coefficients (water → micellar pseudophase) of the corresponding species, F, R, and T are Faraday constant, absolute gas constant, and temperature, respectively, and Ψ is the electrostatic potential in the location of indicator. Usually, this location is assumed to be within the Stern layer of ionic micelles for both charge forms.13 The pKapp = −logKapp value is normally determined via the a a spectrophotometric method accompanied by the pH determination of the bulk (aqueous) phase using the glass electrode in a cell with liquid junction. For instance, the pKa values of the RD in numerous surfactant systems were determined in this laboratory.13 For calculating Ψ via eq 3, one should estimate the term w m log(wγm + −/ γ+ D DH). One of the methods is based on the modeling of this term in ionic micelles by the corresponding value of the same indicator in nonionic micelles, where Ψ → 0. Since, for micelles of cationic and nonionic surfactants, the ET(30) values are rather close, such approach looks reasonable. On the other hand, Drummond et al. assumed some specific interactions between the positive part of the betaine dipole, +D−, and the sulfate groups of the SDS surfactant.11 Hence, the Ψ values obtained for such micelles using the RD as an acid−base probe may be considered as being “not the electrostatic surface potential”.11 The fact that SDS and similar anionic surfactants have notably different (higher) ET(30) values served as an indirect indication of the presence of above interactions. In w m another approach, the equality of wγm γ+DH is assumed + − and D w m w m (and the term log( γ+D−/ γ+DH) is zeroed), grounding on the fact that the indicator molecule has large size and, thus, average nonelectrostatic interaction of each form with a micelle can be thought equal.11 However, wγm values depend on the dye locus in micelles; consequently, both above-mentioned approaches imply some requirements to it. Therefore, the third aim of the present paper is to compare localizations of +D and +DH in SDS and CTAB micelles in order to check the validity of the assumptions that w m w m w m w m (i) wγm γ+DH or (ii) (wγm + − = + −/ γ+ D D DH)SDS = ( γ+D−/ γ+DH)CTAB. Finally, we will compare our results with those of the abovementioned work considering the RD in nonionic block copolymers,29 which will allow us to estimate the similarity between wγm + − in a nonionic supramolecular aggregate and in D cationic and anionic micelles. The rest of the article is organized as follows. In section 2, the technical issues of the presented MD study are discussed. In sections 3.1−3.4, various computed characteristics of the RD molecule locus will be shown. The convergence of the obtained values is discussed in section 3.5. In section 3.6, the comparison between the characterictics of the neutral and protonated forms in SDS and CTAB micelles is made, and the consequences concerning the ET and wγm values of these micelles are deduced. Finally, conclusions about the application of the Reichardt’s dye for measuring polarities and surface potentials of micelles are presented.
2. EXPERIMENTAL SECTION 2.1. Potential Models. Before starting a simulation, it is necessary to choose appropriate potential models for substances involved, which are able to correctly reproduce the properties of interest. There is a large variety of potential models for SDS and CTAB described in literature, 8344
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Figure 1. Initial configurations with SDS (A) for micellization, (B) for collapsing (sliced, the saturation of tail color falls with the distance from the screen plane), and (C) for production run. SDS carbons are colored cyan. The first stage, 10 ns long, was spontaneous forming of a micelle from the initial structure. The latter was a roughly square bilayer consisting of 60 (SDS) or 80 (CTAB) monomers together with their counterions, Figure 1A. Such values correspond to aggregation numbers of these surfactants in wide range of concentrations.45,46 The box size was 8.1 nm for SDS and 9.7 nm for CTAB that resulted in ∼4 nm spacing between the micelle obtained and its periodic images. Next, a cavity was grown in each micelle in order to make space for the dye molecule to be placed. To do this we placed two pseudoatoms in the center of each micelle at a 1 nm distance from each other. The pseudoatoms had the following parameters: zero charge, Lennard-Jones potential parameters σ = 2 nm and ε = 0.4184 kJ/mol. To grow the cavity, the slow-growth algorithm was employed. All interactions between the pseudoatoms and other particles were turned off in the initial state and were gradually enabled during simulation to become fully turned on at t = 2 ns. This led to gradual expansion of the micelle. The pseudoatoms were restrained to their initial positions during runs. We note that the slow-growth algorithm was used for preparing configurations only and not for its usual purpose, which is calculating free energy changes. As a result, we obtained micelles with cavities large enough for an RD molecule to be fitted. Then three configurations were prepared for each surfactant with the dye placed in three different orientations (Figure 1B). The cavities were then collapsed using the slow-growth algorithm applied in the reverse direction. The RD molecules were restrained to their initial positions and orientations, and their interactions with pseudoatoms were always turned off. In such a way, for each of the four systems (+D and +DH in SDS and CTAB), we obtained three equilibrated structures with the RD solubilized in micelle (Figure 1C). Finally, each obtained configuration was used as an initial configuration for a production run 90 ns long (in two cases, 130 ns long). In total, we performed three independent runs for each of the four systems. Additionally, four 31 ns simulations of the RD in pure water were carried out using the same conditions and the cell size of 6.5 nm. In initial configurations that we used, the dye was solubilized in micelles, but to check the correctness of this approach we also performed the simulations of +D in SDS solution from initial configurations having the dye molecule initially located in bulk water. This is discussed in more detail in section 3.5. The VMD software was used for visual examination of the trajectories and preparation of the figures.47
In each simulation, the RD molecule moved from the hydrocarbon core of the micelle to the surface region during the first several nanoseconds of the simulation. The rest of the time it resides at the micelle surface never desorbing to the bulk solution or solubilizing back. However, the phenyl substituents sometimes immerse into the hydrocarbon core. The dye molecule never overlaps surfactant headgroups, i.e., the situation, when a headgroup is located on a line between the micelle center and the dye never appears. The reverse situation, when a surfactant ion lies between the dye and water, appears infrequently for short (tens of picoseconds) time periods. Most of the time, the molecule is aligned flatwise on the surface of the hydrocarbon core, i.e., all phenyl rings lie on the surface. This makes the whole molecule exposed to water. The rotation of phenyl rings as well as the rotation around the PyPh bond are possible as in bulk water. In the less frequent orientation, the molecule is “inserted” into the micelle, i.e., one ortho-phenyl of the phenolate part and the nearest ortho-phenyl of the pyridinium part are immersed in the hydrocarbon core, while two other ortho-phenyls are surrounded with water. In order to provide a qualitative idea of typical dye orientations on studied micelles, several snapshots from MD trajectories are presented in Figures S1 and S2. We note that they are not a result of processing or averaging but are just instantaneous configurations. Now we will quantitavely describe the properties of the adsorbed dye. The last 80 ns of MD trajectories were used for computations, while the first 10 ns when the dye relocated from the micelle interior to the surface were not accounted for. For each system, values obtained from each of three independent runs were averaged, thus the results reported in the article correspond to 240 000 processed configurations. In two runs out of 12, the dye did not leave the micelle interior for 10 ns and stayed partially immersed for ∼40 ns; therefore, in these two cases, the simulations were extended by 40 ns, and the calculations were performed in 50130 ns intervals instead of 1090 ns. 3.2. Localization. The most common characteristics of the system structure are its radial distribution functions (RDFs). They can show the average localization of the dye in micelle, and, to the some extent, indicate its orientation. We plotted RDFs between (i) the micelle center of mass (COM) and (ii) N and O atoms of the dye and S (N) atoms of the surfactant (Figure 2). Each point of an RDF curve shows the scaled probability, g(r), of finding an atom of the given kind (dye N or O or surfactant S or N)
3. RESULTS AND DISCUSSION 3.1. General Overview. At first, we describe the picture qualitatively, in a general outline. Each micelle consists of a relatively dense hydrocarbon core, covered by a sparse layer, composed from headgroups, water molecules, and counterions. This layer is called the surface region or the Stern layer. 8345
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Figure 2. Radial distribution functions micelle COM−RD N (blue curves, 1) and micelle COM−RD O (red curves, 2) in comparison with RDFs micelle COM−surfactant S (N) (black curves, 3). Left: SDS solutions, right: CTAB solutions, top row: the neutral form, bottom row: the protonated form.
Figure 3. Left: sketch depicting the definition of the pitch angle θ, right: probability distributions of the angle θ. Blue curves (1) are for SDS solutions, red curves (2) are for CTAB solutions. Solid lines are for the neutral form, dashed lines with underlined numbers are for the protonated form.
on a particular distance, r, from the micelle COM. Consequently, the abscissas of peaks correspond to the preferable locations of these atoms relative to the micelle COM. The S (N) peak of the surfactant indicates both the radius and the thickness of the headgroups layer, which are related to those of the Stern layer. Therefore, it serves as a reference for estimating dye localization. On the other hand, the maximum on the dye N atom peak simultaneously shows the preferential location of the dye COM because these points are very close. At first, we examine the neutral form. It can be seen that, for each surfactant, the nitrogen atom is farther from water than the oxygen atom, and both atoms are located behind headgroups (looking from water). These observations suggest that in SDS micelles, the oxygen atom is better exposed to water, and in micelles of both kinds, the molecule is not parallel to the surface but is considerably pitched having the O atom protruding in water. The localization of the protonated form is similar to that of the neutral form, but the orientation is opposite. The molecule is pitched on the opposite side, i.e., the oxygen atom is located farther from water than the nitrogen atom. Moreover, in SDS
micelles, the O peak has considerable height near the origin, which indicates the occurrence of the orientation in which the phenolate part is deeply immersed into the micelle and the pyridinium part is pushed to the water. The area of the peak slice between 0 and 0.7 nm is 7.3% of the total peak area. We notice that in the case of micelle−dye systems, RDFs with respect to the micelle COM have intrinsic uncertainty because micelles have ellipsoidal, not spherical forms. Thus, the micellar surface is located not at a single distance from the center, but on distances ranging from the minor semiaxis to the major one. This also causes widening of the peaks on RDFs. However, this circumstance does not diminish the informativity of such RDFs. 3.3. Orientation. The next step is the more detailed description of the orientation of the RD molecule. In order to quantify it, we plotted a distribution function of the angle between (i) the vector from the micelle COM to the dye N atom, and (ii) the vector between dye N and O atoms, θ, Figure 3. It will be called the “pitch angle”. The dipole moments of both forms have nearly the same directions, which are close to the N−O axis of the molecules. Zero value of θ corresponds to the dye alignment along the micelle radius, when the N atom is immersed into 8346
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Figure 4. Left: definition of parts of the dye molecule, for which NCH values were calculated; right: their NCH values. The parts contained hydrogen atoms bonded to carbon atoms. Blue curves (1) are for SDS solutions, red curves (2) are for CTAB solutions. Solid lines are for the neutral form; dashed lines with underlined numbers are for the protonated form.
small rotations of the latter lead to large displacements of the former. In addition to average NCH values of groups, we also calculated average magnitudes of the differences between solvation numbers of ortho-phenyl substituents connected to the same ring (either phenolate or pyridinium). These ΔNCH values clearly indicate the average inclination of the dye molecule around the N−O axis: the highest magnitudes are achieved when one Ph substituent is deeply immersed into a micelle core, while the second Ph substituent is predominately surrounded by water. On the contrary, when both phenyls are located in the same region, this difference is close to zero. The NCH and ΔNCH values are collected in Table S1 and also plotted in Figure 4 to facilitate the comparison between all four systems. The uncertainties are calculated based on the variation of the same quantity between three runs. We also found the maximum solvation numbers, which were reached during MD runs, in order to establish the scale of NCH values, Table S2. They were calculated as the highest average values observed on short 10 ps trajectory intervals. The obtained numbers vary around ∼48 atoms for phenyl rings and around ∼13 for the O atom. First, this information allows one to estimate the significance of the difference between calculated NCH values. Second, the fact that the maximum NCH are similar for SDS and CTAB micelles proves that NCH values are accurate measures of the dye orientation, independent from the surfactant tail length and details of the micelle shape. The obtained results agree with those of the geometry-based approaches but are more exact. For the neutral form, the trend of changing NCH values along the dye molecule proves the conclusion that in micelles of both kinds, the molecule is advanced to water with the phenolate part, while the pyridinium part is immersed into the micelle. The pitch angle is higher on an SDS micelle. Interestingly, as it follows from the average magnitude of the difference between solvation numbers of the phenolate phenyl substituents, ΔNCH, in CTAB micelles, the phenolate part of the dye molecule is aligned considerably more aslant to the surface than in SDS ones (ΔNCH is higher on 6.2 atoms), while the inclinations of the pyridinium part are similar. The protonated form is oriented in a similar way in micelles of both kinds too, and has the phenolate part immersed into micelle deeper than the pyridinium part. 3.4. Microenvironment. The localization and orientation of the dye molecule themselves do not determine the spectrum of the RD. The final factor that impacts measured polarity
micelle and the O atom is pushed to water, and the value 180° indicates the inverse orientation. The right angle corresponds to the orientation with both N and O atoms located in the same micelle region at equal distances from its center. It should be noted that in the case of micellar systems, this angle describes the orientation only approximately because micelles have nonspherical and very rough shape; therefore, the surface around a given point is usually not perpendicular to its radius vector. For the neutral form, it can be seen that (i) the preferential/ average θ values are from narrow to right (74°/66° in SDS micelles and 82°/75° in CTAB ones), which means that the O atom protrudes into water, and (ii) in SDS this effect is more pronounced than in CTAB. The protonated form (i) is aligned oppositely with corresponding preferential/average θ values from right to obtuse (90/102° and 108/102° in SDS and CTAB micelles correspondingly), (ii) has a much broader distribution of orientations, and (iii) for SDS micelles, there is a pronounced peak at 127°, corresponding to a distinct secondary orientation with the N atom strongly protruded in water. This analysis confirms the conclusion made during RDF examination and shows that, in general outline, each form is oriented similarly in micelles of both kinds, while the more detailed examination shows a considerable difference (∼9° for the neutral form). Because the described characteristics have the intrinsic uncertainty caused by the complex character of micelle shape, we also employed an approach that does not require assumptions about micelle shape. In order to accurately assess the average orientation of the dye molecule, we calculated the numbers of contacts between different parts of the molecule and the micelle hydrocarbon core, NCH. This quantity was defined as the average number of C and H atoms, belonging to surfactant ions, found in a 0.4 nm vicinity of a given group of atoms. For CTAB, the CHn groups bonded to the N atom were considered as belonging to the headgroup and excluded from the NCH computations. For simplicity, NCH will be called the “solvation number”. If a group has the same solvation numbers in micelles of both kinds, we can assume that it is positioned on average in the same region of the micelle-water interface. Consequently, the set of solvation numbers of all groups define the average localization and orientation of the whole molecule, and do this in a way that is convenient for quantitative comparison. For phenyl rings, we used only carbon atoms in the 3′, 4′, and 5′ positions and hydrogen atoms bonded to them in calculations (Figure 4) because these atoms are located far from each other and, thus, have nonintersecting microenvironments. Moreover, they are located far from the center of the dye molecule, therefore 8347
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Table 1. Average Numbers of Various Atoms in Microenvironments of the Whole Dye Molecule and Its O Atom on Different Micellesa system
micelle core
water
headgroups
counterions
total
0.37 ± 0.03 0.34 ± 0.016
218 ± 11 214 ± 7 202 ± 7 220 ± 3 213 ± 6 206 ± 6
Dye Molecule D in SDS D in CTAB
120 ± 5 132 ± 3
89 ± 5 65 ± 4
DH in SDS DH in CTAB
123.2 ± 1.7 118 ± 3
82.8 ± 1.6 85 ± 3
+
D in SDS + D in CTAB
2.6 ± 0.17 3.9 ± 0.10
10.29 ± 0.04 5.06 ± 0.06
+
8.3 ± 0.3 7.1 ± 0.8
3.2 ± 0.2 3.3 ± 0.6
+ +
+ +
8.4 ± 0.7 17.0 ± 0.3 4.8 ± 0.1 13.5 ± 0.16 9.0 ± 0.4 2.2 ± 0.11
0.29 ± 0.03 0.52 ± 0.03
O Atom
DH in SDS DH in CTAB
+
a
0.032 ± 0.007 4.5 ± 0.16 1.40 ± 0.08 0.38 ± 0.06 1.3 ± 0.3 0.35 ± 0.09
0.10 ± 0.02
