Effects of Hydrotropic Salt on the Nanoscopic Dynamics of DTAB

Article pubs.acs.org/JPCB

Effects of Hydrotropic Salt on the Nanoscopic Dynamics of DTAB Micelles V. K. Sharma,† H. Srinivasan,† S. Mitra,† V. Garcia-Sakai,‡ and R. Mukhopadhyay*,† †

Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India ISIS Facility, Science and Technology Facilities Council, Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom

‡

ABSTRACT: Effects of a hydrotropic salt, sodium salicylate (NaSal), on the dynamic behavior of cationic dodecyltrimethylammonium bromide (DTAB) micelles as studied using dynamic light scattering (DLS) and quasielastic neutron scattering (QENS) techniques are reported here. DLS study showed that the addition of NaSal leads to a decrease in the apparent diffusion coefficient of the whole micelle indicating micellar growth. QENS data analysis suggested that observed dynamics involves two distinct motions, lateral motion of the surfactant over the curved micellar surface and localized segmental motion of the surfactant. It is found that the addition of NaSal slows down the lateral motion of DTAB while the localized segmental motion of the DTAB chain is not affected much. An atomistic molecular dynamics (MD) simulation was performed to gain further insight into the underlying phenomena. MD simulation results are found to be consistent with the experimental observations. MD simulation revealed that location of the salicylate ions on the micellar surface and their strong electrostatic association with their oppositely charged surfactant headgroup are the major factors in slowing down the lateral motion of the DTAB molecule. In the present work, a quantitative description of the effects of NaSal on the nanoscopic dynamics of DTAB micelles and its correlation with the microstructure of the micelle is provided.

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has been studied extensively.4−10 It has been shown that the salicylate counterion interacts with the surfactant electrostatically as well as hydrophobically, and the orientation of the salicylate ion at the micellar surface has a predominant role in the growth of the micelles. Rheology measurements have also shown interesting viscoelastic properties of cationic micelles such as double peak behavior in the zero shear viscosity as a function of concentration of NaSal.6 Small angle neutron scattering (SANS) measurements5−7 showed that the addition of NaSal induces micellar growth, and rodlike micelles are formed. However, the effect of NaSal on the dynamic behavior of micelles and the correlation with their microstructures has not been investigated in detail. The local dynamics of micelles is important in understanding various properties such as the release mechanism of solubilized drugs, micellar breaking time, and synthesis of nanoparticles, among others. The mobility of the aliphatic chains gives indications of how different species diffuse within the micelles through its interior. Different kinds of motion take place in micellar solutions such as diffusion of whole micelles, lateral motion of the surfactant molecules over the curved surface of the aggregates, segmental motions of the surfactant chain, and torsional motions, etc.11−14 Dynamics of self-assembled aggregates can

INTRODUCTION Surfactant molecules in aqueous solution, above the critical micelle concentration, self-assemble into a wide variety of morphological structures like micelles, lamellar sheets, bicontinuous phases, etc. The size and shape of the aggregates is a complex interplay of geometry, charge, concentration of surfactant, and physicochemical conditions such as temperature, ionic strength, and concentration of the electrolyte.1,2 The geometry of the aggregates formed by the surfactant molecules is a consequence of a delicate balance of two opposing forces. The tail−tail attractive hydrophobic interaction provides the driving force for the aggregation of surfactant molecules, while the electrostatic and steric repulsion between headgroups limits the size of micelles. Electrostatic repulsion between the charged headgroups can be screened by the addition of electrolyte or salt which induces the micellar transition from spherical to rodlike structures. Compared to inorganic counterions, organic counterions bind more strongly to the micellar surface and are highly efficient in promoting micellar growth or inducing wormlike micelles.3,4 Here, our interest is in an important class of organic salts, sodium salicylate (NaSal), which belongs to the hydrotrope family. Hydrotropes are a class of compounds which enhance the solubility of hydrophobic compounds in water. NaSal is also an analogue of aspirin, and acts as nonsteroidal anti-inflammatory drug for antipyretic and analgesic actions. The effect of NaSal on the structure and macroscopic behavior of cationic micelles © 2017 American Chemical Society

Received: March 29, 2017 Revised: May 1, 2017 Published: May 11, 2017 5562

DOI: 10.1021/acs.jpcb.7b02976 J. Phys. Chem. B 2017, 121, 5562−5572

Article

The Journal of Physical Chemistry B

Figure 1. Variation of autocorrelation functions with delay for (a) DTAB micelles with and without NaSal at 300 K and (b) DTAB micelles with NaSal at three different temperatures, namely, 300, 315, and 330 K. Inset shows variation of obtained apparent diffusion coefficient from DLS data with temperatures. (c) Size distribution of DTAB micelles at 300 K and DTAB micelles with NaSal at 300, 315, and 330 K.

NaSal at 300 K using nanoparticle size analyzer SZ-100 (Horiba). The wavelength of the incident laser light was 5320 Å, and the data were collected at the scattering angle 173° using a photomultiplier tube detector. For an investigation of the effect of temperature, DLS measurements have also been carried out on DTAB micelles with NaSal at 315 and 330 K. QENS experiments have been carried out on 300 mM DTAB micellar solution with and without NaSal at 300, 315, and 330 K using the high energy resolution IRIS spectrometer at ISIS facility, UK.28 It would have been ideal to use fully deuterated NaSal in the QENS experiment. However, protonated NaSal has been used which contributes about 6% to the total scattering signal. IRIS was operated with the pyrolytic graphite (002) analyzer in the offset mode. For the chosen experimental setup, the spectrometer had an energy resolution 17 μeV (full width at half-maximum), and the energy transfer range was −0.3 to 1.0 meV. The wave-vector transfer (Q) range covered was 0.5−1.8 Å−1. QENS spectra were also recorded from pure D2O at 300, 315, and 310 K for reference. For the instrument resolution, QENS measurements were carried out on a standard vanadium sample. The samples were placed in an annular aluminum can with an internal spacing of 1 mm to minimize multiple scattering and have reasonable measuring statistics. MANTID software29 was used to carry out standard data reduction including background subtraction and detector efficiency corrections.

be studied experimentally using dynamic light scattering (DLS),3,15,16 nuclear magnetic resonance (NMR),11,17 tracer diffusion,14,18 and quasielastic neutron scattering19−26 techniques. While diverse experimental techniques have been used to study the dynamics of micelles, most of these are only capable of observing a single aspect of the dynamics on a limited time and length scale. DLS is widely used to measure diffusion on the length scale of over a micrometer and the time scale longer than nanoseconds.15,16 Quasielastic neutron scattering (QENS) is suited for the study of the microscopic dynamics of micelles on a pico- to nanosecond time scale and on a length scale from angstroms to tens of nanometers.23−26 Molecular dynamics (MD) simulations cover the same length and time scales as QENS and can be used in synergy to provide a detailed picture of the relaxation process in the micellar systems.4,26,27 Here, we report the effects of NaSal, a salt with pharmaceutical significance, on the dynamic behavior of cationic dodecyltrimethylammonium bromide (DTAB) micelles as studied using DLS, QENS, and MD simulation techniques. The effect of salt on the diffusion of the whole micelle has been investigated using DLS. Lateral and segmental motions of surfactant molecules within the micelles and the effect of NaSal on these motions have been investigated using QENS and MD simulation techniques. The results obtained from DLS, QENS, and MD simulation have provided a comprehensive picture of the effects of NaSal on the dynamics of the micelle in a wide range of time scales from microseconds to picoseconds.

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EXPERIMENTAL DETAILS DTAB, NaSal, and D2O (99.9% atom D purity) were purchased from Sigma-Aldrich. Micellar solutions were prepared by dissolving DTAB in D2O with and without NaSal salt. For the present study, the molar ratio between NaSal and DTAB was kept fixed and equal to 1. DLS measurements have been carried out on 50 mM DTAB solution with and without 50 mM

RESULTS AND DISCUSSION

Dynamic Light Scattering. In a dynamic light scattering measurement, the characteristic time of fluctuations in the scattered intensity is measured, and it depends on the diffusion coefficient of the particles undergoing Brownian motion.15,16 The normalized time correlation function of the scattered intensity at a particular angle, g2(τ), is given as 5563


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Figure 2. (a) Typical observed QENS spectra for DTAB micellar solution and D2O at 300 K. Contribution of pure DTAB micelles after subtracting the contribution of D2O is also shown. Peak normalized QENS spectra for DTAB micelles with and without NaSal at (b) 300, (c) 315, and (d) 330 K. Instrument resolution as measured from standard vanadium is also shown in the right top panel. All the QENS spectra shown here are at Q = 1.22 Å−1.

g 2 (τ ) =

I (t ) I (t + τ ) I (t ) 2

The intensity autocorrelation function for DTAB micelles with and without NaSal at 300 K as measured using DLS is shown in Figure 1a. It is clear from Figure 1a that, because of the addition of NaSal, the autocorrelation function showed much slower decay compared to that of pure DTAB micelles. This suggests a decrease in the diffusion coefficient of the whole micelle. Figure 1b shows measured autocorrelation functions for DTAB micelles with NaSal at three different temperatures. It is evident that, as the temperature increases, the autocorrelation function decays more quickly indicating faster diffusion of the micelle. The combination of both the effects, i.e., increase in the thermal energy and decrease in the micellar size, is responsible for the faster decay of the autocorrelation function at higher temperature. Measured autocorrelation functions are analyzed using eqs 2 and 4, and for DTAB micelles at 300 K, the apparent diffusivity of the whole micelles (Da) is found to be 8.1 × 10−7 cm2/s. This is in very good agreement with the value (∼9 × 10−7 cm2/ s) obtained for diffusion of DTAB micelles using the tracer diffusion technique.18 It is found that, because of the addition of NaSal, Da of DTAB micelles reduces to 1.9 × 10−7 cm2/s. The variation of Da with temperature for DTAB micelles with NaSal is shown in the inset of Figure 1b. It is evident that, as the temperature increases, Da increases. The observed trend in the apparent diffusion coefficients can be correlated to the changes in the microstructure. The size distributions of the DTAB micelles with and without NaSal salt, obtained by employing CONTIN analysis,31 are shown in Figure 1c. It is evident that, because of the addition of NaSal, the mean of the size distribution shifts to a larger value indicating growth of the micelles. It is also clear that, at 300 K, in the presence of NaSal, the size distribution of DTAB micelles is much broader, which could be due to the combined effects of a rodlike structure and a relatively higher polydispersity. This is consistent with the earlier SANS studies which had indicated an induced growth of the micelles because of the addition of NaSal salt.5−7 It has been shown that the size of rodlike micelles follows an exponential distribution, which gives rise to high polydispersity.6 As the temperature increases, the mean of the size

(1)

where τ is the correlation delay time. I(t) and I(t + τ) represent the intensity of the scattered light at time t and (t + τ). For photo counts obeying Gaussian statistics, g2(τ) is related to the first-order autocorrelation function of the electric field g1(τ) by the relationship15 g 1(τ ) = [g 2(τ ) − 1]0.5

(2)

For a suspension of monodisperse, spherical particles undergoing Brownian diffusion, the field autocorrelation function decays exponentially. However, in the case of a polydisperse continuous distribution, the field autocorrelation function can be written as g 1(τ ) =

∫0

∞

G(ΓDLS) exp( −ΓDLSτ ) dΓDLS

(3)

The distribution G(ΓDLS) represents the relative intensity of light being scattered with relaxation rate ΓDLS and will be a function of the number and size of scatterers. For narrow polydispersity, the above expression can be simplified to the well-known cumulant expansion30 ln(g 1(τ )) = b − ΓDLSτ +

μ2 τ 2 2

(4)

where the first and second cumulants, ΓDLS and μ2, give the mean and variance, respectively. The ratio of the variance to the square of the mean is a measure of the polydispersity in the diffusion coefficient and is represented by the polydispersity index (PI). From the average relaxation rate ΓDLS, the apparent diffusion coefficient of the particle Da can be obtained using ΓDLS = DaQ2. The value of Da is apparent since the presence of intermicellar interaction and anisotropy influences the diffusion of the whole micelle. For the minimization of intermicellar interaction in pure DTAB micelles, DLS experiments were carried out in dilute solution (50 mM DTAB) and in the presence of a small amount of electrolyte (50 mM NaCl). 5564


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The Journal of Physical Chemistry B distribution shifts to a lower value indicating that temperature has the reverse effect as compared to that from the addition of salt; the size of micelles reduces, and they tend toward a spherical shape. Size distribution of the micelles is also found to be narrower with increasing temperature because of the lower polydispersity at higher temperature. Even at 330 K, the mean of the size distribution of DTAB with NaSal is larger compared to that of pure DTAB micelles at 300 K. Neutron Scattering. As stated earlier, different kinds of motion exist in micelles such as the diffusion of whole micelles, lateral motion of the surfactant molecules, and segmental motion within surfactant chains, etc. To proceed with the data analysis, it is customary to separate the contribution from different kinds of motions according to their time scales. It is assumed that these contributions are independent of each other. It is also known that, with the addition of organic salt, the size of the micelles increases drastically. Since the global diffusion of the whole micelles is directly related to size of the micelles through the Stokes−Einstein relation, the addition of salt is expected to alter the global diffusion of the whole micelle. Our present DLS study also showed this (Figure 1a). However, no such correlation between the size of the micelles and the lateral motion of the monomers is known. For pure micelles, since the time scales of the lateral motion of the surfactant and global motion of the micelles are very similar,23,32 it is difficult to identify which motion is actually contributing to the QENS data. The present QENS study on DTAB micelles with and without NaSal may help to resolve whether lateral or global motion is contributing to the QENS data. For the QENS experiments, D2O is used as the solvent to minimize the scattering contribution from the solvent. Spectra from D2O are scaled by the volume fraction of the solvent in the micelles and are subtracted from those measured for the micellar solutions. Subtracted QENS spectra correspond solely to the contribution from the micelles. A comparison of QENS spectra for DTAB micellar solution and D2O at 300 K at Q = 1.22 Å−1 is shown in Figure 2a. Prior to any quantitative analysis, we first start with a qualitative data comparison between DTAB micelles with and without NaSal to examine the trend. Significant quasielastic broadening is observed for micelles with and without NaSal over the instrument resolution as shown in Figure 2b. Furthermore, broader quasielastic spectra are observed for pure DTAB micelles compared to those for the DTAB with NaSal at all the measured temperatures (Figure 2b−d) indicating that the addition of salt hinders the dynamic motion of micelles. Dynamic susceptibility is a powerful tool to find out the number of relaxation processes without employing any detailed data analysis. This approach is possible since a relaxation process with a characteristic time (τ) shows a peak in the dynamic susceptibility at energy transfer E = ℏ/τ, where ℏ is the reduced Planck’s constant. The scattering data was converted into the imaginary component of dynamic susceptibility, χ″(E), by dividing the Q-averaged intensity, S(E), with Bose population factor, nB(E) ≈ kBT/E (under the approximation that E ≪ kBT), where kB is the Boltzmann constant and E = ℏω is energy transfer. Profiles of χ″(E) versus E for DTAB micelles with and without NaSal at 300 K are shown in Figure 3. A major conclusion that can be drawn from the susceptibility spectra is that the dynamics of DTAB micelles with and without NaSal cannot be viewed as a single relaxation process. The occurrence of minima in the susceptibility spectra indicates that there are two relaxation

Figure 3. Dynamic susceptibility, χ″(E), values for the DTAB micelles in the presence and absence of NaSal salt at 300 K.

processes present in the micelles both with and without NaSal salt. This minimum separates the faster dynamics observable at higher energy transfer from the slower dynamics at ∼0.1 meV. Earlier QENS studies on micelles13,23−25 showed that slower dynamics is purely translational and faster dynamics is localized in nature. Slower purely translational motion could be either global motion of the whole micelle or the lateral motion of the monomers, while faster localized dynamics could be segmental motion of the monomers. Average characteristic relaxation times (τ’s) from the first peak of the dynamic susceptibility are obtained to be 7.3 and 6.3 ps for DTAB micelles with and without NaSal, respectively. It is evident that τ is found to increase with the inclusion of NaSal, indicating hindrance in the dynamics in DTAB micelles with NaSal. Average relaxation times are obtained for other temperatures as well and found to decrease with the increase in temperature for both the systems. Our DLS measurement revealed that, at 300 K, the global diffusion coefficient for the pure DTAB micelle changes from ∼0.8 × 10−6 to 2 × 10−7 cm2/s with the addition of NaSal. If one assumes that the nonlocalized translational motion is global motion of the whole micelle, then, in the case of DTAB micelles with salt, only segmental motion should contribute to the QENS data since the time scale corresponding to a global diffusion coefficient of 2 × 10−7 cm2/s is not accessible by IRIS spectrometer (fwhm = 17 μeV). In that case, one elastic component is expected in the QENS spectra because of the localized nature of segmental motion. However, data analysis showed that no such elastic component is necessary to describe the QENS data from micelles with salt, and two distinct motions are observed to be very similar to those of the pure DTAB micelles. This indicates that dynamics present in the QENS spectra other than the segmental motion of the alkyl chain cannot be the global motion of the whole micelle. With the consideration of this motion as lateral motion of the monomer and the approximation that lateral and segmental motions are decoupled, the Q-averaged scattering law of micelles can be written as Smicelles(Q , ω) = [S lat(Γlat, ω) ⊗ Sseg(Γseg , ω)]

(5)

where Slat(Γlat, ω) and Sseg(Γseg, ω) represent the scattering law values corresponding to the lateral and segmental motions of the surfactant molecules, respectively. Lateral motion of the surfactant is characterized by continuous diffusion,20−22 and hence, the associated scattering law can be expressed as 5565


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Figure 4. Typical fitted QENS spectra for (a) DTAB micelles and (b) DTAB micelles with NaSal assuming the model scattering function as described in eq 8 at Q = 1.22 Å−1 at different temperatures.

S lat(Q , ω) = L lat(Γlat, ω) =

Γlat 1 π Γlat 2 + (ℏω)2

above scattering law describes the observed QENS data well for micelles with and without salt for all available Q values at all the measured temperatures. Typical fitted QENS spectra for DTAB micelles with and without salt at Q = 1.22 Å−1 at different temperatures are shown in Figure 4. Lateral Motion. Variation of the HWHM of the Lorentzian function (Γlat), corresponding to the lateral motion, with Q2 for DTAB micelles with and without NaSal is shown in Figure 5. It is clear that Γlat increases linearly with Q2 indicating that the lateral motion follows continuous diffusion, which can be described by a simple Brownian motion using Fick’s law, Γlat = DlatQ2, where Dlat is the lateral diffusion coefficient. Solid lines in Figure 5 correspond to the description as per Fick’s law. Variation of Dlat as obtained for DTAB micelles with and without NaSal with temperature is shown in Figure 6. It is evident that the lateral diffusion coefficient for DTAB is found to be lower in micelles with NaSal compared to that in pure micelles at each measured temperature. For example, at 300 K, the lateral diffusion coefficient, Dlat, for pure DTAB micelles is found to be (3.1 ± 0.2) × 10−6 cm2/s which is in close agreement with the value (4.7 × 10−6 cm2/s) obtained for the lateral diffusion coefficient of DTAB by the tracer diffusion technique.14 It is found that, because of the addition of NaSal, the lateral diffusion coefficient of DTAB at 300 K reduces to (2.4 ± 0.1) × 10−6 cm2/s. At 330 K, Dlat for pure DTAB micelles is found to be (5.2 ± 0.3) × 10−6 cm2/s, which reduces to (3.5 ± 0.2) × 10−6 cm2/s for DTAB micelles with NaSal. It is evident that the addition of NaSal restricts the lateral motion of DTAB. Electrostatic interaction between the salicylate counterion and cationic headgroup, obstruction and reduction in free volume, might lead to the hindrance in the lateral diffusion of the surfactant.

(6)

where Γlat is the HWHM of the Lorentzian corresponding to lateral motion of the surfactant. For the segmental motion of the surfactant, which is localized in character, the scattering law can be written as19 Sseg(Q , ω) = A(Q ) δ(ω) + (1 − A(Q ))Lseg (Γseg , ω) (7)

where the first term represents the elastic component, and the second term represents the quasielastic component. The fraction of elastic scattering in the total spectra is called the elastic incoherent structure factor (EISF). Therefore, A(Q) in eq 7 is nothing but the EISF, which represents the space Fourier transform of the particle distribution, taken at infinite time and averaged over all the possible initial positions. The EISF provides information about the geometry of the molecular motion. Γseg is the HWHM of the Lorentzian corresponding to segmental motion. Hence, the resultant scattering law for micelles can be written as Smicelles(Q , ω) = [A(Q )L lat(Γlat, ω) + (1 − A(Q ))L tot(Γlat + Γseg , ω)]

(8)

For QENS data fitting, eq 8 has been convoluted with the instrumental resolution function as measured with a vanadium standard, and the parameters A(Q), Γlat, and Γseg were determined by a least-squares fit of the measured spectra. No parameter is constrained or fixed during the fitting. Program DAVE33 developed at the NIST Center for Neutron Research was used for the fitting of the QENS data. It is found that the 5566


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diffusion within a confined space.19,34 More quantitative and detailed models of the segmental motion23,24,26 have been used under the assumption that the hydrogen atoms at different positions along the chain can move within spheres of different radii, because of the flexibility of the alkyl chain. Here, we have employed a rather simple model mainly to estimate the effect of salt on the segmental dynamics. In this model, it is assumed that only a fraction of hydrogen atoms are undergoing localized translational diffusion within a sphere. This model could describe the data reasonably well for DTAB micelles with and without NaSal. EISF for this model can be written as13,25 ⎡ 3j (QR ) ⎤2 ⎥ A(Q ) = px + (1 − px )⎢ 1 ⎣ QR ⎦

(9)

where px is the fraction of hydrogen atoms that are immobile on the observation time scale, and R is the radius of the assumed spherical domain of dynamics. Equation 9 has been used to describe the observed EISF, and as evident from Figure 7a, this model successfully describes the observed EISF for DTAB micelles with and without salt. At 300 K, for DTAB micelles, px = 35%, and R = 2.5 Å indicating that on average about 65% of the hydrogen atoms are participating in the segmental motion, undergoing localized translational diffusion within a sphere of radius 2.5 Å. As the temperature increases, though the fraction of immobile hydrogen atoms decreases, the radius of the sphere remains more or less the same. This can be explained by the fact that as temperature increases, a higher proportion of hydrocarbon chains take part in the dynamics. It is found that the addition of NaSal does not affect the segmental motion of DTAB, and the values of px and R are very close to those of a pure micellar system. For example, at 330 K, for DTAB micelles with NaSal, px and R are found to be 22% and 2.8 Å, respectively, which are very similar to those found for pure DTAB micelles. The obtained values of px and R at different temperatures for DTAB and DTAB + NaSal micelles are given in Table 1. The time scale of the segmental motion can be quantitatively obtained by the detailed analysis of the HWHM of the Lorentzian function. For the fractional localized translational diffusion model, the scattering law can be written as34

Figure 5. Variation of HWHM of the Lorentzian corresponding to lateral motion of the surfactant in DTAB micelles with and without NaSal salt, at different temperatures.

⎡ ⎡ 3j (QR ) ⎤2 ⎤ ⎥ ⎥δ(ω) Sseg(Q , ω) = ⎢px + (1 − px )⎢ 1 ⎢ ⎣ QR ⎦ ⎥⎦ ⎣

Figure 6. Comparison of the lateral diffusion coefficient in DTAB micelles with and without NaSal salt. It is evident that at all the measured temperatures lateral diffusion of DTAB is restricted because of the presence of NaSal salt.

⎡ 1 + (1 − px )⎢ ⎢⎣ π

Segmental Motion. As described earlier, the scattering law (eq 8) for micelles has contributions from the lateral motion of the surfactant and the segmental motion within it. The segmental motion is characterized by the EISF and HWHM of the Lorentzian function (eq 7). However, as can be seen from eq 8, the width of the second Lorentzian is actually the sum of the widths of the Lorentzians corresponding to lateral and segmental motions. As the width of the lateral motion is already known, the HWHM corresponding to segmental motion, Γseg, can be obtained by subtracting the width of the first Lorentzian, Γlat, from the width of the second Lorentzian. The Q dependence of the EISF and HWHM corresponding to segmental motion is shown in Figure 7a,b, respectively. It is evident from Figure 7b that, for DTAB micelles with and without NaSal, Γseg flattens at low Q. However, at higher Q, it increases as Q2. This is a signature of localized translational

∑ {l , n} ≠ {0,0}

(2l + 1)A nl(QR )

(xnl)2 Dseg /R2 l 2 [(xn) Dseg /R2]2 + (ℏω)2

⎤ ⎥ ⎥⎦

(10)

where with (n, l ≠ 0, 0) is the quasielastic structure factor, and values of it for different n and l can be calculated by using the values of x1n.34 Dseg is the diffusion coefficient for segmental motion. Since no analytical expression exists for the HWHM of the quasielastic part unlike that for the EISF, the HWHM can be calculated numerically (using eq 10) for given values of R and Dseg. The least-squares fitting method is used to describe the observed Γseg with Dseg as parameters, while the value of R is already known from the fit of the EISF. It is found that the model describes the obtained HWHM well as shown by  in Figure 7b. The diffusion coefficient corresponding to segmental motion for pure DTAB micelles, Dseg, at 300 K is found to be (11.1 ± 0.7) × 10−6 cm2/s which increases to (15.2 ± 0.8) × 10−6 cm2/s at 330 K. Addition of NaSal does not Aln(QR)

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Figure 7. (a) EISF and (b) HWHM for segmental motion of DTAB within micelles in the absence and presence of NaSal. Solid lines are the fits assuming the fractional localized translational diffusion model as described in the text.

Table 1. Fraction of Immobile Hydrogen Atoms, Radius of the Spherical Domain of Dynamics, and Diffusivity Corresponding to the Segmental Motion of the DTAB Molecules for DTAB Micelles with and without NaSal Salt DTAB temp (K) 300 315 330

−6

Dlat × 10

2

cm /s

3.1 (2) 4.4 (2) 5.2 (3)

DTAB + NaSal

px (%)

R (Å)

35 (2) 32 (2) 21 (2)

2.5 (2) 2.6 (2) 2.8 (2)

−6

Dseg×10

2

cm /s

11.1 (7) 13.7 (7) 15.2 (8)

−6

Dlat × 10

2

cm /s

2.4 (1) 3.0 (2) 3.5 (2)

px (%)

R (Å)

Dseg×10−6 cm2/s

41 (3) 33 (2) 22 (2)

2.5 (2) 2.6 (2) 2.8 (3)

10.3 (6) 13.4 (7) 14.1 (7)

Figure 8. Snapshots of (a) cylindrical pure DTAB micelles at 0, 2, and 3 ns, and (b) cylindrical DTAB micelles in the presence of NaSal at 0, 5, and 20 ns.

Molecular Dynamics Simulation. MD simulations can offer microscopic insights, which can aid us in understanding the obtained experimental results. Therefore, we have carried out atomistic MD simulations using NAMD 2.1135 with CHARMM 3636 force field parameters and the TIP3P37 water model. CGenFF (force field version 3.0.1) was used to obtain the charges and the parameters for the salicylate ion.38 The equations of motion were integrated at a time step of 1 fs. Electrostatic interactions were treated using the particle-mesh

affect the segmental motion much; for example in the case of DTAB micelles with NaSal, at 300 K, Dseg is found to be (10.3 ± 0.6) × 10−6 cm2/s which is slightly lower than the observed value for pristine DTAB micelles. As the temperature increases, Dseg for DTAB micelles with NaSal increases, and at 330 K it is found to be (14.1 ± 0.7) × 10−6 cm2/s. Our study reveals that the addition of the organic salt affects the lateral motion of the surfactant significantly while the segmental motion of the surfactant is more or less unaffected. 5568


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Figure 9. Intermediate incoherent scattering function, I(Q, t), calculated from MD simulation at different Q values.

cylindrical micelle suggesting a strong interaction of salicylate ions with DTA+ surfactants. The stability of spherical and cylindrical DTAB micelles in the absence and presence of NaSal, respectively, is in good agreement with the experimental observations.6,7,41 For a comparative study of the dynamics of pure DTAB micelles with respect to DTAB micelles in the presence of NaSal, a simulation of pure DTAB spherical micelles was also carried out. There were 50 DTA+ monomers arranged in a spherical micellar form and then solvated with water and bromide ions using Packmol. Equilibration runs of 20 and 10 ns were carried out for cylindrical DTAB micelles with NaSal and spherical pure DTAB micelles, respectively. This was followed by a production run of 5 ns for both the systems, with a trajectory recording interval of 2 ps. The incoherent intermediate scattering function, I(Q, t), for all hydrogen atoms of DTAB micelles was calculated for both the systems in the Q range 0.6−1.8 Å−1 for a comparison with the neutron scattering results. Typical calculated I(Q, t) values for DTAB micelles with and without NaSal are shown in Figure 9 at different Q values. It is evident from Figure 9 that the I(Q, t) decays much faster, at all the Q values, for pure DTAB micelles compared to that of DTAB micelles with NaSal, indicating restricted micellar dynamics because of the addition of NaSal. It has been found that the calculated I(Q, t) for DTAB micelles with and without NaSal could be described well assuming three dynamic processes corresponding to lateral, segmental, and faster torsional motions of the surfactant. These three processes had been observed in the QENS data in a wide energy transfer range for CTAB micelles.12 In that case, I(Q, t) could be written as

Ewald sum with a grid size of 1 Å. Short-range forces were modeled with a Lennard-Jones interaction with a cutoff of 12 Å. The Langevin piston method39 was used to keep the temperature and pressure constant to simulate the system in an NPT (constant temperature, constant pressure) ensemble. The temperature of the system was set to 300 K, and the target pressure was set to 1 bar. Semi-isotropic pressure coupling was enforced where the z-direction of the box was allowed to vary independently of the x- and y-directions. In general, DTAB surfactant forms spherical micelles in aqueous solution. However, in the presence of the external electrolyte NaSal, the structure becomes modified, and rodlike micelles are observed.5−7 Molecular dynamics simulations have been carried out for cylindrical DTAB micelles with and without equimolar NaSal. A method used by Wang and Larson4 was used to assemble a cylindrical micelle. A circular slice of DTA+ monomers with their principal axis along radial directions and with an angular spacing of 40° was constructed. There were 20 such slices stacked along the z-direction of the box with an initial spacing of 5 Å, with each subsequent slice rotated by 20° around the z-axis. The radius of the inner void, which is the distance between the cylindrical axis and the terminal carbon atom in the tail of the assembled structure, was set to be 3 Å initially. The arranged cylindrical micelle was made of 180 DTA+ monomers. The cylindrical micelle was then solvated with water, NaSal, and bromide ions using the Packmol package.40 It is found that, in the absence of NaSal salt, cylindrical micelles break into smaller spherical micelles within 3 ns. Figure 8a shows snapshots of this at t = 0, 2, and 3 ns. The cylindrical micelle breaks into three parts, which is in concurrence with the typical aggregation number of pure DTAB spherical micelles in water.41 However, in the presence of equimolar NaSal, the simulation was extended to 75 ns just to verify the stability of the cylindrical micelle, and it was found to remain intact. The snapshots of the DTAB micelles in the presence of NaSal at t = 0, 5, and 20 ns are shown in Figure 8b. It is evident that, at ∼20 ns, the salicylate ions become condensed at the surface of the

I(Q , t ) = A1 exp( −Γlatt ) + A 2 exp( −Γlat + segt ) + (1 − A1 − A 2) exp(−Γfastt )

(11)

A typical fit of I(Q, t) for the DTAB micelle with NaSal at Q = 1.0 Å−1 is shown in Figure 10. The Γ corresponding to the fast component (∼1 ps−1) is beyond the range of the present neutron spectrometer, IRIS. The Γ values corresponding to the 5569


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Figure 12. Angular distribution of the angle between the axis of the DTAB and nearby salicylate ions within a radius of 5 Å from the DTAB headgroup (inset shows the specified angle).

Figure 10. Typical fit of the I(Q, t) at Q = 1.0 Å−1 for DTAB + NaSal assuming eq 11.

lateral and segmental motions, as obtained from the fit for DTAB micelles with and without NaSal, are found to agree well with the experimental values. Figure 11a shows the variations of Γlat and Γseg obtained from both the MD simulation for the DTAB micelle with NaSal and the neutron experiments for direct comparison. As can be seen from Figure 11a, the Γlat and Γseg values as obtained from QENS experiments corroborate with those of the MD simulation. The variation of the Γlat for DTAB micelles with and without NaSal, as obtained from MD simulation, with Q2 is shown in Figure 11b. It is evident that lateral diffusion follows Fick’s law as shown by solid lines in Figure 11b, and the lateral diffusion coefficients for DTAB monomers in the absence and presence of NaSal are found to be 2.6 × 10−6 and 1.3 × 10−6 cm2/s, respectively. These are in good agreement with those obtained from neutron experiments. As already pointed out, salicylate ions condense onto the surface of the DTAB micelle. Therefore, investigating the orientational profile of salicylate ions with respect to the micellar surface can help in understanding the role played by them in slowing down the lateral motion of the DTA+ surfactants. The distribution of the angle between the axis of the DTA+ and salicylate ions, within a radius of 5 Å from the DTAB headgroup, is calculated and depicted in Figure 12. The definitions of the axes and specified angle between them are displayed in the inset of Figure 12. This demonstrates that salicylate ions are oriented mostly within 15−30° with respect to the molecular axis of DTAB, and the hydrophilic parts (carboxylate moiety) of salicylate ions are facing toward the

water. With salicylate ions being amphiphilic in nature, it is expected that their hydrophilic part tends to face water, and their hydrophobic region avoids it. In the presence of DTA+ ions, it is observed from Figure 12 that they orient themselves such that their hydrophilic group stays at the surfactant headgroup region, and the hydrophobic group is partially embedded into the hydrophobic core of the micelle. This is consistent with the recent MD simulation study4 on a different cationic surfactant, cetyltrimethylammonium chloride (CTAC). From the orientational profile of the salicylate ion, it is conspicuous that there is a strong electrostatic interaction between anionic salicylate and the cationic headgroup of the surfactant. Hence, it can be asserted that, because of strong electrostatic interaction, the finite size of the salicylate ion and its location near the headgroup of the micelle could be the major factors for hindrance to the lateral motion of the surfactant. Earlier, it was reported that the structure of the ionic micelles was found to be altered significantly with the addition of an electrolyte.5−7 Here, we have shown that the dynamics of ionic micelles also gets modified, particularly when the electrolyte is an organic salt. We have also found that the QENS data are not affected much if the additive salt is inorganic. It has been shown4 that inorganic counterions are weakly associated with the charged headgroup in comparison to organic counterions. Moreover, because of the absence of a hydrophobic part, the inorganic counterions are not embedded within the micelle. Hence, in contrast to that with their organic counterparts, motion of the surfactant molecules is not significantly affected.

Figure 11. Variation of (a) Γlat and Γseg (■ and ▲, respectively) as obtained from the fits of I(Q, t) assuming eq 11 for DTAB micelles with NaSal salt. For direct comparison, the Γ values obtained from the neutron experiments at 300 K are shown by □ and △. (b) Γlat for DTAB micelles with and without NaSal salt. The solid lines correspond to the description assuming Fick’s law. 5570


The Journal of Physical Chemistry B Our MD simulation indicates that salicylate ions are strongly associated with the charged headgroup of the surfactant and are located at the micellar surface. This significantly affects the lateral motion of the surfactant rather than the segmental dynamics of CH2 units in the alkyl chain. This is also consistent with the experimental results that the parameters corresponding to the segmental motion did not change much via the addition of NaSal salt as the salicylate ion. These results are in line with our recent observations of the effects of membrane active peptides (e.g., amyloid β, antimicrobial, etc.) on the dynamics of the phospholipid membrane.20,21 At low concentration, these peptides are located near the surface of the membrane and have been found to alter mainly the lateral motion of the lipids. On the other hand, segmental motion of the lipid has been found to remain unaffected in the presence of the additive. Our present study provides microscopic insights on the effects of hydrotropic salts on the nanoscopic dynamics of ionic micelles which can be correlated with the more complex system such as the membrane active peptide and cell membrane which has more physiological relevance.

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ACKNOWLEDGMENTS

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REFERENCES

Authors would like to acknowledge Dr. V. K. Aswal, Dr. P. A. Hassan, and Dr. N. Choudhury from BARC, India, for fruitful discussion.

(1) Degiorgio, V., Corti, M., Eds.; Physics of Amphiphiles: Micelles, Vesicles and Microemulsions; North-Holland: Amsterdam, 1985. (2) Chevalier, Y.; Zemb, T. The Structure of Micelles and Microemulsions. Rep. Prog. Phys. 1990, 53, 279−371. (3) Hassan, P. A.; Raghavan, S. R.; Kaler, E. W. Microstructural Changes in SDS Micelles Induced by Hydrotropic Salt. Langmuir 2002, 18, 2543−2548. (4) Wang, Z.; Larson, R. G. Molecular Dynamics Simulation of Threadlike Cetyltrimethylammonium Chloride Micelles: Effects of Sodium Chloride and Sodium Salicylate Salts. J. Phys. Chem. B 2009, 113, 13697−13710. (5) Das, N. C.; Cao, H.; Kaiser, H.; Warren, G. T.; Gladden, J. R.; Sokol, P. E. Shape and Size of Highly Concentrated Micelles in CTAB/NaSal Solutions by Small Angle Neutron Scattering (SANS). Langmuir 2012, 28, 11962−11968. (6) Aswal, V. K.; Goyal, P. S.; Thiyagarajan, P. Small-Angle NeutronScattering and Viscosity Studies of CTAB/NaSal Viscoelastic Micellar Solutions. J. Phys. Chem. B 1998, 102, 2469−2473. (7) Joshi, J. V.; Aswal, V. K.; Goyal, P. S. Effect of Sodium Salicylate on the Structure of Micelles of Different Hydrocarbon Chain Lengths. Phys. B 2007, 391, 65−71. (8) Rodrigues, R. K.; da Silva, M. A.; Sabadini, E. Worm-like Micelles of CTAB and Sodium Salicylate under Turbulent Flow. Langmuir 2008, 24, 13875−13879. (9) Zhang, Y.; Li, Y.; Song, Y.; Li, J. Properties and Sodium Salicylate Induced Aggregation Behavior of a Tail-Branched Cationic Surfactant with a Hydroxyl-Containing Hydrophilic Head. RSC Adv. 2015, 5, 105952−105960. (10) Šarac, B.; Cerkovnik, J.; Ancian, B.; Mériguet, G.; Roger, G. M.; Durand-Vidal, S.; Bešter-Rogač, M. Thermodynamic and NMR Study of Aggregation of Dodecyltrimethylammonium Chloride in Aqueous Sodium Salicylate Solution. Colloid Polym. Sci. 2011, 289, 1597−1607. (11) Söderman, O.; Carlstrom, G.; Olsson, U.; Wong, T. C. Nuclear Magnetic Resonance Relaxation in Micelles. Deuterium Relaxation at Three Field Strengths of Three Positions on the Alkyl Chain of Sodium Dodecyl Sulphate. J. Chem. Soc., Faraday Trans. 1 1988, 84, 4475−4486. (12) Sharma, V. K.; Mitra, S.; Garcia-Sakai, V.; Hassan, P. A.; Embs, J. P.; Mukhopadhyay, R. The Dynamical Landscape in CTAB Micelles. Soft Matter 2012, 8, 7151−7160. (13) Brocca, P.; Cantu, L.; Cavatorta, F.; Corti, M.; Del Favero, E.; Deriu, A.; Di Bari, M. Dynamics of Ganglioside Micellar Solutions by Quasielastic Neutron Scattering. Phys. B 2004, 350, E619−E622. (14) Kandori, K.; McGreevy, R. J.; Schechter, R. S. Solubilization of Phenol and Benzene in Cationic Micelles: Binding Sites and Effect on Structure. J. Phys. Chem. 1989, 93, 1506−1510. (15) Hassan, P. A.; Rana, S.; Verma, G. Making Sense of Brownian Motion: Colloid Characterization by Dynamic Light Scattering. Langmuir 2015, 31, 3−12. (16) Pecora, R. Dynamic Light Scattering; Plenum: NewYork, 1985. (17) Belmajdoub, A.; Elbayed, K.; Brondeau, J.; Canet, D.; Rico, I.; Lattes, A. Comparative Investigation of Cetyltrimethylammonium Bromide Micelles in Water and Formamide by Nuclear Magnetic Relaxation. J. Phys. Chem. 1988, 92, 3569−3573. (18) Tominaga, T.; Nishinaka, M. Tracer Diffusion of Ionic Micelles: Effects of Size and Interactions. J. Chem. Soc., Faraday Trans. 1993, 89, 3459−3464. (19) Bée, M. Quasielastic Neutron Scattering; Adam Hilger: Bristol, 1988. (20) Sharma, V. K.; Mamontov, E.; Tyagi, M.; Qian, S.; Rai, D. K.; Urban, V. S. Dynamical and Phase Behavior of a Phospholipid

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CONCLUSIONS The effects of a hydrotropic salt, sodium salicylate (NaSal), on the dynamics of DTAB-based cationic micelles are studied and reported here. The diffusion coefficient of whole DTAB micelles obtained from the dynamic light scattering experiments at room temperature is found to be slower with the addition of NaSal. This is consistent with the earlier small angle neutron scattering (SANS) results5−7 which suggested that the addition of NaSal induces growth of DTAB micelles. Observed QENS data were explained by a model consisting of two distinct motions. The slower motion is identified as the lateral motion, and the other one corresponds to the segmental motion of the surfactant. Lateral motion is found to be Fickian in nature, and segmental motion is described using a model in which a fraction of surfactant hydrogen atoms undergoes localized translational diffusion within spherical domains. It is observed that the addition of NaSal significantly affects the lateral motion of DTAB, whereas segmental motion remains almost unaffected. These observations are found to be consistent with our atomistic molecular dynamics simulation results. They suggest that lateral motion of the surfactant is hindered because of the stronger association of the salicylate ion with the charged headgroup of the surfactant and its location at the micellar surface. However, segmental motion of the surfactant is localized in nature and mainly dominated by the segmental motion of the alkyl chains which does not have much of an effect because of the addition of NaSal. This study clearly demonstrates the effects of the addition of hydrotropic salt on the nanoscopic dynamics of micelles and establishes the correlation with its microstructure.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91-25594667. Fax: +91-2225505151. ORCID

R. Mukhopadhyay: 0000-0003-0499-2185 Notes

The authors declare no competing financial interest. 5571


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Effects of Hydrotropic Salt on the Nanoscopic Dynamics of DTAB

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