NaSal

Article pubs.acs.org/Langmuir

Shape and Size of Highly Concentrated Micelles in CTAB/NaSal Solutions by Small Angle Neutron Scattering (SANS) Narayan Ch. Das,*,† Hu Cao,† Helmut Kaiser,† Garfield T. Warren,§ Joseph R. Gladden,‡ and Paul E. Sokol*,†,§ †

Low Energy Neutron Source (LENS), Center for the Exploration of Energy and Matter, Indiana University, Bloomington, Indiana 47408, United States ‡ Department of Physics and Astronomy & National Center for Physical Acoustics University of Mississippi, University, Mississippi 38677, United States § Department of Physics, Indiana University, Bloomington, Indiana 47405, United States ABSTRACT: Highly concentrated micelles in CTAB/NaSal solutions with a fixed salt/ surfactant ratio of 0.6 have been studied using Small Angle Neutron Scattering (SANS) as a function of temperature and concentration. A worm-like chain model analysis of the SANS data using a combination of a cylindrical form factors for the polydisperse micellar length, circular cross-sectional radius with Gaussian polydispersity, and the structure factor based on a random phase approximation (RPA) suggests that these micelle solutions have a worm-like micellar structure that is independent of the concentration and temperature. The size of the micelle decreases monotonically with increasing temperature and increases with concentration. These observations indicate that large micelles are formed at low temperature and begin to break up to form smaller micelles with increasing temperature.

1. INTRODUCTION Surfactants are amphiphilic molecules with both a bulky hydrophilic head, which is often charged, and a relatively short and slender hydrophobic tail. Above their critical micelle concentration (CMC), surfactant molecules spontaneously selfassemble into aggregates to form micelles in aqueous solutions. Depending on the size of the headgroup, length of tails, charge of the surfactant, temperature, concentration and even the flow condition, these large aggregates can form into a number of different shapes, including spherical and wormlike micelles, vesicles, and lipid bilayers.1 When micelles grow and become wormlike, these aggregates are much like polymers and entangle in three-dimensional networks above the CMC. Wormlike micelles (WLMs) are long, flexible threadlike surfactant aggregates exhibiting a hierarchy of length scale and striking viscoelastic behavior.2−6 The viscoelastic wormlike micelles are already extensively used in consumer and personal care products.7,8 Micelles are well studied structural fluids in which macromolecular structures in an aqueous solution have dramatic effects on rheological properties.9 Cetyltrimethylammonium bromide (CTAB) is one of the surfactants extensively studied in micelle solutions during the last two decades.10−14 The large majority of these studies have been confined to the low to medium surfactant concentration range (0−100 mM). Comparatively little work has been done on high concentration solutions despite the fact that concentrations of up to 1 M surfactant are accessible and the structure at such high © 2012 American Chemical Society

concentrations is still an open question. There are also practical applications for these solutions in the high concentration range that motivate a better understanding of these unique materials. For instance, above several hundred mM, these solutions begin to mimic a soft gel rather than a fluid, flowing for slow shear stresses and tearing for faster shears, and thus probe the boundary between fluid and solid.15 Additionally, they are birefringent with stress optic coefficients that scale with concentration so that ever smaller stresses can be visualized through crossed polarizing filters in ever increasing concentration micelle solutions. It is well-known that CTAB grows from globular to wormlike shapes when salts, such as KBr, NaSal (sodium salicylate), NaNO3, etc., are added. The association of halide anions (Cl− and Br−) with surfactant cations (CTA+) is moderate, and thus the growth of micelles is gradual.16 However, with the association of strongly binding counterions, such as Sal−, these surfactants immediately form into wormlike micelles even at low concentrations, without passing through an intermediate spherical morphology, which was exemplified in the CPCL (cetylpyridinium chloride) + NaSal system.17−19 Small Angle Neutron Scattering (SANS) is a powerful tool for studying surfactant polymorphism because of the large scattering contrast between the hydrogenated surfactants and Received: June 15, 2011 Revised: June 12, 2012 Published: July 24, 2012 11962

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nitrogen-cooled liquid ethane, only crystalline samples were produced. Extensive efforts to produce vitrified samples suitable for imaging were unsuccessful.

deuterated water (D2O) as the solvent. In addition, the structural parameters, like the length and radius of micelles fall in the wave-vector range covered by the SANS technique (Q ≈ 10−3 to 0.4 Å−1). This technique can provide important information about the shapes, sizes, and even parameters of interaction between micelles. So far, most of the SANS studies on CTAB/NaSal micelle solutions have been reported only on low surfactant and salt concentrations. In the concentration range of about 1−30 mM CTAB and salt/surfactant ratio of 0.6, it is known that the surfactant molecules self-assemble into long tubular (wormlike) structures with diameters on the order of ∼22 Å and lengths that can be tens of micrometers at room temperature16 (and shorter at higher temperatures). However, CTAB/NaSal micelle solutions at high concentrations (100 − 800 mM/L) and their temperature dependence have not been studied as well and little structural information exists in the literature, although nematic and hexagonal phases have been observed.12 Therefore, the micelle solutions of interest in this study are highly concentrated CTAB (100, 200, 400, 600, 800 mM) with a fixed ratio of CTAB/NaSal = 0.6 in D2O as a function of temperature from 20 to 60 °C. Our SANS studies clearly illustrate that highly concentrated CTAB/NaSal micelles have a wormlike structure. Second, there is no structural transition observed in the studied temperature range and concentrations. These wormlike micelles shrink linearly in particle size with increasing temperature and increases with concentrations.

3. THEORETICAL MODEL AND DATA ANALYSIS METHODS CTAB/NaSal solutions generally form in two basic shapes, ellipsoidal and rodlike (or wormlike) micelles. Their scattering profiles are quite different, especially in the low-Q range. In practice, the data analysis of the scattering spectrum provides information on the structural parameter, such as the shape, size of the particles, and its size distribution. Specifically, the scattering intensity from wormlike micelles provides information about three lengths in direct space: contour length, Lc, persistence length, lp, and the cross sectional radius, rcs, with its size distribution. The modeling and data analysis of the scattering spectrum for the micelles sample is extremely difficult due to intermicellar interactions. Meanwhile, in the presence of correlations between the micelles, the scattered intensity, I(Q) is no longer simply expressed by a single-particle form factor, F(Q). Hence for micelles in general, the total I(Q) can be expressed as follows:20−22 I(Q ) = nmF(Q )S(Q ) + Ibkg

(1)

where nm is the normalization factor, which includes the number density of micelles, F(Q) is the form factor, connected with the intramicellar particle resulting from the size and shape of the micelle, S(Q) is the interparticle structure factor, which specifies the correlation between the centers of neighboring micelles, and Ibkg is the incoherent background intensity, mainly due to the hydrogen in the sample, where it is assumed that the effect of polydispersity in F(Q) and S(Q) can be separated. The form factor was modeled for semiflexible self-avoiding cylinders with a circular cross-section, as described by the wormlike chain model with excluded volume interactions developed by Pedersen and Schurtenberger.23 It depends on three parameters: Lc, lp (or the Kuhn length b = 2lp), and rcs. Since the micelles are expected to have polydispersity of the length and cross-section, the form factor with the polydispersity is defined by the following:

2. EXPERIMENTAL SECTION The SANS experiments were performed at the Low Energy Neutron Source (LENS) located at the Center for Exploration of Energy and Matter (CEEM), Indiana University. LENS is a novel, university-based pulsed neutron source based on a high-current, variable-pulse-width proton accelerator to produce either short or long neutron pulses. LENS utilizes a low energy p-n reaction in Be, a water reflector and a solid methane moderator to produce a high flux of low energy neutrons. The SANS Instrument at LENS is a conventional neutron “time-of-flight” instrument. The incident flight path is 8.6 m and uses pinhole collimation to provide a beam with a divergence of 7 mrad at the sample position. A cooled Beryllium filter is used to reduce fast neutron backgrounds and limits the shortest wavelength available to 4 Å. The sample-to-detector distance is variable, from 1.1−4.2 m and, for these measurements, 2.2 m was used allowing us to cover a Q-range of 0.008−0.3 Å−1 utilizing λ = 4−18 Å neutrons. For these measurements, the accelerator was operated at 13 MeV with a peak current of 20 mA, pulse width of 600 μS and repetition rate of 20 Hz yielding an average power on target of 3 kW. CTAB (99%, ρ = 0.39 g/cm3) and NaSal (99%, ρ = 0.32 g/cm3) were obtained from Sigma-Aldrich. Micelle solutions with five concentrations (100/60, 200/120, 400/240, 600/320, 800/480 mM/ L) were prepared in D2O, which provides a better neutron scattering contrast between the micelle solution and the solvent. The micelle solutions were held in a quartz banjo cell with a thickness of 2 mm. The raw data were circularly averaged after background correction due to sample cell and detector noise and then converted into absolute units by comparison with a water standard, taking into account the transmission of the samples. The data were collected in the Q-range of 0.008 to 0.25 Å−1 for the temperature range of 20 to 60 °C. Imaging of the samples using a CryoTEM was also attempted but the high viscosity of the samples frustrated these efforts. A Vitrobot Mark III freezing robot was used to prepare the samples which allowed the entire freezing chamber to be heated to 50 °C. However, even at these elevated temperatures, the viscosity of the sample remained high enough that standard techniques (pipetting followed by blotting) failed to produce an appropriate thin film. A free-standing film within a wire loop was produced but upon freeing, by submersion in liquid-

F(Q ) = (Δρ)2 Lc2FL(Q )Fcs(Q )

(2)

where Δρ (= ρm − ρs) is the difference in scattering length density between the micelles and the solvent, ρm and ρs are the scattering length density of the micelles and solvent, respectively, and FL(Q) and Fcs(Q) are the polydisperse form factor for the length and cross-section. The longitudinal polydisperse form factor is expressed by the following: ∞

FL(Q ) =

∫2r f (L)FL(q , L) dL c

∞

∫2r f (L) dL

(3)

c

with a polydispersity given by an exponential distribution ⎛L⎞ f (L , Lc) = exp⎜ ⎟ ⎝ Lc ⎠

6

(4)

Assuming that the micelles have a cyclindrical cross-section with Gaussian polydispersity in the cross-sectional radius, rc., the cross-sectional form factor can be expressed by the following: 11963

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Figure 1. Neutron scattering intensity versus Q as a function of temperature for CTAB/NaSal micelle solutions with a molar ratio of CTAB/NaSal = 0.6, (a) 100/60 mM, (b) 200/120 mM, (c) 400/240 mM, and (d) 600/360 mM. Symbols indicate experiential data. The solid curves through symbols represent best fit of WLM model. ∞

FCS(Q ) =

actions to accurately determine structural parameters such as the contour length, Kuhn length, and cross-sectional radius of the micelles. Several scattering experiments and Monte Carlo simulations have demonstrated the importance of including intermicellar interactions when determining structural parameters.24,25 The structure factor, S(Q) in the presence of intermicellar interactions can be expressed using a random phase approximation (RPA) and PRISM type interactions.26,27

∫0 fcs (rc)Fcs(q , rcs) drcs ∞

∫0 fcs (rcs) drcs

(5)

and the cross-section scattering function for micelles with a circular section of radius, rc is as follows: ⎛ 2J (Qrc) ⎞ ⎟ Fcs(Q ) = (πrc2)2 ⎜ 1 ⎝ Qrc ⎠

(6)

where J1(x) = (sinx − x cosx)/x is the first-order spherical Bessel function and Gaussian distribution of the cross-sectional radius is as follows: 2

f (rc) =

⎛ (r − r )2 ⎞ 1 c ⎟ exp⎜ − 2 2 2σ ⎠ ⎝ 2πσ

S(Q ) =

1 1 + βFL(Q , L)

(8)

where FL(Q,L) is the longitudinal length form factor and β = [1 − S(0)]/S(0) is a parameter representing the strength of the intermicellar interaction, where S(0) is the forward contribution to the structure factor. An explicit functional form of S(0) has been formulated using a renormalization-group method28 originally developed for semidilute polymer solution for analyzing the measured apparent molar mass of the micelles. Later, several authors successfully employed the following functional form:22,26,29

(7)

where r and σ are the average and dispersity index of the crosssectional radius, respectively. Worm-like micelles are open coil-like structures that interact with each other in the solvent, even at low concentrations. Those intermicellar interactions not only influence high q-data, they also influence the corresponding scattering data at lower qvalues and consequently the inferred overall size of the micelles. Thus, it is important that the structure factor, which represents intermicellar interactions, adequately incorporates these inter11964

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S(0) = 1 +

2ln(1 + X ) ⎞ 1⎛ ⎜9X − 2 + ⎟ ⎠ 8⎝ X

⎧ ⎡1 ⎤⎫ ⎛ 1 ⎞ exp⎨0.25⎢ + ⎜1 − 2 ⎟ln(1 + X )⎥⎬ ⎝ ⎣X ⎦⎭ X ⎠ ⎩

(9)

where X = 42.1 ϕeff. The effective volume fraction, ϕeff of chains can determined by the following: ⎛ r + k−1 ⎞⎛ rg ⎞ ⎟⎜⎜ ⎟⎟φ φeff = ⎜ cs ⎝ rcs ⎠⎝ rg,u ⎠

(10)

where ϕ is the volume fraction of micelles, rcs is the crosssectional radius, k−1 (= √lp) is the Debye length, and r and rg,u are the theoretical radius of gyration of a completely charge and uncharged chain, respectively. The relationship between r and rg,u for a given contour length can be estimated using the empirical relationship as presented by Pedersen.23,26 Latter, Helgeson et al. also successfully employed the same empirical relationship to calculate r and rg,u.22 The SANS data obtained for highly concentrated micelles containing CTAB/NaSal in the D2O were analyzed with the WLM model in eqs 1−10. The fitting routine written in Mathcad was used to fit the SANS data in which the average contour length, polydispersity index, and cross-sectional radius are adjusted to minimize the average aggregate squared normalized standard error.

Figure 2. Neutron scattering intensity versus Q as a function of concentration at room temperature 20.5 °C for CTAB/NaSal micelle solutions. The solid lines through experimental data represent the model scattering intensity for wormlike micelles.

The scattering intensity from wormlike micelles typically display three spectral regions containing information about three length in direct Q space: the contour length, Lc, the persistence length lp, and the cross sectional radius rcs as discussed earlier. In the case of long wormlike aggregates, the cross section is generally well separated in the q space from the contour or persistence length. In very small Q region, the decay of I(Q) follows the Guinier law (I(Q) ≈ e−(Q2R2g/3)) allowing the determination of radius of gyration, or equivalent of contour length (⟨R2g⟩ ≈ (bL/6)). The power law decay of I(Q) with Q represent the chain flexibility and parametrized by the Kuhn length. The region at higher Q is followed by decay of I(Q) contains information regarding the micellar radial cross section. The model fitting of scattering function containing L, b, r, and Q over full range of scattering curve can provide quantitative structural informations. Figure 3 shows a representative SANS spectrum for a sample of 200/120 mM CTAB/NaSal in D2O at 20.5 °C. The absolute scattering intensity was fitted using the Schurtenberger WLM model as described in the previous section. The scattering length density of the surfactant and solvent were estimated using standard methods.30 The volume of micelles was estimated based on the total volume fraction of surfactant in solution from the solid density of CTAB. The remaining parameters of contour length, Kuhn length, the micellar radius, and radius polydispersity were fitted to SANS data using combination of eqs 1−10. The solid line through symbols in Figure 3 indicates the fitting result of representative data. The WLM model gives a good fit to the data over the entire q-range, providing an excellent description of the experimental results. The best fit parameters Lc, b, rcs, and σ for 200/120 mM CTAB/NaSal micelle at 20.5 °C are 6, 5, 2, and 0.035, respectively. In this study, the solvent (D2O) scattering length density is ρs = 5.76 × 10−6 Å−2 and the 800/480 mM micelle scattering density is calculated to be ρm ≈ 1.1 × 10−7 Å−2 (smaller for 600/360 mM and lower concentrations), which could be neglected compared to ρs. The inset in Figure 3 presents the structure factor, S(Q) and form factor F(Q) with polydisperse contour length and cross-sectional radius with Lc = 69 nm, b = 5 nm, rcs = 2 nm, and σ = 0.035, indicating a marginal contribution of intermicellar interaction. These wormlike micelles are similar to polymers in that they are quite flexible with typical persistence length 2−2.5 nm (Kunh

4. RESULTS AND DISCUSSION SANS measurement were performed on CTAB/NaSal micelles with varying surfactant concentration at fixed of 0.6 CTAB/ NaSal and temperature to directly measure micelles shape and size. Figure 1 shows the measured SANS data for four CTAB/ NaSal micelle solutions as a function of temperature from 20 to 60 °C. The symbols represent the experimental data, and the curves are the best fit using WLM model according to eqs 1−10. No abnormal changes in scattering intensities were found in these micelle solutions. At each of the concentrations, it was found that the scattering intensity at large Q > 0.08 Å−1 is independent of the temperature, whereas the scattering intensity monotonically decreases at low Q < 0.08 Å−1 on heating. The observed scattering behaviors in these four solutions suggest that the cross-sectional radius of the micelles, which is reflected in the large Q behavior, is not significantly affected, whereas the contour length, which is reflected in the small Q behavior, actually becomes shorter with increasing temperature. Figure 2 shows scattering profiles of five micelle solutions at 20.5 °C. With increasing concentration as shown Figure 2, the overall scattering intensity increases. Increase in the scattering intensity at low q-range is due to the concentration induce micellear growth and number density of micelles. However, the scattering intensity of 600/360 mM micelle is very close to that of 800/480 mM micelle, indicating that micelles have reached the limit in the size and number of micelles at such high concentrations. In addition, the interference effects of scattering from different micelles at higher concentration due to intermicellar interaction decrease the scattering intensity at low scattering.29 The combination of these opposing effects of intermicellar interactions and concentration induced growth at high concentration, resulting in a marginal increase of scattering intensity or decrease in the relative change of scattering intensity. 11965

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Figure 3. Neutron scattering intensity versus Q for 200 mM CTAB with 120 mM NaSal micelle at 20.5 °C. Curve gives best fit to the WLM scattering model as described in section 3. The inset shows the wormlike micelle form factor F(Q) and structure factor S(Q) based on random phase approximation (RPA).

length = 4−5 nm),31,32 and this persistence length is independent of temperature and concentration at a fixed surfactant and salt ratio.22,33 This persistence length represents the distance over which the micelle shows rigidity or nonflexibility. In other words, a wormlike micelle behaves as a rigid rod when its length Lc ≤ lp and a flexible when Lc > lp. The cross section radius obtained from WLM model fitting of our studies is close agreement with previous measurement for CTAB/NaSal micelles assuming ellipsoidal micellar34 or CTAB/NaNO3 wormlike micelles structures.22 The best fit results, the solid curve through the symbol of experimental data, of WLM model to experimental SANS data at different temperatures 20−60 °C and different concentrations of 100/60, 200/120, 400/240, and 600/360 mM CTAB/NaSal at fixed ratio = 0.6 are shown in Figure 1a−d . Overall, the fits to the WML model describe the experimental data remarkably well. Small deviations from the model at low q values are observed in some samples, which may be due to neglect of electrostatic interaction between micellar segments.26 The fit values of Lc over temperature range of 20 to 60 °C for five different concentrations 100/60, 200/120, 400/240, 600/ 360, and 800/480 mM of CTAB/NaSal from WML model fitting is shown in Figure 4. Specifically, the contour length increases significantly with surfactant concentration and decreases with increasing temperature at a fixed CTAB/NaSal ratio, as shown in Figures 4 and 5. The Lc values obtained from WML model fitting for 100 mM and 800 mM CTAB micelles are ∼600 and 760 Å at 20 °C, respectively. The contour length of these highly concentrated micelles shows similar behavior as seen very low concentrated micelles22 for CTAB/NaNO3 and CTAB/NaSal.35 Since the total volume fraction of the micelle remain unchanged with an increase in temperature, the rodlike or wormlike micelles probably break along the growth direction to form shorter ones upon heating. The similar observation has also been reported in CTAB/NaSal 100/20 mM micelles.35 A recent rheology and SANS study of CTAB and sodium nitrate (NaNO3) has revealed wormlike micelles from 40 mM

Figure 4. Contour length versus temperature as a function of concentration for CTAB/NaSal micelle solutions.

up to 100 mM of CTAB concentration. It is well-known that wormlike micelles can be easily formed at the low concentration of CTAB with the addition of strongly bonding salt, following a transition from spherical or ellipsoidal to long rodlike or wormlike micelles. However, as concentration of CTAB increases with a fixed ratio (=1.0) of surfactant/salt, the contour length of wormlike micelles exponentially increase, reaching ∼192 nm in CTAB 100 mM and ∼118 nm in 40 mM. However, our study of highly concentrated CTAB/NaSal micelles from 100/60 mM up to 800/480 mM is not inconsistent with low concentrated CTAB/NaNO3 wormlike micelles.22 In addition, the high q behavior which represents cross sectional of our data appears to be independent of surfactant concentration at fixed surfactant/salt ration is consistent with CTAB/NaNO2 micelles system.22 Figure 6 shows the temperature dependence on the contour length (Lc) of micelles for five concentrations. The dashed lines 11966

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5. CONCLUSIONS In summary, highly concentrated CTAB/NaSal micelles with a fixed salt/surfactant ratio of 0.6 have been studied by SANS as a function of temperature and concentration. The modeling analysis results of the SANS data suggest that these studied micelle based on CTAB/NaSal solutions form wormlike micelle structures and the micelle structural parameters, like contour length, varies with concentration and temperature, whereas the Kunh length and cross-sectional radius are independent of concentration and temperature. The contour length decreases monotonically with increasing temperature or increases with concentration and reaches the limit at high concentrations of 600/360 and 800/480 mM micelle solutions. Since the total volume of wormlike micelles stays unchanged, these observations indicate that long micelles start to break up as the temperature increases, and those broken surfactant molecules coalesce again to form more micelles.

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Figure 5. Contour length as a function of concentration for CTAB/ NaSal micelle solutions at 20 and 60 °C.

AUTHOR INFORMATION

Corresponding Author

*Email: [email protected] (N.Ch.D.); [email protected] (P.E.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This report was prepared by Indiana University under Award No. 70NANB10H255 from the National Institute of Standards and Technology, U.S. Department of Commerce. The statements, findings, conclusions, and recommendations are those of the authors and do not necessarily reflect the views of the National Institute of Standards and Technology or the U.S. Department of Commerce. Construction of LENS was supported by the National Science Foundation Grants Nos. DMR-0220560 and DMR-0320627, the 21st Century Science and Technology fund of Indiana, Indiana University, and the Department of Defense. Operation of LENS is supported by the Office of the Vice Provost for Research at Indiana University.

Figure 6. Micelle length (contour length, Lc) as a function of temperature. The dashed lines represent the fitted Arrhenius behavior of Lc ≈ exp(E/kbT).

present the fitted Arrhenius behavior (L ≈ exp(Es/kbT)) where Es is typically associated with the scission energy of the micelle, kb is Boltzmann’s constant, and T is absolute temperature. The temperature dependence of micelle length has been the subject of many studies in the literature. An often cited theoretical work by Cates and Candau presents a mean field approach to the problem which results in an Arrhenius type scaling of length with temperature.6 This type of scaling has been verified experimentally through linear rheology,22,36,37 however certain types of micelle structures have been shown to exhibit opposite temperature trends (e.g., lengthening).38 The linear dependence of the ln(L) vs 1/RT plots in Figure 6 for each concentration and over all temperatures strongly suggest that there are no structural transitions for these micelles over this temperature range. The scission energy is often found from the slope of the fitted lines and can vary widely depending on the type of micelle and surfactant to salt ratio. Our values range from Es = 3.3 to 4.0 kbT, which is lower than other commonly reported values (∼10−20 kbT) for lower concentrations.22,37 It should be noted however that because of the small contour length of our micelles, the length range spans only a partial decade between 20 and 55 °C and thus resulting scission energies may lack accuracy.

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REFERENCES

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dx.doi.org/10.1021/la2022598 | Langmuir 2012, 28, 11962−11968