Impact of Salt Co- and Counterions on Rheological Properties and

Nov 17, 2016 - Rheological properties of aqueous solutions of long-tailed cationic surfactant erucyl bis-(hydroxyethyl)methylammonium chloride (EHAC) ...
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Impact of Salt Co- and Counterions on Rheological Properties and Structure of Wormlike Micellar Solutions Alexander L. Kwiatkowski,† Vyacheslav S. Molchanov,† Anton S. Orekhov,‡ Alexander L. Vasiliev,‡ and Olga E. Philippova*,† †

Physics Department, Moscow State University, 119991 Moscow, Russia National Research Centre “Kurchatov Institute”, 123182 Moscow, Russia

‡

ABSTRACT: Rheological properties of aqueous solutions of long-tailed cationic surfactant erucyl bis-(hydroxyethyl)methylammonium chloride (EHAC) were examined as a function of concentration Cs of different inorganic salts (KCl, CaCl2, and LaCl3) at a fixed surfactant concentration of 0.6 wt %. The structural evolution of micelles was followed by smallangle neutron scattering and cryogenic transmission electron microscopy. It was observed that, upon addition of salt, the zero-shear viscosity η0 of semidilute surfactant solutions goes through a maximum by passing the following three regimes: η0 ∼ Cs10 (regime I), η0 ∼ Cs3.5 (regime II), and η0 ∼ Cs−2 (regime III). In regime I, the micelles grow in length; in regime II, the linear growth of micelles proceeds simultaneously with their branching; and in regime III, the branching becomes dominating. With increase in the salt valence, the viscosity curves shift to a lower salt content, indicating that these salts are more effective in inducing micellar elongation and branching, as they contain a larger amount of anionic species Cl− screening the repulsion between cationic surfactant heads. Diverse roles of salt co- and counterions (i.e., salt ions that are similar and oppositely charged with respect to surfactant head groups) at different salt concentrations were demonstrated. It was shown that at low salt concentrations corresponding to the rising branch of the viscosity curve (regimes I and II), salt counterions (Cl−) fully determine the rheological behavior of the system. At high salt concentrations, when the electrostatic repulsions between micelles and salt co-ions are essentially screened, the co-ions start affecting the rheological properties. Under these conditions, monovalent co-ions (K+) provide much lower viscosity of surfactant solutions than the multivalent ones (Ca2+, La3+), which is consistent with theoretical predictions that suggest the penetration of K+ inside the micellar corona increasing the charge of the micelles and therefore hindering their growth.

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INTRODUCTION Wormlike surfactant micelles represent giant self-assembled chains that can form transient networks in an aqueous medium. Such networks exhibit extraordinary viscoelastic properties.1−4 Because of the self-assembled nature of micellar chains, these properties are very sensitive to many factors, including temperature, shear, concentration of added salt, presence of hydrophobic or amphiphilic substances, and so forth.4−13 Adaptive viscoelastic properties of wormlike micellar solutions have been put to practical use in several areas, including oil industry, where these solutions are applied for formulation of fracturing and drilling fluids.14−18 In the case of ionic surfactants, the formation of wormlike micelles is usually induced by the added salt. Salt screening repulsion between similarly charged surfactant head groups favors their closer packing, leading to the transition from spherical to cylindrical micelles and their further growth in length to reduce the number of thermodynamically unfavorable spherical end-caps. When the repulsions are significantly screened, the linear micellar chains transition into branched © 2016 American Chemical Society

ones and then into multiconnected network, which does not contain any end-caps.1 Such transitions were visualized by cryogenic transmission electron microscopy (cryo-TEM).19,20 The efficiency of salts to induce the elongation and branching of micellar chains depends essentially on the nature of the salt. The most effective are hydrotropic salts such as sodium salicylate,21,22 3-hydroxy-naphthalene-2-carboxylate,23 p-toluene sulfonate,24 and so forth for cationic surfactants or ptoluidine hydrochloride,25 benzyltrimethylammonium bromide,26,27 choline chloride,28 and so forth for anionic surfactants. The ions of these salts, which are oppositely charged with respect to surfactant heads, contain hydrophobic groups. These groups are rather small so that the ions cannot form micelles by themselves,29 but they can embed the existing surfactant micelles. The hydrophobic parts of such ions penetrate into the nonpolar core, whereas the ionic groups Received: September 28, 2016 Revised: November 10, 2016 Published: November 17, 2016 12547

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components of fracturing fluids together with KCl and CaCl2 salts. Microscopic origin of the rheological changes in the system under study was examined by small-angle neutron scattering (SANS) and cryo-TEM. It was observed that the rheological behavior of EHAC solutions at low salt concentrations is fully determined by salt counterions, whereas at high salt concentrations the co-ions come into play and affect significantly the maximum viscosity that can be reached in the system.

localize adjacent to the oppositely charged surfactant heads.30,31 Intercalation of hydrotropic counterions among the head groups strongly reduces the micellar charge promoting growth of wormlike micelles at a much lower salt/surfactant ratio32,33 in comparison to nonpenetrating salts (e.g., NaCl, KCl), which are able to bind to the micelles only through the polarizability effect.34 At the same time, hydrotropic counterions may induce the precipitation of surfactants;25,30 therefore, use of nonpenetrating salts is preferable for several applications.34 Salt counterions (oppositely charged with respect to the surfactant head groups) were suggested to contribute mainly to the screening of electrostatic repulsion on the surface of micelles, leading to their elongation and branching. The action of salt co-ions (similarly charged with respect to surfactant head groups) is much less understood. Recent theoretical studies35 demonstrated that the effect of co-ions should be observed mainly at a high salt content, when the repulsion of co-ions from similarly charged micelle is strongly screened, and the coions can approach the micelles triggered, for example, by dispersion attraction. Co-ions coming closer to the micellar surface increase the net charge of micelles, which opposes micellar growth and branching.35 To the best of our knowledge, there is only one experimental paper36 devoted to the effect of salt co-ions on viscoelastic properties of wormlike micellar solutions. It deals with the anionic surfactant sodium dodecyl sulfate (SDS). In this article, Kabir-un-Din et al.36 studied the dependence of the viscosity of 0.3 M SDS solutions on the concentration of different ammonium salts (NH 4 Cl, NH 4 Br, NH 4 I, NH 4 NO 3 , NH4SCN). It was shown that the type of salt co-ion affects the value of viscosity, both before and after its maximum value. The differences in viscosities reached more than 1 order of magnitude, the highest viscosity being observed for NH4SCN solution, the lowest for NH4Cl solutions, which was attributed to the effect of hydrophobic interactions on the micellar size.36 By light scattering, it was shown37 that co-ions (F−, Cl−, Br−, I−, SCN−) indeed affect the size of rodlike micelles of SDS; however, in NaSCN solution, the size of micelles was much smaller than that in NaCl solution, which is inconsistent with the aforementioned viscosity results.36 Therefore, the data on the effect of salt co-ions on rheological properties of surfactants are very scarce and still poorly understood. At the same time, many practical applications of wormlike micellar solutions suggest the presence of salts with different co-ions. In particular, it concerns the formulation of various oil field fluids.14−18 In such systems, mainly based on cationic surfactants, usually different low molecular weight salts are present, KCl and CaCl2 being the most common ones. Although there are many papers devoted to cationic wormlike micelles/KCl systems, the effect of CaCl2 on the behavior of these micelles was not studied. At the same time, a detailed study of the dependence of the rheological properties on the amount and type of nonbinding electrolyte is quite important to get the desired material properties for specific applications. In this article, the viscoelastic properties of aqueous solutions of cationic surfactant erucyl bis-(hydroxyethyl)methylammonium chloride (EHAC) were studied in a wide range of concentrations of three inorganic salts (KCl, CaCl2, and LaCl3) bearing the same anion as surfactant counterions and different cations, which enables uncovering the effects of salt counter- and co-ions on the rheological behavior. The chosen surfactant is widely used in oil recovery14,15 as one of the main

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EXPERIMENTAL SECTION Materials. Aqueous solution of EHAC (C22 surfactant with a cis unsaturation at the 13-carbon position5,19,32) containing 25 wt % 2-propanol was provided by AkzoNobel. To obtain a pure surfactant, the commercial solution was diluted by deionized water (1:10) and freeze-dried as described elsewhere.5 Potassium chloride from Sigma-Aldrich (>99.8% purity), calcium chloride dihydrate from Fluka (>99.5% purity), and lanthanum chloride heptahydrate (>99.99% purity) from Sigma-Aldrich were used as received. Water was purified by Millipore Milli-Q system. Samples Preparation. Surfactant solutions were prepared by mixing appropriate quantities of aqueous stock solutions of the surfactant and the salt with distilled−deionized water. The samples were stirred for 1 day and left for equilibration at room temperature for another 1 day. In the resulting solutions, EHAC concentration was fixed at 0.6 wt % (0.0144 M). The concentrations of the salts were varied in the following ranges: 0.007−0.7 M KCl, 0.004−0.36 M CaCl2, and 0.007−0.26 M LaCl3. Rheology. Steady shear and dynamic shear (i.e., frequency sweep) rheological measurements were performed on a controlled-stress rheometer Anton Paar Physica MCR 301 at 20.5 °C. For the experiments, cone-plate (diameter 50 mm, cone angle 1°) or coaxial cylinders (inner diameter 24 661 mm, outer diameter 26 667 mm) measurement cells were used for viscoelastic and low viscous samples (η0 < 0.01 Pa s), respectively. From steady shear viscosity data, the values of the zero-shear viscosity η0 and the terminal relaxation time λ that is inversely proportional to the critical shear rate γ̇ (λ = 1/γ̇), at which the viscosity starts to decrease, were estimated by fitting the data with the Carreau−Yasuda model, which makes an interpolation between the zero-shear viscosity and infinite-shear viscosity in the case of shear-thinning liquids38 η(γ )̇ = η∞ + (η0 − η∞)[1 + (λγ )̇ a ]n − 1/ a

where η∞ is the infinite-shear rate viscosity, corresponding here to the viscosity of the solvent (0.001 Pa s), n > 0 is a power-law index describing the degree of shear thinning, and a is a constant, which characterizes the size and curvature of the transition region between Newtonian and shear-thinning behavior. All of the frequency sweep experiments were performed in the linear viscoelastic regime in the frequency range 10−3−34 rad/s. In steady shear experiments, the shear rate was varied between 2 × 10−4 and 10 s−1. SANS. SANS measurements were carried out with two detector system on the time-of-flight YuMO high-flux pulsed reactor IBR-2M at the Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, Russia. The experiments were performed at 20 °C at scattering vectors Q 12548

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Figure 1. Flow curves of 0.6 wt % aqueous solutions of EHAC at increasing concentrations of the added salt CaCl2: 0.05 M (triangles), 0.08 M (circles), 0.10 M (squares), 0.13 M (reverse triangles), 0.22 M (diamonds), and 0.36 M (hexagons) at 20.5 °C.

Figure 2. Frequency dependences of storage G′ (filled symbols) and loss G″ (open symbols) moduli for 0.6 wt % aqueous solutions of EHAC at increasing concentrations of the added salt CaCl2: 0.05 M (triangles), 0.08 M (circles), 0.10 M (squares), 0.13 M (reverse triangles), 0.22 M (diamonds), and 0.36 M (hexagons) at 20.5 °C.

ranging from 0.006 to 0.14 Å−1. All data were treated according to standard procedures of small-angle isotopic scattering.39−41 The samples were prepared using heavy water D2O to obtain higher contrast. The neutron scattering length density of D2O is 6.38 × 10−6 Å−2, whereas that of EHAC (without counterion) is −0.14 × 10−6 Å−2. Cryo-TEM. The cryo-TEM specimens were prepared in the following way: the sample was applied onto the grid manually via the side port of the Vitrobot (FEI) directly onto the Lacey carbon-coated side of the 300 mesh copper TEM grid using a pipette. The Vitrobot parameters are described elsewhere.42 After the sample deposition, the grid was blotted and immediately plunged into liquid ethane. All samples were studied in bright-field TEM in a Titan Krios 60-300 TEM/ STEM (FEI, OR) equipped with a spherical aberration corrector (image corrector), a direct detection camera Falcon II (FEI), and postcolumn energy filter (Gatan, Pleasanton, CA). The microscope was operated at 300 kV. The micrographs were obtained in low dose mode with total electron dose of less than 15 e/Å2. Digital Micrograph (Gatan) and TIA (FEI) softwares were used for image processing.

the alignment of micelles along the direction of the flow. The inverse value of the shear rate corresponding to the onset of the shear thinning was used to estimate the terminal time of stress relaxation.43 Figure 2 shows the results of dynamic rheological measurements. They demonstrate a typical behavior of viscoelastic fluid with the crossover of G′(ω) and G″(ω) curves. It is seen that with increase in the salt concentration from 0.05 to 0.1 M, the storage modulus G′ becomes higher and less frequency dependent. In 0.1 M CaCl2, a plateau on G′(ω) dependence appears, indicating the formation of a network of entangled wormlike micelles.5 The evolution of the rheological properties (the zero-shear viscosity, the terminal relaxation time, and the plateau modulus) of EHAC solutions with increasing concentration of salt is demonstrated in Figure 3 for three inorganic salts, KCl, CaCl2, and LaCl3. These salts have the same anion as surfactant counterions (Cl−) and cations with different charges. At the same time, the radii of these cations do not differ too much and are equal to 2.8, 2.5, and 2.5 Å for hydrated K+, Ca2+, and La3+ ions, respectively.44 From Figure 3, it is seen that the viscosity passes through a maximum at increasing salt concentration for all of the three salts under study. This behavior is quite similar to that observed for many surfactant/ salt systems and is explained by the increasing length of the micellar chains and their further branching as a result of enhanced screening of electrostatic repulsion between the surfactant head groups.19,45−47 In the presence of a small amount of added salt, the samples demonstrate low viscosity of 10−3 Pa s, close to that of a pure solvent. Under these

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RESULTS AND DISCUSSION Rheological properties of 0.6 wt % EHAC solutions were studied both in steady state and in dynamic regimes at different concentrations of salts varying over 2 orders of magnitude. Figure 1 shows typical results of steady-state measurements for CaCl2 salt. One can see a Newtonian plateau at a low shear rate followed by a pronounced shear thinning, which can be due to 12549

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so that its further growth does not affect the number of entanglements in the system. These results are consistent with literature data. In particular, a very weak dependence G0 ∼ Cs0.77 was shown for EHAC/KCl at somewhat higher surfactant concentration (2.25 wt % EHAC).49 Note that the branching of micelles is not expected to have any impact on the plateau modulus taking into account that the saturated multiconnected network containing only branching points without any entanglements demonstrates a Newtonian flow without any elastic response.50 Figure 3a shows that with increasing salt valence the viscosity curve shifts toward a lower salt content, suggesting that a small amount of salt is needed to induce the growth of micelles in length and their further branching. To prove this, the average length of micellar chains L was estimated from the rheological data using the following equation51 G0 L ≈ le G″min

where G″min is the value of the loss modulus at the high frequency minimum (Figure 2) and le is the entanglement length, that is, the contour length between two successive entanglements. The entanglement length was determined from the G0 value by using the following expression52,53 G0 ≈

kT le9/5lp6/5

where lp is the persistence length, which amounts to 30 nm for EHAC wormlike micelles.54 The above model of estimation of the contour length of micelles is valid34 for the system of entangled wormlike micelles with le ≫ lp and with the breaking time much higher than the Rouse time of a chain with the length equal to le. These requirements are fulfilled in the studied system. If the micelles are branched, an effective contour length Lc should be used47 instead of L. The effective length Lc corresponds to the contour length of linear wormlike micelles forming a network, which has the same rheological properties as the network of the branched micelles. The L (or Lc) values thus obtained are plotted as a function of salt concentration in Figure 4. It is seen that in the presence of multivalent salt the micelles are longer. The effect of different salts on the growth of the micelles can also be demonstrated by SANS data. For cylindrical micelles,

Figure 3. Zero-shear viscosity η0 (a), terminal relaxation time λ (b), and plateau modulus G0 (c) of 0.6 wt % aqueous solutions of EHAC as a function of the concentration of added salts: KCl (triangles), CaCl2 (circles), and LaCl3 (squares) at 20.5 °C.

conditions, the solutions contain spherical or short cylindrical micelles that do not entangle with each other, that is, the solution is in the dilute regime.43 At a higher salt concentration, the viscosity starts to increase considerably, indicating the transition from dilute to semidilute regime, when the growing micelles become sufficiently long to entangle with each other. In this regime, the viscosity sharply increases by up to 5 orders of magnitude due to increasing contour length of micelles. Then, at some concentration of salt, the maximum viscosity is reached, after which the viscosity starts to decrease; this was attributed to the branching of micelles.19,20,48 Branching induces the appearance of a new relaxation mechanism, where the branching points slide along the main chain, which speeds up the relaxation processes and decreases the viscosity. Figure 3b shows that the terminal relaxation time mirrors the change in the viscosity (Figure 3a). At the same time, the plateau modulus, which was obtained only for samples with rather high viscosity, varies only slightly with salt concentration (Figure 3c), indicating a constant density of cross-links. Under these conditions, the length of micelles becomes large enough

Figure 4. Average contour length L (of linear micelles) or effective length Lc (of branched micelles) in 0.6 wt % aqueous solutions of EHAC as a function of the concentration of added salts: KCl (triangles) and CaCl2 (circles) at 20.5 °C. 12550

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The Journal of Physical Chemistry B ⎛ πcM (Δρ)2 ⎞ R g2Q 2 L ⎟ ln(QI ) = ln⎜⎜ − ⎟ 2 2 ⎝ NaρB ⎠

the scattering intensity in low-Q region is known to scale as3,55,56 I ∼ Q−1. In the case of very short rodlike micelles, for which spherical end-caps make a significant contribution to scattering compared to that of cylindrical central part, the dependence I(Q) is weaker.56 From Figure 5, it is seen that at

where c is the concentration of the surfactant, ρB is the bulk density of the surfactant, and Δρ = ρEHAC − ρD2O is the scattering contrast. Rg and ML values together with the radii of wormlike micelles Rc deduced from Rg values as20,57 Rc = √2Rg are presented in Table 1. Despite the fact that the formula used to estimate Rc is valid in the case of uniform distribution of the neutron scattering length along the micelle cross section, it was commonly applied in the analysis of the scattering data from wormlike micelles of EHAC.19,20 The estimated Rc values are close to those obtained in refs 19, 20, but they are larger than the length of the alkyl tail of EHAC, equal to11 ca. 2.4 nm. Most probably, Rc values contain the contributions of both the alkyl tail and the bulky quaternary ammonium head group. From Table 1, it is seen that the Rc values of the radii of micelles remain unaltered by the amount and valence of the added salt ions. As to ML values, Table 1 shows that they are only slightly affected by the type of salt, but increase with increasing salt concentration, indicating tighter packing of the surfactant molecules in the micelles. This is obviously due to the enhanced screening of the repulsion of similarly charged head groups of EHAC. The values obtained are in good agreement with the ML values previously reported for EHAC micelles: 1.9 × 10−13 g/cm for 4.5 wt % EHAC solution in 1−12 wt % of KCl19 and 3.0 × 10−13 g/cm for 4.5 wt % EHAC solution in 2, 6, and 12 wt % of KCl,58 but the ML values reported in the literature were not significantly influenced by salt content.19,58 Thus, in this article, we first observe by SANS a tighter packing of EHAC molecules within the micelles upon increasing salt concentration. Note that in contrast to the literature data19,58 where the total salt concentration range corresponds to long wormlike micelles, we compare the long wormlike micelles (in 0.09 M salt) with the short rodlike ones (in 0.007 M salt), for which spherical end-caps are non-negligible in comparison with the cylindrical central part. Thus, the shift in the viscosity curve indicates that, in the presence of salt with multivalent cations, the growth of the micelles and their branching proceed at lower salt concentrations. The main reason for this may consist in more effective screening of charges of surfactant head groups by these salts as they contain a larger amount of anionic species Cl− oppositely charged with respect to the head groups. To check this suggestion, viscosity was plotted as a function of the concentration of chloride ions (Figure 7). It is seen that the ascending branches of the curves coincide perfectly and independently of the type of added salt (Figure 7). Therefore, in this range of salt concentrations, salt counterions fully determine the viscosity of the surfactant solution. At the same time, the maxima and the descending branches of the curves diverge for different salts (Figure 7), indicating that in this range of salt concentrations, co-ions have a significant impact on the viscosity. These results are in complete agreement with the recent theoretical predictions.35 According to the theory, the influence of salt co-ions on the micellar growth in EHAC solutions should be different at low and high salt contents. At low salt contents, the co-ions reside far from micelles because of their strong repulsion from similarly charged surfactant head groups and therefore their effect should be small. Under these conditions, the micellar growth is affected primarily by salt

Figure 5. SANS profiles for 0.6 wt % aqueous solutions of EHAC containing 0.007 M of added salts: KCl (triangles), CaCl2 (circles), and LaCl3 (squares). Solid lines show the slopes of I ∼ Q−1 and I ∼ Q0 dependences. The inset is an enlargement of the low-Q data.

low salt concentration (0.007 M), the slope of log−log plot I(Q) in low-Q region increases with increasing valence of cations and reaches a value of −1 for LaCl3. These data indicate the elongation of micelles upon increasing the valence of cations, which coincides with rheological results obtained at higher salt concentrations. Guinier plots are depicted in Figure 6 in the Q-range 2π/lp ≤ Q ≤ 1/Rg, where Rg is the cross-sectional radius of gyration of wormlike micelles of EHAC. It is seen that these plots represent straight lines. From their slopes and intercepts, the values of Rg and of the mass per unit length ML, respectively, were obtained using the following equation19

Figure 6. Dependences of ln(QI) on Q2 for 0.6 wt % aqueous solutions of EHAC containing 0.007 M (top) and 0.09 M (bottom) of salt: KCl (triangles), CaCl2 (circles), and LaCl3 (squares). 12551

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Table 1. Values of Cross-Sectional Radius of Gyration Rg, Radius Rc, and Mass Per Unit Length ML of Wormlike Micelles in 0.6 wt % Aqueous Solutions of EHAC Containing 0.007 or 0.09 M KCl, CaCl2, or LaCl3 0.007 M salt

0.09 M salt

salt

Rg, nm

Rc, nm

ML, 10−13 g/cm

Rg, nm

Rc, nm

ML, 10−13 g/cm

KCl CaCl2 LaCl3

2.1 ± 0.4 2.1 ± 0.4 2.4 ± 0.4

3.0 ± 0.6 3.0 ± 0.6 3.4 ± 0.6

2.13 ± 0.03 2.09 ± 0.02 2.33 ± 0.02

2.4 ± 0.2 2.3 ± 0.2 2.4 ± 0.2

3.4 ± 0.3 3.2 ± 0.3 3.4 ± 0.3

2.62 ± 0.03 2.79 ± 0.03 2.62 ± 0.03

Figure 8. Cryo-TEM picture of 0.6 wt % EHAC solution containing 0.2 M KCl. Branching points are marked by arrows.

It is interesting that at somewhat higher temperature (40 °C) the second slope of the viscosity curve disappears (Figure 7a), indicating an abrupt transition from the regime of micellar growth in length to the regime of micellar branching. This behavior can be explained as follows. When the added salt makes the spherical end-caps more unfavorable, their amount is reduced. It can occur in one of two ways: either by increasing the length of micelles or by their branching. Both processes reduce the entropy. However, if the length of chains is sufficiently long, the branching results in less significant decrease of entropy, as the branches keep the possibility to freely slide along the main chain. Higher temperature, which makes the entropic contribution to the free energy more important, is thus expected to favour the branching process. Therefore, when the conditions make the branching possible, at higher temperature, the system switches abruptly to branching, whereas at lower temperature, the branching can still coexist with the growth of micelles in length. The exponents of power-law dependences of viscosity η0 on the salt concentration in regimes I and II, kI, kII, are compiled in Table 2. It is seen that they are almost independent of the type of salt (KCl, CaCl2, and LaCl3). Thus, the behavior of the system in the rising part of viscosity curve is fully determined by salt counterions and does not depend on the type and the valence of salt co-ions. Now, let us consider the part of viscosity curves affected by salt co-ions (regime III). It includes the viscosity maximum and the descending branch, which are determined by the behavior of linear micelles of maximum length and branched micelles, respectively. The transition to regime III proceeds at 0.22 M

Figure 7. Zero-shear viscosity η0 of 0.6 wt % aqueous solutions of EHAC as a function of the concentration of anions Cl− of added salts: KCl (triangles), CaCl2 (circles), and LaCl3 (squares) at 20.5 °C in double logarithmic (a) and semilogarithmic (b) coordinates. Diamonds (a) show the zero-shear viscosity η0 data for 0.6 wt % aqueous solutions of EHAC in KCl at 40 °C. Reprinted with permission from ref 5. Copyright 2005 American Chemical Society.

counterions, which is indeed observed experimentally in regimes I and II (Figure 7). At the same time, at high salt concentration providing a strong screening of the electrostatic repulsion, the influence of salt co-ions becomes significant because they can come closer to the surface of micelles. Such behavior was observed experimentally in regime III (Figure 7). Let us first consider in more detail a rising branch of the curves controlled by salt counterions (regimes I and II). In this branch, a sharp increase in viscosity (regime I) is followed by its moderate enhancement (regime II) just before reaching a maximum value (Figure 7a). A less pronounced increase in viscosity can be because of the onset of the branching of micellar chains proceeding simultaneously with the growth of micelles in length. Indeed, some branching points can be detected on cryo-TEM image before the viscosity maximum (Figure 8). The branching points have three arms in contrast to overlapping micelles showing four arms at intersection. Note that, under these conditions, the micelles are very long; their contour length exceeds few microns. 12552

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micellar chains making their scission easier and therefore reducing their average contour length. Shortening of the maximum length of surfactant micelles decreases the maximum viscosity of EHAC solutions in the presence of KCl. The viscosity curves in the presence of Ca2+ and La3+ co-ions are very close to each other (Figure 7). This may indicate that these co-ions reside far from similarly charged micelles because of their high charge and therefore do not influence the rheological properties of solutions. Table 2 shows that the slopes of the descending branches of the viscosity curves are almost the same for all three salts. Therefore, probably, potassium co-ions affect mainly the maximum length of the micelles, whereas their contribution to the branching process is much weaker. It should be pointed out that the observed slope of the descending branch is smaller than that reported in the literature (η0 ∼ Cs−3.37) for the EHAC/KCl system at a higher EHAC concentration (2.25 wt %).49 Therefore, the slope is sensitive to surfactant concentration: the higher the surfactant concentration, the sharper the salt-induced drop in viscosity. This fact seems to be quite reasonable taking into account that the increase in the concentration of surfactant favors branching.59 Also, at higher surfactant concentration, the micelles are longer and hence the branches can slide over larger distances along the main chains, thus facilitating the stress relaxation and therefore reducing the viscosity. Note that despite the decrease in viscosity, the value of plateau modulus G0 remains almost constant (Figures 1 and 3c). It indicates that the density of the entanglements in the network does not change upon branching. This is in accordance with the fact that multiconnected networks behave as Newtonian fluids50 without any viscoelastic response. It means that the branching points do not act as entanglements and do not contribute to the elastic modulus. Valuable information about the behavior of the system in regime III can be extracted from the analysis of Cole−Cole plots (Figure 10), representing the imaginary part of the shear modulus G″ plotted against the real part G′. The Cole−Cole plots with G′ and G″ values normalized by the value of G″ at the maximum in the low-frequency range43 are presented in Figure 10 for different concentrations of KCl and LaCl3. In these plots, an ideal semicircle corresponds to the Maxwellian viscoelastic liquid with single relaxation time.60−63 From Figure 10, it is seen that all of the studied systems become closer to Maxwellian ones when salt concentration is increased. Such behavior was previously described in many papers,43,47,64−67 and it was attributed to the increase in the micellar contour length making the breaking time τb much shorter than the reptation time τrep: τb ≪ τrep. Indeed, by increasing the length of micelles, their reptation time increases, whereas the breaking time becomes shorter as, in longer micelles, there are more places where the breaking can occur. As a result, during reptation, the micelles break and reform many times, which averages the relaxation processes leading to monoexponential stress decay. However, all of these observations in the literature were made at salt concentrations corresponding to the rising branch in the viscosity curve.43,47,64−67 Branched chains (after viscosity maximum) were shown to keep a Maxwellian response attained at increasing viscosity.68 In contrast, the present system does not show a Maxwell behavior even at highest viscosity corresponding to wormlike micelles of maximum length (Figure 10): 0.22 M KCl and 0.08 M LaCl3. Most probably,

Table 2. Values of the Power-Law Dependences of ZeroShear Viscosity η0 of 0.6 wt % Aqueous Solutions of EHAC on the Salt Concentrations for Different Regimes Indicated in Figure 7 salt

kI

kII

kIII

KCl CaCl2 LaCl3

10.6 ± 0.8 9.1 ± 0.9 10.1 ± 0.4

3.3 ± 0.1 3.6 ± 0.2 3.6 ± 0.5

−2.0 ± 0.1 −2.0 ± 0.2 −1.7 ± 0.3

KCl, 0.13 M CaCl2, and 0.08 M LaCl3, which correspond to the Debye screening lengths κ−1 of 0.65, 0.49, and 0.44 nm, respectively, indicating that under these conditions the electrostatic repulsion is essentially shielded. A fairly higher κ−1 values for KCl suggest that K+ co-ions start influencing the rheological properties when the micellar charge is less screened, which may be due to the lower charge of these ions. Meanwhile, from Figure 7b, it is seen that in KCl solutions, the maximum viscosity is lower than that in CaCl2 and LaCl3; therefore, in the presence of potassium co-ions, the maximum length of linear wormlike micelles is shorter. According to molecular thermodynamic theory,35 at high salt concentrations, when the electrostatic repulsion is rather weak and unable to keep the salt co-ions far from the micellar surface, the co-ions triggered by dispersive attraction can get inside the corona of micelles. In this case, the localization of salt co-ions becomes the governing factor that influences the growth of micelles. In our system, one can suggest that among the three co-ions (K+, Ca2+, La3+), potassium ions could come closer to the micelles because of their smaller charge and therefore weaker repulsion with the similarly charged surfactant head groups. In addition, according to theoretical considerations,35 at high salinity, K+ coions can penetrate deep inside the corona of EHAC micelles as a result of the dispersion interaction of the ions with the micelle and dehydration of the ions in the corona. The theory predicts35 that surprisingly K+ co-ions can reside even closer to the core of EHAC micelles than Cl− counterions (Figure 9). Such a specific location of K+ ions increases the charge of

Figure 9. Schematic representation of the distribution of salt co- and counterions around wormlike micelle of cationic surfactant EHAC at high salt contents. Cloud of counterions Cl− (minuses) is localized around the micelle; some of the K+ co-ions, which are able to penetrate inside the corona area,35 when the electrostatic repulsion is strongly screened, are located even closer to positively charged head groups of micelles than Cl− counterions. 12553

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The Journal of Physical Chemistry B

the three salts studied, the viscosity passes through a maximum with increasing salt concentration, with the curve being shifted to lower salt content for salts with higher ion valence. These results suggest that multivalent salts favor the linear growth of micelles and their branching. However, when the viscosity is plotted as a function of salt anions, the rising branches of the curves for all of the salts perfectly coincide with each other, indicating that mainly salt ions oppositely charged with respect to surfactant molecules determine the growth of micelles in length. As to the effect of salt cations, it appears only at viscosity maximum and its further decrease, when the electrostatic interactions become highly shielded. Therefore, salt ions similarly charged with surfactant ions affect mainly the maximum length of micelles and their further branching. More specifically, it was found that the maximum viscosity of EHAC in KCl solution is ca. 2-fold lower than that in CaCl2 and LaCl3 solutions. We believe that the main reason for this effect is related to deep penetration of K+ co-ions inside the corona of micelles, leading to the increase in the net charge of the micelles and therefore hindering their growth. These observations fully coincide with the recent theoretical predictions,35 showing that micelles with charged surfaces can bind not only salt counterions but also co-ions, provided that the electrostatic repulsions between the micelles and similarly charged salt ions are significantly screened. The results obtained are important for the proper design of wormlike micellar systems, suggested to be used in different salt-containing media.

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Figure 10. Normalized Cole−Cole plots for 0.6 wt % aqueous solutions of EHAC at different concentrations of the added salts: KCl (top) and LaCl3 (bottom) at 20.5 °C.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +7 495 9391464. Fax: +7 495 9392988.

this is because of a low concentration of the surfactant, which does not allow the formation of long enough linear micelles providing τb much shorter than τrep: τb ≪ τrep, and therefore exhibiting a wide range of relaxation times. Yet, the most important observation is that the present system continues to approach Maxwell behavior at decreasing viscosity (regime III), when a pronounced branching of micelles occurs. It indicates that branching narrows the spectrum of relaxation times, that is, makes the scission/ recombination processes faster than the reptation. Acceleration of the scission/recombination processes can be because of very short lifetime of branching points69,70 and the fastening of micellar reformation at strong screening of electrostatic repulsion at a high salt content.66 Multivalent salt is more effective in bringing the system closer to the Maxwellian one when compared to monovalent salt (Figure 10), which is obviously due to larger micelles in the former case. Thus, salt co-ions affect the rheological behavior of wormlike micellar solutions at high salt concentrations when the electrostatic repulsion cannot keep these ions far from the similarly charged micelles. The most pronounced effect is produced by co-ions of smaller charge (K+). They are able to approach closer to the micelle, increasing its effective charge and thereby opposing its growth.

ORCID

Olga E. Philippova: 0000-0002-1098-0255 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Russian Science Foundation (Project no. 15-13-00114).

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REFERENCES

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CONCLUSIONS In this article, the rheological properties of cationic surfactant EHAC solutions with added inorganic mono- and multivalent salts (KCl, CaCl2, and LaCl3) having a common counterion with the surfactant were examined. SANS and cryo-TEM data were used to shed light on the microstructural changes underlying the rheological ones. It was shown that for all of 12554

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