Rheological Behavior of Oil-Swollen Wormlike Surfactant Micelles

Article pubs.acs.org/JPCB

Rheological Behavior of Oil-Swollen Wormlike Surfactant Micelles Andrey V. Shibaev, Vyacheslav S. Molchanov, and Olga E. Philippova* Physics Department, Moscow State University, 119991 Moscow, Russia ABSTRACT: We study the rheological properties of wormlike micellar aqueous solutions of an anionic surfactant potassium oleate containing solubilized 1-phenyldodecane. We show that upon increasing the amount of absorbed hydrocarbon the rheological behavior of semidilute micellar solutions changes drastically, showing a sequence of different regimes: (i) a “fast-breaking” entangled regime, when very long micellar chains form a network; (ii) an “unbreakable” entangled regime, when the shortening of the micelles leads to the decrease of their reptation time up to the values close to the breaking time; (iii) an unentangled regime (for the first time evidenced for wormlike micelles), where the micelles are so short that they cannot interlace. Within the entangled regime, an unusual rheological behavior has been discovered, probably characterized by the dominant role of end or bond interchange reactions or “breathing” modes, which leads to a novel hypothesis that hydrocarbon is distributed nonuniformly along the micellar length, thus increasing the probability of micellar breakage at certain points.

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INTRODUCTION

However, when the amount of absorbed hydrocarbon is small, wormlike micelles still persist, and their properties depend significantly on the nature of hydrocarbon, which determines the site of its location in the micellar core. When the solubilization proceeds preferentially in the interior part of the core far from the micellar surface (like in the case of highly hydrophobic long n-alkanes), it induces the radial growth of micelles.17−19 Such swelling decreases the curvature of the cylindrical part of wormlike micelles making it closer to the curvature of the semispherical micellar end-caps, which results in the drop of scission energy and hence of the average micellar length. By contrast, when the solubilization proceeds preferentially at or near the micellar surface (like in the case of solubilization of benzene20 or cycloalkanes21 in cationic surfactant micelles or m-xylene in nonionic poly(oxyethylene) alkyl ester micelles22), the micelles grow in length and do not change their radius. There are only few works, in which the rheological behavior of oil-swollen wormlike micelles is treated. For instance, Hoffmann et al.13 studied a particular case of perfluorinated surfactants with absorbed fluorocarbon and observed the lowering of viscosity, plateau shear modulus, and relaxation time with increasing amount of fluorocarbon, which was explained by the shortening of micellar chains and the diminution in the number of entanglements between them. Prud’homme et al.23 observed the decrease of scission energy, micellar length, and viscosity upon absorption of n-hexane by wormlike micelles of a cationic surfactant erucyl bis(hydroxyethyl)methylammonium chloride. Aramaki et al.24−26

Equilibrium “living” networks based on small self-assembling molecules have become an object of considerable attention in the past decade due to their remarkable rheological behavior and highly responsive properties.1−5 Among them, networks of wormlike surfactant micelles have been extensively studied, since they possess a number of advantages over the other responsive systems.3−5 The micellar chains can overlap and form a network with high viscosity (up to ∼104 Pa s) and pronounced viscoelastic properties at very low surfactant concentrations. Since the networks are built by small molecules linked by weak noncovalent bonds, the degradation of their mechanical properties at high shear or elevated temperatures is completely reversible. Strong viscoelasticity of the micellar solutions combined with commercial availability of many surfactants which form wormlike micelles gave rise to their numerous applications as thickening agents in cosmetics, drag reduction, oil industry, etc.6,7 The self-assembled nature of the micellar chains confers them high responsiveness to multiple factors: light, pH, CO2, hydrocarbons, etc.8−10 Among them, the responsiveness to hydrocarbons is one of the most important because this is a key property determining a wide application of wormlike micellar systems for hydraulic fracturing in oil recovery.11 This application resides on the fact that large amounts of hydrocarbons lead to a drop of viscosity of wormlike micellar solutions by several orders of magnitude and a complete loss of viscoelastic properties. Such behavior is due to the solubilization of hydrocarbons inside the micellar hydrophobic cores, resulting in the disruption of wormlike micelles and their transition to microemulsion droplets.12−16 © 2015 American Chemical Society

Received: October 27, 2015 Revised: December 6, 2015 Published: December 9, 2015 15938

DOI: 10.1021/acs.jpcb.5b10505 J. Phys. Chem. B 2015, 119, 15938−15946

Article

The Journal of Physical Chemistry B

regime far above an overlap concentration C*, which has been reported to be approximately 0.1 wt %.15 These solutions contain long wormlike micelles as was previously evidenced by cryo-TEM and small-angle neutron scattering (SANS).15,31 The concentration of low-molecular-weight salt KCl has been fixed at 6.5 wt %. It corresponds to the maximum of the bell-shaped dependence of viscosity on KCl concentration, which ensures the formation of linear wormlike micelles of maximum length. In the absence of hydrocarbons such solutions possess high viscosity (Figure 1) and pronounced viscoelastic properties

reported the drop of viscosity by several orders of magnitude upon addition of fluorinated oils to wormlike micelles formed by a mixture of nonionic perfluorinated surfactants (C8F17EO20 and C8F17EO1). But, to the best of our knowledge, a detailed description of the sequence of rheological regimes upon gradual increase of the amount of absorbed hydrocarbon has never been presented. This paper is aimed at studying the changes in rheological behavior of oil-swollen wormlike micelles with increasing amount of solubilized hydrocarbon. The investigations were performed on an example of C18-tailed anionic surfactant potassium oleate. For these studies, we used a hydrocarbon of the phenylalkane family (1-phenyldodecane), which has a rather long C12 alkyl tail and an aromatic ring. Since different effects of aliphatic and aromatic hydrocarbons on the rheology and structure of wormlike surfactant micelles have been reported in the literature, it is interesting to investigate how hydrocarbon with both of these moieties affects the micellar solution properties.

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EXPERIMENTAL SECTION Materials. Potassium oleate (Aldrich, 40 wt % solution in water), potassium chloride (Panreac, purity >99.8%), and 1phenyldodecane (Aldrich, purity >97%) were used without further purification. Distilled deionized water was purified by the Millipore Milli-Q system. Rheology. Rheological measurements were made with a stress-controlled rotational rheometer Haake Rheostress 150L. The temperature was controlled with a water circulating bath and held constant at 20.5 ± 0.2 °C. For highly viscous and viscoelastic samples, a cone−plate geometry with 35 mm diameter and 2° cone angle was used, whereas for low-viscous samples, the experiments were performed with double-gap coaxial cylinders (19.14 mm average radius, 55 mm height). A specially constructed vapor lock was used to prevent solvent evaporation from the sample. The samples were equilibrated for 10−15 min in the measurement cell prior to investigation. In steady shear measurements different shear stresses (0.005−10 Pa) were applied to the sample, and the value of viscosity on the plateau at low stresses was taken as the zeroshear viscosity. In oscillatory shear (dynamic) measurements, the stress amplitude was chosen in the linear viscoelastic regime as determined by dynamic stress sweep measurements to ensure that the storage modulus (G′) and the loss modulus (G″) are independent of the applied stress. The Cox−Merz rule28 was tested to hold for most of the investigated viscoelastic samples. Dynamic Light Scattering (DLS). DLS experiments were performed on an ALV/DLS/SLS-5000 goniometer system (Langen, Germany) with a helium−neon laser (wavelength 632.8 nm). ALV-5000 digital time correlator was used for the calculation of the correlation functions. The details of the data treatment are described elsewhere.29,30 For the measurements, the solutions preliminarily filtered through 0.22 μm poly(vinylidene fluoride) filters (Millipore) were put into cylindrical cells with a diameter of 10 mm. The cells were immersed in an index-matching fluid (toluene).

Figure 1. Dependences of shear viscosity η on shear rate for 2.5 wt % potassium oleate solution in the presence of 6.5 wt % KCl and different concentrations of 1-phenyldodecane: 0 wt % (filled circles), 0.012 wt % (open circles), 0.025 wt % (filled triangles), 0.033 wt % (open triangles), 0.041 wt % (filled stars), 0.076 wt % (open stars), 0.11 wt % (filled squares), 0.125 wt % (open squares), 0.135 wt % (filled reverse triangles), 0.155 wt % (open reverse triangles), and 0.22 wt % (filled diamonds). Temperature: 20 °C.

(Figure 2) with G′ much higher than G″ in a wide range of frequencies and a plateau on G′(ω) dependence, indicating that the wormlike micelles interlace and form a network. Figure 1 demonstrates the effect of 1-phenyldodecane on the viscosity of 2.5 wt % potassium oleate solutions. It is seen that the solution without hydrocarbon has a zero-shear viscosity of 110 Pa s, which is 5 magnitudes higher than the viscosity of water. The viscosity decreases progressively as hydrocarbon is

Figure 2. Frequency dependences of the storage modulus G′ (filled symbols) and of the loss modulus G″ (open symbols) for 2.5 wt % potassium oleate solution in the presence of 6.5 wt % KCl and different concentrations of 1-phenyldodecane: 0 wt % (circles), 0.033 wt % (triangles), 0.041 wt % (stars), 0.076 wt % (squares), and 0.11 wt % (diamonds). Temperature: 20 °C. Gray solid lines represent the theoretical dependences calculated according to the Maxwell model.

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RESULTS AND DISCUSSION In this paper, the studies were performed with 1−5 wt % potassium oleate aqueous solutions in the presence of KCl. The concentrations of surfactant correspond to the semidilute 15939


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The Journal of Physical Chemistry B added, reaching finally that of pure water. Simultaneously with the decrease of viscosity we observe a drop of G′ and G″, the increase of frequency at which G′ = G″ and the disappearance of the plateau on G′(ω) dependence (Figure 2). A thorough analysis of the rheological data at different amounts of absorbed hydrocarbon allows one to distinguish several regimes in the rheological behavior of oil-swollen micellar chains. They are discussed in detail below. “Fast-Breaking” Entangled Semidilute Regime. This regime corresponds to small hydrocarbon concentrations: 0− 0.041 wt % (for 2.5 wt % of surfactant), at which the viscosity is rather high (>10 Pa s), and one can still observe the plateau on G′(ω) dependence, indicating the presence of an entangled network. Within this regime, the rheological behavior of the solutions is well-described by Maxwell model with a single relaxation time τ, what is evident from fitting of the experimental data by the theoretical frequency dependencies of storage (G′) and loss (G″) moduli for a Maxwell fluid (Figure 2). The relaxation time can be determined as τ = 1/ωr from the frequency ωr, at which G′(ω) and G″(ω) intersect. Such simple rheological behavior is a common feature of viscoelastic surfactant solutions containing long entangled wormlike chains.5,32 As the hydrocarbon concentration increases, a progressive shift of the intersection point of G′(ω) and G″(ω) to higher frequencies is seen (Figure 2), indicating the decrease of the relaxation time τ. As shown by Cates,33 stress relaxation in the entangled wormlike micellar solutions is defined by two main processes, reptation and reversible chain scission, and the relaxation time depends on two characteristic times, reptation time τrep and breaking time τbr. Namely, in the presence of fast reversible scission reactions34

τ=

τrepτbr

Figure 3. Cole−Cole plots for 2.5 wt % potassium oleate aqueous solutions in the presence of 6.5 wt % KCl and different concentrations of 1-phenyldodecane: (1) 0 wt %, (2) 0.012 wt %, (3) 0.025 wt %, (4) 0.033 wt %, (5) 0.041 wt %, (6) 0.076 wt %, and (7) 0.11 wt %. Semicircle (8) represents the theoretical dependence calculated according to the Maxwell model. Temperature: 20 °C.

with corrections according to the results of computer modeling for different systems.35,36,39 Knowing the relaxation time τ for Maxwell solutions from the intercept of G′(ω) and G″(ω) and using eqs 1 and 2, reptation and breaking times were calculated separately. The values of τbr and τrep for oil-swollen wormlike micellar solutions of potassium oleate at different content of 1phenyldodecane are shown in Figure 4. It is seen that in the

(1)

Thus, the dependences of the reptation and breaking times on hydrocarbon concentration should be addressed in order to understand the observed decrease of τ. Separate determination of these times from the rheological data can be done by using the Cole−Cole plots, which represent the dependences of G″ on G′ normalized by the maximum value of the loss modulus at low frequencies G″max. Cole−Cole plots for 2.5 wt % potassium oleate solutions at different hydrocarbon concentrations are depicted in Figure 3. Semicircle also shown in this figure represents an ideal Maxwell fluid. It can be seen that the deviations from the semicircle occurring at high values of G′ (that is, at high frequencies) grow with increasing hydrocarbon content, indicating the progressive divergence from the Maxwell behavior. Cates and co-workers showed35,36 that the magnitude of these deviations is determined by the ratio of breaking and reptation time τbr/ τrep. The system can be roughly considered as a Maxwell fluid only if the length β of the segment, which is cut off on the G′axis by a straight line fitting the data at high frequencies, does not exceed 3.1−3.2, which corresponds to τbr/τrep less than 0.3−0.5. As it is seen from Figure 3, according to such treatment, our solutions can be regarded as Maxwellian only at hydrocarbon concentrations less than ∼0.041 wt %. The ratio τbr/τrep was determined from the Cole−Cole plots using an approximate equation37,38 2 ⎛ 1 ⎞ τbr /τrep = ⎜1 − ⎟ β − 1⎠ ⎝

Figure 4. Reptation time (black symbols) and breaking time (gray symbols) as functions of concentration of 1-phenyldodecane for 2.5 wt % potassium oleate aqueous solutions in the presence of 6.5 wt % KCl. Temperature: 20 °C.

absence of hydrocarbon and at its very small concentrations the breaking time is much shorter than the reptation time (τbr ≪ τrep), which corresponds to the so-called “fast-breaking” regime.40 In this regime, wormlike micelles break and recombine many times during the time of reptation. This results in the averaging of the relaxation processes, which acquire one characteristic relaxation time, monoexponential stress relaxation function, and Maxwell behavior. Now let us consider how the concentration of surfactant in the solution of oil-swollen wormlike micelles affects the rheological behavior. For this study we fixed the molar ratio [1-phenyldodecane]/[potassium oleate] at 1/80 (what corresponds to the hydrocarbon concentration of 0.025 wt % at 2.5 wt % surfactant), and obtained the dependences of viscosity,

(2) 15940


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Thus, at very low concentrations of solubilized hydrocarbon the solutions of oil-swollen wormlike micelles are in the “fastbreaking” regime and retain Maxwell behavior, which is explained by the presence of long entangled micellar chains. “Unbreakable” Entangled Semidilute Regime. As seen from Figure 4, the reptation time drops significantly as the hydrocarbon concentration increases and at ∼0.041 wt % of hydrocarbon nearly reaches the value of the breaking time, which indicates that the system leaves the “fast-breaking” regime (τbr ≪ τrep) and approaches the regime of “unbreakable” chains, for which τbr ≥ τrep. In this regime, reptation occurs fast enough, so that the micelles do not break and recombine many times during τrep and behave like ordinary polymer chains. For “unbreakable” wormlike micelles, reptation is the principal mechanism of stress relaxation, which is characterized by a spectrum of relaxation times, and the stress relaxation function is strongly nonexponential.40 It is likely that the transition from “fast-breaking” to “unbreakable” regime, which takes place upon increasing concentration of hydrocarbon, is provoked by the shortening of oil-swollen wormlike micelles. Indeed, the “fast-breaking” regime is usually observed for rather long wormlike micellar chains,4,40,41 since the longer is the micelle, the more places along its length exist where it can break, and thus the frequency of the breaking process is high enough. Given the fact that the reptation time increases with the mean micellar contour length L according to the equation4,40

relaxation time, and plateau storage modulus on surfactant concentration, which are shown in Figure 5 (curves b). It is

τrep ∼ L3C 3/2

(3)

where C is the concentration of the surfactant, and the breaking time is inversely proportional to the contour length (since the probability of scission is assumed constant over the whole length of the micelle)4,40 τbr = (kL)−1

(4)

it can be easily seen that the condition τbr ≪ τrep holds only for relatively large values of L. The decrease of L results in the lowering of τrep, which causes the transition from the “fastbreaking” to the “unbreakable” chains. It is seen from Figure 4 that the breaking time is almost unaffected by the content of hydrocarbon in oil-swollen micelles. This behavior, which seems rather unexpected, can be due to the fact that two oppositely acting tendencies affect the value of τbr. On the one hand, the solubilization of hydrocarbon may result in the weakening of bonds between surfactant molecules in the micelle, thus favoring the disruption of the micelles. On the other hand, the shortening of surfactant micelles upon absorption of hydrocarbon should increase the breaking time, since the number of places where the chain can be broken is reduced. As a result of these two competing tendencies, the breaking time does not significantly change with the concentration of hydrocarbon. To the best of our knowledge, this is the first work presenting the dependences of the reptation and breaking times on the amount of hydrocarbon in oil-swollen wormlike surfactant micelles. These times are microscopic parameters related to different mechanisms of stress relaxation; therefore, their determination is essential for understanding the dynamics of micellar chains. Figure 5 (curves c) shows the dependences of the rheological properties on surfactant concentration at fixed molar ratio [1phenyldodecane]/[potassium oleate] = 1/40 (which corre-

Figure 5. Dependences of zero-shear viscosity (A), relaxation time (B), and plateau storage modulus (C) on surfactant concentration for potassium oleate aqueous solutions in the presence of 6.5 wt % KCl and 1-phenyldodecane at different molar ratios [1-phenyldodecane]/ [potassium oleate]: 0 (a), 1/80 (b), 1/40 (c), 1/12 (d, only the viscosity graph is shown). Temperature: 20 °C.

seen that these dependences obey the following scaling laws: η0 ∼ C3.7, τ ∼ C1.5, and G0 ∼ C2.25, which are close to those theoretically predicted for the “fast-breaking” regime in the presence of reversible scission reactions.40 Similar dependences are observed in the absence of hydrocarbon at surfactant concentrations higher than ∼0.7 wt % (Figure 5, curves a). Therefore, the “fast-breaking” regime is preserved when a very small amount of hydrocarbon is solubilized inside wormlike micelles, but it is “shifted” to higher surfactant concentrations (Figure 5A, cf. curves a and b). For convenience, all the slopes observed experimentally in this work and predicted theoretically for the corresponding regimes are summarized in Table 1. 15941


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Table 1. Power Laws of the Dependences of Zero-Shear Viscosity η0, Relaxation Time τ, and Plateau Storage Modulus G0 on Surfactant Concentration at Different Molar Ratios [1-Phenyldodecane]/[Potassium Oleate] (Theoretical Values from Ref 40) η0 hydrocarbon/surfactant molar ratio 0 (low surfactant concentrations) 0 (intermediate surfactant concentrations) 0 (high surfactant concentrations) 1/80 1/40 (low surfactant concentrations) 1/40 (high surfactant concentrations) 1/12

experiment

τ theory

experiment

G0 theory

experiment

theory

rheological regime

2.0 ± 0.4

1.9

unentangled

5.8 ± 0.3

5.7

entangled, “unbreakable”

3.7 ± 0.2

3.7

1.3 ± 0.2

1.4

2.25 ± 0.15

2.3

entangled, “fast-breaking” (reversible scission)

3.7 ± 0.2 5.7 ± 0.3

3.7 5.7

1.5 ± 0.2 3.5 ± 0.3

1.4 3.4

2.25 ± 0.10 2.15 ± 0.10

2.3 2.3

entangled, “fast-breaking” (reversible scission) entangled, “unbreakable”

3.0 ± 0.2

2.6− 3.5 1.9

0.7 ± 0.2

0.3− 1.2

1.7 ± 0.3

entangled, “fast-breaking” (bond or end interchange, or “breathing” modes) unentangled

Cates,40 they can be explained by the domination of the end interchange (or bond interchange) reactions instead of reversible scission. Thus, the lower exponents in our system may indicate that the solubilization of hydrocarbon inside the micelles changes the kinetics of reversible scission or makes interchange reactions more favorable. One can suppose that it may happen if hydrocarbon is not distributed uniformly along the micelle, but accumulates, for example, in the form of droplets in the micellar ends, thus favoring end interchange, or in the cylindrical body, making the bond interchange more preferable. The hypothesis of nonuniform distribution of hydrocarbon along the micelle has been recently proposed by us on the basis of theoretical considerations43 showing that the hydrocarbon is accumulated preferentially in the energetically unfavorable parts of wormlike micelles − hemispherical endcaps, reducing their curvature and thus making them more energetically favorable. Another explanation of the lower exponents can be the transition to the “breathing” modes regime, for which τbr/τrep ≪ 1/NT, where NT is the number of tube segments in the chain (usually for the micelles NT ∼ 10− 50).40 In any case, the rheological regime observed by us at high surfactant concentrations is still “fast-breaking”, since τbr/ τrep ≪ 1, and the observed exponents allow unambiguously distinguishing it from the regime of “unbreakable” chains. Thus, entangled oil-swollen wormlike micelles change their rheological behavior from the “fast-breaking” to the “unbreakable” regime either at increasing content of hydrocarbon (when the concentration of surfactant is fixed) and at decreasing concentration of surfactant (when the content of hydrocarbon is constant), which is explained by the shortening of the micellar contour length. Unentangled Semidilute Regime. At even higher hydrocarbon concentrations: 0.11−0.22 wt % (for 2.5 wt % of surfactant) the solutions of oil-swollen micelles lose viscoelastic behavior, which is seen from the frequency dependences of G′ and G″ (Figure 2): at 0.11 wt % of hydrocarbon there is no crossover point between G′ and G″ and no plateau on the dependence G′(ω). The Cole−Cole plot has a form very different from a semicircle (Figure 3). However, in the most part of this range of hydrocarbon concentrations the viscosity is much higher than the viscosity of water, which means that the micelles overlap and the solutions are in the semidilute regime. The sharp drop of viscosity and the absence of viscoelastic properties can be explained by the disruption of the entangled

sponds to 0.05 wt % hydrocarbon at 2.5 wt % surfactant). Two slopes can be clearly seen on the concentration dependences of viscosity and relaxation time. At low surfactant concentrations (C < 2.7 wt %) η0 ∼ C5.7 and τ ∼ C3.5, which corresponds to the regime of “unbreakable” chains.40 Note that nearly the same slope η0 ∼ C5.8 is seen in the absence of hydrocarbon, but at lower surfactant concentrations (Figure 5A, curve a). It indicates that the “unbreakable” regime is preserved for oilswollen wormlike micelles, but it is shifted to higher surfactant concentrations, since the oil-swollen micelles are shorter than those in the absence of hydrocarbons. At high surfactant concentrations (C > 2.7 wt %) η0 ∼ C3.0 and τ ∼ C0.7, which corresponds to the regime of “fastbreaking” chains.40 Thus, the transition from the “unbreakable” to the “fast-breaking” regime is observed upon increasing surfactant concentration at a fixed molar ratio [1-phenyldodecane]/[potassium oleate]. This is quite similar to the behavior of ordinary (oil-free) wormlike micelles (Figure 5A, cf. curves a and c). For oil-free wormlike micelles the transition from the “unbreakable” to the “fast-breaking” regime upon increasing surfactant concentration was explained14 by the growth of micelles in length, which leads to the increase of the time of their reptation τrep and the decrease of their breaking time τbr (eqs 3 and 4), thus approaching the system to the condition of “fast-breaking”: τbr ≪ τrep. One can assume that the same reason is valid for oil-swollen wormlike micelles, too. Thus, the oil-swollen wormlike micelles similar to their oil-free counterparts become longer with increasing surfactant concentration. The concentration dependence of the plateau storage modulus G0 shows only one slope of 2.15 (Figure 5C, curve c), which confirms the presence of entangled micellar chains in both the “fast-breaking” and “unbreakable” regimes.40,42 The most important observation concerns the fact that in the “fast-breaking” regime observed at higher content of hydrocarbon (at molar ratio [1-phenyldodecane]/[potassium oleate] = 1/40) the exponents of power law dependences of viscosity and relaxation time on the surfactant concentration (η0 ∼ C3.0, τ ∼ C0.7) are much smaller than in the “fast-breaking” regime observed at lower concentration of hydrocarbon (at molar ratio [1-phenyldodecane]/[potassium oleate] = 1/80) and in the absence of hydrocarbon (η0 ∼ C3.7, τ ∼ C1.5). As was mentioned above, the last exponents coincide with theoretical predictions for the “fast-breaking” chains in the presence of reversible scission reactions. As to the lower exponents, according to 15942


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The Journal of Physical Chemistry B network of oil-swollen wormlike micelles. The disappearance of entanglements is confirmed by the dependence of viscosity on surfactant concentration at fixed molar ratio [1-phenyldodecane]/[potassium oleate] = 1/12 (which corresponds to 0.15 wt % hydrocarbon at 2.5 wt % surfactant), which shows a slope of 1.7 (Figure 5A, curve d) close to the theoretical value for the unentangled regime (Table 1). Indeed, short unentangled chains in semidilute regime obey Rouse dynamics with η0 ∼ LC1.3 in a good solvent,44,45 where C is the concentration of chains and L is their length. For surfactant micelles4 L ∼ C0.6, thus giving η0 ∼ C1.9. To the best of our knowledge, the semidilute unentangled regime in wormlike micellar solutions has never been directly evidenced by means of rheology. This is presumably due to the fact that both the number and the length of wormlike micelles grow when the surfactant concentration is increased, so that they start to form entanglements soon after leaving the dilute regime (contrary to ordinary polymers, which do not change their length, and for which the entanglement concentration is usually 5−10 times higher than the overlap concentration46). In this work, the slope indicating the unentangled regime is seen for the first time at the concentration dependence of viscosity for wormlike surfactant micellar solutions. It is observed for both oil-swollen and oil-free micelles, but in the case of oilswollen micelles this regime occurs at much higher surfactant concentration (Figure 5A, cf. curves a and d). In order to fully understand the reasons for the network disruption, the solutions at hydrocarbon concentrations 0.18− 0.30 wt % (close to the end of unentangled regime) were studied by DLS. As seen from Figure 6, the hydrodynamic radii

Figure 7. Dependences of the relaxation rates Γ of the fast (gray symbols) and slow (black symbols) modes on the square of the scattering vector q2 for 2.5 wt % potassium oleate aqueous solution in the presence of 6.5 wt % KCl and 0.2 wt % 1-phenyldodecane. Temperature: 20 °C.

radius 1.3−1.9 nm surrounded by one layer of surfactant molecules with a thickness of 1.9 nm. Thus, it is reasonable to assume that in the DLS data the fast mode is due to the microemulsion droplets, and the slow mode refers to cylindrical micelles. Indeed, the values of Rh for the fast mode vary in the range of 2.7−3.8 nm (Table 2), which is close to the radii expected for microemulsion droplets. It can be seen that the size of microemulsion droplets grows as the hydrocarbon content is increased. Table 2. Hydrodynamic Radii for the Fast and Slow Modes and the Ratio of Areas under Peaks Obtained from DLS Data for the Solutions Containing 2.5 wt % Potassium Oleate and 6.5 wt % KCl at Different Hydrocarbon Concentrations 1phenyldodecane concentration, wt %

Rh1, nm (fast mode, microemulsion droplets)

0.18 0.20 0.25 0.30

2.7 3.1 3.6 3.8

Rh2, nm (slow mode, cylindrical micelles)

ratio of areas under peaks (Sfast/Sslow) × 103

18.3 17.8 19.7

2.9 7.1 46.0

As concern the slow mode, it is consistent with the literature data48 showing that cylindrical surfactant micelles near the overlap concentration should give a similar broad peak on the hydrodynamic radii distribution. At these conditions the cylindrical micelles are expected to be rather short. The movement of a cylindrical particle in a solution is a combination of a translational and rotational diffusion. However, it is known49,50 that for short rods (for which qL < 3, where L is their mean length) the rotational diffusion does not significantly contribute to the scattering. Thus, one could assume that the slow mode refers to the translational diffusion of short cylindrical micelles. The length of the cylindrical micelles can be very roughly estimated from the DLS data assuming that the micelles are rigid rods. Using the dependence Γ = DTq2 for the slow mode presented in Figure 7, one can calculate the translational diffusion coefficient of the cylinders DT, which is related to the cylinder length by the equation51

Figure 6. Distribution functions of hydrodynamic radii Rh obtained by the Contin method for 2.5 wt % potassium oleate aqueous solutions in the presence of 6.5 wt % KCl and different concentrations of 1phenyldodecane: 0.18 wt % (open diamonds), 0.20 wt % (full squares), 0.25 wt % (open triangles), 0.3 wt % (full circles). Scattering angle θ = 90°. Temperature: 20 °C.

(Rh) distribution functions in this range of hydrocarbon concentrations are bimodal. The dependences of the relaxation rates Γ = 1/τ (τ is the characteristic relaxation time) of the both modes on the square of the scattering vector q2 are linear (Figure 7), which means that the both modes are diffusive.47 In our recent work43 it was shown by SANS that potassium oleate solutions with added hydrocarbon at the conditions close to the overlap concentration contain a mixture of short cylindrical micelles with a radius of ∼1.9 nm and small spherical microemulsion droplets with a radius of ∼3.2−3.8 nm, the microemulsion droplets consisting of a hydrocarbon core with a 15943


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The Journal of Physical Chemistry B DT =

⎞ kT ⎛ ⎜⎛ L ⎟⎞ ⎜ln + ξ⎟ ⎠ 3πηsL ⎝ ⎝ d ⎠

value by choosing a certain radius of a microemulsion, so that the free energy is not increased. Thus, the free energy of the surfactant layer does not significantly change upon transition from wormlike micelles to microemulsion droplets, which allows for their coexistence. At the same time, the formation of many small microemulsion droplets compared to cylindrical micelles is favorable for entropic reasons. Thus, in the unentangled semidilute regime, where the oilswollen wormlike micelles are so short that they do not entangle with each other, the microemulsion droplets coexisting with oil-swollen wormlike micelles are observed. Effect of Hydrocarbon Structure. Since the hydrocarbon under study contains both aromatic and aliphatic parts, it was of interest to compare its effect on the rheological properties of wormlike micelles with the effect produced by purely aliphatic43 or purely aromatic20 hydrocarbons. As reported in the literature, aromatic hydrocarbons are often solubilized at or near the micellar corona,20 especially when their content is low and there are still vacant places in the corona area. This induces the growth of wormlike micelles in length and, hence, the viscosity enhancement. From Figure 1 it is seen that 1-phenyldodecane even at very low concentrations does not induce any increase in viscosity. By contrast, the viscosity decreases. A progressive loss of viscoelastic properties of the solutions and the transition between “fast-breaking”, “unbreakable”, and unentangled regimes observed at the addition of 1-phenyldodecane are due to the shortening of wormlike micelles. Such shortening is usually explained23,24 by hydrocarbon solubilization inside the micellar cores (far from the polar heads). This allows suggesting that despite having an aromatic ring, 1-phenyldodecane preferentially solubilizes in the center of the hydrophobic core of wormlike micelles, and not near the surfactant polar heads, since its alkyl tail is too long to reside near the micellar surface. So, the behavior of 1-phenyldodecane is more reminiscent of that of aliphatic hydrocarbons. At the same time, comparison with the data obtained for a similar system, but with n-dodecane as a hydrocarbon,43 shows that 1-phenyldodecane is more effective in the disruption of wormlike micelles. Indeed, only one 1-phenyldodecane molecule per 8 surfactant molecules is necessary to achieve the viscosity of the solution close to that of pure water (Figure 1), whereas one needs to add 2-fold more ndodecane molecules to get the same effect.43 One of the possible reasons for this may be connected with larger volume of 1-phenyldodecane molecule compared to n-dodecane. Thus, upon the increase of 1-phenyldodecane concentration a drastic drop of viscosity and a complete loss of viscoelastic properties of the solutions are seen, which are due to the disappearance of entanglements between the oil-swollen micellar chains, probably caused by their shortening, and to the appearance and growth of microemulsion droplets, which do not significantly contribute to viscosity but contain surfactant molecules and thus effectively reduce the amount of surfactant in wormlike micelles.

(5)

where d is the diameter of the micelles, k is the Boltzmann constant, T is the absolute temperature, ηs is the solvent viscosity, and ξ is a parameter nearly equal to51 ξ = 0.312 + 0.5656d /L − 0.1d 2/L2

(6)

SANS data43 show that the radius of the cylindrical micelles of potassium oleate does not significantly change upon absorption of hydrocarbon due to the packing constraints of surfactant molecules and is roughly equal to 1.9 nm. Using this value, the mean length of cylindrical micelles can be estimated to be L ∼ 90 nm at 0.2 wt % hydrocarbon. At the scattering angle θ = 90° q = 0.0187 nm−1, and thus qL ≈ 1.8 and the condition for the absence of rotational diffusion impact on scattering is satisfied. However, given the fact that the persistence length of potassium oleate micelles is ca. 14−20 nm,43,52 it can be seen that the micelles with L ∼ 90 nm cannot be treated as rigid rods, and therefore the estimation of L based on DLS data is only qualitative. Table 2 shows the ratio of areas under the peaks of fast and slow modes at different hydrocarbon concentrations. It can be seen that this ratio increases upon addition of hydrocarbon. In order to understand this fact, one should take into account that the area under each peak is proportional to the intensity scattered by each type of particles, which is in turn proportional to their number N and the squared volume of each particle V02.47 The experimental data show that the ratio Sfast/Sslow grows much faster than the squared volume of a single microemulsion droplet: it increases by a factor of ca. 16 (Table 2), whereas V02 increases only by a factor of ca. 5.7, when hydrocarbon concentration is raised from 0.18 to 0.25 wt %. Thus, it can be concluded that Sfast/Sslow grows not only due to the increase of the microemulsion droplets radius but also due to the growth of their number and, probably, to the decrease of the length of cylindrical micelles. To the best of our knowledge, this is the first observation of coexistence of cylindrical micelles and microemulsion droplets and a transition between them made by DLS. Note that the hydrodynamic radius of microemulsion droplets reaches the value of 3.8 nm (Table 2), which is 2fold larger than the length of a fully extended alkyl tail of potassium oleate R0 = 1.9 nm. Existence of an optimal radius of microemulsion droplets of 3.8 nm can be easily understood using the concept of packing of surfactant molecules in the micelles. According to Helfrich,53 free energy of a unit surface of a surfactant layer can be calculated as F = const −

Kc1 K + R 2R2

(7)

where 1/R is the mean curvature, K is a constant describing the elasticity of the layer, and c1 is the spontaneous curvature. Literature data suggest that a hydrocarbon, which is solubilized in the micellar core and which does not significantly penetrate into the volume of surfactant tails, does not affect the properties of the layer, namely, the values of K and c1.54 Furthermore, it can be easily seen that the mean curvature of a cylinder with a radius R0 equals to that of a sphere with a radius 2R0. Therefore, if under certain conditions surfactant molecules are optimally packed in a cylinder, upon solubilization of hydrocarbon the layer adapts its curvature to the optimal

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CONCLUSIONS In this article, the rheological behavior of oil-swollen wormlike surfactant micelles was investigated in a wide range of oil-tosurfactant ratios. The study of various rheological parameters (zero-shear viscosity, plateau modulus, relaxation, breaking and reptation times) allowed us to distinguish several rheological regimes in semidilute solutions of oil-swollen worms as the amount of absorbed 1-phenyldodecane is increased: (i) “fast15944


Article

The Journal of Physical Chemistry B breaking” entangled regime, (ii) “unbreakable” entangled regime, and (iii) unentangled regime. This is done by examining the dependences of the rheological characteristics on surfactant concentration at the constant molar ratio [hydrocarbon]/[surfactant] as well as by the direct calculation of the reptation and breaking times of the micelles as functions of the content of absorbed hydrocarbon, which has never been done before. It was shown that the changeover from one regime to another is due to the progressive shortening of the micellar chains with increased amount of absorbed oil, which provokes first (i) the decrease of their reptation time, so that it becomes close to the breaking time, and then (ii) the disappearance of entanglements. To the best of our knowledge, the existence of the unentangled regime has for the first time been evidenced in semidilute solutions of wormlike micellar chains. It can occur both for oil-free and oil-swollen wormlike surfactant micelles. In addition to this, an unusual regime with weak dependences of the viscosity and relaxation time on surfactant concentration is found, which might indicate the dominant role of end or bond interchange reactions in the micellar kinetics. It allows suggesting that hydrocarbon is distributed nonuniformly along the micellar length and probably accumulates in the form of droplets in some parts of micelles. These droplets, located at the ends or along the cylindrical body of the micelles, may serve as points where end or bond interchange is favored, thus changing the micellar reaction kinetics. The remarkable rheological properties of viscoelastic wormlike micellar solutions combined with their high responsiveness to hydrocarbons are the key properties for their use as fracturing fluids in oil recovery. Therefore, the new findings of this article concerning the rheological behavior of oil-swollen wormlike micelles are of obvious importance for the development of highly responsive surfactant-based systems for petroleum industry.

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(6) Rose, G. D.; Foster, K. I. Drag Reduction and Rheological Properties of Cationic Viscoelastic Surfactant Formulations. J. NonNewtonian Fluid Mech. 1989, 31, 59−85. (7) Maitland, G. C. Oil and Gas Production. Curr. Opin. Colloid Interface Sci. 2000, 5, 301−311. (8) Chu, Z.; Dreiss, C. A.; Feng, Y. Smart Wormlike Micelles. Chem. Soc. Rev. 2013, 42, 7174−7203. (9) Lu, H.; Shi, Q.; Huang, Z. pH-Responsive Anionic Wormlike Micelle Based on Sodium Oleate Induced by NaCl. J. Phys. Chem. B 2014, 118, 12511−12517. (10) Feng, Y.; Chu, Z.; Dreiss, C. A. Smart Wormlike Micelles: Design, Characteristics and Applications; Springer-Verlag: Berlin, 2015. (11) Chase, B.; Chmilowski, W.; Marcinew, R.; Mitchell, C.; Dang, Y.; Krauss, D.; Nelson, E.; Lantz, T.; Parham, C.; Plummer, J. Clear Fracturing Fluids for Increased Well Productivity. Oilfield Rev. 1997, 9, 20−33. (12) Hoffmann, H.; Ulbricht, W. Transition of Rodlike to Globular Micelles by the Solubilization of Additives. J. Colloid Interface Sci. 1989, 129, 388−405. (13) Hoffmann, H.; Würtz, J. Unusual Phenomena in Perfluorosurfactants. J. Mol. Liq. 1997, 72, 191−230. (14) Shashkina, J. A.; Philippova, O. E.; Zaroslov, Yu. D.; Khokhlov, A. R.; Pryakhina, T. A.; Blagodatskikh, I. V. Rheology of Viscoelastic Solutions of Cationic Surfactant. Effect of Added Associating Polymer. Langmuir 2005, 21, 1524−1530. (15) Molchanov, V. S.; Philippova, O. E.; Khokhlov, A. R.; Kovalev, Yu. A.; Kuklin, A. I. Self-Assembled Networks Highly Responsive to Hydrocarbons. Langmuir 2007, 23, 105−111. (16) Philippova, O. E.; Molchanov, V. S. Polymer-Surfactant Networks Highly Responsive to Hydrocarbons. Macromol. Symp. 2010, 291−292, 137−143. (17) Menge, U.; Lang, P.; Findenegg, G. H. From Oil-Swollen Wormlike Micelles to Microemulsion Droplets: A Static Light Scattering Study of the L1 Phase of the System Water + C12E5 + Decane. J. Phys. Chem. B 1999, 103, 5768−5774. (18) Menge, U.; Lang, P.; Findenegg, G. H. Structural Transition of Oil-Swollen Cylindrical Micelles of C12E5 in Water Studied by SANS. J. Phys. Chem. B 2003, 107, 1316−1320. (19) Miyake, M.; Asano, A.; Einaga, Y. Size Change of the Wormlike Micelles of Pentaoxyethylene, Hexaoxyethylene, and Heptaoxyethylene Dodecyl Ethers with Uptake of n-Dodecane. J. Phys. Chem. B 2008, 112, 4648−4655. (20) Kumar, S.; Bansal, D.; Kabir-ud-Din. Micellar Growth in the Presence of Salts and Aromatic Hydrocarbons: Influence of the Nature of the Salt. Langmuir 1999, 15, 4960−4965. (21) Törnblom, M.; Henriksson, U. Effect of Solubilization of Aliphatic Hydrocarbons on Size and Shape of Rodlike C16TABr Micelles Studied by 2H NMR Relaxation. J. Phys. Chem. B 1997, 101, 6028−6035. (22) Sato, T.; Acharya, D. P.; Kaneko, M.; Aramaki, K.; Singh, Y.; Ishitobi, M.; Kunieda, H. Oil-Induced Structural Change of Wormlike Micelles in Sugar Surfactant Systems. J. Dispersion Sci. Technol. 2006, 27, 611−616. (23) Siriwatwechakul, W.; LaFleur, T.; Prud’homme, R. K.; Sullivan, P. Effects of Organic Solvents on the Scission Energy of Rodlike Micelles. Langmuir 2004, 20, 8970−8974. (24) Sharma, S. C.; Acharya, D. P.; Aramaki, K. Viscoelastic Micellar Solutions in a Mixed Nonionic Fluorinated Surfactants System and the Effect of Oils. Langmuir 2007, 23, 5324−5330. (25) Sharma, S. C.; Shrestha, R. G.; Shrestha, L. K.; Aramaki, K. Viscoelastic Wormlike Micelles in Mixed Nonionic Fluorocarbon Surfactants and Structural Transitions Induced by Oils. J. Phys. Chem. B 2009, 113, 1615−1622. (26) Sharma, S. C.; Rodriguez-Abreu, C.; Shrestha, L. K.; Aramaki, K. Oil-Induced Anomalous Thermoresponsive Viscoelasticity in Fluorinated Surfactant Systems. J. Phys. Chem. B 2007, 111, 12146−12153. (27) Molchanov, V. S.; Shashkina, Y. A.; Philippova, O. E.; Khokhlov, A. R. Viscoelastic Properties of Aqueous Anionic Surfactant (Potassium Oleate) Solutions. Colloid J. 2005, 67, 606−609.

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Fax +7 495 9392988; Tel +7 495 9391464 (O.E.P.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was supported by the Russian Foundation for Basic Research (project 14-03-32085_mol-a).

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Rheological Behavior of Oil-Swollen Wormlike Surfactant Micelles

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