Wormlike micelles in mixed surfactant solutions

Advances in Colloid and Interface Science 123–126 (2006) 401 – 413 www.elsevier.com/locate/cis

Wormlike micelles in mixed surfactant solutions Durga P. Acharya ⁎, Hironobu Kunieda Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan Available online 24 July 2006

Abstract Small micellar aggregates of some surfactants exhibit enormous growth in one dimension and form very long and flexible wormlike micelles. Depending on the nature of the surfactant, such micellar growth can be induced in different ways, for example by adding cosurfactants or salts. Above a system-dependent concentration of surfactant, these giant micelles are entangled to form a transient network, and exhibit viscoelastic behavior analogous to a flexible polymer solution. However, unlike polymers in solutions, wormlike micelles undergo breaking and recombination, and, therefore, exhibit complex rheological behavior. Information on the evolution of aggregate morphology can be obtained from rheological study. In this article formation of wormlike micelles and the evolution of rheological properties in different mixed surfactant systems is discussed. Besides, a brief overview on the salt-induced micellar growth in ionic surfactant systems and reverse micellar systems induced by adding certain polar additives has also been presented. © 2006 Elsevier B.V. All rights reserved. Keywords: Wormlike micelles; Micellar growth; Viscoelastic micellar solution; Phase behavior; Rheology; Rheological behavior

Contents 1. 2. 3.

Introduction . . . . . . . . . . . . . . . . . . . . . Rheology of wormlike micelles: theory . . . . . . Wormlike micelles in mixed surfactant systems . . 3.1. Ionic surfactant + cosurfactant systems. . . . 3.2. Mixed nonionic surfactant systems . . . . . 3.3. Mixed cationic–anionic surfactant systems . 4. Wormlike micelles in ionic surfactant + salt systems 5. Reverse wormlike micelles . . . . . . . . . . . . . 6. Summary . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction In aqueous media, surfactant molecules self-assemble to form aggregates of different microstructures and shapes depending on the composition, temperature and type of the amphiphile. At a surfactant concentration just above the critical micelle concentration (cmc), micelles are usually spherical in ⁎ Corresponding author. Tel./fax: +81 45 339 4300. E-mail addresses: [email protected], [email protected] (D.P. Acharya). 0001-8686/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cis.2006.05.024

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401 402 404 404 406 409 410 411 412 412

shape. The aggregate geometry may be predicted on the basis of the packing of the surfactant molecules in the aggregate, usually expressed in terms of “critical packing (CP) parameter” [1], which is defined as v/lcas, where v is the volume of the lipophilic chain having maximum effective length lc, and as is the cross-sectional area of the head group at the interface. For CP ≤ 1/3 spherical micelles are expected; when 1/3 ≤ CP ≤ 1/2, cylinders are expected. The sphere–rod transition in the micellar shape can be induced by different ways such as increasing surfactant concentration, salinity or temperature, depending on the type

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of the surfactant. However, in certain conditions, the micelles undergo enormous elongation and form very long and highly flexible aggregates, called “wormlike” or “threadlike” micelles. In the rodlike micelles, the curvature of the end caps is higher than the spontaneous curvature of the aggregate at the cylindrical part. One-dimensional (1D) micellar growth may be considered as a tendency of the system to minimize the excess free energy by reducing the number of end caps in spite of the counteracting entropy factor. Above a system-dependent concentration of surfactant, called the overlap concentration (c⁎), the wormlike micelles are sufficiently close with each other and hydrodynamic interaction occurs between the aggregates and viscosity increases sharply with increasing surfactant concentration. Entanglement of wormlike micelles into a transient network imparts viscoelastic properties to the surfactant solution, which are analogous to those observed in polymer solutions. Wormlike micelles have drawn considerable interest in basic research and applications. In the late 1980s and early 1990s, theoretical modelling as well as an extensive study on the dynamics and rheological behavior of wormlike micelles began in long-chain cationic surfactant systems in the presence of added salt [2–16]. It has been found that different mixed surfactant systems, for example, cationic–anionic [17–19], ionic–zwitterionic [20–22], zwitterionic–nonionic [23] and ionic–nonionic [24–27] systems formed viscoelastic solutions containing wormlike micelles. Recently, viscoelastic solutions have been reported in mixed nonionic surfactant systems as well [28–30]. While numerous aqueous surfactant systems have been found to form wormlike micelles, only lecithin in organic solvents is known to form wormlike reverse micelles upon addition of a small amount of water or certain polar solvents [31,32]. In this article, first a brief theoretical discussion on the rheological behavior of viscoelastic wormlike micelles is presented. It is followed by discussion on the formation of viscoelastic wormlike micellar solutions in different mixed surfactant systems, their rheological behavior and the evolution of aggregate structure and micellar growth as obtained from rheological and other measurement techniques. A brief discussion on the salt-induced viscoelastic wormlike micelles formed in ionic surfactants and viscoelastic solution of reversed wormlike micelles is given. 2. Rheology of wormlike micelles: theory The viscoelastic behavior of wormlike micelles arises due to entanglement of the flexible aggregates to form a transient network analogous to a polymer network. However, the wormlike micelles are dynamic systems, and, therefore, undergo breaking and recombination, which makes the rheological behavior of these “living polymer” different from that of a polymer in solution. Several models have been proposed to explain the complex rheological behavior of wormlike micellar solutions. In steady-state rheological measurements, wormlike micellar solutions with low viscosity show Newtonian type of behavior,

with viscosity independent of shear rate. As the viscoelasticity of the micellar system increases, shear thinning is observed at high shear rate, which may be attributed to the deformation of the network and alignment of the wormlike micelles in the shear flow. The zero-shear viscosity (η0) can be obtained by extrapolation of the viscosity curve to zero-shear rate. Shear thickening, which corresponds to the increase in viscosity over a range of shear rate, has been observed in several surfactant systems [33]. In oscillatory-shear measurements, the sample is deformed by applying small-amplitude sinusoidal shearing so as not to disturb the fluid structure. In this case, the stress measured during oscillatory deformation is controlled by the spontaneous rearrangements or relaxation. The wormlike micelles have an equilibrium conformation in the network. The micelles constantly undergo translational diffusion process, and they also break and recombine. When the network of wormlike micelles is deformed or conditions are suddenly changed from the equilibrium state, the relaxation occurs and the equilibrium condition is restored again. For the deformation with a time period shorter than the relaxation time τR, the system exhibits an elastic property characteristic of a solid material with a Hookean constant G0, called the shear modulus [34]. For a slow deformation, however, the network has sufficient time to dissipate the stress, and the viscoelastic system behaves as a viscous fluid with a zero-shear viscosity, η0. The dynamic rheological behavior of a viscoelastic micellar solution is described by a mechanical model, called the Maxwell model, consisting of an elastic component (spring) with the Hookean constant G0 and a viscous component (dashpot) with viscosity η0. When a sudden strain is applied to the system for a short time, the stress (σ) relaxes exponentially with a time constant τR, i.e., r ¼ r0 expðt=sR Þ

ð1Þ

sR ¼ g0 =G0

ð2Þ

It is possible to obtain different rheological parameters by following the stress decay as a function of time. Alternately, the rheological properties of a viscoelastic material can be investigated by applying a sinusoidal deformation of angular frequency ω. From the phase angle between sinusoidally varying stress and strain signals, the elasticity (storage) modulus G′, the viscous (loss) modulus G″, and the magnitude of complex viscosity |η⁎| can be calculated. For a Maxwell fluid, the following relations are obtained [35]: G VðxÞ ¼

x2 s2R G0 1 þ x2 s2R

GWðxÞ ¼

jg⁎j ¼

xsR G0 1 þ x2 s2R

ðG V2 þ GW2 Þ1=2 g0 ffi ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x 1 þ x2 s2R

ð3Þ

ð4Þ

ð5Þ

D.P. Acharya, H. Kunieda / Advances in Colloid and Interface Science 123–126 (2006) 401–413

where G0 is called shear (plateau) modulus. At low ω, and ωτR ≪ 1, G′ becomes proportional to ω2 whereas G″ is proportional to ω, with G″ > G′. This region is called terminal zone, and the system behaves as a simple liquid (Fig. 1). It can be seen that for ωτR ≫ 1, G′ approaches a constant limiting plateau value equal to shear modulus (G0), with G′ > G″ and the system behaves as an elastic material. The plateau modulus G0 is related to the number density of entanglement (v) at a temperature T, according to the following relation: G0 ¼ vkT

ð6Þ

where k is the Boltzmann constant. The relaxation time, τR, is given by the inverse of the ω (expressed in rad s − 1 ) corresponding to G′–G″ cross-over in a G′, G″–ω plot. In addition to Eq. (2), Eq. (5) allows one to estimate η0 from the oscillatory-shear measurement by extrapolating |η⁎| to the zero oscillatory frequency. From above equations, it follows that    2 G0 2 G0 2 GW þ G V ¼ ð7Þ 2 2 which means that for viscoelastic materials with Maxwellian behavior, the linear plot of G″ as a function of G′, known as the Cole–Cole plot, should show a semicircle centred on the G′ axis (Fig. 1, inset). In contrast to the fixed molecular weight distribution (MWD) of ordinary polymer solutions, “living polymer” model proposed by Cates and coworkers [2–4] considers the MWD of wormlike micelle to be in thermal equilibrium. The MWD of the equilibrium polymer is calculated using statistical mechanics (mean-field approach). The viscoelastic behavior of the entangled wormlike micelles is described by considering two processes–reptation, i.e., reptile-like motion of the micelle along its own contour, and reversible scission of micelles– taking place at two time scales, namely, reptation time τrep and breaking time τb. The τrep is the time taken by the wormlike micelle of length L to pass through the hypothetical tube and the

403

τb is the average time taken by the chain of average length L to break into two pieces. It is assumed that when a chain breaks, two product chains become uncorrelated, and recombine with the micellar end in a random way. For an extremely slow scission kinetics (τb > τrep), stress relaxation occurs by reptation, and the stress relaxation function becomes non-exponential [2]: r ¼ r0 exp½const:ðt=srep Þ1=4 

ð8Þ

However, in the fast-breaking regime (τb ≪ τrep), a single exponential stress decay is observed and the viscoelastic behavior of such systems at low frequency follows the Maxwell model with a single relaxation time τR given by (τb · τrep)1/2. Although the Maxwell equations predict a monotonous decrease of G″ in the high frequency region (shown by the solid lines in Fig. 1), the wormlike micelles deviate from this behavior, showing an upturn in G″ in this region, and a deviation from the semicircle as well as a depression in the Cole–Cole plot. This deviation is often associated with the stress relaxation by additional ‘faster’ relaxation processes, such as the Rouse modes of cylindrical micelles, analogous to a polymer chain. The minimum value of G″ in the high frequency region is related to the micellar contour length according to the following relation [3]: GWmin le c G0 L¯

ð9Þ

where le is the entanglement length, i.e., the contour length of the section of wormlike micelles between two entanglement points, and ¯L is the contour length of the whole wormlike micelle. For flexible micelles, the correlation length, ξ, which gives the mesh size of the micellar network, is related to le and G0 according to the relations [3]: le cn5=3 =lp2=3

ð10Þ

 1=3 kT n¼ G

ð11Þ

Combining Eqs. (10) and (11) yields a relation which relates G0 to le kT G0 c 9=5 ð12Þ le

Fig. 1. Typical pattern of the oscillatory-shear response of the viscoelastic solution of wormlike micelles. G′ (circles) and G″ (squares) are the storage and loss moduli, and η⁎ (triangles) is the complex viscosity. The solid lines are the Maxwell fittings to the data points. The Cole–Cole plot of the same system is shown in the inset.

The persistence length, lp, gives an estimate of micellar flexibility. Even though the wormlike micelles are flexible, at a small length scale comparable to lp, they behave as a rigid rod. For wormlike micelles of ionic surfactants in the presence of salt, lp is dependent on the ionic strength of the solution and structure of surfactant monomer. For example, lp is about 15– 20 nm for hexadecylpyridinium bromide (CPyB)/NaBr system, whereas it is about 137 nm for (hexadecyltrimethylammonium salicylate (CTASal)/sodium salicylate (NaSal) system, with alkyltrimethylammonium halide (CnTA-halide) and sodium dodecylsulphate (SDS) systems having lp values in the range of 50 and 70 nm respectively. Different techniques such as small angle neutron scattering [36,37], static and dynamic light scattering [38,39], rheo-optical measurements [40] or their

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combination have been used to estimate the lp of wormlike micelles. Comparison of the persistence length of wormlike micelles in different surfactant systems is available [41]. In the limit τb ≪ τrep, the theoretical model predicts the following scaling laws for the viscoelastic parameters as a function of the volume fraction of surfactant (ϕ) [4]: G0 f/2

f2:25

ð13Þ

sR f/1:25

ð14Þ

g0 f/3:25

ð15Þ

If excluded volume interactions are taken into account, slightly different exponents of the above scaling laws are obtained.

3. Wormlike micelles in mixed surfactant systems 3.1. Ionic surfactant + cosurfactant systems Incorporation of a cosurfactant in the palisade layer of micellar aggregates of ionic surfactants decreases the average area of surfactant head group, as, resulting in an increase in CP or a decrease in the interfacial curvature of the aggregate. It is, therefore, reasonable to expect one-dimensional micellar growth upon the addition of cosurfactant to the surfactant solution. Nonionic amphiphiles like poly(oxyethylene)dodecylether (C12EOn) of small head group size (n = 2–4) as well as alkanolamide type foam-boosters such as dodecanoyldiethanolamide (LDEA), dodecanoyl-N-methylethanolamide (NMEA12) and its homologue NMEA-16, have been found to be suitable to form viscoelastic micellar solutions in dilute solutions of different classes of surfactants—from ionic surfactants such as SDS, hexadecyltrimethylammonium bromide (CTAB) and dodecyltrimethylammonium bromide (DTAB) [24–27] to nonionic surfactants such as ethoxylated sterols [28,30,42], sucrose alkanoates [29], as well as anionic dimeric surfactants [43]. The studies show that the extent of micellar growth and formation of viscoelastic solution relies on the careful selection of the

cosurfactant depending on the type, and especially the chain length, of the surfactant used. Fig. 2 shows phase diagram of CTAB and DTAB/NMEA-n/water systems [25]. The maximum viscosity region inside the single-phase micellar domain (shown by the shaded area or dotted line in the phase diagram) extends toward the water-rich region from the protruded part of the H1 phase, which indicates that the cylindrical growth of the micelles is highly favorable in this region. Herb et al. have shown that along the line of maximum viscosity, the packing parameter attains a maximum but constant value (∼0.45), which favors the formation of cylindrical aggregates [24]. Since, the average area of surfactant head group, as, decreases with increasing surfactant concentration, an extensive micellar growth occurs at lower cosurfactant/surfactant mixing ratio as the surfactant concentration increases. As a result, the locus of the high-viscosity region is nearly parallel to the water–surfactant binary axis. Similar phase behavior is observed in the aqueous systems of CTAB/C12EO3 and DTAB/C12EO3 [27], as well as SDS/NMEA-n (n = 12 and 16) [26] and SDS/LDEA [24]. With increasing chain length of surfactants, the evolution of the aggregate morphology is rapid but phase separation occurs at a lower cosurfactant/surfactant mixing ratio, as expected. On the other hand, with a short-chain cosurfactant, for example NMEA-8, the micellar domain is very wide but viscosity growth does not occur [26]. Recently, a salt-free aqueous solution of anionic dimeric (gemini) surfactant (disodium 2,3-didodecyl-1,2,3,4-butanetetracarboxylate, abbreviated as GS) in the presence of various short-EO-chain amphiphiles, CmEOn (m, n = 12, 2; 12, 3; 12, 4 and 16, 4) [43], has been reported to form highly viscoelastic micellar solutions. The GS has no spacer group and two monomers are connected by a covalent bond. No viscoelastic solution is formed in the GS–water binary system, but on adding the cosurfactant a highly viscoelastic solution is formed. The phase diagrams (Fig. 3) show that with increasing hydrophilicity of the cosurfactant, the domain of the viscoelastic micellar region shifts to lower GS concentrations, and with C12EO4, the viscoelastic solution is formed at very low GS concentration. The effect of the variations of surfactant and additive concentration on the rheological behavior of wormlike micellar

Fig. 2. Partial phase diagrams of CTAB/NMEA-n/water and DTAB/NMEA-n/water systems at 25 °C. The viscoelastic micelle region within the Wm-domain is shown by shaded area. In the DTAB systems, the dotted lines within the Wm-domain show the locus of maximum viscosity. H1: hexagonal liquid crystals, S: solid, W: water. The H1 domain in the phase diagram includes single-and two-phase regions containing hexagonal phase (redrawn from Ref. [25]).

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Fig. 3. Partial phase diagram of GS/CmEOn/water systems (a: C12EO2, b: C12EO3, c: C12EO4 and d: C16EO4) at 25 °C. Shaded region inside the Wm-region shows the region of viscoelastic micellar solution (redrawn from Ref. [43]).

solution has been studied in various systems. The typical patterns of cosurfactant-induced evolution of viscosity in ionic surfactant systems are shown in Figs. 4 and 5 as a function of the mixing fraction, X, of cosurfactant (by mole) in the total surfactant at a fixed surfactant concentration. Usually three regimes of viscosity growth are observed in a plot of viscosity

Fig. 4. (a) Variation of η0 as a function of the mixing fraction of NMEA (X) in 0.15 M CTAB or DTAB–NMEA systems: (A) CTAB + NMEA-12, (B) CTAB + NMEA-16, (C) DTAB + NMEA-16 and (D) DTAB + NMEA-12 systems at 25 °C. Variation of G0 and τR for CTAB–NMEA-12 system is shown in (b) (from Ref. [25]).

Fig. 5. Variation of η0 as a function of the mixing fraction of C12EO3 (X) in 0.15 M CTAB + C12EOn (open symbols) and DTAB + C12EOn (filled symbols) systems at 25 °C (from Ref. [27]).

as a function of X. At low cosurfactant concentration, the viscosity is nearly similar to that of water. However, above a critical concentration called overlapping concentration c⁎, a rapid micellar growth occurs and the viscosity increases sharply within a narrow range of X to a peak value, often followed by a decrease. At the boundary between these regimes, the rheological parameters such as η0, G0, τR change dramatically, which is reflected in the discontinuity of the slope in the plots of these parameters as a function of composition. Usually, in the regime of sharp micellar growth, the low-frequency oscillatory shear behavior of the viscoelastic samples approaches Maxwellian behavior. The validity of the scaling law proposed by the Cates model is tested in this regime. As the viscosity decreases after the maximum, so does τR, and the system progressively deviates from the Maxwellian behavior. The discontinuity in the evolution of η0, τR and G0, as shown in Fig. 4 implies structural changes in the network that allow stress relaxation by some “faster” mechanism other than the reptation process. The plausible explanation is the progressive increase in the number density of saddle-shaped micellar joints, which can slip along the micellar length, thereby allowing stress relaxation [12,44]. Since the surfactant molecules in the aggregate are not chemically connected, surfactant molecules are expected to form this type of interconnection readily if they do not strongly resist a negative Gaussian curvature. In some surfactant systems, micellar connections or branching points have been detected by cryogenic transmission electron microscopy (cryoTEM), especially in the region where the viscosity decreases after the maximum [20,45–47]. The viscosity growth in a mixed system is sensitive to sizes of both head and tail groups of both the cosurfactant as well as the surfactant. The viscosity–composition curves clearly show that decreasing head group size and increasing alkyl chain length of the cosurfactant increases the steepness of the viscosity curve. However, the value of X at which the viscosity rapidly increases depends mainly on the chain length of the surfactant, with relatively small contribution from the cosurfactant. The composition–viscosity plots in other mixed

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surfactant–cosurfactant systems [26,27,42,43] are in agreement with this result. A plausible explanation for this behavior is that at a low mixing fraction of cosurfactant (below c⁎), the cosurfactant molecules are preferably incorporated in the cylindrical part of the aggregate, whereas the hemispherical end caps of the cylindrical micelles are mainly occupied by the surfactant molecules with bigger head group so as to reduce the curvature free energy, although entropically such segregation is not favorable [48,49]. Hence, the free energy of the end caps, and, therefore, the micellar growth at a low surfactant concentration is likely to be affected mainly by the packing behavior of the surfactant occupying the end caps. At high cosurfactant mixing fractions, the micellar growth is promoted by increasing chain lengths and decreasing head group sizes of both surfactant and cosurfactant. With very long tail or very small head group, however, the aggregate curvature decreases too rapidly leading to a phase separation at low cosurfactant mixing fractions. Fig. 6 shows the η0–composition curves for CTAB/ NMEA-12 systems at different CTAB concentrations [25]. With increasing CTAB concentration, micellar growth can be induced at lower concentration of cosurfactant, but the maximum viscosity values are nearly similar. In the maximum viscosity region, the network density (or G0) increases with surfactant concentration whereas τR shows a decrease (Fig. 7), most probably due to increasing number density of micellar joints with increasing CTAB concentration. In mixed ionic–nonionic surfactant systems the scaling of viscosity is far from the theoretical prediction. For example, for CTAB + NMEA-12 system, following scaling of rheological parameters as a function of total surfactant (ionic and nonionic) weight fraction are observed: (w) η0 ∼ w14.5 , G0 ∼ w7.0, and τR ∼ w8.2, which are significantly higher than those predicted by the theoretical model. When the micellar surface has a high surface charge density, the aggregate becomes rigid with high persistence length (lp). Moreover, the electrostatic repulsion between the micellar aggregates makes the network more rigid. As a result, a large deviation is observed from the theoretical model.

Fig. 6. Variation of η0 as a function of the mixing fraction of NMEA-12 (X) at different CTAB concentrations: (A) 0.20 M, (B) 0.15 M, (C) 0.10 M, and (D) 0.05 M. (from Ref. [25]).

Fig. 7. Variation of plateau modulus, G0 (circle) and relaxation time (τR) (square) with CTAB concentration for the compositions corresponding to maximum viscosity in CTAB + NMEA-12 systems (from Ref. [25]).

Zwitterionic surfactants such as alkyldimethylamineoxides (CnDMAO) are also known to form wormlike micellar solutions in the presence of cosurfactants such as long-chain alcohols [23]. With successive addition of alcohol, viscosity increases and passes over a maximum, and long-chain (C8, C10) alcohols are more effective in inducing micellar growth than the shortchain (C6) one. In fact, C14DMAO itself forms viscoelastic solution in water at high concentration (∼1 M); in the presence of alcohol the micellar growth occurs at low concentrations. 3.2. Mixed nonionic surfactant systems Although the micellar growth leading to the formation of wormlike micelles has been observed in several nonionic surfactant systems [50,51], the formation of highly viscoelastic solutions in dilute solutions of nonionic surfactants has been reported recently in long-chain (C12 and C16) sucrose alkanoates as well as the cholesterol based surfactant (ChEOm, m = 10 and 15) systems upon addition of the lipophilic amphiphiles such as C12EOn, NMEA-n, and monolaurin (C12-MG). In the sucrose alkanoate (CmSE)/C12EOn/water systems, viscoelastic micellar solutions are formed over a wide concentration range. Aqueous solutions of these surfactants are known to form viscous micellar solutions at high surfactant concentrations [52]. With the addition of the cosurfactant, viscoelastic solutions are formed even at low surfactant concentrations. Phase diagrams of the sucrose ester/nonionic surfactant/water systems in water-rich region are shown in Fig. 8. One interesting feature of the phase diagram of the sucrose hexadecanoate (C16SE)/C12EOn/water system is that the maximum viscosity region is located near the surfactant– water binary axis in the phase diagram (Fig. 8) at a low C12EO n/C16SE mixing ratio (∼ 1/9 at 5 wt.% of total surfactant). With successive increasing mixing fraction of the cosurfactant, the viscosity decreases as a result of gradual disruption of the micellar network structure, as suggested by the light scattering data, and ultimately the lamellar phase separates out. In the sucrose dodecanoate (C12SE)/CmEOn/

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Fig. 9. Variation of zero-shear viscosity (η0) in C16SE + cosurfactant system as a function of the weight fraction of cosurfactant in cosurfactant + C16SE (W1) at 30 °C (redrawn from Ref. [29]).

Fig. 8. Partial phase diagrams of sucrose hexadecanoate (C16SE)/cosurfactant/ water and sucrose dodecanoate (C12SE)/cosurfactant/water systems. CmEOn stands for polyoxyethylene alkylether with n oxyethylene units and alkyl chain containing m carbons, and C12-MG stands for monolaurin (from Ref. [29]).

water systems, viscoelastic micellar phase is formed near the phase boundary of the micellar phase. On increasing the head group size of cosurfactant, a higher cosurfactant/surfactant ratio is required to form viscoelastic solution, which is attributed to the decreased ability of the cosurfactant to reduce the aggregate curvature. ChEO10/C12EO3/water system [28] and also other mixed systems of ethoxylated sterol systems [42] show phase behaviors similar to that of C12SE/CmEOn/ water, with the viscoelastic solution formed in the vicinity of the micellar phase boundary. Variation of η0 in a mixed nonionic system, namely, C16SE/ C12EOn/water system, as a function of mixing ratio of C12EOn/ C16SE at fixed (5 wt.%) total surfactant concentration is shown in Fig. 9. The effect of EO chain length of C12EOn on the viscosity observed in the system is similar to that observed in the ionic–nonionic systems discussed before. However, in the C16SE system, rapid increase in viscosity of several orders of magnitude is obtained with relatively small mixing fraction of the cosurfactant. A direct evidence for the micellar growth in a surfactant system can be obtained by small angle scattering techniques. However, there are only few reports on the study of the evolution of micellar growth in wormlike micelles by small angle scattering employing X-rays (SAXS) or neutrons (SANS). The small-angle scattering intensity data can be

analysed by indirect Fourier transformation followed by deconvolution to obtain information on the shape and size of the scattering particles (micelles) [53,54]. If we consider scattering by particles in dilute solution (negligible interparticle interaction), the scattered intensity, I(q), is given by: Z l sinqr dr ð16Þ I ðqÞ ¼ 4p pð r Þ qr 0 where p(r) is the pair-distance distribution function (PDDF), involving the information about the size, shape and internal core-shell structure of particles and q is the magnitude of scattering vector which is related to the angle θ between the incident and scattered beams of wavelength λ by the relation: q = (4π/λ)sin(θ/2). The intraparticle scattering contribution is called the form factor, P(q), which theoretically corresponds to the Fourier transform of p(r). Fig. 10 shows the PDDF function of 5% (C16SE + C12EO3) at different mixing fractions of C12EO3 (W1) at compositions indicated by arrows in the η0–W1 plots shown in Fig. 9 [55]. The local maximum and minimum in the p(r) function in the low-r region arise essentially from the productive contribution

Fig. 10. Pair-distance distribution function (PDDF) for 5% (C16SE + C12EO3) system at different mixing fractions of C12EO3, W1 (from Ref. [55]).

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of the micelles with addition of C12EO3. Further increase in C12EO3 concentration decreases the aggregate size, in consistence with the rheological data. Evidence for one-dimensional micellar growth based on SANS measurement in dilute mixed nonionic system (ChEOm + C12EOn) has been provided recently [57]. SANS provides a higher resolution in comparison to SAXS because of higher contrast between the particles and the solvent, but the information about the internal structure is lost. Fig. 11(a) show the PDDFs obtained from SANS scattering intensity profiles for 1% ChEO10 + C12EO3 systems at different concentrations of C12EO3. The effect of the head group size of C12EOn on the micellar growth can be seen in Fig. 11(b). The PDDFs show that C12EO4 does not induce micellar growth. However, upon decreasing the head group size of C12EOn, micellar growth becomes increasingly favorable. The effects of head group and alkyl chain length of added cosurfactant on the sphere–rod shape transition and onedimensional micellar growth can be explained in terms of a simple model based on packing constraints. Incorporation of

Fig. 11. Pair-distance distribution functions (PDDFs) from SANS scattering experiments carried out on 1 wt.% ChEO10 + C12EOn systems. Effects of the concentration of C12EOn and EO-chain length on the micellar growth are illustrated in (a) and (b) plots, respectively (redrawn from Ref. [57]).

of the negative and positive electron densities (in comparison to average value) from the hydrophobic core and hydrophilic shell respectively, which gives us the information about the internal structure of micelles. The value of r corresponding to the maximum inflexion after the second maxima of p(r) function gives the cross-sectional diameter of cylindrical aggregate, including the head group. Theoretically, the largest distance, rmax, at which the p(r) function decays corresponds to the size of the aggregate. However, this value may be biased by the resolution limit of the experiment. The PDDF plots in Fig. 10 are typical of cylindrical aggregates [56], with non-linear (slightly convex) decay at large r values which corresponds to polydispersity in length. It can be seen that even in C16SE–water binary system the maximum dimension of the aggregate is ∼ 12.5 nm which is twice the diameter of the aggregate. In fact, the viscosity of the micellar solution is significantly higher than that of water, which is attributed to the presence of elongated aggregates. With addition of C12EO3, the maximum length increases and at a composition corresponding to the maximum viscosity, the maximum length of ∼ 23 nm is obtained. It should be noted that this length is significantly lower than the expected length of wormlike micelles in a viscoelastic solution, which is often measured in several hundred nanometers or even micrometer. The measurement of the actual length is limited by the resolution limit, nevertheless, the data confirm the elongation

Fig. 12. (a) Phase diagram showing solubilization of decane in 10% (C16SE + C12-MG) system as a function of mixing fraction of C12-MG in the total surfactant, W1. The effect of different types of oil on the zero-shear viscosity is shown in (b) (redrawn from Ref. [58]).

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Fig. 13. Partial phase diagram of hexadecyltrimethylammonium tosylate (CTAT)/ sodium dodecylbezenesulphonate(SDBS)/water system. Wm(R) is the micellar phase consisting of rodlike aggregates; V is the vesicular phase; I, II are the twophase regions. Compositions are in wt.% (redrawn from Ref. [18]).

cosurfactant into surfactant micelles decreases the average cross-sectional area of the head group at the interface, or in other words, interfacial curvature of the aggregate decreases by an extent depending on the size of the cosurfactant head group. Similar effect is observed upon increasing the alkyl chain of the amphiphiles. Thus, the extent of one-dimensional micellar growth and viscoelastic properties of wormlike micellar solutions in mixed surfactants can be tuned by a careful selection of cosurfactants. It is well known that addition of oil to surfactant aggregates produces morphological changes. For example, flexible nonpolar oils such as long-chain hydrocarbons solubilize in the core of the aggregate and tend to increase the interfacial curvature,

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which is opposite to the effect of cosurfactants. Fig. 12(a) shows the variation in the capacity of the wormlike micellar solution in 5% and 10% (C16SE + C12-MG) systems to solubilize decane. With increasing surfactant concentration, the solubilizing capacity increases and reaches its maximum value around the composition corresponding to the maximum viscosity. The effect of the addition of two different types of oil on the viscosity of wormlike solution is shown in Fig. 12(b) [58]. The presence of decane reduces the viscosity by reducing the extent of micellar growth. However, p-xylene behaves differently although both decane and p-xylene are nonpolar oils. Due to rigid structure and elongated shape of p-xylene molecule, it is not solubilized in the micellar core, rather it is preferentially solubilized in the palisade layer. Due to this orientation, it behaves as a cosurfactant and increases the viscosity sharply even in C16SE–water binary solution. As a result, the maximum in viscosity is achieved at comparatively lower concentration of C12-MG (i.e., smaller W1) and the overall η0–W1 curve in Fig. 12(b) appears to be shifted toward lower W1 side. 3.3. Mixed cationic–anionic surfactant systems Some mixed ionic (cationic–anionic) surfactants, including combination of zwitterionic surfactant with cationic or anionic surfactant, are known to form viscoelastic solutions containing wormlike micelles [18–22]. In 1970s, Baker et al. studied the phase and rheological behavior of viscoelastic micellar solution formed in alkyltrimethylammonium bromide–SDS aqueous system [17]. Another cationic–anionic mixed system known to form viscoelastic wormlike micelles is hexadecyltrimethylammonium tosylate (CTAT)/sodium dodecylbenzenesulphonate

Fig. 14. Variations of rheological parameters as a function of surfactants compositions in the aqueous CTAT + SDBS system (from Ref. [18]).

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(SDBS)/water system, studied by Kaler and coworkers [18]. The phase diagram of this system in the water-rich region is shown in Fig. 13. The viscoelastic micellar phase is formed in the CTAT-rich region—with its domain extending from CTAT– water axis to a composition corresponding approximately to SDBS/CTAT mixing ratio of 10/90, with the maximum viscoelasticity being observed at an intermediate mixing ratio. With further increase in the anionic surfactant concentration, a two-phase region consisting of wormlike micelles and vesicular dispersion is observed. In the micellar solution formed in the SDBS-rich region, however, the aggregates are spherical. The wide domain of bilayer structures such as vesicle and lamellar phases indicates a strong interaction between the oppositely charged head groups which leads to a sharp decrease in aggregate curvature. Similar phase behavior has been reported for SDS/C8TAB/water and SDS/hexadecyldimethylammoniopropane sulphonate (HDPS)/water systems [21]. However, in the SDS/C8TAB/water system, the micellar domain is wide, and the region of clear viscoelastic micellar solution shifts to intermediate (about 7:3) SDS/C8TAB mixing ratio, which is near the micellar phase boundary. A very narrow micellar domain is formed at very high C8TAB mixing fraction but the viscosity is very low. In the mixed cationic–anionic systems, the rheological properties are sensitive to the mixing ratio of the surfactants as well as the surfactant concentration. Fig. 14 shows variations of different rheological parameters as a function of surfactant mixing ratio and total surfactant volume fractions in the aqueous CTAT/SDBS system [18]. With the SDBS/CTAT mixing ratio within a narrow range, both the viscosity and relaxation time sharply increase to maximum values at an intermediate mixing ratio within the concentration range of micellar regime, followed by a decrease. It can be seen that with increasing surfactant volume fraction (ϕ), G0 scales with an exponent very close to that predicted by the Cates model, but both η0 and τR increase with large exponents at low surfactant concentrations, and show a decrease after the maxima. The variation in the micellar charge density, for example, by changing the surfactant mixing ratio or adding salt, strongly influences the rheological behavior of wormlike micelles. It has been found that the rheological parameters are highly sensitive to the concentration of the salt and its ability to bind to the surfactant head group [59]. With NaCl which screens the electrostatic interaction between the head groups, η0 and τR both decrease, and the maximum in the τR–ϕ plot disappears, with τR decreasing in a monotonous way in the surfactant concentration range shown in Fig. 14. With a relatively small concentration (0.25 wt.% in the system described in Fig. 14) of hydrotropic salt sodium tosylate, which is incorporated at the hydrophilic–hydrophobic interface and is capable of screening the electrostatic repulsion more effectively, the maxima in both η0– and τR–ϕ plots disappear and the magnitudes of η0 and τR sharply decrease by about 2 orders of magnitude in comparison to the system without salt and the exponents of η0 and τR approach closer to the theoretical value. In addition to the micellar charge density, the alkyl chain length of the surfactants also affects the evolution of aggregate

Fig. 15. Variation of zero-shear viscosity (η0), relaxation time (τR) and shear modulus (G0) as a function of the mixing fraction of CnTAB in 3% (NaOA + CnTAB) aqueous system (obtained from Ref. [19]).

morphology in cationic–nonionic mixed surfactant systems. In dilute systems of sodium oleate (NaOA) and CnTAB (n = 10, 12) at fixed (3 wt.%) total surfactant concentration, micellar solution is formed at NaOA-rich or CnTAB-rich compositions and a two-phase region containing bilayer aggregates appears at intermediate NaOA/CnTAB mixing ratio. Viscoelastic micellar solution is formed in NaOA-rich as well as CnTAB-rich micellar regions in the vicinity of the phase boundary. Upon increasing the asymmetry between the alkyl chain, i.e., in NaOA/C6TAB and NaOA/C8TAB systems, a single micellar phase region is formed in the entire range of surfactant mixing ratio, with a highly viscoelastic micellar phase forming at 7/3 NaOA/C8TAB mixing ratio. Rheological pattern observed in the aqueous NaOA + C8TAB system is similar to that of CTAT/SDBS system, although the viscosity maximum occurs at a different mixing ratio and the variation in viscosity extends over a wide range of mixing ratio in the former system [19]. The variation of rheological parameters as a function of the mixing ratio of NaOA and CnTAB is shown in Fig. 15. 4. Wormlike micelles in ionic surfactant + salt systems Most widely studied systems for the formation of viscoelastic wormlike micelles are the long-chain cationic surfactants such as hexadecyltrimethylammonium (CTA+) and hexadecylpyridinium (CPy+) ions in the presence of inorganic as well as organic counterions such as Br−, Cl−, ClO3−, CH3COO−, salicylate (ohydroxybenzoate, Sal−), tosylate (p-methylbenzenesulphonate,

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T−), and 3-hydroxy-2-naphthalenecarboxylate (HNC−) [9–16]. The extent of micellar growth is sensitive to the binding strength of the counterions to the surfactant head group. Weakly-binding counterions such as Br−, Cl−, ClO3−, CH3COO− are attached to the oppositely charged head groups of the amphiphiles by electrostatic interactions and the binding strength to the head group follows the Hofmeister series: CH3COO− < Br− < ClO3−, which means that with the increased degree of hydration of the counterion, the ability to bind to the head group and induce micellar growth decreases [63,64]. However, aromatic counterions such as Sal−, T− and HNC− are incorporated at the hydrophilic–hydrophobic interface, and, therefore, behave like a cosurfactant. These strongly-binding counterions reduce the curvature of the micelles more effectively even at low concentrations [5,60] or in some cases, in the absence of added salts [61–64]. Structure of the aromatic counterions that favors solubilization of the aromatic part in the palisade layer favors one-dimensional micellar growth. For example, no micellar growth is observed when isomers m- or p-hydroxybenzoate are used instead of o-hydroxybenzoate (Sal−) [65] in the surfactant system. Salt-induced one-dimensional micellar growth has also been observed in aqueous solutions of anionic surfactants such as SDS and sodium dodecyl trioxyethylene sulphate, in the presence of bivalent or trivalent counterions [66–68]. In aqueous SDS/Al(NO3)3 system, viscoelastic solution is formed at relatively high salt concentration. With monovalent ion such as Na+, formation of viscoelastic micellar solution has not been reported yet, although a noticeable micellar growth occurs [69,70]. Aqueous solutions of several oligomeric (gemini) cationic surfactants consisting of quaternary ammonium moieties linked at the level of head group by a spacer (often –(CH2)n–) have been reported to form viscoelastic solutions of wormlike micelles in the absence of salt and at low surfactant concentration (< 10 wt.%) [71–73]. Linking of conventional molecules by a spacer or simply by a covalent bond in the gemini surfactant affects packing of the molecules in the aggregates and their shapes. Moreover, the end-cap energy is expected to be large since packing the bulky alkyl chain into hemispherical end caps with respect to cylindrical part is energetically less favorable, and, therefore, sphere–rod transition in micellar shape occurs at low concentration. The viscoelastic properties of ionic surfactant systems are strongly dependent on the salt/surfactant ratio. At a low salt concentration, high surface charge density of the aggregate reduces the flexibility of the cylindrical aggregates and increases the persistence length (lp). Moreover, the electrostatic repulsion between the cylindrical aggregates makes the network more rigid which is expected to contribute to G0. In this condition, the rheological behavior deviates significantly from the Cates model. In presence of high counterion concentrations, however, the systems approach theoretical behavior [10]. At very high salt concentration also, the systems show a large deviation from the Cates model, which is attributed to the branching of the wormlike micelles, leading to saturation of network at high salt concentration [12,66,71,73].

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Several review papers on the rheological behavior of wormlike micelles in cationic surfactant + salt systems are available [23,34,41,44,74]. 5. Reverse wormlike micelles Phosphatidylcholine, a natural phospholipid commonly known as lecithin, forms reverse aggregates in many organic solvents at low lecithin concentrations. Fig. 16 shows the phase diagram of lecithin/water/cyclohexane system [75]. With increasing lecithin concentration in the lecithin/cyclohexane binary system, reverse micelle (Om)–reverse nematic (N2)– reverse hexagonal (H2) phase transition takes place. Upon adding a small amount of water to the Om solution at a fixed volume fraction of lecithin (composition change along direction a in Fig. 16), one-dimensional micellar growth occurs and reverse wormlike micelles are formed. Upon increasing the volume fraction of the dispersed phase (lecithin + water) along the direction b in Fig. 16, the wormlike micelles begin to entangle and at a high volume fraction of the dispersed phase, a transient network is formed and a viscoelastic solution, often called organogel, is obtained. It should be noted in the phase diagram (Fig. 16) that the region of the highly viscoelastic micelles within the Om domain is located very near the domain of N2 phase which is composed of long, stiff, rod-like aggregates with a net average orientation. Beside cyclohexane, various organic solvents such as linear and cyclic alkanes, esters of fatty acids and amines are known to form organogels above a system-dependent concentration of water, often expressed in the molar ratio of water to lecithin, nw [31]. The critical value of nw for the formation of an organogel, and also the location of the phase boundary of the Om phase exhibit strong solvent dependence, with cycloalkanes showing high values (nw = 6–14) whereas alkanes show low values (nw = 1–2) [32,76,77]. Another factor that affects the formation of an organogel is the lipophilic chain length of lecithin. Reverse micellar solutions of short-chain (C10 or shorter) synthetic lecithins in oil exhibit a poor water solubilizing capacity but addition of relatively large amount of a short-chain alcohol as cosolvent

Fig. 16. Phase diagram of lecithin/water/cyclohexane system at 25 °C. Phase notations are as follows. Om: reverse micellar, N2: reverse nematic, H2: reverse hexagonal, Lα: lamellar. The arrows a and b indicate directions of composition change (for detail, see text) (redrawn from Ref. [75]).

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increases the solubilizing capacity. While a variation of the hydrocarbon chain length influences the location of the phase boundary of the Om phase, the overall micellar shape remains spherical and wormlike micelles are not formed in the shortchain lecithin systems [78]. In the long-chain lecithin, however, solubilization of considerable amount of water in the reverse micelles of lecithin/oil system takes place in the absence of cosolvent, and a one-dimensional micellar growth is induced. The rheological behavior of viscoelastic solutions of wormlike reversed micelles formed in lecithin/water/organic solvents can be described, in general, by the Maxwell model [79–82] with single relaxation time, although in some cases the rheological behavior can be best described by combination of two Maxwell elements of different relaxation times in parallel [83]. The rheological properties of the organogels are sensitive to the concentration of water [80]. At water content below the critical value nw, viscosity growth is gradual but above the critical value, viscosity increases sharply with increasing water content and the system gradually approaches closer to Maxwellian behavior. At high water content, however, the evolution of the rheological parameters deviates from the initial trend [80,82,84]. This is taken as an indication that the successive addition of water first induces a linear growth of the micelles, however, above a certain limit, it also induces branching in the structure. There are evidences that the rheological behavior of the reverse wormlike micelles depends on the type of polar group also. Using glycerol as a polar additive, the viscosity growth becomes noticeable at a significantly lower molar ratio of polar additive to lecithin and micellar growth occurs more swiftly than that observed with water [79]. Although glycerol can form a network with higher number of entanglements, but the micelles are shorter, and therefore, the relaxation time is significantly shorter. The addition of a sugar-containing surfactant to the lecithin/water/decane system induced branching in the network and modified the rheological behavior [81]. 6. Summary In dilute surfactant solutions, one-dimensional micellar growth leading to the formation of wormlike micelles may be induced by tuning the packing properties of the surfactants, which can be brought about by adding a suitable salt or a cosurfactant to the surfactant solution. The phase behavior of the surfactant systems mentioned above provides some understanding of the conditions that favor the formation of wormlike micelles. Information on the effects of the surfactant and additive (salts or cosurfactants) concentrations on the viscoelastic behavior and solution properties of the wormlike micelles can be obtained from rheological studies. The structural evolution such as entanglement, micellar growth and branching can be predicted on the basis of the rheological behavior and small-angle scattering techniques using X-rays or neutrons which provide direct evidences of micellar growth. In a surfactant–cosurfactant mixed system, the size of the head and tail groups of the surfactant as well as the cosurfactant tail group

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