Self-Aggregation of Mixtures of Oppositely ... - ACS Publications

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Self-Aggregation of Mixtures of Oppositely Charged Polyelectrolytes and Surfactants Studied by Rheology, Dynamic Light Scattering and Small-Angle Neutron Scattering Ingo Hoffmann,*,†,‡ Peggy Heunemann,†,‡ Sylvain Pr
evost,†,§ Ralf Schweins,‡ Norman J. Wagner,|| and Michael Gradzielski*,† †

)

Stranski Laboratorium f€ur Physikalische und Theoretische Chemie, Technische Universit€at Berlin, Straβe des 17. Juni 124, 10623 Berlin, Germany ‡ LSS Group, Institut Laue-Langevin, 6 rue Jules Horowitz BP 156, F-38042 Grenoble, Cedex 9, France § Helmholtz-Zentrum Berlin, D-14109 Berlin, Germany Department of Chemical Engineering, Center for Molecular and Engineering Thermodynamics, University of Delaware, Newark, Delaware 19716, United States

bS Supporting Information ABSTRACT: In this study, the phase behavior, structure and properties of systems composed of the cationic, cellulose-based polycation JR 400 and the anionic surfactants sodium dodecylbenzenesulfonate (SDBS) or sodium dodecylethoxysulfate (SDES), mainly in the semidilute regime, were examined. This system shows the interesting feature of a very large viscosity increase by nearly 4 orders of magnitude as compared to the pure polymer solution already at very low concentrations of 1 wt %. By using rheology, dynamic light scattering (DLS), and small-angle neutron scattering (SANS), we are able to deduce systematic correlations between the molecular composition of the systems (characterized by the charge ratio Z = [þpolymer]/[
surfactant]), their structural organization and the resulting macroscopic flow behavior. Mixtures in the semidilute regime with an excess of polycation charge form highly viscous network structures containing rodlike aggregates composed of surfactant and polyelectrolyte that are interconnected by the long JR 400 chains. Viscosity and storage modulus follow scaling laws as a function of surfactant concentration (η ∼ cs4; G0 ∼ cs1.5) and the very pronounced viscosity increase mainly arises from the strongly enhanced structural relaxation time of the systems. In contrast, mixtures with excess surfactant charges form solutions with viscosities even below those of the pure polymer solution. The combination of SANS, DLS, and rheology shows that the structural, dynamical, and rheological properties of these oppositely charged polyelectrolyte/surfactant systems can be controlled in a systematic fashion by appropriately choosing the systems composition.

’ INTRODUCTION Systems composed of oppositely charged polyelectrolytes and surfactants show a rich and complex self-aggregation behavior. The structures formed vary over a large size range, as well as with respect to their detailed structural organization, and such mixtures have many applications, e.g., in cosmetics, detergency, and drug delivery. Therefore they have attracted quite some interest in the past decades1
22 and substantial efforts have been devoted to the study of complexes formed by block or graft polyelectrolytes with oppositely charged surfactants and hydrophobically modified polymers with surfactants23
28 in the dilute29
35 and in the semi dilute regime.27,36
38 Already in rather dilute mixtures of polyelectrolyte containing double-hydrophilic block copolymer and oppositely charged surfactant, such as poly(sodium acrylate)-b-poly(acrylamide) (PANa-b-PAM) and dodecyltrimethylammonium bromide (DTAB) relatively complex core
shell structures containing surfactant micelles in the core have been observed.39,40 In a similar fashion of ionic coassembly, r 2011 American Chemical Society

mixtures of double hydrophilic block copolymers with oppositely charged polyelectrolytes41 or other double hydrophilic block copolymers with an oppositely charged block42 result in the formation of aggregates. Also mixtures of cross-linked polyelectrolyte and linear neutral polymers can lead to the formation of gels with remarkable mechanical properties.43,44 Alternatively to ionic coassembly, one may also have hydrophobically driven assembly. For instance, hydrophobically modified polymers can be involved in the formation of aggregates with either surfactants or other polymer molecules via their hydrophobic side chains, which can lead to the formation of network structures with surfactants. Oppositely charged polymer/surfactant systems possess similar qualities once surfactant molecules are bound to the polymer with their charged group, Received: November 18, 2010 Revised: March 6, 2011 Published: March 23, 2011 4386

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Langmuir thereby forming hydrophobic, micelle-like domains. Together with other surfactant decorated polymers, they can now form interconnected network structures as well that typically are highly viscous or even gel-like. Therefore by combining oppositely charged polyelectrolytes and surfactants, one does not only induce the formation of aggregated structures, but is also able to exert control over the dynamical and rheological properties of these systems. This means one can design systems of potential interest for encapsulation and release.18,45 Accordingly, such mixed polyelectrolyte/surfactant systems are of potential interest for many applications from the fields of detergency, rheological modification, and formulation science. Complexes of polyelectrolytes and oppositely charged surfactant have been intensely studied for the case of polyelectrolytes with high charge density along the polymer backbone (such as polyacrylate (PA), polymethacrylate (PMA), or polystyrene sulfonate (PSS)) for equimolar mixtures. Such complexes are insoluble in water, typically exhibit a high degree of ordering, and are interesting composite materials.11,46 For instance, mixtures of PANa and alkyltrimethylammonium bromide (CnTAB) have been intensely studied. Here it has been observed that over a very extended range of concentrations phase separation occurs.47 However, this strong tendency for phase separation appears to be linked to the high charge density present in the polyelectrolyte, as it was also observed that for sodium hyaluronate with its somewhat lower charge density the range of colloidal stability is significantly larger.48 At high PANa concentration, some small increase of viscosity has been observed upon addition of CTAB or DTAB beyond the critical micelle concentration (cmc).49 Very interesting in that context is that previous studies of more dilute PANa solutions have shown that their solution viscosity decreases largely already upon addition of very small amounts (Z . 1) of DTAB,50 and similar observations have been reported for the addition of DTAB to copolymers of acrylamide and sodium 2-acryl-amido-2methylpropanesulfonate.51 This is in striking contrast to the observations reported in our investigation. Our aim then was to use a structurally different type of polyelectrolyte and to develop a systematic approach to systems based on a commercially relevant polyelectrolyte of lower charge density and oppositely charged surfactants with a particular emphasis on controlling the rheological properties of such systems. This is of high practical importance; such systems have hardly been studied so far, and their use could be of significant relevance in order to control the properties of surfactant/ polyelectrolyte formulations with as little material as possible in order to save resources. For that purpose, in the present study we investigate systems composed of the cationic, cellulose based polymer JR 400 and the anionic surfactants SDBS and SDES. This is still a rather simply built system, but with relevance to practical applications. They were studied as a function of the mixing ratio and the total concentration. In contrast to many other commonly investigated high-charge density polyelectrolytes, such as PSS or sodium polyacrylate (PAA) (which have charge densities along the polymer chain of about 4 charges/nm), the average distance between charges along the polymer backbone of JR 400 is of the order of about 2 nm, which is well above the Bjerrum length, which is 0.714 nm in water. Compared to conventional high charge density polyelectrolytes, we may expect a much broader colloidal stability in the mixtures with oppositely charged surfactant for JR 400, especially since the uncharged monomeric units are relatively hydrophilic. Therefore it can be expected that they

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Figure 1. Chemical structure of JR 400 and SDBS (from left to right); 27% of JR 400 monomer units are charged.

stabilize charge compensated complexes in aqueous solution. The phase behavior of the polycation/anionic surfactant mixtures was studied over a large range of mixing ratios and total concentration. In the studied system, remarkable changes of the macroscopic flow properties were observed already in the rather dilute regime. By combining small-angle neutron scattering (SANS), rheology, and dynamic light scattering (DLS), a comprehensive physicochemical characterization was done, which allowed us to correlate the microscopic structural changes directly with the change of the dynamical properties in the microscopic and macroscopic domain. Thereby a relation between the molecular composition of the mixed system and its macroscopic properties can be obtained.

’ MATERIALS AND METHODS Materials. JR 400 (Dow Chemical, USA; see Figure 1) is a cationically modified cellulose ether with a molecular weight of about 500 000 g/mol52 and a degree of substitution of 0.27, resulting in a charge density of 1000 g/mol of positive charges.53 It was used without further purification. Linear alkylbenzenesulfonate (LAS) (gift from Henkel KGaA, Germany) is an anionic surfactant, consisting of a benzenesulfonate headgroup and a secondary alky chain with an average length of about 12 carbon atoms and statistically linked to the benzene ring, i.e., it is not a molecularly pure compound where a single cmc is to be expected. It has an average molecular weight of 318 g/mol, determined by titration with NaOH. Equimolar amounts of NaOH (97%, Merck, Germany) were added to obtain (mainly) sodium dodecylbenzenesulfonate (SDBS). The cmc varies depending on the chain length and the position of the benzenesulfonate group along the alkyl chain. The value for a commercial sample has been reported as 2.4 mM.54 Texapon N70 (Cognis GmbH, Germany) is a sodium dodecylethersulfate (SDES) surfactant with a mass average molecular weight of 337 g/mol, as determined by electrospray ionization mass spectrometry (ESI-MS), assuming equal ionisability of all species. Mainly chains with 12 and 14 carbon atoms and 0 to 3 ethylene oxide groups are present in the mixture. According to the supplier, the main component is sodium 2-(2-dodecyloxyethoxy)ethyl sulfate. The cmc of sodium 2-(2-dodecyloxyethoxy)ethyl sulfate has been reported to be 2.88 mM.55 For simplicity, it will be referred to as SDES. For the mixtures, the characteristic charge ratio Z is given as the ratio between the concentration of the positive polymer charges and that of the negative surfactant charges, Z = [þpolymer]/[
surfactant]. Mixtures of polymer and surfactant were prepared by mixing stock solutions with the same polymer concentration, one of them containing no surfactant the other one containing enough surfactant, so that Z < 1. All samples were 4387

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prepared at least 24 h prior to the measurements and stored at room temperature. Water was taken from a Millipore System and had a specific conductivity of 0.06 μS/cm. SANS samples were prepared in D2O (99.9% isotopic purity, Euriso-top, France) so as to keep the molar concentrations identical to the corresponding samples in H2O. Methods. Rheology. Rheology data were measured with a TA Instruments AR G2 Rheometer and a Malvern Instruments Gemini 200 HR both with cone and plate geometry with a 4 cm cone with a cone angle of 4° and 0.15 mm gap. All measurements were carried out at 25 °C. The shear rate dependence was measured with increasing and decreasing shear rate. For measurements with the Gemini 200 HR, a delay time and an integration time of 10 s each were chosen, while on the AR G2 consecutive measurements with an integration time of 10 s were carried out until 3 consecutive measurements agreed with each other within 5% tolerance or a maximum time of 5 min was exceeded. Oscillatory measurements were all carried out in the linear viscoelastic regime as was ascertained by prior strain sweeps. Typical measurements took less than 30 min in order to mitigate evaporation. The critical shear rate was taken as the onset of the decrease in viscosity. The exact value was determined by the intersection of two lines extrapolating the low shear rate plateau and the high shear rate decreasing region, respectively (for an example, see Figure S9, Supporting Information). DLS. DLS measurements were performed at 25 °C with a setup consisting of an ALV 7004 Correlator, an ALV CGS-3 Goniometer and a He
Ne Laser with a wavelength of 632.8 nm. Cylindrical sample cells were placed in an index matching vat filled with toluene. Autocorrelation functions were recorded under different angles between 50° and 150°. The magnitude of the scattering vector q is related to the angle by q = (4πn/λ) sin(θ/2), with n being the refractive index of the medium, λ being the wavelength in vacuo, and θ being the scattering angle. The measured intensity autocorrelation function g(2) is related to the field autocorrelation function g(1) by the Siegert relation:56 g ð2Þ ¼ 1 þ Bjg ð1Þ j2

ð1Þ

The mode coupling theory (MCT) has been successfully applied to describe the dynamics of semi dilute polymer solutions.57
59 According to the approach taken by Ngai and co-workers,60,61 the correlation function of semidilute solutions of entangled polymers can be described with a combination of an exponential function at short times and a stretched exponential at long times: g ð1Þ ðtÞ ¼ Afast expð
t=τfast Þ þ Aslow expð
ðt=τslow Þβ Þ

ð2Þ

While the decay at short times, described by τfast, is related to the collective motion of single chains with the diffusion coefficient D = (τfastq2)
1, the slow mode, described by τslow, accounts for the dynamics of larger clusters. The exponent of the stretched exponential is related to the coupling parameter n via β = 1
n. The theory assumes that below a certain critical time tcrit, the dynamics of the chains are not perturbed by the formation of clusters and the correlation function can be described by a single exponential decay g(t) = exp(
t/τfast). For times longer than tcrit, the dynamics of the clusters start to influence the correlation function, and a second slow mode is required to describe its behavior. The decay time of the slow mode is related to τfast, tcrit, and n as τslow 1/(1
n) (q) = (t
n . While the fast time shows diffusive q
2 critτfast(q)) behavior, the q dependence of τslow is proportional to q
2/(1
n), as follows from inserting the q
2 dependence into the expression for τslow. SANS. SANS experiments were performed on the instrument D11 at the Institut Laue Langevin (ILL) in Grenoble, France and on the instrument V4 at the Helmholtz-Zentrum Berlin f€ur Materialien und Energie (HZB), Germany. To cover a large Q-range, measurements were done at a wavelength of 0.6 nm and for sample-to-detector distances of 1.2, 8, and 32 m (ILL) and 1 and 4 m (HZB), respectively. Transmissions were measured with the attenuated direct beam at 8 m.

Figure 2. Phase diagram for SDBS/JR 400 and SDES/JR 400 mixtures. Solid outline with white background: two-phase region of SDBS/JR 400 mixtures; dashed outline with gray background: two-phase region of both SDBS/JR 400 and SDES/JR 400 mixtures. Water was used as a standard to obtain absolute intensities and to account for the detector efficiency. D2O was used as a solvent to improve contrast and lower the incoherent background. Standard procedures62 for data reduction were applied using the software package Bersans.63 The scattering behavior could be described as follows: I(Q) = φVP(ΔSLD)2F2(Q), with the volume fraction φ, the particle volume VP, the difference in scattering length density between solvent and particles ΔSLD, and the scattering amplitude F(Q). For a cylinder of length L and radius R, F(Q) is given as64 pffiffiffiffiffiffiffiffiffiffiffiffi Z 1 4J1 ðQR 1
x2 Þ sinðQLx=2Þ pffiffiffiffiffiffiffiffiffiffiffiffi FðQ Þ ¼ dx ð3Þ Q 2 R 1
x2 Lx 0 with the length of the rod L, its radius R and the first order Bessel function J1. The scattering from solutions with an excess of surfactant charges could be described as that of a sphere. The scattering amplitude of a sphere with radius R is given as64 sinðQRÞ
QR cosðQRÞ FðQ Þ ¼ 3 ðQRÞ3

ð4Þ

The scattering from pure polymer solutions could be described as that of Gaussian coil: expð
ðQRG Þ2 Þ
1 þ ðQRG Þ2 IðQ Þ ¼ φVP ðΔSLDÞ2 2 ðQRG Þ4

ð5Þ

with the radius of gyration RG and the forward scattering intensity I(0) = φVP(ΔSLD)2. Unless stated differently, the incoherent background has not been subtracted.

’ RESULTS AND DISCUSSION Phase Behavior. As a first step we studied the phase behavior of mixtures of the cationic polymer for a large Z-range, i.e., upon the addition of increasing amounts of anionic surfactant (while keeping the polymer concentration constant), in a range of polymer concentration of 0.005 to 1 wt %. Thereby we cover from the dilute to the concentrated range of such mixtures. Right after mixing all samples show precipitation or at least pronounced turbidity, yet after stirring overnight, samples in the single phase regions are clear and have reached a stable state. The phase diagrams for the SDBS/JR 400 and the SDES/JR 400 system in Figure 2 show a precipitation region near the point of charge equivalence (Z = 1) and single phase regions for both an 4388

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Figure 3. SANS data (ILL) of SDBS/JR 400 mixtures for different Z (O 3, 0 3.9, ) 5.9, Δ 7.8, 3 29, left-4 pure polymer) Lines are best fits using eq 5 (pure polymer) or eq 3 (mixtures), polymer concentration was fixed at 1 wt % at 25 °C.

excess of polymer charges as well as for an excess of surfactant charges. The region of precipitation apparently becomes smaller upon dilution on the polymer-rich side. While the region with Z > 1 (i.e., with an excess of polymer charges) shows a pronounced increase in viscosity as the phase boundary is approached, no viscosity enhancement is observed for the Z < 1 region. Although the viscosity increases largely as the phase boundary is approached from the Z > 1 side, all samples still flow under the influence of gravity, i.e., none of them behaves like a gel having a yield stress. Precipitates can easily be redissolved by both surfactant and polymer excess, making it likely that the structures formed are in equilibrium. These observations hold true for both surfactants. Some care should be taken with the exact location of the phase boundaries. On one hand, the high viscosity of some samples might prevent the dissolution of remaining precipitate and thereby extending the apparent phase boundary to higher Z, while on the other hand the very small amounts of precipitate in samples with very low concentrations can be difficult to detect, which is probably also the reason for the apparent absence of the two-phase region in mixtures of SDES and JR 400 for small JR 400 concentrations, i.e., they might simply not be discerned by our visual determination. The similarities in the phase behavior lead to the conclusion that the phase behavior of these systems is generic and dominated by electrostatic effects, as has been shown previously for similar systems.1,37,65 SANS. In order to gain insight into the structure of the solutions from a microscopic point of view, we carried out SANS experiments on samples with 1 wt % JR 400 and variable SDBS or SDES concentrations on both sides of the phase boundary. The obtained scattering curves are depicted in Figure 3 and Figure 4 (the same data, but with the incoherent background subtracted are also given in a bending rod plot, i.e., IQ vs Q, in the Supporting Information as Figure S5 and Figure S6, respectively). While there are differences in the details, the qualitative behavior of the SANS curves is the same for mixtures of JR 400 with SDBS (Figure 3) and SDES (Figure 4). The pure polymer displays only very weak scattering, and the structure visible could be described by a random coil structure according to eq 5 with a radius of gyration of about 2 nm, which changes slightly upon increase of polymer concentration (see Figure S3 and Table S1). The scattering of the polymer is too weak to account for the entire amount of polymer present in the sol ution, as typically observed for polyelectrolyte solutions in the

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Figure 4. SANS data (ILL) of SDES/JR 400 mixtures for different Z (O 2.5, 0 3.3,) 5.0, Δ 6.6, 3 25, left-4 pure polymer) Lines are best fits using eq 5 (pure polymer) or eq 3 (mixtures), polymer concentration was fixed at 1 wt % at 25 °C.

Figure 5. SANS data of SDBS/JR 400 mixtures with excess of polymer charges (open symbols) and excess of surfactant charges (closed symbols) at 25 °C (O SDBS Z 3; b SDBS Z 0.1); lines are best fits using eq 4 (Z = 0.1) or eq 3 (Z = 3).

semidilute regime,66,67 and what is observed is some correlation length. See the Supporting Information for details. Addition of surfactant causes a continuous increase in scattering intensity with roughly a Q
1 slope. At the highest surfactant content (excess of surfactant charges) one sees a different scattering pattern where a plateau is reached at low Q, and the shape of the scattering curves is that of globular aggregates with the size of a typical surfactant micelle (see Figure 5). The Q
1 slope at intermediate Q indicates the presence of rodlike structures (Figure 3 and Figure 4). These structures grow in length as more surfactant is added (as evidenced from the extended Q
1 range and increasing scattering intensity at low Q);their radius, however, is again of the order of magnitude of surfactant micelles and does not change significantly as the mixing ratio is changed. From a quantitative analysis using eq 3 to describe the scattering curves, the size parameters length and radius can be deduced, and they are summarized in Table 1. From that analysis it can also be concluded that the structures formed in SDBS/JR 400 mixtures are slightly thinner (by about 0.2 nm) than those in the SDES/JR 400 mixtures, presumably due to the longer average surfactant chain of SDES (see Table 1). As the phase boundary is approached, a shoulder can be observed around 0.1 nm
1, corresponding to a spacing of roughly 60 nm, that can be interpreted as being due to a typical mesh size of the rodlike aggregates. This is in contrast to the typical behavior of semidilute wormlike micelles, where normally no correlation peak is observed. However, it 4389

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Table 1. Fit Parameters and Concentrations of SANS Samples with Polymer Surfactant Mixtures in the Polymer Excess Regimea surfactant

Z

ΔSLD2 [nm
4]

φfit

R [nm]

SDBS

29

3.2  107

0.0013

1.1

SDBS

7.8

3.2  107

0.0013

1.5

SDBS

5.9

3.2  107

0.0013

SDBS

3.9

3.2  107

SDBS

2.9

3.2  107

SDES

25

SDES

φs

φtot

11

0.0001

0.0058

6

20

0.0004

0.0060

81

8

1.8

24

0.0005

0.0062

180

10

0.0017

1.7

>150

0.0008

0.0064

1200

8

0.0021

1.6

>150

0.0010

0.0067

1300

7

3.2  107

0.0012

1.2

13

0.0001

0.0058

12

7

6.6

3.2  107

0.0014

1.9

20

0.0005

0.0061

140

11

SDES SDES

5.0 3.3

3.2  107 3.2  107

0.0016 0.0020

1.9 1.8

40 >150

0.0006 0.0009

0.0063 0.0066

340 1400

11 9

SDES

2.5

3.2  107

0.0023

1.9

>150

0.0013

0.0069

1700

8

L [nm]

NAgg,SANS

Npol 6

φfit: fitted aggregate volume fraction; R: fitted radius of aggregate; L: fitted length of aggregate; φs: surfactant volume fraction; φtot: total volume fraction of polymer and surfactant; NAgg,SANS: number of surfactant molecules per aggregate; Npol: estimated number of polymer chains per aggregate. a

should be noted that also for such system the SANS curves can only be described appropriately by taking into account a structure factor.68 The different behavior in our case can be explained by the fact that the bridging between the aggregates is done by the polyelectrolyte chains, and it is not the aggregates themselves that are entangled as with wormlike micelles; therefore a typical spacing between the aggregates can be observed in the scattering pattern. In addition, it should also be noted that in our surfactant/polyelectrolyte complexes, no extended wormlike micelles are claimed, but still relatively short rodlike micelles. For the highest concentrations of SDES, one even observes a change of the shape of the scattering curves at lower Q that indicates the formation of larger globular structures. This would not be surprising given the fact that here relatively large amounts of surfactant are present, and the formed rodlike aggregates might locally become bundled together in an overall globular shape. If an excess of surfactant is added to the polymer, the rodlike structures are dissolved, as can be seen by the lower intensity at very low Q (see Figure 5), and the curve is dominated by the scattering of spherical micelles. It is difficult to tell whether these micelles are free micelles or bound to the polymer, as in the generally accepted necklace model,69 probably a mixture of both is present. The decrease in intensity shows that the rodlike structures present before the phase boundary have disappeared while a relatively sharp peak can be seen in pure micellar solution, the curve is relatively flat in the case of a mixture with comparable surfactant concentration and additional polymer. However, the same effect is seen if salt is added to the micellar solution (Figure S1), where the number of charges per volume introduced by adding the KH2PO4 is about a factor of 2 higher than that for the investigated JR 400 solution. Accordingly, this is largely a screening effect induced by the binding of the polyelectrolyte JR 400 onto the micellar surfaces. The higher intensity observed at lower Q for the JR 400 may be attributed to an effective attraction introduced by bridging neighboring aggregates. A comparison of the surfactant volume fraction in the sample φs and the volume fraction of the rodlike structures obtained from fits with eq 3 φfit shows that the aggregates have to be composed of both surfactant and polymer since the samples do not contain enough surfactant to account for the observed scattering intensity. Accordingly, mixed aggregates of surfactant and JR 400 must be present. Figure 6 shows that the ratio between the aggregate volume fraction from the fits and the surfactant volume fraction decreases as the phase boundary is

Figure 6. Ratio of surfactant volume fraction to polymer volume fraction in aggregates calculated from SANS (open symbols, left axis), line: Z
1 and ratio of fitted aggregate volume fraction to surfactant volume fraction (closed symbols, right axis), SDBS O, SDES 0.

approached but remains larger than 1, so that the ratio of surfactant to polymer volume in the aggregate is increasing, but the aggregates are always composed of both polymer and surfactant in the whole polymer excess region. This assumes that φfit is composed of the surfactant volume fraction and the volume fraction of polymer in the aggregates φpol (φfit = φpol þ φs). Furthermore we can infer from these findings that the aggregates are not just formed from surfactant molecules arranged along one polymer chain, i.e., no pearl necklace structure is formed, but that many polymer chains are held together by those aggregates in a compacted fashion (see Scheme 1). If we assume rodlike micelles along the backbone of a single polymer chain, the fraction of polymer in the aggregate would have to be much smaller. The effective cross section of the polymer backbone, using eqs S1 and S2 (Supporting Information) is 0.45 nm. Therefore, with an aggregate radius of 1.5
2 nm and a single polymer chain in it, the surfactant to polymer volume fraction in the aggregate would be on the order of at least (φfit
φpol)/φpol = (R2
r2)πL/r2πL ≈ [(1.5 nm)2
(0.45 nm)2]/(0.45 nm)2 = 10, but the experimental values are smaller by 1 order of magnitude and more. If we assume a stretched conformation of the polymer chains along the whole length of the aggregate, we can estimate the number of polymer chains per aggregate: Assuming that φs/φpol = 1 and taking the same radii as before the number of polymer chains in the aggregate Npol would be R2/(1 þ φs/φpol)r2 = Npol = 1.52/ (1 þ 1)0.452 ≈ 6. This means that, on average, six polymer 4390

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Scheme 1. Schematic Representation of Structures Formed by Oppositely Charged Polymer Surfactant Mixturesa

Figure 7. Zero shear viscosity η0 of SDBS(b) and SDES/JR 400 (0) mixtures for different Z; polymer concentration was fixed at 1 wt % at 25 °C. Solid straight line Z
4. a

The charges along the polymer backbone are compensated by single surfactant molecules. As more surfactant is added, polymer chains are held together by rodlike mixed aggregates. Addition of even more surfactant causes the dissolution of these structures, and single spherical aggregates are formed along the polymer backbone.

chains are incorporated along the line of rodlike surfactant/ polyelectrolyte complex aggregates (see Scheme 1). The number of surfactant molecules per aggregate (see Figure S2) can be calculated as NAgg,SANS = (VAgg/Vs) 3 (φs/φfit), with the volume of the aggregates VAgg and the volume of a single surfactant molecule Vs. The obtained values are very similar for both surfactants and reflect the growth of the structures as more surfactant is added. The occurrence of a peak at low Q for samples near the phase boundary in the polymer excess region shows that the mesh size of the network formed by the rodlike surfactant/polyelectrolyte complexes is becoming smaller as more surfactant is added, as to be expected for a constant thickness of the rods. A detailed summary of all parameters is given in Table 1. For the case of excess surfactant, one observes a scattering pattern that resembles that of a pure surfactant solution (Figure 5). The larger structures present at lower surfactant content vanish and are replaced by smaller micellar units upon addition of more surfactant. This finding is consistent with the observation that, at the same time, the viscosity of these samples is largely reduced. Compared to a pure micellar solution, the scattering at low Q is somewhat enhanced (see Figure S1), which points to the presence of a pearl necklace structure in which the micelles experience an effective attractive interaction due to bridging by the polyelectrolyte. The obtained radius of the micelles is 2.1 nm, which is slightly larger than the radii of the cylinders. The volume fraction obtained from the fit is 0.027, which corresponds to the volume fraction of the surfactant in the sample. Still it is difficult to say whether the polymer is included in the spheres since the volume fraction of the polymer is quite small compared to the surfactant volume fraction and the position of the low Q plateau might be somewhat disturbed by structure factor effects. Rheology. In order to obtain information about the macroscopic properties, rheology measurements were performed. Mixtures of JR 400 with SDES and SDBS with a constant JR 400 concentration of 1 wt % and solutions of pure JR 400 at different concentrations were examined by viscosimetry and oscillatory measurements.

Figure 8. Critical shear rate γ_ crit of SDBS(b) and SDES/JR 400 (0) as a function of Z; polymer concentration was fixed at 1 wt % at 25 °C, straight line: Z2.7.

The zero-shear viscosity is given in Figure 7 and shows an increase by 4 orders of magnitude upon addition of anionic surfactant to the 1 wt % JR 400 solution. For still higher surfactant concentrations beyond the precipitate region, the viscosity is reduced again to values lower than that of the pure JR 400 solution. The behavior is very similar for both anionic surfactants, but with somewhat higher absolute values for the case of SDBS. In contrast, for the surfactant-rich side, a much lower viscosity is observed for the case of SDBS, which indicates that the SDBS is apparently effectively able to suppress the polyelectrolyte properties of JR 400 at these concentrations. Solutions of JR 400 with a concentration of 1 wt % or higher show shear thinning behavior as can be seen in Figure S8. At a critical shear rate γ_ crit, a decrease in viscosity is observed. The shear thinning is significantly more pronounced if some surfactant is added. The type of anionic surfactant used does not seem to be of great importance since both SDBS and SDES behave quite similarly. As the surfactant excess regime is reached, however, no shear thinning can be observed. Both zero shear viscosity (η0) and γ_ crit change systematically as Z is decreased (i.e., if surfactant is added). On approaching the phase boundary, γ_ crit does not change much above Z ≈ 10, but decreases by an order of magnitude until the phase boundary is reached (γ_ crit µ Z2 to Z3) (Figure 8). The change in η0 seems to be correlated to the change in γ_ crit. η0 shows a slight increase with added surfactant, and as Z ≈ 10 is reached, addition of more surfactant causes a steep rise in viscosity by roughly 4 orders of magnitude until precipitation begins. Note that the Z value at which the flow behavior starts to change dramatically coincides 4391

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Figure 9. Elastic modulus G0 (filled symbols) and viscous modulus G00 (open symbols) as a function of angular frequency ω for SDBS/JR 400 (1 wt %) mixtures at different Z (b 3, 9 5, ( 8).

Figure 10. Mesh size of mixtures of JR 400 (1 wt %) and SDBS (b) and SDES (0), as a function of Z.

Table 2. Parameters Obtained from Oscillatory Shear Rheology of SDBS/JR 400 Mixtures Z

ωcross

τcross

G0

N

dmesh

NAgg,

[rad/s]

[ms]

[Pa]

[m
3]

[nm]

Rheo

1

30

38

165

1.3

3.2  10

150

635

10 8

36 37

175 170

5.0 7.2

1.2 1021 1.8 1021

94 83

496 430

7

36

175

10

2.5 1021

74

347

6

29

217

13

3.1 1021

69

328

5

20

314

17

4.2 1021

62

286

4

11

571

26

6.3 1021

54

238

3

4.8

1310

45

1.1 1022

45

184

20

Table 3. Parameters Obtained from Oscillatory Shear Rheology of SDES/JR 400 Mixtures Z

ωcross

τcross

G0

N

dmesh

NAgg,

[rad/s]

[ms]

[Pa]

[m
3]

[nm]

Rheo

4.5

21

1

17

37

170

1.1  10

97

275

8.6

26

242

10

2.4  1021

74

248

6.9

18

353

15

3.6  1021

65

206

6

12

537

18

4.4  1021

61

197

5.2

9.4

671

25

6.1  1021

55

165

4.3

6.5

971

29

7.0  1021

52

171

3.4 2.6

3.0 1.4

2100 4460

35 45

8.5  1021 1.1  1022

49 45

177 184

well with the value for which formation of rodlike structures is observed in SANS (Figure 3 and Figure 4). The other remarkable point is that this increase of viscosity is by more than 4 orders of magnitude already for a concentration of 1 wt % JR 400 and about 0.1 wt % anionic surfactant. Frequency sweeps (Figure 9) demonstrate that the more viscous samples show viscoelastic behavior, as typically found for entangled networks of wormlike surfactant solutions.70
72 One observes a crossover between G0 and G00 , which indicates an effective structural relaxation time τcross, which is shifted toward lower frequencies with increasing surfactant content. At the same time, the values for the shear modulus become larger. The corresponding rheological parameters are summarized in Table 2 and Table 3 for the SDBS/JR 400 and SDES/JR 400 cases, respectively.

Figure 11. Plateau modulus G0 of SDBS (O) and SDES (0)/JR 400 (1 wt %) mixtures and η0 3 γ_ crit of SDBS (b) and SDES (9)/JR 400 (1 wt %) mixtures as a function of Z; solid line: Z
1.5.

The plateau value of G0 (taken as the average of G0 at the four highest frequencies) allows for the calculation of a network junction density 1N via G0 = 1NkBT with the network junction density 1N, temperature T, and Boltzmann's constant kB. This in turn can be used to calculate a mesh size dmesh = 1/1N(1/3) and give a rough estimate for the number of surfactant molecules per junction NAgg,Rheo = 1Ns/1N with the number density of surfactant molecules 1Ns. This number should overestimate the aggregation number because it is assumed that all surfactant molecules are involved in the formation of aggregates that tie together polymer chains. On the other hand, there are probably junctions that consist of polymer chains only, which would lead to an underestimation of the aggregation number. Especially, the fact that rheology counts the number of surfactant molecules per junction and not the number of surfactant molecules per aggregate should lead to significantly smaller numbers in rheology than in SANS. In fact, the values found are on the order of a few hundred surfactant molecules, which is smaller than the numbers found by SANS by a factor of about 5 in the case of samples near the phase boundary where values of about 1000 surfactant molecules are found in SANS. This finding supports the proposed structure of multibridging mixed aggregates (Scheme 1). Furthermore the mesh size of samples near the phase boundary coincides very well with the spacing of 60 nm deduced from the correlation peak in SANS samples with the same composition. It is interesting to note that G0 rises systematically upon approaching the precipitate phase boundary (Figure 11), but to a much lesser extent than the zero-shear viscosity. This means that the high zero-shear viscosity observed just before reaching the 4392

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ARTICLE

precipitate region arises from a systematic increase of the structural relaxation time of the viscoelastic network, which for a simple Maxwell fluid is given by the plateau values of the shear viscosity and the shear modulus by η ð6Þ τ¼ 0 G0 This is consistent with the finding that the critical shear rate γ_ crit, which is expected to be inverse to the structural relaxation time, changes in this range by 2 orders of magnitude. In fact, almost quantitative agreement is found between the scaling of G0 with Z, which is found to be about
1.5. The scaling of η0 (
4) and γ_ crit (2.7) should result in G0 µ γ_ critη0 µ Z
4þ2.7 µ Z
1.3, which is in good agreement with the experimental value. The product γ_ critη0 is compared to G0 in Figure 11, and one finds a very similar trend (while the absolute numbers differ by a constant factor, presumably due to the fact that γ_ crit is directly proportional to 1/τ, but not identical to it). The rheology of viscoelastic surfactant solutions has been extensively studied70,72
74 and similar scaling laws75 with surfactant concentration (Z µ c
1 s ) have been found for these systems. Scaling exponents found for G0 vary between 1.8 and 2.4, which is slightly larger than the value found here. That the elastic values increase less strongly with surfactant concentration is not surprising, as to a significant extent it will also rely on the presence of the polyelectrolyte whose concentration remains constant throughout the variation of Z. For η0 values of the exponent between 1 and 4 have been reported, which is in agreement with our value of about 4. However, the systems under investigation are not simple Maxwell fluids, as can be seen by the discrepancy between the relaxation times obtained from the crossover between G0 and G00 and eq 6 (Table 2 and 3). In addition, it was not possible to obtain reasonable fits with the Maxwell model. Furthermore, it should be noted that despite the pronounced viscoelastic properties, these gels do not possess a yield stress as demonstrated in Figure S10. DLS. Further information regarding the dynamic properties of the system is accessible by DLS. This is particularly interesting, as especially for viscoelastic systems one can expect that the relaxation spectrum observed in rheology is also reflected in DLS.76 DLS probes the dynamics of the system on a microscopic scale, and the results can be correlated with the behavior on a macroscopic scale as seen by rheology and the microscopic structure as obtained from SANS. By combining this information, it should be possible to relate the behavior on a microscopic level to the macroscopic properties. The field correlation functions (Figure 12) obtained via eq 1 show the complex behavior predicted by theory (eq 2) and as conventionally observed for polyelectrolytes under salt-free conditions.77
79 Pure JR 400 solution already shows a two-step relaxation process, with a very slow nonexponential mode. The addition of small amounts of anionic surfactant leads to a substantial shift of the correlation functions such that the amplitude of the fast relaxation becomes much smaller. However, the two relaxation modes remain observable. The fast relaxation time remains almost unchanged for all samples and exhibits diffusive behavior, i.e., a conventional q
2 dependence and a zero intercept in a plot of the reciprocal time versus the scattering vector (see Figure S13). The hydrodynamic radii (Figure S16 and Table 4), obtained from the Stokes
Einstein equation, show accordingly almost constant values of around 2 nm (that increase slightly with decreasing Z). This value is the same as the structural

Figure 12. Field autocorrelation function g(1) of SDBS/JR 400 (1 wt %) mixtures at a scattering angle of 150° for different Z: O pure polymer, 0 28, ) 8, Δ 6, 3 5, left-4 4, right-4 0.2.

Table 4. Parameters Obtained from DLS Measurements, Stretch Parameter β, Amplitude of the Fast Mode Afast at a Scattering Angle of 150° and Hydrdynamic Radius RH Obtained from the Fast Mode Z

β

Afast

RH [nm]

pure polymer

0.49

0.13

1.13

0.14 28

0.47 0.51

0.62 0.04

3.68 1.32

9.7

0.43

0.01

2.2

7.8

0.42

0.03

2.16

5.8

0.41

0.04

2.16

4.9

0.39

0.04

2.42

3.9

0.37

0.03

2.38

Figure 13. Slow mode τslow as a function of q of SDBS/JR 400 (1 wt %) mixtures for different Z: O pure polymer, ) 8, Δ 6, 3 5, left-4 4, right-4 0.2; line: q
4. The strong q dependence shows the nondiffusive character of the slow mode.

size observed by SANS. This implies that the fast dynamics are due to polymer subunits (polymer blobs), that remain widely unaffected by the formation of superstructures in the sample. The slow relaxation time, which is related to these superstructures of the network (presumably like a breathing mode of this network), shows a stronger q dependence of about q
4 (Figure 13) and 4393

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Langmuir

Figure 14. Stretch parameter β of SDBS/JR 400 (1 wt %) mixtures as a function of Z, the decrease toward the phase boundary indicates an increase in coupling strength.

Figure 15. Structural relaxation time τcross (b) (from intersection of G0 and G00 ), structural relaxation time from η0/G0 (3) and τslow at a scattering angle of 150° (0) of SDBS/JR 400 (1 wt %) mixtures as a function of Z. All quantities follow the same trend.

dominates the correlation function except for the sample with Z < 1. The stretch parameter β decreases, and the amplitude of the slow relaxation time increases as the phase boundary is approached from the Z > 1 side. These two findings both indicate that the coupling is increased as Z is decreased. The slow relaxation time is clearly correlated to the structural relaxation time seen in the rheology experiments, and clearly is a nondiffusive relaxation mode. Although τslow is systematically larger than τcross, both quantities show a qualitatively similar trend as a function of Z, as a plot of the inverse cross over frequency together with the slow time at an angle of 150° divided by 2π in Figure 15 clearly shows. An even more quantitative agreement is achieved when τslow is compared with the structural relaxation time determined by eq 6. It should be noted that the relative amplitude of the slow relaxation time for the sample with Z = 0.2 is even below that of the pure polymer, which is consistent with the lower viscosity of the system in the surfactant excess regime. Conclusions. By combining DLS, rheology and SANS measurements we were able to show that oppositely charged polymer surfactant systems composed of the cationically modified cellulose derivative JR 400 and anionic surfactants (SDBS or SDES) form highly viscoelastic networks of rodlike aggregates at surfactant concentrations somewhat below charge equivalence, i.e., at Z values above 2, where Z is defined as the charge ratio [þpolymer]/[
surfactant]. An increase of viscosity by more than

ARTICLE

4 orders of magnitude can be induced by adding to a 1 wt % polycation (JR 400) solution about 0.1 wt % anionic surfactant (Z ∼ 3). For larger amounts of anionic surfactant, i.e., around charge equivalence precipitation of a polycation/surfactant complex is observed. As the surfactant concentration is further increased beyond the phase boundary, this complex becomes redissolved, and the viscosity drops below the value of even that of the pure polymer. SANS measurements in this regime of excess surfactant show the presence of spherical aggregates, which have the size of pure surfactant micelles and presumably are arranged in the frequently observed pearl necklace model structure. Much more interesting is certainly the enormous viscosity enhancement that can be induced in the polycation rich regime by the addition of rather small amounts of oppositely charged surfactant. For such mixtures with Z > 2, SANS shows the presence of rodlike surfactant/polyelectrolyte complexes that increase in length with increasing relative surfactant content. They must contain many JR 400 chains in order to account for the observed intensity, and these long JR 400 chains (stretched length of 600
800 nm) are also responsible for interconnecting many such rods. This then explains the tremendous increase in viscosity. The onset of formation of these rodlike structures (3.5) coincides with a pronounced increase of the zero-shear viscosity η0, which follows a scaling law of cs4 at constant polymer concentration. At the same time, the elastic modulus G0 of these viscoelastic systems follows a power law of 1.5 with respect to the surfactant concentration. These scaling laws show that a large part of the viscosity increase must be due to a very pronounced increase of the structural relaxation time of the system caused by the complexation of the JR 400 by anionic surfactant. This is presumably due to the largely increasing interconnection of the growing rod-like structures with increasing surfactant content. Accordingly, the large increases in elastic and viscous properties, as well as the enhancement of the structural relaxation time of the surfactant/polyelectrolyte mixtures is in very good agreement with the structural model of interconnected “polyelectrolyte enforced” rodlike surfactant/polyelectrolyte complexes. Although a comparison between macroscopic (rheology) and microscopic (DLS) relaxation shows quantitative differences in the relaxation time (by about a factor 10), the two measurements follow the same trend; thus, the microscopic dynamics appears to be directly related to the macroscopic rheological behavior of the system. This is an interesting observation that rewards further experimental investigation and might also be of interest for further theoretical investigations. Furthermore, the comparison of SANS and rheology shows good agreement between microstructure and macroscopic dynamics, as the mesh size calculated from rheology coincides well with the spacing seen in SANS. The aggregation numbers for the rod-like aggregates deduced from both methods are well comparable. In summary, the formation of polyelectrolyte-rich complexes in the JR 400/anionic surfactant system allows for control of the rheological properties over an extended range by the addition of rather small amounts of surfactant. A “gelling” of the system becomes already possible for very low polymer/surfactant concentrations of about 1 wt %. The properties observed are well explained by a model of polyelectrolyte enforced mixed rodlike aggregates (Scheme 1). They form a network structure as evidenced in SANS, and the mesh size of 26 deduced is in good agreement with the one deduced from rheology. The large increase in viscosity of these systems is simply due to the formation of rather rigid rodlike surfactant/polyelectrolyte 4394

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Langmuir complexes that are intereconnected by the long and flexible JR 400 chains. The stability of these systems is related to the fact that the charge density of the polyelectrolyte is not too high, thereby effectively allowing for the formation of such extended rodlike structures. The behavior of these mixtures does not depend on the particular choice of anionic surfactant but is generic and apparently controlled by electrostatics. By appropriate choice of the mixing conditions, it is thus possible to tune structural and rheological properties over a wide range of values. This renders such systems from polyelectrolyte and ionic surfactant very interesting candidates for many applications, especially in formulation science.

’ ASSOCIATED CONTENT

bS

Supporting Information. Additional measurements. This material is available free of charge via the Internet at http://pubs.acs.org/.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: ingo.hoff[email protected] (I.H.); michael.gradzielski@ tu-berlin.de (M.G.).

’ ACKNOWLEDGMENT This international cooperation and the research stays at the University of Delaware were supported by the Deutsche Akademische Austausch Dienst (DAAD) (PPP 50021532). SANS measurements were supported by the European Commission under the seventh Framework Programme through the Key Action: Strengthening the European Research Area, Research Infrastructures. Contract No.: 226507 (NMI3). The authors thank the ILL for granted beam time, Ms. Maria Schlangen for ESI-MS measurements, and the Henkel KGaA for support of this project. M.G. would like to thank the Institut Laue-Langevin (ILL, Grenoble, France) and the DFG (Project GR1030/10) for hospitality and funding of his sabbatical stay during which a larger part of this manuscript was produced. ’ REFERENCES (1) Goddard, E. D.; Hannan, R. B. J. Colloid Interface Sci. 1976, 55, 73–79. (2) Zhang, H.; Li, Y.; Dubin, P.; Kato, T. J. Colloid Interface Sci. 1996, 183, 546–551. (3) Antonietti, M.; Burger, C.; Th€unemann, A. Trends Polym. Sci. 1997, 5, 262–267. (4) Claesson, P. M.; Fielden, M. L.; Dedinaite, A.; Brown, W.; Fundin, J. J. Phys. Chem. B 1998, 102, 1270–1278. (5) Kosmella, S.; Koetz, J.; Shirahama, K.; Liu, J. J. Phys. Chem. B 1998, 102, 6459–6464. (6) Kwak, J. C. T., Ed. Polymer
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