Yield Stress and Scaling of Polyelectrolyte Multilayer Modified

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Yield Stress and Scaling of Polyelectrolyte Multilayer Modified Suspensions: Effect of Polyelectrolyte Conformation during Multilayer Assembly Andreas Hess*,† and Nuri Aksel‡ †

Department of Mechanics and Fluid Dynamics, Freiberg University of Mining and Technology, Freiberg, Saxony, D-09596 Germany, and ‡ Department of Applied Mechanics and Fluid Dynamics, University of Bayreuth, Bayreuth, Bavaria, D-95440 Germany ABSTRACT: The yield stress of polyelectrolyte multilayer modified suspensions exhibits a surprising dependence on the polyelectrolyte conformation of multilayer films. The rheological data scale onto a universal master curve for each polyelectrolyte conformation as the particle volume fraction, ϕ, and the ionic strength of the background fluid, I, are varied. It is shown that rough films with highly coiled, brushy polyelectrolytes significantly enhance the yield stress. Moreover, via the ionic strength I of the background fluid, the dynamic yield stress of brushy polyelectrolyte multilayers can be finely adjusted over 2 decades.

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concentration of the aqueous deposition solution.7 Due to counterion screening, high salt concentrations, c ≥ 0.5 mol/L, lead to highly coiled, brushy polyelectrolytes with linearly growing film thickness.8 Contrary to high salt concentrations, adsorption from salt free or low salt concentrations c < 0.5 mol/L, results in flatly adsorbed polyelectrolytes which build comparatively thinner films.5 Via the polyelectrolyte conformation, the salt concentration also moderates the roughness of the PEM film, which increases with increasing brushiness of the polyelectrolyte building blocks.5,7 Moreover, the changes in surface roughness are also reflected in the evolution of the surface morphology toward evolving wormlike patterns, as visualized by Figure 1. The changing surface morphology agrees very well with the observations made on polyelectrolyte multilayers which were assembled onto flat substrates.7 As a main advantage, the polyelectrolyte conformation, and thus the roughness of the PEM film, is conserved, when the PEMs are transferred from the deposition solution to another aqueous medium.9 Furthermore, the PEM films are kinetically stable for ionic strengths of the background fluid up to I ≈ 1 mol/L monovalent salt.10−12 This should allow us to tailor the interparticle interactions, and consequently the dynamic yield stress, ex situ, that is independent of pH and ionic strength of the background fluid.13,14 In contrast, competing surface functionalization approaches result in a strong coupling to the chemical composition of the background fluid.

INTRODUCTION Control over the yield stress of colloidal suspensions is crucial for many industrial processes and basic research, including soft matter physics, materials engineering, food, and biotechnology. Colloids, per se, have great potential as building blocks for functional nanostructures, but often lack essential features like biocompatibility, dispersibility, or sedimentation stability in aqueous and ionic media. To improve their applicability, the surface of the colloids has to be functionalized . Due to their huge internal surface, nanometer thin polyelectrolyte multilayer (PEM) films, which are composed of alternating polyanion and polycation layers, are interesting materials for surface functionalization.1,2 Thereby, the physicochemical properties of the PEM films greatly benefit from the polymeric and ionic nature of the polyelectrolytes. The physicochemical properties of the PEM film, like hydrophobicity, porosity, surface charge, and roughness, can be precisely adjusted by pH and ionic strength during PEM film assembly.3,4 For example, increasing ionic strength during multilayer formation results in rougher PEM films.5 Herein, we use two of the most studied strong polyelectrolytes, poly(diallyldimethylammoniumchloride) (PDADMAC) and poly(styrenesulfonate) (PSS), to create the multilayer films. Strong polyelectrolytes completely dissociate in aqueous media for wide range of pH values. Thus, the conformation of the used polyelectrolytes depends on their chemical structure and on the ionic strength. We systematically vary the conformation of the polyelectrolytes during PEM film assembly, and study the effect of the polyelectrolyte conformation on the dynamic yield stress, which proves to be a well-defined material property.6 The polyelectrolyte conformation is, to a large extent, set by the salt © 2013 American Chemical Society

Received: May 3, 2013 Revised: August 16, 2013 Published: August 16, 2013 11236

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Figure 1. Topography images of (PDADMAC/PSS)4 modified particles. The PEMs were assembled at (a) c = 10−2 mol/L KCl, and (b) c = 1 mol/L KCl. The AFM experiments were performed in dry air.

Figure 2. Topography images of (a) (PDADMAC/PSS) and (b) (PDADMAC/PSS)4 modified particles. The PEMs were assembled at c = 1 mol/L. The AFM experiments were performed in dry air.

While many applications require the dispersion of PEM modified colloidal particles in liquid media, and even though the use of PEMs as particle coating is often mentioned as a tool to stabilize colloids in suspension,15,16 only a few works deal with the rheology of polyelectrolyte multilayer modified suspensions. In a previous work,17 we investigated the dependence of the static yield stress6,18 of dense suspensions on the number of adsorbed polyelectrolyte layers. The surface roughness decreases with increasing layer number, which is exemplarily visualized by Figure 2 for PEM-modified particles with 2 and 8 polyelectrolyte layers, assembled at c = 1 M NaCl. The static yield stress becomes independent of the surface properties of the colloidal template when the PEM film consists of more than about 6 layers.17 In this multilayer regime, the interparticle interactions are solely determined by the terminating polyelectrolyte layer. The dependence of the rheological properties on the outermost polyelectrolyte layer was expected for the used strong polyelectrolytes. We like to emphasize, that the correlation of the PEM properties to the terminating polyelectrolyte might be less pronounced in case of exponentially growing or strongly stratified PEM’s. While this first study validated the capability of PEM modified suspensions, a more detailed picture of the micromacro interaction mechanism is essential for further applications. With the present work, we take advantage of our previous findings to investigate the micromacro interaction in more detail. We focus on the multilayer regime and limit our study to films with 8 layers and PSS termination. Using PSS as the terminating layer, greatly reduces hydration changes and swelling of the PEM films when the ionic strength of the background fluid was varied.19 Also, for PSS terminated (PDADMAC/PSS) multilayers there exists no significant charge overcompensation when assembled at different salt concentrations.20

We report on tailoring the dynamic yield stress by controlling the polyelectrolyte conformation during (PDADMAC/PSS)4 film assembly. For a specific polyelectrolyte conformation, values of the measured shear stress, σ, can be scaled onto a single master curve. When the polyelectrolytes evolve to brushy conformations, the dynamic yield stress, σy, increases dramatically, and we observe a behavior similar to the variation of particle volume fraction, ϕ, or ionic strength of the background fluid, I. Our results clearly show that the polyelectrolyte conformation is an effective and precise control parameter for the dynamic yield stress.

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MATERIALS AND METHODS

Materials. We use the layer-by-layer (LbL) self-assembly technique21 to build the PEM films onto self-made polystyrene particles. Contrary to state-of-the-art techniques, LbL self-assembly is not restricted to surface charge, size, or shape of the colloidal template. Also, the PEMs can be created from a huge variety of polyanion/ polycation and polyelectrolyte/template pairings. Polystyrene Particle Manufacturing and Characterization. Polystyrene (PS) particles were prepared via dispersion polymerization of styrene in ethanol,22 because of the high monodispersity of the samples and the up-scaling ability for the synthesis.23 Alcohol soluble styrene monomer, initiator, 2,2′-azobis(2-methylbutyronitrile) (AMBN), stabilizer, poly(vinylpyrrolidone) (PVP K30), and costabilizer, Triton X-305, were purchased from Sigma Aldrich and used without further purification. The synthesis route was similar to Song et al.21 About 80% of the styrene monomer (200 g), stabilizer (PVP K30, 32 g), costabilizer (Triton X-305, 11.2 g), and 800 g ethanol were weighed into a 2 L three-neck reaction flask. The filled flask was placed in a 75 °C oil heating bath and continuously stirred at 70 r/min. A starter solution with styrene monomer (40 g) and initiator (AMBN, 8 g) was mixed in a glass beaker and homogenized by a magnetic stirrer, during heating. When the starter solution reached 40 °C, it was poured 11237

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allow the microstructure to rebuild. We use the transient elastic shear modulus, G′(t), to follow this aging during tw by oscillatory shear (oscillation frequency ω = 10 rad/s) with small amplitude, γ0 = 10−2. An example is given in Figure 3. Similar rejuvenation-aging protocols are proved and tested for the investigation of colloidal suspensions that exhibit yield stress behavior.24−27

into the polymerization solution. After 24 h, the solution was cooled to room temperature to stop the synthesis. The particles were washed by centrifugation at 3000 r/min and subsequently decanting the supernatant. Fresh ethanol was added and the washing procedure was repeated 4 times. In a final step, the particles were dried at 30 °C in vacuum, and sieved through a mesh with 20 μm pore size. The particle size is estimated by dynamic light scattering (Mastersizer 2000, Malvern), which reveals a mean radius a = 2.5 μm and a polydispersity of about 3%. The surface charge of the particles, ζ = −55 mV, was determined by electrophoresis experiments (Zetasizer Nano, Malvern). Dry particles were suspended in ultrapure water (Milli-Q, Millipore) at a concentration of 1 g/L to obtain a master suspension. Because the zeta potential measurement suffers from too high particle concentrations, a fraction of the master suspensions was separated and subsequently diluted. The zeta potential was estimated at each dilution step. Values of the zeta potential became independent of the particle concentration at 10−3 g/ L and througout this work, the presented zeta potential values were obtained at this concentration. Polyelectrolyte Multilayer Formation and Characterization. Polyelectrolyte multilayer films with in total 8 individual polyelectrolyte layers were assembled onto the PS spheres by consecutively adsorbing polycations, poly(diallyldimethyhlammonium chloride) (PDADMAC), and polyanions, poly(sodiumstyrene sulfonate) (PSS), from aqueous KCl solutions. The used polyelectrolytes, PDADMAC (Mw = 100 000−200 000 g/mol, and PSS (Mw = 70 000 g/mol) were purchased from Sigma Aldrich and used as received. Aqueous deposition solutions of 10−2 mol/L polyelectrolyte were prepared by the use of ultrapure water (Milli-Q, Millipore). The deposition solutions were adjusted to the desired ionic strength by adding the desired amount of the monovalent salt KCl. The (PDADMAC/PSS)4 films were built from the three salt concentrations, c = 10−2 mol/L KCl, c = 5 × 10−1 mol/L KCl, and c = 1 mol/L KCl. Between the adsorption of successive polyelectrolyte layers, the particles were washed 3 times with polyelectrolyte and salt-free Milli-Q water by centrifugation at 3000 r/m and subsequently decanting and replacing the supernatant. Each adsorbed layer reverses the surface charge of the particles. The charge-reversal was checked by zeta potential measurements (Zetasizer Nano, Malvern), which reveal a zeta potential of about ζ = −55 mV for PSS, and ζ = 25 mV for PDADMAC termination. The PEM modified particles were stored in salt-free Milli-Q water. Suspension Preparation. Prior to each experiment, we wash the particles three times with the aqueous background fluid, which we adjust to the desired ionic strength, ranging from I = 10−3 − 5 × 10−1 mol/L KCl. The particles were stored for 24 h at the specific ionic strength.10 The suspensions were concentrated by sedimentation under gravity and removing the supernatant. Visual inspection of the sedimentation process shows that the occurrence of a liquid phase and a particle sediment became apparent at the time scale of days, and hence the samples are stable against sedimentation on the experimental time scale of several hours. Rheological Setup and Measurement Protocol. A disposable pipet was used to fill in one step about 4 mL of the concentrated suspensions into a concentric cylinder geometry with 0.71 mm gap width. During the experiments, a solvent trap is used to prevent evaporation. Steady shear experiments were performed on a MCR 500 rheometer (Anton Paar), which operates in controlled strain mode. The shear stress response of a decreasing strain rate γ̇, starting at 1000 s−1, is recorded. In order to enhance the reproducibility, the suspensions were presheared at high strain-rates, γ̇ = 500 s−1, to completely erase their mechanical history. At this high strain rate, the viscosity of the suspensions became independent from the strain rate, which indicates that the microstructure is broken down into single particles. Subsequently, the suspensions were left at rest for 2 h for the microstructure to rebuild in a reproducible manner. Aging Protocol. The rejuvenation during preshear resets the time, t, of the sample history. Thus, a waiting time tw = 7200 s is necessary to

Figure 3. Microstructure build up during aging with the transient elastic shear modulus, G′, as a function of time, t. The same data are plotted in the inset in semilogarithmic scales, where the solid line is the logarithmic fit to G′(t) for t > 100 s. The dashed line indicates the structural relaxation time, ts = 300 s, at which G′(t) approaches logarithmic behavior. Volume Fraction Estimation. We estimate the volume fraction from the measured high-shear viscosity,28 −2 ⎛ ϕ ⎞ η∞ = ηf ⎜⎜1 − eff ⎟⎟ ϕ∞ ⎠ ⎝

(1)

with the background fluid viscosity ηf, the effective, and shear dependent volume fraction, respectively, ϕef f, and ϕ∞ = 0.71.29 The presence of electrostatic or steric interactions, as discussed before, may significantly enlarge the effective particle size, and hence ϕeff = (1 + λ/a)3ϕ. To evaluate this effect, we use the characteristic length scales λ of both forces, namely the Debye length κ−1 and the polymer layer thickness δ. First, we evaluate the Debye length for monovalent salt, κ−1 = 0.304 nm/√I, with I denoting the ionic strength of the background fluid.30 In our experiments, the lowest ionic strength is I = 10−3 mol/L KCl, leading to a Debye length κ−1 max = 10 nm. Now we turn to the polymer layer thickness. The largest polymer layer thickness arises in the case of brushy polyelectrolyte conformation. Our most brushy (PDADMAC/PSS)4 multilayers, assembled at c = 1 mol/L KCl, are about δ = 100 nm thick.10,31 The addition of such a relatively thin layer does not significantly increase the effective particle radius. Hence, the effective volume fraction is less than 4% and has no noticeable effect on the rheological properties of the suspensions.32 Consequently, we estimate all volume fractions by the use of eq 1, where we replace ϕeff by ϕ.

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RESULTS AND DISCUSSIONS From the example of Figure 4, we first investigate the rheological properties as a function of the volume fraction when the polyelectrolyte conformation and the ionic strength of the background fluid are fixed. Volume fractions ranging from ϕ = 0.10 to 0.60 were studied. Below a critical volume fraction, ϕc ≈ 0.10 and 0.20, respectively for high, I = 5 × 10−1 mol/L KCl, and low, I = 10−3 mol/L KCl, ionic strength of the background fluid, the measured shear stress decreases linearly with the applied strain rate. This is exemplarily depicted by the lowest curve in Figure 4(b). Such samples behave Newtonian, with their viscosity exceeding that of the background fluid. This is characteristic for dilute suspensions. Larger volume fractions 11238

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To further investigate the rheological properties, we fix the polyelectrolyte conformation and the particle volume fraction and vary the ionic strength of the background fluid. Comparing Figure 4, part (a) with part (b), exemplarily demonstrates that the ionic strength greatly affects the dynamic yield stress. Values of σy drop by more than one order in response to a reduction of the ionic strength from I = 5 × 10−1 mol/L KCl to I = 10−3 mol/L KCl. In conclusion, the data for ϕ > ϕc, suggest that the dynamic yield stress behaves similar at different ϕ and I. To compare these data with respect to the polyelectrolyte conformation, we scale the measured shear stress and the applied strain rate, respectively, by the scaling factors ã and b̃. Curves of different ϕ and I collapse onto a single master curve for each polyelectrolyte conformation. This is visualized by Figure 5(a) for the limiting cases flat and brushy, with the

Figure 4. Representative flow curves for increasing volume fraction from ϕ ≈ 0.20 over ϕ ≈ 0.40 to ϕ ≈ 0.50 at fixed polyelectrolyte conformation and ionic strength. The plotted data contrast the effect of (a) high, I = 5 × 10−1 mol/L KCl, and (b) low, I = 10−3 mol/L KCl, ionic strength of the background fluid. The PEMs were assembled at c = 5 × 10−1 mol/L KCl.

lead to more complex material behavior, as the recorded shear stress becomes more and more nonlinear at low applied strain rates and finally reaches a plateau value. This kind of material behavior can be modeled as a Herschel-Bulkley (HB) fluid,

σ(γ )̇ = σy + kγ ṅ

(2)

with the dynamic yield stress, σy, the consistency index, k, and the positive power-law exponent, n, accounting for either shearthinning, n < 1, or -thickening, n > 1. The consistency index, k, might be interpreted as an apparent viscosity. Fitting eq 2 to our rheological data reveals an excellent agreement where σy corresponds to the plateau stress, and the exponent correctly captures shear-thinning. Because the Hershel--Bulkley (HB) model describes steadystate flow curves, we are now interested in the relevant time scales that enter the description of our samples. We found typical viscoelastic relaxation times, η∞/G0, of the order of 10−3 to 10−2 s. We determine the high shear viscosity, η∞, at γ̇ = 500 s−1 in the Newtonian regime of the flow curve. We define the elastic shear modulus, G0, as the value when G′(t) approaches logarithmic behavior during aging.33 This is illustrated in Figure 3, where we further define the structural relaxation time, ts, when G′(ts) = G0. We like to note that other methods also exist to determine the structural relaxation time.34−36 The ratio of the both time scales gives a dimensionless number, D = η∞/ (G0ts), that indicates nonthixotropic materials for D close to unity, and thixotropic materials for D ≪ 1.37 Typical structural relaxation times, ts, of our samples are ts < 300 s. Then, D < 10−4 and we deal with thixotropic materials. Hence, we have to validate that a steady-state is reached and we choose a waiting time per measurement point, twp = 300 s, so that twp > ts at each imposed strain rate.38−41

Figure 5. Using the polyelectrolyte conformation of the PEM’s to tune the dynamic yield stress. (a) Typical curves of normalized shear stress, σã, as function of normalized strain rate, γḃ .̃ The closed symbols denote different volume fractions, ϕ, while the open symbols denote different ionic strength, I, of the background fluid. The upper master curve (triangles) is for brushy PEMs, assembled at salt concentrations of c = 1 mol/L KCl, the lower master curve (squares) for flat PEMs, assembled at c = 10−2 mol/L KCl. For each polyelectrolyte conformation, the dynamic yield stress value at ϕ = 0.60 sets the reference for the scaling. The corresponding scaling factors are plotted in (b), where the open symbols denote values for I = 10−3 mol/L KCl, the closed symbols for I = 10−1 mol/L KCl. Flat PEMs are less sensitive to I. Hence, low values of the dynamic yield stress can be achived either by flat PEMs (□, ■) or by brushy PEMs which were dispersed in a low I background fluid (Δ).

PEMs assembled at c = 10−2 and c = 1 mol/L KCl, respectively. This scaling demonstrates that the modification by brushy PEM films significantly enhances the dynamic yield stress by more than one order in magnitude. To comprehend the meaning of the scaling, the horizontal scaling factor b̃ is normalized by the high shear viscosity, η∞, to account for the particle loading. The factors ã and b/η∞ are plotted in Figure 5(b). Because ã and b/η∞ are linearly related, 11239

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6(a) nicely visualizes the rise of the dynamic yield stress with increasing ionic strength, I of the background fluid. Now we turn to the effect of the polyelectrolyte conformation on the dynamic yield stress. For this, we vary the brushiness, and thus the roughness of the PEM film,5 and plot in Figure 6(b) representative σy values at fixed ionic strength, I = 10−1 mol/L KCl. Remarkably, values of the dynamic yield stress increase with increasing volume fraction according to σy ∝ ϕ3. Furthermore, the dynamic yield stress increases with increasing salt concentration, c, of the deposition solution. Surprisingly, at low, I = 10−3 mol/L KCl, and high, I = 5 × 10−1 mol/L KCl, ionic strength of the background fluid, the brushiness plays a minor role and values of σϕ(c) of the different polyelectrolyte conformations are approximately equal. The results from Figure 6, parts (a) and (b), clearly show that different routes exist to tune the yield stress of PEMmodified suspensions. Low yield stress values can be achieved by the following: (i) flat PEMs, assembled from polyelectrolytes which were adsorbed at low salt concentrations c or (ii) by brushy PEMs, with polyelectrolytes adsorbed at high c, which were dispersed in a low ionic strength background fluid. About 2 decades higher yield stress values can be tailored by brushy PEMs in high ionic strength background fluids, as seen by Figure 6(a). It turns out from Figure 5(b), that flat PEMs are less sensitive to the ionic strength of the background fluid than brushy PEM’s. First, we will discuss the effect of I on σϕ. Generally, the interactions between polyelectrolyte multilayers are a superposition of electrostatic and steric forces. Unfortunately, systematic studies of the interactions between PEMs are scarce, and the interaction mechanisms are not fully understood. Using the surface force apparatus (SFA) and colloidal probeforce measurements (CP-AFM), the dominating interactions between PEMs assembled at high, c ≥ 0.5 mol/L, monovalent salt concentration, were recently investigated.50−52 In these experiments, the polyelectrolyte conformation was fixed and the ionic strength of the background fluid was varied. The experiments reveal the dominance of steric over electrostatic interactions above ionic strength of the background fluid of I ≈ 10−3 mol/L. Please note that our experiments were conducted at similar ionic strength I ≥ 10−3 mol/L. The steric interactions originate from tails and loops of the terminating polyelectrolyte that expand from the PEM surface into the surrounding solution. Thus, we can think of a hairy corona around the PEM coated colloids. Recent experiments performed with the support of the osmotic stress technique arrived at the same solid core-PEM shell-hairy corona picture.53 In a first approximation, we hypothesize that the hairy corona behaves similarly to PSS monolayers,54,55 which shrink with decreasing ionic strength of the background fluid according to ∝ I−1/3. A qualitatively similar behavior is observed for (PDADMAC/PSS) multilayers,19 which also shrink with increasing ionic strength I. Hence, we anticipate that the tails and loops of the hairy corona were most extended at low I. Then, the expanding polyelectrolyte chains experience electrostatic self-repulsion, which tends to stretch the polyelectrolyte chains and is balanced by their elasticity. Increasing I leads to an imbalance which results in chain softening and lastly in a collapse of the hairy corona. We speculate that thereby the effective interparticle attraction increases.

the scaling represents a shift along the viscosity of the background fluid.42 Interestingly, the scaling factors in Figure 5(b) expand over two decades for brushy PEM films (triangles), whereas for flat PEM films (squares) they accumulate in a half decade. This much narrower distribution implies that the modification by flat PEM films is less sensitive to the ionic strength of the background fluid and will be discussed later. Remarkably, in Figure 5(a), we observe negative slopes in the I = 10−3 mol/L KCl flow curves for the brushy samples at low strain rates. Similar behavior is observed for other soft colloids, like colloidal star polymers, and related to shear banding.26,40,43,44 The flow curves in Figure 4, together with the master curves in Figure 5, suggest that the fluid changes to a jammed solid, either if the volume fraction or the interparticle interaction exceeds their corresponding critical values ϕc ≈ 0.2 or Uc, implying that I is related to the interparticle interaction, U(I) . Thus, the dynamic yield stress denotes the critical stress at the jamming phase boundary, described by σy = σϕ(ϕ − ϕc)ν, where σϕ sets the stress scale of the yield stress, and ν is an exponent which is related to the microstructure of the sample.45 We focus on high volume fractions, and thus this equation simplifies to the following:46,47

σy = σϕϕv

(3)

As an example, Figure 6(a) shows the dynamic yield stress as a function of the volume fraction for brushy, PE’s adsorbed at c = 1 mol/L KCl, colloids.

Figure 6. Alternative routes to tune the dynamic yield stress: (a) Fine tuning by the ionic strength I of the background fluid for brushy PEMs and (b) tailoring the dynamic yield stress by the polyelectrolyte conformation during multilayer assembly. Low yield stresses can be achieved either by brushy samples dispersed in a low ionic strength background fluid (▼) or by flat PEMs (▲). In (a), the brushy polyelectrolyte multilayers were assembled at c = 1 KCl. The dynamic yield stress increases with increasing I. Values of the ionic strength during measurement are I = 10−3 mol/L (▼), I = 10−2 mol/L (⧫), I = 10−1 mol/L (●), and I = 5 × 10−1 mol/L (⬟) KCl. The experiments shown in (b) are performed at I = 10−1 mol/L KCl. The dynamic yield stress increases with increasing polyelectrolyte conformation, from flat, c = 10−2 mol/L KCl (▲), over c = 5 × 10−1 mol/L KCl (■) to brushy, c = 1 KCl (●). In both figures, solid lines are fits of eq 3 to the data with the slope 3.

The plotted solid lines denote fits of eq 3 to the dynamic yield stress data obtained at ionic strengths between I = 10−3 mol/L and I = 5 × 10−1 mol/L KCl. As expected from eq 3, the dynamic yield stress increases proportional to a constant power of the volume fraction, σy ∝ ϕν, with ν = 3. This value is reasonable, since values of ν between 1.4 and 5.5 are typically observed in suspensions of weakly attractive particles that form scale invariant particulate networks.46,48,49 Moreover, Figure 11240

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CONCLUSIONS Using strong polyelectrolytes, we demonstrate that control over the polyelectrolyte conformation of PEM films serves as a versatile tuning parameter for the dynamic yield stress of colloidal suspensions. Using this tuning parameter opens up the possibility to tailor the dynamic yield stress. In particular, low dynamic yield stress values can be achieved by adsorbing the polyelectrolytes in a flat conformation, where the ionic strength of the background fluid has less impact on the yield stress. As an alternative route, low yield stress values can also be produced by adsorbing the polyelectrolytes in a brushy conformation and dispersing them in a low ionic strength background fluid. In contrast, to achieve high yield stress values, the polyelectrolytes have to be adsorbed in a brushy conformation and dispersed in a high ionic strength background fluid. Hence, for brushy polyelectrolyte multilayers, a fine-tuning over 2 decades of the dynamic yield stress is possible via the ionic strength of the background fluid. Using simple scaling arguments, we draw a first picture of the interaction mechanisms that motivate further study. Our results show that well-defined, homogeneous polyelectrolyte multilayers are a promising method for the design of colloidal suspensions.

The interactions of PSS monolayers are strongly correlated to the thickness, L, of the highly coiled polyelectrolytes. This thickness is proportional to the decay length of the steric repulsion,56 and hence, for the PSS terminated multilayers we expect the effective attraction U ∝ L−1. This is reasonable since in Figure 5(b), the scaling factors for the flat PEMs, assembled at c = 10−2 mol/L, lie closer together as the scaling factors for the brushy PEMs, assembled at c = 1 mol/L. Increasing the ionic strength of the background fluid, I, collapses the hairy layer according to L ∝ (Is2)−1/3, where, in the case of PSS monolayers, s2 is related to the chain length of polyelectrolytes.14,56 For the PSS terminated multilayers, we pragmatically use s as a dimensionless scaling factor. Using eq 3 together with the scaling,49 σy ∝

Uϕν a2

Article

(4)

recently proposed for weakly attractive particles with ν close to 3, relates the extra stress to the interparticle interactions, σϕ ∝ U. Hence, we expect the normalized yield stress to scale as σy/ (Is2)1/3 ∝ ϕ3, which we plot in Figure 7(a). Remarkably,

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the reviewers for their instructive comments, and gratefully acknowledge the financial support of the German Research Foundation (FG 608 “Nonlinear Dynamics in Complex Media”). We thank Andreas Fery for inspiring discussions. Many thanks to Melanie Poehlmann, who performed parts of the AFM measurements.

Figure 7. Scaling of the normalized dynamic yield stress, σy/(Is2)1/3, as a function of particle volume fraction, ϕ. The plotted data are obtained for increasing brushiness, or roughness, from triangles (PEMs assembled at c = 10−2 mol/L KCl) over squares (PEMs assembled at c = 5 × 10−1 mol/L KCl) to circles (PEMs assembled at c = 1 mol/L KCl), respectively with the scaling factors s = 0.01, 0.04, and 0.1. For each polyelectrolyte conformation, the variation of the different ionic strength of the background fluid I during measurement is visualized by the colors green (I = 10−3 mol/L KCl), black (I = 10−2 mol/L KCl), blue (I = 10−1 mol/L KCl), and red (I = 5 × 10−1 mol/L KCl). Please note that data for I = 5 × 10−1 mol/L KCl are not shifted.

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samples up to I = 10−1 mol/L KCl follow this scaling and collapse onto the unshif ted data for I = 5 × 10−1 mol/L KCl. We hypothesize that at this high ionic strength, I = 5 × 10−1 mol/L KCl, charges of the hairy layer are largely neutralized, and the interactions become dominated by nonspecific interactions, such as bridging.57,58 On the basis of Figure 7, we discuss the effect of brushiness, and hence PEM film roughness,5 on σϕ. We estimate s = 0.01, 0.04, and 0.1, ordering from flat to brushy adsorbed polyelectrolytes. This ordering corresponds to increasing PEM film roughness,5 as visualized by Figure 1. The increasing PEM film roughness leads to rising attractive interparticle interactions,51 which is in good accord with our observed increasing values of s, and hence σϕ. Our findings are also in good qualitative agreement with colloidal probe force measurements14 as well as yield stress measurements59,60 on brushy, or rough, polyelectrolyte monolayers. 11241

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