Yield Stress and Scaling of Polyelectrolyte Multilayer ModifiedSuspensions: Effect of Polyelectrolyte Conformation duringMultilayer AssemblyAndreas Hess*,† and Nuri Aksel‡
†Department of Mechanics and Fluid Dynamics, Freiberg University of Mining and Technology, Freiberg, Saxony, D-09596Germany, and‡Department of Applied Mechanics and Fluid Dynamics, University of Bayreuth, Bayreuth, Bavaria, D-95440 Germany
ABSTRACT: The yield stress of polyelectrolyte multilayermodified suspensions exhibits a surprising dependence on thepolyelectrolyte conformation of multilayer films. The rheo-logical data scale onto a universal master curve for eachpolyelectrolyte conformation as the particle volume fraction, ϕ,and the ionic strength of the background fluid, I, are varied. Itis shown that rough films with highly coiled, brushypolyelectrolytes significantly enhance the yield stress. More-over, via the ionic strength I of the background fluid, thedynamic yield stress of brushy polyelectrolyte multilayers canbe finely adjusted over 2 decades.
■ INTRODUCTION
Control over the yield stress of colloidal suspensions is crucialfor many industrial processes and basic research, including softmatter physics, materials engineering, food, and biotechnology.Colloids, per se, have great potential as building blocks for
functional nanostructures, but often lack essential features likebiocompatibility, dispersibility, or sedimentation stability inaqueous and ionic media. To improve their applicability, thesurface of the colloids has to be functionalized . Due to theirhuge internal surface, nanometer thin polyelectrolyte multilayer(PEM) films, which are composed of alternating polyanion andpolycation layers, are interesting materials for surfacefunctionalization.1,2 Thereby, the physicochemical propertiesof the PEM films greatly benefit from the polymeric and ionicnature of the polyelectrolytes.The physicochemical properties of the PEM film, like
hydrophobicity, porosity, surface charge, and roughness, canbe precisely adjusted by pH and ionic strength during PEM filmassembly.3,4 For example, increasing ionic strength duringmultilayer formation results in rougher PEM films.5 Herein, weuse two of the most studied strong polyelectrolytes, poly-(diallyldimethylammoniumchloride) (PDADMAC) and poly-(styrenesulfonate) (PSS), to create the multilayer films. Strongpolyelectrolytes completely dissociate in aqueous media forwide range of pH values. Thus, the conformation of the usedpolyelectrolytes depends on their chemical structure and on theionic strength. We systematically vary the conformation of thepolyelectrolytes during PEM film assembly, and study the effectof the polyelectrolyte conformation on the dynamic yield stress,which proves to be a well-defined material property.6 Thepolyelectrolyte conformation is, to a large extent, set by the salt
concentration of the aqueous deposition solution.7 Due tocounterion screening, high salt concentrations, c ≥ 0.5 mol/L,lead to highly coiled, brushy polyelectrolytes with linearlygrowing film thickness.8 Contrary to high salt concentrations,adsorption from salt free or low salt concentrations c < 0.5mol/L, results in flatly adsorbed polyelectrolytes which buildcomparatively thinner films.5 Via the polyelectrolyte con-formation, the salt concentration also moderates the roughnessof the PEM film, which increases with increasing brushiness ofthe polyelectrolyte building blocks.5,7 Moreover, the changes insurface roughness are also reflected in the evolution of thesurface morphology toward evolving wormlike patterns, asvisualized by Figure 1. The changing surface morphology agreesvery well with the observations made on polyelectrolytemultilayers which were assembled onto flat substrates.7
As a main advantage, the polyelectrolyte conformation, andthus the roughness of the PEM film, is conserved, when thePEMs are transferred from the deposition solution to anotheraqueous medium.9 Furthermore, the PEM films are kineticallystable for ionic strengths of the background fluid up to I ≈ 1mol/L monovalent salt.10−12 This should allow us to tailor theinterparticle interactions, and consequently the dynamic yieldstress, ex situ, that is independent of pH and ionic strength ofthe background fluid.13,14 In contrast, competing surfacefunctionalization approaches result in a strong coupling tothe chemical composition of the background fluid.
Received: May 3, 2013Revised: August 16, 2013Published: August 16, 2013
While many applications require the dispersion of PEMmodified colloidal particles in liquid media, and even thoughthe use of PEMs as particle coating is often mentioned as a toolto stabilize colloids in suspension,15,16 only a few works dealwith the rheology of polyelectrolyte multilayer modifiedsuspensions. In a previous work,17 we investigated thedependence of the static yield stress6,18 of dense suspensionson the number of adsorbed polyelectrolyte layers. The surfaceroughness decreases with increasing layer number, which isexemplarily visualized by Figure 2 for PEM-modified particleswith 2 and 8 polyelectrolyte layers, assembled at c = 1 M NaCl.The static yield stress becomes independent of the surfaceproperties of the colloidal template when the PEM film consistsof more than about 6 layers.17 In this multilayer regime, theinterparticle interactions are solely determined by theterminating polyelectrolyte layer. The dependence of therheological properties on the outermost polyelectrolyte layerwas expected for the used strong polyelectrolytes. We like toemphasize, that the correlation of the PEM properties to theterminating polyelectrolyte might be less pronounced in case ofexponentially growing or strongly stratified PEM’s. While thisfirst study validated the capability of PEM modifiedsuspensions, a more detailed picture of the micromacrointeraction mechanism is essential for further applications.With the present work, we take advantage of our previous
findings to investigate the micromacro interaction in moredetail. We focus on the multilayer regime and limit our study tofilms with 8 layers and PSS termination. Using PSS as theterminating layer, greatly reduces hydration changes andswelling of the PEM films when the ionic strength of thebackground fluid was varied.19 Also, for PSS terminated(PDADMAC/PSS) multilayers there exists no significantcharge overcompensation when assembled at different saltconcentrations.20
We report on tailoring the dynamic yield stress bycontrolling the polyelectrolyte conformation during (PDAD-MAC/PSS)4 film assembly. For a specific polyelectrolyteconformation, values of the measured shear stress, σ, can bescaled onto a single master curve. When the polyelectrolytesevolve to brushy conformations, the dynamic yield stress, σy,increases dramatically, and we observe a behavior similar to thevariation of particle volume fraction, ϕ, or ionic strength of thebackground fluid, I.Our results clearly show that the polyelectrolyte conforma-
tion is an effective and precise control parameter for thedynamic yield stress.
■ MATERIALS AND METHODSMaterials. We use the layer-by-layer (LbL) self-assembly
technique21 to build the PEM films onto self-made polystyreneparticles. Contrary to state-of-the-art techniques, LbL self-assembly isnot 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 polymerizationof styrene in ethanol,22 because of the high monodispersity of thesamples and the up-scaling ability for the synthesis.23 Alcohol solublestyrene monomer, initiator, 2,2′-azobis(2-methylbutyronitrile)(AMBN), stabilizer, poly(vinylpyrrolidone) (PVP K30), and costabil-izer, Triton X-305, were purchased from Sigma Aldrich and usedwithout further purification. The synthesis route was similar to Song etal.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 wereweighed into a 2 L three-neck reaction flask. The filled flask was placedin a 75 °C oil heating bath and continuously stirred at 70 r/min. Astarter solution with styrene monomer (40 g) and initiator (AMBN, 8g) was mixed in a glass beaker and homogenized by a magnetic stirrer,during heating. When the starter solution reached 40 °C, it was poured
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/LKCl. 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.
into the polymerization solution. After 24 h, the solution was cooled toroom temperature to stop the synthesis.The particles were washed by centrifugation at 3000 r/min and
subsequently decanting the supernatant. Fresh ethanol was added andthe washing procedure was repeated 4 times. In a final step, theparticles were dried at 30 °C in vacuum, and sieved through a meshwith 20 μm pore size.The particle size is estimated by dynamic light scattering
(Mastersizer 2000, Malvern), which reveals a mean radius a = 2.5μm and a polydispersity of about 3%. The surface charge of theparticles, ζ = −55 mV, was determined by electrophoresis experiments(Zetasizer Nano, Malvern). Dry particles were suspended in ultrapurewater (Milli-Q, Millipore) at a concentration of 1 g/L to obtain amaster suspension. Because the zeta potential measurement suffersfrom too high particle concentrations, a fraction of the mastersuspensions was separated and subsequently diluted. The zetapotential was estimated at each dilution step. Values of the zetapotential became independent of the particle concentration at 10−3 g/L and througout this work, the presented zeta potential values wereobtained at this concentration.Polyelectrolyte Multilayer Formation and Characterization.
Polyelectrolyte multilayer films with in total 8 individual polyelec-trolyte layers were assembled onto the PS spheres by consecutivelyadsorbing 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 = 70000 g/mol) were purchased from Sigma Aldrich and used as received.Aqueous deposition solutions of 10−2 mol/L polyelectrolyte wereprepared by the use of ultrapure water (Milli-Q, Millipore). Thedeposition solutions were adjusted to the desired ionic strength byadding 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-Qwater by centrifugation at 3000 r/m and subsequently decanting andreplacing the supernatant. Each adsorbed layer reverses the surfacecharge of the particles. The charge-reversal was checked by zetapotential measurements (Zetasizer Nano, Malvern), which reveal azeta potential of about ζ = −55 mV for PSS, and ζ = 25 mV forPDADMAC termination. The PEM modified particles were stored insalt-free Milli-Q water.Suspension Preparation. Prior to each experiment, we wash the
particles three times with the aqueous background fluid, which weadjust 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 ionicstrength.10 The suspensions were concentrated by sedimentationunder gravity and removing the supernatant. Visual inspection of thesedimentation process shows that the occurrence of a liquid phase anda particle sediment became apparent at the time scale of days, andhence the samples are stable against sedimentation on theexperimental 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 concentratedsuspensions into a concentric cylinder geometry with 0.71 mm gapwidth. During the experiments, a solvent trap is used to preventevaporation. Steady shear experiments were performed on a MCR 500rheometer (Anton Paar), which operates in controlled strain mode.The shear stress response of a decreasing strain rate γ, starting at 1000s−1, is recorded. In order to enhance the reproducibility, thesuspensions were presheared at high strain-rates, γ = 500 s−1, tocompletely erase their mechanical history. At this high strain rate, theviscosity of the suspensions became independent from the strain rate,which indicates that the microstructure is broken down into singleparticles. Subsequently, the suspensions were left at rest for 2 h for themicrostructure 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
allow the microstructure to rebuild. We use the transient elastic shearmodulus, 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 protocolsare proved and tested for the investigation of colloidal suspensions thatexhibit yield stress behavior.24−27
Volume Fraction Estimation. We estimate the volume fractionfrom the measured high-shear viscosity,28
η ηϕϕ
= −∞∞
−⎛⎝⎜⎜
⎞⎠⎟⎟1f
eff2
(1)
with the background fluid viscosity ηf, the effective, and sheardependent volume fraction, respectively, ϕef f, and ϕ∞ = 0.71.29
The presence of electrostatic or steric interactions, as discussedbefore, may significantly enlarge the effective particle size, and henceϕeff = (1 + λ/a)3ϕ. To evaluate this effect, we use the characteristiclength scales λ of both forces, namely the Debye length κ−1 and thepolymer layer thickness δ. First, we evaluate the Debye length formonovalent salt, κ−1 = 0.304 nm/√I, with I denoting the ionicstrength of the background fluid.30 In our experiments, the lowestionic strength is I = 10−3 mol/L KCl, leading to a Debye length κmax
−1 =10 nm. Now we turn to the polymer layer thickness. The largestpolymer layer thickness arises in the case of brushy polyelectrolyteconformation. 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 significantlyincrease the effective particle radius. Hence, the effective volumefraction is less than 4% and has no noticeable effect on the rheologicalproperties of the suspensions.32 Consequently, we estimate all volumefractions by the use of eq 1, where we replace ϕeff by ϕ.
■ RESULTS AND DISCUSSIONSFrom the example of Figure 4, we first investigate therheological properties as a function of the volume fractionwhen the polyelectrolyte conformation and the ionic strengthof the background fluid are fixed. Volume fractions rangingfrom ϕ = 0.10 to 0.60 were studied. Below a critical volumefraction, 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 thebackground fluid, the measured shear stress decreases linearlywith the applied strain rate. This is exemplarily depicted by thelowest curve in Figure 4(b). Such samples behave Newtonian,with their viscosity exceeding that of the background fluid. Thisis characteristic for dilute suspensions. Larger volume fractions
Figure 3. Microstructure build up during aging with the transientelastic shear modulus, G′, as a function of time, t. The same data areplotted in the inset in semilogarithmic scales, where the solid line is thelogarithmic fit to G′(t) for t > 100 s. The dashed line indicates thestructural relaxation time, ts = 300 s, at which G′(t) approacheslogarithmic behavior.
lead to more complex material behavior, as the recorded shearstress becomes more and more nonlinear at low applied strainrates and finally reaches a plateau value. This kind of materialbehavior can be modeled as a Herschel-Bulkley (HB) fluid,
σ γ σ γ = + k( ) yn
(2)
with the dynamic yield stress, σy, the consistency index, k, andthe positive power-law exponent, n, accounting for either shear-thinning, n < 1, or -thickening, n > 1. The consistency index, k,might be interpreted as an apparent viscosity. Fitting eq 2 toour rheological data reveals an excellent agreement where σycorresponds to the plateau stress, and the exponent correctlycaptures shear-thinning.Because the Hershel--Bulkley (HB) model describes steady-
state flow curves, we are now interested in the relevant timescales that enter the description of our samples. We foundtypical viscoelastic relaxation times, η∞/G0, of the order of 10
−3
to 10−2 s. We determine the high shear viscosity, η∞, at γ = 500s−1 in the Newtonian regime of the flow curve. We define theelastic shear modulus, G0, as the value when G′(t) approacheslogarithmic behavior during aging.33 This is illustrated in Figure3, where we further define the structural relaxation time, ts,when G′(ts) = G0. We like to note that other methods also existto determine the structural relaxation time.34−36 The ratio ofthe both time scales gives a dimensionless number, D = η∞/(G0ts), that indicates nonthixotropic materials for D close tounity, and thixotropic materials for D ≪ 1.37 Typical structuralrelaxation times, ts, of our samples are ts < 300 s. Then, D <10−4 and we deal with thixotropic materials. Hence, we have tovalidate that a steady-state is reached and we choose a waitingtime per measurement point, twp = 300 s, so that twp > ts at eachimposed strain rate.38−41
To further investigate the rheological properties, we fix thepolyelectrolyte conformation and the particle volume fractionand vary the ionic strength of the background fluid. ComparingFigure 4, part (a) with part (b), exemplarily demonstrates thatthe ionic strength greatly affects the dynamic yield stress.Values of σy drop by more than one order in response to areduction of the ionic strength from I = 5 × 10−1 mol/L KCl toI = 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 comparethese data with respect to the polyelectrolyte conformation, wescale the measured shear stress and the applied strain rate,respectively, by the scaling factors a and b .Curves of different ϕ and I collapse onto a single master
curve for each polyelectrolyte conformation. This is visualizedby Figure 5(a) for the limiting cases flat and brushy, with the
PEMs assembled at c = 10−2 and c = 1 mol/L KCl, respectively.This scaling demonstrates that the modification by brushy PEMfilms significantly enhances the dynamic yield stress by morethan one order in magnitude.To comprehend the meaning of the scaling, the horizontal
scaling factor b is normalized by the high shear viscosity, η∞, toaccount for the particle loading. The factors a and b/η∞ areplotted in Figure 5(b). Because a and b/η∞ are linearly related,
Figure 4. Representative flow curves for increasing volume fractionfrom ϕ ≈ 0.20 over ϕ ≈ 0.40 to ϕ ≈ 0.50 at fixed polyelectrolyteconformation and ionic strength. The plotted data contrast the effectof (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.
Figure 5. Using the polyelectrolyte conformation of the PEM’s to tunethe dynamic yield stress. (a) Typical curves of normalized shear stress,σa , as function of normalized strain rate, γ b. The closed symbolsdenote different volume fractions, ϕ, while the open symbols denotedifferent ionic strength, I, of the background fluid. The upper mastercurve (triangles) is for brushy PEMs, assembled at salt concentrationsof c = 1 mol/L KCl, the lower master curve (squares) for flat PEMs,assembled at c = 10−2 mol/L KCl. For each polyelectrolyteconformation, the dynamic yield stress value at ϕ = 0.60 sets thereference for the scaling. The corresponding scaling factors are plottedin (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 lesssensitive to I. Hence, low values of the dynamic yield stress can beachived either by flat PEMs (□, ■) or by brushy PEMs which weredispersed in a low I background fluid (Δ).
the scaling represents a shift along the viscosity of thebackground fluid.42
Interestingly, the scaling factors in Figure 5(b) expand overtwo decades for brushy PEM films (triangles), whereas for flatPEM films (squares) they accumulate in a half decade. Thismuch narrower distribution implies that the modification by flatPEM films is less sensitive to the ionic strength of thebackground 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 lowstrain rates. Similar behavior is observed for other soft colloids,like colloidal star polymers, and related to shear band-ing.26,40,43,44
The flow curves in Figure 4, together with the master curvesin Figure 5, suggest that the fluid changes to a jammed solid,either if the volume fraction or the interparticle interactionexceeds 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 thejamming phase boundary, described by σy = σϕ(ϕ − ϕc)
ν,where σϕ sets the stress scale of the yield stress, and ν is anexponent which is related to the microstructure of the sample.45
We focus on high volume fractions, and thus this equationsimplifies to the following:46,47
σ σ ϕ= ϕv
y (3)
As an example, Figure 6(a) shows the dynamic yield stress asa function of the volume fraction for brushy, PE’s adsorbed at c= 1 mol/L KCl, colloids.
The plotted solid lines denote fits of eq 3 to the dynamicyield 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, thedynamic yield stress increases proportional to a constant powerof the volume fraction, σy ∝ ϕν, with ν = 3. This value isreasonable, since values of ν between 1.4 and 5.5 are typicallyobserved in suspensions of weakly attractive particles that formscale invariant particulate networks.46,48,49 Moreover, Figure
6(a) nicely visualizes the rise of the dynamic yield stress withincreasing 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 varythe brushiness, and thus the roughness of the PEM film,5 andplot in Figure 6(b) representative σy values at fixed ionicstrength, I = 10−1 mol/L KCl. Remarkably, values of thedynamic yield stress increase with increasing volume fractionaccording to σy ∝ ϕ3. Furthermore, the dynamic yield stressincreases with increasing salt concentration, c, of the depositionsolution.Surprisingly, at low, I = 10−3 mol/L KCl, and high, I = 5 ×
10−1 mol/L KCl, ionic strength of the background fluid, thebrushiness plays a minor role and values of σϕ(c) of thedifferent polyelectrolyte conformations are approximatelyequal.The results from Figure 6, parts (a) and (b), clearly show
that different routes exist to tune the yield stress of PEM-modified suspensions. Low yield stress values can be achievedby the following: (i) flat PEMs, assembled from polyelectrolyteswhich were adsorbed at low salt concentrations c or (ii) bybrushy PEMs, with polyelectrolytes adsorbed at high c, whichwere dispersed in a low ionic strength background fluid. About2 decades higher yield stress values can be tailored by brushyPEMs in high ionic strength background fluids, as seen byFigure 6(a). It turns out from Figure 5(b), that flat PEMs areless sensitive to the ionic strength of the background fluid thanbrushy PEM’s.First, we will discuss the effect of I on σϕ. Generally, the
interactions between polyelectrolyte multilayers are a super-position 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 probe-
force measurements (CP-AFM), the dominating interactionsbetween PEMs assembled at high, c ≥ 0.5 mol/L, monovalentsalt concentration, were recently investigated.50−52 In theseexperiments, the polyelectrolyte conformation was fixed andthe ionic strength of the background fluid was varied. Theexperiments reveal the dominance of steric over electrostaticinteractions above ionic strength of the background fluid of I ≈10−3 mol/L. Please note that our experiments were conductedat similar ionic strength I ≥ 10−3 mol/L. The steric interactionsoriginate from tails and loops of the terminating polyelectrolytethat expand from the PEM surface into the surroundingsolution. Thus, we can think of a hairy corona around the PEMcoated colloids. Recent experiments performed with thesupport of the osmotic stress technique arrived at the samesolid core-PEM shell-hairy corona picture.53
In a first approximation, we hypothesize that the hairy coronabehaves similarly to PSS monolayers,54,55 which shrink withdecreasing 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 withincreasing ionic strength I. Hence, we anticipate that the tailsand loops of the hairy corona were most extended at low I.Then, the expanding polyelectrolyte chains experience electro-static self-repulsion, which tends to stretch the polyelectrolytechains and is balanced by their elasticity. Increasing I leads toan imbalance which results in chain softening and lastly in acollapse of the hairy corona. We speculate that thereby theeffective interparticle attraction increases.
Figure 6. Alternative routes to tune the dynamic yield stress: (a) Finetuning by the ionic strength I of the background fluid for brushy PEMsand (b) tailoring the dynamic yield stress by the polyelectrolyteconformation during multilayer assembly. Low yield stresses can beachieved either by brushy samples dispersed in a low ionic strengthbackground fluid (▼) or by flat PEMs (▲). In (a), the brushypolyelectrolyte multilayers were assembled at c = 1 KCl. The dynamicyield stress increases with increasing I. Values of the ionic strengthduring 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 experimentsshown in (b) are performed at I = 10−1 mol/L KCl. The dynamic yieldstress 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 datawith the slope 3.
The interactions of PSS monolayers are strongly correlatedto the thickness, L, of the highly coiled polyelectrolytes. Thisthickness is proportional to the decay length of the stericrepulsion,56 and hence, for the PSS terminated multilayers weexpect the effective attraction U ∝ L−1. This is reasonable sincein Figure 5(b), the scaling factors for the flat PEMs, assembledat c = 10−2 mol/L, lie closer together as the scaling factors forthe 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, inthe case of PSS monolayers, s2 is related to the chain length ofpolyelectrolytes.14,56 For the PSS terminated multilayers, wepragmatically use s as a dimensionless scaling factor. Using eq 3together with the scaling,49
σ ϕ∝νU
ay 2 (4)
recently proposed for weakly attractive particles with ν close to3, 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,
samples up to I = 10−1 mol/L KCl follow this scaling andcollapse 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 nonspecificinteractions, 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 adsorbedpolyelectrolytes. This ordering corresponds to increasingPEM film roughness,5 as visualized by Figure 1. The increasingPEM film roughness leads to rising attractive interparticleinteractions,51 which is in good accord with our observedincreasing values of s, and hence σϕ. Our findings are also ingood qualitative agreement with colloidal probe force measure-ments14 as well as yield stress measurements59,60 on brushy, orrough, polyelectrolyte monolayers.
■ CONCLUSIONSUsing strong polyelectrolytes, we demonstrate that control overthe polyelectrolyte conformation of PEM films serves as aversatile tuning parameter for the dynamic yield stress ofcolloidal suspensions. Using this tuning parameter opens up thepossibility to tailor the dynamic yield stress.In particular, low dynamic yield stress values can be achieved
by adsorbing the polyelectrolytes in a flat conformation, wherethe ionic strength of the background fluid has less impact onthe yield stress. As an alternative route, low yield stress valuescan also be produced by adsorbing the polyelectrolytes in abrushy conformation and dispersing them in a low ionicstrength background fluid. In contrast, to achieve high yieldstress values, the polyelectrolytes have to be adsorbed in abrushy conformation and dispersed in a high ionic strengthbackground fluid. Hence, for brushy polyelectrolyte multilayers,a fine-tuning over 2 decades of the dynamic yield stress ispossible 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 resultsshow that well-defined, homogeneous polyelectrolyte multi-layers are a promising method for the design of colloidalsuspensions.
■ ACKNOWLEDGMENTSThe authors thank the reviewers for their instructive comments,and gratefully acknowledge the financial support of the GermanResearch Foundation (FG 608 “Nonlinear Dynamics inComplex Media”). We thank Andreas Fery for inspiringdiscussions. Many thanks to Melanie Poehlmann, whoperformed parts of the AFM measurements.
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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 obtainedfor increasing brushiness, or roughness, from triangles (PEMsassembled at c = 10−2 mol/L KCl) over squares (PEMs assembledat c = 5 × 10−1 mol/L KCl) to circles (PEMs assembled at c = 1 mol/LKCl), respectively with the scaling factors s = 0.01, 0.04, and 0.1. Foreach polyelectrolyte conformation, the variation of the different ionicstrength of the background fluid I during measurement is visualized bythe 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). Pleasenote that data for I = 5 × 10−1 mol/L KCl are not shifted.
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