Polymer-Mediated Clustering of Charged Anisotropic ColloidsAnand K. Atmuri† and Surita R. Bhatia*,†,‡,§

†Department of Chemical Engineering, University of Massachusetts Amherst, Amherst, Massachusetts 01003, United States‡Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, United States§Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11793, United States

ABSTRACT: Formation of stable, dense nanoparticle clusters isinteresting due to both the underlying physics and use ofnanoclusters in applications such as digital printing, imaging andbiosensing, and energy storage. Here, we explore formation ofnanoparticle clusters in dispersions of the model disk-shaped colloidLaponite. Under basic conditions, the model disk-shaped colloidLaponite forms a repulsive glass in water due to strong electrostaticinteractions. Addition of a nonadsorbing polymer, the sodium salt ofpoly(acrylic acid) (PAA), induces a depletion attraction betweenparticles. Through dynamic light scattering (DLS) and rheology, wesee that the polymer initially causes a transition from the glassy phaseto an ergodic fluid. Samples at higher particle concentration age to a weak nonergodic state, while samples at lower Laponiteremain as fluids. As the strength of attraction between particles is increased, we find an increase in the fast relaxation timemeasured via dynamic light scattering (e.g., slowing of the short-time diffusion of a single particle). While this may in part beattributed to an increase in the ionic strength, the aging behavior and glass-fluid transition we observe appear to be unique to thepresence of polymer, suggesting that depletion plays an important role. DLS data on the fluid samples were consistent with twowidely spaced diffusive relaxation modes, corresponding to motion of single particles and motion of large clusters, although otherslow dynamic processes may be present. On the basis of the estimated volume fraction and depletion attraction, we believe theLaponite-PAA suspensions to be either fluids of stable clusters or glasses of clusters, although it is possible that the nonergodicstate we observe is instead a gel of clusters. Additionally, the cluster size was found to be stable for at least 120 days and wasdirectly related to the polymer concentration. This may serve as an important means of tuning cluster size in products andprocesses based on dense nanoparticle assemblies.

■ INTRODUCTION

The existence of dense colloidal aggregates that are stable insize has garnered significant interest. From a fundamental pointof view, the specific shape and type of interparticle potentialsthat lead to phases of stable clusters, rather than the morewidely seen fractal aggregates or phase separation, remains anactive area.1−3 There are also current and emerging applicationsthat rely on controlled aggregation of nanoparticles into stabledense clusters, including assemblies for digital printing,4

biosensors and cellular imaging,5,6 drug delivery,7 and energystorage.8 For these applications, it is important to understandthe physical parameters that can be used to control cluster sizeand morphology.Although clustering has been seen in purely repulsive

systems,9,10 the literature on attractive colloids is more relevantto the systems that we study. There have been a number ofstudies devoted to hard-sphere colloids with nonadsorbingpolymers, which have a short-range attraction. At low colloidvolume fractions, experiments2,11 and numerical simulations12

show gelation that occurs with a spinodal decompositionprocess. However, a recent study shows that for volumefractions above 0.2, gelation occurs without competition formacroscopic phase separation.13,14 In the intermediate volumefraction range, depletion suspensions exhibit interesting

structure15−17 and mechanical properties18 that can beattributed to formation of a transient network of clusters. Alocal “frozen” cage structure is observed, and large fluctuationsemerge at small wave vectors due to heterogeneities or clusters.At higher volume fractions, two different types of glassyarrested states can be present.19−21 In a recent study, Zukoskiand co-workers observed transitions from different arrestedstates (glass to fluid to gel) by changing the interactionpotential from repulsive, to near hard, to attractive in sphericaland anisotropic particle suspensions where particles interactonly by van der Waals forces and a soft electrostaticrepulsion.22,23

A different scenario is seen in particles with short-rangeattraction complimented by long-range repulsion. In this case,competition between aggregation from the attractive portion ofthe potential and the stabilizing role of repulsion has beenobserved. When the repulsion is short-range (<0.5σ, where σhardcore diameter of the particle), it was observed inexperiments24 and simulations25,26 that elongated clusters ofparticles would form at low enough temperature. However, at a

Received: October 12, 2012Revised: February 12, 2013Published: February 18, 2013

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larger volume fraction (but less than 0.2), clusters are found tomerge into a percolating network. When the range of repulsionis appreciably long (>σ), simulations3,27 show formation ofboth Wigner fluids of clusters would form and a glass transitiondriven by the repulsive interaction.In all the cases studied above, particles are spherical and the

polymer is uncharged. Here we report clustering, dynamics, andrheology in a model disk-shaped colloid with a chargednonadsorbing polymer. The colloid we use is Laponite, a disk-shaped particle with a diameter of 30 and 1 nm thick. TheLaponite crystal is composed of 1500 unit cells28 with theempirical formula Na+0.7[(Si8Mg5.5Li0.3)O22(OH)4]

−0.7. Manystudies suggest that Laponite disks have a slight positive chargealong the rim and slowly dissociate when pH is less than 9,while the pH > 9, the disk has a uniform negative charge.29

These conditions correspond to repulsive electrostatic inter-particle interactions.30 In aqueous dispersions at pH > 9,Laponite forms a disordered gel-like solid. Evidence fromscattering (small-angle X-ray scattering (SAXS), small-angleneutron scattering (SANS), and light) confirms that this phaseis a repulsive colloidal glass.31,32 However, a recent analysissuggests there may be some positive charge on the edge even athigher pH, with roughly 10% of the edge groups beingpositively charged and slightly decreasing with increasing pHfor pH < 11.33 As the surface charge is pH dependent, there hasbeen much debate on whether the structural arrest arises due tothe repulsions from overlapping of double layers or fromaggregation due to attractive interactions between the edgesand faces.31 However, several studies from the literature nowgenerally agree that, with no added salt, Laponite at basic pHforms a repulsive glass.33

The interactions between Laponite particles can be tunedwith the addition of salt or polymer. Ruzicka et al. have done akinetic study on the aging dynamics on Laponite at differentparticle concentrations34 with added salt35 and have observeddifferent routes for structural arrest. At low concentrations ofcolloids and high salt concentrations, suspensions form a geldriven by attractions, whereas at higher colloid concentrationand low salt concentration, the structural arrest is driven byrepulsive interactions and a glassy phase is observed. Mongodryet al.36 observed slowing down of the formation of Laponitegels with salt in the presence of pyrophosphate andpoly(ethylene oxide) (PEO). In the former case the rim chargeis screened by adsorption of four valence ions, which increasesthe activation energy for binding, whereas steric hindrance ofchains adsorbed onto the Laponite particles slows downaggregation in the latter case. Similarly, Zulian et al.37 havedone a kinetic study on the aging dynamics of the repulsiveLaponite glass with addition of PEO and observed a slowing ofthe aging dynamics upon addition of polymer. Labanda andLlorens38 developed a phase diagram for a system of Laponite-sodium polyacrylate at different ionic strengths, and in thepresence of salt they also observed a variation of viscoelasticproperties of the suspension with different molecular weights39

and concentrations40 because of the change in the electrostaticinteraction between the particles.41

In our previous studies of Laponite with an adsorbingpolymer, PEO, we have explored long-term aging dynamics byvarying the length42 and concentration43 of polymer chains andhave observed a type of re-entrant behavior, where elasticity islost or decreased upon addition of polymer. However, thepresence of bridging chains complicates analysis of thesesystems. In this report we present a dynamic light scattering

(DLS) and rheology study of the aging dynamics of discoticclay particles with a low molecular weight nonadsorbingpolymer, the sodium salt of poly(acrylic acid) (PAA). Weconsider this polymer to be nonadsorbing, as the surface ofLaponite is dominated by negative charges at the conditions ofthis study (pH = 10),33 and the polymer is anionic and nearlyfully charged at this pH. Because addition of PAA results in anincrease in the ionic strength of the solution, the effects of PAAaddition on the interparticle interactions are complex.However, comparison of our data with previous studies onLaponite dispersions with added salt35,44,45 suggest that theresults we observe are primarily due to a depletion attractioncaused by the polymer and are not the result of electrostaticscreening. Some of the behavior we observe appears to beanalogous to phenomena seen in glasses of spherical colloidswith short-range attractions caused by nonadsorbing poly-mer.46,47

■ MATERIALS AND METHODSLaponite RD was obtained from Southern Clay Products (Gonzales,TX). Single platelets of Laponite have a diameter of approximately 30nm and are 1 nm thick. The sodium salt of PAA with a molecularweight of 5.1 kg/mol was purchased from Sigma-Aldrich. Sampleswere prepared by first adding the clay to nanopure water adjusted to apH of 10 by the addition of NaOH. A T25 Basic UltraTurraxhomogenizer was used for about 1 min to fully disperse the clay andbreak up any large aggregates. Suspensions were then stirred for 20min using a magnetic stirrer and filtered using a 0.45 μm filter. PAAwas then added to obtain the desired polymer concentration, cp, andsamples were again stirred for 1−2 min to dissolve the polymer.Samples were prepared at two concentrations of Laponite (2 wt % and3 wt %) and cp varying from 0 to 0.75 wt %. Addition of PAA results inan increase in the ionic strength of the solutions; the concentrationswe have chosen lead to samples with an ionic strength of 0.1 mM−1.5mM. We consider an aging time t = 0 to be the time after the polymeris completely dissolved and stirring has been stopped.

Table 1 shows some parameters important for our datainterpretation for these experimental conditions, including the effective

volume fraction of particles, accounting for the electrical double layer;the polymer concentration scaled by c*; and an effective strength ofdepletion attraction arising from the polymer chains, calculated fromthe Asakura−Oosawa (AO) potential. Neat Laponite at a concen-tration of 2 wt % at pH = 10 forms a repulsive glass,31,32 with a higheffective volume fraction due to electrostatic repulsions. With thechange in ionic strength resulting from added PAA, the effectivevolume fraction is lower; nevertheless, at both 2 wt % and 3 wt %Laponite, the samples are fairly crowded. Addition of PAA is expectedto induce a weak depletion attraction (<1 kT). All polymerconcentrations are in the dilute regime.

Dynamic light scattering (DLS) was performed to obtain thenormalized auto correlation function g2(τ). A 200-mW Innova Ar-ionlaser of wavelength of 488 nm with a Brookhaven Instruments BI-9000AT correlator was used. Data was taken at an incident angle of90° and sampled for 1 min with delay times of 0.1−107 μs. All samples

Table 1. Estimated Effective Volume Fraction, c/c*, andStrength of Depletion Attraction for Samples under Study

Laponite cp, wt % Φeff c/c* −U/kT

2 wt % 0.25 0.26 0.06 0.150.50 0.26 0.11 0.300.75 0.26 0.17 0.46

3 wt % 0.25 0.39 0.06 0.210.50 0.39 0.11 0.420.75 0.39 0.17 0.63

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were given a slight rotation after each run to obtain data at 20−50different positions for each sample. The average of the ensemble isreported.48 For such measurements on nonergodic systems, thenumber of positions that need to be sampled to get an accurate valueof g2(τ) is system-dependent, with some systems requiring as few as 10positions sampled49 and others requiring several hundred. Exper-imentally, we found 20−50 sample positions sufficient to yield anensemble average that did not appreciably change with additionalmeasurements. Following Bonn and co-workers,42,50 we can define theergodic break point as the aging time when the time-averagecorrelation function is no longer equal to the ensemble-averagecorrelation function.Oscillatory shear rheological experiments were conducted using a

AR-G2 stress-controlled rheometer from TA Instruments. Dynamicstress sweeps were performed at 1 Hz to determine the linearviscoelastic region (LVE), and then a frequency sweep was performedwithin the bounds of LVE.

■ RESULTS AND DISCUSSIONFigure 1 shows the ensemble-averaged normalized autocorre-lation function, g2(τ), measured at an angle of 90° (q = 0.024

205 nm−1), for a fixed Laponite concentration of 3 wt % andvarying cp, after 1 day and 30 days of aging. For clarity, everytenth data point in each series is plotted. After 1 day, the neatLaponite dispersion shows dynamics of an arrested state. Thesystem shows nonergodic behavior (data not shown), and g2(τ)plateaus to a value of approximately 0.4 at long delay times.The plateau value can be interpreted as the fraction of frozen-indensity fluctuations in a glass, in other words, it is theprobability that caged particles in an arrested state can straddlearound their metastable equilibrium positions.19 Addition ofpolymer dramatically changes the state of the suspension. At t =1 day, all samples with polymer behave as ergodic fluids, andg2(τ) decays to zero (Figure 1a). The dynamics are dependentupon the concentration of polymer in the system. As thesamples age, g2(τ) at long delay times becomes nonzero andsamples become nonergodic, suggesting that for a Laponiteconcentration of 3 wt %, even samples with polymer age to a

structurally arrested state over sufficiently long times (Figure1b). The time scale for reaching an arrested state is 7−30 daysand depends on polymer concentration; the time to reach theergodic break point is shown quantitatively in Figure 4 and isdiscussed further below. Note that the sample at cp = 0.25 isonly very weakly nonergodic at 30 days; the value of g2(τ) atlong decay times is small but nonzero, and the DLSmeasurements are dependent upon sample position. Recallthat, for the nonergodic samples, these data are ensemble-averages of measurements taken at 20−50 points in the sample,thus the relative error bars on individual data points are small.We consider this sample to be very close to the liquid-glass orliquid-gel transition. This is supported by the rheology for thissample, discussed below, where G′ ∼ G′′ over the measurablefrequency range. This is characteristic of a sample very close tothe liquid-gel or liquid-glass transition.Figure 2 shows g2(τ) for samples at 2 wt % Laponite and

varying cp after 1 day and 30 days of aging. Samples with

polymer are still fluids with ergodic behavior, whereas the neatLaponite suspension at this concentration initially an ergodicfluid transforms to a soft elastic solid. Thus, for the same cp,samples at high Laponite concentration eventually age to anonergodic state, while those at a lower concentration remainliquids over the time period we have studied.The melting of the Laponite glass and delay in formation of

the arrested state upon addition of PAA is similar to behaviorobserved in repulsive glasses of hard-sphere colloids,19 whereaddition of small amounts of nonadsorbing polymer induces aweak depletion attraction that speeds dynamics and melts theglass into a liquid state. As noted above, addition of PAA alsoincreases the ionic strength of the solution, so PAA modifiesthe interparticle interactions in a complex manner. The freePAA chains will increase the attraction between Laponiteparticles due to depletion effects, with a weak attractionestimated to be <1 kT (Table 1). The increase in ionic strengthwill also cause an effective increase in the interparticle

Figure 1. Normalized autocorrelation function measured at an angle of90° (q = 0.024 205 nm−1) for 3 wt % Laponite and differentconcentrations of polymer, cp, after (a) 1 day and (b) 30 days of aging.For clarity, every 10th data point is shown in each series. The lines forthe data series with polymer are fits to eq 1.

Figure 2. Normalized autocorrelation function measured at an angle of90° (q = 0.024 205 nm−1) for 2 wt % Laponite and differentconcentrations of polymer, cp, after (a) 1 day and (b) 30 days of aging.For clarity, every 10th data point is shown in each series. The lines forthe data series with polymer are fits to eq 1.

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attraction, as the additional counterions present will partiallyscreen electrostatic repulsion between Laponite particles.However, contrasting the behavior we observe with that seenin Laponite dispersions with added salt highlights somedifferences in the system physics. The phase behavior ofLaponite with added salt has been explored by manygroups33,35,44,51,52 Although there have been some differencesin the detailed phase diagrams reported, it is important to notethat none of them show a transition from an arrested state to aliquid state as the salt concentration is increased. Rather, moststudies show transitions between two types of arrested states(e.g., a transition from a repulsive glass/Wigner glass to eitheran attractive glass or a gel as ionic strength increases).33 Theionic strengths explored in these studies have been in the rangeof 0.1−10 mM, comparable to or higher than the ionic strengththat we estimate in our Laponite-PAA dispersions. Additionally,while added salt acts to speed the aging from an ergodic to anonergodic state as compared to Laponite dispersions with noadded salt,44,45 for our systems the addition of polymer slowsthe aging process as compared to neat Laponite.To develop a physical interpretation of our DLS data, we

must understand the nature of the multiple dynamic processesthat are present. For the 2 wt % series of samples, which remainergodic fluids over long periods of time, we performed DLS atdifferent angles after a set period of aging. To simplify theinterpretation, we analyzed the data as having two distinctrelaxation processes, a fast and slow mode. Figure 3 shows a

representative set of data for the decay rate, Λ, obtained usingthe NNLS algorithm for the fast and slow mode, as a functionof the scattering vector q, for 2 wt % Laponite with 0.25 wt %polymer after aging for 300 days. (Note that the decay rate istypically given the symbol “Γ” in light scattering literature; herewe use the symbol Λ to avoid confusion with the mathematicalgamma function used in eq 2, below). Figure 3 shows that Λvaries linearly with q2, indicating that both relaxation processesare diffusive in nature. We surmise that the fast mode describesthe motion of single particles of Laponite, whereas the slowmode describes movement of larger clusters of particles. As acheck on this intrepretation, we can estimate a particle andcluster size by extrapolating these data to q = 0 and using theStokes−Einstein relation and assuming isotropic entitites. Forthe fast mode, this yields an effective size of 21.8 nm, which isslightly larger than we might expect for the Laponite particlesbut in the correct range. A similar analysis gives a cluster size of145.5 nm, which as discussed further below is in goodagreement with our detailed fits of the autocorrelation function.To quantify the dynamics, we fit g2(τ) for the samples

containing polymer to a sum of an exponential decay and astretched exponential decay:42

τ = + − +τ τ ττ− −

β⎡⎣⎢

⎤⎦⎥

( )g A p p C( ) e (1 )e2( / ) ( )

21 2

(1)

where A, p, τ1, τ2, β, and C are fitting parameters. Note that thisdata fitting was only performed for samples containingpolymer; the dynamics of neat Laponite are such that fittingthis type of model over the data range that we have would yieldunphysical results. Lines in Figures 1 and 2 are the fits of thedata to eq 1. The goodness of the fit is evident, although this isperhaps not surprising given the large number of parameters inthe model. However, the interpretation that can be assigned toseveral of the parameter values are physically reasonable,lending credibility to the fit. The parameter τ1 is the firstrelaxation time, representing dynamic processes that occur atshort time scales. For glassy systems, τ1 describes themovement of a particle in a cage of neighbors.37 Thus, ahigher value of τ1 indicates slower movement of individualparticles and can be related to an increase in the depth ofattraction between particles. Dynamic processes that occur on alonger time scale are described by a stretched exponentialfunction, characterized by the parameters τ2 and β. There arevarious ways in which we can interpret this slow relaxationtime. One interpretation is that this corresponds to escape ofparticles from a cage or similarly to disruption of clusters, whichis also known as the α relaxation process. We may also interpretthis time as corresponding to the diffusivity of large entities orclusters. We feel that the latter interpretation is more plausiblein this system. There is some evidence in the literature that theformer process (escape from cages) leads to a nonlineardependence of the decay rate on q2 for glassy systems.47

Additionally, as seen from Figure 3 we have relaxation at twodifferent length scales which are diffusive under the lengthscales probed, suggesting the integrity of the large structuresthat are formed. The mean relaxation time τm associated withthe slow dynamics which can be used to quantify thenonergodicity of the system is calculated as34,45,53

τ τβ β

= Γ⎛⎝⎜

⎞⎠⎟

1 1m 2

(2)

where Γ is the gamma function.Figure 4 shows the first relaxation time, τ1, for various cp at a

fixed Laponite concentration of 3 wt % at different days of

aging. The ergodic break point teb is indicated with a smallvertical line.44 For the samples with polymer, τ1 increasesslightly as the samples age until the ergodic breaking point isreached. After this time, there is no increase in τ1. As cpincreases, particle motion retards gradually, and when anarrested state is reached, the value of τ1 saturates. This is

Figure 3. Λ vs q2 for 2 wt % Laponite and 0.25% polymer after agingfor 300 days. Lines are guides to the eye.

Figure 4. First relaxation time, τ1, as a function of aging time forsuspensions of 3 wt % Laponite at different polymer concentrations.The vertical lines indicate the ergodic break point, as defined by Bonnand co-workers.44,50.

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consistent with aging behavior seen in attractive glasses ofspherical colloids47 and in Laponite suspensions with addedsalt.44 Increasing cp increases the strength of attraction betweenparticles via a depletion mechanism, hindering particle diffusionand leading to a higher value of τ1 (i.e., slower particlediffusion). For the case of 0.25 wt % polymer, the systemreaches a nonergodic state at approximately 30 days, and hencethere is a monotonic increase in this relaxation time until thispoint. Rheology data further confirms below that this phase isarrested after 30 days (a weak “gel” rheologically).The mean relaxation time for this same series of samples,

varying cp at a fixed Laponite concentration of 3 wt %, is shownin Figure 5. We have plotted the mean relaxation time

normalized with the value at tw ∼ 0 (Figure 5a). The meanrelaxation time grows exponentially with time, which is typicallyseen in glassy systems, not in gels.34,44,50 The mean relaxationtime has a low value when the sample is ergodic. As the samplegradually transforms from an ergodic liquid to a nonergodicphase, τm increases by orders of magnitude. The small verticallines in Figure 5b show the ergodic break point teb for thesystems studied. As can be seen from the figure, this point isdependent on the polymer concentration. Samples with ahigher cp need less time to undergo structural arrest. The trendsin this mean relaxation are consistent with the relaxation timeobserved in Laponite with salt.45,53 So, the trends show anexponential behavior with waiting time until the ergodic breakpoint and has a linear behavior thereafter, which is consistentwith what has been observed in other glassy systems.34,44,50

To compare the relaxation processes for different Laponiteconcentrations, we have plotted τ1 and τm as a function of cp forboth Laponite concentrations in Figures 6 and 7. Figure 6shows that the behavior of single particles progressively departsfrom free diffusion as the interparticle attraction in-

creases,16,17,21 as evidenced by an increase in τ1 with cp forboth 2 wt % and 3 wt % Laponite. Interestingly, the magnitudeof τ1 and its dependence on cp are similar for both the 2 wt %and 3 wt % series of samples, even though their overall behaviorand bulk rheology (discussed below) are drastically different.Thus, the local environment seen by a particle in the 2 wt %series is similar to that experienced by a particle in the morecrowded 3 wt % series. This is in sharp contrast to the behaviorof τm, which is 3−4 orders of magnitude slower for the 3 wt %series than for the 2 wt % series (Figure 7).Neat Laponite dispersions at pH = 10 are dominated by

repulsive forces and form a glass at both 2 wt % and 3 wt%.33,35,44,51,52 The addition of nonadsorbing PAA causes aneffective increase in interparticle attractions, likely through botha depletion mechanism and electrostatic screening. Thesuspension transforms from a state in which a single plateletof Laponite acts as a single entity in the nonergodic state(repulsive glass) to a state in which the clusters of particlesformed with the addition of polymer acts as the basic entity.For the samples with polymer, τ1 is weakly dependent on the

Laponite concentration and is mainly determined by theamount of polymer. Thus, the strength of the attractionbetween particles and the structure of particle clusters is similarfor both the 2 wt % and 3 wt % series. The mean relaxationtime represents the cluster−cluster dynamics, and the presenceof neighboring clusters affects these dynamics. It is very clearfrom Figure 7 that this slow relaxation process is orders ofmagnitude higher for the 3 wt % Laponite samples. In the 3 wt% series of samples, movement of clusters is hindered, and thesuspensions undergo structural arrest. Table 2 gives theparameters obtained by fitting the DLS data to eq 1 forsamples after 30 days of aging.From Table 2, it can be seen that for a 2 wt % Laponite

suspension, as polymer concentration is increased, the value ofp decreases from 0.42 to 0.25. This indicates that there is agreater weight on the portion of g2 arising from clusters asopposed to single particles, which makes sense as cp increases.On the other hand, for the 3 wt % series, p is lower and remainsat a constant value of 0.22 with polymer concentration,

Figure 5. (a) Mean relaxation time normalized by the initial meanrelaxation time versus time normalized on the time to reach theergodic break point. (b) Mean relaxation time as a function of agingtime for suspensions of 3 wt % Laponite at different polymerconcentrations. The vertical lines indicate the ergodic break point, asdefined by Bonn and co-workers.36,42.

Figure 6. First relaxation time, τ1, as a function of polymerconcentration for different Laponite concentrations for samples aged30 days.

Figure 7. Mean relaxation time as a function of polymer concentrationfor different Laponite concentrations for samples aged 30 days.

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signifying that the number of particles participating in clustersdoes not change once the arrested state is formed. Theparameter β indicates the distribution of formed clusters. Forboth the 2 wt % and 3 wt % series, the variation in β withpolymer concentration is not significant (e.g., within the errorof the fit parameter). However, the clusters appear to be morepolydisperse for the 2 wt % series.In the 2 wt % series, the samples with PAA remain in the

liquid state for long times, and it appears that the clusters thatare present undergo diffusive motions (Figure 3). We cancalculate an effective size of the cluster from τm using theStokes−Einstein equation. Figure 8a shows τm over time; since

the value of τm is relatively constant, this implies that the clustersize is stable over long periods of time, up to 120 days (Figure8b). From the data in Figure 3, we estimated a cluster size of145.5 nm for 2 wt % Laponite and 0.25 wt % polymer. Thisagrees fairly well with the size of the clusters obtained from thefits of the data to eq 1. This also supports the accuracy, validity,and interpretation of the fits. We attempted to further verify thecluster sizes using cryo-transmission electron microscopy(TEM); however, such experiments are extremely challengingon soft solids that contain a high amount of water, and in spiteof the large literature on Laponite systems, there are very fewthat report TEM data. We have obtained some evidence fromcryo-TEM of clusters with diameters of 300−400 nm. Effortsare underway to refine these images and quantify cluster sizeindependently; these will be reported in an upcomingpublication. Thus, the 2 wt % samples with added PAA areliquids comprised of large, stable clusters that are free to diffusein solution. Again, interestingly, this is different than what isobserved in Laponite dispersions with added salt33,35,44,51,52

even though both salt and nonadsorbing polymer lead to anincrease in the interparticle attractions.We have performed rheological characterization of these

samples to confirm the results from DLS. Figure 9 shows the

variation of elastic and viscous modulus with frequency fordifferent polymer concentrations and different Laponiteconcentrations after 30 days of aging. Note that we haveshifted the data for visual clarity, multiplying the moduli byfactors of 10, 0.01, and 0.1 for the samples with no polymer,0.25 wt % polymer, and 0.50 wt % polymer, respectively. Forthe same polymer concentration, samples at 3 wt % Laponitewith added PAA behave rheologically as gels, while samples at 2wt % Laponite with added PAA behave as viscoelastic liquids.The sample at 3 wt % Laponite, cp = 0.25 appears to be veryclose to the critical point, displaying the behavior G′ ∼ G′′ overthe measurable frequency range. There is a small variation inthe frequency dependence of G′ and G′′, and thus a crossoverpoint can be observed. However, this sample is very close to aliquid-gel point or a glass transition.We can compare relaxation times obtained from rheology

with those obtained via DLS. For the 3 wt % Laponitesuspensions with polymer, the relaxation time obtained fromthe inverse of the crossover frequency of the elastic and viscous

Table 2. Parameters from the Fits of the DLS Data after 30 Days of Aging to Equation 1

Laponite-polymer (wt %) A p C τ1 (μs) τ2 (μs) B

2−0.25 0.990 ± 0.003 0.42 ± 0.04 0.0003 ± 0.0005 128 ± 5 300 ± 20 0.59 ± 0.032−0.5 1.060 ± 0.004 0.29 ± 0.03 0.004 ± 0.003 180 ± 10 810 ± 80 0.64 ± 0.022−0.75 1.010 ± 0.001 0.247 ± 0.005 0.004 ± 0.001 245 ± 5 1590 ± 30 0.642 ± 0.0063−0.25 1.11 ± 0.01 0.217 ± 0.004 0.031 ± 0.001 178 ± 4 3.9 × 104 ± 0.3 × 104 0.200 ± 0.0043−0.5 0.98 ± 0.01 0.217 ± 0.005 0.139 ± 0.002 260 ± 10 4.0 × 104 ± 0.4 × 104 0.194 ± 0.0053−0.75 1.03 ± 0.01 0.215 ± 0.005 0.103 ± 0.003 340 ± 20 9 × 104 ± 1 × 104 0.188 ± 0.006

Figure 8. (a) Mean relaxation time and (b) effective size of clustersderived from the mean relaxation time for 2 wt % Laponite at differentpolymer concentrations as a function of time.

Figure 9. Elastic modulus as a function of frequency for differentpolymer concentrations (shown in the legend) after 30 days of agingfor Laponite concentrations: (a) 3 wt % and (b) 2 wt %. For visualclarity, data have been shifted by factors of 10, 0.01, and 0.1 forsamples with no polymer, 0.25 wt % polymer, and 0.50 wt % polymer,respectively.

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modulus is 0.9, 7.9, and 15.8 s for cp = 0.25, 0.50, and 0.75,respectively. This is consistent with the mean relaxation timeobtained from fitting the DLS data to eq 1. These resultsconfirm the behavior observed in DLS. So, both Laponite andpolymer concentration affect the elasticity of the suspension.After the system reaches the nonergodic state, the elasticmodulus depends strongly on the concentration of polymer,but to reach this state, both Laponite and polymerconcentration play a crucial role.Structurally, are the samples at 3 wt % Laponite with added

polymer a gel of clusters or a glass of clusters? Both rheologyand DLS show evidence of a slow relaxation process. Therheology is reminiscent of what is observed in the transientnetwork, although such profiles have also been predicted forglassy systems depending upon the measurement window. If weconsider the relaxation time measured via rheology to beassociated with formation of a transient network of clusters, wecan estimate the energy of association between two clusters insuch a network, Ea, by the expression τx = τdiff exp(Ea/kT),where τx is the relaxtion time estimated from the crossoverpoint in rheology and τdiff is the diffusion time for a cluster,estimated from the sizes measured on the 2 wt % Laponitesamples (Figure 8). This analysis yields an association energy of8−9 kT. Physically, it is not clear what mechanism would leadto such an association between clusters and hence whatmechanism would drive formation of such a transient network.We still expect an electrostatic repulsion between clusters dueto the charge on the Laponite particles, even though this hasbeen partially screened through counterions associated with theadded PAA. The depletion attraction arising from PAA chains isrelatively weak, < 1 kT (Table 1), much lower than theestimated Ea and more characteristic of a glass than a gel.Finally, the aging behavior of the sample, shown in Figure 5a, ismore consistent with a glass. The mean relaxation time growsexponentially until the ergodic break point, more characteristicof a glass than a gel.34,44,50 Thus, while certain behaviors ofthese systems are characteristic of both gels and glasses, theaging behavior and energetics are more consistent with thephysical picture of a glass.A balance between the short-range attractions induced by the

addition of polymer and long-range electrostatic repulsion playsa crucial role in the dynamics of these complex systems. In thecase of suspensions with 3% Laponite, with the addition ofpolymer, clusters of particles are formed but the movement ofclusters is hindered because of the presence of other clusters. Inother words, we believe our data to be consistent with a glass ofclusters; the clusters themselves are caged by neighbors. Thispicture is further supported by the effective volume fraction andour initial TEM results, although other interpretations of theslow relaxation mode are possible. By contrast, suspensions at 2wt % Laponite with polymer behave as fluids of clusters, withclusters that are stabilized with long-range electrostaticrepulsions up to 120 days.

■ CONCLUSIONIntroduction of a nonadsorbing polymer, PAA, to repulsiveglasses of Laponite changes the structure, dynamics, andrheology. The polymer initially causes a transition from theglassy phase to an ergodic fluid; for samples at 3 wt % Laponitethe fluid eventually ages to a nonergodic state, but samples at 2wt % Laponite remain as fluids. This transition can be seen inboth the DLS and rheology data. We find that the polymerincreases the fast relaxation time, signaling that attractions have

been introduced between particles. While increasing the ionicstrength will also result in an effective increase in interparticleattractions, the aging behavior and glass-fluid transition weobserve have not been seen in previous studies of Laponite withadded salt, suggesting that depletion plays a role in thephenomena we observe. The fast relaxation time is similar forboth concentrations of Laponite we explored, while the slowrelaxation time is orders of magnitude higher for the 3 wt %Laponite samples. In the ergodic samples, both the fast andslow mode were found to be diffusive in nature, suggesting thatthe samples of 2 wt % Laponite with PAA are fluids of stableclusters that are electrostatically stabilized. For 3 wt % Laponitewith PAA, we believe clusters (as opposed to particles) aretrapped within repulsive cages of neighboring clusters and theglass transition of these clusters is responsible for nonergodicbehavior, although it is also possible that a gel of clusters isformed. Our results also show that in the 2 wt % series, thecluster size is stable over long periods of time and theconcentration of PAA can be used to control the cluster size.This may have implications for development of products andprocesses based on dense assemblies of nanoparticles.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: surita.bhatia@stonybrook.edu.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

The authors gratefully acknowledge financial support from anNSF GOALI award (Grant CBET-0853551), the NSF-fundedCenter for Hierarchical Manufacturing (Grant CMMI-1025020), and Xerox Corporation. We appreciate helpfuldiscussions with Prof. Paul Dubin on interpretation of the DLSresults.

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