Poroelastic Consolidation in the Phase Separation of Vesicle-PolymerSuspensions

Ji Yeon Huh,†,‡ Matthew L. Lynch,§ and Eric M. Furst*,†

Department of Chemical Engineering and Center for Molecular and Engineering Thermodynamics, UniVersityof Delaware, Colburn Laboratory, 150 Academy Street, Newark, Delaware 19716, and The Procter andGamble Company, 8256 Union Centre BouleVard, CP-426 West Chester, Ohio 45069

The addition of the polymer poly(diallyl dimethyl ammonium chloride) (polyDADMAC) to multilamellarvesicle dispersions of ditallowethylester dimethyl ammonium chloride (DDAC) causes the vesicle particlesto aggregate and form a space-spanning network. These networks collapse under their own buoyant weight.The time evolution of the vesicle network height is investigated as a function of polymer concentration,vesicle volume fraction, and initial sample height. A poroelastic consolidation model accurately relates thetime scales of the network collapse to the balance of gravitational, viscous, and elastic forces. Network formationis consistent with an arrested spinodal decomposition of the colloid-polymer mixture; however, while suchnetworks usually lead to nonequilibrium gels, the buoyant stresses are sufficient to drive the phase separationof this colloid-polymer mixture to completion.

I. Introduction

When sufficient polymer is added to an otherwise stablecolloidal suspension, the suspension may phase separate or gel.1

For instance, polymer molecules that adsorb to the surface ofparticles can induce bridging flocculation by binding multipleparticles together. Interparticle attractions can be also inducedvia the depletion mechanism, in which nonadsorbing polymerexcluded from between particles pushes them together byosmotic pressure.2,3 The phase separation and gelation inducedby these attractive interactions affect the processing, stability,and final properties of foods, personal care products, agro-chemicals, paints, inks, and numerous other products andmaterials. Therefore, understanding these phenomena is of greatinterest toward the industrial applications of dispersed colloids,emulsions, and proteins.

Fundamentally, the connection between phase separation andgelation phenomena remains enigmatic and therefore also ofsignificant interest. Previous research has explored the relation-ship between gel formation and the underlying phase behaviorof colloidal suspensions.4-7 This large body of work has soughtto understand whether gelation is a consequence of an arrestedphase separation, and if so, the mechanism of the arrest and itsimplications for the microstructure, rheology and, stability ofthe suspension. It is thought, for instance, that as the attractiveglass line crosses the phase diagram binodal for attractivespheres, nonequilibrium states consisting of dynamically arrestedand structurally percolated microstructures form that mechani-cally behave as elastic solids, or gels.8

The mechanical properties and gravitational stability ofcolloidal gels have also been the subject of a number ofexperimental and theoretical studies.9-19 Furthermore, forsuspensions with a density mismatch between the particles andsuspending solvent, gel formation is constrained by gravity andcan be mechanically unstable, leading to collapse.11-17 This

collapse may occur smoothly, at a rate that decreases with time,which is known as a steady or creeping sedimentation. Asattractive interactions between colloidal particles decrease, itcan alternatively occur with an initial slow sedimentation for afinite time, followed by a catastrophic collapse. This delayedsedimentation has been reported for a variety of weaklyaggregated colloidal systems, including poly(methyl methacry-late),8,11 silica,12,13,15 and oil-in-water emulsions,19 but it stillremains poorly understood.

Recently, we reported a transition from phase separation tocreaming of gels for vesicle-polymer mixtures as the polymerconcentration increased.18 Such vesicle dispersions are of interestnot only for their use in consumer products, foods, cosmetics,plastics, paints, medical imaging, and gene therapies20 but alsobecause of the complexity that arises from their polydispersity,softness, and shape compared to model colloidal systems suchas monodisperse hard spheres.21 Surprisingly, at short times,we found that the initial rate of rising (analogous to sedimenta-tion) increases as the polymer concentration increases, leadingto faster consolidation, unlike other colloidal gels. This unex-pected behavior was explained by correlating the porousmicrostructure, characterized by microscopy, with the perme-ability obtained from the initial rising velocity. The porosity,and thus permeability, was found to increase with increasingpolymer concentration.18

In this paper, we characterize this collapse behavior ofvesicle-polymer solutions beyond the initial rising period,which provides a potential to understand and control theconsolidation of these materials in terms of process andformulation variables. Following the details of our experimentalmethods, we present the time evolution of the height of thesuspensions over a range of both vesicle and polymer concen-trations, and initial sample heights. From these results, we extractthe characteristic consolidation time scales of vesicle gels. Wediscuss the effect of network elasticity, permeability, and initialheight on the collapse by comparing with the theory ofporoelastic consolidation. Finally, we conclude with summaryand future direction of this work.

* To whom correspondence should be addressed. E-mail: furst@udel.edu. Tel.: (302) 831-0102. Fax: (302) 831-1048.

† University of Delaware.‡ Current address: Polymers Division, National Institute of Standards

and Technology, 100 Bureau Drive, Gaithersburg, MD 20899-8542.§ The Procter and Gamble Company.

Ind. Eng. Chem. Res. 2011, 50, 78–8478

10.1021/ie1004543 2011 American Chemical SocietyPublished on Web 05/21/2010

II. Experimental Section

A depletion interaction is induced between cationic vesicleswith a nominal mean diameter, 2a ) 256 ( 25 nm by theaddition of cationic poly(diallyl dimethyl ammonium chloride)(polyDADMAC, Aldrich, No. 522376) with MW ) 14.5 kDaand Rg ) 11.2 nm, leading to the size ratio, Rg/a ≈ 0.09.18 Thevesicle dispersion is prepared from an aqueous solution ofdichain cationic surfactant, ditallowethylester dimethyl am-monium chloride (Goldsmith) with standard milling manufactur-ing process. It is a quaternary ammonium compound that hastwo long fatty acid chains with two weak ester linkages. In theabsence of electrolytes, the zeta potential of the vesicledispersion is +49 ( 5 mV. The vesicles are buoyant due to thelower density than the suspending fluid (∆F ≈ 50 kg/m3) andexhibit the polydisperse distribution of diameters between 100nm and 10 µm.18

The stiffness of the vesicles is quantified by calculating theYoung’s modulus E from atomic force microscopy (AFM)measurements. All AFM experiments are carried out with aBioscope II (Veeco, Inc.) on an Axiovert 200 (Zeiss, Inc.) Weuse silicon nitride tips (Veeco Probes, Inc.) with a nominal tipradius of 20 nm on V-shaped 180 µm long silicon nitridecantilever (Veeco Probes, Inc.) with a nominal spring constantof 0.03 N/m. Prior to each measurement, silicon nitride tips arecalibrated using the thermal tuning method. The probe is rampedat a velocity of 4 µm/s, and the measurements are averagedover 50 times. Approximately 10 µL of samples at φ ≈ 10-4

are placed on a glass slide. The Young’s modulus is given byE ) (�π/2)(1 - V2)(S/�A) where V is the Poisson ratio, S isthe contact stiffness, and A is an area function related to theeffective cross-sectional or projected area of the indenter.22,23

In general, the Poisson ratio V ) 0.5 is used.24,25 The contactstiffness is estimated from S ) dP/dh where P is the appliedforce and h is the indentation length. We then calculate theYoung’s modulus as E ) 2.8 ( 1.5 kPa. This reflects thewaxlike structure of the partiles below the Kraft temperature,Tk ≈ 50 °C. As a consequence of the relative insolubility ofthe surfactant and high Kraft temperature, the vesicles do notOstwald ripen, complex with the polymer, coalescence, ordeform significantly in the consolidation experiments.

Vesicle samples are prepared from a stock solution. Thevolume fraction of the stock dispersion is determined to be 0.46by separating a vesicle layer with centrifugation using 40 000rpm for 18 h at 25 °C and adjusting it by a factor of 0.7, thepacking efficiency of polydisperse spheres. This volume fractionis confirmed by weighing vesicle suspensions after drying 24 h.

The polymer overlap concentration is Cp* ≈ 7 wt % based

on the sudden rapid increase in viscosity in a frequency sweeprheology experiment. We find that the overlap concentrationcalculated using the relationship Cp

* ) (3MW/4πRg3NA) ≈ 0.04

wt % significantly underestimates the experimental value.26

For Cp g 0.3 wt %, we observe a highly turbid vesicle-richphase on top and a clear, vesicle-free subphase on the bottom.18

The sample height h(t) is defined as the interface between thesetwo phases, as shown in Figure 1. It is measured as a functionof both vesicle and polymer concentrations. The gel boundarywas previously determined by observing the phase behavior andmeasuring the viscoelastic properties using both bulk andmicrorheology. It corresponds to UAO ≈ 15kBT using the averageof the polydisperse vesicle diameters.1,18 All samples areprepared in a cylindrical glass column with a diameter of 1.8cm. We mix the samples at high speed prior to each measure-ment, to ensure good dispersion.

Rheology experiments are performed using a Couette cell (AR2000 and AR-G2, TA Instruments) to maximize the sample-toolarea contact. Creamed suspensions are carefully removed witha laboratory spatula and placed in the rheometer. An attempt ismade to disturb the sample as little as possible in order to avoidgross changes in the microstructure and rheology. Oscillatoryfrequency sweep measurements are made at constant stressamplitude σ0 ) 0.01 Pa from 0.01 to 10 Hz at 25 °C. The storage(G′) and loss moduli (G) are obtained as a function of frequency.

Confocal microscopy is used to visualize the microstructuredirectly (Nipkow confocal, Yokogawa Electric. Co. Model CSU10). The vesicle dispersions are stained using Nile Red dye(Aldrich, No. N3013). Nile Red dye is dissolved in dimethyl-formamide (DMF) at 0.1 wt %. Approximately, 20 µL of dyesolution is added to 4 mL of the vesicle solution prior to theaddition of the polymer. Images are captured using a 10-bitintensified charge-coupled device (CCD) camera (StanfordPhotonics XR-MEGA/10). We use thin sample cells (height 200µm) and image approximately 100 µm from the sample bottom.Such images are representative of the suspension structure inthe absensce of significant gravitational consolidation.

III. Results

A. Time-Evolution of the Suspension Height. The time-evolution of the suspension sample height h(t), defined in Figure1, over a range of vesicle and polymer concentrations (φ )0.05-0.3 and Cp ) 0.3-2.0 wt %) is shown in Figure 2. Ingeneral, the consolidation of the suspension occurs smoothlyto an equilibrium height and eventually forms a weak gel atthe top of the container. The vesicle network collapses fasteras the polymer concentration increases, as indicated by the arrowin Figure 2, which is opposite to the collapse behavior of gelsreported for model colloidal systems such as monodisperselattices or silica particles.9,11-13,15

B. Equilibrium Height. The initial sample height is h0 ) 4cm for all of the samples shown in Figure 2. However, the finalheight hf, defined as the suspension height as it approaches anequilibrium plateau, is a strong function of polymer concentra-tion, as shown in Figure 3a. The final height increases withincreasing vesicle volume fraction, while it decreases withincreasing polymer concentration, consistent with Figure 2. Thecorresponding final vesicle volume fraction φf, calculated fromφf ) φ(h0/hf) is shown in Figure 3b.

As the initial vesicle volume fraction φ increases, φf alsoincreases and approaches a maximum φf ≈ 0.56. More interest-ingly, φf increases with increasing polymer concentration,resulting in a denser structure. Recently, Gopalakrishnan et al.reported similar behavior for silica-decalin-polystyrene (PS)mixtures.17 They found that φf appears independent of Rg/a andφ, while it weakly depends on the free polymer concentrationCp,free, which is the polymer concentration based on the volume

Figure 1. Sample height h(t) defined as the interface between a turbidvesicle-rich and a clear polymer-rich phase.

Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011 79

in which the polymer coils can freely move.27 Here, we estimateCp,free using the solvent volume fraction in the suspension,(1 - φ). In Figure 3, we also plot φf as a function of Cp,free. Thefinal volume fractions for φ ) 0.15, 0.2, and 0.3 nearly collapseonto a single curve when Cp is replaced by Cp,free, as shown inFigure 3b. Furthermore, the data for φ ) 0.05 is clearly distinctand results in lower density sediments, which suggests adifferent consolidation process related to the microstructure atthis volume fraction.

Using confocal microscopy, the microstructure is imaged asthe vesicle volume fraction increases at Cp ) 2.0 wt %,corresponding to Cp/Cp

* ≈ 0.3. The images in Figure 4a suggesta tenuous microstructure for the vesicle dispersion at φ ) 0.05.In contrast, a thick, bicontinuous interpenetrating network ofvesicles and large voids forms for φ g 0.15 (Figure 4b-d),similar to our previous work.18 In addition, we measured theviscoelastic moduli of the vesicle-rich phases at φ ) 0.3 andCp ) 0.3-2.0 wt % by frequency sweep experiments with σ0

) 0.01 Pa. All samples are mixed and allowed to rest quiescentlyuntil they are in the regime close to the final equilibrium state(φf ) 0.46-0.56), as indicated in a final plateau in Figure 2d.As shown in Figure 5, the storage modulus G′(ω) is greaterthan the loss modulus G(ω) for all polymer concentrations,verifying that a gel network has formed. Furthermore, G′(ω)increases with increasing polymer concentration. A possibleexception is the Cp ) 0.3 wt % sample. In this case, thefrequency dependence of the storage modulus is significantlystronger and may cross through the loss modulus at low

Figure 2. Time-evolution of the height as a function of polymer concentra-tion at φ ) (a) 0.05, (b) 0.15, (c) 0.2, and (d) 0.3 for Cp ) 0.3 wt % (filledtriangles), 0.6 wt % (open triangles), 0.9 wt % (filled squares), 1.2 wt %(open squares), 1.6 wt % (filled circles), and 2.0 wt % (open circles). Thearrow indicates increasing polymer concentration.

Figure 3. Suspension height after 30 days. (a) Final height hf and (b) finalvesicle volume fraction φf as a function of polymer concentration Cp at φ

) 0.05 (diamonds), 0.15 (squares), 0.2 (circles), and 0.3 (triangles). Thepolymer concentration based on free volume Cp,free is also shown as opensymbols for comparison.

Figure 4. Confocal images obtained immediately after samples are preparedat φ ) (a) 0.05, (b) 0.15, (c) 0.2, and (d) 0.3 for Cp ) 2 wt %.

Figure 5. Storage G′(ω) (closed symbols) and loss G(ω) (open symbols)moduli of the final suspension measured at φf ) 0.46 - 0.56 for Cp ) 0.3wt % (double green triangles), 0.6 wt % (blue upward triangles), 0.9 wt %(yellow circles), 1.2 wt % (black downward triangles), 1.6 wt % (reddiamonds), and 2.0 wt % (purple squares).

80 Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011

frequencies. Clearly, this represents the lower concentration limitfor gel-like rheology.

IV. Discussion

A. Theory of Poroelastic Consolidation. Two distinctregimes of initial volume fraction are observed for the consoli-dation data shown in Figure 3. It has been suggested thatsuspensions exhibit percolation only above φ > 0.05, and thus,it is difficult to develop a microstructure capable of resistinggravitational stresses at or below this dilute volume fraction.28

Fractal models of flocculation predict percolation at infinitesimalconcentrations, but these are typically unreachable due to theeffect of gravitational stresses.29 This leads to cluster sedimenta-tion (rising in this study), consistent with the clusters observedby confocal microscopy. At φ g 0.15, a bicontinuous networkforms consisting of a dense, percolated structure of vesiclesinterpenetrated by pores of nearly pure solution. Earlier, wedemonstrated that the compactness of the network and size ofthe pores both increases as the polymer concentration in-creases;18 our rheological measurements further confirm thetransition to a percolated structure occurs. The consolidationof this network structure can be understood in terms of aporoelastic material that consists of a solid matrix permeatedby an interconnected network of pores.30 Colloidal particles arebound together by colloidal forces (here the depletion attractioninduced by the addition of nonadsorbing polymer suspendingfluid), leading to the elastic network and pores filled with theviscous suspending fluid. The suspension settling is caused bya gradual adaptation of colloidal particles to the gravitationalload.

Biot established the general theory of consolidation, whichis valid for an arbitrary load that is variable with time.31 Briefly,the theoretical model considers the compaction of fluid saturatedsolids under the stresses due to the hydrostatic pressure of thewater filling the pores, and the average stress in the networkdue to body forces. Assuming the solid has isotropic mechanicalproperties, stress-strain relations reduce to Hooke’s law foran isotropic elastic body. For a column of completely saturatedsolids supporting a load p0 ) -σz with no lateral expansion,the increment of water pressure is derived in the form of a series

where p0 is the hydrostatic pressure due to the weight of thefluid, a is the final compressibility a ) (1 - 2ν)/(2G(1 - ν))with the shear modulus G and the Poisson ratio ν, and k is thecoefficient of permeability of the colloidal network from Darcy’slaw for the flow in a porous medium. This system is incom-pressible if no water is allowed to permeate out, and thus, thechange of the volume is equal to the volume of water leavingthe elastic structure. The displacement of colloid interface inthe z-direction, w ) h0 - h(t) is given by integrating ∂w/∂z )a(σ - p0), leading to

Equation 2 can be simplified further by assuming that thePoisson ratio is zero V ) 0 and truncating the faster relaxationtime scales13

where the total change in the height is ∆h ) (∆Fgφh02)/2G,

the time scale for collapse is τ ) (2h02η)/(π2Gk), g is the

gravitational acceleration, and η is the fluid viscosity. Ashortcoming of eq 3 is that it cannot capture the changingmicrostructure during consolidation, including changes in thefluid permeability and elastic modulus. Kim and co-workersrecently extended the poroelastic model to account for changesin particle concentration during sedimentation (creaming);19

however, the resulting diffusion-advection problem for ourconditions is stiff, and numerical solutions are difficult to obtain.Nonetheless, as we discuss below, eq 3 provides a reasonabledescription of the experimental data.

We compare the consolidation of depletion-induced vesiclegels due to gravity to Biot’s theory. The collapse of the gelnetwork, w ) h0 - h(t) is obtained from the experimental heightdata shown in Figure 2. We normalize w by the total change inthe height ∆h ) h0 - hf, which is determined from the finalequilibrium height. The normalized displacement profile w/∆his fit using eq 3 with the relaxation time τ as an adjustableparameter, as shown in Figure 6. The theory is in goodagreement with the experimental data for φ ) 0.15-0.3 inFigure 6b-d, whereas it deviates for φ ) 0.05 in Figure 6a.This may reflect the fact that eqs 1-3 apply rigorously for apercolated network, which is only satisfied for φ > 0.05. Figure7 shows τ obtained from Figure 6 as a function of polymerconcentration at all vesicle volume fractions. We find that thehighest and lowest values of the collapse time scale are τ )107 h for φ ) 0.3 and Cp ) 0.3 wt % and τ ) 1.2 h for φ )0.05 and Cp ) 2.0 wt %. Clearly, as the vesicle volume fractionincreases, τ also increases, corresponding to slower compactionof the vesicle gel. This is consistent with the shear and bulkmoduli increasing more sharply with particle volume fractionthan the gravitational load.32,33 However, τ decreases withincreasing polymer concentration. For instance, at φ ) 0.3, ittakes more than 4 days for the vesicle dispersion with Cp ) 0.3wt % to consolidate, while gels with Cp ) 2.0 wt % collapse in20 h.

To validate eq 3 further, we investigate the effect of initialsample height h0 on the consolidation. All samples are preparedin a cylindrical glass column with a diameter of 1.8 cm and h0

is varied from 1.3 to 5.5 cm. We measure the sample heighth(t) at φ ) 0.2 for Cp ) 0.3 and 2.0 wt %. As h0 increases, thevesicle network consolidates more slowly for both polymerconcentrations. The collapse time scale in colloidal gels coulddepend on the initial sample height and the shape of thecontainer based on a stress transmission length scale.11,14 It isdefined as the ratio of the bulk viscosity of the network and thecoefficient of drag due to solvent backflow. In particular, if thesample is sufficiently tall, the network is unable to transmitgravitational stress to the bottom and settles at its terminalvelocity, supported by drag only. We expect that the sampleheights discussed here are shorter than such a characteristiclength scale and therefore that the consoidation becomes afunction of the height. Indeed, in Figure 8, the gel collapse timeis shown to scale as τ ∼ h0

2, which is the scaling behavior fromthe theory.

According to Biot’s theory, both the network elasticity andpermeability govern the suspension consolidation time scale.Note that there is a relatively small increase in the solventviscosity η with increasing polymer concentration, η ) 8-14cP for Cp ) 0.3-2.0 wt %, and consequently, a significantinfluence on the collapse time scale is not expected to arise

σ ) 4π

p0{exp[-( π2h0

)2ka

t]sinπz2h0

+ 13

exp[-( 3π2h0

)2ka

t] ×

sin3πz2h0

+ · · ·} (1)

w ) 8

π2ah0 p0 ∑

0

∞1

(2n + 1)2{1 - exp[-((2n + 1)π2h0

)2ka

t]}(2)

w ) ∆h[1 - exp(- tτ)] (3)

Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011 81

from changes in the fluid viscosity. To test this scenario, firstwe estimate the solvent permeability k, by assuming that thelinear relationship between the porous microstructure andpermeability is valid at long times. Previously, we found a nearlyone-to-one correlation between the number-averaged pore area⟨�⟩n

2, determined by confocal microscopy, and the initialpermeability k0 obtained from the initial rising velocity at shorttimes.18 In addition, we assume that the pore volume ⟨�⟩n

3 isproportional to the sample volume calculated from the heighth(t). This assumption is reasonable when the deformation ofthe vesicles is negligible, as expected based on their Young’smodulus, E ) 2.8 ( 1.5 kPa. The extrapolated permeability atlong times for Cp ) 0.3-2.0 wt % and φf ) 0.46-0.56 is k(φf)) 2-9.4 µm2 as shown in Figure 9a. Finally, in Figure 9b, weplot the collapse time from versus the network elasticity andpermeability. The scaling is in good agreement with the abovetheoretical prediction τ ∼ 1/(G · k) indicated by the solid line inFigure 9b, for all but the lowest polymer concentration (Cp )0.3 wt %). The deviation probably arises from the lower networkelasticity, consistent with the bulk rheology of the creamedsuspension reported in Figure 5.

B. Phase Separation and Gelation. The results of ourstudies of vesicle-polymer solutions are summarized in the statediagram shown in Figure 10. The behavior of the vesicle-poly-mer mixtures divides into two primary regimes: (1) the gradualseparation into distinct phases at low polymer concentration,

Figure 6. Sediment height compared to the poroelastic model, eq 3 withthe consolidation time scale, τ as a fitting parameter: φ ) (a) 0.05, (b)0.15, (c) 0.2, and (d) 0.3 for Cp ) 0.3 wt % (gray filled triangles), 0.6 wt% (red open triangles), 0.9 wt % (blue filled squares), 1.2 wt % (purpleopen squares), 1.6 wt % (blue filled circles), and 2.0 wt % (black opencircles).

Figure 7. Consolidation time scale, τ at φ ) 0.05 (filled triangles), 0.15(open triangles), 0.2 (filled squares), and 0.3 (open squares).

Figure 8. Consolidation time scale τ depenence on the initial suspensionheight h0 for φ ) 0.2; (a) Cp ) 0.3 wt % (triangles) and (b) 2.0 wt %(circles). Lines show least-squares linear fits to the experimental data witha 95% confidence interval.

Figure 9. Final permeability, k(φf), for φf ) 0.46-0.56 and h0 ) 4 cm, (a)extrapolated from the initial values as a function of polymer concentration(Cp ) 0.3-2.0 wt %). (b) The consolidation time scale τ is proportional to1/(G · k).

82 Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011

indicated by the solid triangles, and (2) the formation of “gel”states that consolidate over time (open symbols). As wedemonstrated above, the gel states are further divided into alow and high volume fraction regime, depending on whetherthe particle concentration is sufficiently high to form a percolatedmicrostructure. In the low volume fraction case, more or lessisolated clusters of aggregated vesicle particles form, whicheventually cream (circles), while for higher volume fractions,the bicontinuous structure evolves in a manner consistent withporoelastic consolidation (squares). This general state diagramhighlights several interesting similarities and differences whencompared to the behavior of other colloid-polymer solutionsstudied in the literature.

An important similarity of the current work to previous studiesof phase separation, gelation, and collapse of colloid-polymersolutions is the existence of a bicontinuous phase at sufficientlyhigh polymer concentrations and vesicle volume fractions. Thepercolated structure and dynamic arrest of the vesicle particlessuggest in every way the formation of a gel from the arrestedphase separation of the suspension. In this view, a coarseningsuspension microstructure is initiated by the spinodal decom-position of the colloid-polymer solution.10,34-37 This phaseseparation halts due to a glasslike arrest of the constituentparticles in the developing microstructure combined with thelow interfacial energy driving the coarsening. The poroelasticconsolidation of the suspension is strong evidence that themicrostructure, albeit weak, forms with the mechanical char-acteristics of an elastic solid that are typical of a gel. The keydifference for the vesicle-polymer suspensions is the micro-structure is unable to support the gravitational stresses causedby the buoyancy of the particles, which leads to the consolidationof the structure.

In the absence of the internal stresses due to the vesiclebuoyancy, it is not difficult to imagine that the gel microstructurewould remain arrested indefinitely, in exactly the mannerreported for depletion gels in the literature.38 However, thepresence of the buoyant force allows the phase separation toreach completion. In Figure 10, we plot the final sedimentvolume fraction (crossed squares) as a function of free polymerconcentration. The curve is suggestive of the high volume

fraction branch of a phase envelope, which coexists with a dilutecolloidal gas phase. This hypothetical phase envelope is shownby the solid line a. Althought the position and shape of thisphase envelope is conjecturedsthe phase behavior of highlypolydisperse suspensions are expected to be significantly morecomplex than those composed of monodisperse particles39-42sit provides an intriguing perspective, which we now discuss.

With this phase envelope in mind, that sedimentation behaviorof this study bears a striking resemblence to an example of thecompetition between phase separation (spinodal decomposition)and dynamical arrest recently reported by Cardinaux and co-workers.8 In their study using lysozyme as a model colloid withshort-range attractions, protein solutions exhibited gelation forquenches below a critical temperature within the metastablebinodal, reflecting a local arrest of the protein-rich phase duringspinodal decomposition. Similar to the vesicle gels, this leadsto a percolated, elastic microstructure. The critical temperatureis believed to occur at the point the attractive glass line intersectsthe two-phase region. For quenches below this temperature, theprotein-rich phase reaches the attractive glass line before phaseseparation can complete. Using centrifugation and rheology ofthe gelled solutions, Cardinaux and co-workers traced theattractive glass line through the two-phase region.

In Figure 10, we propose that the current vesicle results canbe explained in a manner analogous to the results of Cardinauxet al. Line b represents the hypothetical attractive glass line,which intersects the two-phase region. For polymer concentra-tions within the two-phase region but below this intersection,the suspension will phase separate normally into vesicle-richand vesicle-lean phases, indicated by line c. This correspondsapproximatley to Cp e 0.3 wt % in our experiments. Belowline c, kinetic arrest of the phase separation occurs, and thesuspensions consequently form gels. Unlike the lysozyme case,these arrested states eventually phase separate by poroelasticconsolidation, as described above. Furthermore, this implies thatthe lower volume fraction limit where we observe sedimentingclusters represents conditions that lie in the nucleation regionof the phase envelope, rather than the spindodal region, denotedby the dashed line d. Such nucleated phases probably miss adynamic percolation threshold in which the kinetically arrestedstructure simply fails to connect.39

V. Conclusions

We presented the buoyant rising of vesicle suspensionsdispersed in nonadsorbing polymer solutions with variouspolymer concentrations, vesicle volume fractions, and the initialsample heights. The suspension consolidates faster as thenetwork elasticity and permeability increase and the initial heightdecreases, which are in good agreement with the theory ofporoelastic consolidation. Our results provide a potential tounderstand and control the consolidation of a weakly aggregatedcolloidal suspensions in terms of process variables captured inthe poroelastic model, which affects the stability of manyindustrial applications. Overall, it appears that the vesicle-poly-mer suspensions phase separate under circumstances thatnormally would lead to arrested gels. While bicontinuousmicrostructures form at sufficiently high polymer and vesicleconcentrations, consistent with spinodal decomposition of themixture, the buoyancy of the vesicles is sufficiently strong todrive the phase separation.

What role, if any, the suspension polydispersity plays in thereported behavior is a significant and open question. Asmentioned earlier, the surfactant vesicles used in this study arepolydisperse in size distribution. Such polydispersity is ubiq-

Figure 10. State diagram summarizing the behavior of vesicle-polymermixtures as a function of volume fraction and free polymer concentration.Suspensions exhibit poroelastic consolidation (open squares), clustersedimentation (open circles), and phase separation (solid triangles). Thefinal sediment volume fraction is given by the crossed squares forsuspensions that exhbit poroelastic consolidation. Overlayed on the statediagram is a hypothetical phase envelope (a). Lines b-d represent theattractive glass line, corresponding boundary between equilibrium andkinetically arrested phases, and spinodal line, respectively.

Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011 83

uitous in many suspensions found in practical applications andcan consist of not only of size, but also their charge, shape,and density. A suspension with significant polydipsersity canseparate into many coexisting phases due to a large number ofdegrees of freedom.39-42 Furthermore, phase separation of apolydisperse colloidal dispersion implies size fractionation,which significantly affects the macroscopic physical behavior.This is an exciting opportunity for future work with potentiallystrong impact for the applications of colloid-polymer solutions.

Acknowledgment

We thank P. Schurtenberger, W. Poon, D. Weitz, A. Fernan-dez-Nieves, and W. Russel for helpful discussions and ElizabethAdams for assistance with atomic force microscopy. Thisresearch was supported by the International Fine ParticlesResearch Institute (IFPRI) and the Procter and Gamble Company.

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ReceiVed for reView March 1, 2010ReVised manuscript receiVed April 30, 2010

Accepted May 3, 2010

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84 Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011