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J. Non-Newtonian Fluid Mech. 87 (1999) 283305

The rheology of aqueous polyurethane dispersions

G.L. Flickinger, I.S. Dairanieh b,, C.F. Zukoski aa Department of Chemical Engineering, University of Illinois, Urbana, IL 61801, USA

b Amoco Chemicals, Naperville, IL 60566-7011, USA

Received 4 April 1999; received in revised form 7 June 1999

Abstract

The rheological properties of aqueous polyurethane dispersions are reported from the dilute regime up to mass

concentrations in excess of 40 wt.%. Particle size decreases and the particles are more resistant to shear induceddeformation with increasing ionic strength and, at very low ionic strength, the reduced viscosity passes through a

minimum with increasing concentration. As the mass fraction of polyurethane increases, the dispersions shear thin.

The zero shear rate viscosity diverges with the development of an apparent yield stress at the highest concentrations

probed. Stress sweep experiments show that deviation from linear viscoelasticity occurs at strains of less than 0.05%

for the moderately concentrated dispersions. The CoxMerz rule is obeyed by these dispersions only at strains in

the linear viscoelastic region and at concentrations below the gel point. As the ionic strength is increased at fixed

particle concentration, viscosities pass through a minimum. These phenomena are discussed in terms of particle

deformability and an interplay of electrostatic and steric repulsive forces. 1999 Elsevier Science B.V. All rights

reserved.

Keywords:Polyurethane

1. Introduction

Driven by environmental regulations, water-borne coatings and adhesives are of steadily growingimportance. Replacement of the organic solvent by water not only protects the environment but alsoleads to reduced product costs. A major class of water-borne polymeric dispersions where flow propertiesare poorly studied are those prepared by polycondensation followed by water dispersion [1]. A primeexample of these materials are aqueous rheological polyurethanes.

The chemical difference between the conventional water insoluble polyurethanes and those dispersiblein water lies in the incorporation of hydrophilic segments in the polyurethane backbone. These built-in

Dedicated to Professor David V. Boger on the occasion of his 60th birthday. Corresponding author.

0377-0257/99/$ see front matter 1999 Elsevier Science B.V. All rights reserved.

PII: S0377-0257(99)00068-3

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284 G.L. Flickinger et al. / J. Non-Newtonian Fluid Mech. 87 (1999) 283305

internal emulsifiers are nonionic, cationic or anionic; examples of such moieties can be found in a reviewpaper by Dieterich [2]. Depending on the chemical structure and the concentration of the monomers,aqueous polyurethane (PU) dispersionscan be tailor made for a variety of applications [2,3]. The influenceof variations in preparation proceduresand/or reactants have been correlatedwiththe performance of thesedispersions in coatings and adhesives [47]. The synthesis process results in the polymers being sphericalparticles of relatively narrow size distribution suspended in an aqueous electrolyte. Upon drying, these

dispersions coalesce to form barrier coatings. Despite the industrial significance of PU dispersions, little isunderstood about their rheological properties [5,6,8,9]. This paper presents the results of a detailed studyof the rheological properties of anionic aqueous PU dispersions and is written in honor of Dave Bogeron the event of his sixtieth birthday. From Dave we have learned much about non-Newtonian mechanicsand the excitement of developing fundamental understanding in pursuit of technological advances.

As a starting point, we anticipate that the particles will have flow properties similar to soft spheres.This assumption is based on morphological studies indicating that aqueous PU dispersions are wellcharacterized as consisting of spherical particles [1]. These particles have a narrow but not monodispersesize distribution and contain internal pockets of water. The base case rheology for these systems is thatof hard spheres where the zero shear rate viscosity (o) data has been correlated over a wide range ofvolume fractions () by

ro = oc=

1 m

2, (1)

wherecis the continuous phase viscosity and mis the volume fraction at close packing [10]. For hardspheres in the low shear limit, m= 0.63. This correlation describes the concentration dependence ofparticles exhibiting soft interactions such as electrostatic or steric repulsions, but the parameterm, mustbe adjusted to account for the effective increase in particle size due to repulsion [11,12].

Asincreases, the viscosity of suspensions of hard and soft particles displays high shear rate and highshear rate limiting plateau viscosities,oand, respectively. This shear thinning behavior is often welldescribed by the Cross equation [13] in terms of critical stress (c):

o =

1

1+ (/c), (2)

or in terms of critical shear rate (c)

o =

1

1+ ( /c), (3)

where and are order one quantities.The rheological properties of a variety of suspensions containing deformable particles have been in-

vestigated where the thickness of the soft or deformable layer increases relative to the size of the particleshard core. Hard particles with thin steric layers are well described by the hard sphere scaling with mbeing adjustable to account for the adsorbed layer thickness [12,1418]. Hard core particles with thicksoft layers, on the other hand, show deviations from hard sphere scalings. In particular, they display amore rapid increase in oas increases. The ability of Eq. (1) to describe the volume fraction dependence

ofoalso breaks down nearmwhere these suspensions exhibit drastically different dynamic propertiesdue to particle interactions [12,19].

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G.L. Flickinger et al. / J. Non-Newtonian Fluid Mech. 87 (1999) 283305 285

The rheology of suspensions containing soft or gel particles is exemplified by crosslinked polymerparticles swollen by good solvent. These suspensions show similar behavior to hard core particles withthick stabilizing layers up to m [2023]. However above m, as the particles remain deformable, thesuspensions respond as if they are a continuous polymer network. As the particle crosslink densityincreases, these suspensions approach the hard sphere limit [21].

In comparing PU dispersion rheology with observations on other systems one of the key issues is the

determination of the sample concentration in terms of volume fraction. This is typically done by assumingthat the reduced viscosity (r) of the system in the dilute limit is described by the Einstein equation:

limeff0

r =

c= 1+ 2.5eff= 1+ []c, (4)

where c is the continuos phase viscosity and effis the effective volume fraction. From Eq. (4), themeasured mass concentration (c) can be linked to volume fraction through

eff=[]

2.5c , (5)

where [] is the intrinsic viscosity. Although this link is established in the dilute regime, the connectionbetween andcis extrapolated into the dense suspension region by assuming that the particles maintainthe same size and shape [18,2429]. The PU dispersions investigated here contain highly charged particles

suggesting that repulsive interactions will be important. In addition, these particles deform under shear. Asthe system ionic strength increases, the particles shrink, become less deformable and ultimately becomeattractive and aggregate. As a consequence, care must be taken in assuming behavior at low c can beextrapolated to highc.

Below in Section 2 we describe our experimental techniques which include static and dynamic lightscattering to determine particle molecular weight and second virial coefficient and size. In addition flowbirefringence is used to establish that the particles deform under flow. In Section 3 we first discussproperties of dilute PU dispersions prior to characterizing dense dispersion properties. In Section 4 wedraw conclusions.

2. Experimental

2.1. Materials

The polyurethane particles studied in this work are commercially available from Zeneca Resins (Wilm-ington, MA) under the trade name Neorez R-9637. This system is an aliphatic polyester resin that iswidely used both as a stand-alone dispersion and in blends with other dispersions. The particles aresynthesized by the prepolymer mixing process and contain in-built carboxyl stabilizing groups which areprovided by dimethylolpropionic acid (DMPA). These particles are highly charged. Based on the chem-ical formula for this system, there should be one carboxylic acid group per 1878 atomic weight units(AMU). A conductometric titration of the actual experimental system suspended in DI water carried outin our laboratory indicated that there is one charged group per every 2573 AMU. The number of chargesper particle can be estimated by converting the moles of carboxylic acid groups per gram of PU with the

molecular weight (obtained from static light scattering). The reaction stoichiometry predicts 676 chargesper particle while we calculate 494 charges per particle from conductometric titration data.

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Dynamic light scattering data analyzed by Contin [30] and the method of cumulants indicates thatthe average particle diameter in a dispersion dialyzed to equilibrium against deionized water is approx-imately 34 nm with a standard deviation of15 nm. Solution density measurements indicate that theparticle density is 1.150.01 g/ml (gram dry polymer per ml occupied in solution). This value is in closeagreement with the value of 1.14 g/ml reported in the technical information bulletin provided with theR-9637 samples. The as-received dispersion is at a pH of 8 and has a solids concentration of 35% by

weight. The dispersion contains the following volatile organic compounds on a weight percent basis:8.4%N-methyl-2-pyrrolidone and 2.0% triethylamine. TheN-methyl-2-pyrrolidone is a high boiling co-alescent solvent used to enhance film formation [3]. The triethylamine is a neutralizing base and a chainextender used in the polyurethane synthesis [31].

The manufacturer suggests that the system stabilization arises solely from the ionized carboxylic groups[1,32]. Polyurethanes stabilized by carboxylic groups display a distinct instability at a pH near the pKaofthe stabilizing acid group. The R-9637 dispersion aggregated at a pH near 5. Increases in ionic strengthto 0.2 M also induced aggregation.

2.2. Sample preparation

Prior to experimental use, the dispersions were thoroughly washed by dialysis to remove the excess

organic solvents and any possible unknown salts. To accomplish this, the dispersions were placed inindividual dialysis membranes and submerged in deionized (DI) water. Due to large osmotic pressuredifferences, the dispersions swell. The dialysis sacks were then submersed in polyethylene glycol (PEG)solution with a higher osmotic pressure and the suspensions were allowed to equilibrate resulting in anincrease in PU concentration. This procedure is repeated in fresh solutions of PEG and DI water until theconductivity of the dialysate held constant at the value measured initially for DI water. The sample is thenreconcentrated using PEG. This concentrated sample is then diluted with DI water to obtain the desiredconcentrations for study. When salt is added to the system, the same procedure as outlined above wasfollowed with the only exception being that the solution outside the membrane was held at the desired saltconcentration. In this case, the concentrated master batch was diluted to the appropriate concentrationusing the matching molarity KCl solution.

The diluted specimens were mixed at high speed for 1 h and then left to sit for 2 days, ensuring a

homogenous concentration. The mass concentration of the samples was determined by the weight lossof drying at 100C. A sample volume fraction could be determined from the measurements of the massconcentration using the measured solution density and the density of the particles as a conversion.

2.3. Particle characterization measurements

Dynamic light scattering experiments were performed using a Spectra-Physics 60 mW HeNe laser ata wavelength of 632.8 nm, a Brookhaven Instruments BI-200SM goniometer, and a photomultiplier tubewith the output signal processed by a BI-9000AT digital correlator. The data were analyzed by Contin andthe method of cumulents to obtain an average particle size and an approximate particle size distribution.

Static light scattering experiments were performed with a DAWN DSP-F laser photometer manufac-tured by Wyatt Technology Corporation. The apparatus is equipped with a vertically polarized, 5 mW,

632.8 nm wavelength laser. The scattered intensity of the incident laser light is measured by an array of18 photodiodes mounted at fixed angles. Toluene was used as the reference for calibration of absolute

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intensities. The data were plotted on a standard Zimm plot in order to determine the particle molecularweight (Mw), radius of gyration (Rg), and second virial coefficient (A2).

Static light scattering experiments were performed on sample concentrations ranging from 2.0 104

to 2.0 105 g/ml. Extremely small PU concentrations were necessary, because sample scattering wasintense. Using a Zimm plot, we extrapolate toc = 0 and apply the fundamental equation for static lightscattering [33]:

KcR

= 1MW

+ 2B2NA

M2Wc, (6)

whereKis the systems optical constant

K =4 2[no(dn/dc)]

2

NA4 . (7)

c is the particle concentration, Ris the Rayleigh ratio, MW is the particle weight average molecularweight,nois the solvent refractive index, dn/dcis the refractive index increment, ois the wavelength ofthe light source in vacuum,is the detector angle, andNA is Avogadros number.

Flow birefringence experiments were performed using a system constructed in the laboratory of A.J.McHugh. A complete description of the optical bench, the experimental procedures and data analysis

procedures used for the birefringence measurements is available elsewhere [34]. A couette flow cell withshear rates in the range of 0.001600 s1 was used to measure the flow birefringence and the orientationangle of several dispersions. The requirement of a clear, transparent sample limited the measurements tothe dilute range.

Solution densities were determined using a Mettler/Kem DA-100 density meter. Particle charge mea-surements were conducted using a standard conductometric titration procedure with 0.024 M HCl as thetitrating acid and 0.02 M NaOH as the titrating base. A YSI model 34 conductance-resistance meter witha standard dip type cell having a constant of 1.0 mho/cm was used to measure solution conductivities.

2.4. Rheological measurements

Dilute rheological data were collected using a standard CannonFenske 50 capillary viscometer. The

viscometer was immersed in an insulated, constant temperature bath at 25C. DI water was used as thereference standard, since it is the continuous phase for the PU dispersion. All samples were temperatureequilibrated to 25C prior to data collection. Capillary viscometry experiments were repeated 34 timesto ensure measurement accuracy.

A constant stress (Bohlin CS-10) and a constant shear rate (Bohlin VOR) rheometers were used toobtain the steady state shear flow and dynamic oscillatory measurements. Both rheometers are equippedwith a temperature control unit capable of maintaining the sample temperature at0.2C of the set point.For the constant stress rheometer, two measuring systems were used to cover the stress range requiredfor obtaining flow curves of the dispersions with various concentrations. A cone and plate (cp 4/20)with 4 angle was used for the concentrated samples whereas a cup and bob (c14) was used for the lessconcentrated specimens.

The samples were loaded in the rheometers using a syringe with no needle (cp 4/20 geometry) or a

pipette (c14 geometry). The samples were covered with a solvent trap to ensure no evaporation took placeand measurements were taken immediately. Even after more than 2 h of measurements, no drying of the

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specimen was observed or detected. The rheological measurements included stress viscometry, stresssweeps and oscillatory shear flow. All rheometer measurements were conducted at 20C.

3. Results and discussion

3.1. Dilute dispersions

3.1.1. Static light scattering experiments

Static light scattering measurements of PU dispersions suspended in deionized water as a functionof concentration yield a particle Mw = 1.270.08 106 g/mol and an average second virial coefficientfor the system of 3.54 0.061015 cm3. For rigid particles, the second virial coefficient can also bederived from statistical mechanics [3536],

B2 = 2

0

x2(eV(x)/kT 1)dx, (8)

wherex is the distance between particle centers, V(x) is an interparticle pair potential, kis Boltzmans con-stant, and Tis the absolute temperature. To estimate the magnitude of the attractions and repulsions giving

riseto B2, the measured value is generally compared to the second virial coefficient for an equivalent hardsphere repulsion BHS2 = 2

3/3 where, is the particle diameter. IfB2/BHS2 >1, the particles have a net

repulsive interaction while ifB2/BHS2

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Fig. 1. Change in specific refractive index increment from flow birefringence measurements with shear rate for the R-9637 PU

dispersion at several concentrations and ionic strengths.

3.1.3. Capillary viscometry

Capillary viscometry experiments were performed on PU dispersions ranging in concentration from0.004 to 0.17 g/ml. The intrinsic viscosity data of PU dispersions at different ionic strengths showsbehavior expected for highly charged polymers [8,3942] or highly charged, rigid, colloidal particles[41,4346] (Fig. 2). At low suspending medium ionic strength, the upturn in red for c < 0.05 g/ml isindicative of double layer expansion and the resulting increase in the effective particle size. The minimuminrednear 0.05 g/ml is associated with increased domination of hydrodynamic interactions.

For background ionic strengths capable of swamping contributions to the ionic strength from thepolyurethane particles, we expect:

red =/c 1

c

= []+ kH[]2c, (9)

where kHis the Huggins coefficient. For flexible polymer chains in a good solvent, kHis between 0.3 to 0.5[42,47,48]. Systems with macromolecular associations display higher values of the Huggins coefficient[42]. For particle systemskH, is a measure of the strength of particle interactions increasing from a valueof approximately unity as attractions or repulsions grow [10]. The measured Huggins coefficients givenin Table 1 are all larger than unity.

As shown in Fig. 3, increases in concentration of PU dispersion (dialyzed to equilibrium againstdeionizedwater) dramatically increases the dispersion conductivity, K. The solid line inFig.3 is calculatedfromK= KoAcwithKo=0 andA = 7.56 whereKhas units of mMho/cm andchas units of g/ml. Theseresults suggest that when PU particles are suspended in deionized water or 104 M KCl, the effect of thecounter ions on the intrinsic viscosity will only be felt when c 0.01 g/ml. When the suspending mediumhas an ionic strength of 103 M KCl, the effect of counter ions can only be neglected for c < 0.03 g/ml.

Not surprisingly, the reduced viscosity curves in Fig. 2 converge for c > 0.05 g/ml for PU dispersions indeionized water, 104 M KCland 103 M KCl. The effect of counter ions associated with the PU particles

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Fig. 2. Reduced viscosity measurements as a function of concentration for PU dispersions suspended in ionic strengths ranging

from DI water to 101 M KCl.

Table 1

Low volume fraction characterization of PU dispersions

[I] [] (ml/g) KH Rh (nm) []2.5 (ml/g) C (g/ml)

DI water 9.4a 12.4 3.76 0.17

104 MKCl 8.4a 11.9 3.36 0.19103 MKCl 7.73 1.05 11.6 3.09 0.21

5 103 M KCl 3.57 6.04 9.0 1.43 0.45

102 M KCl 2.82 7.19 8.3 1.13 0.57

101 M KCl 3.04 2.42 8.5 1.22 0.52

a These values weredetermined by truncating thecapillary viscometry dataat lowconcentration wherethe viscositydivergence

occurs.

is less important as the ionic strength of the suspending fluid is increased. Thus the reduced viscositycurves show less convergence with increasing concentration for ionic strengths greater than 5 103 M.

Treating the PU dispersion as consisting of spheres, the particle hydrodynamic radius (RH) can beestimated from capillary viscometry data by

RH =

3qMw

4NA

1/3

, (10)

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Fig. 3. Conductivity of PU samples dialyzed against DI water as a function of concentration in g/ml. Horizontal lines indicate

the conductivity of KCl solutions of the indicated ionic strengths.

Fig. 4. Average PU particle diameters from a second cumulant analysis of dynamic light scattering data () and from intrinsic

viscosity measurements ().

whereq = []/2.5 andNAis Avagadros number. For deionized water and 104 M KCl, [] is determined

by extrapolation of the linear portion of the reduced viscosity curve. Results of these calculations aresummarized in Table 1 where it is seen that RH decreases with increasing ionic strength.

Similar trends are seen for the particle sizes extracted from dynamic light scattering measurements(Fig. 4). Discrepancies in these two estimates of particle radius are poorly understood, but may be

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attributable to particle deformability at the high shear rates where [] is measured and the broad particlesize distribution (which influences the value of molecular weight used in Eq. (10)). Both estimates,however, show a decrease in size as ionic strength increases.

As the particle concentration increases, the effective ionic strength increases. The resulting changein ionic strength of the suspending medium will result in a shrinking of the particles. The combinedparticle size and suspension conductivity data, suggest that forc > 0.15 g/ml all dispersions will exist in

a state similar to that when dilute dispersions are suspended in a continuous phase with an ionic strengthbetween 101 and 102 M. Table 1 suggests that in this state, the particles have reached a minimumsize withRH= 89 nm (or a dynamic light scattering radius of 14 nm). This observation has a dramaticimpact on the concentration where the dispersion viscosity will diverge. This critical concentration canbe estimated to occur at an effective volume fraction of eff= 0.63. Using dilute suspension propertiesthis corresponds to a mass concentrationC = 0.63/q. As shown in Table 1 for background ionic strengthsof 103 M and below,C drops to values less than 0.17 g/ml, well below the value where the zero shearrate viscosity diverges. These results add weight to the birefringence and particle size data suggestingthat with increasing ionic strength or concentration, particle repulsions are diminished and the particlesshrink in size.

From the dilute solution characterization, we conclude that when PU dispersions are approximated asdeformable spheres. The sphere diameter and deformability decrease as the background ionic strength

increases. The counter ions balancing the particle charge contribute in a substantial manner to the disper-sions effective ionic strength. As a consequence, the effects of the counter ions can only be swampedwhen the dispersion concentration is kept below a critical value. For a supporting medium ionic strengthof 103 M, this concentration is approximately 0.02 g/ml while for 102 M this critical value is 0.15 g/ml.While double layer repulsions will remain a function of PU concentration, the particle size shrinks to aconstant size forc > 0.15 g/ml or ionic strengths greater than 102 M.

3.2. Concentrated dispersions

In characterizing the flow properties of dense dispersions, we focus initial attention on suspensionsdialyzed to equilibrium against deionized water. After discussing these suspensions we turn to the effectsof increasing the background ionic strength.

3.2.1. De-ionized water dispersions

3.2.1.1. Steady state shear viscosity. Viscosity measurements in the concentrated regime were per-formed at a sample temperature of 20C with a solvent trap. For T> 20C viscosity increases with timewere observed. This was attributed to solvent losses due to drying. Shear rate dependant thickening wasnot observed for this system at any concentration for the experimentally accessible shear rates.

Even in the most concentrated suspensions studied, steady state viscosity was obtained only secondsafter stress application. At 20C, suspension viscosities were found to remain constant for time periodsin excess of 2 h. Viscosities were independent of the rheometer tool geometry. The flow curves wereextremely reproducible not only between sample loadings, but also with increasing and decreasing stresssweeps.

Flow curves for PU dispersions in deionized water are shown in Fig. 5. Three types of behavior areapparent. The first extends up to a mass concentration c0.35 g/ml where a Newtonian response is

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Fig. 5. Relative viscosity of PU dispersions suspended in deionized water as a function of shear rate at several concentrations

expressed in g/ml.

obtained at all shear rates. The second covers the concentration range of 0.36 g/ml < c < 0.42 g/ml wherea Newtonian low shear (zero-shear) plateau viscosity is observed followed by shear thinning. Finallywhenc > 0.43 g/ml, the behavior is that of a shear thinning fluid with an apparent yield stress. The zeroshear rate viscosity could not be measured and the viscosity decays as x with x1 indicating theonset of a yielding type of response.

The flow properties of PU dispersions will be governed by interparticle thermodynamic and hydrody-namic forces. The thermodynamic forces arise primarily from particle charge, and from the loops andtails of the polymer comprising the particles. Evidence for the particulate nature of these suspensions canbe developed by comparing the characteristic Peclet number for shear thinning for PU dispersions and forhard sphere suspensions [10,49]. The Peclet number, Pecharacterizes the relative rates of deformationand diffusion:

P e =a2

Do=

6ca3

kT, (11)

whereDois the particle diffusivity,ais the particle radius and the shear rate. A Peclet number charac-terizing shear thinning,Pec can be defined from the shear rate, c, required for the viscosity to decreaseto halfway between the limiting high and low shear rate viscosities, o and respectively. For densesuspensions o/ 1 and Pec occurs at a shear rate where =0.5o. Due to difficulties in definingan effective volume fraction for the PU dispersions, rather than comparing Pec at equal values of , wecompare Pecat equal values ofo/c. Rueb and Zukoski [50] report that hard sphere suspensions with zeroshear rate relative viscosities of 104 and 3 105, havePec 2 10

3 and6 105 respectively. Usinga radius of 14 nm at the same zero shear rate relative viscosities, the PU dispersions havePec 1 10

3

and 3 105 respectively. The similarity of values ofPec suggests that shear thinning and the rapid

decrease inPec as particle concentration is increased have the same physical origins in hard sphere sus-pensions and in PU dispersions. Thus ascincreases, we conclude that the increases in viscosity and rapid

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Table 2

Cross-equation parameters for concentrated dispersions

[I] Concentration (g/ml) o (Pa s) c(s1)

DI 0.436 5024 80 0.096 0.003 0.81

0.415 365 2 1.58 0.04 0.82

0.413 294 2 2.02 0.07 0.82

0.402 12.80.1 65.1 1.2 0.90

0.385 9.60.1 91.2 2.5 0.90

102 M KCl 0.457 943 4 0.79 0.02 0.81

0.432 219 1 3.1 0.1 0.83

0.425 100 1 6.5 0.1 0.83

0.416 28.90.1 23.8 0.7 0.86

0.405 10.40.1 85.5 3.6 0.86

0.401 4.10.1 248 4 0.95

101 M KCl 0.421 5864 175 0.023 0.002 0.80

0.413 846 7 0.158 0.004 0.78

0.403 455 4 0.20 0.01 0.73

0.370 1.620.01 106 2 0.79

increases in characteristic stress relaxation times are associated with the approach of the close packinglimit where the particle long time self diffusivity goes to zero [29,49].

The particulate nature of the PU dispersion is further supported by comparing the full shear ratedependence of the flow curves of PU and hardcore dispersions. Shear thinning in hard core suspensions iswell described by Eq. (3). For our system, o and the data is well described by the Cross equationin the following form:

o=

1

1+ ( /c). (12)

Fits to Eq. (12) are summarized in Table 2. The values compare well with those obtained by Jones et. al.[18] on hard sphere suspensions 0.50 < < 0.73 and those obtained by Jones et al. [19] 0.547 < < 0.815and Mewis et al. [12] 0.708 < < 1.15 on sterically stabilized suspensions. Mewis et al. [12] were able

to measure high shear plateau viscosities () for particles with diameters of 1220, 475, and 84 nm. Highshear plateau viscosities were obtained for Pe > 10, suggesting that will not be reached for the PUdispersions studied here until 105 s1.

The flow properties of the PU dispersions at different volume fractions and ionic strengths can becollapsed onto a single master curve (Fig. 6). The master curve can be constructed by normalizing theviscosity and shear rate with oand c, respectively. This allows one to capture the flow behavior of thePU system from Eq. (12) with only two parameters (o(c), c). This curve is well approximated with= 0.8 independent ofc or ionic strength. To achieve a similar collapse for the sterically stabilized systemof Jones et al. [19], was found to be a function of concentration.

The stress characterizing shear thining can be calculated from c = 0.5oc To compare suspensionscomposed of particles of different size we work with the hard sphere scaling, where the reduced criticalshear stress is define:

rc =ca3

kT. (13)

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Fig. 6. Master curve created by normalizing the sample viscosity by the zero shear viscosity(o) and the shear rate by the critical

shear rate (c) Values ofo and c were determined by fitting Eq. (12) To the flow curve data of PU dispersions suspended in

deionized water (0.385 c 0.436), 102 M KCl (0.405 c 0.457) and 101 M KCl (0.370 c 0.413). A summary of the

values foro and c and are given in Table 2.

Papir and Krieger [51] originally assumed that rc= 1 for hard sphere suspensions independent of particlesize and concentration. Later, de Kruif et al. [24] showed thatrcis concentration dependant with a max-imum at approximately = 0.50. This maximum occurs at the concentration where hard spheres undergoa disorder to order transition. Although the magnitude of the peak for a model soft sphere suspension wassmaller than obtained for hard spheres, Mewis et al. [12] argued that soft sphere suspensions displayed thesame transition and concluded that rcwas not very sensitive to particle hardness. Rueb and Zukoski [50]found thatrcis weakly dependant on the strength of particle attraction.For their micogel system, Wolfeand Scopazzi [21] report that the magnitude of the maximum in rc in agreement with linear polymer

behavior. Wolfe and Scopazzi also showed that the volume fraction at the maximum in rcincreased withincreasing particle crosslink density (hardness). This was attributed to two ompeting effects: (1) particledeswelling at higheffand (2) polymer segment tails at the particle surface which enhance longer rangeparticle interactions. Particle deswelling will dominate the behavior for particles with high cross-linkdensities, acting to increase effat rcmaximum. With low particle cross-link densities, polymer tails areexpected to dominate the behavior eff at rc maximum. The critical reduced stress for the PU systemsuspended in deionized water is plotted with the calculated eff= cq in Fig. 7. In this work we use qdetermined from intrinsic viscosities measured for particles suspended at an ionic strength of 102 M.For purposes of comparison in Fig. 7 are also plotted the data of Wolfe and Scopazzi [21] for microgelparticles containing 0.25 and 4.0% crosslinker and data from Jones et al. [19] on 59 nm diameter softspheres. These results suggest to PU dispersions have a softness between the microgel particles of Wolfeand Scopazzi.

The divergence of the zero-shear viscosity is indicative of a transition from a disordered fluid to aglassy solid. This transition will occur as the system approaches the limit of close packing of equivalent

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Fig. 7. Reduced critical stress calculated from Eq. (13) as a function of the concentration expressed in effective volume fraction.

Also presented are data on microgel particles containing 0.25% and 4.0% crosslinker from Wolfe and Scopazzi (1989) and data

on sterically stabilized soft spheres from Jones et al. (1992).

Fig. 8. Relative zero shear viscosity as a function of effective volume fraction. Also plotted are data on charged spheres from

Buscall et.al. (1982). Thesolid line shows the prediction for model hard spheresuspensions. The line through the data of Buscall

et al. is drawn from Eq. (1) with m= 0.144. Also shown is Eq. (1)with m= 0.50 (dash-dotted line) intermediate concentrations.

A better fit is obtained if the exponent in Eq. (1) is set at 3 (dotted line).

hard spheres (meff) [49,52,53]. An example of this divergence for highly charged, hard core particles

can be found in the work of Buscall et al. [11] who fit their data exceptionally well with Eq. (1) by lettingm= 0.144 (Fig. 8). Data for model soft sphere systems with small soft layers has also been fit effectively

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using an effective hard sphere volume fraction [12,14]. As the particle softness increases, Mewis et al.[14] showed that Eq. (1) becomes less effective at describing the data.

Eq. (1) was used to fit the PU data in Fig. 8 with m= 0.50. Eq. (1) under predicts the viscosity at inter-mediate concentrations and over predicts the viscosity high concentrations. The smaller value of do/dat high concentration is attributable to the PU particles ability to deform and compress. The enhancementof viscosity at intermediate concentrations is suggestive of longer range interactions. Wolfe and Scopazzi

[21] observed this same behavior for low crosslink density polymethylmethacrylate microgels. For thissystem, the viscosity enhancement was attributed to increased interparticle interactions from low polymersegment density tails at the particle surface. This effect was more pronounced for the lower cross-linkdensity microgels. The behavior of the PU data in Fig. 8 can be captured much more effectively if theexponent in Eq. (1) is changed from (2) to (3).

Despite the failure of hard sphere based models to capture the divergence ofo asc is increased, weanticipate that atmthe particles become close packed. This assumes that in this low shear environment,electrostatics will be the dominant interaction and thus the deformation seen at elevated shear rates willnot be important. If we choose a hardcore approach, we can relate the effective maximum packing fraction,meff, to that where hard spheres of diameter dform a glass by

meff= 0.642a

d

3

, (14)

where a is the particle radius and dis the effective hard sphere particle diameter [10]. For hardcoreparticles of radiusaexperiencing electrostatic repulsions, can be estimated from

d=1

ln

ln(/(ln . . . ) )

(15)

where1 is the Debye length and is defined by

=4 o

2sa

2k exp(2ak)

kT, (16)

where ois the permittivity of free space, is the relative permittivity of the suspending medium, and sis

the particle surface potential [10]. For the data of Buscall et al. [11], a surface potential of 2535 mV yieldsmeff= 0.15 and Eq. (1) predicts experimental data well. For the PU system, using meff= 0.50, a =14nm,and an ionic strength of 5 102 M, Eqs. (1416) yield d= 30.4nm and s= 22 mV. The surface potentialcan be related to the number of charges on theparticle surface by thelinearized PoisonBoltzmanEquation[10,54] yielding 200 charges per PU particle. The calculated charge is lower than the 494 charges perparticle obtained from a conductometric titration. As much of the particle charge will be internal to theparticle and thus screened, it is not surprising that the estimation from meffyields a lower charge thanthat determined by titration.

3.2.1.2. Dynamic oscillation. Above meff the dispersion behaves as a viscoelastic solid. Dynamicstress sweeps were performed at a constant frequency of 1 Hz to obtain values of the storage modulus

(G), the loss modulus (G), and the complex viscosity (). Fig. 9 shows the variation ofG with thestrain for various PU concentrations. Forc < 0.41 g/ml (eff< 0.49 calculated from Eq. (5)) the storage

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Fig. 9. The elastic modulus of PU dispersions suspended in deionized water as a function of strain at a frequency of 1 Hz. The

PU dispersion concentration is given in g/ml.

modulus is small as would be expected for a disordered fluid. For c > 0.41 g/ml the particles begin tointeract strongly as indicated by the increase in G. As the strain increases, this structure is destroyed,resulting in a decrease in G. The extent of the linear viscoelastic response, characterized by a constant G,is concentration dependent. Higher concentrations lead to a reductionin the critical strain (crit) separatingthe linear and the nonlinear viscoelastic response. If the cut-off between the two responses (linear andnon-linear) is chosen as the point whereG is 90% of the plateau value, increasing the mass concentrationfrom 0.41 to 0.43 g/ml (effof 0.49 and 0.51) reducescritfrom 0.056 to 0.036. These critical strains aretypical of gels composed of charge stabilized particles as opposed to aggregated suspensions [55,56].

The concentration and strain dependencies ofG are shown in Fig. 10. Several features may be noted.First, G increases with increasing concentration. Again moderate increments in c lead to orders of

magnitude increase inG. Secondly,G > G forc < 0.42 g/ml (eff< 0.50). However, for c > 0.43 g/ml(eff> 0.50) and with the formation of an apparent gel,G

becomes higher thanG. Thirdly, a differentbehavior is observed for the highest concentration measured. G first increases, reaches a maximum andthen decreases; such a behavior has been associated with materials having yield stresses [20].

Dynamic oscillatory flow experiments were conducted at a strain of 2% (ensuring linear viscoelasticresponse) and over the frequency range of 0.0130 Hz. Figs. 11 and 12 show, the variation of the G andG with , the angular frequency. At low concentrations, terminal behavior is observed with G increasingwith 2 andG as . As concentration is increased, near c = 0.42 g/ml the relaxation rate (as characterizedwhereG = G) decreases rapidly. This behavior occurs over a very narrow concentration range (i.e., thecharacteristic relaxation time moves from 10 s to

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Fig. 10. The loss modulus of PU dispersions suspended in deionized water as a function of strain at a frequency of 1 Hz. PU

concentrations are expressed in g/ml.

Fig. 11. The elastic modulus of PU dispersions suspended in deionized water at a strain of 0.02 as a function of frequency. PU


The CoxMerz correlation is obeyed by this system only in regions where the system can obtain aNewtonian shear plateau. As can be seen from Fig. 13, the CoxMerz rule where () = ( )is onlyfound to be applicable in the region of small and and for c less than the gel concentration or theonset of an apparent yield point for the system. In the regions of shear thinning, the dynamic viscosity

() is always greater than the shear viscosity (). This result is observed in several structured systems[20]. This result lends further support to our essentially particulate description of the PU dispersions.

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Fig. 12. The loss modulus of PU dispersions suspended in deionized water at a strain of 0.02 as a function of frequency. PU


Fig. 13. Viscosity as a function of shear rate for constant deformation rate experiments (closed symbols) and complex viscosity

(open symbols) as a function of frequency. PU dispersions are suspended in deionized water and concentrations are reported in

g/ml. The CoxMerz rule is only obeyed in the low shear viscosity limit.

3.2.2. Effect of the ionic strength

The results discussed in the previous section are associated with samples diluted with deionized water.To investigate the effect of screening the double layer repulsion, the flow properties of dense PU samples

were measured in 102 and 101 M KCl. Due to difficulties in dialyzing these PU samples to specificconcentrations, experimentally tested samples were made from a concentrated master batch dialyzed to

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Fig. 14. Zero shear relative viscosity as a function of the effective volume fraction determined from Eq. (5). Shown are data for

PU dispersions suspended in deionized water, 102 M KCl, and 101 M KCl.

equilibrium with 101 or 102 M KCl by dilution with the appropriate ionic strength solvent. For boththe 101 M and the 102 M KCl dispersions. the trends in the viscosity-shear rate experiments, the stresssweep experiments, and the frequency sweep experiments were very similar to the deionized dispersion.

The best fit parameters extracted from the Cross equation for each ionic strength are shown in Table2. The master curve in Fig. 6 clearly shows that shear thinning occurs in a similar manner for all ionicstrengths investigated.

The relative zero shear viscosity (or) at each ionic strength as a function of effective volume fraction(eff) calculated from Eq. (5) is presented in Fig. 14. As expected, at low to medium concentrations, boththe 102 and 101 M KCl samples display lower viscosities than an equivalent concentration dispersiondialyzed to equilibrium against deionized water. This behavior is consistent with the findings of numerousstudies on dense charge stabilized suspensions [11,55,57]. The decreases in viscosity with increasing

ionic strength are associated with compression of the electrostatic double layer by the inert electrolyte.A detailed analysis of this result is complicated by a lack of knowledge of the specific ionic condition inthe sample. At higher PU concentrations, the 102 M dispersion continues to follow this trend.

Forc > 0.45 g/ml, the zero shear rate viscosities of the dispersion in 101 M KCl are higher than therespective deionized samples. At an ionic strength of 0.2 M KCl, the PU dispersions aggregate. Secondvirial coefficient measurements suggest the particles are less repulsive with increasing ionic strength.These results suggest that attractions become important as the ionic strength increases. The data in Fig.14 indicates that these attractions are weak but grow for c > 0.45 g/ml when the background ionic strengthis 101 M.

Reduced critical stresses for each ionic strength and concentration are shown in Fig. 15. The 101 Msamples display slightly different values than the lower ionic strength samples. Using octadecyl silica indecalin, Rueb and Zukoski [50] found that attractions made very little difference in the reduced critical

stress behavior of hard core systems. The relative magnitude and flattening behavior of the 101 M KCldata are similar to that obtained on soft 42 nm PMMA particles [16,17]. Frith associated flattening of the

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Fig. 15. Reduced critical stress calculated from Eq. (13) as a function of the effective volume fraction determined from Eq. (5)

for PU suspended in deionized water, 102 M KCl, and 101 M KCl. Also shown are data obtained by Frith (1986).

reduced critical stress with increasing particle softness [16,17]. This conclusion is not consistent with thePU dispersions where increases in ionic strength appear to increase particle rigidity.

A simple Maxwell model with a single relaxation time could not be used to fit the frequency depen-dencies ofG andG. TheG data of Fig. 11 along with the data for the other ionic strengths was fit to asystem of Maxwell elements in parallel such that a high frequency limiting storage modulus, G, couldbe estimated. As the concentration of the dispersions increases, additional relaxation times were requiredto fit the modulus data. As a result, a single characteristic relaxation time for each respective sample wasunattainable. Fig. 16 shows the G values obtained for each PU sample. The data of Fig. 16 indicatethat there is virtually no mechanical differences between the glassy structures formed by the PU particlesat elevated concentrations. This result is not surprising as the ion concentrations in the three dispersionswill be very similar at these elevated PU concentrations.

4. Conclusions

Here we present a detailed study of the rheological properties of a commercial aqueous PU dispersion.These systems are composed of soft particles whose size is a function of both ionic strength and dispersionconcentration. Flow birefringence experiments demonstrate that the PU particles deform and orient in ashear field. These findings support the soft nature of the particles suggested by Satguru et al. [1,32].Due to the small particle size, shear thinning does not occur for c < 0.35 g/ml. For higher concentrations,shear thinning is observed and the zero shear rate viscosity diverges near c 0.42 g/ml (eff0.50).

Strong interactions and glassy responses are observed at concentrations below that for randomly packedhard spheres and many sterically stabilized systems [12,17,19]. However, these PU particles are highly

charged. In addition, their polyelectrolyte nature suggests polymer chains or tails may extend fromthe particle core. As a consequence, either through electrostatic repulsions or a combination of charge

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Fig. 16.The asymptotic high frequencyelasticmodulus of PU dispersions suspendedin deionizedwater,102 MKCland101 M

KCl as a function of the effective volume fraction determined from Eq. (5).

and steric effects, these systems gel or form glasses at volume fractions near 0.5. The approach to glassformation is characterized by the rapid change in frequency where G = G and the rapid decrease in Pecas the particle concentration is increased.

While we anticipated thatbackground ionic strength would play a significant role in dispersion rheology,as the particles themselves carry a substantial charge, in a dense suspension, the effects of the addition ofinert electrolyte are muted up to a point where a combination of ions balancing particle charge and thosefrom the background electrolyte approach an effective ionic strength of0.1 M. At this point interparticleattractions can become important.

Acknowledgements

This work was supported by the Materials Research Laboratory at the University of Illinois at Cham-paign-Urbana by the U.S. Department of Energy through Grant DEFG02-96-ER-45439. Additional sup-port was provided by the 3M Company St. Paul, Minnesota. The authors would like to thank A.J. McHughfor the use of his flow birefringence apparatus.

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