Journal of Colloid and Interface Science 297 (2006) 312–316www.elsevier.com/locate/jcis

Dynamics of shear-thinning suspensionsof core–shell structured latex particles

Hiroshi Nakamura ∗, Kazuyuki Tachi

Toyota Central Research & Development Laboratories, Inc. 41-1, Yokomichi, Nagakute, Aichi-gun, Aichi, 480-1192, Japan

Received 31 May 2005; accepted 5 October 2005

Available online 9 November 2005

Abstract

The rheological behavior and microstructure of shear-thinning suspensions of core–shell structured carboxylated latex particles were examined.The steady shear viscosity of the suspension increased with increasing dissociation of the carboxyl groups or increasing particle concentration,however the critical shear stress σc and inter-particle distance ξ of the microstructure did not change. With increasing particle diameter, σcincreased and ξ decreased. These results were consistent with a Brownian hard sphere model, in which competition exists between the bulkmass transfer due to the applied field and diffusion of the particles. We confirmed that σc depends on ξ , as expressed by σc = 3kT /4πξ3. Thisrelationship is consistent with the dynamics of a Brownian hard sphere model with particle diameter ξ . Thus the dynamics of shear-thinningsuspensions of core–shell particles can be explained by a Brownian thermodynamic model. 2005 Elsevier Inc. All rights reserved.

Keywords: Suspension rheology; Core–shell particle; Carboxylated latex; Critical shear stress; Inter-particle distance; Brownian dynamics

1. Introduction

Core–shell structured particles consisting of a hard sphereand an adsorbed or grafted soft layer display characteristic be-havior in terms of particle swelling and suspension rheology.Core–shell structured latex particles with a mantle core poly-mer and a shell polymer layer having carboxyl groups swellwith addition of base in an aqueous medium [1]. An aqueoussuspension of these swelling particles displays shear-thinningflow at low concentrations; for non-swelling particles, New-tonian flow would normally be observed. This characteristicrheological behavior enables control of the rheological behav-ior of paints, inks, foods and other products [2–4].

It is well known that when acrylic acids containing latexpolymers are neutralized to an alkaline pH, there is a markedincrease in the viscosity of the system [4–8]. Verbrugge mea-sured viscosity versus pH for a large number of methacrylicacids containing latexes of high and low Tg and similar hy-drophilicity [5,6]. Quadrat demonstrated that changes observed

* Corresponding author. Fax: +81 561 63 6507.E-mail address: nakamura@mosk.tytlabs.co.jp (H. Nakamura).

0021-9797/$ – see front matter 2005 Elsevier Inc. All rights reserved.doi:10.1016/j.jcis.2005.10.006

in the flow curves of carboxylated acrylate latex suspensionsduring alkalinization could be described in terms of parametersof the Cross theory of aggregation of disperse particles, and de-scribed the flow mechanism of latex suspensions in which theparticles have dissociable groups [7,8].

In previous work, we have found that shear-thinning flowsuspensions of core–shell structured carboxylated latex parti-cles display elastic solid-like behavior in dynamic rheologi-cal testing [9]. Moreover, from small angle X-ray scattering(SAXS) measurements, the pseudo-lattice structure was de-tected in the suspension. However, this lattice-like microstruc-ture was not permanent but instead was a metastable structuredeformed by thermal motion, the behavior was represented bytime–temperature conversion as represented by the Arrheniusequation [9]. This behavior of the core–shell particles is thussimilar to that of hard spheres or polymerically stabilized parti-cles [10–17]. The shear-thinning rheological behavior of poly-merically stabilized colloidal suspensions are usually predictedand correlated on the basis of data and scaling laws for Brown-ian hard sphere models. In Brownian hard sphere models, therheological behavior is explained based on the correlation be-tween bulk mass transfer and diffusive mass transfer. If the ap-plied fields are greater than the particle diffusion, the viscosity

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does not change; however, if the particle diffusion dominates,the viscosity falls. At this critical shear stress σc, the bulk masstransfer due to the applied field is greater than the particle dif-fusion.

In this article, the rheological behavior and microstruc-ture of shear-thinning suspensions of core–shell structuredcarboxylated latex particles are examined under various de-grees of neutralization, and various concentrations and parti-cle diameters. The dynamics of the shear-thinning is analyzedbased on Brownian hard sphere models using the critical shearstress σc.

2. Experimental

2.1. Preparation of suspension of carboxylated core–shellparticles

Carboxylated core–shell particles CS-1, CS-2, CS-3, andCS-4 were obtained by semi-continuous two-stage feed emul-sion polymerization [1,9,18]. In all particles, mantle core poly-mers were crosslinked and shell polymers were linear andgrafted to the core. The crosslinked core was synthesized usingmethyl methacrylate (MMA), n-butyl acrylate (n-BA) and al-lyl methacrylate (AMA), and the linear shell using methacrylicacid (MAA), containing carboxyl groups, 2-hydroxyethyl acry-late (HEA), n-BA and MMA. The weight ratio of monomersof the core polymer/shell polymer was 100/29.5. Monomercompositions are shown in Table 1. Though core and shellcompositions of all the particles were the same, particle di-ameters were varied by controlling the initiator weight. Theseparticles swelled with addition of a base in aqueous medium.Table 2 shows the diameters of non- and fully neutralizedparticles as measured using dynamic light scattering (OtsukaElectronics ELS-800) in dilute suspension (0.1 wt%). The alka-line agent used for neutralization was 2-dimetylaminoethanol(DMAE).

Suspensions of the core–shell particle were prepared withvarious degrees of neutralization up to the full amount of car-boxyl groups in the shell polymer and at various particle con-centrations. The neutralized agent was DMAE and the degreesof neutralization ranged from 0–100%. The particle concentra-tion was varied from 15–22 wt%.

2.2. Measurements of rheological behavior andmicrostructure of the suspension

Steady shear rate viscosity η was measured by changing theshear rate γ̇ from 1 × 10−2 s−1 to 1 × 103 s−1. Shear mod-ulus G′ was measured using an oscillation frequency ω from1 × 10−2 rad s−1 to 1 × 102 rad s−1 in the linear region. Theseexperiments were measured using a rotational type rheometer(Rheometrics ARES) equipped with a conical-cylinder fixture.The critical shear stress σc at which the flow behavior of thesuspension changes from Newtonian to shear-thinning was esti-mated as the intersection point of the low shear rate Newtonianregion and the shear-thinning region in a plot of η versus σ

(= ηγ̇ ).

Table 1Monomer compositions of the core–shell particles

Weight ratio

First stage (core) Second stage (shell)

MMA 47 24n-BA 50 38AMA 3MAA 18HEA 20

Table 2Diameters of the core–shell particles non-neutralized (d0) and fully-neutralized(d100) by 2-dimetylaminoethanol as measured by dynamic light scattering

Diameter (nm)

d0 d100

CS-1 109 176CS-2 35 55CS-3 65 103CS-4 191 291

Table 3Conditions of SAXS measurements

Target CuKβ filter NiVoltage, current 50 kV, 300 mAAngle range 0.0150–0.15◦Step angle 0.003◦Slits Entrance slit 0.015 mm

Receiving slit 0.02 mmScatter slit 0.08 mmHeight limitter 25 mm

Sampling time 50 s (10 s × 5)

The microstructure of the suspension of the core–shell par-ticles was estimated by small-angle X-ray scattering (SAXS)measurements. The conditions for SAXS are shown in Table 3.The inter-particle distance ξ , which measures between adjacentparticle centers in the lattice-like microstructure, was derivedfrom the first peak position in a plot of the scattering vector Qversus X-ray intensity.

3. Results and discussion

3.1. Rheological behavior and microstructure of thesuspension of core–shell particles

Fig. 1 shows the steady shear rate viscosity η of a 20 wt%suspension of the core–shell particles as a function of shearrate γ̇ with various degrees of neutralization. With increasingdegree of neutralization, η and the degree of shear-thinning in-creased. For the non-neutralized suspension, Newtonian flowwas obtained. At intermediate degrees (30–80%), the suspen-sions moved from Newtonian at low shear rates to shear-thinning at high shear rates. At high degrees (90–100%), thesesuspensions indicated shear-thinning only.

Fig. 2 shows the storage modulus (G′) of a 20 wt% suspen-sion of the core–shell particles as a function of frequency forvarious degrees of neutralization. At non-neutralized and lower

314 H. Nakamura, K. Tachi / Journal of Colloid and Interface Science 297 (2006) 312–316

Fig. 1. Steady shear rate viscosity η of a 20 wt% suspension of the carboxylatedcore–shell particles as a function of shear rate γ̇ for various degrees of neutral-ization of the carboxyl groups: (") 0, (Q) 30, (2) 60, (F) 70, (!) 80, (P) 90,and (1) 100%.

Fig. 2. Dynamic shear modulus G′ of a 20 wt% suspension of the carboxylatedcore–shell particles as a function of angular frequency ω for various degrees ofneutralization of the carboxyl groups: (") 0, (Q) 30, (2) 60, (F) 70, (!) 80,(P) 90, and (1) 100%.

degrees, the behavior was consistent with that of an inelasticfluid; i.e., G′ was quite low and increased rapidly with fre-quency. At intermediate degrees more pronounced viscoelasticbehavior was seen, with G′ flattening out at high frequencies.At high degrees elastic solid-like behavior was observed. Here,G′ was high and almost independent of frequency. These re-sults support those of Fig. 1 and are very similar in form tothose observed for hard sphere suspensions in the transitionfrom liquid-like to solid-like behavior.

To clarify the relationship between the rheological behav-ior and the microstructure, η is plotted against shear stress σ

(Fig. 3). Over the entire σ range, η increased with increasingdegree of neutralization as seen in Fig. 1 but surprisingly thecritical shear stress σc at the transition from Newtonian flow toshear-thinning was almost the same (1 Pa) in spite of the chang-ing degree of neutralization. For most practical purposes thiscritical stress can be considered a yield stress. The above re-sults suggest that the yield stress of the suspension of the sameparticle composition and diameter is constant over various de-grees of neutralization.

Fig. 3. Steady shear rate viscosity η of a 20 wt% suspension of the carboxy-lated core–shell particles as a function of shear stress σ for various degrees ofneutralization of the carboxyl groups substituting γ̇ with σ (= ηγ̇ ) from Fig. 1.The critical shear stress σc is about 1 Pa.

Fig. 4. Steady shear rate viscosity η of a 100% neutralized suspension of thecarboxylated core–shell particles as a function of shear stress σ for variousconcentrations: (") 15, (Q) 18, (2) 20, and (F) 22 wt%. The critical shearstress σc is about 1 Pa.

Fig. 4 shows η vs σ over various particle concentrations. Itcan be seen that η increases with increasing degree of neutral-ization, but that σc remains the same (1 Pa) despite the changein particle concentration. This behavior has been reported in therheology of hard sphere suspensions [7–10].

Thus suspensions of core–shell particles of the same com-position and diameter show a constant critical shear stress re-gardless of the degree of neutralization and concentration; inother words, the yield stress that deforms the microstructure byshear flow is constant. Because the yield stress corresponds tointeraction between neighboring particles in the microstructure,the interaction between the particles must be independent of thedegree of neutralization and concentration.

Fig. 5 shows SAXS profiles of the shear-thinning suspen-sions. Diffraction peaks originating from ordered particle struc-tures were detected for all suspensions. From the peak positionin the profiles, the inter-particle distances ξ of the microstruc-ture were found to be almost identical (Table 4). This supportsthe assumption that the interaction between particles in theshear-thinning suspensions is almost the same. As such, the crit-ical shear stress σc correlates with the inter-particle distance ξ

of the microstructure.

H. Nakamura, K. Tachi / Journal of Colloid and Interface Science 297 (2006) 312–316 315

Fig. 5. SAXS profiles of various degrees of neutralization and concentration:(2) 100% (18 wt%), (F) 80% (20 wt%), (!) 90% (20 wt%), (P) 100%(20 wt%), (1) 100% (22 wt%).

Table 4Inter-particle distance ξ of the microstructures in the suspensions for variousdegrees of neutralization and concentrations of the core–shell particles

Degree of neutralization (concentration) Distance ξ (nm)

100 (22) 126100 (20) 12690 (20) 12680 (20) 125

100 (18) 125

3.2. Correlation between rheological behavior andmicrostructure

We consider that the rheological dynamics of the shear-thinning suspensions of core–shell structured latex particles canbe probed by the relationship between σc and ξ , which involvesdiffusion of the particles in the microstructure and scaling basedon a Brownian hard sphere model [10–17]. The ratio of bulkmass transfer to diffusive mass transfer is represented by thePeclet number Pe. In the low stress regime, the stress does notperturb the system until a critical stress σc is reached and theviscosity falls. At this stress, the bulk mass transfer due to theapplied field is greater than the Brownian motion in the sys-tem and the existing order of the suspension is disrupted. Pe isexpressed as,

(1)Pe = LV/D,

where L is the length scale, V is the applied velocity, and D isthe diffusion coefficient of the particles. If a continuous shearfield is applied with a shear rate γ̇ to a suspension of particleswith radius a, the following is obtained:

(2)Pe = a2γ̇ /D.

Taking the diffusion coefficient as expressed by the Stokes–Einstein law, D = kT /6πη0a, gives

(3)Pe = 6πη0γ̇ a2/kT .

At the critical shear stress, the Peclet number should be 1, yield-ing the following:

(4)σc = kT /6πa3.

However, this equation is based on Stokes–Einstein diffu-sion of the particle, which is concerned only with dilute sus-pensions. A general expression for diffusion of the particle in

Fig. 6. Steady shear rate viscosity η of a 100% neutralized 18 wt% suspen-sion of the carboxylated core–shell particles as a function of shear stress σ forvarious diameters: (") CS-4, (Q) CS-1, (2) CS-3, (F) CS-2. With increasingdiameter, the critical shear stress σc decreases; CS-4: 0.02 Pa, CS-1: 0.1 Pa,CS-3: 0.35 Pa, CS-2: 5 Pa.

Table 5Inter-particle distance ξ of the microstructures in the suspensions for variousdiameters of the core–shell particles

Distance ξ (nm)

CS-1 126CS-2 37CS-3 78CS-4 225

a shear-thinning suspension has not been determined. Instead,we derived the diffusion constant of the particle in the shear-thinning suspension by scaling equation (4). When σc was 1 Pa,the particle radius derived from Eq. (4) was 60 nm. This derivedradius does not agree with ξ but is close to ξ/2. This indicatesthat the diffusion coefficient of the particle in the suspensionmust correlate with ξ in a similar way to the correlation thatexists between the diffusion coefficient and correlation lengthin a three dimensional gel [19,20]. These results indicate thatthe dynamics of shear-thinning suspensions of core–shell par-ticles can be expressed by scaling the Brownian dynamics ofhard spheres, and that particle diffusion corresponds to that ofa hard sphere with diameter ξ . We have determined that σc isrelated to ξ by

(5)σc = 3kT /4πξ3.

3.3. Rheological behavior and microstructure with differentparticles

For the same particle composition and diameter, σc and ξ

are almost the same with changing degree of neutralization orconcentration, respectively. To clarify the relationship obtainedabove, σc and ξ were measured with core–shell particles ofvarious diameters. Fig. 6 shows the relationship between shearstress σ and viscosity η with various particle diameters. η andσc decreased with increasing diameter along with ξi (Table 5).If we assume a hard sphere suspension following Brownian dy-namics and apply equation [4], it can be seen that σc decreaseswith increasing diameter. Fig. 7 shows the relationship between

316 H. Nakamura, K. Tachi / Journal of Colloid and Interface Science 297 (2006) 312–316

Fig. 7. The relationship between 1/ξ3 and σc for various diameters of thecore–shell particles: (") CS-4, (Q) CS-1, (2) CS-3, (F) CS-2. The slope ofthe straight line is kT /6π .

1/ξ3 and σc with various suspensions of different particle size.In the log–log plot, σc is proportional to 1/ξ3 and the slopeof the relationship is 3kT /4π . This confirms that the diffusioncoefficient of the particles in the shear-thinning suspensions ofcore–shell particles is consistent with a particle of diameter ξ .From these results, the dynamics of the suspension of the core–shell particles can be explained by the Brownian hard spheremodel, in which there is competition between the bulk masstransfer due to the applied field and diffusion of the particles inthe suspension.

4. Summary

The rheological behavior and microstructure of aqueous sus-pensions of core–shell structured carboxylated latex particleswere examined. The critical shear stress σc and inter-particledistance ξ of the microstructure did not change with changingdegree of neutralization and concentration. However, with in-creasing particle diameter, σc increased and ξ decreased. Thesebehaviors were found to be consistent with the Brownian hardsphere model, in which competition exists between the bulk

mass transfer due to the applied field and diffusion of theparticles in the suspension. It is widely accepted that at lowshear rates, where there is a Newtonian plateau, the suspen-sion microstructure is not significantly perturbed by the shear.At higher shear rates the hydrodynamic forces begin to dom-inate and shear-thinning occurs. We experimentally confirmedthe dependence of σc on ξ , as expressed by σc = 3kT /4πξ3.This relationship corresponds to a Brownian hard sphere modelwith a particle diameter of ξ . These results demonstrate that thedynamics of shear-thinning suspensions of the core–shell parti-cles is explained well by a Brownian thermodynamic model.

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