Controlled Clustering and Enhanced Stability of Polymer-Coated Magnetic Nanoparticles

7/31/2019 Controlled Clustering and Enhanced Stability of Polymer-Coated Magnetic Nanoparticles

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Controlled Clustering and Enhanced Stability ofPolymer-Coated Magnetic Nanoparticles

Andre Ditsch, Paul E. Laibinis, Daniel I. C. Wang, and T. Alan Hatton*

Department of Chemical Engineering, Massachusetts Institute of Technology,Cambridge, Massachusetts 02139

Received November 30, 2004. In Final Form: March 23, 2005

The clustering and stability of magnetic nanoparticles coated with random copolymers of acrylic acid,styrenesulfonic acid, and vinylsulfonic acid has been studied. Clusters larger than 50 nm are formed whenthe coatings are made using too low or too high molecular weight polymers or using insufficient amountsof polymer. Low-molecular-weight polymers result in thin coatings that do not sufficiently screen van derWaals attractive forces, while high-molecular-weight polymers bridge between particles, and insufficientpolymer results in bare patches on the magnetite surface. The stability of the resulting clusters is poor,but when an insufficient polymer is used as primary coating, and a secondary polymer is added to coatremaining bare magnetite, the clusters are stable in high salt concentrations (>5 M NaCl), while retainingthe necessary cluster size for efficient magnetic recovery. The magnetite cores were characterized by TEMand vibrating sample magnetometry, while the clusters were characterized by dynamic light scattering.The clustering and stability are interpreted in terms of the particle-particle interaction forces, and theoptimal polymer size can be predicted well on the basis of these forces and the solution structure andhydrophobicity of the polymer. The size of aggregates formed by limited polymer can be predicted with

a diffusion-limited colloidal aggregation model modified with a sticking probability based on fractionalcoating of the magnetite cores.

Introduction

Colloidally dispersed magnetic nanoparticles showconsiderable promise for a wide range of applications assealants,1 damping agents,2 drug-delivery vehicles,3 con-trast agents in magnetic resonance imaging,4 and separa-tion aids.5-7 In many cases, these colloidal dispersions, ormagnetic fluids, consist of magnetite (Fe3O4) nanopar-ticles, typically 10 nm in size, coated with surfactantsor polymers6-15 both to stabilize the particles in suspen-sion and to provide favorable surface properties tailoredfor specific applications of interest. The small size of the

stabilized particles results in dispersions that remainsuspended indefinitely in gravitational and moderate

magnetic fields.10 Large surface areas per unit volumemake the particles ideally suited for use in adsorptiveseparations6,7 since their capacity for targeted solutes isconsiderably greater than the capacity of commercialresins. Thesurface area is availablewithoutinternal pores,and thus, separations are not limited by pore diffusionand can, in principle, be performed much more quicklythan with standard porous materials.

In separation processes, the magnetic properties of theloaded nanoparticles can be exploited in their recoveryfrom process streams by using high-gradient magneticseparation (HGMS) technology.6,7 This process relies onthe fact that the force acting on a magnetic particle in amagnetic field depends on the particle size and themagnetic field gradient according to

where Vis the volume of the magnetic nanoparticle andMis itsmagnetization in a given field,H.AnHGMSsystemtypically consists of a column packed with a bed ofmagnetically susceptible wires, on the order of 50 m indiameter, placed between the poles of an electromagnet.The wires dehomogenize the applied magnetic field toestablish the large field gradients near the wire surfacesrequired for capturing the particles. HGMS has been

examinedfor thecapture of magneticnanoparticles6,7,16-18whereit has been demonstrated, both experimentally andtheoretically, that individual nanoparticles cannot becaptured effectively by HGMS because diffusional anddrag forcescan overcome theforcesof magnetic attractionto the wires, and the particles are swept through thecolumn relatively unimpeded. Small clusters of magnetic

* Author to whom correspondence should be addressed. E-mail:[email protected]. Tel: 617-253-4588. Fax: 617-253-8723.

Department of Chemical Engineering, Rice University, Hous-ton, Texas, 77005.

(1) Rosensweig, R. E. Chem. Eng. Prog. 1989, 85, 53-61.(2) Raj, K.; Moskowitz, R. J. Magn. Magn. Mater. 1990, 85, 233-

245.(3) Lubbe, A. S.; Bergemann, C.; Brock, J.; McClure, D. G. J. Magn.

Magn. Mater. 1999, 194, 149-155.(4) Kawaguchi, T.; Yoshino,A.; Hasegawa, M.;Hanaichi, T.; Maruno,

S.; Adachi, N. J. Mater. Sci.-Mater. Med. 2002, 13, 113-117.(5) Safarik, I.; Safarikova, M. J. Chromatogr. B 1999, 722, 33-53.(6) Moeser, G. D.;Roach, K. A.;Green, W. H.;Laibinis, P. E.;Hatton,

T. A. Ind. Eng. Chem. Res. 2002, 41, 4739-4749.(7) Bucak, S.; Jones, D. A.; Laibinis, P. E.; Hatton, T. A. Biotechnol.

Prog. 2003, 19, 477-

484.(8) Jones, F.; Colfen, H.; Antonietti, M. Colloid Polym. Sci. 2000,278, 491-501.

(9) Mendenhall, G. D.; Geng, Y. P.; Hwang, J. J. Colloid InterfaceSci. 1996, 184, 519-526.

(10) Rosensweig, R. E. Ferrohydrodynamics; Cambridge UniversityPress: London, 1985.

(11) Shen,L. F.;Laibinis, P. E.;Hatton, T. A.J. Magn. Magn. Mater.1999, 194, 37-44.

(12) Shen, L. F.; Laibinis, P. E.; Hatton, T. A. Langmuir 1999, 15,447-453.

(13) Shen, L. Ph.D. Thesis, MIT, Cambridge, MA, 2000.(14) Shen, L. F.; Stachowiak, A.; Fateen, S. E. K.; Laibinis, P. E.;

Hatton, T. A. Langmuir 2001, 17, 288-299.(15) Wooding, A.; Kilner, M.; Lambrick, D. B. J. Colloid Interface

Sci. 1992, 149, 98-104.

(16) Moeser,G.D.;Roach,K.A.;Green,W.H.;Laibinis,P.E.;Hatton,T. A. AIChE J. 2004, 50, 2835-2848.

(17) Fletcher, D. IEEE Trans. Magn. 1991, 27, 3655-3677.(18) Gerber,R.; Takayasu, M.;Friedlaender,F. J.IEEE Trans.Magn.

1983, 19, 2115-2117.

F ) -0VMH

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10.1021/la047057+ CCC: $30.25 2005 American Chemical SocietyPublished on Web 05/18/2005


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particles on the order of 50 nm or larger can, however, beremoved efficiently from process streams using HGMS.Thus, it is desirable to synthesize clusters of the particlesto provide the size needed for the particle recovery butwithout compromising the adsorptive capacity nor thestability of the suspension.

Due to their small size and large surface area, magneticnanoparticles will tend to aggregate to reduce their surfaceenergy. Nanoparticle dispersions can, however, be sta-bilized by use of a suitable surface coating, typically a

surfactant or polymer, and the many polymer coatingsthat have been examined formagnetic nanoparticlesvaryfrom simple homopolymers to graft and block copoly-mers6,8,9,15 Thesynthesis of stableclustersof these particlesis a difficult prospect since the primary particles must beunstable toformthe initial clusters andthe clusters formedare therefore themselves on the threshold of stability andare prone to further aggregation with small changes insolutionconditions. Unless thereis a method for removingthe initial instability that permits cluster formation, it ishighly unlikely that the resulting clusters will be stable.For example, a common situation is when attractive vander Waals interactions initially overcome electrostaticrepulsion forces to allow cluster formation but where theelectrostatic energy barrier to coagulation increases asclusters grow so that beyonda finite cluster size no furthergrowth occurs.14 However, if the ionic strength of themedium is increased, these clusters aggregate further toform permanent precipitates that cannot be resuspended.In separation processes, particularly for biological ap-plications, the ionic strength can vary over a wide rangeand multivalent ions may be present. These ions greatlychangethe strength and rangeof electrostatic interactions,leading to instability and coagulation of poorly coatednanoparticles at moderate ionic strengths. Whenparticlesare formed withcoatings thatproviderobust stabilization,such as those that repel each other sterically and providethermodynamic stability,6,19,20 the particlesdo notclusterand are difficult to capture.6,16,21 If we can control thestability of clusters formed under incipiently unstableconditions, then many applications requiring capture ofthese clusters and their reuse in adverse environmentscan be realized.

It is the purpose of this paper to demonstrate both thatclusters of controlled size can be synthesized readily andthat the required stability can be achieved through post-treatment with no further growth of these clusters. Themagnetic nanoparticles are coated with random co-polymers of acrylic acid, styrene sulfonic acid, and vinylsulfonic acid, which are suitable for adsorptive ion-exchange purification of proteins. This simple polymersystem also allows independent tuning of the molecularweight, attachment density, and hydrophobicity of thecoatings, allowing a systematic study of the effects of the

coating properties on the resulting particle clusters to beperformed. We have explored the clustering of nanopar-ticles by three methods: (i) using a low-molecular-weightpolymer that provides a coating of insufficient thicknessto provide steric stabilization against the van der Waalsinteractions; (ii) using a high-molecular-weight polymerto bridge between particles; and (iii) using a moderate-molecular-weightpolymer in a limited amountto coattheparticles partially. We show that all three methods resultin clusters large enough for capture in an HGMS column.

When a polymer is either too large or too small, theinstability that causes clustering could not be removedeasilyand highlystable clusters could notbe synthesized.

The instability that causes clustering with a limitedamount of low-molecular-weight polymer was easilyremoved by using a polymer that coats well in limitedamounts as the first coating followed by the subsequentaddition of more polymer to stabilize the clusters formedduring the first step. The clustering and stability of thenanoparticles were analyzed on the basis of calculatedenergies of interaction of the particles, and from thisanalysis, we outline models for the formation of clustersand for determining the optimum molecular weight of apolymer coating.

Experimental Section

Materials. Ferricchloride hexahydrate(97%), ferrouschloridetetrahydrate (99%), vinylsulfonic acid sodium salt (technical,25% in water), 4-styrenesulfonic acid sodium salt hydrate(technical), acrylic acid (99%), potassium persulfate (99% ACSreagent), (ar-vinylbenzyl)trimethylammonium chloride (99%),and 3-acrylamidopropyltrimethylammonium chloride (75 wt%in water)were obtainedfrom Sigma-Aldrich andused as received.

Acetone, ammoniumhydroxide (29.7%in water),sodiumchloride,and sodium metabisulfate were obtained from Mallinckrodt andused as received.

Synthetic Procedure. Polymer Synthesis. A wide range ofrandomco-polymersof varyingcompositionand molecular weightwas prepared by aqueous free-radical polymerization of sty-renesulfonic acid, vinylsulfonic acid, and acrylic acid withpotassium persulfate as the initiator, as shown in Figure 1.Molecular weightwas controlled via chain transfer with sodiummetabisulfate, as described by Bokias et al.22 The reaction wasperformed as follows. Monomer (0.028 mol) was dissolved in

Milli-Q water, and0.37 mmol of potassium persulfate and0 -10.5mmol (typically 2.6 mmol) of sodium metabisulfate were added.The final volume was adjusted to 22 mL, and the mixture wasplaced in a sealed glass vial and heated to 80 Cfor 3 h. Cationicpolymers were made following the same procedure, with 0.007mol of acrylic acid and 0.021 mol of either 3-acrylamidopropy-ltrimethylammonium chloride or vinylbenzyltrimethylammo-nium chloride used as monomers.

Particle Synthesis. Themagnetic nanoparticleswere producedby chemical co-precipitation, as shown in Figure 2. In a typicalprocedure, 2.35 g of iron(III) chloride hexahydrate and 0.86 g ofiron(II) chloride tetrahydrate were added to 40 mL of deoxy-genated water. The deoxygenation was achieved by bubbling(19) Bagchi, P. J. Colloid Interface Sci. 1974, 47, 86-99.

(20) Napper, D. H.Polymeric Stabilization of Colloidal Dispersions;Academic Press: Orlando, 1983.

(21) Ditsch, A. P.: Lindenmann, S.; Laibinis, P. E.; Wang, D. I. C.;Hatton, T. A., submitted for publication.

(22) Bokias, G.; Durand, A.; Hourdet, D. Macromol. Chem. Phys.1998, 199, 1387-1392.

Figure 1. Polymer synthesis. The monomers are mixed inaqueous solution with potassium persulfate as a free-radicalinitiator, and sodium metabisulfite as a chain-transfer agent.The result is a random copolymer in which hydrophobicity(styrene sulfonic acid), attachment density (acrylic acid), andmolecular weight can be independently tuned.

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nitrogen through the solution in a vigorously stirred 100 mLthree-necked flask. The resulting Fe3+ and Fe2+ concentrationswere 0.22 and 0.11 M, respectively, resulting in therequired 2:1ratio for magnetite (Fe3O4) production. The nitrogen bubblingwasceased,and themixturewas then heatedto 80 C.A mixtureof 5 mL of 28% ammonium hydroxide and various amounts of

polymer dissolved in 5 mLof water,typically 7 mmol of monomerunits, was added to the three necked flask. The mixtureimmediately turned black, indicating the precipitation of mag-netite. After 15 min, additional polymer, typically 4 mmol on amonomer basis, was added to ensure complete coating of theexposed particle surfaces. The reaction was allowed to proceedfor 15 more minutes (30 min total) before cooling to roomtemperature. The magnetic fluid was then precipitated with50-100 mL of acetone, magnetically decanted, and resuspendedin 30 mL of Milli-Q water and sonicated for 30 s with a Bransonsonifier 450 at an output of 40%.

Molecular Weight Determination. Molecularweights weredetermined with a Brookhaven BI-200SM lightscattering systemusing the provided Zimm plot software at angles from 30 to150.The polymers weredissolvedat fiveconcentrations,typically2-10 mg/mL in 1 M NaCl to limit interparticleinteractions. Thesampleswerefiltered through a 0.22m syringe filter toeliminate

dust. Refractive indexes were determined for each polymercompositionand concentrationto enableanalysis of thescatteringdata to give the weight-averaged molecular weight. For eachmonomer composition studied, at least four different molecularweights were obtained at varying chain transfer amounts andfit to eq 1:

where XW is the weight averaged degree of polymerization, X0is thedegree of polymerization when no chain transfer is added,CS is the chaintransfer coefficient, [S] is themolar concentrationof chain transfer agent, and [M] is the total molar concentrationof the monomer.

Dynamic LightScattering. Dynamic lightscattering (DLS)experiments were performed with the Brookhaven BI-200SMlight scattering system at a measurement angle of 90. Theautocorrelation function was fit with an exponential fittingsoftware program to extract the diffusion coefficient, and theStokes-Einstein equation was used to convert the diffusioncoefficient to the hydrodynamic diameter. Intensity-averagedsize distributions were converted to volume-averaged andnumber-averaged sizedistributionsfor further analysis.Quotedparticle sizes are volume averages and are the average of fourmeasurements. Mostsamples werefiltered with a 0.45msyringe

filter to remove dust. If evidence of particles larger than thefilter pore size was observed, either by visually inspecting thefilter, or if the particle size distribution indicated that particlesgreater than 0.45 m were present, the measurement wasrepeated several times without filtering to obtain the true sizedistribution.

Electron Microscopy Measurements. Transmission elec-tron microscopy (TEM) experiments were performed on a JEOL200CX (200 kV) instrument. Samples were prepared by evapo-rating dilute suspensions on a carbon-coated film. The mediansizeand polydispersity of themagnetiteparticleswere determinedby visually measuring themajor andminor axes of 150 particlesand taking their averages.

Vibrating Sample Magnetometry (VSM). VSM measure-ments were performed on 30L samples of magnetic fluid usingan ADE 880 VSM instrument. The magnetic field was varied

from-

1 to 1 and back to-

1 T in steps of 0.05 T at roomtemperature to obtain the magnetization of each sample as afunction of the applied field.

Zeta PotentialMeasurement. Thezeta potentialsof particlesuspensions were measured on a Brookhaven ZetaPals ZetaPotential Analyzer. Particle suspensions were diluted to 0.005wt%Fe3O4 with0.1 M NaCl prior to measurement.Two millilitersof the sample were loaded into the electrode cell. The electro-phoretic mobility (e) of theparticles measuredover 25 electrodecycles was converted to the zeta potential () using the Smolu-chowski equation:

where and are the viscosity and dielectric constant of the

dispersionmedium,respectively. The quoted zetapotentialis anaverage of five measurements. Equation 2 is only valid when a. 1,24,25 where is theinverse Debye lengthand a is theparticleradius. As all samples were run in 0.1 M NaCl, with particleslarger than 70 nm, this condition was always satisfied since a> 100.

Stability Determination. Magnetic fluids were diluted to0.025 wt%in solutions of varioussodiumchloride concentrations,from 0.1 to 5.0 M, at increments of approximately 1 M, mixedwell with a vortex mixer, and left at room temperature for aminimum of 24 h. They were then mixed again and centrifugedfor 15 min at 4000 rpm in an Eppendorf 5810R centrifuge. Thehighest concentration at which no particle coagulation occurredwasnoted, andthe experiment wasthen repeated in incrementsof 0.1M NaCl to just above thehigheststable concentration. Thehighest concentration that resulted in no particle sedimentation

was reported as the critical coagulation concentration.

Characterization of Polymers and MagnetiteNanoparticles

In this section, we provide primary characterization ofthe polymers and the isolated magnetic nanoparticles. Adetailed discussion of the characteristics of the nanopar-ticle clusters and their stability is given in subsequentsections.

(23) Odein, G. Principles of Polymerization, 3rd Edition ed.; JohnWiley and Sons: New York, 1991.

(24) Hiemenz, P. C., Rajagopalan,R.Principlesof Colloid and SurfaceChemistry; Marcel Dekker: New York, 1997; Vol. 3.

(25) Hunter, R. J. Introduction to Modern Colloid Science; OxfordUniversity Press: New York, 1998.

Figure 2. Magnetic fluid synthesis. The magnetic nanopar-ticles are produced by chemical co-precipitation of iron salts inan aqueous solution of a limited amount of SSA/VSA/AAcopolymer. The resulting particles are clustered and notcompletelycoated.A second polymeraddition providescompletecoating,greatly stabilizingthe clusterswithoutaffectingclustersize.

1XW

)1

X0+ CS

[S]

[M](1)

)

e (2)

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Polymer Characterization. Thepolymersystem waschosen to allowindependent tuning of hydrophobicityandattachment density through selection of the relativemonomer fractions and of the molecular weight throughthe chain transfer agent concentration. Polymers with awide range of monomer compositions and molecularweights were synthesized.

Thehydrodynamic diameter of thepolymer in 1 M NaClsolution, obtained using DLS, correlated well with thetotal number of repeat units in thebackbone of thepolymer(XW) for all compositions synthesized, in agreement withpublished data for poly(acrylicacid),26 as shown inFigure3. The molecular weightfor a polymer composed of heaviermonomers, such as styrene sulfonic acid, will be propor-tionally higher for the same XW than one composed oflighter monomers, such as vinyl sulfonic acid or acrylicacid. Throughout this paper, therefore, polymers arecompared on the basis ofXW and not on molecular weight.

At high ionic strength, the polymer size scales withXW tothe 0.55 power and the polymer conformation is ap-proximately that of a random coil.26 Thus, in subsequentanalyses, the end-to-end distance and radius of gyration

are approximated by the known expressions for randomcoil polymers.TEM Size Distributions. The size distribution of

magnetic nanoparticles formed by chemical precipitationcan often be fit by a log-normal size distribution6,11

where Rc,med is the median core radius and c is the corepolydispersity. For the particles shown in Figure 4a-c,the median diameter is 7.5 nm with a polydispersity of0.26 as shown in Figure 4d. Due to the low contrastof thepolymers relative to that of the carbon substrate, only themagnetite cores can be seen in the micrograph. The

clusters observed in TEM measurements may simply beartifacts of the preparation method since the particlesmust be deposited on a grid and may be aggregateddifferently than when in solution. TEM cannot generallybe used to ascertainthe sizes of theclusters in suspension;DLS was used for this purpose. However, below a certainoverall particle concentration, the cluster size observedon the TEM grid was constant, which may imply that noadditional clustering or artifacts were introduced duringthe preparation of the TEM sample. Indeed, since thecluster sizes shown in Figure 4a and b for measurementsmade at low concentrations (


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basis, given by the slope of the magnetization curve at H) 0, is the volume fraction of particles, Md is thesaturation magnetization of bulk magnetite on a volumebasis, and H is obtained from the M ) 0 intercept of agraph of M versus 1/H at high applied fields. Thesaturation magnetization of the fluids in the limit as Hf can be determined from the intercept at 1/H ) 0 ofaplotofMversus 1/H; an averagevalue of63 emu/g Fe3O4wasdeterminedfor theparticles.The median size obtainedfrom this analysis was Dcore ) 6.4 nm and ) 0.35.

The core magnetization of our particles is lower thanthe saturation magnetization of bulk Fe3O4, 87 emu/g,12

butistypicalofthatforFe3O4 nanoparticles, which usuallyhave a saturation magnetization of 50-70 emu/g.6,9,12 Thelower magnetization is attributed to formation of anonmagnetic layer owing to disruption of the magneticmoments of atoms on the surface of the magnetite core.10

Usually, this nonmagnetic layer results in the magneticdiameter being significantly smaller than the TEMdiameter, as was seen in our analysis.

Zeta Potential Results. For magnetic nanoparticlesto be useful for charge-based separations, it is desirablethat they be strongly charged over a wide pH range, bothfor affinity for the targeted solutes and for stabilizationof the nanoparticles. The zeta potential of the particlesshows strongly negativelycharged surfacesfor allparticlestested over a wide range of pH, as shown in Figure 5. Forparticles with 25% acrylic acid groups, there is very littledependence of the zeta potential on pH, possibly becauseall the carboxyl groups are chelated with the surface Featoms on theparticles. Forparticleswith 50% acrylic acidgroups, there is a steady drop with pH in the magnitudeof the surface charge below a pH of 5, and a leveling outof the curves at higher pH, consistent with the deproto-nation of freecarboxyl groups (i.e., those not chemisorbedon the particle surfaces) of the poly(acrylic acid) withincreasing pH below its pKa. The salt concentration wasrelatively high, at 0.1 M, to ensure that the concentrationof protons, even at low pH, did not significantly affect theionic strength and to evaluate the surface charge at ionicstrengths similar to those found in fermentation broths,where the charged particles can be used for proteinseparations.7 Thus, the relatively low magnitude of theZeta potential (-30 mV) is due to the highly compresseddouble layer. The zeta potential of the same particles atlow ionic strength is around -50mV at neutral pH.

Clustering of Nanoparticles

The VSM and TEM results indicate that the magnetitecores produced by our synthesis method are typical ofthosemadeby chemical co-precipitation.It hasbeen shownpreviously16-18,21 that such nanoparticles are too small to

be recovered efficiently from the dispersion medium. Ifthese particles are to be useful for separations, they mustbe recoverable, which makes clustering of the nanopar-ticlesessential. Theclustersmust also be stableto furtheraggregation and sedimentation for practical use. We willshow in the following sections that several methods canbe used to create clusters sufficiently large for capture,but unless the clustering and stabilizing steps are de-coupled, the resulting clusters are not sufficiently stablefor many applications in which they are exposed to high-

ionic-strength environments. When a goodcoating polymerthat results in single nanoparticles is used in a limitedamount during synthesis to form clusters, the clusterscan be stabilized by later addition of a second polymer,resulting in extremely stable clusters of any desired size.

Effect of Primary Polymer Molecular Weight onCluster Size and Stability. Clusters were synthesizedwith excess polymer to evaluate the effect of molecularweight (from 2000 to as high as 300 000; XW from 15 to2500)on clustering. The clustering falls intothree distinctregimes, as shown in Figure 6a. When the polymermolecular weight is small, the size of the clusters is large,on theorderof 200nm. As themolecular weightincreases,the clusters decrease in size until a minimum is reachedatXmin, attributedpartially to enhanced stericstabilizationdue to the thicker polymer coatings on the primaryparticles; at this point, the particles are dispersedindividually and do not participate in cluster formation.With further increases in molecular weight, the polymerbegins to bridge between the particles and the clustersagain begin to form. Oncethe polymerbecomes sufficientlylargethat bridging predominates,the cluster sizeincreasesrapidly and the clusters approach a micrometer in size.Theselarge bridged clusters have a significantly differentmorphology from that of the large clusters formed withsmall polymers, as they are stable to centrifugation atmuch larger sizes, up to 800 nm as compared to 150 nmfor clusters formed with small polymers, and form muchmore viscous magnetic fluids at the same magnetitecontent. This indicates that the large aggregates consistmainly of an extended network of hydrated polymerbridges, with relatively low magnetitecontent, while low-molecular-weight polymers yield dense clusters of mag-netite nanoparticles.

Stability of Nanoparticle Clusters Formed WithExcess Polymer. The intrinsic stability of the nanopar-ticle clusters shown in Figure 6a was assessed bydetermining the critical NaCl concentration at whichcoagulation occurs. The cluster stability very closelymirrors the cluster size, with small clusters exhibitingthe greater stability, as shown in Figure 6b. The largerclusters formed at very low and very high molecularweights arenot stable, evenin 0.1M NaCl. Clusters formednearXmin are stablein 5 M NaCl(the highestconcentration

tested), with the maximum stability occurring withpolymers slightly larger thanXmin. However, these stableclusters are too small for efficient HGMS capture, whileclusters large enough for capture are not stable to highsalt concentrations. None of the clusters formed by usinga singlepolymer coatingwas both stable and recoverable,and thus, these clusters are not useful for separationprocesses. Thus, varying molecular weight of a singlecoating is notsufficient, and another methodof clusteringmust be utilized.

Effect of Polymer Composition on Xmin. As thefraction of SSA in the polymer increases, and thus alsoits hydrophobicity,Xmin increases sincemore hydrophobiccoatings provide poorer stabilization and thus require athicker coating to preventaggregation. This phenomenon

Figure 5. The zeta potential of particles as a function of pHfor two acrylic acid compositions. The zeta potential indicatesstrongly negative charges. When the acrylic acid content ishigher, the zeta potential is less negative at low pH due to theprotonation of acrylic acid.



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is examined in more detail below when we analyze theparticle-particle interaction energies on the basis ofsimple theoretical models of the clustering processes. To

verify that the observed effect was due to hydrophobicity,we synthesized copolymers of acrylic acid (25mol%) withthe cationic monomers vinylbenzyltrimethylammoniumchloride (VBTMAC) and acrylamidopropyltrimethylam-monium chloride (AATMAC). VBTMAC is more hydro-phobic and results in a higherXmin,as shownin Figure 6c.The effect ofXw on cluster size for the cationic particles

is similar to that for the anionic particles, indicating thatthe observed clustering behavior is due to the hydropho-bicity of the coating. When the results for all particleclusters are plotted in reduced form with D/Dmin as afunction of X/Xmin to account for differences in Xmin, asshown in Figure 6d, the data are represented ap-proximately by a single curve, further indicating thegenerality of the observed phenomena.

Effect of Attachment Group Density. The resultsshown above were obtained for excess polymer added tothe solution and depended only on polymer molecularweight and hydrophobicity, the latter as reflected in theSSA content of thepolymer. Theremainingfraction of thepolymer consisted of acrylic acid and vinyl sulfonic acid,the relative ratios of which do not affect the clusteringbehaviorunderthese excess polymer conditions for acrylicacid fractionsoverthe rangeof 20-75%.(whenthe fractionof acrylic acid is less than 20% or more than 75%, stableparticlesuspensions are not formed; thelatterobservationis consistent with published reports9,15 that PAA itself isincapable of stabilizing particle suspensions).

When the primary polymer molecular weight is nearthat corresponding toXmin, where individual particles arestabilized under excess polymer conditions, clustering ofthese particles can be induced by limiting the amount ofpolymer used or by limiting the fraction of attachmentgroups, i.e., acrylic acid, in the polymer; both strategieslead to incomplete coverage of the particle surfaces andhence some instability in the particle suspension to allow

clustering to occur. Within the range of 20-

75% acrylicacid, the cluster size is a function of the ratio of theconcentration of acrylic acid (chelating groups) to theconcentration of surface Fe2+ andFe3+ (chelated ions)andis independent of the fraction of acrylic acid relative toSSA and VSA on each polymer molecule. When nohydrophobic monomer is present (i.e., for copolymers ofacrylic acid and VSA only), the cluster size decreasesrapidly with increasing attachment group density formolar ratios less than 1.0 and reaches the single coatedparticle size at a ratio of about 1.5, as shown in Figure 7a.For polymers with some hydrophobic character, the clus-ter size starts at a smaller value, presumably due to thelarger polymer size and increased steric repulsion to core-to-core aggregation with incomplete coating. The size of

the clusters coated with more hydrophobic coatingsdecreases more slowly with addition of polymer, reachingthe single particle sizewith 2.5 acrylic acidgroups/surfaceiron ion.

Thestability of theclustersformedwith limited amountsof polymer mirrors the particle size, as shown in Figure7b.Since more than thestoichiometricamountof polymeris required to stabilize individual particles, the cause ofclustering is not an insufficient number of attachmentgroupsbutrather the rate atwhich theparticlesare coated(whichincreasesas theconcentrationof polymer increases)relative to the rate of core-to-core aggregation driven byattractive van der Waals forces. A model based on thismechanism is developed later. As was observedabove with

variations in the polymer molecular weight, only single

Figure6. (a)Clustersizeas a function ofpolymer size (numberof monomer units orXw) in the polymer backbone for polymers

of various styrene sulfonic acid content. The polymer size thatresults in the minimum cluster size, Xmin, increases as thecoating becomes more hydrophobic. (b) Critical coagulationconcentration of particles in (a). The maximum stability of theparticlesoccurs aboveXmin andbelow where significantbridginghas occurred, as shown by the dotted lines connecting themaximum stability to the cluster size in (a). (c) Cluster size vs

Xw for cationic polymer coatings, 75% vinylbenzyltrimeth-ylammonium chloride (VBTMAC) and 75% 3-acrylamidopro-pyltrimethylammoniumchloride(AAPTMAC) with25% acrylicacid. Xmin increases as the coating becomes more hydrophobic,similar to the anionic particles in (a). (d) Cluster size relativeto minimum size as a function ofXw relative to Xmin. When thedifferences in Xmin are accounted for, all particles fall onapproximately the same curve, further indicating that theobserved behavior is similar for allpolymers tested. Secondarybridging particles are bridged by later polymer addition.



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nanoparticles are stable when a single polymer coating isused in limited amounts, and thus, the particles are notwidely useful for separations. However, the instability ofthe clusters formed with limited polymer is not due to thenature of the coating, which is difficult to change, butrather due to the amount of the coating, which is easilychanged by further polymer addition, as will be outlinedbelow.

Cluster Stability and Requirement for SecondaryPolymer

We have shown above that there are many coatingsthat allow formationof clusters that are sufficientlylarge(>50 nm) to be captured by HGMS. These clusters are allstable in pure water due to strong surface charges andthe resulting interparticle electrostatic repulsion but notto moderate changes in ionic strength where chargestabilizing mechanisms break down. These clusters arenot, therefore, particularly suitable for use in separationprocesses performed in high-ionic-strength media. Weshow below that this instability problem can be overcomethrough the addition of a secondary polymer to complete

the coating of the surface sites left vacant because ofinsufficient primary polymer addition.Effect of Secondary Polymer Addition. In Figure

8a, we show the effect on cluster size of the addition of asecondary polymer, poly(acrylic acid), 15 min into theparticlesynthesis.The primaryparticles were synthesizedwith a 1:1 molar ratio of carboxyl groups to surface ironatoms, for which some initial clustering occurs to giveaggregates of 74 nm in diameter. The cluster size isessentially unchanged by the addition of the secondarypolymer when itsmolecular weightis small (


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If polymer with size of approximately Xmin is used inlimited amounts, clusters of controlled size are formed,

but the resulting clusters are also unstable. However, inthis case, the instability is not due to the nature of thecoating, which is difficult to change, but rather due to theamount of the coating, which can easily be changed byaddingmore polymer. With this insight, it follows directlythat the addition of a secondary polymer at a time afterthe clusters are formed should stabilize the clusters,without significantly changing the cluster size. This is infact the case, and the clusters thus formed are extremelystable, with critical coagulation concentrations in NaClin excess of 5 M, while clusters formed by other methodsall have critical coagulationconcentrations in NaCl below1 M, with many below 0.1 M. Without any change in thematerials used, the utility of the particles can be greatlyimproved by a small change in synthesis method.

Analysis of Clustering and StabilitysPredictionof Optimal Polymer

The clusteringbehavioroutlinedin the previous sectionwill now be examined by quantifying the particle interac-tion energies at the synthesis conditions. With thisinformation, we provide a method to predict the optimalsize polymer for stability (Xmin) when excess polymer isused. Then, we postulate a mechanism for cluster growthin the presence of limited polymer, allowing us to predicthow much polymer must be present at nucleation to geta desired final cluster size. The mechanism for growth ofthese clusters indicates the need for a secondary coatingto complete stabilization. Finally, we introduce methods

to predict the size of clusters that result when a polymercoating is used that is too small (Xw < Xmin) or too large(Xw > Xmin). The mechanisms used in predicting the sizeof clusters with nonoptimal polymer coatings provideexplanations for the relative instability of these clusters.With all the models, we are able to predict both the size

and relative stability of clusters resulting from differentpolymer coatings, and we find that it is advantageous touse multiple coatings to get clusters that are stable to awide range of solution conditions.

Prediction ofXmin (Excess Polymer). The first stepin predicting the optimal polymer coating is to find theoptimal polymer size when a large excess of polymer isused. In this section, we will outline a method based onDLVO theory that will allow prediction of Xmin from thesolution structure and hydrophobicity of the polymer.

Particle Interaction Energies. The clustering behaviorof the particles in the absence of bridging is dominated bythe interparticle interactions. For polymer-coated mag-netic particles, the primary forces are the long-range vander Waals interactions, electrostatic interactions, steric

interactions due to interpenetrating polymercoatings, andmagnetic dipole-dipoleinteractions. All theseinteractionscan be estimated as a function of the separation distanceof the particles. In the absence of an applied field, themagnetic dipole-dipole interactions are less than 1kT,and will thus be ignored in this analysis.14 Thus, it isprimarily the nature of the polymer coating that deter-mines particle-particle interactions by modulating the

van der Waals interactions between the cores, enhancingthe effect of the electrostatic interaction contributions,and providing steric repulsion when the polymer layersbegin to overlap.

The main attractive energy for the coated magneticnanoparticles is due to the van der Waals interactions,

with contributions from both the magnetite cores and thepolymer coatings.14 For a core-shell structure, the vander Waals interaction energy is given by28

where

(28) Vold, M. J. J. Colloid Sci. 1961, 16, 1.

Figure 8. (a) Particle size vs size of poly(acrylic acid) secondary polymer for aggregates starting at 74 nm. Minimal changes inparticle size areseen until the secondarypolymer becomes largerthan the primary polymer (primaryXw ) 85)abovewhich bridgingoccurs. This result verifies both that the particles are incompletely coated, allowing bridges to form, as well as that bridging canoccur much later in synthesis than clustering. (b) Cluster sizes obtained with 100 kDa PAA as secondary polymer for polymerswith various ratios of acrylic acid to surface iron. When a large excess of primary polymer is added, the cluster size still increasesbut to a lesser extent than when less primary polymer is added, indicating that bare surfaces are still presentbut to a lesser degree.

Figure9. Stabilityof particles formed withsecondary polymeradded.The total numberof attachment groupsrequiredto formstable clustersis similarfor particlesformed witha large excessof primary polymer and for those where stabilization is bysecondary polymer shown here. In contrast to when moreprimary polymer is added, the clustersize is not reduced whenadditional secondarypolymer is added, allowing stable clustersto be made.

-12uvdw ) (Am1/2

- Ac1/2)2H(s - 2d + 2;1) +

(Ac1/2

- Ap1/2)2H(sd;1) + 2(Am

1/2- Ac

1/2)(Ac1/2

-

Ap1/2)H(s

-

d;d +

d ) (6)



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and Ap, Ac, and Am represent the Hamaker constants forthe particles, coatings, and medium, respectively. Theparticle core surface-to-surface distance is s, the polymercoating thickness is , and the iron oxide core diam-

eter is d. For polymers with hydrophobic domains, theHamaker constant for the polymer layer is different fromthose for both the cores and the suspension medium. Forhydrophilic polymers, however, the Hamaker constantsfor the coating and the medium are essentially the same,so that only the interactions of the magnetite cores willcontribute to the attractive force between the particlesand the interaction energy will reduce to

The particles are coated by polyelectrolytes and thuswill be electrostatically repulsed. Theenergy of interactionbetween two charged spheres can be estimated using29,30

where h ) s - 2, is the surface potential of an isolatedparticle (approximately equal to the zeta potential of theparticle), is the inverse Debye length, is the dielectricconstant, and 0 is the permittivity of free space.

Layer Thickness Required for Stability. When there arehydrophobic domains in thepolymer, suchas the aromaticrings on styrenesulfonic acid, the Hamaker constant ofthe polymer isnot the same asthatof the aqueous medium.In this case, the van der Waals attractive force becomesstrong when the polymer coatings come in close contact.When the attractive forces dominate before the coatingscan touch, the steric interactions of the coatings are nolonger important and the problem reduces to a standardDLVO balance between van der Waals and electrostaticinteractions. In this case, increasing the layer thicknessresults in increased stability, due mainly to increasedelectrostatic repulsion with larger particle diameter, butalso due to reduced van der Waals interactions becauseof the lower Hamaker constant of the polymer relative tothat of the magnetite core. The Hamaker constants forthepolymer were estimated by assumingthat thepolymeris a binary mixture of water and polystyrene, where thetotal volume isthe volume in a sphere with a radius equalto the radius of gyration of the polymer and the numberof styrene molecules equal to the number of styrenesulfonic acid units in a single polymer, with the balancewater,as shown seeFigure 10a. Forthe cationic polymers,the Hamaker constants were evaluated on the basis ofthe number of hydrophobic carbons in the cationic repeatunit relative to those in SSA. Thus, each AAMTMACrepeat unit was assumed to be one-half of an SSA unitfrom the propyl group, and VBTMAC was assumed to beseven-sixths of an SSA from the extra methyl group.

Examples of the interaction energy profiles calculatedusing eqs6 and9 forpolymer layersof differentthickness,, having an effective Hamaker constant of A ) 2.3

10-22 J, near that estimated for 75% SSA, are shown inFigure 10b. When no coating is present, there is littlebarrier to aggregation. As the layer thickness increases,the activation energy for aggregation increases, bothbecause the polymer has a lower Hamaker constant thanmagnetite (4.810-21 J), and because the increasing sizeleads to increased electrostatic repulsion, assuming aconstant interfacial potential of ) -50mV. The layerthickness required for stabilization of the individualnanoparticlesagainst agglomerationis that for which theenergy barrier is at least 15kT.31 In the example given in

(29) Reiner, E. S.; Radke, C. J. Adv. Colloid Interface Sci. 1993, 47,59-147.

(30) Verwey, E. J. W.; Overbeek, J. TH. G. Theory of the Stabiliza-tion of Lyophobic Colloids; Elsevier: New York, 1948.

(31) Vold,R. D.;Vold,M. J. Colloidand Interface Chemistry; Addison-Wesley: London, 1983

H(x;y) )y

x2 + 2xy + x+

y

x2 + 2xy + x + y+

2 lnx2 + 2xy + x

x2

+ 2xy + x + y(7)

-12uvdw ) (Ac1/2

- Ap1/2)2H(sd;1) (8)

ue ) 20a()2

22 + (h/a)

exp(-h) (9)

Figure 10. (a) Schematic of method used to estimate layerthickness () and the Hamaker constant for the coating. TheHamaker constant is estimated by assuming that the polymeris a sphere with radius Rg,poly consisting of a binary mixture ofn styrene molecules (number of SSA repeat units in thebackbone)in a volume ofwater equalto thevolume ofthe sphere.

Thelayerthicknessisassumedtobe2Rg,poly or 7.5nm, whicheveris smaller. (b) Interaction energy for attracting polymers vs (constantHamaker constantA ) 2.310-22 J).When no coatingis present, there is little barrier to aggregation. As the layerthickness increases, the activation energy to aggregationincreases, both because the polymer has a lower Hamakerconstant than magnetite (4.8 10-21 J) and because theincreasingsize increases electrostatic repulsion. Ionicstrength) 0.7 M, ) -50 mV. (c) Comparison of Xmin for severalcompositions of styrenesulfonic acid (closed markers) and forthe SSA fraction that would result in the same hydrophobicityfor cationic polymers (open markers) with theXmin required foran energy barrier of 15kTwith Hamaker constant and of thatpolymer estimated as shown by the solid line, when is limitedto a maximum of 7.5 nm. If no max is used to account forcurvature of the particles, the fit fails at higher hydrophobicities(dashed line).



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Figure 10b, the required layer thickness for stability isabout 8 nm.At thesame ionic strength,this layer thicknesswill be less for more hydrophilic polymers with Hamakerconstants nearer that of water, owing to smaller van derWaals interactions. The height of the energy barrier is astrong function of the ionic strength of the medium,however, and decreases with increasing ionic strength,owing to an increased screening of the interparticleelectrostatic interactions. Thus, for practical applicationsinwhich the ionic strength is higher than that used in the

particle synthesis, should be larger than that requiredfor particle stabilization under synthesis conditions.

Effect of Molecular Weight on and Determination ofXmin. The interaction energy profiles calculated above canbe used to estimate the value of Xmin, the polymer sizethat yields individually coated single nanoparticles thatare stable against aggregation. For this purpose, thedependence of on the polymer molecular weight mustbe known. The layer thickness typically varies as twicethe radius of gyration, i.e., = 2RG, for relatively thinpolymer layers.20,32 For thicker layers, however, thecurvature of the particle will limit themaximum effectivethickness of the coating since the coating far away fromthe surface will tend to be diffuse and provide littlestability.32 We therefore assume that when RG > 1/2DP,the maximum effective layer thickness is simply thediameter of the particle, i.e., max ) 7.5 nm.

With the above assumptions on the composition de-pendence of the Hamaker constants and on the effectivelayer thicknesses, we can estimate the values ofXmin thatwill give energy barriers of 15kT for different polymercompositions, andreport these resultsin Figure10c.Theseestimates agree well with the experimentally determined

values of Xmin for a range of polymer compositionsexpressed in terms of the SSA content or, for the cationicpolymers, the equivalent SSA content. This simple resultindicates that the clustering below Xmin is due to aninsufficient layer thickness and contributions from thepolymer layers to the overall van der Waals interactionsbetween the particles. Thus, we are able to predict themolecular weight required for stabilization on the basisof only the composition of the polymer and the Hamakerconstants of the components, which may be useful as astartingpoint for evaluating the potentialefficacy of otherpolymers for use in stabilizing nanoparticle suspensions.

The maximum stability of the particles occurred withmolecular weights higher than the minimum required forstabilization of individual particles during synthesis,particularly for hydrophobic polymers since, while theseparticles may be stable at the synthesis conditions of 0.7M, a thicker coating is required for the particles to bestable at 5 M.

Prediction of Cluster Size with Limited Polymer(X) Xmin). On the basis of the particle-particle interac-

tions of well-coated particles,we postulate a model for theclustering of particles in the presence of insufficientpolymer. When the polymer is larger thanXmin, but smallenough that bridging is limited, it is expected that coatedsurfaces will not aggregate. However, if the coating is notcomplete, thebarrier for aggregation of uncoated particlesis lowand theaggregation would be expected to be limitedonly by diffusion and the fractional free surface availableto accommodate more polymer adsorption.

If we ignore the kinetics of nucleation and assume thatthecoresare initially7.5 nm uncoated magnetite spheres,we can analyzethe rateof aggregation as diffusion-limitedcolloidal aggregation(DLCA), modified with a probability

of aggregation less than unity, based on the degree ofcoating of the particles. The rate of particle aggregationin such a system will be24,25

whereMis thetotal numberof particles in a given volume, is the viscosity, and PM is the probability of a collisionresultingin aggregation.If a collisionof twobare surfacesresults in aggregation,whileno aggregation occurs if eithersurface is completely coated, the resulting probability is

where is the fractional particle surface inaccessible tothe polymer, either because it is already covered withpolymer or because it is blocked by other particle cores inthe cluster. If we assume that the particle has nm bindingsites, that eachpolymer can block nP sites, where nP isthetotal number of carboxylic acid groups on the backboneof the polymer, and the fractional coating is equal to thefraction of binding sites blocked, then can be calculatedfrom the rate of free polymer adsorption:

where P is the number of polymer molecules in a givenvolume, M0 is the number of magnetite cores initially inthe control volume, andP is the fraction of sites occupiedby adsorbed polymer. The fractional particle surfaceinaccessible to polymer includes both the binding sitesblocked by other cores and those already occupied by thepolymer, and can be approximated by

The rate of polymer disappearance will be related tothe diffusion-limited rate of collisions between magnetitecores and polymer molecules by33

whereRM is the radius of the aggregate core,RG,Poly is theradius of gyration of the polymer, and DM and DP are theparticle and polymer diffusion coefficients, respectively.Sincemagnetite has a pI of about 6, at the pH of synthesis(around 13-14), both magnetite and the polymer arenegatively charged and there will be an activation energy

barrier, Ea, for polymer adsorption.With the preceding equations, the number of particlesin a given volume can be calculated. All that is needed tocalculate the cluster size is to note that the aggregationnumber, or the number of cores in an average cluster, is

M0/M. Sincethe mechanism indicates core-to-corecontact,the core of the cluster will have a size of

whereDF is the fractal dimension of the cluster, expectedto be around 2.0 fordiffusion-limitedcolloidal aggregation.

(32) Aubouy, M.; Raphael, E.Macromolecules 1998,31, 4357-4363. (33) Adachi, Y. Adv. Colloid Interface Sci. 1995, 56, 1-31.

dMdt

) -(4kTM2

2 )PM (11)

PM ) (1 - )2 (12)

dpdt

) -(dPdt )(np

nmM0) (13)

) P +13(1 -

M

M0) (14)

dPdt

) -4(RM + RG,poly)2(DP + DM)(1 - ) e

-Ea/kTMP

(15)

DH ) DP(M0

M)1/DF

+ 4RG,poly (16)



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The size of the coating can be approximated as twice theradius of gyration of the polymer.

These equations were solved for different polymercombinations and fit to the experimental data shown inFigure 7a. The single adjustable parameter in the curvefitting was the activation energy for the polymer-coreinteraction, which was found to be 4.8kT. The fit of themodel is within experimental error for all but the largest

clusters formed with the larger, more hydrophobic poly-mers. When a larger polymer molecule coats the surfaces,the model assumption that clustering occurs until isunity will likelybreak downsincea partially coated surfacewill limit aggregation due to steric effects. The resultingclusters are not stable but can be stabilized with theaddition of smaller, secondary polymers that can accessthe uncoated sites on the particle surfaces. An importantresult of thesimulations is that theclustersize is predictedto be constant after a few milliseconds. Even if the timeprogression is off by several orders of magnitude, thisresult indicates that the cluster size is set well before theaddition of the second polymer at 15 min.

Complete Clustering Model for Excess PolymerAddition. The models presented above were developed

to predict the optimal polymer size (Xmin) and the amountof polymer at Xmin that must be present at nucleation toget the desired cluster size. Although of less importance,it is also of interest to understand the effects of excesspolymer concentration at all values ofX, both below andabove Xmin. In the Appendix, we derive models for thethree specific cases when excess polymer is added and (i)clustering occurs below Xmin, (ii) individual particles arestabilizedby polymers, and(iii) bridging occurs aboveXmin.

An example of the model predictions for the three differentregimes is given in Figure 11a, where it is shown clearlythat the system jumps from one regime to the next as thepolymer molecular weight increases. The model predic-tions are compared with experimental data in Figure 11bfor two polymers with different SSA content. The agree-

mentis remarkable,particularly consideringthe simplicityof the models used to describe these systems. Along withtheclustering model for limited polymer atXmin and thesemodels for clustering away fromXmin, the cluster sizes fora wide range of polymer coatings can be predicted withonly Ea and as fit parameters. The general method andequations should be applicable to a widerange of polymers,allowingrationaldesign of magneticnanoparticle clustersfor specific applications.

ConclusionsWe have introduced a new class of magnetic nanopar-

ticles with controllable cluster size and extreme stabilityin high-ionic-strength media. To obtain particles that areboth stable and can be captured using HGMS, an optimalmolecular weight polymer, nearXmin, was used in limitedamountsto get thedesiredclustersize followed by additionof a secondary hydrophilic, low-molecular-weight polymerfor stabilization. The resulting particles can be made toa desired size, when larger than 50 nm can be capturedinHGMS, and are stableovera widerange ofionic strengthand pH. Clusters of useful size and stability could not besynthesized with the use of a single polymer coating ofany composition or amount, but clusters of a wide range

of hydrophobicityand of both positiveand negativechargecould easily be made by decoupling the clustering andstabilizationsteps.This method shouldbe useful generallyin producing magnetic nanoparticle clusters for a widerange of uses.

The two parameters that are required to make thedesired size and stability are Xmin and the amount ofpolymer in the first coating. The optimum molecularweight (Xmin) can be estimated using standard DLVOanalysis with an estimated polymer Hamaker constantbased on the monomers used and the size of the polymerin solution. The size of the clusters can be estimated withDLCA kinetics modified with a sticking probability basedon fractionalcoating. Both of these approacheshave reliedon minimal fittedconstants andshould be usefulfor many

polymers. The use and optimization of these particles foruse in purification of recombinant proteins from fermen-tation broth is discussed elsewhere.34

Additionally, the cluster sizes obtained using nono-ptimal polymers, either larger or smaller thanXmin, havealso been predicted, with only one adjustable parameter.Both of the mechanisms developed indicate that thestabilityof clusters made with polymers larger or smallerthan Xmin will be strongly dependent on ionic strength,providing further verification of the need for decouplingof the coating and stabilizing steps.

Appendix

Effect of Nonoptimal Polymer on Cluster Size(ExcessPolymer). In theprevious sections, we developed

models to predict the optimal polymer size (Xmin) and theamount of polymer at Xmin that must be present atnucleation to get a desired cluster size. In this section, weprovide models to predict the cluster size both below andaboveXmin. With this information,not only canthe clustersize and morphology resulting from a coating of arbitrarypolymer be explained and predicted, but the relativeinstability of the clusters formed by such methods can beexplained.

Cluster Size Prediction below Xmin. Following theprocedures outlined earlier we are able to predict the sizeof clusters formed with polymers smaller than Xmin. The

(34) Ditsch, A. P.: Yin, J.; Laibinis, P. E.; Wang, D. I. C.; Hatton, T.A., in preparation

Figure 11. (a)Example of the predicted sizes below andaboveXmin. The three relevant sizes are the size that results in anenergy barrier of 15kT, the size of a primary particle, and the

size obtained when bridging occurs. The largest of the threesizes will be the actual size, as shown by the bold line. (b)Predictions for 0% and 75% SSA. Although the models aresignificant oversimplifications of the actualclusteringbehavior,both data setsare fitsemiquantitativelywith only as a globalfit parameter. (See Appendix for details of these calculations)



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interaction energy between fractal clustersand individualnanoparticles has been analyzed by by Shen et al.14 whoassumed that the clusters could be treated as equivalentspheres with constant surface potential and averagedHamaker constant based on the fractal dimensions of thecluster. They assumed that clusters grow until theenergybarrier for aggregation exceeds 15kT and were able toestimate the cluster sizes of surfactant-bilayer-coatednanoparticles, which were in good agreement with dy-namic light scattering, small angle neutron scattering,

andcryo-TEM studies. We apply their analysis to thecaseof our particles with thin polymer coatings (XW < Xmin)

Thevariationof theelectrostaticinteraction energy withinterparticle distance, s, can be approximated by asimplified form of the equations given by Hogg et al.,35 by

where Rcl is the radius of the cluster and Rp is that of theprimary particle. As Rcl increases, the electrostaticinteraction energyincreases, which accounts for the finitecluster sizes formed by primary particles coated withpolymers smaller than Xmin.

Similarly, we can approximate the van der Waalsinteractions by treating the particles and clusters asuniform spheres of constant effective Hamaker constant,

Aeff, according to

and where we assume that we can approximate the vander Waals interactions through a Hamaker constantaveraged over the particle cluster according to

where fis the volume fraction of particles in the cluster,which can be estimated in terms of the fractal dimensionthrough the equation f ) (Rp/Rcl)3-DF. The effectiveHamaker constant for the interaction of the particle withthe cluster depends on the particle density within thecluster, and in particular on the particle density near thecluster surface, as the void spaces are filled with solventand do not contribute to the particle/cluster interactions.Thelargersize increases the electrostatic repulsion of thecluster for a single particle, while the open structurereduces the effectiveHamaker constant. Whenthe clustersize becomes sufficiently large, the activation energybarrier to adding another particle becomes prohibitivelyhigh to permit further growth.

Substituting the new expressions for the interaction

energy of a cluster and primary particle and using theexpressions for and the Hamaker constant from theearlier discussions, we can calculate the cluster sizerequired for the barrier to reach 15kT. The mechanismdevelopedhereis strongly dependenton theionic strengthof the medium, indicating thatcoagulation in a high-ionic-strength medium is to be expected and that ultra stableclusters cannot be formed by simply using a polymersmaller than Xmin. The importance of the layer thicknessand hydrophobicity on the stability of the particles isevident in the extreme stability of clusters formed witha hydrophobic primary coating and a hydrophilic second-

ary coating. The hydrophobic primary coating results ina thicker coating, as evidenced by a later transition tobridging, while the secondary coating will tend to have amoreextended structure andwill dominatethe outer layerof the coating,36 lowering the coating Hamaker constant.Thus, both a thick coating and a reduced Hamakerconstant can be combined in a single particle.

Cluster Size from Bridging (X > Xmin). In the previoussections, the clusters formed by small polymers (below

Xmin) and limited polymer have been described. With the

insights of the kinetics of polymer adsorption from thelimited polymer clustering section, we can also predictthe cluster size due to bridging. Several expressions existfor the size of clusters formed by bridging.33,37,38 However,the existing models are designed to explain the behaviorwhen large polymers(on the order of 106 Da)of an oppositecharge to a colloid adsorb and cause flocculation, such asin wastewater treatment. In such a case, the amount ofpolymer in the system is much less than the amount ofcolloid; since bridging is mostefficient withpartialcoating() 0.5), the polymer adsorption has no significant energybarrier and coagulation occurs on a time scale similar toDLCA. None of these conditions is true in the caseexamined here; bridging occurs after coating is nearlycomplete since theratioof polymer tocolloidis muchhigher

than in the typically modeled case and is characterizedby a sizable activation energy for adsorption. The muchslower rate of bridging relative to coating in our systemis verifiedexperimentallyby theobservation thatbridgingcan be induced readily by the addition of a secondarypolymer 15 min into synthesis when a sufficiently largepolymer is used,while the core-to-coremodel predicts thatcoating will occur over a time scale of milliseconds. Thus,a new model for bridging which accounts for the size ofbridged clusters formed with nearly completely coatedparticles needs to be formulated to explain the observedbridging behavior.

As in the clustering model for polymers smaller thanXmin, we have assumed that bridging stops when theprobability of a bridge forming during a collision isconsistent with an energy barrier of 15kT. We then findthe cluster size by predicting theprobability that a bridgewill form during a collision. The probability consists oftwoparts: (i) that a polymer attached to a primary particlecan contact a magnetite core in a cluster and (ii) that thepolymer-magnetite collision will result in adsorption.

The probabilitythata collision of a particle anda fractalaggregate will result in the extended polymer reaching amagnetite core is equal to the number of layers that thepolymer tail can penetrate times the volume fraction ofmagnetite in that layer. This penetration is illustratedschematically in Figure12a. If we assumethat thepolymersize remains the same asin solution the lengthof the tailswill be 2Rg,poly, and the depth of penetration normalizedto the primary particle size is

whereDpen is thedepth of polymer penetration,Dpoly isthepolymer diameter, is thethickness of theinnerstabilizinglayer, which we have approximated as thelayer thickness

(35) Hogg, R.; Healy, T. W.; Fuerstenau, D. W. Trans. Faraday Soc.1966, 62, 1638.

(36) OShaughnessy, B.; Vavylonis, D. Phys. Rev. Lett. 2003, 90.(37) Healy, T. W.; La Mer, V. K. J. Colloid Sci. 1964, 19, 323.(38) Smellie, R. H.; La Mer, V. K. J. Colloid Sci. 1958, 13, 859.

ue ) 40( RpRclRp + Rcl)()2 ln(1 + exp(-s)) (A-1)

12uvdw ) AeffH( s2Rp;Rcl

Rp) (A-2)

Aeff ) (ApAcl)1/2

) fAp (A-3)

Dpen )Dpoly -

Dp)

2Rg,poly(XW) - (2Rg,poly(Xmin ) + -1)

Dp(A-4)



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atXmin plus the electrical double layer thickness, -1, andDp is the diameter of a primary particle. The probability,Pmag, that thepenetrating polymer tail reachesa magnetitecore is equal to the volume fraction of particles at theouter surface times the volume fraction of magnetite ina primary particle or

whereDcl is thecluster diameter,p is thevolume fractionof magnetite in a primary cluster, andDm is the diameterof the magnetite core. If we assume a fractal dimensionof 2.0 and that the primary particle size is the diameterof the magnetite core plus 2Rg,poly up to a maximum sizeof 22.5 nm, corresponding to a layer thickness of 7.5 nm,then we can calculate the cluster diameter directly. Theremaining component of the bridging probability is theprobability of adsorption after the polymer has come intocontact with a magnetite core. This probability equals

that of a binding site being open times the activationenergy of adsorption or

We assume that the activation energy for bridging is thesame as in the clustering model in the previous section,i.e., 4.8kT. is expected to be a value near to, but slightlyless than, unity since, although sufficient polymer hasbeen added to coat the entire magnetite surface, it wouldbe unfavorable entropically for all sites to be bound,particularly with polymers bound to multiple sites. Theexact value of is not easily estimated, and it is used asa global fit parameter on the assumption that it is thesame for all polymer compositions.

Combining the probabilities derived above and settingthem equal to thetotal probabilityequivalentto an energybarrier of 15kT, i.e., letting

we derive

All parameters in eq A-8 have been estimated above withthe exception of. Cluster diameters for particles formedwith all polymers having polymerization degree greaterthan Xmin are shown as a function of the polymerpenetration depth in Figure 12b together with thepredicted behavior for three different values of. Clearly,the data for all composition ratios, and for both anionicand cationic polymers, are correlated well by eq A-8 whenthe value of is 0.98. Thus, the mechanism indicatedseems to be general and useful for the range of polymersstudied here. The observation that even when a largeexcess of polymer is used there is still incomplete coatingexplains the lack of stability of bridged particles, par-

ticularly in high-ionic-strength media,. To ensure long-term stability, the use of polymers where 2Rg,poly < isdesired, so that bridging cannot occur.

Acknowledgment. This work was supported by theDuPont MIT Alliance. We would like to thank Yuki

Yanagisawa for his help in TEM measurements, VikramSivakumar (MIT, CSME) and Caroline Ross (MIT,CSME)for their assistance in VSM measurements, andSunil Jainand Mariam Kandil for their assistance in particlesynthesis.

LA047057+

Figure 12. (a) Schematic of bridging between a fractal

aggregate and a singleparticle, with the relevant length scalesindicated. The probability of a polymer attaching to a core inthe aggregate increases as the polymer size increases, anddecreases as the aggregate grows. (b) Size data used to fit .Thex axisis made upof all the terms in eqA-8 thatdiffer frompolymer to polymer, allowing a single fit to all data.

Pmag )DF

3 (

Dcl

Dp)

DF-3

pDpen )DF

3 (

Dcl

Dp)

DF-3

(

Dm

Dp)

3

Dpen

(A-5)

PAds ) (1 - ) e-Ea/kT (A-6)

PAdsPmag ) e-15 (A-7)

Dcl )

((

1

3)DFp(Dpoly - )(1 - ) e

15-Ea/kT

)

1/(3-DF)(A-8)


Controlled Clustering and Enhanced Stability of Polymer-Coated Magnetic Nanoparticles

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Transcript of Controlled Clustering and Enhanced Stability of Polymer-Coated Magnetic Nanoparticles