Mechanistic Study on Magnetite Nanoparticle Formation by Thermal

Jan 18, 2011 - coprecipitation is very large as compared to the experimental aging time, resulting in incomplete coagulation, and hence formation of a...
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Mechanistic Study on Magnetite Nanoparticle Formation by Thermal Decomposition and Coprecipitation Routes C. Ravikumar and Rajdip Bandyopadhyaya* Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

bS Supporting Information ABSTRACT: The synthesis of poly (acrylic acid) [PAA]-coated superparamagnetic Fe3O4 nanoparticles was carried out in two ways, either by thermal decomposition of an organometallic iron precursor or by coprecipitation of aqueous solutions of ferrous and ferric chloride salts. PAA-coated particles obtained in the former route were spherical, isolated, and nearly monodisperse, whereas aggregates of coated particles formed in the latter route. A nanoparticle formation mechanism is proposed to explain such contrasting morphology. It is based on estimated time scales of different individual steps in the synthesis routes, diffusion of Fe3O4 nanoparticle over a PAA polymer chain, Brownian collision, and coagulation of particles and experimental aging time. We find that the coagulation time scale is smaller in the thermal decomposition route and is hence essentially complete within the experimental aging time. This results in formation of PAA-coated, isolated Fe3O4 nanoparticles. In contrast, the coagulation time scale in coprecipitation is very large as compared to the experimental aging time, resulting in incomplete coagulation, and hence formation of an aggregated morphology of particles.

1. INTRODUCTION Magnetic nanoparticles, especially magnetite phase of iron oxide (Fe3O4), is of great interest in the development of biomedical applications. Fe3O4 possesses a cubic inverse spinel structure, with only Fe(II) atoms occupying the tetrahedral sites, whereas the octahedral sites are equally occupied by Fe(II) and Fe(III) atoms. It forms a FCC closed packed structure with oxygen.1 In the particle size range 200 °C), especially by thermal decomposition of organometallic precursors in a nonpolar organic solvent.13,20 However, the use of hydrophobic coating agents, for example, oleic acid, oleylamine, etc., was earlier a limitation in thermal decomposition. Hence, particles could be dispersed only in an organic solvent. Further steps like surface modification of the coated particles and phase transfer were required to prepare the desired aqueous dispersion of coated particles. Recently, this problem too was overcome by the use of coating agents that are stable at high temperature and are biocompatible.21-23 Although particles synthesized from either route are being widely used, the particle formation mechanism leading to the two different contrasting morphologies is not understood. In fact, particle morphology plays a very important role in the cellular uptake pathway and its efficiency, by influencing the adhesion and interaction of the particles with the cells.24 For example, isolated, spherical Fe3O4 nanoparticles in the size range 25-30 nm and isolated gold nanoparticles of 50 nm were found to be in the optimum size range for enhanced nanoparticle uptake by different mammalian cells.25,26 Between the above two different routes, there may be significant differences in the operating variables like temperature, Received: June 9, 2010 Revised: December 15, 2010 Published: January 18, 2011 1380

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experimental aging time, particle size, solvent viscosity, molecular weight of polymer, etc. These in turn affect nanoparticle formation by altering the rates of each of the individual steps, adsorption of coating agent on a particle, diffusion of particle on a polymer chain, Brownian collision and coagulation of particles, etc. The relative rates (or in other words the characteristic time scales) of these steps in comparison to the experimentally followed aging time may explain the observed morphological difference in the final aqueous dispersion of coated nanoparticles synthesized. In this article, on the basis of time scale estimates of individual steps, a possible mechanism for these two different morphological outcome is developed, so that one can further optimize the synthesis condition of nanoparticles, depending on required particle size and morphology.

2. EXPERIMENTAL SECTION 2.1. Materials. All chemicals were reagent grade and used without further purification. Ferric chloride hexahydrate (FeCl3 3 6H2O), ferrous chloride tetrahydrate (FeCl2 3 4H2O), sodium salt of poly (acrylic acid) [Mw: 2100], iron(III) acetlyacetonate Fe(C5H7O2)3 [Fe(acac)3], and 2-pyrrolidone (C4H7NO) were purchased from Sigma Aldrich, and 25% ammonium hydroxide (NH4OH) from Qualigens was used. Deionized Millipore-Milli-Q water was used in all the experiments. 2.2. Methods. 2.2.1. Synthesis by Thermal Decomposition. This procedure can be found elsewhere.21,27,28 In a typical synthesis, 20 mL of 2-pyrrolidone (boiling point: 245 °C) was initially taken in a round-bottom flask, equipped with a stirrer and a condenser. 0.9 mmol of Fe (acac)3 and 0.4 mmol of PAA were added to the flask, and nitrogen was purged for 30 min to remove the dissolved oxygen present in the reaction mixture. The mixture was then heated to 210 °C for 30 min, followed by 40 min of reflux at 245 °C, and finally cooled to room temperature. Next, a 5:1 volume ratio of diethyl ether and acetone was added, to separate out the particles from the 2-pyrrolidone solvent. The particles were collected through magnetic separation (0.5 T permanent magnet), and then washed thrice with Millipore water to remove the unadsorbed PAA. Finally, the washed particles were dispersed in water and dialyzed for 3 days using 12 500 kDa cutoff cellulose membrane, to remove the residual, unadsorbed PAA. The final dispersion was stable for several months. To prepare uncoated Fe3O4 nanoparticles, the same procedure was followed in the absence of PAA. For the rest of this article, uncoated and PAA-coated Fe3O4 nanoparticles prepared through thermal decomposition route are denoted by samples A and B, respectively. 2.2.2. Synthesis by Coprecipitation. This too can be found elsewhere.19 For a typical synthesis, 0.9 mmol of FeCl3 3 6H2O, 0.45 mmol of FeCl2 3 4H2O (Fe3þ:Fe2þ = 2:1), and 0.4 mmol of PAA were added in a three necked round-bottom flask, containing 20 mL of water and equipped with a stirrer and a condenser. Using nitrogen, the mixture was purged for 10 min to remove dissolved oxygen and heated to 80 °C. Next, 25% (v/v) of NH4OH was added to the reactor at a rate of 5 mL/min, until the pH of the solution became 12. Addition of NH4OH results in the entire mixture becoming black colored, indicating formation of Fe3O4 nanoparticles. After 15 min of aging, the solution was cooled to room temperature, and the particles were collected through magnetic separation (0.5 T permanent magnet). The particles were washed thrice with Millipore water to remove the unadsorbed PAA, Fe2þ, and Fe3þ cations. Finally, the washed particles were

Figure 1. (a) Bright field TEM image of PAA-coated Fe3O4 nanoparticles (sample B), (b) AFM topograph of PAA-coated Fe3O4 nanoparticles (sample B), (c) bright field TEM image of PAA-coated Fe3O4 nanoparticles (sample D), and (d) AFM topograph of PAA-coated Fe3O4 nanoparticles (sample D). Inset shows HRTEM images of a single particle. Samples B and D were prepared through thermal decomposition and coprecipitation routes, respectively.

dispersed in water and dialyzed to remove the residual, unadsorbed PAA. The resultant dispersion obtained after dialysis was stable up to a month. The same procedure was followed in the absence of PAA. For the rest of this article, uncoated and PAA-coated Fe3O4 nanoparticles prepared through coprecipitation route are denoted by samples C and D, respectively. 2.3. Characterization Techniques. Transmission electron microscopy (TEM) was carried out with a JEOL-JEM 2100F, a field emission electron microscope, operated at 200 kV. For this, a drop of the dispersion was placed on a formvar coated copper grid, followed by drying the grid under IR lamp for 15 min. AFM of samples B and D were performed with Digital Instruments Nanoscope (IV) Multimode SPM. Drop casting of the stable dispersion was made on a cleaned mica substrate and dried under an IR lamp for 30 min. Powder diffraction of all samples were performed in PANalytical X’Pert Pro- XRD (X-ray diffractometer) with a dual goniometer, provided with Cu KR radiation. Prior to XRD analysis, the nanoparticles were dried in an air oven at 80 °C for 30 min. The average crystallite size, corresponding to the highest intensity peak (311) of the particles, was calculated according to Debye Scherer’s formula given below: o

DðA Þ ¼

Kλ β cosðθÞ

ð1Þ

where K is a constant equal to 0.89, λ is the X-ray wavelength (1.54 Å), β is the full-width at half-maximum (fwhm) of the (311) peak expressed in radians, and θ is the Bragg angle (deg) corresponding to that peak. Magnetic measurements of all samples were done in a SQUID magnetometer (Quantum design) at room temperature. To this 1381

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Figure 2. (a) XRD patterns of samples A-D, (b) selected area electron diffraction (SAED) pattern of sample B, (c) magnetization (with respect to Fe3O4) versus applied magnetic field of samples A-D, and (d) zeta potential versus pH of samples A-D. In (d), the lines joining the data points are drawn as a guide to the eye.

end, a few milligrams of the samples were dried at 80 °C for 30 min. Zeta potential was measured at 25 °C by Zeta Sizer NanoS (Malvern Instruments), equipped with a 4.0 mW, solidstate He-Ne laser of wavelength 633 nm. For this, individual dispersions were made by adding dry powder of 0.005 wt % of sample A to D in 0.1 M NaCl. The potential values reported are based on the Smoluchowski equation. Measurement duration was set to be determined automatically, and the data were averaged from at least three runs, with a standard deviation of 4 mV. Cyclic voltammetry of FeCl2 and FeCl3 solutions and solutions containing PAA was carried out in an electrolytic cell having reference electrode (calomel), working electrode, and counter electrode (platinum). 1 M KCl was used as an electrolyte, and measurements were carried out under N2 atmosphere.

3. RESULTS AND DISCUSSION 3.1. Morphology and Surface Characteristics of Nanoparticles. First, we discuss the experimentally obtained morphol-

ogy of PAA-coated Fe3O4 nanoparticles from both routes, followed by other characterizations. Figure 1a,c shows the bright field TEM images of samples B and D, with the inset showing lattice fringes from respective HRTEM images. In Figure 1a, particles of sample B are seen to be spherical, isolated, and nearly

monodisperse, having a mean size of 6 nm with a standard deviation (s.d.) of 1 nm. On the other hand, the morphology of sample D in Figure 1c is found to be aggregated in state. The mean particle size in sample D was found to be 8 nm with a s.d. of 1 nm. In addition to TEM images, the AFM topograph (Figure 1b) also shows that the coated particle morphology of sample B is isolated, whereas that of sample D (Figure 1d) is aggregated. Similar aggregates were observed in coprecipitation (images not shown), when PAA was added after particle formation was over (i.e., post coating), instead of in situ addition, as employed in this article. A detailed discussion on the mechanism leading to such contrasting morphology is given in later sections. Figure 2a confirms that the phase of the nanocrystal is Fe3O4, as the peak positions are the same as in the standard file (JCPDF card: 82-1533, Cu target) of bulk magnetite (Fe3O4), which is a cubic inverse spinel system having a face centered lattice. A vertical guide line to the eye is drawn, joining the (311) planes. Samples B and D (coated particles) in Figure 2a reveal that the presence of PAA did not alter the crystal structure of Fe3O4; only the peak intensities were less, as expected, due to the presence of amorphous coating agents. The calculated average crystallite sizes (from XRD) for samples A and C (uncoated particles) are 8.1 and 9.2 nm, respectively, whereas those of samples B and D are 7.2 and 6.4 nm, respectively. These values are close to the 1382

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The Journal of Physical Chemistry C mean particle sizes of 6 and 8 nm observed from TEM for samples B and D. The decrease in crystallite size for samples B and D from A and C (as observed in Figure 2a) is due to the addition of PAA during synthesis, suppressing further particle growth.14 The selected area electron diffraction (SAED) pattern of sample B acquired from Figure 1a is shown in Figure 2b. The presence of clear rings confirms that sample B is highly polycrystalline. The calculated d-spacing values corresponding to each plane in Figure 2b (from top to bottom) are 2.96, 2.58, 2.05, 1.69, 1.64, and 1.51 Å, which are in very good agreement with the standard (JCPDF card: 82-1533) file of bulk Fe3O4. A similar SAED pattern (not shown) was also observed for sample D. Figure 2c shows magnetization values of all samples (A-D) against the applied external magnetic field. The saturation magnetizations (Ms) of samples A-D are 60, 56.52, 65, and 21.53 emu/g of core Fe3O4 nanoparticle, respectively. All the samples showed immeasurable coercivity and remanence, proving that the particles are superparamagnetic in nature. The magnetization values of PAA-coated samples (B and D) have been corrected for the nonmagnetic contributions of PAA. This has been done on the basis of thermogravimetric analysis (TGA) (refer to Figure S1 of the Supporting Information). The decrease in saturation magnetization values in coated samples (B and D), as compared to uncoated samples (A and C), is likely due to smaller core particle size (due to reduced growth of core particles because of the presence of polymer), weak crystallinity, surface spin canting, surface disorder, etc.29 Zeta potential values of all samples (A-D) at various pH values are given in Figure 2d. We see that for samples A and C, the potential at pH 7.0 is almost zero, while both coated samples (B and D) show a large negative value, which further increases with increasing pH. This indicates that the coated particles acquire a negative charge. This is due to uncoordinated COOgroups of PAA present on the external surface of a particle. The large negative potential values (absolute value above 35 mV) for both samples B and D imply that the particles will have excellent stability in an aqueous medium due to repulsive, interparticle electrostatic force. Similar trend and potential values were also observed by Lin et al.19 Cyclic voltammetric experiments were carried out to determine whether adsorption of PAA takes place either with Fe2þ or with Fe3þ cations of the Fe3O4 nanoparticle. This was achieved by comparing measurements of aqueous solutions of FeCl2 and FeCl3, both before and after PAA addition. In a typical experiment, PAA was added to the aqueous solutions in a roundbottom flask, stirred under N2 atmosphere for 20 min, and then examined. Figure 3a shows the results. In Figure 3a, the voltammogram of FeCl2 solution shows a different trend before and after PAA addition, implying that the Fe2þ cations of FeCl2 coordinate with COO- groups of PAA. On the other hand, similar trends can be seen in FeCl3 solution before and after PAA addition, implying no coordination of Fe3þ with COO- groups of PAA. The same conclusion was reached based on our visual observation. In case of PAA added to FeCl2 solution, a wet, solid precipitate was seen at the flask bottom (Figure 3b), illustrating coordination of Fe2þ cations with the COO- groups of PAA. On the other hand, PAA added to FeCl3 solution showed no precipitate even after 1 week, implying the absence of coordination of Fe3þ cations with PAA (Figure 3c). This again confirms that only Fe2þ cations of Fe3O4 will coordinate and be adsorbed by PAA. This is possible because Fe2þ cation belongs to the d6 system and the calculated crystal field stabilization energy (CFSE) with

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Figure 3. (a) Cyclic voltammogram of iron salt precursors with and without PAA in 1 M KCl solution, done under N2 atmosphere. Round bottom flask showing (b) precipitate of FeCl2 and PAA at the bottom and (c) stable aqueous solution of FeCl3 and PAA.

intermediate strength COO- anion (of PAA) is 0.4Δ0. It adopts high spin state of the COO- ligand and attains more stability. On the other hand, the Fe3þ cation belongs to a d5 system, and its CFSE with COO- anion is zero, resulting in no coordination with PAA.30 3.2. Reaction Steps in Thermal Decomposition. These are given below following Li et al.21 Δ

FeðC5 H7 O2 Þ3 s f FeOOH

ðstep 1Þ

210 °C Δ

C4 H7 NO ð2-pyrrolidoneÞ s f C3 H7 N ðazetidineÞ þ CO 245 °C

ðstep 2Þ FeOOH þ CO þ PAA-Fe3 O4

PAA

Δ

s f

245 °C ðunadsorbed PAAÞ þ CO2 þ H2 O ðPAA-coated Fe3 O4 nanoparticleÞ

ðstep 3Þ

In step 1, iron(III) acetyl acetonate decomposes at 210 °C to the intermediate FeOOH. The FeOOH particles obtained in this step, as expected, were nonmagnetic. In step 2, on increasing reaction temperature to 245 °C, 2-pyrrolidone decomposes to form azetidine and carbon monoxide (CO). Simultaneously, FeOOH will be partially reduced by CO and leads to Fe3O4 (containing Fe2þ and Fe3þ) nanoparticle formation (step 3). Figure 4 shows XRD patterns of the product obtained at each of the reaction steps. The Fe3O4 nanoparticles then diffuse through the reaction medium and adsorb on the PAA polymer chains, through coordination of COO- groups of PAA with Fe2þ cations on the Fe3O4 nanoparticle surface (refer to cyclic voltammetry discussion, section 3.1). 1383

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where x is the root-mean-square distance of the polymer chain (end- to-end distance) and is equal to 0.6(Mw)1/2 (Å),35 Mw is the molecular weight of the PAA polymer, and D is the Stokes diffusivity of a Fe3O4 particle given by: D ¼

kB T 6πμs rp

ð3Þ

In eq 3, kB is Boltzmann’s constant, μs is the viscosity of solvent at temperature T, and rp is the radius of the particle. 3.4.2. Brownian Collision Time Scale of Particles (τc). This depends on Brownian collision rate (k c) and is given by ð4Þ τc ¼ 1=kc

Figure 4. XRD of the reaction mechanism involved in PAA-coated Fe3O4 nanoparticle formation by thermal decomposition. Step numbers shown in the figure refer to steps given in the reaction mechanism in section 3.2.

3.3. Reaction Steps in Coprecipitation. This is explained below.

2Fe3þ þ

ðFe2þ

8OH -

Fe2þ -PAA

cation coordinated with PAAÞ

þ FeðOHÞ2 f

s f 2FeðOHÞ3

PAA-Fe3 O4 ðPAA-coated Fe3 O4 nanoparticleÞ

þ 4H2 O

Before addition of NH4OH, Fe2þ cations in water form coordinate covalent bond with the COO- anions of PAA, based on conclusions from cyclic voltammetric experiments (section 3.1). After addition of NH4OH, COO- coordinates Fe2þ cations, as well as free Fe3þ cations, both of which react with the hydroxyl (OH-) ions of the NH4OH, and forms PAA-coated Fe3O4 nanoparticles along the chains of the PAA polymer itself. 3.4. Mechanism of Nanoparticle Formation from Time Scales. Time scale of an individual step in a synthesis process gives the approximate characteristic time for that specific step to complete. Thus, time scale analysis of an overall synthesis process delineates the slowest, and therefore the rate-determining step, among many concurrent steps. Several works exist on understanding the nanoparticle formation mechanism using time scale analysis.31-33 Time scale estimates of steps like adsorption of PAA on particles, Brownian collision, coagulation, etc., in both routes have been used to explain the contrasting Fe3O4 nanoparticle morphology synthesized in this work. Measured zeta potential shows that PAA has adsorbed on Fe3O4 nanoparticle surface. However, interparticle Brownian collision still occurs for all nanosized particles dispersed in a solvent, while coagulation of particles is important only when the particles are aged at elevated temperatures for longer times. Coagulation of particles in this case occurs due to solid-state diffusion of atoms of the colliding particles. 3.4.1. Diffusion Time Scale of Particle (Along a PAA Polymer Chain) (τd). Diffusion time taken by a Fe3O4 particle (τd) over a PAA polymer chain length (x) during adsorption is calculated by using the two-dimensional Einstein-Smoluchowski random walk equation34 as: τd ¼

x2 4D

ð2Þ

kc ¼ qo No

ð5Þ

8kB T 3μs

ð6Þ

and qo ¼

where kc is defined in Bandyopadhyaya et al.,36 qo is the Brownian collision frequency, and No is the total number of particles undergoing collision in a given volume. 3.4.3. Coagulation Time Scale of Particles (τcoal). To this end, first we calculate the time constant of coagulation (τ) following Ethayaraja et al.37 τ ¼

3 kB Tvp 64π γDs vm

ð7Þ

where vp is the volume of a Fe3O4 nanoparticle, Ds is the solidstate diffusivity, γ is the surface free energy of Fe3O4, and vm is the volume of one molecule of Fe3O4. Ds depends on temperature by Arrhenius form and is given as38   -E Ds ¼ Do exp ð8Þ RT where Do is the pre-exponential factor, E is the activation energy of diffusion, and R is the ideal gas constant. The time scale of coagulation of particles (with 99% volume conversion) is calculated from the time constant of coagulation as37 τcoal ¼ 3τ ð9Þ Table 1 shows the list of variables and their values used in estimating the time scales. Table 2 shows the time scales itself, their comparison with the given experimental aging time, and conclusions thereof. In the thermal decomposition route, time taken by Fe3O4 particles to diffuse over the PAA polymer chain is smaller as compared to the interparticle collision time (τd < τc). Further, the time taken by a PAA polymer chain to diffuse over a Fe3O4 particle, we found, has the same order of magnitude as τd. This implies that the adsorption of PAA on the Fe3O4 particles (limited by diffusion of particles and polymer) is faster compared to collision of particles. See the Supporting Information for approximate adsorption time scale. The time scale of coagulation (0.59 s) (which therefore is the rate-limiting step) is much smaller than our experimental aging time (40 min), implying that the PAA-coated Fe3O4 nanoparticles undergo 1384

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Table 1. Parameters Used for Time Scale Estimation value parameter -3

thermal decomposition

coprecipitation

source

No (no. m )

1.77  10

7.475  10

calculated

T (K)

518

353

experimental condition

rp (m)

3  10-9

4  10-9

observed from TEM

22

vp (m )

1.13  10

2.70  10-25

calculated

μs (kg m-1 s-1)

0.002 (a) (for 2-pyrrolidone)

0.00035 (b) (for water)

(a) extrapolated from data in ref 39; (b) from ref 40

3

-25

21

Table 2. Comparison of Time Scales

a

Ds is calculated from eq 8 using typical values for activation energy (E = 100 kJ/mol), pre-exponential factor (Do = 10-7 m2 s-1) b Refer to section 3.3.

Figure 5. Schematic of (a) isolated and monodisperse versus (b) aggregates of PAA-coated Fe3O4 nanoparticle formation involved in thermal decomposition and coprecipitation routes, respectively.

complete coagulation within the experimental period, resulting in particles to remain as individual, isolated particles, and not as aggregates. Experimental observation by Li et al.21 also showed a uniform increase in size of individual and isolated particles, upon increasing the experimental aging time. Figure 5a shows the event sequence in a schematic. In coprecipitation, in contrast, as discussed in section 3.3, the Fe3O4 particles form initially on the PAA polymer chain itself, so that a separate adsorption step of nanoparticles involving PAA does not take place. However, our experimental aging time of 15 min is far too less than the coagulation time scale (13.7 h), that is,

τa , τcoal, implying formation of aggregates of PAA-coated Fe3O4 nanoparticles, due to the absence of coagulation. Figure 5b shows this schematically. However, it should be also noted that during the early stages of particle formation, that is, during and after nucleation and intraparticle growth, coagulation of small particles can occur, leading to somewhat larger particles. However, the rate of coagulation is dependent on particle size, and at later stages of coprecipitation, as the particle size becomes larger, coagulation slows down and stops. This is reflected in the large value of coagulation time scale for 8 nm diameter particles, as reported in Table 2. 1385

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4. CONCLUSIONS In the present work, PAA-coated Fe3O4 nanoparticle was synthesized by both thermal decomposition and coprecipitation routes. XRD showed that the coated particles were Fe3O4. From TEM and AFM images, individual, isolated Fe3O4 nanoparticles or aggregates of particles were observed for thermal decomposition and coprecipitation, respectively. To understand the morphological difference, we have proposed a mechanism for each route, based on estimated time scales of several steps like diffusion of Fe3O4 nanoparticle over a PAA polymer chain, Brownian collision, and coagulation of particles and on their comparison with the experimental aging time. In thermal decomposition at high temperature, the time scales of diffusion of Fe3O4 nanoparticle over a PAA polymer chain, as also Brownian collision and coagulation of particles, were found to be smaller than the experimental aging time of 40 min [2400 s]. As a result, coagulation between particles that have collided together is complete within the experimental period and results in the formation of final particles in individual, isolated form. On the other hand, in coprecipitation, the estimated time scale of coagulation of particles (13.7 h) [49 320 s] is much larger than the experimental aging time of 15 min [900 s]. Hence, aggregates of PAA-coated Fe3O4 nanoparticles were found due to absence of coagulation. Therefore, thermal decomposition is superior in achieving isolated and monodisperse Fe3O4 nanoparticles, for effective biomedical applications. ’ ASSOCIATED CONTENT

bS

Supporting Information. TGA of samples A-D, and approximate estimate of polymer adsorption time scale. This material is available free of charge via the Internet at http://pubs. acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Phone: 91-22-2576-7209. Fax: 91-22-2572-6895. E-mail: rajdip@ che.iitb.ac.in.

’ ACKNOWLEDGMENT We gratefully acknowledge the sophisticated analytical instrumental facility (SAIF) of the Indian Institute of Technology Bombay for providing TEM and AFM facilities. We gratefully thank Mr. Venugopal, Research scholar, National Chemical Laboratory (NCL), Pune, India, for XRD measurements and Professor A. Q. Contractor and Miss. Chetana B. Saparia, Department of Chemistry, IITB, for cyclic voltammetry measurements. We also thank the Department of Science and Technology, India (DST) [no.: SR/ S3/CE/049/2007], for providing financial support for the work. ’ GREEK SYMBOLS D diffusivity of a Fe3O4 particle in a solvent, m2 s-1 Ds solid-state diffusivity of Fe3O4, m2 s-1 Do pre-exponential factor, m2 s-1 E activation energy of diffusion, kJ mol-1 kB Boltzmann constant, 1.3806  10-23 J K-1 kC Brownian collision rate of Fe3O4 particles, s-1 Mw molecular weight of PAA, 2100 g mol-1 No number of Fe3O4 nanoparticles per unit volume of system, number m-3

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R ideal gas constant, 8.314 J mol-1 K-1 rp radius of Fe3O4 nanoparticle, m qo Brownian collision frequency of Fe3O4 particles, s-1 T temperature, K νm volume of one Fe3O4 molecule, 7.43  10-29 m3 νp volume of one Fe3O4 nanoparticle, m3 μs viscosity of solvent, kg m-1 s-1 γ surface free energy of Fe3O4, 0.1 J m-2 τ time constant of coagulation, s τc time scale of Brownian collision of particles, s τcoal time scale of coagulation of particles, s τd time scale of diffusion of Fe3O4 particle over PAA, s

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