Nanoparticle Composition of a Ferrofluid and Its Effects on the

Langmuir 2004, 20, 2435-2444

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Nanoparticle Composition of a Ferrofluid and Its Effects on the Magnetic Properties K. Bu¨scher,†,‡ C. A. Helm,*,† C. Gross,§ G. Glo¨ckl,§ E. Romanus,§,| and W. Weitschies§ Institute of Applied Physics, University of Greifswald, Jahnstrasse 16, 17487 Greifswald, Germany, Institute of Physical Chemistry, University of Mainz, Welderweg 11, 55099 Mainz, Germany, Institute of Pharmacy, University of Greifswald, Jahnstrasse 17, 17487 Greifswald, Germany, and Institute of Solid State Physics, University of Jena, Helmholtzweg 5, 07743 Jena, Germany Received June 30, 2003. In Final Form: November 12, 2003 Experiments were carried out on a water-based ferrofluid (γ-Fe2O3 with carboxydextran shell) using photon correlation spectroscopy (PCS), atomic force microscopy, and magnetic nanoparticle relaxation measurements. The experiments were designed with the aim to relate the Neél signals that are in theory generated by large single core particles with nanoscopic properties, that is, particle size, particle size distribution, shell properties, and aggregation. For this purpose, the ferrofluid was fractionated by magnetic fractionation and size exclusion chromatography. Nanoparticles adsorbed onto positively charged substrates form a two-dimensional monolayer. Their mean core diameters are in the range of 6 to about 20 nm, and particles above 10 nm are mostly aggregates. The hydrodynamic particle diameters are between 13 and 80 nm. The core diameter of the smallest fraction is confirmed by X-ray reflectometry; the surface coverage is controlled by bulk diffusion. Comparison with the hydrodynamic radius yields a shell thickness of 3.8 nm. Considering the shell thickness to be constant for all particles, it was possible to calculate the apparent particle diameter in the original ferrofluid from the PCS signals of all fractions. As expected, the small cores yielded no Neél relaxation signals in freeze-dried samples; however, the fractions containing mostly aggregates yielded Neél relaxation signals.

Introduction Ferrofluids are colloidal solutions of ferro- or ferrimagnetic nanoparticles in a carrier fluid. Ferrofluids behave like liquid magnets; that is, in the absence of an external magnetic field the magnetic moments of the nanoparticles are randomly distributed, therefore, the liquid shows no net magnetization. When an external magnetic field is applied, the magnetic moments align in the direction of the external field lines, generating a net magnetic moment of the liquid like a ferromagnetic material. Thereby, the magnetic properties of ferrofluids can be compared with the behavior of paramagnetic molecules in a gas phase, while the magnetization is several orders of magnitude higher, due to the ferromagnetic nature of the nanoparticles. Ferrofluids are therefore often referred to as superparamagnetic.1 Ferrofluids are widely used in technical applications that are either mechanical (e.g., seals, bearings, and dampers) or electromechanical (e.g., loudspeakers, stepper motors, and sensors) in nature. Besides these technical applications, ferrofluids are gaining increasing interest for biological and medical applications (e.g., high-gradient magnetic separation techniques,2 magnetic drug targeting,3 magnetic hyperthermia,4 contrast agents for mag* Corresponding author: C. A. Helm, Institute of Applied Physics, University of Greifswald, Jahnstr. 16, 17487 Greifswald, Germany. Phone: +49 3834 864710. Fax: +49 3834 864712. E-mail: helm@ physik.uni-greifswald.de. † Institute of Applied Physics, University of Greifswald. ‡ Institute of Physical Chemistry, University of Mainz. § Institute of Pharmacy, University of Greifswald. | Institute of Solid State Physics, University of Jena. (1) Bean, C. P.; Livingston, J. D. J. Appl. Phys. 1959, 30, 120S. (2) Radbruch, A.; Mechtold, B.; Thiel, A.; Miltenyi, S.; Pfluger, E. Methods Cell. Biol. 1994, 42, 387.

netic resonance imaging (MRI)5) and for the determination of biological binding reactions by measurement of the relaxation of magnetic nanoparticles either by measuring the relaxation of the magnetization of the fluid6,7 or by optically determining the field-induced magnetic transient birefringence of ferrofluids.8 In mechanical or electromechanical applications, highly concentrated ferrofluids are commonly used, to obtain a “liquid magnet” with strong bulk magnetic properties, as a high saturation magnetization. In contrast, the bulk magnetism of the ferrofluid is only of minor importance in most medical and biological applications. Here, the properties of the individual nanoparticles contained in the fluid are more relevant, such as for example a high signal for nanoparticles used as contrast agents in MRI or a high magnetic moment for nanoparticles that are utilized as drug carriers in magnetic targeting or as a separation device in high-gradient magnetic separation techniques. However, the magnetic properties of the individual nanoparticle strongly depend on its volume, that is, the particle diameter, as well as on the shape. In principle, one can distinguish two mechanisms for the relaxation of magnetic nanoparticles: either diffusional rotation of the entire particle in a carrier liquid (Brownian relaxation) or the rotation of the core’s magnetic moment (3) Lu¨bbe, A. S.; Alexiou, C.; Bergemann, C. J. Surg. Res. 2001, 95, 200. (4) Jordan, A.; Wust, P.; Fa¨hling, H.; John, W.; Hinz, A.; Felix, R. Int. J. Hyperthermia 1993, 9, 51. (5) Pouliquen, D.; Perroud, H.; Calza, F.; Jallet, P.; Le Jeune, J. J. Magn. Reson. Med. 1992, 24, 75. (6) Weitschies, W.; Ko¨titz, R.; Bunte, T.; Trahms, L. Pharm. Pharmacol. Lett. 1997, 7, 5. (7) Ko¨titz, R.; Weitschies, W.; Trahms, L.; Semmler, W. J. Magn. Magn. Mater. 1999, 201, 102. (8) Romanus, E.; Gross, C.; Ko¨titz, R.; Prass, S.; Lange, J.; Weber, P.; Weitschies, W. Magnetohydrodynamics 2001, 37, 328.

10.1021/la030261x CCC: $27.50 © 2004 American Chemical Society Published on Web 02/11/2004

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Bu¨ scher et al.

Figure 1. Comparison of the dependence of Brownian (dotted line), Neél (straight line), and effective relaxation time (dashed line) on the particle diameter of spherical magnetic nanoparticles. Assumptions: K ) 20 kJ/m3, T ) 300 K, η ) 1 mPa s.

within the particle (Neél relaxation). This is illustrated as follows: The magnetic moment of a single-domain magnetic nanoparticle is proportional to the amount of magnetic material contained; that is, the magnetic moment increases with the particle volume and thereby with the third power of its diameter. The rotational diffusion time τB, attributed to Brownian relaxation, of a spherical particle is given by9

τB )

3ηVh kT

(1)

where η is the viscosity of the surrounding liquid, k is Boltzmann’s constant, T is the temperature, and Vh is the effective volume of the entire particle (i.e., Vh is the hydrodynamic particle volume in water). In contrast, the Neél relaxation time τN of the magnetic moment within the particle for particles with uniaxial anisotropy is given by10

τN ) τ0 eKVc/kT

(2)

where τ0 is a constant that is usually1 assumed to be in the range of 10-9 s and Vc is the volume of the magnetic core. K is the effective anisotropy constant resulting in a general case from shape and crystallographic and/or surface anisotropies. For magnetic iron oxide nanoparticles, the effective anisotropy mainly results from their shape anisotropy.11 Thereby, when applying an external magnetic field to a liquid containing magnetic nanoparticles, they will align in the direction of the magnetic field, creating as an ensemble a net magnetic moment. After the magnetic field is switched off, the net magnetization will disappear due to the statistical reorientation of the nanoparticles with an effective relaxation time τeff that is given by12

τeff )

τBτN τB + τ N

(3)

Thereby, the faster mechanism is dominating. This is illustrated in Figure 1, where the different relaxation times are plotted for spherical magnetic nanoparticles with a (9) Debye, P. Polar Molecules; Chemical Catalog Co.: New York, 1929. (10) Neél, L. Adv. Phys. 1955, 4, 191. (11) Fannin, P. C.; Kinsella, L.; Charles, S. W. J. Magn. Magn. Mater. 1999, 201, 91. (12) Shliomis, M. I. Sov. Phys.-Uspech. 1974, 17, 153.

core consisting of magnetite that are dispersed in water,13 assuming a uniaxial anisotropy for magnetite. Furthermore, for the sake of simplicity it is assumed that the hydrodynamic diameter and the core diameter are identical. The effective anisotropy of magnetic iron oxide nanoparticles has been determined to be in the range between 1 × 104 and 4 × 104 J m-3.14,15 Accordingly, an effective anisotropy of K ) 2 × 104 J m-3 was taken for the calculation. Obviously, the relaxation time of the magnetic vector is tremendously dependent on the particle core diameter: Below core diameters of ≈13 nm, Neél relaxation is faster; for larger particles in solution, Brownian relaxation dominates. Thereby, for any application where the relaxation behavior of immobilized particles is important, even small changes in the particle size might have dramatic consequences, since the Neél relaxation time increases exponentially with the particle volume. An obvious example is the use of such magnetic nanoparticles as storage material for magnetic recording, where the particles are fixed and only the Neél mechanism is possible. Here, recording media prepared from particles with a core diameter of 21 nm will lose the information (i.e., the magnetic orientation) in less than 20 s, while media using nanoparticles with a core diameter of 26 nm will keep the information for more than 800 years. The nanoparticles in ferrofluids produced by classical chemical syntheses display a rather broad particle size distribution.16 This size distribution may be due to variations of the core size, the thickness of the coating, or different stages of aggregation (Figure 2). In principle, the sizes of the magnetic cores may differ, while the thickness of the stabilizing coating remains constant (Figure 2a) or is also variable (Figure 2b). Furthermore, the individual nanoparticles may be aggregated resulting in stable aggregates with constant (Figure 2c) or variable (Figure 2d) thickness of the coating. Third, the particle sizes may also vary due to the agglomeration of coated nanoparticles with constant (Figure 2e) or variable thickness of the shell (Figure 2f). Unfortunately, the Neél relaxation time τN is not directly experimentally accessible. Actually, magnetization relaxation in most magnetic systems (powders, thin films, etc.) is not exponential, µz ∼ exp(-t/τN) ) exp(-t/(τ0 exp(E/ kT)), as one would expect under the assumption of a thermal relaxation over a single energy barrier E. According to the experimental evidence, magnetic relaxation can be described rather by a linear-logarithmic dependence, µz ) µ0 - S ln(t/t0), where the coefficient S is an experimentally determined constant, called magnetic viscosity. For magnetic systems, the explanation of such a linear-logarithmic behavior was first proposed in ref 17 and generalized in ref 18: such a behavior was attributed to the fact that in any real magnetic system there exist a distribution of energy barriers E, which leads to an exponentially broad distribution of the relaxation times τN (e.g., in a system of fine magnetic particles there exist a distribution of particle core volumes Vc on which τN depends exponentially because the energy barrier height in this case is E ) KVc (cf. eq 2)). (13) Ko¨titz, R.; Matz, H.; Trahms, L.; Koch, H.; Weitschies, W.; Rheinla¨nder, T.; Semmler, W.; Bunte, T. IEEE Trans. Appl. Supercond. 1997, 7, 3678. (14) Fannin, P. C.; Charles, S. W. J. Phys. D: Appl. Phys. 1991, 24, 76. (15) Fannin, P. C.; Charles, S. W. J. Phys. D: Appl. Phys. 1994, 27, 187. (16) Rheinla¨nder, T.; Justiz, J.; Haller, A.; Ko¨titz, R.; Weitschies, W.; Semmler, W. IEEE Trans. Magn. 1999, 35, 4055. (17) Street, R.; Wooley, J. C. Proc. Phys. Soc. A 1949, 62, 562. (18) Gaunt, P. Philos. Mag. 1976, 34, 775.

Nanoparticle Composition of a Ferrofluid

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Figure 2. Schematic illustration of possible particle distributions; in principle, the sizes of the magnetic cores can differ, while the thickness of the stabilizing coating remains constant (2a) or is also variable (2b). Furthermore, the size of the individual nanoparticles may be agglomerated resulting in stable agglomerates with constant (2c) or variable (2d) thickness of the coating. Third, the particle sizes may also vary due to the agglomeration of coated nanoparticles (2e,2f).

At the observation time t, only those particles whose relaxation time τN is close to t contribute to the relaxation; that is, τN ) τ0 exp(KVc/kT) ) τ0 exp(Ec/kT) ∼ t. Namely, only particles with barriers in a narrow interval ∆E ∼ kT around the so-called critical energy Ec ) kT ln(t/τ0) make a substantial contribution to the magnetic relaxation at the observation time t. Therefore, one approximates the critical energy Ec as the boundary between the already relaxed and not yet relaxed particles. The experimentally observed linear-logarithmic dependence of the magnetic relaxation is obtained when one assumes that the energy barrier density F(E) ) dN/dE (dN is the fraction of particles with the energy barriers in the interval [E; E + dE]) varies slowly in the energy interval corresponding to the measurable relaxation times (for the quantitative criterion see refs 17 and 19). One well-investigated system with a focus on single particles is synthetically produced gold colloidals.20,21 This is the temporary state of the art. So it was the aim of this study to describe the composition and size distribution of nanoparticles in a ferrofluid and to investigate their respective importance to the magnetic relaxation derived by the Neél mechanism. For this purpose, a water-based ferrofluid that is already used as a contrast agent in medical diagnostics was investigated by magnetic fractionation and size exclusion fractionation (FPLC) and characterized by photon correlation spectroscopy (PCS), X-ray reflectivity, atomic force microscopy (AFM), and Neél relaxation measurements. Materials & Methods Magnetic Nanoparticles. A water-based ferrofluid (Meito Sangyo, Japan) consisting of magnetic nanoparticles with a core of iron oxide (predominately γ-Fe2O3) and a shell of carboxydextran (Mw of around 2600 Da) was used (Figure 3a). The iron content of the bulk solution was 1.0 mol/L. (19) Berkov, D. V. J. Magn. Magn. Mater. 1992, 111, 327. (20) Schmitt, J.; Ma¨chtle, P.; Eck, D.; Mo¨hwald, H.; Helm, C. A. Langmuir 1999, 15, 3256. (21) Shipway, A. N.; Katz, E.; Willner, I. ChemPhysChem 2000, 1, 18.

Figure 3. Structure formulas of (a) carboxydextran and (b) PEI. Iron Analysis. The iron contents were determined using the chromophore o-phenantroline method.22 In brief, 200 µL of the sample was added to 1 mL of water and 500 µL of concentrated nitric acid. After heating to decolorization and cooling 10 mL of a freshly prepared solution of ascorbic acid (10% (m/m)), 30 mL of acetic buffer (12% (m/m)) and 10 mL of an o-phenantroline solution (0.2% (m/m)) were added and supplemented to 100 mL with water. After 10 min, the sample was spectroscopically characterized by measuring the absorption peak at a wavelength of 511 nm. The calibration curve was obtained using the original ferrofluid with a known iron concentration of 1 mol/L. Fractionation. High-Gradient Magnetic Separation. The ferrofluid was magnetically fractionated by stepwise reduction of a magnetic field generated by an electromagnet (Bruker B-MN 90/30) using magnetic separation columns (MACS Cell Separation Column LS, Miltenyi Biotec). The separation column was fixed between the pole shoes of the electromagnet and rinsed with 2 mL of phosphate buffered saline (PBS, 10 mmol/L phosphate, 130 mmol/L sodium chloride, pH 7.4). For the AFM investigations, the magnetic fractionation was performed as follows: 250 µL of the ferrofluid was added at a current of 4 A. Then, the column was rinsed with the buffer solution until the eluate was clear (4 A fraction). Thereafter, the current was reduced to 1 A and the next eluate was gathered. This procedure was repeated when 0.5, 0.25, 0.125, 0.06, 0.03, 0.015, and 0 A currents were applied. Then, the column was removed from the magnet and the remaining nanoparticles were eluted with water and gathered (22) Ja¨ger, E.-G.; Scho¨ne, K.; Werner, G. Lehrwerk Chemie: Arbeitsbuch 5, Elektrolytgleichgewichte und Elektrochemie; Deutscher Verlag fu¨r Grundstoffchemie: Leipzig, 1999.

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(fraction denoted as “washing solution”). This is necessary as the magnet generates a small remanent magnetic field, even when the applied current is zero. For a further investigation by PCS, an additional magnetic fractionation using a more diluted sample of the ferrofluid was performed. Here, 200 µL of the ferrofluid was diluted with 200 µL of PBS. After 24 h, the fractionation was performed using a new Cell Separation Column at currents of 6, 1, 0.5, 0.25, 0.125, 0.6, 0.3, 0.015, and 0 A and by washing out of the magnet, respectively. The particle sizes were again determined by PCS. Additionally, iron analysis was performed as described above. Size Exclusion Chromatography. Gel filtration was performed on a Fast Performance Liquid Chromatography (FPLC) system (Amersham Pharmacia, Uppsala, Sweden) using Superose 6 prep grade as the size exclusion column material and phosphate buffered saline as the eluent. A flow rate of 2 mL per minute was chosen. The eluate was gathered in fractions of 1 mL. The mean hydrodynamic diameters of the fractions were determined by PCS, and fractions with similar diameters were unified. Thereby, eight fractions and a final washing solution were obtained. Photon Correlation Spectroscopy. The hydrodynamic diameter of the nanoparticles as well as the polydispersity index were determined by PCS using a ZetaSizer 3000HS (Malvern, Germany). The measurements were performed at 298 ( 1 K with a 50 mW laser at a wavelength of 532 nm in an angle of 90°. The mean hydrodynamic diameters were calculated by the determination of the diffusion coefficient from the correlation function by Contin analysis.23 Surface Preparation. Nanoparticle monolayers were prepared on float glass (Rettberg GmbH, Germany) for X-ray experiments and quartz glass (Crystal GmbH, Germany) for UVvis measurements. The substrates were cleaned in piranha solution consisting of 50% H2SO4 and 50% H2O2 and hydrophilized by the RCA method.24 Ultrapure water was prepared by ultrafiltration (Milli-Q, Millipore, Germany). For AFM experiments, clean surfaces were obtained with freshly cleaved mica. All these substrates exhibit a negative surface charge,20 as does the carboxydextran coating of the nanoparticles. As expected from nanoparticles, which are electrostatically repelled from the surfaces, no nanoparticle adsorption onto mica is observed. Clearly, a positive surface charge is crucial. To achieve charge reversal for the chemically very different surfaces, surface functionalization with a nanometer-thick organic polymer layer was employed. The branched polycation poly(ethylene imine) (PEI; Mw ) 50 kDa, Aldrich, cf. Figure 3b) has proved to be an efficient first layer. The substrate is immersed for 20 min in a 0.003 monomol/L PEI solution and then washed in three successive beakers of clean water (soaking time, 1 min each). The thickness of the dried monolayer is about 0.5-1 nm.25 AFM Measurements. AFM measurements were performed with a Multimode equipped with a Nanoscope IIIa controller (Digital Instruments, Santa Barbara, CA) in the tapping mode in air. According to the supplier, the tip radius was 10-20 nm (Digital Instruments). The height of the particles can be determined with AFM within 0.2 nm, if contamination is avoided.26 Yet, it is important to note that the AFM images obtained of nanoparticle monolayers are rather misleading. The lateral particle radius appears to be larger than it is. The AFM image is obtained by convoluting the conical tip shape with the particle. This increases the lateral particle radius by 5-30 nm, depending on the particle height (cf. Supporting Information of ref 20). X-ray Measurements. Small-angle X-ray reflectometry experiments were performed with a Seifert XRD 3003 TT diffractometer (Seifert, Germany) using Cu KR radiation with a wavelength of 1.54 Å. This technique measures the interference between light reflected from the surface layer/air interface and from the substrate/layer interface. While the exact electron density profile necessary to simulate the reflectivity is a complex (23) Provencher, S. W. J. Chem. Phys. 1976, 64, 2772. (24) Kern, W. Purifying Si and SiO2 Surfaces with Hydrogen Peroxide. Semicond. Int. 1984, 7, 94. (25) Schneider, M.; Zhu, M.; Papastavrou, G.; Akari, S.; Mo¨hwald, H. Langmuir 2002, 18, 602. (26) van Noort, S. J. T.; van der Werf, K. O.; de Grooth, B. G.; van Hulst, N. F.; Greve, J. Ultramicroscopy 1997, 69, 117.

Bu¨ scher et al. function (cf. Supporting Information of ref 20), the average diameter 2R of the particles can be determined from the spacing of the interference minima ∆qz of the reflectivity curve according to

2R ) 2π/∆qz

(4)

UV-Vis Absorption Experiments. UV-vis absorption experiments with a nanoparticle solution or a nanoparticle monolayer adsorbed onto functionalized substrates were performed with a UV-vis Lambda 900 spectrometer (Perkin-Elmer, Germany). The extinction coefficient of the nanoparticles of a preselected fraction was determined by measuring the UV-vis absorption spectrum of a particle monolayer on a quartz glass substrate; simultaneously the surface coverage was determined by AFM. Then, the extinction coefficient at a preselected wavelength is determined according to the Beer-Lambert law,

log[I/I0] ) -c0d

(5)

with I being the transmitted and I0 the incident intensity, c0 the concentration, and d the thickness.27 At first, it seems counterintuitive that one can measure both the absorption of the bulk solution and the monolayer, because the two samples differ in thickness by almost 5 orders of magnitude (10 mm and 6-20 nm). Yet the samples differ in filling factors by 5 orders of magnitude; that is, a typical nanoparticle volume in a monolayer is 1000 nm2 × 10 nm ) 104 nm3 (average nanoparticle area multiplied by nanoparticle height). This value is to be compared with a volume per nanoparticle of 0.17 µm3 ) 1.7 × 108 nm3 in the bulk solution as calculated from a nanoparticle concentration of 10-8 mol/L. The corresponding values for c0d amount to 10-3 and 5 × 10-2 nm-2 for the monolayer and the bulk solution, respectively. These values differ by less than 2 orders of magnitude, which is small compared to the 3 orders of magnitude resolution of the spectrometer. Magnetic Nanoparticle Relaxation Measurements. For the determination of the magnetic relaxation signals according to the Neél mechanism, samples of the original ferrofluid were freeze-dried after addition of 5% mannitol (Fluka, Germany). During this process, water evaporation occurs which leads to particle immobilization. The additive mannitol acts as a constituent by forming a framework, that prevents the particles from aggregation. The relaxation signal was measured at room temperature using a measurement device described in detail elsewhere.28 In brief, the measurement system consists of a singlechannel second-order SQUID gradiometer as a magnetic sensor. The magnetization unit is realized by Helmholtz coils. The sample is magnetized for 1 s at 5 mT; then the magnetizing field is switched off, and after a lag time of 20 ms, that is necessary to switch on the SQUID electronics, the relaxing magnetization is measured for 1 s.

Results Characterization of a Nanoparticle Monolayer by AFM. An AFM image of the original sample is shown in Figure 4. For a reliable height profile, the tip must touch the substrate. Therefore, the surface coverage must be rather low. A suitable coverage was achieved by adjusting both the nanoparticle concentration and the absorption time. In Figure 4, the largest particles in the height scan cause the most severe damping in the amplitude scan, indicating that the short-ranged forces between tip and nanoparticles or substrate, respectively, are very similar, presumably just van der Waals forces.29,30 Furthermore, the spatial coincidence of maximum contrast in the (27) Atkins, P. W. Physical Chemistry; W. H. Freeman: New York, 1990. (28) Warzemann, L.; Schambach, J.; Weber, P.; Weitschies, W.; Ko¨titz, R. Supercond. Sci. Technol. 1999, 12, 953. (29) Chen, Y. L.; Helm, C. A.; Israelachvili, J. N. J. Phys. Chem. 1991, 95, 10736. (30) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: London, 1991.


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Figure 4. Height (left) and amplitude AFM images (right) of the original sample obtained in the tapping mode. Bottom left: Height profiles along the x-axis taken at lines A, B, and C as indicated in the height image. The particle heights were determined by the maximum heights found in the x-y scans.

height and amplitude images indicates that the sample is clean. As the particles are negatively charged, they repel each other and do not aggregate on the surface.20 Particles deviating strongly from a spherical shape are therefore interpreted as aggregates that were already present in the solution (“primary aggregates”). This is for example visible for the large particle in height scan C of Figure 4. Furthermore, the particles do not adsorb on top of each other, because they repel each other electrostatically.20 Therefore, structured height profiles that deviate strongly from a symmetrical shape are also strongly indicative for primary aggregates. This is illustrated in scans A and C of Figure 4, while in scan B of Figure 4 a 20 nm particle that is believed to be a single-core particle is depicted. A series of AFM-amplitude images of some of the fractions obtained by magnetic fractionation is shown in Figure 5. While in the AFM-amplitude image of the original ferrofluid before fractionation (Figure 5a) single nanoparticles and agglomerates are present, the nanoparticles gathered at 4 A are basically isolated particles with particle sizes between 4 and 10 nm and a mean diameter of 6.4 ( 0.9 nm. With decreasing current (Figure 5b-e), a growth in diameter up to a mean of 23 nm was observed (Table 1). Diameters above 10 nm were increasingly due to aggregates (Figure 5b-e). The histograms depicted in Figure 5g,h show the particle size distribution, together with a fit. For the size distribution of nanoparticles gathered at high currents, a Gauss

peak provided a suitable fit:31

y)

A

x2πσ

exp

[

]

(y - yc)2 2σ2

(6)

yc is the peak position, which corresponds to the mean particle diameter. A is a normalization factor, and σ is related to the half width at half-maximum (HWHM) of the peak according to

HWHM )

σ 4x2 ln 2

For the less symmetric particle size distributions, that is, those gathered at currents below 1 A, a log-normal function provides a more satisfying fit.

y)

A

x2πwy

[

exp -

]

(ln y - ln µ)2 2w2

(7)

A is again a normalization factor. The mean particle diameter corresponds now to yc ) e(lnµ+w2)/2, and the HWHM is replaced by the variance s, which is given by s ) e2lnµ+w2(ew2 - 1). Also, AFM measurements were performed with the chromatographically fractionated (31) Abramowitz, M.; Stegun, I. A. Mathematical Functions; Dover: New York, 1972.

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Figure 5. Amplitude images of nanoparticles unfractionated (a) and fractionated by a magnetic field with a current of (b) 4 A, (c) 0.125 A, (d) 0.015 A, and (e) 0 A; (f) washing fraction on mica/PEI. (g) Height histograms of nanoparticles fractionated in the magnetic field as indicated, together with a fit to a Gauss function (fractions gathered at 1 A and larger currents) or a log-normal function, respectively. (h) Height histograms of nanoparticles fractionated chromatographically, together with fits to a log-normal function.

particles, which were immobilized on the substrate according to the same procedure as described above. The AFM images are very similar to those shown in Figure 5a-f. However, the largest particles pass the chromatographic columns first (fraction I). The histogram of this fraction is depicted in Figure 5h. Fractions leaving the chromatographic columns later are correspondingly numbered, that is, fractions II, III, and so forth. The particle size distribution could be fitted with a log-normal function. In general, the variance of the size distribution is found to be larger than that of the magnetically fractionated particles (cf. Table 1). On decreasing the current during magnetic fractionation, larger particles are gathered. This trend is reversed for the chromatographic fractionation: the largest particles leave the column first. Yet, there are deviations (cf. Table 1), which may be due to tip contamination. For both methods, the washing fraction contains the largest particles which are mostly aggregates.

To confirm the particle size distribution found with AFM, the magnetically fractionated particles gathered at 4 A were investigated with X-ray reflectometry (cf. Figure 6). For maximum contrast, the highest particle coverage was chosen. Clearly, two interference minima can be distinguished. According to eq 2, the nanoparticle diameter is 5.9 nm, a value which agrees very well with the 6.4 ( 0.9 nm determined by AFM. PCS Measurements. The mean hydrodynamic diameters determined for the original ferrofluid and the fractions obtained by magnetic fractionation and gel chromatography are given in Table 1. The mean hydrodynamic diameter of the primary solution used for the fractionations investigated by AFM is 61.1 nm. The diameters of the fractions obtained by magnetic fractionation range from 13.4 nm for the first fraction (4 A) to 45.6 nm for the last fraction (0 A) and 65.9 nm for the washing solution, respectively. The mean hydrodynamic diameters of the fractions obtained by gel chromatography range


Langmuir, Vol. 20, No. 6, 2004 2441

Table 1. Mean Particle Diameters, Iron Contents of the Fractions, and Presence (+) or Absence (-) of Magnetic Relaxation Signals of Magnetically Fractionated Nanoparticlesa

sample original solution magnetic fraction

FPLC

4A 1A 0.5 A 0.25 A 0.125 A 0.06 A 0.03 A 0.015 A 0A washing solution fraction I fraction II fraction III fraction IV fraction V fraction VI fraction VII fraction VIII fraction IX washing solution

AFM: diameter (nm)

variance or HWHM, respectively

PCS: diameter (nm)

iron content per 100 µL original solution (µmol)

magnetic relaxation signal

14.8 6.4* 6.4* 15.6 9.1 10.0 11.4 15.1 11.7 21.4 22.6

5.4 0.9* 1.4* 3.9 2.4 10.9 4.6 5.1 5.0 11.0

61.1 13.4 15.0 19.0 22.3 29.3 35.8 40.7 44.4 45.6 65.9

100 4.2 9.5 8.0 5.1 5.4 4.8 5.0 2.5 1.1 22.3

+ + + + + +

31.6 28.6 22.5 19.0 18.0 15.3 7.7 8.1

19.0 16.9 5.3 7.8 4.1 7.1 3.4 2.1

32.3

9.2

105.9 82.4 66.0 51.9 41.1 31.2 23.6 19.4 37.4 65.7

4.4 12.5 8.5 6.9 15.0 16.2 23.9 21.9 5.4 4.4

+ + + + + -

a

The particle diameters are derived by PCS and AFM (including variance or HWHM as determined from log-normal fits or Gauss fits, respectively; values determined by Gauss fits are marked by an asterisk).

nanoparticles. To check this idea, the hydrodynamic diameter dh was determined by diffusion experiments. Relevant parameters for such experiments are the nanoparticle concentration c0 and the bulk diffusion constant D. The diffusion constant of a sphere in water with viscosity η is given by the well-known Stokes-Einstein equation:27

D)

Figure 6. X-ray reflectivity measurement of the nanoparticle layer magnetically fractionated at 4 A on glass/PEI.

from 19.4 nm for fraction VIII to 105.9 nm for fraction I. The hydrodynamic diameters of the fractions as determined by PCS are for the magnetic fractionation continuously increasing and for the gel chromatography continuously decreasing. Compared with the diameters determined in a monolayer in air by AFM, the PCS values are always larger (Table 1). In the magnetic fractionation, the main portion of iron was eluted with the washing solution (Table 1), indicating that the column was overloaded with magnetic nanoparticles. Therefore, we performed additional magnetic fractionations using smaller amounts of ferrofluid and we additionally diluted the ferrofluid 24 h prior to the separation using PBS. The results obtained are summarized in Table 3. Here, a mean hydrodynamic diameter of 55 nm was determined after 24 h of incubation in PBS. This indicates that the mean particle size decreases slightly during incubation in PBS which may be attributed to shrinking of the shell or to disaggregation. Adsorption Kinetics: Control of Surface Coverage. So far, the diameters of the nanoparticles gathered at 4 A are determined in air. They are a factor of 2 smaller than the 13.4 nm found with dynamic light scattering. The shrinking may be due to the dehydration of the carboxydextran shell, which in air collapses onto the

kT 3πηdh

(8)

For the early stages of the adsorption, one may assume that every particle that touches the surface sticks. Then we obtain the particle number density on the surface, Γ, with the following equation20,32 as a function of the adsorption time t:

Γ ) 2c0xDt/π

(9)

From eq 9 it is obvious that in the beginning of the adsorption process, the coverage should increase proportionally with the square root of the time, t. Yet, first we need to determine the bulk concentration c0. This is done with UV-vis absorption experiments. To determine the extinction coefficient of a nanoparticle (magnetically fractionated at 4 A), seven samples with different adsorption times were characterized (Figure 7). The surface coverage Γ was determined with AFM, and additionally, with the same monolayer, absorption experiments were performed. From that, at a wavelength of 372 nm, an extinction coefficient of ) 5.8 × 10-15 cm2/particle ) 3.6 × 106 cm2/mmol is found. This value is an order of magnitude larger than for a chromophore molecule with a strong transition but 2 orders of magnitude less than the one found for metallic nanoparticles.20 The simplest approach to determine the surface coverage is to image a sample with AFM and count the particles. For low adsorption times, the surface coverage increases with the square root of the time. This indicates that the (32) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain: Where Physics, Chemistry, Biology, and Technology Meet; VCH: Weinheim, 2001.

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Figure 7. Surface coverage as a function of the immersion time for the nanoparticles fractionated magnetically at 4 A. The surface coverage was determined by counting the particles in AFM images.

size of the adsorbing particles is very homogeneous. If different diameters dh occur in one sample, no square root dependence is found; for instance, it was impossible to describe the adsorption behavior of the primary solution with eq 9. From the extinction coefficient, the particle concentration is 6.1 × 1015 particles/L (1.01 × 10-8 M/L, respectively), with an error of 10%. The diffusion coefficient is D ) 2.3 × 10-11 m2/s, yielding a hydrodynamic particle diameter of 18.6 nm. This value is larger than the one derived from PCS measurements (13.4 nm). The deviation is due to the large error bars in the UV-vis method to determine the particle concentration. Note, however, that both PCS and diffusion measurements yield hydrodynamic diameters which are much larger than the thickness of the dry particles in air, as measured with AFM and X-ray reflectivity. Magnetic Nanoparticle Relaxation Measurements. The relaxation of the nanaoparticles was measured in the time window between 20 ms and 1 s. According to eq 2, Neél relaxation in this time frame should occur for particles with diameters in the range of 20 nm. However, such big homogeneous particles were never found with AFM, only aggregates. Due to the impossibility to determine the relaxation time τN of individual particles by measurements performed on a huge number of different particles,33 we only considered the presence or absence of magnetic relaxation signals (Table 1). Actually, according to AFM Neél relaxation is observed for immobilized particles with average core diameters exceeding 11-16 nm, that is, when aggregates are dominant. These are the particles obtained by magnetic fractionation if the currents were 0.06 A or less and the particles in fractions I-V obtained by FPLC. Discussion During magnetic fractionation, the nanoparticles are separated according to their magnetic moments. As the magnetic moment of a single-domain magnetic nanoparticle is proportional to the amount of magnetic material, that is, the volume of the magnetic core, only particles with very small core sizes pass the column at high magnetic field strengths, that is, high applied currents. By gel chromatography, the particles are separated according to their hydrodynamic diameters; therefore, large particles pass the column faster than smaller ones. Both mechanisms are confirmed by the AFM and the PCS measurements. The AFM images show that the larger nanoparticles are predominantly formed by aggregates of small particles. The observation that large particles are mostly aggregates of smaller ones is consistent with the log-normal size (33) Berkov, D. In Magnetism in Medicine; Wiley-VCH: Weinheim, 1999.

Bu¨ scher et al.

distribution observed for low-current magnetic fractions and the fractions gathered by FPLC. The comparison of the mean particle sizes determined by AFM and PCS further indicates that the mean diameters yielded by PCS measurements are larger than the diameters obtained by AFM. The AFM images of the fractions obtained at the highest currents during magnetic fractionation show single particles, reflecting the fraction of nonaggregated magnetic particles present in the original ferrofluid. Thereby, the 6.4 nm ( 0.9 nm determined by AFM for the 4 A fraction on the dry substrate in air represents the number distribution of the core diameters of nonaggregated single magnetic nanoparticles together with their collapsed shell of carboxydextran molecules. The 5.9 nm yielded for this fraction by X-ray reflectometry is in excellent agreement, especially if one assumes that the reflecting surface is the interface iron oxide to air. Thereby, X-ray reflectometry measures indeed the core diameter dc and the influence of the collapsed carboxydextran shell is too small to be resolved. PCS is performed in a liquid environment, and accordingly, PCS determines the hydrodynamic diameter of the nanoparticles, that is, the core together with the hydrated shell. The PCS-derived hydrodynamic diameter dh of the 4 A fraction was 13.4 nm; assuming that dh ) dc + 2r, the mean thickness r of the carboxydextran shell is about 3.8 nm. The smallest hydrodynamic diameter determined after gel chromatography was 19.4 nm, indicating that it was not possible to separate the nanoparticles as effectively as by magnetic fractionation. The shell consists of carboxydextran polymers; one chain has about 14 monomers of a length of 0.58 nm (according to ChemDraw), yielding a carboxydextran contour length of 8 nm. If one assumes water to be a theta-solvent and the persistence length identical to the monomer length, one would obtain a radius of gyration of 0.9 nm, that is, a brush thickness of 1.8 nm. However, this value is really a lower limit. Water is a good solvent for the sugar polymers. Furthermore, the anchor density is quite large, causing brush stretching. Furthermore, there are experimental considerations: In agreement with the definition of the hydrodynamic radius, neutron and X-ray techniques assume the brush ends when the decay of the segment density profile is steepest. However, light scattering focuses on the hydrodynamic radius, which is determined from the shear plane between polymer brush and water. The shear plane is further away from the grafting surface than the point of steepest decay of the profile, and therefore the hydrodynamic radius determined from light scattering is usually larger than the one from X-ray or neutron scattering.34 There is an additional effect to be considered: each sugar polymer carries one charge, and it is not known how the charge affects the thickness. The thickness of short polyelectrolyte brushes in low solvent conditions (i.e., ion concentrations below 0.1 mol/L) amounts to 5070% of the contour length,35,36 depending on the method. The shrinking of the brushes at high salt conditions (here provided by PBS) is observed with polyelectrolyte brushes. Taking all these considerations together, one may conclude that a carboxydextran thickness of 3.8 nm is a large value, but reasonable. Under the assumption that all fractions are monodisperse and consist of magnetic nanoparticles with one core (34) Eck, D.; Helm, C. A.; Wagner, N. J.; Vaynberg, K. A. Langmuir 2001, 17, 957. (35) Ahrens, H.; Fo¨rster, S.; Helm, C. A. Phys. Rev. Lett. 1998, 81, 4172. (36) Balastre, M.; Li, F.; Schorr, P.; Yang, Y. C.; Mays, J. W.; Tirrell, M. V. Macromolecules 2002, 35, 9480.


Langmuir, Vol. 20, No. 6, 2004 2443

Table 2. Contribution of the Fractions Obtained by the First Magnetic Fractionation to the Particle Sizes Weighted by Number and Intensity (dh6) (All Values Are Related to 100 µL of the Original Solution)

fraction

number of particles

4A 1A 0.5 A 0.25 A 0.125 A 0.06 A 0.03 A 0.015 A 0A washing solution sum

1.193 × 1015 1.422 × 1015 3.210 × 1014 9.606 × 1013 3.095 × 1013 1.247 × 1013 8.082 × 1012 2.899 × 1012 1.205 × 1012 6.577 × 1012 3.094 × 1015

a

contribution to contribution to particle size particle size in number in intensity distribution distribution / a // b dh,i (nm) dh,i (nm) 5.245 6.892 1.971 0.692 0.293 0.144 0.106 0.042 0.018 0.140 16

0.146 0.345 0.407 0.374 0.814 1.333 2.121 1.399 0.700 50.358 58

/ // dh,i ) dh,iNi/N. b dh,i ) dh,iIi/Isum.

of uncoated particles (aggregated or not) that is surrounded by a carboxydextran shell of 3.8 nm thickness, we calculated the number distribution, the volume distribution (weighting by r3), and the intensity distribution (weighting by r6) of the fractions obtained by magnetic separation based on the mean diameter measured by PCS (i.e., we assumed monodisperse fractions). Volume weighting was performed as the iron contents of the fractions are dominated by the volume distribution. Intensity weighting was performed as the PCS signal derived from particles with diameters far below the laser wavelength (here 532 nm) is generated by Rayleigh scattering, and accordingly the intensity of the signal derived from our particles depends to the power of six on the diameter of the particles. The PCS intensity of the original solution could be calculated from the respective contributions of the various fractions, according to the following procedure: (i) One starts with 100 µL of the nanoparticle solution. (ii) Fractionation and PCS measurements of each fractionation are performed, and with iron analysis the iron content is determined. (iii) From PCS measurements, the particle diameter dh,i of fraction i is calculated. Assuming that the particles have Fe2O3 cores and furthermore assuming that the shell thickness is 3.8 nm, the number of particles in the fraction is determined. (iv) The contribution to the overall PCS intensity of each frac6 (Ni is the tion is calculated, according to Ii ) Nidh,i M Ii is the number of particles in fraction i). (v) Isum ) ∑i)1 intensity of the original solution and M is the number of

fractions. Furthermore, the apparent particle diameter of the original solution is calculated, dh,sum ) M M // ∑i)1 (Iidh,i/Isum) ) ∑i)1 dh,i . The apparent particle diameter determined from the fractions agrees remarkably well with the one obtained in the actual measurements (cf. Tables 2 and 3). The mean diameter of the number distribution is 16 nm for the fractions obtained after magnetic fractionation. This value fits excellently the mean diameter of 15 nm determined for the primary ferrofluid by AFM. The mean diameter of the intensity distributions of the fractions is 58 nm. This value is very close to the 61 nm determined by PCS. Because the column was overloaded during the magnetic separation as could be concluded from the poor recovery of iron of about 70%, we repeated the magnetic fractionation using a higher dilution of the ferrofluid and, additionally, we waited for 24 h until the particle diameter was constant at 55 nm after dilution with PBS. Now, we had a nearly perfect recovery of 101% (Table 3). The particle diameters of the fractions were very similar to those from our first magnetic fractionation. The mean diameter of the number distribution was now 14 nm, and that for the intensity distribution was 55 nm. The PCS diameter of the “reconstructed” ferrofluid obtained by mixing all fractions was 53 nm; thereby it can be ruled out that the agglomerates found in the fractions had been formed during the fractionations or that they are artifacts derived from the preparation of the AFM samples. Despite the overloading of the column during the first magnetic fractionation, the same result was obtained, which supports our model. The data indicate that the particle shells are indeed constant for the different particles with a thickness in the range of about 4 nm in PBS, and the core size is rather polydisperse. Furthermore, the result demonstrates that the diameters determined by PCS are heavily dependent on the particle size distribution, due to the intensity averaging of PCS. This should always be kept in mind when interpreting PCS data. As an example, the U.S. Pharmacopeia (Pharmacopeial Forum, volume 24, 1998) describes the ferrofluid investigated by us as “a colloidal aqueous suspension of superparamagnetic iron oxide particles coated with carboxydextran. According to TEM electron microscopy measurements the iron oxide core has a diameter of 3 to 5 nm. The hydrodynamic diameter of the coated particles measured by PCS (photon correlation spectroscopy) is 45 to 65 nm. In the colloidal aqueous suspension, the carboxydextran coat has a thickness of about 25 nm (calculated from PCS measurements)”. The assumed shell thickness is an order of magnitude too

Table 3. Results of the Repeated Magnetic Fractionations (All Values Are Related to 100 µL of the Original Solution)

fraction 6A 1A 0.5 A 0.25 0.125 A 0.063 A 0.03 A 0.015 A 0A washing solution sum original fluid a

diameter dh,i by PCS (nm)

iron content (µmol)

number of particles

contribution to particle size in number / a distribution dh,i (nm)

contribution to particle size in intensity // b distribution dh,i (nm)

12.6 15.4 18.8 22.7 29.0 35.3 40.4 44.5 58.1 77.0

10.6 16.8 11.8 7.5 6.4 6.6 6.0 6.4 24.2 5.0 101.2 100

3.510 × 1015 1.647 × 1015 4.173 × 1014 1.125 × 1014 3.499 × 1013 1.695 × 1013 9.373 × 1012 7.097 × 1012 1.057 × 1013 8.417 × 1011 5.767 × 1015

7.669 4.398 1.361 0.443 0.176 0.104 0.066 0.055 0.106 0.011 14

0.221 0.422 0.432 0.436 0.753 1.445 2.055 3.061 29.479 16.858 55

55

/ // dh,i ) dh,iNi/N. b dh,i ) dh,iIi/Isum.

2444


large; the analysis of the PCS data is obviously a misinterpretation. The determination of Neél relaxation signals in the fractions within a time window of 20 ms to 1 s after switching off a magnetizing field showed that only the original ferrofluid and that in the fractions gathered below 0.06 A or before fraction VI, respectively, yielded magnetic nanoparticle relaxation signals in the experimentally accessible time window. This indicates that only these fractions contain particles with core diameters of about 20 nm as concluded from the theoretical considerations (see Figure 1 and eq 2). However, we did only very rarely observe such large single particles in the AFM images. This might indicate that either the signal is generated by aggregates of small particles or the aggregates contain such large cores. The first hypothesis is to our knowledge not discussed in theoretical physics and seems thereby not very realistic, while the alternative explanation is supported by theoretical calculations, where the presence of individual magnetic nanoparticles above a “critical” diameter in suspension is ruled out, due to the shortranged attractive magnetic forces they are generating.37 Thereby, particles with large cores might act due to their strong magnetic moment as a nucleus for the formation of aggregates during the particle synthesis. Smaller neighbor particles are attracted. During ferrofluid synthesis, the aggregate is finally stabilized by the formation of a carboxydextran shell that stabilizes the particle against further aggregation by steric and electrostatic effects. Conclusions

Bu¨ scher et al.

The fractions obtained by magnetic fractionation and size exclusion chromatography were characterized by AFM and PCS. AFM showed that the particle core sizes range from 6 to about 40 nm; the hydrodynamic particle sizes were between 13 and 80 nm. From AFM, it was concluded that larger particles are predominately aggregates formed by small cores that are often in the range of about 6 nm. This was also the mean core size of the fractions containing the smallest particles which constituted the majority of particles in the original ferrofluid. This predominant core size was confirmed by X-ray reflectivity. Its monodispersity was demonstrated by diffusion measurements. The comparison between the AFM data and the hydrodynamic data in PBS gives evidence for a shell thickness of about 4 nm which is considered to be constant for all particles. With this shell thickness, it was possible to calculate the apparent diameter in the original ferrofluid from the PCS signals of all the fractions. With respect to these data, the ferrofluid investigated consists predominately of isolated small particles and some aggregates. In agreement with theory, the small cores yielded no Neél relaxation signals in a time window of 20 ms to 1 s after switching off a magnetizing field. However, the fractions showing Neél signals were mostly formed by aggregates. Particles with core sizes of about 20 nm, as expected from theory, were hardly found. So far, we conclude that the Neél signals are generated by the aggregates. However, it remains unclear whether just many small aggregated cores generate the signal or it is due to the presence of large cores inside the aggregates, which served as a nucleation center for aggregation during ferrofluid synthesis.

The investigations were performed in order to relate the Neél signals that are in theory generated by large single-core particles (cf. Figure 1) with nanoscopic properties, that is, particle size, particle size distribution, shell properties, and aggregation.

Acknowledgment. We thank H. Ahrens for performing the X-ray reflection measurement, G. Papastavrou for discussing the AFM analysis, and P. Weber for supporting the magnetic relaxation measurements. This research project is supported by the Deutsche Forschungsgemeinschaft DFG: WE 2555/2-3, WE 2555/4-1, HE 1616/7, and HE 1616/10-1.

(37) Charles, S. W. In Studies of Magnetic Properties of Fine Particles and Their Relevance to Material Science; Elsevier: Amsterdam, 1992.

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Nanoparticle Composition of a Ferrofluid and Its Effects on the

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