J. Phys. Chem. C 2008, 112, 7599–7604
7599
Assembly of Superparamagnetic Nanoparticles under Unidirectional External Magnetic Flux: Experimental and Model Establishments K. F. Cedric Yiu,† Chih Hao Yu,‡ Huili Tang,§ Heyong He,§ Shik Chi Tsang,*,‡ and Kin Y. Tam*,| Hong Kong Polytechnic UniVersity, Department of Applied Mathematics, Hung Hom, Kowloon, Hong Kong, People’s Republic of China, UniVersity of Oxford, Inorganic Chemistry Laboratory, South Parks Road, Oxford, OX1 3QR, United Kingdom, Shanghai Key Laboratory of Molecular Catalysis and InnoVatiVe Materials, Fudan UniVersity, Shanghai 200433, People’s Republic of China, and AstraZeneca, Mereside, Alderley Park, Macclesfield, Cheshire, SK10 4TG, United Kingdom ReceiVed: January 10, 2008; ReVised Manuscript ReceiVed: February 15, 2008
Recent development in assembling nanoparticles as building blocks into macroscopic functional structures or devices to harness the size-dependent properties of individual particles is an exciting new direction. Here, it is demonstrated that well-dispersed silica- encapsulated superparamagnetic FePt nanoparticles in solution can be assembled into high-quality, needle- or rod-shaped solid-state supercrystals by applying inhomogeneous external magnetic field together with controlled evaporation. By use of an aggregation model based on the population balance equation technique, this charactersitic morphology of the magnetic asembled crystals can be successfully derived. 1. Introduction One of the main challenges in nanotechnology is to find ways of synthesizing basic nanosize building blocks (bottom-up approach) and assemble them as functional bulk materials not only with the right composition but also having the same size, shape, and patterns. These could provide the basic construction modules in the materials assembly over all scales, a new way of manufacturing electronic, optical, photonic, magnetic, and catalytic functional devices.1–3 Interactions between nano building blocks determine the geometry and distances at which building blocks come to equilibrium in a bulk system. Relative motion between building blocks facilities collisions between them, while energetically allowed aggregation/deaggregation processes and corrective movements of the assembled structure will allow it to attain the most stable form. Provided the building blocks are not too strongly bound in the assembly, it will be able to adjust to an orderly structure. Thus, dynamic effects involving building blocks and assemblies can occur in the liquid phase, at an air-liquid or liquid-liquid interface on the surface of a substrate or within a template coassembly.4,5 The common forces responsible for material assembly at length scales beyond the molecular include capillary, colloidal, elastic, electrostatic, and shear interactions, etc. However, assembly of magnetic nanoparticles as designated ordered/patterned aggregates under inhomogeneous magnetic flux has not been extensively explored despite the fact that this may provide new ways of assembling complex 3-D or hierarchical patterns. One key criterion is that nanoparticles as the building blocks in solution should display superparamagnetism which means that the particles are attracted to a magnetic field but themselves retain no residual magnetism after the field is removed.6 Because * To whom correspondence should be addressed. Phone: +44 (0)1625 230338. E-mail:
[email protected]. † Hong Kong Polytechnic University. ‡ University of Oxford. § Fudan University. | AstraZeneca.
of the extremely small size, properties of these magnetic nanoparticles could be very different from the corresponding bulk material. For instance, magnetic anisotropy, which keeps a particle magnetized in a specific direction, is proportional to the volume of the particle. As the size of the particles decreases the energy associated with the magnetic interactions between particles decreases until thermal energy is sufficient to overcome any preferential orientation of the magnetic moment in the particle. Therefore, suspended individual superparamagnetic particles can be flexibly assembly from solution into designated pattern(s) using an external magnetic field of controllable intensity and direction, before they are preset or molded as solidstate materials on substrate or template. Chemical synthesis of colloidal stable core-shell magnetic nanoparticles could be promising building blocks for this type of assembly. Encapsulation of a wide range of nanosize magnetic materials in silica,7 carbon,8 mesoporous oxides,9 Ti/ SiO2,10 etc. have been recently demonstrated. The shell or external coat is expected to offer the magnetic nanoparticle a physical barrier against uncontrolled aggregation or magnetic perturbation from each other in a close proximity enabling their assembling into ordered array structure with possibly tailored interparticle spacing on a thin supporting film. A strong chemical attachment of the nanosphere to the film can even be designed through specific surface reaction(s).11 Xiong et al. also developed a polymer-assisted magnetic-field-induced assembly to prepare legumelike structures of Co nanoparticles.12 Such core-shell superparamagnetic nanoparticles have potential for many applications in biomedical and catalysis areas.13–15 Recently, Wu et al. has reported an interesting investigation on the effects of external magnetic field on the biodistribution of magnetic nanoparticles, which clearly demonstrated the potential for using magnetic nanoparticles as a drug carrier.16 Depending on the applications, aggregating of magnetic nanoparticles induced by external field may either be required or needed to be avoided. Hence, an understanding of the assembly kinetics and mechanisms would not only help to design colloidal stable magnetic
10.1021/jp800310x CCC: $40.75 2008 American Chemical Society Published on Web 04/19/2008
7600 J. Phys. Chem. C, Vol. 112, No. 20, 2008
Yiu et al.
SCHEME 1: Schematic Diagram Depicting the Growth of Three-Dimensional Core-Shell SiO2-Encapsulated FePt Colloid Crystals under a Unidirectional Magnetic Flux (Extended Magnetic Plate Underneath)a
a The black arrows indicate stacking of the uniform particles into colloid crystals along with the direction of the external magnetic field, and the gray arrows show the gradual evaporation of the ethanol solvent molecules.
nanoparticles but also enable the assembly process to occur in a predictable manner. Following our previous paper reporting a simple synthesis of silica-encapsulated nanosize FePt (a superparamagnet) by microemulsion technique,17 here we report the detailed experimental work of assembling these superparamagnetic nanoparticles in a microscopic compartment under a strong unidirectional magnetic flux (using an extended flat permanent magnet underneath the reactor tube) where the changes in particle size and morphology were monitored. It is interesting to find that the particles are assembled into needle-shaped crystals under the magnetic field. Scheme 1 illustrates the concept of the assembling process. This dynamic magnetic field induced aggregation process is modeled using the population balance equation (PBE) technique, which is commonly adopted for colloidal assembly systems in stagnant conditions.18–21 Such an approach takes mass as the internal coordinate because it is the primary conserved quantity in assembly and is suitable for system of low concentration where all the multibody interactions are negligible. The advantage of the PBE approach is its simplicity, which enables one to model the time evolution of the cluster mass distributions and to gain insight into the assembly kinetics and mechanisms by comparing the theory with the experimental data (e.g., real-time particle size distribution determined by a light-scattering technique). In the present study, in situ light-scattering experiments have been used to monitor the assembly of these silica-encapsulated magnetic nanoparticles in the presence of an external magnetic field. The growth of particle size (log-normal mean diameter) is found to follow a cubic law as a function of time. This result is consistent with the classic Ostwald ripening theory, whereby the growth of larger size particles is favor in the expense of smaller ones, resulting in increase the particle volume as a linear function of time.22,23 Moreover, a PBE model is developed to describe the evolution of particle size distributions with time. Our theoretical derived fractal dimension (Df) close to unity
Figure 1. A typical TEM micrograph shows a ∼33 nm silica particle encapsulating FePt with a narrow size distribution.
(one-dimensional growth) clearly supports our experimental results accounting for the preferred needle-shape magnetic assembled crystals. 2. Experimental Section 2.1. Synthesis of Silica-Encapsulated FePt Nanoparticles. Synthesis of monodisperse iron-platinum (FePt) nanoparticles by coreduction of platinum acetylacetonate and iron(II) chloride tetrahydrate in the presence of oleic acid and oleylamine stablizers was carried out according to Sun et al.,24 which reported the fine controls in FePt particle composition and size. As a result, 394 mg of 1.0 mmol Pt(acac)2, 278 mg of 1.4 mmol FeCl2 4H2O, 1.040 g of 4 mmol 1,2-hexadecanediol, and 50 mL of octyl ether were added to a round-bottom flask under a nitrogen atmosphere attached with a condenser and a thermometer. 0.32 mL of 1.0 mmol oleic acid and 0.34 mL of 1.0 mmol oleylamine were then added into the same flask when the mixture was heated up to 100 °C, and the mixture was sequentially heated to 220 °C over 15 min. LiBEt3H (1 M THF solution, 5.0 mL) was slowly added into the mixture, and the temperature was further kept for 10 more min in order to distill off the low boiling components with nitrogen. The black color soluble product was gradually formed while the mixture was refluxed at 286 °C for 1 h. After cooling the mixture to room temperature, ethanol was added to precipitate the black product, which was repeatedly washed a couple of times by the ethanol with centrifugation (1200 rpm, 1 h) in between. The precipitate was then dried at 150 °C for 1 h as as-synthesized FePt nanoparticles. The redispersed as-synthesized FePt in cyclohexane (1 mg/mL) was prepared prior to the post silica encapsulation treatment according to our previous reported method,25 which demonstrated the ability to tune the thickness of silica overlayer. As a result, 1 mmol of Igepal CO-520 (polyoxyethylene(5)nonylphenyl ether) was predispersed in 9 mL of cyclohexane by sonication for 20 min. After this step, 1.0 mL the FePt solution together with 80 µL of the ammonia
TRH: Assembly of Superparamagnetic Nanoparticles
J. Phys. Chem. C, Vol. 112, No. 20, 2008 7601
Figure 2. (a) Particle size distribution of the silica-encapsulated FePt nanoparticles. The blue shade represents the experimental data as determined using the Nanosight instrument, while the line represents the log-normal distribution (generated by Bestfit (Ithaca, USA)) with mean diameter of 42.6 nm, and variance of 36.0 nm; (b) The cubic of the log-normal mean diameter (〈d〉3) of the silica encapsulated silica encapsulated FePt nanoparticles as a function of time in the presence of an external magnetic field.
solution (35%) was added. Finally, 60 µL of tetraethyl orthosilicate was added, and the mixture was allowed to age for 48 h to complete the hydrolysis and condensation reactions of the precursors to silica. The resulting SiO2@FePt nanoparticles were finally collected by centrifugation, washed, and dried. 2.2. Time-Resolved Light-Scatting Experiments. The lightscatting experiments were performed using the NanoSight LM10 system (NanoSight Ltd., Salisbury, Whitshire, UK), which consists of a class I laser source, a viewing unit, microscope, and charge-coupled device camera together with a computer control unit. The magnetic nanoparticles were dispersed in highperformance liquid chromatography grade water buffered at pH 7.4 in a concentration of about 105 particles/mL. 500 µL of this colloid dispersion was introduced into the viewing unit with a disposable syringe. Magnetic-induced assembly was accomplished by placing a strong permanent magnet (BHmax ) 38 MGOe) underneath the viewing unit. The NTA image analysis software (NanoSight Ltd.) was used to determine the particle size distribution as a function of time. 3. Computational Details The PBE model was coded in Matlab (v7.5, MathWorks Inc., Natick, MA). Data analysis was performed using BestFit (v4.5, Palisade Corp., Ithaca, NY). 4. Results and Discussion A transmission electron microscopy (TEM) image of the silica-encapsulated FePt nanoparticles is shown in Figure 1. It can be seen that a coating containing Si and O (confirmed by EDS data, not shown) surrounds each core nanoparticle, suggesting the nanosized FePt particles are completely encap-
sulated in a silica matrix. The image clearly shows uniform silica particles that are 33.0 ( 0.5 nm diameter encapsulating mostly single but sometimes multiple (typically between zero and five) magnetic nanoparticles. Then, the silica-encapsulated FePt nanoparticles were dispersed in nearly neutral buffered water and studied in the light-scattering experiment. Figure 2a shows the particle size distribution of the silica-encapsulated FePt nanoparticles as measured by NanoSight instrument. It has been suggested that distribution of particle size, particularly in processes of growth, usually obeys a log-normal distribution.26 As shown in Figure 2a, the experimental distribution data fits nicely to a log-normal distribution, with a mean diameter of 42.6 nm, which is in line with the mean particle size of 33 nm as derived from the TEM image (Figure 1). Light scattering depending on the wavelength used tends to give a larger average size than those of TEM results since a significantly larger measurement error is encountered in particle approaching critical size accounting for the observed size discrepancy. 4.1. The Ostwald Ripening. The magnetic induced assembly of the FePt nanoparticles from solution was initiated by placing a strong permanent magnet (BHmax ) 38MGOe) underneath the viewing unit. The colloidal stability of the suspension was then studied by time-resolved light-scattering experiments. Figure 2b shows the cube of the log-normal mean diameter of the particles, 〈d〉3, evolved as a function of time, which is consistent with the case of Ostwald ripening as the volume of the particles is expected to grow linearly with time. As mentioned before, the initial mean particle diameter was 46.2 nm. After 100 min, about a 2-fold increase in particle diameter has been observed.
7602 J. Phys. Chem. C, Vol. 112, No. 20, 2008
Yiu et al.
4.2. The PBE Model. In an assembly system, the population balance has been used to describe the time evolution of the cluster mass distribution.18–21 The discrete form of the PBE model can be written as follows
dNk 1 K NN ) dt 2 i+j)k ij i j
∑
∑ KikNkNi
(1)
i
where Ni represents the number concentration of clusters consisting of i primary particles. The first term in the righthand side of eq 1 accounts for the formation of aggregates of mass k from two small ones (i and j), while the second term accounts for the loss of these aggregates due to their combination with other aggregates. Kij is the matrix of assembly rate constants, which is defined as below
Kij ) K11Bij
(2)
K11 represents the rate constant for doublet formation from the primary particles. Bij denotes the correction factors for the Brownian term, which describes the fractal nature of the aggregates. Bij is defined as19
(
(i1 ⁄ Df + j1 ⁄ Df) 1 + 1 i1 ⁄ Df j1 ⁄ Df Bij ) 4
)
(3)
where Df represents the fractal dimension of the clusters. Equation can be solved numerically by using the particle size distribution in the absence of external magnetic field as boundary conditions (Figure 2a). The remaining unknowns are Df and K11,
which are then treated as adjustable parameters. The problem renders to a nonlinear optimization of K11 and Df to minimize the deviation between the calculated and experimental particle size distributions obtained at various time points. To this end, Nelder-Mead simplex method (in the fminsearch function of Matlab) was utilized for this purpose.27 It was found that the optimization calculation converged to a global solution with K11 ) 5.05 × 10-7 and Df ) 1.01. As shown in Figure 3, the agreement between the PBE model and the time-resolved experimental particle size distribution is apparent. As far as we are aware, there is no published work in open literature concerning the magnetic-induced assembly of silicaencapsulated nanoparticles let alone the quantitative derivations of K11 and Df parameters from experimental particle size distributions. It would be difficult to make any direct comparison on the K11 parameter developed in other aggregation systems, as the magnetic field strength could vary in different experimental setups. However, it is clearly noted that the fractal dimension (Df) derived from this work is very close to unity, which implies that the assembly of the primary FePt nanoparticles in the presence of nonhomogenous external magnetic field from solution occurs in a “linear” manner. Our modeling results undisputedly suggest that the magnetic-induced growth process of magnetic nanoparticles would generate needle or rod-shaped materials, which is in excellent agreement with the experimental work described above. Figure 4 shows the optical, scanning electron microscopy (SEM), and TEM characterizations of the assembled FePt in the presence of external magnetic field with
Figure 3. Size distributions of the dispersed silica-encapsulated FePt nanoparticles as a function of time in the presence of an external magnetic field. Symbols represent experimental data measured using the Nanosight instrument at (a) 0, (b) 9, (c) 27, and (d) 90 min, while the lines represent the theoretical data generated using the PBE model, with K11 ) 5.05 × 10-7 and Df ) 1.01.
TRH: Assembly of Superparamagnetic Nanoparticles
J. Phys. Chem. C, Vol. 112, No. 20, 2008 7603
Figure 4. (a) Magnetic-assembled, centimetre-long, needle-shaped core-shell colloidal crystals composed of 3-nm FePt core in 33-nm silica nanoparticles (SiO2@FePt). (b) An image captured by environmental SEM showing the morphology of the 3-D, assembled acicular colloidal crystals with sharp crystal edges. (c) A high resolution TEM image showing hcp arrangement of the primary SiO2@FePt nanoparticles within the magnetic assembled crystals. (d) A TEM micrograph showing a wide view on assembled 33-nm SiO2@FePt particles as high-quality colloid crystals but a high concentration stacking fault lines (mismatches) is also clearly visible from the TEM image. (e) Corresponding diffuse electron diffraction patterns indicative of a hcp packing with stacking disorders.
Figure 5. VSM measurements of FePt core-shell silica magnetic nanoparticles as a centimetre-length 3-D magnetic colloid crystal (prealigned by external magnetic means) and as a powder (no magnetic alignment).
the aid of slow solvent evaporation. The stacking of the nanoparticles appears to be in form of hexagonal close packing (hcp) with occasionally stacking fault lines (mismatches) clearly visible from the TEM image on our unannealed sample (Figure 4d). The corresponding electron diffraction pattern results (Figure 4e) also suggested self-assembling of monodispersed core-shell magnetic nanoparticles into the macroscopic hcp colloidal crystals with the degree of stacking disorder. It is noted that some silica particles were formed without the incorporation of the FePt nanoparticles. Although it is not yet been able to quantitatively assess the degree of disorders by optical diffraction due to the intense optical absorption of the sample (dark in color), these defects are thought to affect the magnetic
interaction of encapsulated superparamagnetic FePt nanoparticles hence attenuating the overall magnetic properties of the sample. Figure 5 shows the comparison of the magnetic response (vibration saturation magnetization, VSM curves) of the core-shell magnetic nanoparticles before (powder) and after being aligned by the external magnet (3-D crystal). The results clearly indicate that the magnetically aligned supercrystals display much higher magnetic response than corresponding particles without the prealignment. Moreover, the role of silica in reducing the direct interference between FePt particles during assembly of the core-shell magnetic nanoparticles as compared to those without the SiO2 under the same magnetic field has recently been studied.28 Nevertheless, assembly of primary core-shell magnetic nanoparticles under unidirectional field forming needle-shape macroscopic-crystals is clearly evident. While this manuscript was under preparation, two new communications reported by Sun et al.29 on the magnetic-induced assembly of magnetite Fe3O4 nanoparticles and Park et al.30 on the fabrication of highly crystalline assembly of Co nanoparticles using magnetic field were published. Both of these experimental studies also reported the rod-/needle-shaped aggregates. 5. Conclusions To conclude this article we show that our experimental study on assembling core-shell magnetic nanoparticles in the presence of unidirectional magnetic flux form characteristic needle- or rod-shaped supercrystals, the morphology of which can be correctly predicted by our aggregation model based on the population balance equation. This magnetic directing “bottomup” approach and theoretical models as presently demonstrated
7604 J. Phys. Chem. C, Vol. 112, No. 20, 2008 may aid further development in assembling pattern(s) using an applied magnetic field. Acknowledgment. We kindly acknowledge the NanoSight Ltd., Salisbury, Whitshire, United Kingdom, for loading their equipment to the Oxford team as well as providing technical support. References and Notes (1) Murugavel, R.; Walawalkar, M. G.; Dan, M.; Roesky, H. W.; Rao, C. N. R. Acc. Chem. Res. 2004, 37, 763. (2) Lu, W.; Lieber, C. M. Nat. Mater. 2007, 6, 841. (3) Yu, K. M. K.; Yeung, C. M. Y.; Tsang, S. C. J. Am. Chem. Soc. 2007, 129, 6360. (4) Ariga, K.; Nakanishi, T.; Michinobu, T. J. Nanosci. Nanotechnol. 2006, 6, 2278. (5) Li, X. L.; Zhang, L.; Wang, X. R.; Shimoyama, I.; Sun, X. M.; Seo, W. S.; Dai, H. J. J. Am. Chem. Soc. 2007, 129, 4890. (6) Stavroyiannis, S.; Panagiotopoulos, L.; Niarchos, D.; Christodoulides, J. A.; Zhang, Y.; Hadjipanayis, G. C. Appl. Phys. Lett. 1998, 73, 3453. (7) Li, Y.; Zhang, X. L.; Qiu, R.; Qiao, R.; Kang, Y. S. J. Phys. Chem. C 2007, 111, 10747. (8) Fuertes, A. B.; Sevilla, M.; Valdes-Solis, T.; Tartaj, P. Chem. Mater. 2007, 19, 5418. (9) Sadasivan, S.; Sukhorukov, G. B. J. Colloid Interface Sci. 2006, 304, 437. (10) Zhao, G. Y.; Xu, C. L.; Guo, D. J.; Li, H.; Li, H. L. Appl. Surf. Sci. 2007, 253, 3242. (11) Gao, X.; Tam, K.; Yu, K. M. K.; Tsang, S. C. Small 2005, 1, 949. (12) Xiong, Y.; Chen, Q.; Tao, N.; Ye, J.; Tang, Y.; Feng, J.; Gu, X. Nanotechnology 2007, 18, 345301.
Yiu et al. (13) Gao, X.; Yu, K. M. K.; Tam, K.; Tsang, S. C. Chem. Commun. 2003, 2998. (14) Tsang, S. C.; Caps, V.; Paraskevas, I.; Chadwick, D.; Thompsett, D. Angew. Chem., Int. Ed. 2004, 43, 5645. (15) Son, S. J.; Reichel, J.; He, B.; Schuchman, M.; Lee, S. B. J. Am. Chem. Soc. 2005, 127, 7316. (16) Wu, T.; Hua, M. Y.; Chen, J. P.; Wei, K. C.; Jung, S. M.; Chang, Y. J.; Jou, M. J.; Ma, Y. H. J. Magn. Magn. Mater. 2007, 311, 372. (17) Yu, C. H.; Caiulo, N.; Lo, C. C. H.; Tam, K.; Tsang, S. C. AdV. Mater. 2006, 18, 2312. (18) Taboada-Serrano, P.; Chin, C. J.; Yiacoumi, S.; Tsouris, C. Curr. Opin. Colloid Interface Sci. 2005, 10, 123. (19) Lattuada, M.; Sandkuhler, P.; Wu, H.; Sefcik, J.; Morbidelli, M. AdV. Colloid Interface Sci. 2003, 103, 33. (20) Sandkuhler, P.; Sefcik, J.; Morbidelli, M. Langmuir 2005, 21, 2062. (21) Soos, M.; Wang, L.; Fox, R. O.; Sefcik, J.; Morbidelli, M. J. Colloid Interface Sci. 2007, 307, 433. (22) Kabalnov, A. S.; Shchukin, E. D. AdV. Colloid Interface Sci. 1992, 38, 69. (23) Lindfors, L.; Skantze, P.; Skantze, U.; Rasmusson, M.; Zackrisson, A.; Olsson, U. Langmuir 2006, 22, 906. (24) Chen, M.; Liu, J. P.; Sun, S. H. J. Am. Chem. Soc. 2004, 126, 8394. (25) Yu, K. M. K.; Yeung, C. M. Y.; Thompsett, D.; Tsang, S. C. J Phys. Chem. B 2003, 107, 4515. (26) Irani, R. R. J. Phys. Chem. 1959, 63, 1603. (27) Nelder, J. A.; Mead, R. A. Comput. J. 1965, 7, 308. (28) Tang, H.; Yu, C. H.; Oduro, W.; He, H.; Tsang, S. C. Langmuir 2008, 24, 1587. (29) Sun, J.; Zhang, Y.; Chen, Z.; Zhou, J.; Gu, N. Angew. Chem., Int. Ed. 2007, 46, 4767. (30) Park, J. I.; Jun, Y. W.; Choi, J. S.; Cheon, J. Chem. Comm. 2007, 5001, 5003.
JP800310X
