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Magnetic Nanorods for Optofluidic Applications Alexander Tokarev, Binyamin Rubin, Monte Bedford, Konstantin G. Kornev* School of Materials Science and Engineering, 161 Sirrine Hall, Clemson University, Clemson, SC 29634, USA *E-mail: [email protected] Abstract. We have developed a method for laser beam manipulation by using a colloid of nickel nanorods produced by electroplating chemistry. It is shown that the shape of the laser beam passing through a colloid of nickel nanorods can be altered by varying the applied magnetic field. This effect is caused by multiple scattering and diffraction of the laser beam by the nanorods. Compared with spherical nanoparticles, magnetic nanorods are better suited for illumination applications because they are stable in a rotating magnetic field. By rotating the diffraction pattern, one can illuminate a large area. Keywords: nanorods, ferrofluids, optofluidic, magneto-fluidics, magneto-optics, diffraction PACS: 42.25.Fx, 42.62.Be, 81.07.Gf, 78.20.Ls, 85.70.Sq
INTRODUCTION Magnetic fluid is a stable colloidal suspension typically of spherical-shaped magnetic particles of sizes ranging from 5 to 200 nm [1]. Possible applications of magnetic liquids in optofluidics include optical modulators and switches. The properties and behavior of magnetic fluids from spherical nanoparticles have been studied for more than half a century. When a magnetic field is applied to this fluid, the material becomes optically anisotropic, and different magneto-optical effects can be observed. Specifically, optical birefringence, Faraday rotation, dichroism and different types of light scattering were studied [2-5]. One of the most important effects is the diffraction pattern discovered by Haas [6]. In the applied magnetic field, the fluid becomes “frozen”, forming chains of magnetic carriers directed along the field lines. When the light is applied perpendicular to the chains, an elongated characteristic diffraction pattern is formed on the screen (Fig. 1a). While the optical effects from the dispersion of spherical particles were studied by many groups, the fluids with rod-like nanoparticles drew research interest only in recent years [7-10]. Magnetic rods have great potential for applications in optofluidics because of their unique properties of high magnetization and structural stability, in contrast with chains of spherical particles. Template-assisted electrochemical deposition method is widely used for preparation of different magnetic nanonrods [11]. Another way to produce magnetic nanorods is to fill carbon nanotubes with magnetic nanoparticles [8, 9]. Unlike traditional magnetic fluids, colloids of magnetic nanorods have several advantages in optofluidic applications. High magnetization of magnetic nanorods allows one to control the nanorods orientation using a moderate magnetic field. This offers the possibility to use miniaturized magnets with a lab-on-a-chip. Also, the nanorod solidity provides an easy way to manipulate the nanorod as a whole unit. For example, if the magnetic field (Fig. 1a) would rotate in the plane perpendicular to the direction of light propagation, the diffraction pattern would follow this rotation, enabling illumination of a large area. Moreover, by rotating nanorods in the plane perpendicular to the light beam, one can vary the transmission coefficient, enabling intensity modulation [12]. In contrast to nanorods, the nanoparticle chains typically break in the rotating field [13]. In this paper, we show that a suspension of nickel nanorods can be used for optofluidic applications where the precise control of light is needed but mechanical contact is not possible. In particular, we demonstrated that the light beam from a laser can be significantly diffracted by nickel nanorods and by rotating magnetic field one can illuminate a larger area.
AIP CREDIT LINE TO BE INSERTED ON THE FIRST PAGE OF EACH PAPER
CP1311, 8th International Conference on the Scientific and Clinical Applications of Magnetic Carriers edited by U. Häfeli, W. Schütt, and M. Zborowski © 2010 American Institute of Physics 978-0-7354-0866-1/10/$30.00
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EXPERIMENTAL SETUP By means of electroplating chemistry, nickel nanorods (Fig.1 b,c) have been successfully synthesized within the regular pore structure of an anodic aluminum oxide membrane attached to the cathode by a conductive layer. Thus, Ni nanorods were prepared by electrodeposition, reducing Ni+2 ions from an aqueous Watts electrolyte solution, driven by a direct current source. The anode consisted of Ni wire whereby its oxidation replenished the supply of Ni cations.
FIGURE 1. a) Experimental setup for magneto-optical experiments, b) Scanning electron micrograph of nickel nanorods, c) Nickel nanorods aligned in a magnetic field
The electrode was prepared using a copper plate, 76 x 38 x 4.2 mm, wet-sanding the surface with 220 grit silicon carbide paper followed by water and detergent wash while scrubbing with a stiff plastic brush. A Whatman Anodisc® alumina filter membrane, available in three nominal pore sizes, 0.02, 0.1, and 0.2 µm (supported by an annular polypropylene disk, optional and recommended), was covered with Gallium-Indium eutectic liquid by cotton swab. The coated disk was gently pressed to the copper plate and sealed with water-proof tape (vinyl electrical) which had been cut to conform to its edge. Great care was taken to seal the submerged area of electrode from electrolyte seepage. The anode was prepared by coiling a 99.5% pure (metals basis) Ni wire (1.0 mm diameter) for increased electrolyte contact while securing it in a beaker opposite the cathode. From the many possible Watts solutions, the following formulation, 300 g/L NiSO4·6H2O, 45 g/L H3BO3, and 45 g/L NiCl2·6H2O, was used. A constant voltage of 2.0 V was maintained by a Circuit Specialists DC Regulated Power Supply (CSI12001X), with the positive contact attached to anode and the negative to cathode, as this voltage was reported to produce singledomain Ni crystals [11]. No reference electrode was used. The reaction time at ambient temperature varied from about 5 to 40 minutes depending on the desired rod length and reaction kinetics. Average speed of growth is 1 µm per minute resulting in the nanorod length of 5 to 40 µm. Length of the rods was verified by optical and scanning electron microscopy. The membrane was cut from the cathode, wiped with concentrated nitric acid to remove the ·In,Ga and submerged in 6 M NaOH until the alumina was dissolved. The Ni product was separated from the waste and washed well with methanol. In all stages of recovery, cleaning and liquid change, a disk magnet (K&J Magnetics, DY81) was placed against the bottom of the beaker. Thus, the Ni was held firmly while liquid and solid impurities were suctioned, decanted or removed by forceps. Liquid was then added to suspend the nanorods by bath ultrasonication. In the optical experiments, nickel nanorods of about 200 nm in diameter and 25µm in length were suspended in ethylene glycol at different concentrations (0.0015-0.034 wt. %). The rectangular glass cell (1 mm thick) filled with the suspension was placed between two poles of GMW 3470 dipole electromagnet (Fig. 1a). When magnetic field of 0.004 T was applied perpendicular to the direction of beam propagation, we observed that the nanorods aligned along the field lines. He-Ne the laser beam (632.8 nm) illuminated the cell with aligned rods, and the diffraction pattern was observed on the screen located at the distance of 16 cm from the optical cell. This dispersion pattern was similar to that of spherical nanoparticles [11, 14]. CCD camera (Dalsa Falcon 1.4M100) was used to capture the diffraction patterns and the distributions of light intensity were quantitatively analyzed using Matlab. The rotating magnetic field was generated by a custom-built system of four electromagnets (Fig. 2a). Each electromagnet included 6 mm diameter magnetic core and solenoid with 300 turns of copper wire. The magnitude and frequency of the magnetic field were controlled by the LabView program. To observe rotation of the nanorods, the system of electromagnets (Fig. 2a) with a microfluidic chip or a capillary containing the nanorod dispersion was placed under a microscope (Olympus MVX10). High speed digital camera (Motion Pro X3) was used to capture
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images of rotating magnetic nanorods. In order to obtain the magnetic field distribution in the nanorod suspension within the cell, FEM solver COMSOL® was used to simulate the magnetic field (Fig.2b). The validity of these calculations was confirmed by measuring the magnetic field at the center of the optical cell using the digital teslameter (133-DG GMW Inc.). The deviations between the numerical data and the measured value were not greater than 10%.
(b) Location of a glass cell with a dispersion of nickel nanowires
(a) Magnetic cores
y x
10 mm
Magnetic coils B, T
FIGURE 2. a) system of 4 electromagnets for producing a rotating magnetic field, b) simulation of the magnetic field produced by this system
RESULTS AND DISCUSSION The diffraction pattern and the distributions of light intensity along the diffraction wings obtained using the setup shown in Fig. 1a are shown in Fig. 3. We observed that in the range of nanorod concentrations varied between 0.0015 wt. % to 0.034 wt. %, both the illumination intensity and illuminated area have increased monotonously with the nanorod concentration. This effect is explained by the multiple diffraction of light on the layers of nanorods aligned in the applied magnetic field; as the nanorod concentration increases, the light beam finds more obstacles thus enlarging the cone over which the light spreads. This effect was earlier observed for the chains of spherical magnetite nanospheres [12]. As proposed in Ref.[12], one can take advantage of this reconfigurable diffraction pattern and make an optofluidic illuminator by filling a hollow fiber with a suspension of magnetic nanoparticles. When the direction of beam propagation is perpendicular to the magnetic field, the nanoparticles form chains and diffract the light transforming a circular beam into a ribbon and yielding a larger visible area. In order to produce larger spot size, it would be advantageous to rotate this diffraction pattern by spinning the external magnetic field. In contrast with the chains of the magnetite nanospheres, the nanorods are stable in a rotating magnetic field and strongly follow the field. Therefore, they are excellent candidates for this application. Another advantage is that the onset of rotation of the nickel nanorods is observed at lower magnetic fields, much lower than those required to form chains of spherical iron oxide nanoparticles [12]. It is known that the rate of 25 frames per second is close to the limit of naked eye resolution for moving objects. Hence, the diffraction pattern rotating at 25 revolutions per second will be seen as an almost frozen round spot, illuminating an area significantly larger than the original beam spot. In applications to optofluidic illuminators, it is necessary to estimate the relation between the required physical parameters of the nanorods and the frequency of rotating magnetic field. We experimented with nickel nanorods placing them in a capillary and observing the nanorod rotation under the microscope. These experiments were explained theoretically as follows.
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FIGURE 3. The distribution of light along the right diffraction wing (along the white line in the insert) for different mass concentrations of nanorods.
Typically, in rod-like nanoparticles, the axial component of the magnetic moment m is much larger than the transversal component. This makes the description of the nanorod rotation easier, because we can use only axial component of the magnetic moment. To analyze the rotation of magnetic nanorod in rotating magnetic field we used the following equation [8, 13]:
γ 2π f −
dθ dt
mB sin θ =
(1)
where f is the frequency of the rotating magnetic field B, and θ is the angle formed by the nanorod with the field direction. The drag coefficient γ is determined by the nanorod length l, its diameter d, and the ethylene glycol viscosity (η = 16·10-3Pa·s) [8, 13]:
γ=
πη l 3
(2)
l 3ln − 2.4 d
If the nanorod rotates synchronously with the magnetic field, the angle θ is constant, and eq.(1) is simplified as
γ 2π f = mB sin θ
(3) Solving this equation for θ, we can notice that the solution exists if and only if the rotation frequency f is below the critical frequency [8, 13]:
fc =
1 mB 2π γ
Expressing the magnetic moment through the material magnetization M, m = MV, where
(4)
V=
π d 2l 4
is the nanorod
volume, and combining equations (2) and (4) we see that the dimensionless critical frequency does not depend on the particular size of the nanorod, but only on its aspect ratio:
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8πη f c = MB
l 3ln − 2.4 d 2 l d
(5)
In other words, because the viscous torque in eq. (1) is proportional to l3, while the magnetic torque is proportional to d2l, these two torques compensate each other at the critical frequency, resulting in a universal dependence (5). For low magnetic fields, when the magnetization linearly depends on the field, m =
VB χ
µ0
where χ is the magnetic
susceptibility and µ0 is the magnetic permeability of vacuum, the dimensional critical frequency is rewritten as −2
χ B2 l l = fc 3ln − 2.4 8πηµ0 d d
(6)
Therefore, the critical frequency can be increased by reducing the aspect ratio of the rods or by increasing the magnitude of the magnetic field. This dependence of critical frequency on the rod aspect ratio is plotted in Fig. 6, where experimental values are also shown. Experimental values were obtained by analyzing the images of rotating nanorods. The measured magnetic field at the location of a capillary with the nanorod suspension was B = 0.0015±0.0005 T. The literature data on magnetic properties of nickel nanorods demonstrate a significant scatter depending on the parameters used for the nanorod synthesis [14, 15]. This uncertainty suggests considering susceptibility χ as an adjustable parameter and checking whether or not it falls into a range of literature data. We used eq.(6) for the least square fitting the experimental data on critical rotation frequency fc. The obtained best fit value for the susceptibility was χ = 92. This value falls in the range of values reported in the literature for bulk nickel [16]. When the obtained susceptibility χ was substituted into eq. (6), we found a good agreement between the theory and experiments, Fig.6. This theoretical and experimental analysis confirms that nickel nanorod can rotate at the rate as high as 50 revolutions per second in a reasonably weak magnetic field of 0.0015 T. Therefore, the design of optofluidic illuminator proposed in Ref. [12] can be further improved by replacing spherical nanoparticles with nickel nanorods.
Critical frequency, rps
60 Theory Experiment
50 40 30 20 10 0
0
20 10 Aspect ratio
30
FIGURE 4. Critical frequency fc up to which rotation of nickel nanorod is synchronized with rotation of magnetic field as a function of nanorod aspect ratio l/d.
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CONCLUSIONS Nickel nanorods were produced by means of electroplating chemistry. A suspension of these nanorods, aligned in a magnetic field and illuminated by a visible laser beam, was used for the analysis of the diffraction pattern. It was found that increasing the concentration of nanorods in the suspension one can increase the area of diffraction wings. The control of this diffraction pattern is needed in the optofluidic applications where one needs to illuminate a larger area yet no direct mechanical contact with the light source is possible. We showed that the diffraction pattern can be rotated by spinning the magnetic field. The nanorods are stable in rotating magnetic field, i.e. the rotation of the field does not break them as it would with a chain of spherical magnetic nanoparticles. The produced nickel nanorods are able to rotate at the rate as high as 50 revolutions per seconds that is well beyond the limit of naked eye resolution for moving objects. This effect opens an opportunity for use of these colloidal suspensions in medical optofluidic devices producing stationary illuminating spots, for example in endoscopes.
ACKNOWLEDGMENTS We wish to thank David White for his assistance in building the magneto-optical cell. The authors are also grateful for the financial support from the National Science Foundation, Grants CMMI 0826067, CMMI 0825832, and EFRI 0937985.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
R.E. Rosensweig, Ferrohydrodynamics. Cambridge ; New York, Cambridge University Press, 1985. G. Fosa, R. Badescu, and G.C. Calugaru, Czech. J. Phys., 54(9), 989-996, (2004). R.V. Mehta, R. Patel, R. Desai, R.V. Upadhyay, and K. Parekh, Phys. Rev. Lett., 96(12), Article Number: 127402, (2006). K. Yerin and S. Kunikin, Optics and Spectroscopy, 102(5), 765-770, (2007). J. Li, Y. Huang, X.D. Liu, Y.Q. Lin, Q. Li, and R.L. Gao, Phys. Lett. A, 372(46), 6952-6955, (2008). W.E.L. Haas and J.E. Adams, Appl.Phys. Lett., 27(10), 571-572, (1975). A.K. Bentley, A.B. Ellis, G.C. Lisensky, and W.C. Crone, Nanotechnology, (10), 2193-2196, (2005). G. Korneva, H.H. Ye, Y. Gogotsi, D. Halverson, G. Friedman, J.C. Bradley, and K.G. Kornev, Nano Lett., 5(5), 879-884, (2005). K.G. Kornev, D. Halverson, G. Korneva, Y. Gogotsi, and G. Friedman, Appl. Phys. Lett., 92(23), Article Number: 233117 (2008). T. Klein, A. Laptev, A. Gunther, P. Bender, A. Tschope, and R. Birringer, J. Appl. Phys., 106(11), Article Number: 114301, (2009). S. Thongmee, H.L. Pang, J. Ding, and J.Y. Lin, J. Magn. Magn. Mater., 321(18), 2712-2716, (2009). S.Z. Malynych, A. Tokarev, S. Hudson, G. Chumanov, J. Ballato, and K.G. Kornev, J. Magn. Magn. Mater., 322(14), 1894-1897, (2010). E. Blums, A.O. Sebers, and M.M. Maiorov, Magnetic fluids. Berlin ; New York, Walter de Gruyter, 1997. A. Hultgren, M. Tanase, E.J. Felton, K. Bhadriraju, A.K. Salem, C.S. Chen, and D.H. Reich, Biotechnol. Prog., 21(2), 509-515, (2005). A. Prina-Mello, Z. Diao, and J. Coey, J. Nanobiotech., 4(1), PMCID: PMC1592113, (2006). S. Lucyszyn, PIERS Online, 4(6), 686-690, (2008).
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INTRODUCTION Magnetic fluid is a stable colloidal suspension typically of spherical-shaped magnetic particles of sizes ranging from 5 to 200 nm [1]. Possible applications of magnetic liquids in optofluidics include optical modulators and switches. The properties and behavior of magnetic fluids from spherical nanoparticles have been studied for more than half a century. When a magnetic field is applied to this fluid, the material becomes optically anisotropic, and different magneto-optical effects can be observed. Specifically, optical birefringence, Faraday rotation, dichroism and different types of light scattering were studied [2-5]. One of the most important effects is the diffraction pattern discovered by Haas [6]. In the applied magnetic field, the fluid becomes “frozen”, forming chains of magnetic carriers directed along the field lines. When the light is applied perpendicular to the chains, an elongated characteristic diffraction pattern is formed on the screen (Fig. 1a). While the optical effects from the dispersion of spherical particles were studied by many groups, the fluids with rod-like nanoparticles drew research interest only in recent years [7-10]. Magnetic rods have great potential for applications in optofluidics because of their unique properties of high magnetization and structural stability, in contrast with chains of spherical particles. Template-assisted electrochemical deposition method is widely used for preparation of different magnetic nanonrods [11]. Another way to produce magnetic nanorods is to fill carbon nanotubes with magnetic nanoparticles [8, 9]. Unlike traditional magnetic fluids, colloids of magnetic nanorods have several advantages in optofluidic applications. High magnetization of magnetic nanorods allows one to control the nanorods orientation using a moderate magnetic field. This offers the possibility to use miniaturized magnets with a lab-on-a-chip. Also, the nanorod solidity provides an easy way to manipulate the nanorod as a whole unit. For example, if the magnetic field (Fig. 1a) would rotate in the plane perpendicular to the direction of light propagation, the diffraction pattern would follow this rotation, enabling illumination of a large area. Moreover, by rotating nanorods in the plane perpendicular to the light beam, one can vary the transmission coefficient, enabling intensity modulation [12]. In contrast to nanorods, the nanoparticle chains typically break in the rotating field [13]. In this paper, we show that a suspension of nickel nanorods can be used for optofluidic applications where the precise control of light is needed but mechanical contact is not possible. In particular, we demonstrated that the light beam from a laser can be significantly diffracted by nickel nanorods and by rotating magnetic field one can illuminate a larger area.
AIP CREDIT LINE TO BE INSERTED ON THE FIRST PAGE OF EACH PAPER
CP1311, 8th International Conference on the Scientific and Clinical Applications of Magnetic Carriers edited by U. Häfeli, W. Schütt, and M. Zborowski © 2010 American Institute of Physics 978-0-7354-0866-1/10/$30.00
204 Downloaded 16 Dec 2010 to 130.127.15.14. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions
EXPERIMENTAL SETUP By means of electroplating chemistry, nickel nanorods (Fig.1 b,c) have been successfully synthesized within the regular pore structure of an anodic aluminum oxide membrane attached to the cathode by a conductive layer. Thus, Ni nanorods were prepared by electrodeposition, reducing Ni+2 ions from an aqueous Watts electrolyte solution, driven by a direct current source. The anode consisted of Ni wire whereby its oxidation replenished the supply of Ni cations.
FIGURE 1. a) Experimental setup for magneto-optical experiments, b) Scanning electron micrograph of nickel nanorods, c) Nickel nanorods aligned in a magnetic field
The electrode was prepared using a copper plate, 76 x 38 x 4.2 mm, wet-sanding the surface with 220 grit silicon carbide paper followed by water and detergent wash while scrubbing with a stiff plastic brush. A Whatman Anodisc® alumina filter membrane, available in three nominal pore sizes, 0.02, 0.1, and 0.2 µm (supported by an annular polypropylene disk, optional and recommended), was covered with Gallium-Indium eutectic liquid by cotton swab. The coated disk was gently pressed to the copper plate and sealed with water-proof tape (vinyl electrical) which had been cut to conform to its edge. Great care was taken to seal the submerged area of electrode from electrolyte seepage. The anode was prepared by coiling a 99.5% pure (metals basis) Ni wire (1.0 mm diameter) for increased electrolyte contact while securing it in a beaker opposite the cathode. From the many possible Watts solutions, the following formulation, 300 g/L NiSO4·6H2O, 45 g/L H3BO3, and 45 g/L NiCl2·6H2O, was used. A constant voltage of 2.0 V was maintained by a Circuit Specialists DC Regulated Power Supply (CSI12001X), with the positive contact attached to anode and the negative to cathode, as this voltage was reported to produce singledomain Ni crystals [11]. No reference electrode was used. The reaction time at ambient temperature varied from about 5 to 40 minutes depending on the desired rod length and reaction kinetics. Average speed of growth is 1 µm per minute resulting in the nanorod length of 5 to 40 µm. Length of the rods was verified by optical and scanning electron microscopy. The membrane was cut from the cathode, wiped with concentrated nitric acid to remove the ·In,Ga and submerged in 6 M NaOH until the alumina was dissolved. The Ni product was separated from the waste and washed well with methanol. In all stages of recovery, cleaning and liquid change, a disk magnet (K&J Magnetics, DY81) was placed against the bottom of the beaker. Thus, the Ni was held firmly while liquid and solid impurities were suctioned, decanted or removed by forceps. Liquid was then added to suspend the nanorods by bath ultrasonication. In the optical experiments, nickel nanorods of about 200 nm in diameter and 25µm in length were suspended in ethylene glycol at different concentrations (0.0015-0.034 wt. %). The rectangular glass cell (1 mm thick) filled with the suspension was placed between two poles of GMW 3470 dipole electromagnet (Fig. 1a). When magnetic field of 0.004 T was applied perpendicular to the direction of beam propagation, we observed that the nanorods aligned along the field lines. He-Ne the laser beam (632.8 nm) illuminated the cell with aligned rods, and the diffraction pattern was observed on the screen located at the distance of 16 cm from the optical cell. This dispersion pattern was similar to that of spherical nanoparticles [11, 14]. CCD camera (Dalsa Falcon 1.4M100) was used to capture the diffraction patterns and the distributions of light intensity were quantitatively analyzed using Matlab. The rotating magnetic field was generated by a custom-built system of four electromagnets (Fig. 2a). Each electromagnet included 6 mm diameter magnetic core and solenoid with 300 turns of copper wire. The magnitude and frequency of the magnetic field were controlled by the LabView program. To observe rotation of the nanorods, the system of electromagnets (Fig. 2a) with a microfluidic chip or a capillary containing the nanorod dispersion was placed under a microscope (Olympus MVX10). High speed digital camera (Motion Pro X3) was used to capture
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images of rotating magnetic nanorods. In order to obtain the magnetic field distribution in the nanorod suspension within the cell, FEM solver COMSOL® was used to simulate the magnetic field (Fig.2b). The validity of these calculations was confirmed by measuring the magnetic field at the center of the optical cell using the digital teslameter (133-DG GMW Inc.). The deviations between the numerical data and the measured value were not greater than 10%.
(b) Location of a glass cell with a dispersion of nickel nanowires
(a) Magnetic cores
y x
10 mm
Magnetic coils B, T
FIGURE 2. a) system of 4 electromagnets for producing a rotating magnetic field, b) simulation of the magnetic field produced by this system
RESULTS AND DISCUSSION The diffraction pattern and the distributions of light intensity along the diffraction wings obtained using the setup shown in Fig. 1a are shown in Fig. 3. We observed that in the range of nanorod concentrations varied between 0.0015 wt. % to 0.034 wt. %, both the illumination intensity and illuminated area have increased monotonously with the nanorod concentration. This effect is explained by the multiple diffraction of light on the layers of nanorods aligned in the applied magnetic field; as the nanorod concentration increases, the light beam finds more obstacles thus enlarging the cone over which the light spreads. This effect was earlier observed for the chains of spherical magnetite nanospheres [12]. As proposed in Ref.[12], one can take advantage of this reconfigurable diffraction pattern and make an optofluidic illuminator by filling a hollow fiber with a suspension of magnetic nanoparticles. When the direction of beam propagation is perpendicular to the magnetic field, the nanoparticles form chains and diffract the light transforming a circular beam into a ribbon and yielding a larger visible area. In order to produce larger spot size, it would be advantageous to rotate this diffraction pattern by spinning the external magnetic field. In contrast with the chains of the magnetite nanospheres, the nanorods are stable in a rotating magnetic field and strongly follow the field. Therefore, they are excellent candidates for this application. Another advantage is that the onset of rotation of the nickel nanorods is observed at lower magnetic fields, much lower than those required to form chains of spherical iron oxide nanoparticles [12]. It is known that the rate of 25 frames per second is close to the limit of naked eye resolution for moving objects. Hence, the diffraction pattern rotating at 25 revolutions per second will be seen as an almost frozen round spot, illuminating an area significantly larger than the original beam spot. In applications to optofluidic illuminators, it is necessary to estimate the relation between the required physical parameters of the nanorods and the frequency of rotating magnetic field. We experimented with nickel nanorods placing them in a capillary and observing the nanorod rotation under the microscope. These experiments were explained theoretically as follows.
206 Downloaded 16 Dec 2010 to 130.127.15.14. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions
FIGURE 3. The distribution of light along the right diffraction wing (along the white line in the insert) for different mass concentrations of nanorods.
Typically, in rod-like nanoparticles, the axial component of the magnetic moment m is much larger than the transversal component. This makes the description of the nanorod rotation easier, because we can use only axial component of the magnetic moment. To analyze the rotation of magnetic nanorod in rotating magnetic field we used the following equation [8, 13]:
γ 2π f −
dθ dt
mB sin θ =
(1)
where f is the frequency of the rotating magnetic field B, and θ is the angle formed by the nanorod with the field direction. The drag coefficient γ is determined by the nanorod length l, its diameter d, and the ethylene glycol viscosity (η = 16·10-3Pa·s) [8, 13]:
γ=
πη l 3
(2)
l 3ln − 2.4 d
If the nanorod rotates synchronously with the magnetic field, the angle θ is constant, and eq.(1) is simplified as
γ 2π f = mB sin θ
(3) Solving this equation for θ, we can notice that the solution exists if and only if the rotation frequency f is below the critical frequency [8, 13]:
fc =
1 mB 2π γ
Expressing the magnetic moment through the material magnetization M, m = MV, where
(4)
V=
π d 2l 4
is the nanorod
volume, and combining equations (2) and (4) we see that the dimensionless critical frequency does not depend on the particular size of the nanorod, but only on its aspect ratio:
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8πη f c = MB
l 3ln − 2.4 d 2 l d
(5)
In other words, because the viscous torque in eq. (1) is proportional to l3, while the magnetic torque is proportional to d2l, these two torques compensate each other at the critical frequency, resulting in a universal dependence (5). For low magnetic fields, when the magnetization linearly depends on the field, m =
VB χ
µ0
where χ is the magnetic
susceptibility and µ0 is the magnetic permeability of vacuum, the dimensional critical frequency is rewritten as −2
χ B2 l l = fc 3ln − 2.4 8πηµ0 d d
(6)
Therefore, the critical frequency can be increased by reducing the aspect ratio of the rods or by increasing the magnitude of the magnetic field. This dependence of critical frequency on the rod aspect ratio is plotted in Fig. 6, where experimental values are also shown. Experimental values were obtained by analyzing the images of rotating nanorods. The measured magnetic field at the location of a capillary with the nanorod suspension was B = 0.0015±0.0005 T. The literature data on magnetic properties of nickel nanorods demonstrate a significant scatter depending on the parameters used for the nanorod synthesis [14, 15]. This uncertainty suggests considering susceptibility χ as an adjustable parameter and checking whether or not it falls into a range of literature data. We used eq.(6) for the least square fitting the experimental data on critical rotation frequency fc. The obtained best fit value for the susceptibility was χ = 92. This value falls in the range of values reported in the literature for bulk nickel [16]. When the obtained susceptibility χ was substituted into eq. (6), we found a good agreement between the theory and experiments, Fig.6. This theoretical and experimental analysis confirms that nickel nanorod can rotate at the rate as high as 50 revolutions per second in a reasonably weak magnetic field of 0.0015 T. Therefore, the design of optofluidic illuminator proposed in Ref. [12] can be further improved by replacing spherical nanoparticles with nickel nanorods.
Critical frequency, rps
60 Theory Experiment
50 40 30 20 10 0
0
20 10 Aspect ratio
30
FIGURE 4. Critical frequency fc up to which rotation of nickel nanorod is synchronized with rotation of magnetic field as a function of nanorod aspect ratio l/d.
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CONCLUSIONS Nickel nanorods were produced by means of electroplating chemistry. A suspension of these nanorods, aligned in a magnetic field and illuminated by a visible laser beam, was used for the analysis of the diffraction pattern. It was found that increasing the concentration of nanorods in the suspension one can increase the area of diffraction wings. The control of this diffraction pattern is needed in the optofluidic applications where one needs to illuminate a larger area yet no direct mechanical contact with the light source is possible. We showed that the diffraction pattern can be rotated by spinning the magnetic field. The nanorods are stable in rotating magnetic field, i.e. the rotation of the field does not break them as it would with a chain of spherical magnetic nanoparticles. The produced nickel nanorods are able to rotate at the rate as high as 50 revolutions per seconds that is well beyond the limit of naked eye resolution for moving objects. This effect opens an opportunity for use of these colloidal suspensions in medical optofluidic devices producing stationary illuminating spots, for example in endoscopes.
ACKNOWLEDGMENTS We wish to thank David White for his assistance in building the magneto-optical cell. The authors are also grateful for the financial support from the National Science Foundation, Grants CMMI 0826067, CMMI 0825832, and EFRI 0937985.
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