INTRODUCTION
Ferrofluids are synthesized colloidal mixtures of nonmagnetic carrier liquids, typically water or oil, containing single-domain, permanently magnetized particles, typically magnetite, with diameters on the order of 5-15 nm and volume concentration up to about 10%.[1-6] A 10% by volume magnetite ferrofluid would have a saturation magnetization of about 0.0560 T = 560 G (1 T = 10,000 G). Brownian motion keeps the nanoscopic particles from settling under gravity and a surfactant layer, such as oleic acid, surrounds each particle to provide short-range steric hindrance and electrostatic repulsion between particles to prevent particle agglomeration. A polymeric layer surrounding each nanoparticle may also serve this purpose. These nanoparticle coatings allow ferrofluids to maintain fluidity even in intense, high-gradient magnetic fields. The study and application of ferrofluids, invented in the mid-1960s,1-7-1 involves interdisciplinary science and technology integrating chemistry, fluid mechanics, and magnetism. Because of the small particle size, ferrofluids involved nanoscience and nanotechnology from their inception.
Conventional ferrofluid applications use d.c. magnetic fields from permanent magnets for use as liquid O-rings in rotary and exclusion seals,[8-10] bearings, as dampers in stepper motors and shock absorbers, in magnetorheo-logical fluid composites,[11,12] for heat transfer in loudspeakers,1-1-5-1 in inclinometers and accelerometers, for grinding and polishing, and in magnetocaloric pumps and heat pipes.[1,13] Ferrofluid is used in over 50 million loudspeakers each year. Almost every computer disk drive uses a magnetic fluid rotary seal for contaminant exclusion[14] and the semiconductor industry uses silicon crystal-growing furnaces that employ ferrofluid rotary shaft seals. A representative seal can withstand a pressure difference of up to 1.5 MPa 15 atm) at a speed of 7000 rpm.[15] Ferrofluids are also used for the separation of magnetic from nonmagnetic materials and for the separation of materials by their density using a nonuniform magnetic field to create a magnetic pressure distribution in the ferrofluid that causes the fluid to act as if it has a variable density that changes with height.[1,16] Magnetic materials are attracted to the regions of strongest magnetic field, whereas nonmagnetic materials are displaced to the regions of low magnetic field with matching effective density. Magnetomotive separations use this selective buoyancy for sink-float separation of materials such as ore minerals,[16] one novel application being the separation of diamonds from beach sand.[17,18]
Ferrofluids are a multifunctional medium[2] that allow applications in each of its constituent disciplines of chemistry, fluid mechanics, and magnetism. With modern advances in understanding nanoscale systems, current research focuses on synthesis,[19-23] characteriza-tion,[20,22-27] and functionalization[21,22,28-34] of nanopar-ticles with magnetic and surface properties tailored for application as microelectromechanical/nanoelectrome-chanical sensors, actuators, in microfluidic/nanofluidic devices, as nanobiosensors, as targeted drug delivery vectors, in magnetocytolysis of cancerous tumors, in hyper-thermia, in separations and cell sorting, for magnetic resonance imaging (MRI), and in immunoassays.
FERROFLUID SYNTHESIS
Ferrofluid Composition
The current ”nanotechnology” focus on nanoscale devices is new, but the synthesis and formulation of magnetic nanoparticles in ferrofluids has been fairly well established in science and engineering over the last four decades.[1-6,17,32-38] As illustrated in Fig. 1, ferrofluids generally consist of suspensions of permanently magnetized nanoparticles up to about 10% by volume, with diameters on the order of 5-15 nm and with adsorbed surfactant/polymer dispersant layers of approximately 2 nm thickness,[39] undergoing rotational and translational Brownian motion in a suspending fluid. A transmission electron microscopy (TEM) electron micrograph at 500,000 x magnification of approximately 6-nm-diameter iron oxide particles to be utilized in commercial grade ferrofluid is shown in Fig. 2.
Fig. 1 Ferrofluid as a colloidal dispersion of permanently magnetized nanoparticles of radius Rp, on the order of 5 nm, possessing a permanent dipole moment with domain magnetization Md. A stabilizing dispersant layer of thickness d, on the order of 1-2 nm, is adsorbed on the magnetic particle’s surface.
Ferrofluid Colloidal Stability
Colloidal stability involves competition between thermal energy=kT and magnetic energy = m0MdHV, where k = 1.38 x 10"23 J/K is Boltzmann’s constant, T is the absolute temperature [in K], m0 = 4px 10"7 H/m is the magnetic permeability of free space, Md is the particle magnetization [in A/m], H is the magnetic field [in A/m], and V = pD3/6 m3 is the magnetic volume of a spherical ferrofluid nanoparticle of diameter D = 2Rp [in m3].[1]
Stability against settling in a magnetic field requires that the thermal energy be large compared to the magnetic energy:
For the typical magnetite ferrofluid nanoparticle with Md = 4.46 x 105 A/m (or, equivalently, m0Md = 0.56 T) in a magnetic field of H= 104 A/m (m0H«0.013 T) at room temperature (T =298 K), Eq. 1 yields D <11.2 nm.
Commercially available ferrofluids with a volume concentration f of magnetic particles with magnetization Md have a saturation magnetization Ms = fMd up to about 0.1 T, but calculations show that an upper limit of saturation magnetization can be 0.21 T for 16-nm-di-ameter magnetite particles, 0.48 T for 8.7-nm cobalt particles, and 0.55 T for 7.8-nm iron particles.[40]
Ferrofluid Preparation
The two primary methods of preparing particles in the nanosize range are grinding[7] and precipitation.[41] The first commercial ferrofluid was prepared in the mid-1960s by wet grinding of magnetite in kerosene starting from micron-sized particles in a ball mill. It takes about 5001000 hr to reach ~ 10 nm diameter. Chemical precipitation methods are much faster, and thus are most often employed to produce small magnetic nanoparticles.[1-6] The overall chemical reaction for precipitation of ferro-fluid nanoparticles is:[41]
where Fe3O4 is magnetite with a divalent/trivalent iron ion ratio of FeIII/FeII=2. Following precipitation, the small particles are resuspended in a mixture of a surfactant and an organic solvent.
Fig. 2 A TEM electron micrograph at 500,000 x magnification of a mixture of Fe3O4 and Fe3O2 iron oxide particles. The average diameter is 5.9 ± 0.4 nm, with a standard deviation of 2.3 nm. Particles are coated with a surfactant and are utilized in the preparation of a commercial-grade ferrofluid.
An easy and economical method for preparing an aqueous ferrofluid in less than 2 hr reacts iron(II) and iron(III) ions in an aqueous ammonia solution to form magnetite (Fe3O4):
The magnetite is then mixed with an aqueous tetramethyl-ammonium hydroxide [(CH3)4NOH] solution to form a stabilizing surfactant coating.[17]
A ferrofluid using a liquid metal carrier is desirable for high thermal and electrical conductivity applications. A liquid mercury ferrofluid with 2% by weight iron was made with a saturation magnetization of about 700 G. However, stabilizing surfactants have not yet been found for liquid metals, and so, to date, no stable conducting ferrofluid has been made.[1,42,43]
Whereas conventional ferrofluids are opaque, Xerox has developed a new series of water-based ferrofluids based on hydrogel technology with high optical transparency for colored magnetic toner and ink applications.[44] Using maghemite (g-Fe2O3 particles) in the size range of 2-10 nm, Xerox produced transparent colloids ranging in color from light amber to dark red with saturation magnetization greater than 400 G.
FERROFLUID MAGNETIZATION
Magnetization Relaxation Time Constants
When a d.c. magnetic field H is applied to a ferrofluid, just like a compass needle, each magnetic nanoparticle with magnetic moment m experiences a torque mem xH, which tends to align m and H. There are two important time constants that determine how long it takes m to align with H:[1,45]
The Brownian rotational relaxation time tB describes the hydrodynamic process when the magnetic moment is fixed to the nanoparticle and surfactant layer of total hydrodynamic volume Vh, and the whole rotates in a fluid of viscosity z to align m and H. For the spherical nanoparticle in Fig. 1, Vh = 4p/3(Rp+ d)3. The Neel time constant tN is the characteristic time for the magnetic moment to align along the particle’s easy axis with H, without particle rotation. The parameter K is the particle magnetic anisotropy and Vp = 4p/3Rp is the volume of magnetic material alone. The literature gives different values for the anisotropy constant of magnetite, over the range of 23,000-100,000 J/m3, whereas t0 approximately equals 10"9 sec. Recent work[46] has used Mossbauer spectroscopy to show that the value of K is size-dependent, increasing as particle size decreases and gives a value of K = 78,000 J/m3 for 12.6 -nm-diameter magnetite nano-particles. The total magnetic time constant t including both Brownian and Neel relaxation is given by:[1,45]
The time constant t is dominated by the smaller of tB or tN. For K = 23,000 J/m3 with 12.6-nm-diameter magnetite nanoparticles at T = 300 K, tN approximately equals 336 nsec, whereas for the same size particles and temperature with K = 78,000 J/m3, tN approximately equals 368 msec. For a ferrofluid with a representative fluid viscosity of Z = 0.001 Pa sec and with a surfactant thickness d = 2 nm, tB = 1.7 msec. Thus we see that with K = 23,000 J/m3, the effective time constant is dominated by tN, whereas for K = 78,000 J/m3, the effective time constant is dominated by tB. Experiments with ferrofluid particles of the order of 10 nm diameter have found effective magnetic relaxation times by fitting theory to experimental measurements. The computed Brownian relaxation time[47] thus indicated that K has value on the order of 78,000 J/m3, as recently reported[46] rather than previously used values on the order of 23,000 J/m3. Brownian and Neel relaxation are lossy processes leading to energy dissipation and causing complex susceptibility to have an imaginary part measurable using spectroscopic magne-tometry.[48] These losses lead to heat generation using time-varying magnetic fields, which can be used for localized treatment of cancerous tumors.
In rotating magnetic fields, the time constant t of Eq. 5 results in the magnetization direction lagging H; therefore a time average torque acts on each nanoparticle, causing the particles and surrounding fluid to spin.[1,49-62] This leads to new physics as the fluid behaves as if it is filled with nanosized gyroscopes that stir and mix the fluid. In a flow field, if the nanoparticles spin to cause secondary flow in the direction opposite to the local vorticity of the flow, the driving pressure must increase to maintain the initial flow, in the same way as if the fluid viscosity increased. Similarly, if the nanoparticles spin to cause secondary flow in the same direction as the local vorticity of the flow, the driving pressure can decrease for the same initial flow, in the same way as if the fluid viscosity decreased. Thus the nanoscale flow field resulting from the spinning nanoparticles can result in an increase or decrease of effective magnetoviscosity. A decrease in viscosity that is controllable by magnetic field amplitude and frequency has been termed ”negative viscosity.”[64-68] The torques described above can drive ferrofluid flow for microfluidic and nanofluidic pump applications, or generate heat by viscous dissipation of spinning nanoparticles.
Langevin Magnetization Characteristic
Ferrofluid equilibrium magnetization is accurately described by the Langevin equation for paramagnetism:
where M and H are collinear, Ms = Nm = Mdf is the saturation magnetization when all magnetic dipoles with moment m = MdVp and magnetic nanoparticle volume Vp with magnetization Md are aligned with H, N is the number of magnetic dipoles per unit volume, and f is the volume fraction of magnetic nanoparticles in the ferrofluid. For the typically used magnetite nanoparticle (Md = 4.46 x 105 A/m or m0Md = 0.56 T), a representative volume fraction of f = 4% with nanoparticle radius Rp = 5 nm (Vp = 5.24 x 10"25 m3) gives a ferrofluid saturation magnetization of m0Ms = m0Mdf = 0.0244 T and N = f/Vp « 7.6 x 1022 magnetic nanoparticles/m3.
Fig. 3 shows Eq. 6 plotted together with magnetization measurements of four different ferrofluids at various temperatures.[69] At low magnetic fields, the magnetization is approximately linear with H, m=wmH, where:
is the magnetic susceptibility, related to magnetic permeability as m=m0(1 +Wm). For our representative numbers at room temperature and 10-nm-diameter magnetite particles, we obtain wm ~ 4.24 and m/m0 ~ 5.24. The universality of the Langevin curve of Eq. 6 for different ferrofluids, different nanoparticle sizes, and different temperatures is demonstrated in Fig. 3.
Magnetocaloric Effect
The temperature dependence of magnetization causes ferrofluids to exhibit the magnetocaloric effect whereby magnetic materials can heat up in a magnetic field and cool down when the magnetic field is removed.[1,70] This allows a direct and efficient conversion of magnetic work to heat with no mechanical moving parts, or, if the cycle is reversed, refrigeration or heat pumping is obtained. If the magnetic field H of a magnetic material with magnetization M(H,T) is increased by an amount AH, adiabatic demagnetization results in a decrease of temperature:
where CH is the heat capacity at constant H.[38] For example, using iron in a 20-T magnetic field, the adiabatic temperature drop is 53°C.[1]
Fig. 3 Measured magnetization (dots) for four ferrofluids containing magnetite particles (Md=4.46 x 105 A/m, or, equiv-alently, m0Md=0.56 T) plotted with the theoretical Langevin curve (solid line). The data consist of Ferrotec Corporation ferrofluids: NF 1634 Isopar M at 25.4°C, 50.2°C, and 100.4°C, all with fitted particle size of 11 nm; MSG W11 water-based at 26.3°C and 50.2°C, with fitted particle size of 8 nm; NBF 1677 fluorocarbon-based at 50.2°C, with fitted particle size of 13 nm; and EFH1 (positive a only) at 27°C, with fitted particle size of 11 nm. All data fall on or near the universal Langevin curve indicating superparamagnetic behavior.
For a heated magnetic fluid with a change in magnetization of AM in a magnetic field H, the pressure increase is:
Magneto-Optical Effects
Anisotropy from nonspherical nanoparticles orienting in an applied magnetic field causes birefringence (also known as the Cotton-Mouton effect, where the refractive index changes along axes parallel and perpendicular to the magnetic field), dichroism (change in light color dependent on direction of light polarization), and Faraday rotation (the plane of linearly polarized light is rotated when a magnetic field is applied parallel to the direction of light propagation).[71,72] Birefringence causes incident linearly polarized light to become elliptically polarized at some angle to the applied magnetic field. If the birefrin-gent ferrofluid is placed in an optical polariscope, the transmitted light intensity varies with applied magnetic field magnitude and direction. Such a configuration can be used as a light shutter or as a magnetometer. After removing a magnetic field, the transient birefringence can be measured to determine the Brownian relaxation time of Eq. 4 from which the hydrodynamic nanoparticle size can be determined. Such magneto-optical relaxation measurements have also been used to determine the binding reactions of antibodies to their antigens through increases of nanoparticle size.[73]
