Ind. Eng. Chem. Res. 1996, 35, 3027-3031
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Microrheological Study of Magnetic Particle Suspensions M. S. Jhon,* T. M. Kwon,† H. J. Choi,‡ and T. E. Karis§ Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, Department of Polymer Science and Engineering, Inha University, Inchon, 402-751, Korea, and IBM Research Division, Almaden Research Center, San Jose, California 95120
Two different microrheological characterization techniques for the microstructure of complex fluids (i.e. rheomagnetic and rheooptic measurements) were adopted to study the microstructural state of magnetic particle suspensions. These two techniques measure the dispersion state of various single-domain magnetic particles (rodlike γ-Fe2O3 or CrO2 and platelike Ba-ferrite). The techniques complement one other by measuring the order parameter for the magnetic particles in suspension over different concentration ranges. The rheomagnetic measurement is good for on-line characterization of microrheological properties of magnetic particle suspensions. The rheooptical measurement is useful for off-line dispersion microstates and rheological properties of the suspensions. Introduction Particulate magnetic recording media, such as magnetic tapes and floppy disks, consist of a coating of fine magnetic particles on a nonmagnetic plastic substrate. The final product is greatly affected by the dispersion quality of the magnetic particle suspensions (Sharrock, 1989). Although the particulate media industries are mature, an unsolved problem of dispersion quality still remains which plagues any coating process involving unstable particle suspensions. To examine this issue in light of different characterization techniques, we studied a rheomagnetic method for on-line characterization and a rheooptical method for off-line characterization. It is well-known that when magnetic particles are immersed in fluid, there is a dynamic coupling between the fluid and the particles (Brenner, 1972; Smith and Bruce, 1979). In the presence of external fields, suspended particles perturb the fluid media while the fluid changes the dynamics of the particles, especially the orientation (Karis and Jhon, 1986). The dynamic coupling is experimentally observable either by studying the overall suspension behavior or by examining the dynamics of particle orientations (Russel et al., 1989). The orientation of the suspended particles changes dramatically from the initial configuration in the absence of flow and can be measured using rheomagnetic or rheooptic devices depending on the concentration range (Kwon et al., 1992a). Understanding of the complex dynamic coupling between the particles and the fluid in the presence of significant magnetic interactions when the shape of the particles is nonspherical is a challenging problem on a fundamental level, as well as in many technical applications (Karis and Jhon, 1993). The magnetic particle suspension, which is inherently unstable to flocculation due to strong interparticle magnetic forces, is usually prepared by dispersing particulate powder into a suspending fluid (a mixture of binder polymer and solvent). The amount of the flocs that appear in the coating, whose size and distribution is commonly referred to as the “dispersion quality,” is
directly related to the quality of the media (Karis, 1989; Shah et al., 1991). Therefore, characterizing and stabilizing the magnetic particle dispersion is an important engineering consideration in advanced particulate media production. Understanding microrheological characteristics of single domain magnetic particle suspensions is essential for practical applications in obtaining and controlling the state of dispersion at the required level. The rheomagnetic device is based on the principle that the flow-induced particle orientation, which is related to the dispersion quality of the suspension, could be detected as an inductance change through a solenoid coil sensor when the suspension flows through it (Karis and Jhon, 1986). The degree of alignment is found to increase with the flow rate and also depends on the concentration of the suspensions. Although the rheomagnetic technique can be applied in principle to both dilute and nondilute suspensions, the rheooptical technique is used only for dilute suspensions. The rheooptical device uses the principles of polarization modulated linear dichroism to simultaneously measure dichroism and the extinction angle of light passed through the suspension under imposed external fields (hydrodynamic and/or magnetic). Dichroism is related to the degree of particle alignment, which in turn is related to the dispersion quality of the suspension. A pulse of constant magnetic field was applied on a quiescent suspension sample. The dichroism (and hence the degree of particle alignment) was found to increase with applied magnetic field. Relationships between the particle orientation due to the two types of external fields are established through dimensional analysis. The “equivalent magnetic field” is the magnetic field which yields the same magnitude of dichroism as that obtained under shear. Once the equivalent magnetic field plot is obtained experimentally, one can conveniently transform the hydrodynamic field to the equivalent applied magnetic field, and then determine the particle orientation (Choi et al., 1994). Experimental Section
* Corresponding author. T: 412-268-2233. F: 412-2687139. email:
[email protected]. † Present address: LG Chemical Ltd., Science Town, Taejon 305-380, Korea. ‡ Inha University. § IBM.
S0888-5885(95)00749-4 CCC: $12.00
The rodlike γ-Fe2O3 or CrO2 and platelike Ba-ferrite magnetic particles in this study were single-domain particles, similar to those used in magnetic tapes and disks. For both measurements, the suspending fluid was ethylene glycol, which was adopted to simulate the © 1996 American Chemical Society
3028 Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996
below the critical Reynolds number for transition to turbulence in pipe flow (Shah et al., 1991). The inductance (L) of the coil is related to the coil geometry β (β ) 4l/πN2d2, where N is the number of turns of the coil, d is the diameter, and l is the length of the coil) and the permeability µ by
L ) β-1µ
(1)
In practice, we can measure L from the oscillator frequency f in an L-C circuit by means of the relationship
L ) 1/(2πf)2C
Figure 1. Converging flow cell in rheomagnetic device.
actual coating formulation of the magnetic particle suspension. The particles’ size and shape were characterized using a transmission electron microscope (TEM). A vibrating sample magnetometer (VSM) was employed to characterize the particle magnetic properties for randomly oriented dry powders. Details of the TEM and VSM measurements are in Kwon et al. (1992c). The particle density was calculated using the volume increase when a known mass of particles was immersed into a fluid. The coercivity, saturation magnetization, density, diameter, and aspect ratio (length to diameter ratio) are 616 Oe, 77.27 emu/g, 4.6 g/cm3, 0.38 µm, and 7.5 for γ-Fe2O3; 585 Oe, 81.49 emu/g, 4.8 g/cm3, 0.46 µm, and 13 for CrO2; and 635 Oe, 34.97 emu/ g, 5.2 g/cm3, 0.13 µm, and 0.1 for Ba-ferrite. Particle suspensions were prepared in a consistent manner in order to obtain reproducible initial suspension characteristics. For the rheomagnetic measurements, 400 g of the particle powder was combined with 600 mL of suspending fluid in a paint shaker (Red Devil, Model 5410-00) for 10 min. Then, the mixture was passed through a media mill (Eiger Minimotor Mill 0.6 mm ceramic ball media) at 1000 rpm. An additional amount of suspending fluid was stirred into this millbase, and the diluted suspension was once again passed through the mill. No dispersant or surfactant was added. On the other hand, for the reooptical measurement, a concentrated master suspension was prepared by mixing a known amount of magnetic particles into the suspending medium using a volumetric flask and then sonicating the suspension for at least 12 h to properly disperse the particles. Less concentrated suspensions for each experiment were then obtained by diluting the master suspension to a volume fraction between 10-5 and 10-4. The rheomagnetic measurement (Karis and Jhon, 1991; Kwon et al., 1992a; and Kwon et al., 1993a) is a technique for studying the concentration and orientation of magnetic particles in suspensions through inductance measurements. The main element in the test apparatus is an inductor coil and an oscillator circuit. The oscillator method was selected for its low cost and accuracy. Information regarding the state of the suspension flocculation is obtained if the coil is wrapped closely downstream from a circular converging flow of the suspension as shown in Figure 1. The flow cell was made by attaching a 3-mm i.d. glass tube to a 5-cm i.d. tube. The contraction was made abrupt in order to maximize the extensional flow component near the entrance. The coil was located immediately downstream from the contraction formed at the junction of the large and small tube (Jhon and Karis, 1989). The Reynolds number was in the range 1-103, which is well
(2)
where C is capacitance. The most important quantity in characterizing particle orientation is the inductance change (δL), as shown in the following equation,
δL ) L - Ls ) β-1µmφ
(3)
where φ is the volume fraction of particles in the suspension, Ls is the value of L measured with pure suspending fluid, and µm is the permeability contribution of the magnetic particles. µm is obtained by summing the permeability contribution of each particle in the suspension over all possible orientations giving
F(θ) sin θ dθ ∫0π/2[dM dH ]Hf0
µm ) µ0
(4)
where θ is the angle between the direction of flow and the spheroidal particle’s major axis of revolution, µ0 is the permeability of free space, M is the magnetization, and H is the applied magnetic field. F(θ) is the geometrical orientation distribution function of particles, and [dM/dH]Hf0 is related to the intrinsic magnetic susceptibility of the particles. For example, using the Stoner and Wohlfarth coherent rotation model (Stoner and Wohlfarth, 1948), we obtain (Kwon et al., 1992b)
µ0Ms2 dM ) [1 - P2(cos θ)] dH Hf0 3Ku
[ ]
(5)
where P2(cos θ) ) (3 cos2 θ - 1)/2 is the second Legendre polynomial. The saturation magnetization Ms and shape anisotropy coefficient Ku are properties of the magnetic particle. For the dilute system (φ , 1/p2 where p is the aspect ratio of the particles), by neglecting the hydrodynamic interaction between particles, one can obtain F(θ) (Brenner, 1972; Kwon et al., 1992a)
∫-11 exp(3/4qPeξ2) dξ
F(θ) ) F(ξ) ) exp(3/4qPeξ2)/
(6)
where ξ ) cos θ, q ) (p2 - 1)/(p2 + 1), and Pe ) ˘ /Dr which is the rotary Peclet number (i.e., the ratio of convective to diffusive contributions). Here, Dr is the rotary diffusion coefficient, and ˘ is the average elongation rate near the mouth of the small tube (see Figure 1), and is approximated by ˘ ) γQ/d3 (γ ) adjustable hydrodynamic constant; d ) diameter of small tube; Q ) flow rate (see Figure 3)) (Karis and Jhon, 1991). Substituting eqs 4-6 into eq 3, one can get
δL/φ ) (1 - S)/Rβ
(7)
where R ) 3Ku/(µ0Ms)2 is a constant obtained from the magnetic properties of the particle. S is the “order
Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996 3029
axis of the particle relative to the imposed field direction is included in the order parameter. It has been shown in the Rayleigh approximation that the dichroism of the suspension is expressed by
〈∆n′′〉 )
Nns(A| - A⊥) [(〈uxux〉 - 〈uyuy〉)2 + 4〈uyuy〉2]1/2 2 (8)
(Frattini and Fuller, 1984; Frattini et al., 1991). Here, N is the number of the particles per unit suspension volume, ns is the refractive index of the suspending medium, and ui (i ) x, y) are the Cartesian components of the particle orientation unit vector, u. A| and A⊥ are related to the intrinsic optical properties of the particle as follows:
[
Figure 2. Coordinate system adopted for particle orientation.
parameter” defined by 〈(3 cos2 θ - 1)/2〉. The angle brackets indicate an ensemble average of all particle orientations (i.e., 〈B(u)〉 ) ∫B(u)F(u) du with F(u) ≡ F(θ)). For example, the numerical value of S lies between 0 (a random orientation) and 1 (a perfect orientation) for a rodlike particle. The contribution of the magnetic particles to the inductance is related to the projection of the particle’s magnetic moment vector onto the magnetic field vector. For rodlike magnetic particles, the magnetic moment vector is parallel to the major axis of the particles, whereas the magnetic moment vector is perpendicular to the major plane for platelike particles. The inductance measures the orientation of the particles due to the flow field. The principle of the rheomagnetic measurement is based upon the fact that when magnetic particles are in an imposed hydrodynamic field, particles of various shapes orient themselves differently. The magnetic anisotropy induced by the particle orientation, which contains information on the dynamic state of flocs, is detected using a weak magnetic sensing field. This magnetic sensing field is also used to detect the particle concentration of a quiescent suspension (Kwon et al., 1992a). For the dilute suspension of magnetic particles, polarization-modulated linear dichroism, a noninvasive optical technique developed in recent years for studying polymer solutions (Galante and Frattini, 1993) and suspension microrheology (Frattini et al., 1991), was also adopted to investigate the orientational ordering in suspensions of magnetic particles subjected to applied magnetic fields. To study the magnetic particle suspension, we built external magnetic and flow field generating equipment (a plane Poiseuille flow cell and a quadrupole electromagnet) (Kwon et al., 1993b). The polarization modulation dichroism measurement technique, which has the advantage of improved sensitivity and precision over conventional optical measurements, is able to measure the orientation distribution of suspended rod- and platelike particles in the presence of external magnetic and hydrodynamic fields. Linear dichroism measurements provide a degree of particle alignment about the field axis. Linear dichroism, therefore, indirectly measures the intrinsic magnetic properties and shapes of the particles (or flocs of particles). Consider a suspension of axisymmetric particles subjected to incident light traveling along the Z direction of a Cartesian coordinate system as shown in Figure 2. The direction of light propagation is normal to the imposed field direction. The angle of the major
] ]
k3 k3 A| ) 2 |R||2 - ImR| ) Re iR| + 2 R*|R| 3 3
[
k3 k3 A⊥ ) 2 |R⊥|2 - ImR⊥ ) Re iR⊥ + 2 R*⊥R⊥ 3 3
(9) (10)
where Im and Re represent the imaginary and real parts, respectively, k is the wavenumber of the light, and R| and R⊥ are the intrinsic polarizabilities of the particle parallel and perpendicular to the particle’s optical axis, respectively. Rearranging eq 8 for the case of a uniaxial aligning field in the X-Y plane, we obtain
〈∆n′′〉 S ) LDmax S∞ where
LDmax )
Nns(A| - A⊥)S∞ 2
(11)
Here, LDmax is the maximum value of 〈∆n′′〉 and S∞ is the value of S obtained at a perfect particle alignment. Using eq 11, the orientation state of the particles in suspension can be inferred from the experimentally measured dichroism. Results and Discussion The inductance measured for suspensions of three different types of magnetic particles (γ-Fe2O3, CrO2 and Ba-ferrite) is plotted with respect to the volume fraction measured by a thermogravimetric analysis (Karis, 1989), as shown in Figure 3. For all magnetic particle suspensions, the inductance of the suspension showed a linear correlation with the volume fraction of the suspension. Once a concentration calibration curve is prepared, the volume fraction of an unknown suspension can be quickly measured using this inductance measurement. The advantage of the rheomagnetic method compared with other techniques is that it is suitable for on-line characterization of the concentration and orientation of magnetic suspensions during the early stages of slurry production. Typical inductance data obtained from flow orientation measurements are shown in Figure 4. (The vertical axis is a relative scale for the purpose of illustration.) The measured inductance (L) decreases with the flow rate (Q) for a rodlike γ-Fe2O3 suspension, while it increases for platelike Ba-ferrite. During these tests, the flow rate was linearly increased to its maximum
3030 Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996
Figure 3. Correlation between inductance of quiescent suspensions and volume fraction.
f
Figure 5. Typical dichroism data from rheooptical measurement for rod- and platelike particles plotted as a function of the magnetic field.
opposite to that for the platelike particles. The shapes of the curves are different from one another due to the dependence of the torque applied by the field on the type of field and the particle geometry. The rheooptical measurement is complementary to the rheomagnetic measurement, since both techniques measure the orientation of magnetic particles in external fields (hydrodynamic and/or magnetic). It is remarkable to note that the opposite signs of the measured dichroism for the two differently shaped particles (as shown in Figure 5) are similarly observed in the rheomagnetic apparatus (see Figure 4). Both the inductance and dichroism are related to the order parameter (S) as (eqs 7 and 8)
L - Ls ∝ (1 - S), [∆n′′] ∝ S Figure 4. Typical inductance data from rheomagnetic measurement for rod- and platelike particles plotted as a function of flow rate. The vertical scale shows relative changes of inductance.
value over a time of approximately 5 min, and then the flow rate was linearly decreased to zero in the same period of time, without holding it at the maximum rate. Hysteresis of the curves is ascribed to flow-induced microstructural changes in the suspension. Recirculation of the particle suspension through the pump, tubing, and converging flow cell continuously changes the flocculation state of the suspension. An amount of time on the order of hours to days of recirculation is required in order to approach a steady state of dispersion in the present apparatus. Figure 4 is an illustration of the dynamic equilibrium of flocculation in these relatively unstable magnetic particle suspensions. Typical dichroism (∆n′′) dependence of rodlike γ-Fe2O3 and platelike Ba-ferrite particles on the imposed magnetic field is shown in Figure 5. Measured dichroism increases monotonically and approaches a saturation level with the applied magnetic field. The dichroism changes in opposite directions for the two differently shaped particles as with the inductance in Figure 4. Two different types of force were employed to produce the particle orientation shown in Figures 4 and 5. In Figure 4 the particle orientation is produced by a hydrodynamic flow field whereas in Figure 5 the orientation is produced by a magnetic field. In both cases, the alignment of the magnetic moment for the rodlike particles is
(12)
From the definition of the order parameter, S equals 0 for a random orientation of the particles, regardless of particle shape. However, S becomes unity for perfect orientation of rodlike particles, and -1/2 for platelike particles (Kwon et al., 1991). Therefore, for rodlike particles, 0 e S e 1 and S increases with particle alignment, while -1/2 e S e 0 and decreases with particle alignment, in the case of a platelike particle as illustrated in Figure 4 (eq 2). These two techniques focus on orientational characteristics of particles, and the shapes of measured inductance or dichroism curves showed contrasting orientation behaviors of rodlike and platelike particles subjected to external fields. The rheooptical measurement requires extreme dilution of particle concentration (φ ∼ 10-6), while rheomagnetic measurements are applicable to a broad range of high suspension concentrations (up to φ ∼ 10-2). One of the key features of these magnetic particle suspensions is their instability toward flocculation. The instability arises from strongly attractive interparticle forces. Initially the primary particles are separated by the strong shearing forces in the media mill. The suspension is then transferred to the recirculating flow apparatus, during which time flocculation begins to occur. Many hours of recirculation at a steady state are required to achieve a steady state degree of flocculation, as measured by the flow cell coil inductance or the rheooptical dichroism. The dynamic state of dispersion quality measurements is the intended purpose of developing these measurement techniques. The orienta-
Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996 3031
tion theory was developed to interpret these results as completely as possible in terms of the changes being measured in the microstructure of flocculation within the suspension. A unique analytical scheme was established relating the microstructural properties of suspensions to the hydrodynamic orientational characteristics and the intrinsic magnetic properties of the particles. Therefore, the rheomagnetic method is suitable for process control in particulate media production because it can be placed on-line, and measurements can be performed in real time. Acknowledgment One of the authors (H.J.C.) wishes to acknowledge the financial support of the Research Fund for Advanced Materials (1995) through the Korean Ministry of Education and Inha University (1995). Literature Cited Brenner, H. Suspension Rheology in the Presence of Rotary Brownian Motion and External Couples: Elongational Flow of Dilute Suspension. Chem. Eng. Sci. 1972, 27, 1069. Choi, H. J.; Park, Y. D.; Frattini, P. L.; Jhon, M. S. Rheo-optical Measurements on Suspensions of Magnetic Recording Particles. J. Appl. Phys. 1994, 75, 5579. Frattini, P. L.; Fuller, G. G. The Dynamics of Dilute Colloidal Suspensions Subject to Time-Dependent Flow Fields by Conservative Dichroism. J. Colloid Interface Sci. 1984, 100, 506. Frattini, P. L.; Shaqfeh, E. S. G.; Levy, J. L.; Koch, D. L. Observations of Axisymmetric Tracer Particle Orientation During Flow through a Dilute Fixed Bed of Fibers. Phys. Fluids A 1991, 3, 2516. Galante, S. R.; Frattini, P. L. Spatially Resolved Birefringence Studies of Planar Entry Flow. J. Non-Newtonian Fluid Mech. 1993, 47, 289. Jhon, M. S.; Karis, T. E. The Particulate Media for Magnetic Recording: Characterization Techniques for Particle Dispersion and Orientation. In Polymers in Information Storage Technology; Mittal, K. L., Ed.; Plenum Publishing Corp.: New York, 1989; p 299. Karis, T. E. Rapid Determination of Coating Percent Pigment from Magnetic Recording Ink Density and Volume Fraction. In Polymers in Information Storage Technology; Mittal, K. L., Ed.; Plenum Publishing Corp.: New York, 1989; p 421.
Karis, T. E.; Jhon, M. S. Flow-Induced Anisotropy in the Susceptibility of a Particle Suspension. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 4973. Karis, T. E.; Jhon, M. S. Processing Effects on the Flow Orientation Properties of a Magnetic Particle Suspension. Colloids Surf. 1991, 53, 393. Karis, T. E., Jhon, M. S., Guest Eds. Ferro/Electro Fluids and Magnetic Particle Suspensions. Colloids Surf. A 1993, 80, (1). Kwon, T. M.; Jhon, M. S.; Karis, T. E. Concentration and Dispersion Quality Measurement for Ba-Ferrite Particles. J. Magn. Soc. Jpn. 1991, 15, (S2), 663. Kwon, T. M.; Jhon, M. S.; Karis, T. E. A Device for Measuring Concentration and Dispersion Quality of Magnetic Particle Suspension. IEEE Trans. Instrum. Meas. 1992a, 41, 10. Kwon, T. M.; Jhon, M. S.; Karis, T. E. Dispersion Quality of RodLike and Plate-Like Ba-Ferrite Suspensions for Magnetic Recording. Adv. Info. Storage Syst. 1992b, 4, 87. Kwon, T. M.; Jhon, M. S.; Karis, T. E. Rhomagnetic Measurements on Suspensions of Magnetic Recording Particles. J. Appl. Phys. 1992c, 72, 3770. Kwon, T. M.; Jhon, M. S.; Choi, H. J.; Karis, T. E. Rheomagnetic Properties of Mixed Magnetic Particle Suspensions. Colloids Surf. 1993a, 80, 39. Kwon, T. M.; Frattini, P. L.; Sadani, L. N.; Jhon, M. S. RheoOptical Study of Magnetic Particle Orientation under External Fields. Colloids Surf. 1993b, 80, 47. Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: New York, 1989. Shah, M. J.; Karis, T. E.; Cuka, G. M. Effect of Dispersion Quality on Particulate Magnetic Recording Disk Properties. AIChE J. 1991, 37, 394. Sharrock, M. P. Particulate Magnetic Recording Media: A Review. IEEE Trans. Magn. 1989, Mag 25, 4374. Smith, T. L.; Bruce, C. A. Intrinsic Viscosities and Other Rheological Properties of Flocculated Suspensions of Nonmagnetic and Magnetic Ferric Oxides. J. Colloid Interface Sci. 1979, 72, 13. Stoner, E. C.; Wohlfarth, E. P. A Mechanism of Magnetic Hysteresis in Heterogeneous Alloys. Trans. R. Soc. (London) 1948, A240, 599.
Received for review December 15, 1995 Revised manuscript received April 5, 1996 Accepted April 5, 1996X IE950749W X Abstract published in Advance ACS Abstracts, August 15, 1996.
