Evaluation of a magnetic dispersion by interparticle interactions

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Journalof mngnello materials

ELSEVIER

Journal of Magnetism and Magnetic Materials 154 (1996) 279-290

Evaluation of a magnetic dispersion by interparticle interactions Halit GiSkttirk 1, Kazuo Maki * Kao Corporation, Recording and Imaging Science Laboratories, 2606 Akabane, Ichikaimachi, Haga, Tochigi 321-34, Japan

Received 17 October 1995

Abstract

The magnetic, rheological and electrical effects of interparticle interactions in a metal particle dispersion have been investigated experimentally with the aim of understanding the state of the dispersion through such interactions. Samples of different degrees of dispersion were obtained by varying the duration of a sand milling operation. The magnetic interactions were assessed from the hysteresis and remanence curves of frozen dispersion samples. The coercivity and remanence coercivity of the dispersion samples were found to increase with increasing milling time, while the switching field distribution calculated from both the hysteresis and remanence curves decreased. The first normal stress difference, N 1, of the dispersion was measured as a rheological indicator of magnetic interactions. N I decreased with increasing milling time. The dielectric constant and the ac conductivity were investigated for possible electrical particle interactions. Both parameters decreased with increasing milling time, but the results were found to be due to polymer-particle rather than particle-particle interactions. 1. Introduction Particulate magnetic media, currently used as flexible disks and tapes, consist of magnetic particles dispersed in a polymeric binder. The magnetic particles incorporated into the binder are initially in the form of aggregates. During the dispersion preparation, these aggregates are broken down into primary particles and are then distributed within the binder solution. The quality of the dispersion has a significant impact on the media performance [1,2]. Insufficient dispersive or distributive mixing gives rise to problems in the form of rough media surfaces, poor particle orientations, low signal to noise ratios and

* Corresponding author. Fax: + 81-285-687309. i On leave of absence from Highly Filled Materials Institute at Stevens, Hoboken, NJ 07030, USA.

high error rates. Furthermore, the general trend in particulate media is towards the use of smaller magnetic particles in order to achieve higher recording densities [3,4]. These particles are more difficult to disperse, placing more emphasis on the dispersion preparation process. This study is intended to develop new tools for evaluating the state of a magnetic dispersion, preferably in its liquid form, in the hope that it will facilitate the design and optimization of the process. Measurements of the state of a magnetic dispersion are usually performed by first preparing a coating layer on a substrate film and then measuring various properties associated with the coating. One property, which is popular with dispersions of many kinds, is the light reflectance of the film surface [5-7]. As the coating dries, it acquires a surface roughness that is determined by the size of the particle clusters in the dispersion. The degree of light

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H. Gi~kti~rk, K. Maki / Journal of Magnetism and Magnetic Materials 154 (1996) 279-290

reflection, measured as a gloss value, is used as an indicator of the state of the dispersion. Higher gloss values are associated with smoother surfaces with smaller asperities, and hence better dispersion. Although the gloss measurements are easy to perform experimentally, it is more desirable to evaluate the dispersion in its original form rather than after the coating has been made. The drying of the coating alone might change the structure of the dispersion. A number of researchers have studied this problem using different approaches. Sumiya et al. [8] investigated the alignment of magnetic particles under the influence of an external magnetic field, and concluded that the temporal responses of individual particles and aggregates were different. By monitoring the time evolution of the dispersion magnetization they assessed the state of the dispersion. Kwon et al. [9] introduced a rheomagnetic method based on the alignment of particles under the influence of a flow field. They created a flow pattern in which asymmetric particles would align along their long axes as they passed through an inductor. Changes in the inductance of the coil were measured to assess the degree of alignment. Single particles and clusters of particles exhibited different alignment behavior. Mayo et al. [10] measured the lowfrequency B - H loops and isothermal remanence curves of magnetic dispersions. As the particles or particle clusters rotated, the shapes of the two curves changed. By analyzing the combined physical rotation and magnetic switching behavior of the particles they compared different degrees of dispersibility. Sollis et al. [6] measured the transverse susceptibility by applying a small ac field perpendicular to a dc bias field. Individual particles well oriented with the bias field and poorly oriented particle clusters exhibited different transverse susceptibilities. Balkenende [11] measured the magnetic properties of the dispersion while it was being sheared in a manner similar to Couette flow. He related the variations in the magnetic properties to changes in the particle orientations or in the networks established by interacting particles. Overall, the review of the literature indicates that the common denominator in most of these efforts has been the study of differences in the rotation behavior of the magnetic particles. The approach investigated in this study is based on interactions between the filler particles of a dis-

persion. The intention is to take advantage of magnetostatic interactions which exist intrinsically in particulate recording media. Such interactions are inversely related to the separation between the magnetic particles. It is expected that during the mixing process the average interparticle distance would change, giving rise to changes in the intensity of particle interactions. The relation between the average interparticle distance of a good and a bad dispersion can be expressed as (d)good > (d)bad-

(1)

This hypothesis is due to the breaking up of agglomerates and the distribution of the particles within the binder. By measuring the physical parameters which are influenced by interparticle interactions in a well known manner, one can assess ( d ) , and thereby the state of the dispersion. Three possibilities were considered in testing this approach: (a) Magnetic interaction, magnetic measurable: The filler particles interact with each other magnetically, and the physical parameters measured to gauge the intensity of the interaction are also magnetic. Remanent magnetizations of magnetic particles readily give rise to magnetostatic interactions which are inversely related to the particle spacing, d. These interactions affect the magnetic properties of the dispersion, such as the switching behavior [5]. (b) Magnetic interaction, non-magnetic measurable: Particle interactions are magnetic in nature but the measured parameter is a non-magnetic parameter influenced by the magnetic interaction. A good example is the case of the theological properties of a magnetic dispersion. Magnetic particle interactions are known to give rise to a network structure which influences the deformation characteristics of the dispersion [ 12]. (c) Non-magnetic interaction, non-magnetic measurable: The magnetic interaction exists intrinsically in a magnetic dispersion, but other types of interactions can be externally induced. For example, the application of an electric field would polarize the filler particles to create electric dipoles. These dipoles would interact with each other in a manner similar to the magnetic dipoles. Electrical particle interactions can be evaluated from dielectric properties such as the dielectric constant [13]. In this study we have investigated various forms

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PREM1XING Magnetic powder, carbon black, aluminum oxide,

binder polymers, solvent

to improve with longer milling times, giving rise to greater separation distances between the primary particles and fewer interparticle interactions. Material samples obtained before milling and after two passes through the mill were used as 'bad' and 'good' dispersions, respectively, for gross comparisons.

TWIN SCREW EXTRUDER KNEADING

3. Microstructural observations by optical microscopy

DILUTION

,

.

SAND MILLING

LETDOWN

Fig. 1. Schematicof the magneticdispersionpreparationprocess.

of interparticle interactions, as outlined above, with the aim of understanding the state of the magnetic dispersion. It is hoped that the results can be generalized to other types of suspensions or dispersions where particle interactions might be applicable.

2. Materials and processing The magnetic dispersion used in the study was prepared using acicular iron particles 180 nm long, 20 nm in diameter, with specific surface areas of 50 m2/g, and saturation magnetization 125 emu/g. Small amounts of carbon black and alumina were also included in the dispersion. The binder consisted of a mixture of polyvinyl chloride and urethane polyester polymers. The polymers were dissolved in a solvent combination which included cyclohexanone, toluene and methyl ethyl ketone. The processing was performed as outlined in Fig. 1. The ingredients were first mixed in a Henschelltype batch mixer. Then, the premix was kneaded in a co-rotating, intermeshing twin-screw extruder. The kneaded material was diluted and then milled for periods of time corresponding to up to two passes through a sand mill. Before milling and after each pass, material samples were collected for the characterization experiments. The dispersion was expected

Electron microscopy is an important tool used for microscopic examination of material samples, but it is difficult to employ for magnetic dispersions. The volatiles in the dispersion evaporate rapidly in the vacuum environment of the sample chamber, leaving behind a microstructure which is different from that of the original dispersion. Instead, optical microscopy was used here to obtain information on the microstructure of the dispersion in the liquid state. The capabilities of optical microscopy are limited to a maximum magnification of about X 1000, and a maximum resolution of about 1 txm. Primary particles of the fillers, which generally have sub-micron dimensions, cannot be resolved, but aggregates of the primary particles can be observed. The magnetic pigment and the carbon black in the formulation impart an opaque black color to the dispersion. In order to create a thin film suitable for transmission microscopy, a small angle wedge was constructed using microscope cover glasses, as illustrated in Fig. 2. The average thickness of the film corresponding to the first 1 mm from the tip of the wedge was about l0 I~m. Wedge samples were observed with a Nikon microscope, model Metaphot 66, in the transmission mode. Fig. 3(a,b) show sample micrographs of the paint samples obtained before and after milling, respectively. Aggregates, some larger than l0 Ixm in diameter, can be observed in the pictures. After the

Cover glass

0.15 mm

Paint layer

Cover glass

Glass slide

Fig. 2. Constructionof the small angle wedge.

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O

Fig. 4. An ensemble of magnetic particles.

O

pattern of a single magnetized particle. The analytical solution for a uniformly magnetized sphere of radius R is given by Reitz et al. [14]. If the magnetization of magnitude M is chosen in the direction +z, as shown in Fig. 5, the external field can be expressed as a function of the spherical coordinates of radial distance r and polar angle 0 as M R3 H ( r,O) = - 7 X - 7 [ ( 2 c ° s O)u r + (sin O)uo],

(2)

Fig. 3. Micrographs of the dispersion (a) before and (b) after milling.

where u r and u o are the radial and polar unit vectors, respectively. The field magnitude decreases with increasing radial distance, r. Let r = s be the distance at which the magnitude of H diminishes considerably, where 'considerably' is defined as g(s,O) -

milling process, the aggregates diminish in number, their sizes become smaller and their shapes become more rounded. Visual observations confirm the expected improvement in the state of the dispersion as a result of the milling process.

4. Magnetic measurements The interaction between the particles of a magnetic dispersion depends on the magnetization vector of each particle and the distance between the particles. If we consider an ensemble as illustrated in Fig. 4, the local field experienced by each particle would be influenced by the fields of the neighboring particles in addition to any the external field applied to the ensemble. The concentration at which the contribution from the nearby particles starts to become important can be estimated by examining the field

H(R,O) 10

(3)

The corresponding distance of s can be calculated from Eq. (2): R3 s3

1 -

10

or

s ~ 2.15R.

(4)

To generalize the result from a spherical to an acicular particle, R can be considered as the effective radius of a randomly oriented asymmetric particle. For an ensemble of such particles, 2R would represent the average interparticle spacing at maxi-

p

Fig. 5. A uniformly magnetized sphere.

H. G6ktiirk, K. Maki / Journal of Magnetism and Magnetic Materials 154 (1996) 279-290

mum packing. The volume fraction, p, is inversely related to the interparticle spacing, d, as

1 p ( d ) ~ ~-~

erwise, they would tend to move and rotate under the influence of the magnetic field of the VSM and the microstructure would change. The temperature of the samples during the measurements was about - 1 8 5 ° C , as measured by a thermocouple gauge. A magnetic evaluation of a frozen magnetic dispersion has been reported in the literature by Fisher et al. [15], but the results were not interpreted within the context of particle interactions. A sample hysteresis curve and the corresponding derivative of the magnetization with respect to the magnetic field, d M / d H , is shown in Fig. 6. The parameters chosen from the hysteresis curve to understand the intensity of particle interactions were the coercivity, H c, the switching field distribution, SFD, and the coercivity squareness, S* The remanence curve measurements consisted of two parts. The first part was the isothermal remanence curve for which the remanence was measured starting with the particles randomly magnetized and ending with all the particle magnetizations saturated in one direction. The second part was the demagnetization remanence curve for which the remanence was measured starting with magnetizations saturated in one direction and ending with the magnetizations rotated in the opposite direction. Both remanence curves were normalized to the saturation values to eliminate sample specific features like mass. From a knowledge of the normalized isothermal remanence,

1 =

P m a x ¢:X " ~ ,

(5)

R3 p ( s ) =Pmax 7 .

(6)

For a given aspect ratio, Pmax can be calculated following Doyle et al. [13]. The aspect ratio of the metal particles used in the magnetic dispersion of the study is specified as 9, corresponding to a maximum packing fraction of 0.37 and an interaction limit of p ( s ) = 0.037. The volume fraction of the magnetic particles at the milling stage is about 0.06 greater than the estimated interaction limit. Particle interactions can be expected to influence the magnetic properties at the volume fractions used in the experiments. The experimental investigation of magnetic interparticle interactions was performed by measuring the hysteresis and remanence curves of the paint samples by means of a vibrating sample magnetometer. The paint samples were loaded into cylindrical capsules 8 mm long and 6 mm in diameter. They were frozen in liquid nitrogen before and during the measurements using the appropriate accessories of the VSM. This precaution was necessary in order to preserve the spatial arrangements of the magnetic particles. Oth-

5,0000

II:oersted M:emu muir:

L

•

dM

' -

-..,/

I

/

'

Ik..:

/

w

\.

~.'-~,"v\

~3p~..oo....,.,~;,,::':." :':b:'.:~'""":":"i'l . • I~' ~-,.,'~~ ,'%r'~-:,,,'::J"...,,':,...~.:..;::,.,~, ~ ' /" " 4~m~

283

H¢~

,.r:

I', :~.:._......... . . : : . . , , - , " - " . " " ; t " v " ~ : ~ " ' ; ' * ~ °°~:~°~

/-/~

-5.0000

Fig. 6. A samplehysteresiscurve of the magneticdispersion frozen at - 185°C.

H. GSktiirk, K. Maki / Journal of Magnetism and Magnetic Materials 154 (1996) 279-290

284

M r, and the demagnetization remanence, M d, A M function was calculated using [16]: AM=Md-

(1 - 2 M r ) .

(7)

Fig. 7 shows the normalized remanence curves of a frozen magnetic dispersion sample. For randomly oriented acicular particles A M is a bell-shaped curve with a single maximum. The peak value of A M was selected as an interaction parameter. The other interaction parameters chosen from the remanence curves were the remanence coercivity, H r, the switching field distribution, SFD r, and the interaction field factor, IFF, defined in terms of H0.25, H0.7s, H r and H; [17]: Md(Hr) =0,

(8)

Md(Uo.75 ) = - 0.5,

(9)

Md(Ho.25 ) = 0.5,

(10)

Mr(H/) =0.5,

(11)

Ho7 - Ho25

SFDr

,

(12)

nr

Hr-n; mx

-

-

Hc

(13)

The hysteresis and remanence curve measurements were repeated with multiple samples of the magnetic

10

~0.5 0 Ilg 0.0

07 riff 'r~6°O

~

/

!: Ho.25

-0.5

Z

-1.0

n

°°°°e'"

"o i • e •o ~ o °

Peak AM

J ..t.,,,

-4 -3 -2 -1

1 2 3

4

Magnetic Fletd (kOe)

Fig. 7. Sample remanence curves of the frozen magnetic dispersion. Mr is the normalized isothermal remanence, Md is the normalized demagnetization remanence and the filled circles represent the AM function.

Table 1 Comparison of magnetic interaction parameters of paint samples before and after milling; 8 samples per data point. The percentage difference was calculated as 100 x (value before milling minus the value after milling)/value before milling Parameter

Before milling

After milling

% difference

H,. ( k O e ) SFD ~ S* ~ Peak AM Hr (kOe) a SFDr a IFF

1.79+0.02 0.99+0.03 0.47_+0.01 0.31 +0.02 2.32-+0.01 0.47+0.01 0.15_+0.01

1.82+0.02 0.91+0.03 0.48_+0.01 0.31 _+0.02 2.35 ±0.01 0.45+0.01 0.14_+0.01

-2 +8 - 1 +4 -

a The parameter was calculated on the basis o f the applied external field.

dispersions obtained before and after milling. The average values of the interaction parameters calculated from all the measurements are given in Table 1. The ___ error values listed in the results are 95% confidence intervals of the student's t-distribution. The milling process gives rise to an increase in the coercivity and a decrease in the switching field distribution as calculated from both the hysteresis and remanence curves. These changes are indications of decreasing interparticle interactions in the dispersion, as verified by concentration studies where the magnetic particle loading in the binder was varied and trends in the interactions parameters were identified [3,17-20]. Variation of the filler loading is equivalent to changing the average particle distance if the magnetic particles can be redistributed relatively uniformly. The peak values of A M, IFF and S* do not exhibit measurable changes, suggesting that they might be slowly varying functions of the particle interactions at the concentrations used in the milling. The literature includes studies where I F F and S* for acicular particle assemblies were observed to change with the packing fraction [18,19]. The most sensitive of the selected parameters, in terms of the greatest percentage difference between the good and bad dispersions, is the SFD calculated from the hysteresis curves. The accuracy of the data obtained from the remanence curves is better than that of the data from the hysteresis curves, as indicated by the confidence intervals of the results.

H. Gi~kti~rk, K. Maki / Journal of Magnetism and Magnetic Materials 154 (1996) 279-290

5. Rheological measurements

285

gaining an understanding of the variation of the first normal stress difference, N], with variations in the state of the dispersion. The rheological instrument used for the measurements was a Rheometrics Dynamic Analyzer II equipped with both torque and normal force measuring sensors. A cone and plate type fixture 25 m m in diameter and cone angle 0.1 rad (5.7 °) was used. With this fixture, the measured normal force could be related to the first normal stress difference without approximations. The range of usable shear rates was specified as 0 . 0 1 - 1 0 s -1. The measurements were performed using a step shear sequence of 2 min of steady shear at the highest rate of 10 s -] , followed by 2 min of steady shear at 0.03 s - 1. The first part of the sequence was intended as a pre-shear to erase the memory of past deformations accumulated between sampling and measurement. The second step was performed at a low shear rate in order not to perturb the structure due to particle interactions. Spontaneous solvent evaporation from a relatively small volume of the sample (0.5 cm 3) that the cone and plate fixture used limited the duration of shearing. During the experiments the sample was enclosed in an environment enriched with the vapor of the solvent to minimize this problem. To identify the noise level of the measurements,

The polymer solution that serves as the binder for the dispersion contains about 10% by weight of polymer at the concentrations used for the sand milling. It is a nearly Newtonian fluid. When such a fluid is incorporated with asymmetric fillers one of the interesting changes that occur in its rheological properties is the appearance of normal stress effects [21,22]. Such effects are generally observed in polymeric fluids where the stretching and alignment of polymer chains along streamlines gives rise to normal stress differences. The asymmetric filler particles in a Newtonian fluid behave like the molecular chains of polymers. It has been shown that increasing the aspect ratio of the asymmetric filler enhances the normal stress differences [21]. For the dispersions used in magnetic recording, the aspect ratio of the magnetic particles is relatively low, about 10 or less. However, the magnetic forces between the particles couple them to each other and they behave like a weakly connected network rather than as individual short fibers [11,12,23]. Such a network can be expected to exhibit normal stress effects in its deformation behavior. Because of the potential of normal stress differences to serve as an indicator of particle interactions, the experiments were geared towards 1400.0

2000.0

1300.0 1000.0 1200.0 IiO0,O

0.0

I000.0

-lgO0.O

0~0.0 -2000.0

600.0 +% 700,0 "%

°*"

e.+++.+

*~

500.0

.ot .-40GO.O

EO0.O 400,0

'-8000.0

300.0

,-liO~O.D

200.0 lO0.O

0.0 O. 0

] .

.

.

.

.

.

m.o

.

.

.

.

.

.

.

tao.o

.

.

.

.

.

mo.o

.

.

.

B000.0

240.0

time [s]

Fig. 8. Sample data showing the shear stress and the first normal stress difference of the magnetic dispersion for a step shear rate sequence of 2 min at 10 s -l and 2 min at 0.03 s -1 .

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H. Ggktiirk, K. Maki / Journal of Magnetism and Magnetic Materials 154 (1996) 279-290

first, the experiment was performed without any material in the fixture. Peak-to-peak noise values were measured to be approximately 10 d y n / c m 2 for the shear stress and 50 d y n / c m 2 for N I. Second, the experiment was repeated with a Newtonian fluid, standard oil 10P. The measured N 1 was very nearly zero as expected from a Newtonian fluid. Third, the contribution of the binder solution to N] was investigated. N] was measured to be very nearly zero indicating that the binder itself does not exhibit normal stress effects at the concentrations used at the milling stage. Next, the magnetic dispersion samples were tested. A sample result of the experiments with the magnetic dispersions is given in Fig. 8. The magnetic dispersion exhibits a substantial first normal stress difference in addition to the shear stress. The negative sign of N 1 implies that the deformation forces tend to pull the cone and plate together. The magnitude of Nj is higher at the lower shear rate, whereas the magnitude of the shear stress is higher at the higher shear rate. A comparison of the measured data with the results reported in the literature shows that the magnitude of N 1 for the magnetic dispersion is greater than that obtained with fibers of 100 times greater aspect ratio [21]. This result suggests that the NI of the magnetic dispersion might be enhanced by magnetic particle interactions. Steady state values of the shear stress and first normal stress difference were compared for magnetic dispersion samples obtained at different stages of the sand milling process. The variation of shear stress as function of the duration of milling is shown in Fig. 9. At the shear rate of 0.03 s - l the shear stress increases slightly with increasing milling time, whereas at 10 s-1 the increase is not so regular. The difference between the shear stress values of the samples obtained before and after milling is 6% at both shear rates. Fig. 10 shows the variation in the first normal stress difference with milling time. Nj decreases regularly with increasing milling duration at both the low and high shear rates. The differences between N~ values of the samples obtained before and after sand milling were 13% at 0.03 s -I and 28% at 10s -1. The observations that (a) N] is relatively large, despite the low aspect ratio of the particles, (b) N~ increases with decreasing shear rate, (c) N 1 decreases as the dispersion improves, are indications

i

i

i

i

;2l00

o-------~ ~ °

0

150

0 Shear rate 0.03 8 "1 • Shear rate 10 s"1 t i i 0 I 2 Number of sand mllllng passes

Fig. 9. Variation of the steady state shear stress as a function of the milling duration; 10 samples per data point.

that N I can serve as a measure of the magnetic interactions that occur between the particles. A comparison of the current results with those of previous rheological studies shows qualitative agreement. Navarrete [24] and Amari et al. [23] measured the oscillatory deformation behavior of magnetic dispersions. They independently observed that elasticity as described by the storage modulus was more sensitive to changes in the microstructure than viscosity as given by the loss modulus. The storage modulus decreased as the dispersion improved. Kuin [25] measured the steady shear flow properties of magnetic dispersions up to high shear rates of 1500 s -I . His results showed that the parameters associated

-4500

i

i

i

-4000 -3500 A e~ -3000 C "O,-2500

i

-2000 -1500

-I000

0 •

Slmer rate 0.03 s" .L Shmr rate 10 s"1 i i i 0 I 2 Number of sand mllllng passes

Fig. 10. Variation of the steady state first normal stress difference as a function of the milling duration; 10 samples per data point.

H. G6ktiirk, K. Maki / Journal of Magnetism and Magnetic Materials 154 (1996) 279-290 Table 2 Comparison of raw data obtained with magnetic dispersion samples and fixed weights; 10 samples per data point

Normal force (g) Torque (g cm)

Magnetic dispersion

Fixed weight

10.1 +0.60 2.27 + 0.04

10.3 +0.06 2.74 + 0.03

with the elastic deformation of agglomerates (flocs) decreased with increasing degree of dispersion. Kanai et al. [12] measured the rheological properties of magnetic dispersions as a function of the volume fraction of the filler particles. Based on the trends exhibited by the storage modulus, they concluded that an elastic network structure was formed above a critical concentration of about 0.01. This threshold is lower than the one estimated in Section 4. The source of the error that was calculated for the results shown in Figs. 9 and 10 was also investigated. The measurements were repeated using fixed weights which provided about the same order of magnitude torque and normal force as the dispersion samples. The results obtained with the fixed weights and the dispersion samples are compared in Table 2. The confidence interval of the fixed weight measurements shows the instrument accuracy, whereas the confidence interval of the dispersion data also includes errors due to sample-to-sample variations. The error in the torque measurements is close to the instrumental accuracy. The error in the normal force measurements is about 10 times greater. This result indicates that normal force varies more with the slight variations that occur in the sample preparation. Overall, the first normal stress difference was found to be a more sensitive rheological parameter than the shear stress in terms of indicating the state of the dispersion.

6. Electrical measurements

When an electric field is applied to an insulator with incorporated metal particles, surface charges are induced on the conductor particles to make the electric field inside the metal zero. Since the particles have macroscopic dimensions, the dipole moments associated with surface charges become considerable, dominating the polarization properties. Asym-

287

metric conducting particles contribute to the surface polarization more than spherical particles, even when they are randomly oriented [13]. The dielectric properties of a magnetic dispersion employing acicular metal particles in a polymeric binder can be expected to exhibit such enhanced surface polarization effects. If the filler particles are used at low loading, they are separated from each other significantly, and so they respond to an external field like a collection of isolated dipoles. As the loading level is increased, the interparticle distance decreases. The electric dipole fields of the particles start to interact with each other in a manner similar to that of the magnetic dipoles. The limit at which the electrical properties would be effected by particle interactions can be estimated following the same procedure as detailed in Section 4. If a single conducting sphere of radius R is placed in a uniform electric field E 0 chosen in the direction +z, the field outside the sphere can be written in spherical coordinates r and 0 as [14] a3

E( r,O ) = E o k - E 0 ~ - ( 2 c o s

Oa r

+ sin Oao ). (14)

The second term in Eq. (14) is the dipole field of the conducting sphere. The form of the second term is the same as in Eq. (2), with E 0 replaced by M / 3 . If the volume fraction at which electrical interparticle interactions become important is estimated using arguments similar to the magnetic interaction case, the same limit is derived. This result indicates that the intrinsic magnetic interaction is not absolutely necessary for the interparticle interaction approach; the approach can be applied to a broader range of particulate composite materials other than magnetic dispersions. Unlike particle magnetizations, which can be oriented at random along the easy axes, the electrical polarization occurs in the same direction in all the particles and there is no easy axis. The result of the electrical interaction is an enhancement of the local field experienced by each particle. In the comparison of good and bad dispersions, the bad dispersion with more clusters of particles should display a higher dielectric constant and a higher ac conductivity [13]. The experimental setup for the dielectric measure-

H. Gi~ktiirk, K. Maki / Journal of Magnetism and Magnetic Materials 154 (1996) 279-290

288

ments consisted of a low-frequency impedance analyzer equipped with a liquids fixture. The capacitor was modeled as an ideal capacitor, C, in parallel with an ideal resistor, R. The dielectric constant, K, and the ac conductance, G, of material samples were calculated with reference to the values obtained with an empty fixture. The frequency range of the experiment was 500 H z - 3 MHz. The accuracy of the measurements was tested with common liquids such as distilled water, methanol and acetone; the agreement between the measured values and those reported in the reference literature such as the Physics and Chemistry Handbook, was found to be better than 5%. The dielectric properties of the solvent, the polymer solution (solvent + polymer) and the magnetic dispersion (solvent + polymer + fillers) were measured separately to identify the contribution of each component. Fig. 11 shows a comparison of the dielectric constant results obtained for these three cases. The results show different behavior in two frequency regions demarcated by about 10 kHz. In the highfrequency region, f > 10 kHz, the solvent has a dielectric constant, K, of about 9.5. Addition of the polymer increases K by 10% and addition of the fillers increases K by a factor of 2. The fillers make a substantial contribution to the dielectric constant at high frequencies. In the low-frequency region, f < 10 kHz, the dielectric constant of the polymer solution increases rapidly with decreasing frequency. Below about 3 kHz, the dielectric constant values of the lO0 o Solvent v PolymersolulJon Magnetic dispersion

8O

0 U u 1=

V

]i,° _e

D Q

ci

D

20

0

000

0

000

00DO

0

V Ooo 0

........

0.1

i

1

........

,

10

.

.

.

.

.

.

.

.

t

- , ,,,,,,i

100

, ,,

1000

Frequency (kHz) Fig, l l. Polarizability of the components of the dispersion as a function of frequency.

40

~35 C c 0 o

0

15

-

-

0

0

O f=50 kH= •

f'~,,5 kHz I

I

I

0 1 2 Number o f sand a m i n O posses

Fig. 12. Variation of the polarizability of the dispersion as a function of the milling duration; 6 samples per data point,

polymer solution exceed those of the dispersion. The observed trend in the polarizability of the polymer solution suggests that the orientational polarization of the polymer molecules becomes significant in the low-frequency region [14,26]. As the frequency decreases, the polymer molecules have a longer time to align with the external field. Dielectric constant values of the dispersion also become frequency dependent in this region, possibly due to the contribution from the polymer solution. Comparison of the dielectric constant values of paint samples obtained after different degrees of sand milling is shown in Fig. 12. At 50 kHz, the dielectric constant values are very nearly equal, whereas at 0.5 kHz the dielectric constant exhibits a decreasing trend with increasing milling time. The difference between the dielectric constant values of the samples obtained before and after milling is about 10% at 0.5 kHz. The percentage difference increases with decreasing frequency, so that lowfrequency measurements are more desirable to increase the sensitivity. The observed trends are possibly due to the variations in the orientational polarization of the polymer molecules as a function of the degree of dispersion. The rigid filler particles would tend to hinder the orientational polarization. As the sand milling proceeds, the filler particles are dispersed more finely within the polymer solution, creating more barriers for the orientation of polymer molecules. Hence the polarizability at low frequencies decreases with increasing milling times.

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H. Gi~ktiirk, K. M a k i / J o u r n a l o f M a g n e t i s m a n d M a g n e t i c M a t e r i a l s 154 (1996) 2 7 9 - 2 9 0

The conductance part of the dielectric measurement was also investigated for any information it might provide about the dispersion. The measured conductance values of the solvent, the polymer solution and the magnetic dispersion are shown in Fig. 13. At frequencies up to 100 kHz, the conductance values are nearly constant. In this region, the solvent has a conductance value of about 1 txS. Addition of the polymer to the solvent increases the ac conductance by more than two orders of magnitude, to values of about 125 p~S. Addition of the filler particles to the polymer solution introduces another significant change, decreasing the conductance values to about 1.5 p,S. It was originally envisioned that the binder solution of the dispersion would be insulating and that the main contribution to the conductance would come from the metallic cores of the magnetic particles. The results of the measurements show that the main contribution to the conductance comes from the polymer dissolved in the solvent. The magnetic particles dispersed within the binder impede this conduction with their oxide shells. The conductance values of the dispersion samples obtained after different durations of sand milling are shown in Fig. 14. The conductance values exhibit a decreasing trend with increasing milling time. The difference between the conductance values of the samples obtained before and after milling is about 18% at 0.5 kHz. The percentage difference increases with decreasing frequency, again indicating that low-frequency measurements are desirable to in-

135f v 130 f

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v vvv

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crease the sensitivity. The obstruction of the conductance of the polymer solution by the filler particles is possibly the mechanism that creates the differences in the conductivity as a function of milling time. As more of the agglomerates are broken down into primary particles, they impede the conductance more effectively. This phenomenon is the opposite of the electrical percolation of conducting particles in an insulator. It was observed in such composites that percolation could be achieved at lower concentrations of the conductive filler if the chosen particle size distribution of the filler is narrower [27]. Overall, it was found that the dielectric measurements at low frequencies provide information about the state of the magnetic dispersion. The ac conductance is more sensitive than the polarizability in terms of indicating changes in the microstructure. The physical origin of the phenomenon is the interaction of the filler particles with the polymer molecules, rather than the electrical interparticle interactions, as was originally considered.

7. Conclusions 12o1~

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Magnetic interparticle interactions can be evaluated from the hysteresis and remanence curves of magnetic dispersions frozen at low temperatures. The most sensitive of the magnetic parameters, in terms of displaying the highest percentage difference between good and bad dispersions, is the switching

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H. Grktiirk, K. Maki / Journal of Magnetism and Magnetic Materials 154 (1996) 279-290

field distribution obtained from the hysteresis curve. The accuracy of the magnetic parameters from the remanence curves is higher, although the percentage differences between the good and bad dispersions are smaller. The first normal stress difference is a more sensitive rheological parameter than the shear stress in terms of providing information about the state of the dispersion. The first normal stress difference decreases as the dispersion becomes better. The low-frequency dielectric properties of a magnetic dispersion are also useful for understanding the state of the dispersion. Both the polarizability and the ac conductance decrease as a function of the goodness of mixing, although the ac conductance is a more sensitive indicator than the polarizability. Because of the relative simplicity of these electrical and rheological methods, they are promising for the characterization of the state of dispersions on line with manufacturing processes.

Acknowledgements The authors would like to thank Mr Shimizu, Mr Nakamura, Mr Okumura, Mr Sakamoto and Mr Yanagi of Kao Research Laboratories for their assistance with various aspects of the experimental work. One of the authors (H.G.) would also like to express his gratitute to Kao Corporation for the visiting appointment provided at Kao Recording and Imaging Science Laboratory.

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