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Anisotropic aggregates as the origin of magnetically induced dichroism in ferrofluids Wayne Reed and Janos H. Fendler Citation: J. Appl. Phys. 59, 2914 (1986); doi: 10.1063/1.336952 View online: http://dx.doi.org/10.1063/1.336952 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v59/i8 Published by the American Institute of Physics. Related Articles Faraday rotation effect in periodic graphene structure J. Appl. Phys. 112, 023115 (2012) A combined surface stress and magneto-optical Kerr effect measurement setup for temperatures down to 30 K and in fields of up to 0.7 T Rev. Sci. Instrum. 83, 073904 (2012) Study of ultrathin magnetic cobalt films on MgO(001) J. Appl. Phys. 112, 023910 (2012) Collinearity alignment of probe beams in a laser-based Faraday effect diagnostic Rev. Sci. Instrum. 83, 10E320 (2012) Direct observation of magnetization reversal and low field magnetoresistance of epitaxial La0.7Sr0.3MnO3/SrTiO3 (001) thin films at room temperature J. Appl. Phys. 112, 013906 (2012) Additional information on J. Appl. Phys. Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors Downloaded 27 Jul 2012 to 129.81.207.215. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions Anisotropic aggregates as the origin of magneticany induced dichroism in ferrofiuids Wayne Reed a ) and Janos H. Fendlerb) Department of Physics and Department of Chemistry, Clarkson University, Potsdam, New York 13676 (Received 23 April 1985; accepted for publication 5 December 1985) Static and dynamic polarized and depolarized light scattering, static, and time-resolved dichroic anisotropy, as well as conventional magnetization versus applied magnetic field determinations have been carried out on aqueous commercial ferrofluids and on surfactant aggregate stabilized Fe30 4 in aqueous solution. Over a dilution range of more than three orders of magnitude there is no evidence for field-induced cooperative effects. The shape of the dichroic anisotropy versus applied field curve superimposes virtually exactly onto the magnetization curve. Rotational and translational. diffusion coefficients indicate ellipsoidal magnetic aggregates with average minor to major axial ratios around 0.33 and major axis of285 nm, which are insensitive to dilution, and far above the expected value of around 10 nm. Electron micrographs have revealed polydisperse clusters of around 150 nm composed of particles with sizes on the order of 10 nm. The scattered intensity autocorrelation curve shows no appreciable change upon application of a magnetic field to the ferrofluids. Evidence for the shape anisotropy of the presumed 140-nm clusters is apparent in the depolarized light scattering autocorrelation decay curves. In the absence of field-induced particle chaining, aggregation, or shape deformation, the origin of the field-induced dichroism was attributed to the permanent shape anisotropy of the dusters. Subtle field-induced alteration of the spatial arrangement of particJ.es within the stable clusters or an unexpected anisotropic polarizability of the magnetite crystals do not seem to be likely origins of the dichroic effect. I. INTRODUCTION In a continuing effort to gain detailed understanding of magnetic colloids (ferrofiuids) 1 and to develop new applications. studies have been initiated for their formation and stabilization in novel colloidal systems. In particular, it is thought that surfactant vesicles 2 may provide a way of both growing the colloids in situ to desired sizes and stochiometries. and to stabilize them. Vesicle entrapped magnetic particles may function as miniature magnetochemical units, capable of influencing chemical reactions. External magnetic fields have been shown to influence the outcome of a number of photochemical processes. 3 More recently, single-domain coHoidal magnetite particles were shown to influence benzophenone photochemistry in the absence of external. magnetic fieJ.ds in surfactant vesicles. 4 In addition to these photochemical and photophysical applications, magnetic colloids find applications in optical modulation and information storage devices. In an effort to provide a basis for physically characterizing the magnetic colloids, several optical techniques have been implemented. The aim of the current article is to report the results of these techniques on commercial aqueous suspensions of magnetite and to assess the val.ue of the information yielded with respect to guiding the development of new magnetic colloids. These techniques include static and timeresolved magneto-optical dichroism measurements, static and dynamic light scattering measurements and the nonop- tical. detennination of magnetization versus applied magnetic field. The determined optical parameters in a commercial ferrofluid and in surfactant vesicle entrapped Fe3 0 4 , in contrast to previous reports,5--9 failed to indicate magnetic field dependent chaining or aggregation. II. MATERIALS AND METHODS A. Magnetic colloids studied The main magnetic colloid used in the following studies was a commercially available magnetite from the Georgia Pacific Co. (Lignosite). 10 The stock solution contains 10% iron, or about 14% magnetite by weight. Lignosite powder consists of calcium lignin sulfonates to the extent of 80%, together with about 15% of carbohydrates and carbohydrate sulfonates, and about 5% other constitutents. Its exact description is not known since the structure of lignins are still imperfectly understood. Lignosite is generally accepted to be made up of poly phenylpropane with molecular weights ranging from several hundred to above one hundred thousand. Other colloids used in the experiments induded those prepared from hydroxide solutions injected into solutions containing dissolved iron saIts and subsequently stabilized by dioctadeyldimethylammonium chloride (DODAC) vesicles, or by ammonium laurate and lauric acid. 4 B. Static and dynamic measurements of magnetically Induced dichroism. "Current address: Department of Physics, Tulane University, New Orleans, LA 70118. b) Current address: Department of Chemistry, Syracuse University, Syracuse, NY 13210. 2914 J. Appl. Phys. 59 (6). 15 April 1986 Among other optical effects, linear dichroism is induced in ferrofiuids when an external magnetic field is applied. The effect was first reported in 1902. II Linear dichroism can be 0021-8979/86/082914-11 $02.40 @ 1986 American Institute of Physics Downloaded 27 Jul 2012 to 129.81.207.215. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 2914 observed by applying a unifonn magnetic field to the colloid sample, usually in the plane perpendicular to the incident unpolarized analyzing light which passes through the sample. The transmitted light is then simultaneously analyzed into its parallel and perpendicular components with respect to the magnetic field by means of a polarizing beam splitter and detected by a system of two balanced, identical photomultiplier tubes. The system used in this laboratory employs a 450 W mercury or xenon lamp for the unpolarized analyzing light, an electromagnet with adjustable 3.5-cm pole faces, a polarizing beam splitter from Karl Lambrecht, Inc., and two magnetically shielded Hammamatsu IP28 photomultiplier tubes for detection. The difference between transmitted parallel and perpendicular intensity components is fonned by a differential amplifier and the signal processed by a Tektronix R7912 waveform digitizer which is controlled by a DEC PDPl1/34A minicomputer. The magnitude of the resulting anisotropy A between the paraI1el transmitted intensity 1/, and the perpendicular transmitted intensity I, is defined by (1) where I, in this work is taken as perpendicular to the ground, and 1/ parallel to the ground. Except where otherwise noted the applied magnetic field was paranel to the ground. The quantity A, according to Eq. (I) was always positive in this configuration, which corresponds to the definition of positive dichroism in the general literature. A circuit was designed and built which allows the applied magnetic field in the anisotropy apparatus to be turned offin less than 20 f-tS.12 This allows the resu:lting decay of the anisotropy signal (l, - 1/, or either intensity component separately) to be followed in time. Since rotational diffusion of magnetite particles above about 10 nm is the mechanism of the magnetization relaxation (as opposed to Ned relaxation) , I it is possible to relate the directly detennined relaxation time (obtained from an exponential decay analysis of the anisotropy curve) to the particles' hydrodynamic volume and rotational diffusion coefficient according to the relations VH = kTtJ1], t, = 1/6A, (2a) (2b) where k is Boltzmann's constant, T the solution temperature, 1] the solution viscosity, t, the rotational relaxation time, and A the rotational diffusion coefficient. Equation (2a) assumes that the particles are spherical, at least to a first approximation. The above equations also hold for aggregates of particles, as long as the rotational relaxation of the entire cluster governs the net magnetization relaxation of the cluster. field induced aggregation or other detectable phenomena occurred. Static light scattering measurements were first carried out to determine if there was any element of magnetic dipole scattering in the scattered light mixed with the electric dipole scattering. Static measurements were than also made on the colloid solutions with and without an applied magnetic field. Dynamic and static light scattering was carried out using the goniometer and photomultiplier system supplied by Brookhaven Instruments. The photomultiplier output was split off with a BNC T connector and half the signal was fed into the Brookhaven M2000 autocorre1ator, and the other half into an ORTEC digital counter. The incident ray for the scattering experiments, vertically polarized with respect to the ground, was obtained by a beam splitter which picked off about 25 mW of the 514.3-nm line of an argon-ion laser, whose main beam pumped a dye laser for unrelated experiments. For the depolarized dynamic light scattering measurements discussed below it was necessary to direct the entire beam through the solution (at about 2-W optical power) in order to obtain a reasonable count rate for autocorrelation. The relative scattering intensity from the colloid solution was integrated by the digital counter for several 30-s counting periods, and the results averaged for each data point. The background scattering count, obtained at 90 deg for pure solvent, was subtracted from each intensity point. The intensity autocorrelation function was collected over either 64 or 256 data channels of the Brookhaven M2000 autocorrelator, and the resulting curve was analyzed according to In[CEy(t)] = -Gt+ut 2 12, where CEy(t) is the scattered electric field autocorrelation function, observed through an analyzer set at vertical polarization, and is equal to the square root of the baseline-subtracted scattered intensity autocorrelation function, provided that the scattering solution is dilute enough to neglect particle-particle interactions and multiple scattering. G represents the mean relaxational frequency of the electric field autocorrelation function, and u is the second moment ofthe relaxational frequency over the vesicle distribution. The polydispersity index, or "Q value," is defined as Q= u/2G 2 (4) and can be interpreted as a measure of the variance of the (Gaussian) particle popUlation from the mean hydrodynamic diameter calculated according to DH = kTq2/6mJG, (5) where q is the magnitude of the scattering vector defined as q = (41Tn/A)sin(e /2), C. Static and dynamic light scattering measurements Dynamic light scattering measurements were used to measure the magnetic particles' translational diffusion coefficient and to calculate their hydrodynamic diameters and first-order polydispersity index ("Q value"). Magnetic fields were also applied to the colloid solutions during the dynamic scattering experiments to ascertain whether any 2915 J. Appl. Phys., Vol. 59, No.8, 15 April 1986 (3) (6) where n is the index of refraction of the solvent, A the wavelength of the incident light, and the angle of measurement in the scattering plane. Eq. (5) also assumes that the particles are spherical. Deviations from sphericity can be determined by monitoring the depolarized component of the scattered Ught, thus building up CEH (t); i.e., the autocorrelation function for the scattered light passed through the analyzer e W. Reed and J. H. Fendler Downloaded 27 Jul 2012 to 129.81.207.215. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 2915 >- >- 0.8 Co 0 .. -... Co 0 - 0 0 CII III c: < C < u u ...0 ...0 .c: .c: u u C C 0 0 0.5 200 400 1.0 600 H(Gauss) Absorbance FIG. 1..: Dichroic anisotropy of Lignosite; X: magnetization of Lignosite scaled to dimensionless anisotropy; and .. : scaled magnetization of magnetite stabilized in lauric acid. FIG. 2. Dichroic anisotropy vs absorbance... : Lignosite; .: magnetite sta· bilized in DODAC vesicles; X: magnetite stabilized in lauric acid. set horizontal to the ground. The details of these measurements are discussed below. distribution. The latter information can thus be correlated with the results obtained from the anisotropy and scattering measurements. D. Polarimetry measurements ill. RESULTS AND DISCUSSION A very simple polarimeter arrangement was used to determine the phenomenological depolarization matrix of the transmitted light, and to relate this matrix to the dichroism data. A 25-mW He-Ne vertically polarized laser was used as the incident beam on magnetic colloid solutions immersed in magnetic fields at different orientations with respect to the plane of polarization. Transmitted light was passed through an analyzing polarizer and the intensity measured on a standard laser power meter. Figure I shows the results of both magnetization and dichroic anisotropy versus applied magnetic field for Lignosite plotted on the same graph. The dichroic units follow Eq. ( 1 ), whereas the 0-600 G portion of the entire Lignosite magnetization curve was scaled to the anisotropy curve at the 500 G mark. The very close overlap of the two curves is probably no coincidence and seems to indicate that the dichroic anisotropy is governed by the same mechanism that governs the magnetization curve, i.e., the progressive alignment of the magnetic dipoles of the particles along the applied field axis. Furthermore, the shape of the curve in Fig. 1 is concentration independent for at least up to dilutions of the stock magnetite suspension of over 1500/1. The magnetization curve in Fig. 1 was obtained for the stock magnetite suspension and separately for a lOll dilution with water. The anisotropy data overlapping with the same curve was taken at a dilution of the stock of 300/1. Figure 2 shows the value of the dichroic anisotropy versus aqueous dilution of the suspension over approximately an order of magnitude. The dichroic anisotropy versus dilution is linear, and so the curve in Fig. 1 could be expected to remain the same for dilutions of at least 1. 500/ 1. Figure 2 also shows the dichroic anisotropy behavior versus concentration of magnetite stabilized in DODAC and in lauric acid. For a given concentration of magnetite, observing the dichroic anisotropy at different wavelengths, and hence different absorbances, yielded values equivalent to the values obtained for solutions of varying concentrations at corresponding absorbances when observed at a fixed wavelength. The source of such concentration-independent behavior of both the anisotropy and magnetization is most probably due to the lack of any cooperative effects between the magnetite colloids in suspension. That dichroic anisotropy effects are stilI observable in the absence of cooperative effects, E. Magnetization curve determinations Initial attempts to measure the magnetization curves of dilute solutions of magnetite in vesicles using a commercial vibrating magnetometer were frustrated by the lack of sensitivity of the apparatus. Accordingly, the design and construction of a new magnetometer was undertaken. 12 This system, which provides the necessary sensitivity, allows the ferrotluid sample to sit statically in one coil of a dual pickupcoil arrangement aligned within a uniform external magnetic field. Inductive pickup in the sample-containing coil is achieved by running the magnet power supply current up and down with a 1 Hz specially formed pulse abstracted from a I-MHz oscillator signal that simultaneously synchronizes data acquisition through a microcomputer-based AID broad. The induction occurring in the sample-containing coil due to the time-modulated external field, as well as the noise picked up, are compensated for by subtracting the equal induction and noise of the identical., nonsample-containing coil, thus leaving the pure magnetization signal of the ferrofiuid. The synchronous, repetitive modulation of the external field allows signal averaging to be performed up to any desired degree of precision. The magnetization curves resulting from this apparatus give valuable information concerning the saturation magnetization and particle size and 2916 J. Appl. Phys., Vol. 59, No.8, 15 April 1986 W. Reed and J. H. Fendler Downloaded 27 Jul 2012 to 129.81.207.215. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 2916 however, indicates that the anisotropy cannot be the result of field-induced chaining, aggregation, or cooperative phenomena, as has been variously suggested: CoateS observed dielectric anistropy in magnetite particles dispersed in nonpolar solvents when subjected to an ac electric field. He attributes the origin of the effect to chains of magnetite particles. Goldberg et al. 6 have observed the dichroic effect for magnetite dispersed in both aqueous and nonpolar media and have concluded that the magnetite particles assemble in lines under the influence of an external magnetic field. Maiorov and T sebers7 consider the pairwise spatial correlation of particles in externally induced magnetic alignment and relaxation phenomena for fine magnetite particles in any carrier medium. Scholten9 variously analyzes the possibility of the magneto-optical effects as a result of orientation of preexisting small aggregates, field-induced aggregation of single particles into strings, anisotropic spatial ordering of single particles, orientation of single superparamagnetic particles through weak shape anisotropy, and orientation of single particles with permanent dipoles. He concludes that orientation of small aggregates, and secondary aggregation of large aggregates into strings are the most likely causes of the anisotropies. Recently obtained electronmicrographs reveal aggregates of small particles. The size and shape of these aggregates, as judged by time resolved dichroism decay and dynamic light scattering data, however, do not seem to change, within the limits of each technique'S resolution, upon dilution or application of an external field. Figure 1 also shows the magnetization curve of magnetite stabilized in lauric acid versus the applied magnetic field. The curve has been scaled to the near-saturation value of the Lignosite curve at around 2500 G in order to contrast the difference in magnetization behavior of the two different preparations. Both curves must be analyzed with the Langevin function weighted appropriately for the polydispersity of each solution. Chantrell et al.13 have given a method for lognormal particle size distributions from a ferroftuid's room-temperature magnetization curve. The initial slope of the magnetization curve depends most sensitively on the particle diameter. The Langevin function for particles of diameter D and saturation magnetization M. is given by M (H) = bM. [coth(a)-1/a], (7) where b isthe volume fraction of particles with the saturation magnetization M., and a = D 3MsH /24kT. (8) Since both the Lignosite and the lauric acid stabilized magnetite are assumed to be single-crystal particles of Fe304' their M. values are the same ( 480 G), so that the differences in the magnetization curves should be due only to the differences in the magnetically active diameters of the different particles. It should be noted that this magnetically active diameter must be less than the hydrodynamic diameter of the entire conoid, as the polymer or surfactant coat on the particles obviously does not contribute any magnetic moment. Furthermore, the magnetite particles themselves might have a chemically reacted, nonmagnetic layer l4 which further reduces the active magnetic diameter. Finally, dilu2917 J. Appl. Phys., Vol. 59, No.8, 15 April 1986 1 r!-'----"-<-/.;\".;:7:.>"..,.\-::.I . . Le(_.''--'--'---'--' 1 2 2.lr~~~',~;00~~~L~.~~~~~;~~ ..... 10 III 1 '03 .s ~ let- , b . '.. ".__~ .b . - ,)i1 ~ . --' 10 1 .~ ~ 100'--'~1~~2~-3~-4~~5 Time ems) FIG. 3. (a) Time-resolved dichroic anisotropy of Lignosite and (b) magnetite in ammonium laurate, along with the residuals corresponding to single exponential fits. The respective exponential decay times are 630 and 400 p.s, respectively. tion independent clusters of smaller particles would further reduce the magnetically active volume below the hydrodynamic volume of the cluster, due to incomplete space filling in the cluster. It should thus be possible to estimate the percentage of magnetically active material in a colloid by comparing the hydrodynamic diameter, corrected for the polymer or surfactant coat, with the magnetically active diameter obtained from the slope of the Langevin function by (9) This comparison win require a careful fitting of the magnetization curves with the appropriate polydispersity distribution and a corresponding correlation with the hydrodynamic and polydispersity data obtained from dynamic light scattering. In the case of clustering, the packing would also have to be taken into account. The anisotropy data shown in Figs. 1 and 2 were obtained with the external field applied perpendiCUlarly to the direction of propagation of the analyzing light. Furthermore, the external field is parallel to the parallel transmitted intensity component 1/, which is defined as being horizontal with respect to the ground. The fact that the dichroic anisotropy is positive indicates that less light is transmitted, i.e., more is scattered, in the plane parallel to the external field. Separate measurements of 1/ and Ir show that the intensity of light transmitted perpendicular to the field increases as the magnetic field is increased. The effects of the increased perpendicular transmission and decreased parallel transmission can be observed visually by placing a polarizer after the sample and shining the transmitted light on a screen. The interpretation of the increased scattering parallel to the field is W. Reed and J. H. Fendler Downloaded 27 Jul 2012 to 129.81.207.215. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 2917 directly substantiated by the static light scattering experiments described below. When the applied field is oriented parallel to the direction of propagation, however, no dichroic effect was observed within the limit of resolution of the system. Figure 3 shows time resolved anisotropy decay curves for Lignosite and magnetite stabilized in ammonium laurate. The curves analyze quite well to a single exponential and yield rotational relaxation times of 630 and 400 J.lS, respectively. These relaxation times correspond to rotational diffusionconstants [Eq. (2b)] of 265 and 415 rad/s. UsingEq. (2a) to obtain the hydrodynamic volumes of the colloids yields values of 2.91 X 10- 15 and 1.87X 10- 15 cm 3, respectively, which correspond to particle hydrodynamic diameters of 177 and 153 nm. The fact that the curves analyze so well under one exponential decay indicates that either there is very little shape anisotropy associated with the particles, and that they must indeed be very close to spherical in shape, or that the single exponential decay only measures the rotational relaxation relevant to the randomization of the dichroic axis; e.g., to rotations perpendicular to the axis of symmetry if the particles were ellipsoids of rotation. In general, however, anisotropically shaped particles, linear chains, or other nonspherical aggregates would be expected to manifest multiexponential decays, corresponding to combinations of relaxations about the principal axes. The dynamic anisotropy data is not sufficient to distinguish between pure spherical symmetry and relaxation of the symmetry axis of an ellipsoid of revolution. The question of the particle's shape was finally resolved using depolarized light scattering measurements, discussed below. It should be mentioned that the amount of time the field was left on before turning it off and measuring the relaxation varied between 1 sand 1 min, all runs yielding identical decay curves. The buildup of the anisotropy to full value occurred within buildup time of the applied field itself, which was about 1 ms. A determination of the anisotropy buildup time would require modification of the circuit used. Nonetheless, it is evident that full dichroic anisotropy is reached in less than a miHisecond, and although subsequent chaining or ordering of the magnetic colloid could conceivably occur if the field were left on, such a phenomenon would seem unrelated to the magnitude and decay behavior of the dichroism actually observed: Peterson and Krueger,I5 for example, found evidence for the reversible agglomeration of water dispersed magnetite particles, with the diameters around 10 nm, into clusters containing from 107 to 109 particles, when full-strength solutions were subjected to dc magnetic fields from 2 min up to many hours. The smaller initial slope of the magnetization curve for magnetite in ammonium laurate seen in Fig. 1 is consistent with the above interpretation that the vesicle-entrapped colloids are smaner than the Lignosite. This consistency of result also strengthens the interpretation of the magnetization decay as originating in hydrodynamic rotational relaxation, as opposed to the Neel mechanism. Static light scattering was employed to ascertain whether there was a component of magnetic dipole scattering mixed with the presumed electric dipole scattering. The scattering cross section for a scatterer whose size is much 2918 J. Appl. Phys., Vol. 59, No.8. 15 April 1986 1.32 1.24 1.17 1.10 o ~ 1.04 1.00 E", 0.9 0.84 0.78 o 2 4 8 6 rei. H-field FIG. 4. Relative scattering at 90" for Lignosite vs relative magnetic field .•; H applied parallel to electric vector of polarized incident laser beam; 0; H applied parallel to the direction of propagation of the beam; X; H applied perpendicularly to both the incident electric po1arization and direction of propagation. smaller than the wavelength of the incident light 4, for incident light with polarization vector eand direction of propagation ii when observed in direction it' with a polarizer at orientation e' is given byl6 dO"=k4{~, - e·p+ (~' nxe~') ·m}2 dO E2 ' (10) where k is the wave number and E the electric field strength of the incident light, and p and m are, respectively, the induced electric and magnetic dipoles in the scatterer. If the incident polarization is perpendicular to the scattering plane, then the scattering intensity analyzed parallel to the polarization vector of the incident light, mapped out by sweeping through the scattering plane should be given by (11 ) where () is the angk of observation in the scattering plane, having a value of zero in the direction of incident propagation. Corrections to the intensity, as I sin () must be made at each observation point to correct for the increasing parallelepiped of observed scattering volume. The scattering intensity as a function of angle turned out to be a constant within error bounds, indicating Rayleigh-type scattering of the purely electric dipole type. Lest a small. component of magnetic dipole radiation escape notice next to the predominant electric dipole scattering, a half-wave plate was placed in the path of the incident light so that the initial. polarization was parallel to the scatteringplane. In this case, observing with a polarizer parallel to the scattering plane should show an angular scattered intensity distribution given by 10:: (m+pCOS(})2 (12) Observing 90· should yield a scattering intensity due purely to magnetic dipole scattering. Within the background noise level, no discernible scattering intensity was observed at 90·, and it is concluded that the scattering mechanism for the colloids is purely of the electric dipole type. W. Reed and J. H. Fendler Downloaded 27 Jul 2012 to 129.81.207.215. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 2918 G bC, ' a w Ii A • Gl ::l ~[.'~"~"'. [ '.' • 'I~ • .. + ".J - 13375 III I C o ;; 10700 ('II Qj Time (ms) 1.28 ~ 8025 u o ~ 5350 ~ >- :t:: bc, l!! GI 2675 S o ? 400 800 1200 1600 2000 Time (fIS) o Time (ms) t'", 0.64 ......: : / ", FIG. 5. (a) Background substracted scattering intensity autocorrelation function Lignosite and (b) magnetite in ammonium laurate. Curve 1 in each figure is in the presence of a transverse magnetic field. curve 2 in the absence of field. When the static scattering intensity was measured in the presence of a magnetic field in three different orientations, again with the initial electric polarization perpendicular to the scattering plane, the data shown in Fig. 4 was obtained. This is entirely consistent with the dichroic anisotropy results, in that when the applied field is parallel to the initial polarization vector there is more scattering, as observed at 90'. When the field was oriented perpendicularly to both the initial polarization vector and the direction of propagation, the scattering intensity fell off as a function of the applied field. When the field was aligned axially with the direction of incident propagation there was no observed change in the 90· scattering count within the resolution of the technique. Unfortunately, the physical arrangement of the goniometer and magnet arrangement did not allow precise determination of the magnetic field at the scattering center, so that the relative scattering intensity is plotted versus relative magnetic field. The highest field strength on the upper-right most curve corresponds to roughly 350 G. Once again the shapes of the curves, except for the axially aligned case, seem to follow the form of the magnetization and anisotropy curves. Dynamic light scattering was carried out on the Lignosite and magnetite stabilized in ammonium laurate. Absorbances for these substances were typically less than 0.1 and they were thus very dilute. Figures 5 (a) and 5 (b) show plots of the scattered intensity autocorrelation functions for the two different samples with and without an applied magnetic field. These measurements were carried out simultaneously with the static measurements. The autocorrelation traces analyzed according to a single-exponential decay yielded hydrodynamic diameters for the Lignosite and ammonium laurate stabilized magnetite of 183 and 119 nm and polydis2919 J. Appl. Phys., Vol. 59, No.8, 15 April 1986 ~ ~ 800 GI :5 ~oo o (b) o 100 200 300 Time <..s) 400 500 FIG. 6. (a) Plot of polarized scattered intensity autocorrelation vs time for OA-1Lm filtered Lignosite at 8 = 60". T = 298 K. TJ = 0.008 cP, and..1. = 514 nm. (b) Plot of depolarized autocorrelation vs time for same solution under same conditions. The faster time scale, as compared to (a), shows the contribution of the rotational relaxation to the autocorrelation function decay according to the exponent in Eq. (14b). persity indices of 0.24 and 0.32, respectively. These values are in reasonable agreement with those obtained from the time-resolved dichroic anisotropy measurements considering the uncertainities introduced by the particles' polydispersity. The fact that no significant change in the autocorrelation function was observed when the colloids were subjected to an applied field also argues against any type of field-induced aggregation or chaining phenomenon taking place. If any chaining or aggregation did take place it would be natural to expect that the translational diffusion constant of the resulting aggregate or chain would be measurably different than that obtained in the absence of applied fields and presumed chaining or aggregation. The lack of a change in the polarized scattering autocorrelation function CEV (t) upon application of a magnetic field indicated that an inherent shape anisotropy of the particles was possible. Accordingly, the depolarized light scattering intensity was autocorrelated W. Reed and J. H. Fendler Downloaded 27 Jul 2012 to 129.81.207.215. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 2919 tion, the actual points representing the reciprocal lifetime for the best fit to the majority popUlation, The results are interpreted in the following manner: If the scattering particle has an anisotropic polarizability tensor a due to shape anisotropy or other factors, then the tumbling of the particles will introduce a fluctuating intensity component of the scattered light on top of the intensity fluctuations due to the particles' translational diffusion. If the particle has cylindrical symmetry, e.g., an ellipsoid ofrevolution, then the polarizability tensor can be diagonalized in a coordinate frame from coincides with the particle's principal axes, o (13) o 0.2 0.4 2 sin 0.6 en 0.8 o 1.0 FIG. 7. Reciprocal intensity autocorrelation decay lifetime vs sin 2 for depolarized data. 0 for polarized data. f) /2 - .i [ CEH (t) ], by placing the analyzer's polarization state at right angles to the vertically polarized incident laser beam. The depolarized count was typically 0.37% of the polarized scattering count. To reduce the polydispersity problem, the Lignosite solution was first filtered through a 0.4O-,um nuc1eopore filter. A plot of the polarized autocorrelation function measured at 60 deg for this solution without applied magnetic field is shown in Fig. 6(a). As seen, this curve analyzes well according to two exponentials, indicating a majority population whose decay constant is 640 s, which corresponds to a translational diffusion coefficient of 2.96 X 10- 8 cm 2Is, and to a hydrodynamic diameter of 165 nm for the spherical approximation ofEq. (5) (T= 298 K, 11 = 0.0089 cP,A = 514 nm. The solution is dilute enough to use the viscosity of water). The second, larger population has a decay time of 930 ps, yielding a hydrodynamic diameter of 240 nm. The ratio of autocorrelation exponential decay amplitudes for the majority to the minority population was roughly 4 to 1. A rough estimate of the relative numbers of particles, according to the 6th power law for Rayleigh scattering is that 97% of the particles fall into the majority distribution and 3% into the minority distribution. It should be noted that the curve represented in Fig. 6(a) corresponds to the decay of the intensity autocorrelation function, so that the actual decay time of the electric field autocorrelation is one half this value, according to the Gaussian approximation for dilute solutions explained earlier. Figure 6(b) shows a depolarized intensity autocorrelation function decay for the same solution under the same conditions but a shorter time scale. This curve is likewise analyzable under two exponentials which yield characteristic decay times of 180 and 400 ps, respectively. The polarized and depolarized intensity autocorrelation functions were measured for the solution at various angles and the reciprocal lifetimes for the majority popUlation in these measurements are plotted versus sin 2 012 in Fig. 7. The error bars in the graph result chiefly from the polydispersity of the solu2920 J. Appl. Phys., Vol. 59, No.8, 15 April 1986 where a 1 = a;u = ayyazz = all' For such a cylindrically symmetric particle the translational diffusion coefficient breaks down into terms representing diffusion paranel DII and perpendicular Dl to the symmetry axis. In the same way the rotational diffusion coefficient breaks down into components all and a p corresponding to rotations paranel and perpendicular to the symmetry axis. Ifneither DII - Dl nor all - a 1 is too large, as would be the case with eUipsoids of low to medium eccentricity, then the translational rotational diffusions are uncoupled from each other and the field autocorreIations, CEV (t) and C EH (t) can be given, respectively, by!7 CEV(t) = (N)a 2e- q'Dt + 434 (N) ( all-a1 )2e - (M! + riD) r , )2 -(M!+q'D)f, C EH (t) --J(N)( -13 all - a 1 e (14a) (l4b) where (N) represents the average number ofpartic1es in the observed scattering volume and + 2a !(DII + Wi)' a = j(all D= (l5a) 1 ), (I5b) D and a thus represent the angle-averaged translational diffusion coefficient and polarizability, respectively, and can be interpreted as the factors responsible for the large isotropic part of the scattering. The ratio of the anisotropic (second) term in Eq. (14a) to the isotropic term is M (all - a 1 )laj2, which is much smaller than unity, even for highly eccentric ellipsoids or rods. The second term in Eq. (14a) is thus very small and difficult to resolve experimentaHy, so that CEV(t) is dominated by the isotropic scattering. Indeed, the clear extrapolation of the reciprocal lifetime versus sin 2 (J /2 to the origin in Fig. 7 for CEV(t) demonstrates its pure dependence on translational diffusion (q2 D). The fact that the extrapolated reciprocal lifetimes of the CEH (t) frunction in Fig, 7 intercepts the y axis at a nonzero value demonstrates that the particle does have an anisotropic polarizability tensor. The y intercept directly yields the value of the component of the rotational diffusion coefficient perpendicular to the symmetry axis of the particle. The significantly faster time scale of the depolarized autocorrelation decay in Fig. 6(b), as comW. Reed and J. H. Fendler Downloaded 27 Jul 2012 to 129.81.207.215. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 2920 TABLE!. Translational diffusion coefficient [from slope of Cuu (t) in Fig. 7] Hydrodynamic diameter, spherical approximation Ratio of depolarized to polarized intensities (angle independent) from 50-100· Rotational diffusion coefficient (from Yintercept of IhvH in Fig. 7) G(p) = [r 3 (p) (I-p2)]1[(2-p) r (p) - I ] Eccentricity [from Eq. (19»), b la = p r (p), prolate case [from Eq. (19») Major axis of ellipsoid Eq. (2a) Minor axis of ellipsoid Eq. (2b) Hydrodynamic diameter of sphere of equivalent volume (D H ) 150nm± 5% 0.00367 ± 5% 250 radls 2.61 ± 26% 0.32(0.23 41<0.53 ) 1.90 [ 1.47 <r<p) <2.21] 285 nm [230«2a)<31Onm) 91 nm [53«2b)<165 nm) 133 nm (86<D H <204 nm) pared to the time scale of decay in Fig. 6 (a), clearly shows the contribution of the rotational diffusion term to hastening the depolarized autocorrelation decay, in accord with Eq. (14b). In the absence of convincing evidence for an innate anistropic polarizability of the magnetite particle, the anisotropic polarizability is assumed to have its origin in the shape anisotropy of the clusters. It should be pointed out that the preexponential coefficients in Eqs. (14a) and ( 14b) apply only to lossless dielectric particles in the Rayleigh approximation, restrictions not fully satisfied by the particles at hand. The data analysis presented herein, however, makes use only ofthe exponents, which are purely hydrodynamic terms, devoid of complications due to complex dielectric constants and Mie scatterers. Perrin 18.19 has developed a hydrodynamic model for rotational and translational diffusion of ellipsoids, assuming "stick" boundary conditions, and derived that D=KB Tf(p)l67n]a, (16) and Ai = 3KB TI167T1/a 2{[(2 _p2) r (p) -1]/(l-p4)}, (17) where p = b la is the ratio of the semiminor to semimajor axis of the ellipsoid. For prolate ellipsoids (a < 1) r (p) = (l_ p 2)- J/2 :in( 1 + (1;p2)1/2). (p) = (p2 _ 1) 1/2p tan- J [(p2 _ 1) 1/2]. 41 (I8b) Having experimentally determined D and A" from CEV(t) and CEH (t) it is then possible to determine p by D3 2 (kBn2r3(p) (l_p4) = Ai 81 ~172 [ (2 - p2) r (p) - 1] , J. Appl. Phys., Vol. 59, No.8, 15 April 1986 :EIII rJ) 19180 CII co I C 15344 .2 1G Q) (19) hence, a, and then b, can be determined by direct substitution back into Eqs. (16) or (17). Since the anisotropy results showed that transmission parallel to the orienting field diminishes, and static light scattering results showed that the scattering parallel to the applied field increases, it was assumed that the particles were prolate ellipsoids and Eq. (18a) was used for r (p). Elementary energetic considerations also support the idea that a cluster of dipoles would tend to elongate in the direction of the magnetic dipole of the cluster. Table I summarizes these 2921 calculations for the filtered lignosite solutions. It should be noted that the extrapolated value for Ai of250 radls corresponds very wen to the value of 265 rad/s for the rotational diffusion coefficient determined by the time-resolved dichroism measurements. This means that the rotational relaxation observed in these latter measurements was due purely to the rotational diffusion of the symmetry axis. Although it was possible to determine D and Ai to reasonable accuracy (5% and 15%, respectively), it was difficult to determine the ellipticity to high accuracy, first of all because the errors for D and A1 are significantly propagated in Eq. (19), and second of all, because the ratio ofEq. (19) is not very sensitive to ellipticity, ranging from a value of 1.5 for p = 1.0 to 3.7 for p = 0.2. Indeed, Perrin 18 noted in his .calculations that the difference in rotational relaxation times between extremely long prolate ellipsoids and spheres of equal volume amounts to only about a third, and thus explained the apparent success that researchers in the 19308 were having in fitting Debye's spherical hydrodynamic formulation to patently nonspherical molecules. Additionally, in the case of magnetic particles it is probable that ellipticity is an increasing function of size, so that polydispersity leaves no unique value of ellipticity for the entire solution. Figure 8 shows the depolarized autocorrelation func- (l8a) and for oblate ellipsoids (p > 1) r ± 15% t: 11508 : :I 7672 0 u 0 < >:t:: rJ) c: .... 41 3836 .5 a 0 100 200 300 ~OO 500 TIme (lIS) FIG. 8. Depolarized intensity autocorrelation function for O.4-llm filtered Lignosite without applied field and with 220 G field applied parallel to laser polarization, at 8 = 90", T = 298 K. TJ = 0.0089 cP, A. = 514 nm' W. Reed and Downloaded 27 Jul 2012 to 129.81.207.215. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions J. H. Fendler 2921 2.0 - < :x ic 1.0 :::J ;:; e. B(GBussl FIG. 9. Relative depolarized scattering vs magnetic field applied parallel to laser polarization, for O.4-J.lm filtered Lignosite, at 0 = 9(1', T = 298 K, 1/ = 0.0089 cP, A = 514 nm. tions measured at 90· in the absence of an applied magnetic field and with an applied vertical field of220 G. No measurable differences in the short- or long-time components were detectable within the limits of error. This indicates that the applied field does not induce any additional shape anisotropy to the colloids, although slight changes may occur within the error limits. It is puzzling, however, that the applied field does not seem to significantly restrict the rotational diffusion of the particles. That the transl.ational diffusion should not change is to be expected, as there is no energetic preference for an oriented magnetic dipole translating in any direction ______________~~~~~_r~~~~~~900 ana zer perpendicular to polarization ot the laser b&i:lM) 0 0 (analyzer paraDeI to polarization of the laser beam ) FIG. 10. Polar plots of transmitted intensity through Lignosite vs angle of analyzing polarizer with respect to laser polarization (a) with no applied magnetic field, (b) field applied parallel to incident polarization, and (c) field applied perpendicularly to incident polarization. Upper-right-hand comer is an enlargement of the diagram for angles close to 9(1', showing the depolarization at these angles. 2922 J. Appl. Phys.• Vol. 59, No.6, 15 April 1966 in a uniform field. At a 90· observation angle the invariability of the translational diffusion may overshadow any small changes in the rotational diffusion. Furthermore, at 220 G and at room temperature, the particles are still. only partially aligned with respect to the applied field. and azimuthal rotational. diffusion should not be hindered, although altitude angle diffusion should be. Figure 9 shows the relative intensity of the depolarized scattering as a function of the magnetic fie1d applied vertically; i.e., in the direction of the incident laser beam polarization. It is seen that the intensity drops off as a function of applied field. This is reasonable behavior, as the alignment of the symmetry axis of the elliptical particles with the applied field, and hence also with the laser polarization state, reduces the contribution to the scattered ray from the a xx and a yy diagonal terms in the polarizability tensor a. Presumably, complete alignment of the particles with the field and the incident polarization vector, at low temperatures and high field strengths, would completely eliminate the depolarized scattering. Likewise, orienting the magnetic field at an angle <p with respect to the laser polarization vector should cause maximum depolarized scattering for <p satisfying (20) To conclude the optical characterization, polarimetric measurements were made on the Lignosite solution in an attempt to deduce the phenomenological depolarization matrix for the transmitted laser beam. As the deduced matrix is phenomenological it does not depend on the actual mechanism of depolarization with which it is associated, although the weight of evidence at this point leans in favor of shape anisotropy. Figure 10 shows polar plots of the transmitted intensity of a linearly polarized He-Ne laser through a Lignosite solution (a) with no applied field, (b) with an applied field of 180 G parallel to the initial polarization vector, and (c) with an applied field of 180 G perpendicular to the polarization vector. Aligning the field along the axis of beam propagation produced no observable changes from the no-field case, strengthening the notion that the colloids are ellipsoids of revolution. Let E represent the electric field vector of the beam transmitted through magnetite in the absence of an applied external magnetic field, with parallel. E, and perpendicular Er components, where parallel indicates paral.leHty to the external magnetic field vector which is subsequently applied. Let E' represent the transmitted electric field vector with the external field applied, with parallel and perpendicular components similarly defined. Let U (B,abs) represent the depolarization matrix, whose components are a function of both the applied magnetic field strength and the absorbance of the sample. Then E and E' are related to each other by E = UE = e :) (!J, (21) where the elements of U are possibly complex quantities. In the case where E is initially polarized in the parallel. direction: (22) W. Reed and J. H. Fendler Downloaded 27 Jul 2012 to 129.81.207.215. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 2922 FIG. II. Electron micrograph is the sodium laurate stabilized ma.gnetic particles (74 000 X magnification). where t/J is the angle between the initial polarization of the incident beam and the analyzing polarizer. The transmitted intensity is the observed quantity, whose form follows from Eq. (22): I (t/J) = (a*a cos 2 t/J + c*c sin2 t/J)Ei. (23) The moduli of a and c are readily obtained from the data in Fig. 10(b) and are [a] = 0.85 and [c] = 0.212. Similar reasoning is used for obtaining the moduli of the matrix parameters band d when the incident beam is polarized in the perpendicular direction, and the values obtained from Fig. 6(c) are [b] = 0.084 and [d] = 1.11. These values for the matrix parameters are valid only for the conditions under which they were calculated, namely, that H = 180 G and absorbance = 0.85. Figures 1 and 2 can be used to obtain the elements of U on the basis of U (180 G, 0.85). The depolarization matrix can be related to the dichroic anisotropy by considering the incident unpolarized light to be composed of equal components of E, and E r • The expressions for the perpendicular and paranel intensities, calculated from the depolarization matrix are given by = [a*a + b *b + a*b + b *a] E2/2, I; = [c*c + d *d + c*d + d *c] E 2/2. I; (24) (25) The dichroic anisotropy defined in Eq. (1) is then: A = [(c+d)*(c+d) - (a+b)*(a+b)]I [(c + d)*(c + d) + (a + b)*(a + b)]. (26) If all the phase information carried in the depolarization matrix is suppressed, because it is still unknown at this point, then the dichroic anisotropy calculated from Eq. (26) and the above numerical value of the moduli of the components isA = 0.33. Using Figs. 1 and 2 to find the dichroic anisotropy under these conditions yields A = 0.195. This difference lies outside of the bounds of experimental error and so it 2923 J. Appl. Phys., Vol. 59, No.8, 15 April 1986 must be concluded that the components of the depolarization matrix are indeed complex quantities and not amenable to approximation by real values, except for the case where the incident light is linearly polarized and there is no mixing of matrix terms. It is easy to show that Eq. (26) will yield a smaller value when the quantities a,b,c, and d are complex than when they are real, their moduli being equal in both cases. The fact that the depolarization components are complex means that birefringent effects should be observable if differential phase information is contained in the matrix components. Birefringence under applied fields has indeed been observed and studied by a number of investigators. 21-24 The possibility of modulating the anisotropy on the time scales of hundreds of microseconds could allow interesting laser applications in which the transmitted light is alternately polarized and partially or completely depolarized. Understanding the origin of the optical effects could help in the development of magnetic colloids which would give maximum dichroism with a minimum of attenuation, thus allowing the development of magnetically modulated ferrofluids for switching and depolarization applications. Enhancing colloidal magneto-optical effects ties into the magnetics industry'S efforts to make improved, higher density storage media which are "read" by rotations of the plane of polarization oflasers. Recent electron micrographs were obtained for the magnetite in DODAC on a Phillips EM200 instrument. Colloids were, without staining, evaporated on a 200 mesh copper grid (Formvar support). 20 Figure 11 clearly shows the existence of clusters of a smaller magnetite particle where sizes are consistent with the dynamic li!ybt scattering and anisotropy data obtained. Thus, it seems likely that these clusters are not artifacts of evaporation, although nothing can be deduced from the electron micrographs concerning the shape of these dusters in their native aqueous environment. As already explained, the duster sizes and ellipsoidal shapes appear to be independent of dilution and the application of magnetic fields. Thus, the anisotropy, while due chiefly to the existence of the ellipsoidal aggregates, may also be weakly linked to internal spatial ordering or cooperative phenomenon within, but not between, the clusters. IV. SUMMARY The following summary can be made concerning the origin of the dichroism of the systems studied: None of the techniques reveals any type of cooperative behavior as a field is applied to the magnetic solutions. The concentration independence of the magnetization curves and the dichroism argue in this direction. The invariance of the scattering intensity autocorrelation curves under applied magnetic fields also argues strongly against the notion of field-induced chaining or aggregation. The consistency of the hydrodynamic diameters obtained from the dichroism decay curves and the scattering intensity autocorrelation function decays indicates that the clusters behave as autonomous units as concerns both rotational and translational diffusion. The unambiguous detection of shape anisotropy in the depolarized scattering intensity autocorrelation function indicates that the particles are ellipsoids of revolution with a ratio of semiminor to W. Reed and J. H. Fendler Downloaded 27 Jul 2012 to 129.81.207.215. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 2923 TABLE II. Summary of optical experiments. Technique Infonnation Static dichroic anisotropy Follows magnetization curve, scales linearly with concentration, no dichroism when H is parallel to analyzing light direction of propagation. Time-resolved dichroic anisotropy tR = 630Jls, DH = 177 nm, ~ = 265 radls for Lignosite tR = 400 JlS, DH = 153 nm, ~ = 415 radls for magnetite in ammonium laurate micelles Dynamic light scattering t, = 360 Jls, Q = 0.24, DH = 183 nm, ± 5% for Lignosite t, = 220 Jls, Q = 0.32, DH = 118 ± 5% magnetite in ammonium Iaurate micelles No measurable change in values under applied magnetic field. See Table I for results of depolarized light scattering. single exponential decay for spherical approximation Eqs. (3),(4), and (5) Static light scattering No magnetic dipole scattering, polarized scattering at 90 deg increases when H parallel to incident polarization. Polarized scattering decreases when field applied perpendicular to both initial polarization and direction of propagation. No detectable polarized scattering change when H parallel to laser propagation direction. Polarimetry Depolarized scattering decreases when H parallel to incident polarization. Initially polarized light is partially depolarized due to birefringence. Depolarization matrix obtained. semimajor axes in the neighborhood of 0.32. The electronmicrographs reveal that these particles are actually aggregates of much smaller spherical crystals. The shape anisotropy of the aggregates is sufficient to produce an anisotropic pol arizability tensor for the colloids, which accounts for the observed dichroic effects without the need for introducing more complicated or sophisticated origins such as cooperative effects, spatial ordering, or inherent optical anisotropy of the magnetic crystal. Table II summarizes the information and conclusions from each optical technique. If the central finding presented in the article is correct, namely, that the pronounced magnetodichroic effect is due to large anisotropic clusters of smaller particles, then the dichroic effect has a very useful function in guiding magnetic particle preparations: if small particles (e.g., 10 nm diam) are individually dispersed and not aggregated then the dichroic effect should be absent, or nearly so (see Scholten 9 for the calculation of a tiny dichroic effect based on single-particle anistropy). Thus, a magnetic dichroism test can indicate whether a particular preparation or dispersion material or technique is effective. This is particularly true in the case of vesicle stabilized single-magnetite particJ.es, where the vesicle is much larger than the particles (roughly 150 vs 1.0 nm) and no simple light scattering experiments can distinguish between entrapped clusters and entrapped individual particles. ACKNOWLEDGMENTS Support of this work by 3M Corporation is gratefuUy acknowledged. We thank Mr. M. Brandt for his aid in instrumentation and Mr. Pascal Herve for providing samples of his surfactant aggregate entrapped magnetites. 2924 J. Appl. Phys .• Vol. 59, No.8, 15 April 1986 IS. W. Charles and J. Popplewell, in Ferromagnetic Material, Vol. 2, edited by E. P. Wohlfarth (North-Holland, New York, 1980), p. 509; E. P. Wohlfarth, J. Magn. Magn. Mater. 39, 39 (1983). 2J. H. Fendler, Membrane Mimetic Chemistry (Wiley-Interscience, New York, 1982); J. H. Fendler, Ace. Chern. Res. 13, 7 (1980). 3R. Haberkorn, Chern. Phys. 19, 165 (1977); A. L. Buchachenko, Russ. Chern. Rev. (Engl. Trans.) 45, 761 (1976); N. J. Turro and B. Krautler, Ace. Chern. Res. 13, 369 (1980); V. Steiner, Ber. Bunsengecell. Phys. Chern. 85, 228 (1981); J. C. Scaiano, E. B. Abrin, and L. C. Stewart, J. Am. Chem. Soc. 104, 5673 (1982). ·P. Herve, F. Nome, and J. H. Fendler, J. Am. Chern. Soc. 106, 8291 (1984). 5C. Coate, J. Magn. Magn. Mater. 39, 85 (1983). 6p. Goldberg, J. Hansford, and R. G. Van Heerden, J. Appl. Phys. 42,3874 (1971 ). 7M. M. Maiorov and A. O. Tsebers, Kolloidn. Zh. 39, 1087 (1977). 8E. E. Bibik, Magn. Gidrodin. 3, 25 (1973). "P. C. Scholten, IEEE Trans. Magn. 16,2 (1980). I°Georgia Pacific Company, P. O. Box 1236, Bellingham, WA 98227. 110. Majorana, Atti. Linc.ll, 531 (1902). 'ZWe are grateful to Mr. Michael Brandt for building this circuit. 13R. W. Chantrell, J. Popplewell, and S. W. Charles, IEEE Trans. Magn. 14,975 (1978). 14R. Kaiser and G. Mickoizey, J. Appl. Phys. 41, 1064 (1970). 15E. A. Peterson and D. A. Kruger, J. Colloid Interface Sci. 62, 24 (1977). 16J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 413. 17B. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976), Chap. 7. IIF. Perrin, J. Phys. Radium V, 497 (1934). 19p. Perrin, J. Phys. Radium YD, I (1936). rowe are grateful to Arnold J. Drube, Science Research Laboratory, Central Research, 3M Company, St. Paul, MN, for taking the electron micrographs. 21A. Martinet, Rheol. Acta. 13, 260 (1974). 21D. Y. Chung, T. R. Hickman, R. P. DePaula, and J. H. Cole, J. Magn. Magn. Mater. 39, 71 (1983). 23Davies and Llewellyn, J. Phys. D. 12, (1979). 24G. A. Jones and I. B. Puchalska, Phys. Status Solidi 51,549 (1979). W. Reed and J. H. Fendler Downloaded 27 Jul 2012 to 129.81.207.215. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 2924