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Anisotropic aggregates as the origin of magnetically induced dichroism in
Wayne Reed and Janos H. Fendler
Citation: J. Appl. Phys. 59, 2914 (1986); doi: 10.1063/1.336952
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Published by the American Institute of Physics.
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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 within the stable clusters or an unexpected anisotropic
polarizability of the magnetite crystals do not seem to be likely origins of the dichroic effect.
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.
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.
Current address: Department of Chemistry, Syracuse University, Syracuse, NY 13210.
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
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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
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
= kTtJ1],
t, = 1/6A,
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
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
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,
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
J. Appl. Phys., Vol. 59, No.8, 15 April 1986
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
W. Reed and J. H. Fendler
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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
D. Polarimetry measurements
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
J. Appl. Phys., Vol. 59, No.8, 15 April 1986
W. Reed and J. H. Fendler
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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],
where b isthe volume fraction of particles with the saturation
magnetization M., and
= D 3MsH /24kT.
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
. . Le(_.''--'--'---'--'
..... 10
'.. ".__~
. -
. --'
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,
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
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
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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
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
J. Appl. Phys., Vol. 59, No.8. 15 April 1986
E", 0.9
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
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
- e·p+ (~'
nxe~') ·m}2
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
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
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' a
• 'I~
Time (ms)
~ 5350
Time (fIS)
Time (ms)
......: : /
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
Time <..s)
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
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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
FIG. 7. Reciprocal intensity autocorrelation decay lifetime vs sin 2
for depolarized data. 0 for polarized data.
/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)(
all - a 1 e
where (N) represents the average number ofpartic1es in the
observed scattering volume and
+ 2a
!(DII + Wi)'
a = j(all
1 ),
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
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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,
Ai = 3KB TI167T1/a 2{[(2 _p2)
(p) -1]/(l-p4)},
where p = b la is the ratio of the semiminor to semimajor
axis of the ellipsoid. For prolate ellipsoids (a < 1)
(l_ p 2)- J/2
:in( 1 + (1;p2)1/2).
(p) = (p2 _ 1) 1/2p tan- J [(p2 _ 1) 1/2].
Having experimentally determined D and A" from CEV(t)
and CEH (t) it is then possible to determine p by
2 (kBn2r3(p) (l_p4)
81 ~172 [ (2 - p2) r (p) - 1] ,
J. Appl. Phys., Vol. 59, No.8, 15 April 1986
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
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-
and for oblate ellipsoids (p > 1)
± 15%
: :I
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
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J. H. Fendler
ic 1.0
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
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.
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
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
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
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,
where the elements of U are possibly complex quantities. In
the case where E is initially polarized in the parallel. direction:
W. Reed and J. H. Fendler
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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.
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.
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)].
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
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.
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
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TABLE II. Summary of optical experiments.
Static dichroic
Follows magnetization curve, scales linearly with
concentration, no dichroism when H is parallel to analyzing
light direction of propagation.
dichroic anisotropy
tR = 630Jls, DH = 177 nm, ~ = 265 radls
for Lignosite
tR = 400 JlS, DH = 153 nm, ~ = 415 radls
for magnetite in ammonium laurate
Dynamic light
= 360 Jls, Q =
0.24, DH
= 183 nm,
± 5% for Lignosite
t, = 220 Jls, Q = 0.32, DH = 118 ± 5%
magnetite in ammonium Iaurate
No measurable change in values under applied magnetic field.
See Table I for results of depolarized light scattering.
for spherical
Eqs. (3),(4), and (5)
Static light
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.
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, 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.
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.
J. Appl. Phys .• Vol. 59, No.8, 15 April 1986
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by E. P. Wohlfarth (North-Holland, New York, 1980), p. 509; E. P.
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'ZWe are grateful to Mr. Michael Brandt for building this circuit.
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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).
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W. Reed and J. H. Fendler
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