The nonflat distribution function G͑E͒ =sech

͑E/2kT͒,
with

=3, however, has been introduced as an excellent al-
ternative for fitting the field dependence of the DS peak
frequency.
14
Using the nonflat description Eq. ͑1͒ is reduced
to
f
P
͑H͒ =
͵
A exp͑− KV/kT͒tanh͑E/2kT͒P͑V͒dV. ͑2͒
The solid lines in Fig. 2 represent the best fit of the
experimental data according to Eq. ͑2͒. In contrast, the use of
a flat G͑E͒ function replaces, in Eq. ͑2͒, the asymptotic
tanh͑E/2kT͒ by the divergent sinh͑E/2kT͒, not accounting
for the saturation behavior observed in Fig. 2. At this point
two aspects of the nonflat distribution function, G͑E͒, should
be emphasized. First, from the mathematical point of view
Eq. ͑2͒ is exactly obtained from Eq. ͑1͒, as long as G͑E͒
=sech
3
͑E/2kT͒. Second, from the physical point of view the
nonflat distribution function, G͑E͒, deviates very little from
the Boltzmann distribution function. In other words, the
good agreement between the data and the model proposed in
the present study, which uses the nonflat distribution func-
tion, indicates that the asymmetry parameter ͑E͒ may follow
a classical distribution function. Though empirical, the
present approach represents a step forward as compared to
the use of a flat distribution function.
The parameters obtained from the fitting of the DS data
͑solid lines in Fig. 2͒ are in excellent agreement with the data
provided by the TEM micrographs. The log-normal fit shown
in Fig. 3 for the dextran-coated ͑DMSA-coated͒ sample
gives 3.1±0.3 nm ͑5.6±0.2 nm͒ and 0.26±0.02 ͑0.22±0.01͒
for the mean particle diameter and diameter dispersion, re-
spectively. The particle polydispersity parameters obtained
from the fitting of the TEM data were used as initial values
͑guess values͒ in the fitting procedure ͑least-squares fit͒ of
the DS data using Eq. ͑2͒. The fitting of the DS data ͑solid
lines͒ shown in Fig. 2 was performed with 3.7±0.5 nm
͑6.1±0.5 nm͒ and 0.27±0.04 ͑0.25±0.03͒ for the mean par-
ticle diameter and diameter dispersion of the dextran-coated
͑DMSA-coated͒ sample, respectively. Furthermore, the aver-
age anisotropy values we found from the DS analysis of the
dextran-coated and DMSA-coated samples were ͑1.2±0.4͒
ϫ10
4
and ͑1.6±0.3͒ϫ 10
4
J/m
3
, respectively. Considering
the uncertainties, the anisotropy values we found are in ex-
cellent agreement with the value reported for the anisotropy
of bulk magnetite ͑1.9ϫ 10
4
J/m
3
͒.
15
Finally, the average
magnetization obtained from the DS analysis of both
samples was 110±8 emu/g. Though upshifted from the satu-
ration magnetization value reported in the literature
16
͑84 emu/g for magnetite͒ the fitted value still falls in the
expected range. The observed difference in saturation mag-
netization, i.e., the value reported in the literature versus the
value found from the susceptibility data may indicate the
presence of a nonmagnetic surface layer in the magnetite
nanoparticles. Similar investigation, namely, the field depen-
dence of the imaginary peak susceptibility, has been reported
in the literature with no model picture supporting quantita-
tive explanation for the data.
17
Note that measurements
available from the literature present data recorded in the
range of 0 to about 1 kG. In such a low-end side of magnetic
fields a linear dependence of the peak frequency shift has
been observed,
17
similar to the data reported in this study.
In conclusion, magnetite-based biocompatible magnetic
fluid samples were investigated using room-temperature dy-
namical susceptibility measurements. The multipeak compo-
nent observed in the susceptibility curves can be explained in
terms of the presence of monomers and dimers ͑fanning and
coherent͒ in the magnetic fluid samples; the dimers induced
by a weak magnetic field due to the Robinson oscillator su-
perimposed to the external steady field. We found, in addi-
tion, that the fanning configuration of the dimer is more
likely to occur than the coherent one, indicating that the
DMSA-coated magnetite nanoparticles built up essentially
the fanning dimer whereas the dextran-coated magnetite
nanoparticles form both fanning and coherent dimers. Con-
sidering the uncertainty related to the polydispersity param-
eters obtained from both dynamical susceptibility and trans-
mission electron microscopy data, the present investigation
highlights the capability of the susceptibility measurements
in assessing the mean size and size dispersion of magnetic
nanoparticles in magnetic fluid samples. In addition, the field
dependence of the main susceptibility peak allows estimation
of the saturation magnetization ͑110±8 emu/g͒ and magne-
tocrystalline anisotropy ͑1.2±0.4ϫ 10
4
and 1.6±0.3
ϫ10
4
J/m
3
͒ values associated with molecular-coated mag-
netite nanoparticles. Indeed, the field dependence of the main
susceptibility peak has been described via a relaxation pic-
ture of the magnetic moment of an isolated nanoparticle in
an asymmetric double-well potential.
ACKNOWLEDGMENTS
This work was supported by the Brazilian agencies
CNPq, FINEP, and FINATEC.
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