Quantitative analysis of the a.c. susceptibility of core–shell nanoparticles

RESEARCH PAPER

Quantitative analysis of the a.c. susceptibility of core–shellnanoparticles

M. A. Lucchini • P. Riani • F. Canepa

Received: 14 November 2012 / Accepted: 22 March 2013

� Springer Science+Business Media Dordrecht 2013

Abstract Magnetite (Fe3O4) and silica-coated mag-

netite (Fe3O4@SiO2) nanoparticles (NPs) were syn-

thesized and characterized by scanning and

transmission electron microscopy and by a.c. suscep-

tibility measurements as a function of the frequency

both at room temperature and 80 K. A new mathe-

matical approach based on the explicit coexistence (at

room temperature) of Brownian and Neel contribu-

tions is proposed: the magnetic data were quantita-

tively analyzed following this approach and the results

well agree with microscopic data. This mathematical

procedure allows the achievement of the complete size

distribution of coated magnetic NPs in solution as well

as the real dimension of the magnetic nuclei.

Keywords Core–shell nanoparticles �Ac susceptibility � Nanoparticle magnetism

Introduction

Magnetic nanoparticles (MNPs) are extensively stud-

ied due to their possibility to be chemically or

biologically functionalized for different applications

in medicine and bioanalytics like drug delivery (Veiseh

et al. 2010), Magnetic resonance imaging contrast

enhancement (Na et al. 2009), protein separation (Kim

et al. 2010), and hyperthermia (Laurent et al. 2011). All

these applications require the minimization of the

dipole–dipole magnetic interactions to reduce the

possibility of agglomeration among the different

MNPs. A successful method to stabilize these nano-

particles (NPs) is their coating with an organic

(Griffete et al. 2012) or inorganic shell (Mahmoudi

et al. 2010). In both cases, a reduction of the magnetic

interactions is obtained: An inorganic coating like Au

or SiO2 can be easily detected by transmission electron

microscopy (TEM) analysis (Im et al. 2005) and

scanning probe microscopy (both atomic force, AFM

Colombo et al. 2012, and tunneling, STM Koo et al.

2012), while an organic one is usually invisible to this

type of technique. An alternative method is dynamic

light scattering (DLS); in this technique, the signal is

mainly due to the larger particles or the aggregates

M. A. Lucchini

Dipartimento di Chimica e Chimica Industriale,

Via Dodecaneso 31, 16146 Genoa, Italy

P. Riani

INSTM-UdR Genova and Dipartimento di Chimica e

Chimica Industriale, Via Dodecaneso 31, 16146 Genoa,

Italy

F. Canepa (&)

CNR—Unita di Genova and Dipartimento di Chimica e

Chimica Industriale, Via Dodecaneso 31, 16146 Genoa,

Italy

e-mail: [email protected]

123

J Nanopart Res (2013) 15:1601

DOI 10.1007/s11051-013-1601-x

present in the sample: the scattered light intensity

shows a quadratic dependence on the volume of

scattering particles according to the classical Rayleigh

theory (Kerker 1969), so the contribution of larger

molecules is more pronounced in a polydispersed

sample1 (Sipos et al. 2003).

Another method to detect the dimensions of MNPs in

solution, based on a.c. susceptibility measurements, was

developed some years ago by Kotitz et al. (1995), and

later modified (Connolly and St Pierre 2001; Nutting

et al. 2006). This approach, adopted for magnetic

particles in the superparamagnetic regime, is based on

the Debye theory developed to describe the dielectric

dispersion on dipolar fluids (Debye 1929), leading to an

expression for the frequency dependence of the complex

magnetic susceptibility. Recently (Ludwig et al. 2009),

the magnetorelaxometry and the a.c. susceptibility of

Fe3O4 MNPs with polyacrylic acid shells were analyzed

in the framework of Brownian and Neel mechanisms. In

the Brownian mechanism, the whole MNP rotates

including shell and attached solvent molecules, while in

the Neel mechanism, only the magnetic moment inside

the MNP can flip by thermal activation. The authors

took into account the fact that both mechanisms are

present due to a large size distribution function observed

from TEM measurements on several hundreds of NPs,

and they fixed an effective relaxation time given by

seff = (sBsN)/(sB ? sN) where sB is the Brownian

relaxation time and sN is the Neel relaxation time

(Shliomis and Raikher 1980).

However, up to now, very few data on MNPs and

composite MNPs, related to the frequency dependence

of the complex susceptibility at low temperatures, i.e.,

when the Brownian contribution vanishes, are known.

This fact prevented the determination by magnetic

measurements of dimensional parameters of compos-

ite NPs in solution. So, in this paper, the results

obtained preparing magnetite NPs and covering them

with silica in order to obtain Fe3O4@SiO2 MNPs were

reported. Both sets of NPs were characterized by TEM

and a.c. susceptibility measurements at room temper-

ature (RT) as well as at 80 K. The analysis of the

magnetic results was performed taking into account

both the Brownian and Neel contributions and the

results are reported here.

Experimental details

Magnetite NPs were prepared by coprecipitation using a

modified Massart method (Riani et al. 2011). Once

obtained, the MNPs were coated with silica by hydro-

lysis and condensation following the Stober process

(Stober et al. 1968): 5.4 mmol of tetraethyl orthosilicate

was added to 200 ml of ethanol and 4 ml of water. The

reaction occured at a temperature of 40 �C (water bath)

for 20 min and at basic pH (pH [ 9 by NH3(aq)) to

advantage the condensation over the hydrolysis (Schu-

bert and Husing 2005) of silica NPs. Once the silica

primary NPs were obtained, 8 ml of Fe3O4 NPs solution,

with a concentration of 60 mg/l, was added and the

solution was mechanically stirred for 2 h (Lu et al.

2008). The final solution was then centrifuged to collect

the coated MNPs as well as the SiO2 NPs formed: The

solvent in excess was eliminated to stop the reaction.

The NPs were again dispersed in pure ethanol and finally

the Fe3O4@SiO2-composite NPs were collected and

separated from the SiO2 NPs by means of magnetic

levitation with a permanent magnet.

The morphology of the Fe3O4 and Fe3O4@SiO2

MNPs was detected by microscopic techniques like

TEM (JEOL JEM 2010 200 kV) and a field emission

scanning electron microscope (FE-SEM, ZEISS

SUPRA 40 VP) equipped with an energy dispersive

X-ray spectrometer (EDX-OXFORD ‘‘INCA Energie

450 9 3’’) for microanalysis. a.c. susceptibility mea-

surements were obtained using an OXFORD Mag-

lab2000 magnetic measurements system operating in

the 1–104 Hz frequency range with an a.c. magnetic

field of 10 Oe. The resolution of the a.c. signal was

better than 10-7 emu.

Results and discussion

Magnetic relaxations in a ferrofluid

When an alternate magnetic field is applied to a

ferrofluid formed by superparaMNPs, two different

relaxation mechanisms can take place: the Brownian

relaxation and the Neel relaxation.

In the Brownian relaxation, the whole magnetic

nanoparticle with the solvent molecules bound to it by

ionic interactions can rotate with the a.c. field and, in

this case, the time constant sB, i.e., the time that a

particle needs to complete the rotation, is related to the

1 Thiele G, Poston M, Brown R. A case of study in sizing

particles. Micromeritics analytical services.

www.particletesting.com

Page 2 of 10 J Nanopart Res (2013) 15:1601

123

hydrodynamic radius of the NP (under the assumption

of a spherical shape) and to the viscosity of the solvent

by the equation

sB ¼4p � g � r3

h

kB � Tð1Þ

where g is the solvent viscosity, rh is the hydrody-

namic radius of the NP, kB is the Boltzmann constant,

and T is the absolute temperature.

In the Neel relaxation, only the magnetic moment

of the spherical core of the NP can rotate with the a.c.

field, and the corresponding time constant sN is related

to the anisotropy energy following the equation

sN ¼ s0 � exp4p � r3

c � Ka

3kB � T

� �ð2Þ

where s0 is a constant with values ranging in the order

of 10-9 7 10-13 s, rc is the magnetic core radius, and

Ka is the magnetic anisotropy constant. The sB and sN

time constants are related to the experimental applied

frequency m by the relation s = 1/(2pm).

In the framework of the Debye model (Debye 1929;

Fannin and Coffey 1995), the real and imaginary

components of the a.c. susceptibility are given by

v mð Þ ¼ v0 mð Þ � iv00ðmÞ ð3Þ

v0 ¼ v1 þv0 � v1

1þ x � sð Þ2and

v00 ¼ v0 � v1ð Þ � x � s1þ x � sð Þ2

ð4Þ

where v0 and v00 are the real and imaginary component

of the a.c. susceptibility, respectively, v0 is the

susceptibility at zero frequency (static approxima-

tion), v? is the susceptibility at the highest frequency,

x is 2pm, and s is the relaxation time.

To take into account the size dispersion distribu-

tion, typically a log-normal distribution is considered:

p r½ � ¼ 1

r � r �ffiffiffiffiffiffi2pp � e

� ln rrmð Þ

2

2r2

h ið5Þ

where rm is the mean particle radius and r is the

standard deviation. As can be found in the reference

(Riani et al. 2011), more than one population can be

considered and, in this case, the total distribution will

be the weighed sum of all components.

Using formulas (1) and (2), it is possible to

calculate the Brownian rotation frequency and the

Neel rotation frequency as a function of the hydrody-

namic and magnetic core radius, respectively, and the

results are reported in Fig. 1 at the two different

B

Fig. 1 Relation between

the relaxation frequency and

dimension of the system for

Brownian (300 K) and Neel

relaxation (80 K e 300 K)

J Nanopart Res (2013) 15:1601 Page 3 of 10

123

temperatures of 80 and 300 K. At RT, in the

100–104 Hz frequency range of the instrumentation

adopted here, the Brownian relaxation occurs for NPs

or aggregates of NPs with a radius between 20 and

180 nm; the Neel relaxation, under the hypothesis that

s0 = 9 9 10-13 s and Ka = 3.56�105 J/m3 (Goya

et al. 2003), is restricted to NPs with a magnetic core

radius between 3.6 and 4.0 nm. At 80 K, obviously,

only the Neel relaxation exists and our frequency

window allows the detection of NPs with a magnetic

radius between 2.3 and 2.6 nm. This simulation

suggests the contemporary presence of the two

Fig. 2 Transmission

electron microscope image

of Fe3O4 NPs. As inset the

distribution of radii,

obtained by several TEM

images can be found

Fig. 3 TEM photograph of Fe3O4@SiO2 NPs; a dark Fe3O4 NP

aggregates imbedded in gray silica sphere can be observed. The

chemical composition of the gray spheres b and of the embedded

darker aggregates c has been characterized by EDX analysis

carried out with a 5-nm-diameter electron probe. Cu contribu-

tion is related to the supporting grid

Page 4 of 10 J Nanopart Res (2013) 15:1601

123

different relaxation mechanisms at RT, and this

evidence was taken into account to obtain the fit of

experimental data.

Microscopic results

Figure 2 reports a typical example of magnetite NPs:

The MNPs present a spherical shape with small

dimensions; as an inset of Fig. 2, a size distribution

histogram of the radius of the NPs, obtained from the

measurements of one hundred NPs, is presented. The

histogram presents a distribution of radii between 2

and 8 nm and an average radius around 4 nm. Since

the critical radius for superparamagnetism is 6.5 nm

(O’Handley 2000), this value confirms that our MNPs

are in the superparamagnetic regime.

Figure 3a shows TEM image of Fe3O4@SiO2

MNPs: The small dark magnetite NPs are enclosed

in the clearly visible silica shell with mean radius

around 20 nm. This core–shell structure has been also

confirmed by the EDX spectra reported in Fig. 3b, c.

Polycondensation occurs among the different coated

NPs. The TEM images are very similar to those

obtained by Lu et al. (2008). Figure 4 displays a FE-

SEM image of a similar sample: single composite NPs

with a radius similar to the previous one can be seen.

Also, in this case, the presence of magnetite inside the

silica shell was confirmed by EDX analyses and one of

these was reported as the inset.

Magnetic results

Fe3O4 nanoparticles

Figure 5 shows the real and imaginary components of

the room temperature a.c. susceptibility of a magnetite

NP sample as a function of the frequency. The data

were corrected by the not negligible contribution of

the solvent, as already demonstrated (Lucchini and

Canepa 2012). To complete the magnetic character-

ization, the ferrofluid was cooled down to 80 K and the

results are presented as insets in the same figure. As is

possible to see from the insets, both components of the

a.c. susceptibility present, also at low temperature, a

slight but visible dependence from frequency. Since at

that temperature the solvent is frozen and conse-

quently the Brownian contribution is reduced to zero,

this dependence must be attributed only to Neel

relaxation. So, taking again s0 = 9 9 10-13 s and

Ka = 3.56 9 105 J/m3 (Goya et al. 2003), we obtain a

good fit for the low T data using a log-normal

distribution centered in a mean core radius value (rc)

of 2.75 nm and a standard deviation r = 0.11. The fit

is reported, as a continuous line, in the same insets.

This result confirms that a not negligible Neel

contribution is present in our susceptibility data and

must be taken into account to achieve the best fit, also

at room temperature. The value of rc is consistent with

our frequency window at 80 K (displayed in Fig. 1)

Fig. 4 SEM photograph of

Fe3O4@SiO2 NPs with

corresponding EDX spectra

as inset. The EDX analysis

presenting iron, silicium,

and oxygen peaks confirms

the core shell structure of the

NPs. The image has been

acquired collecting

secondary electron signal.

Cu contribution is related to

the supporting grid

J Nanopart Res (2013) 15:1601 Page 5 of 10

123

and with the distribution obtained by TEM images (see

Fig. 2).

The RT susceptibility data were consequently

analyzed using both the Neel and Brownian contribu-

tions and the results are reported, as continuous lines,

again in Fig. 5. The Neel contribution is ascribed to

NPs with a magnetic core radius of 4.0 nm and

standard deviation of 0.018. The Brownian contribu-

tion is due to a bimodal log-normal distribution with

rm1 = 22.5 nm (r1 = 0.41, 88 %) and rm2 =

125.0 nm (r2 = 0.5, 12 %). We emphasize here the

agglomeration of the NPs in small and large aggre-

gates due to the strong dipole–dipole interactions

present in water in the absence of surfactants.

Fe3O4@SiO2 nanoparticles

Different samples of MNPs coated by silica were

prepared and magnetically measured: Here, the results

concerning the a.c. susceptibility data and the analyses

of two of these samples are presented. Both specimens

were measured at room temperature. Furthermore, for

one of the samples, the a.c. susceptibility at 80 K was

obtained in order to check, also in this case, if a Neel

contribution is present at low temperatures. The results

are shown in Figs. 6 and 7 for samples A and B,

respectively. In the inset of Fig. 6, the complex v data

for sample A at 80 K are reported. The low temperature

data of Fe3O4@SiO2, showing a flat decrease of the real

susceptibility with frequency, confirm the existence of

the Neel contribution. A fit with only this term, reported

as a continuous line, gives a value of 2.62 nm for the

magnetic core with a standard deviation of 0.07. This

average value of the magnetic core radius agrees well

with that obtained from the pure MNP sample.

The room temperature a.c. susceptibility data of the

two silica-coated samples are very similar: in both

cases, the real susceptibility shows an evident decrease

at increasing frequency with a change of slope around

50 7 150 Hz. The imaginary component is more

intriguing: A broad maximum, consistent with an

evident Brownian relaxation, is present in the two

samples. On the basis of the protocol followed for

Fe3O4 NPs, the complex susceptibility data of both

samples were fitted with a sum of the Brownian and

Neel relaxation terms. The data are reported in

Table 1, together with those already obtained for the

bare NPs. The fit is sketched, as a continuous line, in

Figs. 6 and 7 for samples A and B, respectively. In

Fig. 7, the two single contributions for Brownian and

Neel relaxation (empty dot and empty square, respec-

tively) are also presented.

Fig. 5 AC Susceptibility of

Fe3O4 NPs at room

temperature and at 80 K;

experimental data (emptydot) and fit (line) are

reported

Page 6 of 10 J Nanopart Res (2013) 15:1601

123

Discussion

The control of the dimensions of the functionalized

MNPs is very important and, typically, it is analyzed

by microscopic techniques (SEM, TEM, AFM). If the

NPs are functionalized, the possibility to detect the

functionalization strongly depends by its nature. An

organic functionalization of the NP can be hardly

detected by standard electron microscopy. So, to

obtain the size distribution of the functionalized

Fig. 6 AC Susceptibility of

Fe3O4@SiO2 NPs (sample

A) at room temperature and

at 80 K; experimental data

(empty dot) and fit (line) are

reported

Fig. 7 AC Susceptibility of

sample B of Fe3O4@SiO2

NPs: fit of the experimental

data is reported as total

contribution (line) and as

single contribution

Brownian (circle) and Neel

(square)

J Nanopart Res (2013) 15:1601 Page 7 of 10

123

MNPs, the use of an alternative method based on the

measurement of a physical property related to the

dimension of the nanoparticle, and its optimization,

seems to be an interesting target to reach. Within this

assumption, the use of the a.c. susceptibility is very

promising, either for the high sensitivity achievable by

this technique or by the possibility to know, from non-

destructive measurements, the behavior of a real

magnetic drug delivery system.

Our low temperature analyses of different systems

of bare or coated MNPs always evidenced the

existence of a Neel contribution. Furthermore, differ-

ent tentatives to fit the room temperature data (both

real and imaginary components of the complex

susceptibility) with a simple Brownian term were

made, mainly for the Fe3O4@SiO2 NPs where an

evident maximum in v00 was observed in each studied

system. In any case, the fit was unsatisfactory. These

results suggested that we adopt a different approach to

that used up to now, i.e., the use of an effective

relaxation time. We hypothesized an effective inde-

pendence between Brownian and Neel rotations with a

mathematical system based on a sum of the two

contributions. Under this hypothesis, some mathemat-

ical corrections have been taken into account:

• The experimental susceptibility will be the sum of

the Brownian contribution and Neel contribution;

• The experimental susceptibility at zero frequency

(v0) is the sum of two different values arising from

the two different contributions, i.e., the Brownian

and Neel ones;

• The v? value in v00 formula for Brownian relax-

ation for coated MNPs is fixed equal to zero since,

as it is enhanced in the mathematical analysis of

Fig. 7, the imaginary contribution of the Brownian

relaxation of our coated MNPs approaches zero at

high frequency.

Using this correction, the new model proposed is

based on the following equations:

vexp ¼ vB þ vN

v0 mð Þ ¼ v0B mð Þ þ v0N mð Þv00ðmÞ ¼ v00BðmÞ þ v00NðmÞ

ð6Þ

where the two contributions can be considered as

follows:

v0 mð ÞB¼ v1 þZr2

r1

PB rð Þ � v0B � v1ð Þ

1þ 2p � m � 4p�gkB�T � r

3h

� �2dr ð7Þ

v00 mð ÞB¼Zr2

r1

PB rð Þ � ðv0B � v1Þ � 2p � m � 4�p�gkE�T � r3

h

� �1þ 2p � m � 4�p�g

kB�T � r3h

� �2dr

ð8Þ

for the Brownian contribution, where PB(r) is the

radius distribution for Brownian relaxation (see Eq.

(5)) and rh is the hydrodynamic radius of the particles.

v0 mð ÞN¼ v1 þZr2

r1

PN rð Þ � v0N � v1ð Þ

1þ 2p � m � eKa4�p�r3

c3�kB �T

� �2dr ð9Þ

v00ðmÞN ¼Zr2

r1

PN rð Þ � ðv0N � v1Þ � 2p � m � eKa4�p�r3

c3�kB �T

� �

1þ 2p � m � eKa4�p�r3

c3�kB �T

� �2dr

ð10Þ

for Neel contribution, where PN(r) is the radius

distribution for Neel relaxation (see Eq. (5)) and rc is

the radius of the magnetic NPs.

So, the data obtained from the different fits are

totally self-consistent: Brownian radii obtained for the

Fe3O4 NPs are in excellent agreement with data from

the reference (Riani et al. 2011). The Neel mean radius

calculated at room temperature presents the same

value for the Fe3O4 and Fe3O4@SiO2 NPs, as

presented in Table 1, and this value is in complete

agreement with the mean value obtained from TEM

images. The reason for the existence of the Neel

contribution, together with the Brownian one, can be

Table 1 Summary of data obtained by fit of experimental data

for bare magnetite and silica-covered magnetite NPs

rm Brownian (nm)

(distribution)

rm Neel (nm)

(distribution)

Fe3O4 (80 K) – 2.75 (0.11)

Fe3O4 (300 K) 22.5 (0.41)a 4.0 (0.02)

Fe3O4@SiO2 (80 K) – 2.62 (0.07)

Fe3O4@SiO2 (300 K)

(sample A)

118 (0.57) 3.56 (0.07)

Fe3O4@SiO2 (300 K)

(sample B)

70 (0.45) 3.46 (0.06)

a For this sample, only the main population (88 %) is reported

Page 8 of 10 J Nanopart Res (2013) 15:1601

123

deduced from Fig. 7, where, as an example, the

experimental data of the B-Fe3O4@SiO2 sample with

the two relaxation contributions to the fit are reported.

As is possible see from the plot, the slow but

continuous increase of Neel relaxation with the

synchronous decrease of the Brownian relaxation

toward zero values at higher frequencies must be

explained in terms of progressive freezing of the

dynamic rotation motion of the NPs in solution. When

the NPs are blocked, the magnetization vector of the

magnetic core of the NPs begins to rotate with the

applied alternate magnetic field, thus giving the Neel

contribution to the overall susceptibility.

This approach, which can be easily adopted for any

other magnetic nanosystem characterized by a higher

or lower complexity without worsening of the solu-

tion, allows to know accurately the dimensional

distribution of composite NPs irrespective of the type

(and number) of coatings used as well as the dimen-

sion of magnetic nuclei.

Quantitative magnetic analyses on Fe3O4@SiO2

NPs functionalized with fluorescent molecules are

now in progress at our laboratory to confirm the

present mathematical approach.

Conclusions

Magnetite NPs were coated with silica following the

literature data. These core–shell NPs were characterized

by electron microscopy and ac susceptibility measure-

ments at 300 and 80 K. The data were quantitatively

analyzed with a new mathematical approach based on

the coexistence of Brownian and Neel rotations in the

same fluid. The results are in agreement with direct

microscopic observations and the literature data. The

adopted procedure seems a good starting point to

quantitatively evaluate the morphology of complex

functionalized MNPs not discernible in other way.

Acknowledgments The support of Miss. Agnese Carino is

gratefully acknowledged.

References

Colombo C, Palumbo G, Ceglie A, Angelico R (2012) Char-

acterization of synthetic hematite (a-Fe2O3) Nanoparticles

using a multi-technique approach. J Colloid Interface Sci

374:118

Connolly J, St Pierre TG (2001) Proposed biosensors based on

time-dependent properties of magnetic fluids. J Magn

Magn Mater 225:156

Debye P (1929) Polar molecules. Chemical Catalog Company,

New York

Fannin PC, Coffey WT (1995) Contribution of particles inertial

effect to resonance in ferrofluid. Phys Rev E 52:6129

Goya GF, Berquo TS, Fonseca FC, Morales MP (2003) Static

and dynamic magnetic properties of spherical magnetite

nanoparticles. J Appl Phys 94:3520

Griffete N, Clift MJD, Lamouri A, Digigow RG, Mihut AM,

Fink A, Rothen-Rutishauser B, Dietsch H (2012) Amino

covalent binding approach on iron oxide nanoparticle

surface: toward biological applications. Colloids surf A

415:98–104

Im SH, Herricks T, Lee YT, Xia Y (2005) Synthesis and char-

acterization of monodisperse silica colloids loaded with

superparamagnetic iron oxide nanoparticles. Chem Phys

Lett 401:19

Kerker M (1969) The scattering of light. Academic Press, New

York, p 414

Kim J, Piao Y, Lee N, Park YI, Lee I, Lee J, Paik SR, Hyeon T

(2010) Magnetic nanocomposite spheres decorated with

NiO nanoparticles for a magnetically recyclable protein

separation system. Adv Mater 22:57

Koo H, Kano S, Tanaka D, Sakamoto M, Teranishi T, Cho G,

Majima Y (2012) Charcaterization of thiolfunctionalized

oligo(phenylene-ethynylene)-protected Au nanoparticles

by scanning tunneling microscopy and spectroscopy. Appl

Phys Lett 101(083115):1–5

Kotitz R, Fannin PC, Trahms L (1995) Time domain study of

Brownian and Neel relaxation in ferrofluids. J Magn Magn

Mater 149:42

Laurent S, Dutz S, Hafeli UO, Mahmoudi M (2011) Magnetic

fluid hyperthermia: focus on superparamagnetic iron oxide

nanoparticles. Adv Colloid Interface Sci 166:8

Lu Z, Dai J, Song X, Wang G, Yang W (2008) Facile synthesis

of Fe3O4/SiO2 composite nanoparticles from primary sil-

ica particles. Colloids Surf A 317:450–456

Lucchini MA, Canepa F (2012) Brownian relaxation of mag-

netic nanoparticles in fluid: the effect of the solvent.

J Nanopart Res 14:809

Ludwig F, Heim E, Schilling M (2009) Characterization of

magnetic core–shell nanoparticles by fluxgate magnetore-

laxometry, ac susceptibility, transmission electron

microscopy and photon correlation spectroscopy-a com-

parative study. J Magn Magn Mater 321:1644

Mahmoudi M, Sant S, Wang B, Laurent S, Sen T (2010) Su-

perparamagnetic iron oxide nanoparticles (SPIONs):

development, surface modification and applications in

chemotherapy. Adv Drug Deliv Rev 63:24

Na HB, Song IC, Hyeon T (2009) Inorganic nanoparticles for

MRI contrast agents. Adv Mater 21:2133

Nutting J, Antony J, Meyer D, Sharma A, Qiang Y (2006) The

effect of particle size distribution on the usage of the ac

susceptibility in biosensors. J Appl Phys 99:08B319

O’Handley RC (2000) Modern magnetic materials: principles

and applications. Wiley-Interscience, New York

Riani P, Napoletano M, Canepa F (2011) Synthesis, character-

ization and a.c. magnetic analysis of magnetite nanoparti-

cles. J Nanopart Res 13:7013–7015

J Nanopart Res (2013) 15:1601 Page 9 of 10

123

Schubert U, Husing N (2005) Synthesis of inorganic materials.

John Wiley & Son, New York

Shliomis MI, Raikher YL (1980) Experimental investigations of

magnetic fluids. IEEE Trans Magn 16:237

Sipos P, Berkesi O, Tombacz E, Pierre TG, Webb J (2003)

Formation of spherical iron(III) oxyhydroxide nanoparti-

cles sterically stabilized by chitosan in aqueous solutions.

J Inorg Biochem 95:55

Stober W, Fink A, Bohn E (1968) Controlled growth of mono-

disperse silica spheres in the micron size range. J Colloid

Interface Sci 26:62

Veiseh O, Gunn JW, Zhang M (2010) Design and fabrication of

magnetic nanoparticles for targeted drug delivery and

imaging. Adv Drug Deliv Rev 62:284

Page 10 of 10 J Nanopart Res (2013) 15:1601

123