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Influencing factors in the CO-precipitation process of superparamagnetic iron
oxide nano particles: A model based study
Article in Journal of Magnetism and Magnetic Materials · March 2015
DOI: 10.1016/j.jmmm.2014.10.074
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Journal of Magnetism and Magnetic Materials 377 (2015) 81–89
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials
journal homepage: www.elsevier.com/locate/jmmm
Influencing factors in the CO-precipitation process of
superparamagnetic iron oxide nano particles: A model based study
Hans-Christian Roth a, Sebastian P. Schwaminger a, Michael Schindler a,
Friedrich E. Wagner b, Sonja Berensmeier a,n
a
b
Bioseparation Engineering Group, Technische Universität München, Boltzmannstraße 15, Garching d-85748, Germany
Technische Universität München, Physics Department El5, Garching d-85748, Germany
art ic l e i nf o
a b s t r a c t
Article history:
Received 19 March 2014
Received in revised form
27 August 2014
Accepted 16 October 2014
Available online 22 October 2014
The study, presented here, focuses on the impact of synthesis parameters on the co-precipitation process
of superparamagnetic iron oxide nanoparticles. Particle diameters between 3 and 17 nm and saturation
magnetizations from 26 to 89 Am2 kg 1 were achieved by variation of iron salt concentration, reaction
temperature, ratio of hydroxide ions to iron ions and ratio of Fe3 þ /Fe2 þ . All synthesis assays were
conceived according to the “design of experiments” method. The results were fitted to significant models.
Subsequent validation experiments could confirm the models with an accuracy495%. The characterization of the chemical composition, as well as structural and magnetic properties was carried out using
powder X-ray diffraction, transmission electron microscopy, Raman and Mössbauer spectroscopy and
superconducting quantum interference device magnetometry. The results reveal that the particles' saturation magnetization can be enhanced by the employment of high iron salt concentrations and a molar
ratio of Fe3 þ /Fe2 þ below 2:1. Furthermore, the particle size can be increased by higher iron salt concentrations and a hyperstoichiometric normal ratio of hydroxide ions to iron ions of 1.4:1. Overall results
indicate that the saturation magnetization is directly related to the particle size.
& Published by Elsevier B.V.
Keywords:
Iron oxide nanoparticles
Design of experiment
Magnetite
Alkaline co-precipitation
Mössbauer spectroscopy
X-ray diffraction
1. Introduction
Superparamagnetic nano-particles (MNP) have been studied
intensively in the last decades, due to fundamental scientific interest and the wide range of applications. Particularly, their chemical, physical and especially magnetic properties predestine
them as excellent materials for a variety of research fields. The
applications range from wastewater treatment [1,2], to electrode
material in lithium ion batteries [3–5], magnetic fluids respectively
ferrofluids [6–8], used e.g. as magnetic inks for jet printing [9,10],
biosensing applications [11,12], medical applications, such as targeted drug delivery [13,14], contrast agents in magnetic resonance
imaging [15–20], and also biotechnological processing [21–24] and
carrier materials for biocatalysts [25], to sum up a few. All of these
applications require high magnetization values and a narrow
particle size distribution.
Numerous synthesis methods have been developed to satisfy the
demand for MNP with controlled properties including sol–gel
syntheses [26], hydrothermal reactions [27], sonochemical procedures
[28], hydrolysis and thermolysis of precursors [29], electrospray
n
Corresponding author. Tel.: +49 89 289 15750; fax: +49 89 289 15766.
E-mail address: s.berensmeier@tum.de (S. Berensmeier).
http://dx.doi.org/10.1016/j.jmmm.2014.10.074
0304-8853/& Published by Elsevier B.V.
synthesis [30] and the synthesis from microemulsions [31]. However,
one common and economic method for the controlled synthesis of
large amounts of superparamagnetic MNPs, without any stabilizing
surfactant agents, is the chemical co-precipitation of iron salts in an
alkaline environment, [32–38] known as the Massart process [39,40].
The chemical reaction of dissolved iron salts to magnetite (Fe3O4) can
be formulated according to Eq. (1) [41].
Fe2 þ þ2Fe3 þ þ8OH -Fe3O4 þ 4H2O
(1)
As is well known, certain reaction conditions in this process
and the dimensions of the nanocrystals have a significant impact
on the physical, chemical, structural and magnetic properties of
the MNP [42–44]. Therefore, our motivation is to predict the effect
of reaction conditions on particle properties, with this being the
key to produce customized MNPs for a variety of applications.
In this study, we proceeded with a statistical approach to describe and predict the impact of the main synthesis parameters in
the Massart process on the properties of obtained MNP. We chose
the Fe3 þ /Fe2 þ -ratio, the ratio of hydroxide to iron ions with respect to Eq. (1), the synthesis temperature and the concentration
of iron salts as parameters of interest in our investigation. All
syntheses were operated in a well-defined and controlled reaction
setup. Magnetic properties of MNP were characterized by a superconducting quantum interference device (SQUID), chemical
82
H.-C. Roth et al. / Journal of Magnetism and Magnetic Materials 377 (2015) 81–89
and structural properties by powder X-ray diffraction (XRD),
electron microscopy (TEM) and Mössbauer- and Raman spectroscopy. All experiments were planned by the software Design Expert
8 (Stat-Ease, Inc. USA), based on the method “design of experiments” (DoE). Resulting models were confirmed by validation
experiments.
2. Experimental
2.1. Synthesis and characterization of MNPs
All syntheses of iron oxide nanoparticles were processed by the
co-precipitation of Fe2 þ and Fe3 þ aqueous salt solutions in alkaline environment as reported previously [40]. Ferric chloride
(FeCl3∙6H2O) and sodium hydroxide (NaOH) were purchased from
AppliChem GmbH, Germany. Ferrous chloride (FeCl2∙4H2O) was
purchased from Bernd Kraft GmbH, Germany. Aqueous solutions of
iron salts and sodium hydroxide were prepared with degassed and
deionized water. The precipitation of iron oxide nanoparticles was
performed under nitrogen atmosphere in order to prevent oxidation of the precursors and the product. Process conditions, such as
temperature, pH value, dosing rate and stirring speed, were controlled and monitored by the fully automated OptiMax™ synthesis
station (Mettler–Toledo GmbH, Germany).
The reaction setup was prepared as follows: The reactor vessel
was filled with 500 mL of a sodium hydroxide solution. The desired reaction temperature was adjusted while the solution was
stirred under a steady flow of nitrogen. Ferric- and ferrous chloride
solutions were prepared separately and mixed thoroughly in a
flask maintained under nitrogen atmosphere. Using a dosing
pump, the iron salt mixture was added to the stirred reactor vessel
with a constant volumetric flow of 150 mL min 1. Instantly, a
brown-black precipitate was formed and the reaction proceeded
for 30 min under mechanical stirring. In order to lower the content
of salt and residual sodium hydroxide, the precipitate was washed
several times with degassed and deionized water-using a NdFeB
permanent magnet to support separation of the precipitate from
solution. The washing procedure was performed until the solution′
s conductivity dropped below 200 mS cm 1. A colloidal sample
was stored under nitrogen atmosphere for transmission electron
microscopy (TEM) imaging while the rest of the precipitate was
lyophilized with an ALPHA 1-2LDplus (Martin Christ Gefriertrocknungsanlagen GmbH, Germany).
Crystal structure and phase purity of the precipitates were
examined at room temperature via powder X-ray diffraction (XRD)
from the lyophilized samples. The Stadi-P (STOE & Cie GmbH,
Germany), employed in this work, is equipped with a molybdenum source (Ge (111) monochromator, Kα1 radiation
(λ ¼0.7093 Å) and a Mythen 1 K detector (DECTRIS Ltd., Switzerland). Data was collected in the range from 2° to 50° (2θ). The
software package STOE WinXPOW (STOE & Cie GmbH, Germany)
was used for indexing and refinement purposes. For more detailed
information about phase purity, the colloidal samples were frozen
and analyzed via 57Fe Mössbauer spectroscopy at 4.2 K in a liquid
He bath cryostat. Data was recorded with a source of 25 mCi of
57
Co in Rh in transmission geometry using a conventional spectrometer with sinusoidal velocity waveform. Both, the absorber
and the source were held at 4.2 K throughout all measurements.
The spectra were fitted with a superposition of Lorentzian lines
grouped into sextets for ferric and octets for ferrous iron ions
using MOS90 software version 2.2. The fitted components often
show broadened lines and have to be considered as representing
distributions of magnetic hyperfine fields. The chemical composition was also determined by Raman spectroscopy. A Senterra
Raman spectrometer (Bruker Corporation, USA), equipped with a
785 nm laser, was used for the analysis of particles produced. Low
laser powers were chosen in order to prevent oxidation of samples. A baseline correction was accomplished, applying the rubber
band method, by the software OPUS for each spectrum measured
by Raman spectroscopy.
The mean diameters (dp) of the precipitated crystallites were
estimated from XRD-data using the Scherrer equation employing a
shape factor of 0.89 for spherical magnetite particles [45]. Additionally, the particle dimensions were assessed by transmission
electron microscopy (TEM) using a JEM 100-CX (JEOL GmbH,
Germany). For the TEM measurements the colloidal samples were
diluted in degassed and deionized water and sonicated in order to
disperse any agglomerates. Dilution of the samples was controlled
by visual light spectroscopy at 475 nm, measured in polystyrene
cuvettes with 10 mm optical path length with the Infinites 200
Pro (Tecan Group Ltd., Switzerland). Values of adsorption were
adjusted from 0.2 to 0.25. All samples were repeatedly homogenized by sonication, without addition of any stabilizing surfactant agents, before placing a droplet of each 5 mL on a carbon
coated copper grid (Quantifoil Micro Tools GmbH, Germany), respectively. The grids were allowed to dry under ambient conditions. In order to cover a representative imaging of the samples,
each copper grid was evaluated with a number of three pictures
from different locations. The pictures were manually processed in
ImageJ (java based open source). A number of 100 particles per
sample were measured in randomized order.
Magnetic properties of the precipitates were characterized
with a superconducting quantum interference device (SQUID)
magnetometer MPMSs (Quantum Design Inc., USA) at a temperature of 300 K. The magnetic flux density was varied from 5 T
to þ5 T.
2.2. Experimental design
The setup of reaction conditions was planned using “design of
experiments”. Response surface methodology (RSM) was used to
create a central composite face centered design (CCF). Four parameters, discussed in the literature [16,46,47] to have significant
influence on saturation magnetization (MS) and particle size (dp),
were embedded into the design. Variables chosen for the design
are the total amount of iron (A), synthesis temperature (B), the
molar ratio of Fe3 þ to Fe2 þ (C) and the ratio of sodium hydroxide
to iron salts (D). Factor D is defined as a variable, which indicates
whether the ratio of sodium hydroxide to iron ions is hypostoichiometric (D o1), stoichiometric (D ¼1) or sodium hydroxide
is present in excess (D41) with respect to Eq. (1). The range and
levels of investigated parameters are listed in Table 1 and were
chosen to model the widest possible sector of reaction conditions
within physically and technically reasonable borders.
The influence was evaluated according to the CCF design with
five repetitions at the center point (0 0 0 0) (Table 2). Saturation
magnetization and mean particle diameter were chosen as response parameters for the design. In analogy to DoE, all assays
were carried out in randomized order. Graphical analysis and regressions of obtained data were carried out with the software
Design Expert 8.
The DoE model was validated with three randomly chosen
values within the range of the CCF design for the factors A, B, C and
D, shown in Table 3.
3. Results and discussion
Iron oxide nanoparticles were prepared from iron salts in alkaline environment, according to a modified Massart porcess [39,40].
Synthesis assays were processed with parameter combinations
H.-C. Roth et al. / Journal of Magnetism and Magnetic Materials 377 (2015) 81–89
Table 1
Factor levels used according to the CCF design.
Variable parameter
Level
A: total amount of iron (mol)
B: temperature (°C)
C: Fe3 þ /Fe2 þ ratio (mol mol 1)
D: NaOH/Fe ratio
1
0
þ1
0.006
5
1.5
0.8
0.303
47
2.25
1.4
0.6
90
3
2
Table 2
Values for saturation magnetization (Ms) and mean particle diameter (dp) (XRD)
according to the CCF design.
Assay
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Variable
Response
A
B
C
D
MS (Am2 kg 1)
dp (nm)
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
þ1
þ1
þ1
þ1
þ1
þ1
þ1
þ1
þ1
0
þ1
þ1
þ1
1
1
1
þ1
1
0
0
0
0
0
1
þ1
0
0
0
0
0
þ1
þ1
0
1
þ1
1
þ1
1
1
0
þ1
þ1
0
0
þ1
þ1
1
1
0
1
0
0
0
0
0
þ1
0
0
0
0
þ1
þ1
0
1
1
1
1
þ1
þ1
0
1
þ1
þ1
þ1
þ1
1
1
1
0
0
0
1
0
0
0
0
0
þ1
0
0
þ1
1
0
þ1
1
1
þ1
1
þ1
89.19
33.01
33.58
79.37
66.95
26.76
2.06
67.27
40.51
65.08
82.48
56.15
63.79
71.40
75.42
71.36
61.77
74.53
76.69
73.23
77.06
60.67
59.52
81.22
70.45
78.93
73.26
79.31
16.70
59.18
15.2
6.3
6.4
12.5
9.0
3.3
n.a.
10.4
8.0
8.3
16.3
13.3
10.4
12.1
12.1
13.7
9.7
15.2
15.7
13.7
13.7
11.5
11.5
15.7
14.7
15.7
17.0
17.0
14.2
10.9
n.a.¼ not accessible
Table 3
Factors used for validation of the DoE model.
Variable parameter
A: total amount of iron (mol)
B: temperature (°C)
C: Fe3 þ /Fe2 þ ratio (mol mol 1)
D: NaOH/Fe ratio
Validation assays
V01
V02
V03
0.4
85
1.7
1.2
0.5
25
1.9
1.8
0.2
70
2.6
1.0
shown in Table 2. All samples were characterized by powder X-ray
diffraction. Particle mean diameters were estimated by aid of the
Scherrer equation and are presented in Table 2. The mean diameters
of the iron oxide nano-particles range from 3 nm to 17 nm, which is
in good agreement with values reported in literature [42,48]. Results of assays 7 and 29 are not included in the DoE model. Due to
unfavorable synthesis parameters in assay 7, no precipitation occurred and a red salt solution remained. Therefore, neither powder
XRD nor SQUID analyses could be performed on this assay. The
results of assay 29 are discussed separately.
83
Powder XRD patterns of samples representing the change of
one single synthesis condition from center point configuration
(0 0 0 0) are displayed in Fig. 1. Within the detection limit, peaks of
all patterns could be attributed to the Bragg positions of magnetite
given by the WinXPOW database. The decrease in peak width with
increasing values for factor A, is evidenced by our measurements.
This means an increase in particle size with higher iron salt concentrations in the synthesis assays. In classical nucleation theory
[49,50] the formation of crystals in the co-precipitation process is
described by two single steps, in which a short burst of nucleation
from a supersaturated solution is followed by a slow growth of the
crystals. Therefore, an increase of factor A is thought to enforce the
nucleation process by elevating the relative supersaturation of the
solvent. As a result, more nuclei are formed, leading to smaller
particles. It is conceivable, that our reaction set up with a good
homogenization of the reaction volume in combination with a
defined dosing of the iron salt solution leads to a decrease of relative supersaturation. Compared to an instantaneous addition of
the iron salts, this might enforce the process of particle growth.
This effect is described in literature, where the addition of the iron
salt solution to alkaline solution is performed at defined dosing
rates [16,32]. Within our reaction setup, the particle size is barely
affected by changes of factor B, tending to bigger particles at
higher temperatures [16,41]. It is well known that the ratio of
Fe3 þ /Fe2 þ in the co-precipitation method strongly affects the
properties of iron oxide products [46,48]. The mean particle size
rises with decreasing values of factor C [51]. This effect can be
explained by an analysis of the reaction pathway of iron oxides.
Hence, primary nuclei, formed after super saturation of an iron salt
solution, consist of Fe3 þ -species [52]. Thus, higher values of factor
C lead to a larger number of nuclei and therefore to more, but
smaller particles for an equal amount of iron salts. The ratio of
sodium hydroxide to the total amount of iron salt reduces the final
particle diameter for D ¼0.8. Taking into account, that the formation of magnetite takes place at pH values exceeding 8 [53], the
formation of byproducts is likely, when the reaction has consumed
the limited amount of base [47]. As the byproducts are produced
only at the very end of the synthesis, when the pH value drops
below 8, their amount proves to be very low and might be lost in
the magnetic washing procedure after synthesis. The reaction
pathway of iron to magnetite switches to the formation of byproducts like lepidocrocite and goethite [52] for values of factor
Do1, leading to smaller MNPs. There is no significant influence of
factor D on the particle diameter for D ¼1.4 and D¼ 2. This result is
in good accordance with the data of Khalafalla and Reimers [38].
According to the thermodynamics of the chemical reaction
described in Eq. (1), the complete precipitation of Fe3O4 should be
expected at a pH between 8 and 14, with a molar Fe3 þ /Fe2 þ -ratio
of 2 in a non-oxidizing environment. [53]. Reaction conditions that
strongly differ from the ideal reaction parameters of magnetite can
lead to various byproducts [52,54]. A good example is assay 29
(Table 2), where factor C is 3 mol mol 1 and factor D is 0.8. The
powder XRD pattern of sample 29 in Fig. 2 can be attributed to
iron oxyhydroxide species. Corresponding Bragg reflections are
listed in Table 4.
In order to confirm XRD-data concerning phase and composition, Mössbauer spectroscopic analyses were carried out on selected samples. All spectra attest to the presence of a nanoscale
magnetite phase, except for sample 29. Mössbauer patterns of
assay 29 and the samples prepared with the center point parameters are presented in Fig. 3. Parameters of fitted spectra are
summarized in Table 5. The isomer shift was received from the
experiment without further manipulation, i.e. with respect to the
source of 57Co in Rh at 4.2 K. To refer them to metallic iron at
ambient temperature, 0.24 mm s 1 have to be added.
84
H.-C. Roth et al. / Journal of Magnetism and Magnetic Materials 377 (2015) 81–89
Fig. 1. Powder X-ray diffractograms of magnetic iron oxide nano-particles synthesized with variation in a) total amount of iron salts, b) reaction temperature, c) Fe3 þ /Fe2 þ
ratio, and d) NaOH/Fe ratio. All other parameters are based on the center point assay (Table 2).
Table 4
Characteristic Bragg reflection angles (XRD) with corresponding lattice planes of
iron oxides contributed to sample 29 (Fig. 2).
Lepidocrocite
Fig. 2. Powder X-ray diffractogram of sample 29 consisting of lepidocrocite and
goethite.
The Mössbauer data confirms the powder XRD results concerning phase composition of sample 29. The fitted parameters are
in good accordance with literature and imply the presence of
goethite, lepidocrocite and maghemite [55,56]. The presence of
ferrous chloride (FeCl2) in sample 29 can be explained by the hypostoichiometric ratio of sodium hydroxide to iron salts with respect to Eq. 1. Once, the sodium hydroxide is consumed in the
reaction, the excess amount of FeCl2 remains in sample 29. Although the washing procedure was carried out thoroughly, some
residual FeCl2 could be detected by Mössbauer spectroscopy.
An additional investigation towards the chemical composition of
precipitated iron oxides was accomplished by Raman spectroscopy.
Goethite
Angle (2θ)
Plane
Angle (2θ)
Plane
6.47
12.34
13.67
16.44
17.23
19.49
21.02
23.56
26.83
29.47
020
120
011
031
111
060
200
151
231
112
8.13
9.68
15.10
15.74
17.98
020
110
130
021
210
Data of all samples was acquired at a low laser power of 0.1 mW by
a 785 nm laser source. All spectra but samples 7 and 29 evidence
the presence of magnetite while maghemite and other iron oxides
are not indicated.
Raman spectra confirm the Mössbauer and XRD data concerning the compositions of the samples investigated. Characteristic Raman shifts for magnetite could be detected and are demonstrated for a center point sample in Fig. 4b). Here the typical
main band at 667 cm 1 and also minor peaks at 536 and 310 cm 1
can be observed, which are in good agreement with literature
values [56–59]. Though, assay 29 shows characteristic iron oxide
and iron oxyhydroxide peaks. What is more, the Mössbauer and
XRD data is confirmed by Raman spectroscopy as consisting of
goethite, lepidocrocite and maghemite which can be detected
here. The Raman shifts 385 and 299 cm 1 indicate goethite while
H.-C. Roth et al. / Journal of Magnetism and Magnetic Materials 377 (2015) 81–89
85
Fig. 3. Mössbauer spectra of a) assay 29 and b) center point.
Table 5
Parameters of Mössbauer spectra displayed in Fig. 3.
Sample
Iron oxide
ΔEQ
δ
Bhf
Area (%)
29
Goethite
Lepidocrocite
Maghemite (A)
Maghemite (B)
Ferrous chloride
Magnetite (A)
Magnetite (B1)
0.171
0.018
0.015
0.000
3.285
0.029
0.057
0.278
2.126
0.631
0.513
1.104
0.26
0.25
0.10
0.3
1.09
0.15
0.32
0.24
0.80
0.79
0.82
0.96
49.5
45.4
50.7
51.5
–
50.6
52.8
50.0
48.8
49.2
44.5
39.2
31.1
38.1
14.0
15.2
1.6
37.6
18.2
15.8
12.2
6.5
6.0
3.7
Center point
Magnetite (B2)
Quadrupole splittings (ΔEQ) and isomer shifts (δ) given in mm s 1; magnetic hyperfine fields (Bhf) in T.
the bands at 250 and 528 cm 1 demonstrate the presence of lepidocrocite and the band at 730 cm 1 can be referred to maghemite [56–58].
Magnetic properties of all samples were characterized by a
SQUID magnetometer at 300 K in hysteresis mode, varying the
magnetic flux density from 5 to 5 T. Values obtained for saturation magnetization MS of the samples range from 16.7 to
89.19 Am2 kg 1, which is in good agreement with iron oxide nanoparticles synthesized by co-precipitation [41]. All samples tend to
show superparamagnetic behavior, characteristic for iron oxide
particles with a mean diameter smaller than 20 nm [60,61]. Values
of remanence vary from 0.03 to 1.67 Am2 kg 1 and indicate the
superparamagnetic character of the MNPs. Hysteresis loops of
magnetization (M) versus magnetic flux density (B) for samples,
a
b
intensity (a.u.)
intensity (a.u.)
100
representing the change of one single synthesis condition from the
center point configuration, are displayed in Fig. 5. Results show that
values for MS of the iron oxide nano-particles can be tailored from
65 to 81 Am2 kg 1 by changing factor A from 0.006 to 0.6 mol, respectively. The variation of factor B barely modifies MS in our reaction setup. Therefore, MS can be elevated from 62 to 82 Am2 kg 1
by reducing values of factor C from 3 to 1.5 mol mol 1, respectively.
A similar impact on MS by the Fe3 þ /Fe2 þ -ratio is reported in literature [46,51]. The increase of factor D from 0.8 to 2 leads to an
increase of MS from 64 to 77 Am2 kg 1. Iron oxide particles synthesized at D¼1.4 and 3 barely differ in their values of MS. Particles
prepared at D¼0.8 show a significant drop in MS which can be
attributed to byproducts with lower saturation magnetization than
magnetite occurring at pH valueso8 [62].
Magnetic properties of iron oxide nanoparticles strongly depend
on crystallinity and particle size [63,64]. Values of saturation magnetization reported for nanoscale material (65 to 70 Am2 kg 1)
range below the values of bulk material (92 to 100 Am2 kg 1) [54].
The discrepancy in MS between the bulk and the nanoscale material
can be explained by the higher number of lattice defects with increasing surface to volume ratio for smaller particles. This correlation is visualized in Fig. 6, where MS is plotted versus the corresponding particle diameter of the iron oxide nanoparticles prepared
in this work. Data sets of samples containing other materials than
magnetite are not included. Though, all samples prepared in this
study are proven to be nanoscaled by XRD measurements, high
saturation magnetizations close to those reported for bulk material
could be achieved for assay 01, 11 and 24.
The decrease of MS from about 83 Am2 kg 1 to about
27 Am2 kg 1 at particle diameters from 16 nm to 3 nm in this
study suggests a linear dependence of MS on particle size.
300
500
700
900
Raman shift (cm-1)
1100
1300
1500
100
300
500
700
900
Raman shift (cm-1)
Fig. 4. Raman Spectra of a) assay 29 and b) center point at 0.1 mW laser power.
1100
1300
1500
86
H.-C. Roth et al. / Journal of Magnetism and Magnetic Materials 377 (2015) 81–89
a 100
40
B = 90°C
B = 47.5°C
B = 5°C
80
60
M (Am2 kg-1)
M (Am2 kg-1)
60
100
b
A = 0.6 mol
A = 0.303 mol
A = 0.006 mol
80
20
0
-20
-40
40
20
0
-20
-40
-60
-60
-80
-80
-100
-100
-6
-4
-2
0
2
4
6
-6
-4
-2
B (T)
c 100
40
2
4
6
2
4
6
D=2
D = 1.4
D = 0.8
80
60
M (Am2 kg-1)
M (Am2 kg-1)
60
100
d
C = 3 mol mol-1
C = 2.25 mol mol-1
C = 1.5 mol mol-1
80
0
B (T)
20
0
-20
-40
-60
40
20
0
-20
-40
-60
-80
-80
-100
-100
-6
-4
-2
0
2
4
6
B (T)
-6
-4
-2
0
B (T)
Fig. 5. SQUID measurements of MNPs synthesized with variation in a) the total amount of iron salts, b) the reaction temperature, c) the ratio of Fe3 þ /Fe2 þ and d) the ratio of
NaOH/Fe. Other parameters are based on the center point assay (Table 2).
Fig. 6. Correlation of saturation magnetization of iron oxide nano-particles with
the particle diameter.
Geometric properties of the produced iron oxide nanoparticles
were investigated by TEM imaging to confirm the particle size
estimated from powder XRD-data via the Scherrer equation. Assay
conditions were selected randomly. Particle size was determined
manually using the software ImageJ. TEM images and determined
particle size distributions of sample 10 and 19 are shown in Fig. 7.
All TEM images show a roughly gaussian-shaped particle size
distribution. The mean particle diameter of sample 19 and sample
10 is determined as 15.1 nm and 8.2 nm, respectively, which is in
very good agreement with the particle diameters determined from
powder XRD data. A more detailed discussion referring to the
correlation of colloidal particle sizes obtained from XRD and TEM
can be found in [65]. TEM images show that most particles, with a
diameter smaller than 10 nm, have a spherical shape, while bigger
particles often have a distinct octahedral shape.
All data from powder XRD and SQUID analysis was incorporated in Design Expert 8 and computed to a model with a
quadratic approach. Manual optimization was carried out by purging the model of insignificant terms and interactions (P o0.3).
Table 6 summarizes the results of the statistical analyses for the
response parameters dp and MS.
In our model, each of the investigated synthesis parameters
proves to affect the saturation magnetization of the particles
prepared with a statistical significance above 96.8% confidence
level. Interaction effects of the factors BC, BD and CD and the
quadratic influence B2 were excluded from the quadratic model as
their significance is below 95% confidence level. The final equation,
in terms of coded factors suggested for our model, is given by
Eq. (2).
MS (Am2 kg 1) ¼74.92 þ10.14A þ5.07B 12.23C þ4.31D 3.79AB þ
4.41AC 4.08AD 4.53B2 5.56C2 7.44D2
(2)
The model is highly significant with a value of P o0.0001, as
can be seen in the analysis of variance (ANOVA) in Table 7.
The model′s coefficient of determination is R2 ¼0.91. The predicted R2 of 0.85 is in good agreement with the adjusted R2 of 0.88.
In regard to the mean particle diameter, all factors except D
show no statistical significance at less than 99.2%. Although the
effect of factor D (P ¼0.1478) on dp is not significant, the factor is
included in the model due to the models hierarchical structure.
The final equation in terms of coded factors suggested for our
model is given in Eq. (3).
H.-C. Roth et al. / Journal of Magnetism and Magnetic Materials 377 (2015) 81–89
87
120
frequency (%)
100
80
60
40
20
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
particle size (nm)
a
120
frequency (%)
100
80
60
40
20
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
particle size (nm)
b
Fig. 7. TEM images of a) Assay 19 and b) Assay 10.
Table 6
Estimated coefficients and standard errors for mean particle diameter (dp) and
saturation magnetization (MS) using the CCF design.
Factor
Intercept
A: total amount of iron
(mol)
B: temperature (°C)
C: Fe3 þ /Fe2 þ ratio
(mol mol 1)
D: Fe/NaOH ratio
AB
AC
AD
A2
C2
D2
Table 8
Analysis of variance (ANOVA) for the representative model of the particle mean
diameter in the studied range of parameters.
MS (Am2 kg 1)
dp (nm)
Source
SS
d.f.
MS
F-value
P
Coefficient Standard
error
Coefficient Standard
error
Model
Residual
Lack of fit
Pure error
Total
306.08
31.85
24.78
7.05
337.92
6
21
16
5
27
51.1
1.52
1.55
1.41
33.64
o 0.0001
1.10
0.5013
74.92
10.14
2.19
1.85
13.43
3.19
0.36
0.31
5.07
12.23
1.84
1.84
0.94
2.66
0.32
0.32
R2 ¼ 0.86; C.V. ¼ 10.16%; SS ¼ sum of squares; d.f. ¼ degrees of freedom; MS ¼ mean
square
4.31
3.79
4.41
4.08
4.53
5.56
7.44
1.84
1.98
1.98
1.98
4.24
4.24
4.24
0.48
0.61
–
–
–
2.80
–
0.32
0.33
–
–
–
0.48
–
The determination coefficient of the model is R2 ¼0.86. The
predicted R2 of 0.74 is in good agreement with the adjusted R2 of
0.77 and the model is significant at a confidence level greater than
99.99% (Po 0.0001).
The resulting models are valuable tools for the prediction of
factor interactions and their influence on the response parameters
within the studied area of design. This can be seen, when the results of the validation experiments are compared to the forecasted
values by the models. It is remarkable that the predicted values
meet the reality with a confidence greater than 95%. Results are
summarized in Table 9.
Contour plots indicating the predicted parameter interactions
are displayed in Fig. 8 with actual factors corresponding with the
center points.
The model (Fig. 8a)–c)) predicts a strong influence of factor A
on MS with an increase of MS for higher values of factor A. This
prediction is in good agreement with the SQUID measurements
presented in Fig. 5a). Elevated magnetization properties at higher
synthesis temperatures are suggested by several authors due to
improvement in crystal formation [16,47]. This effect of factor B is
predicted by our model (Fig. 8a)), even though the influence is
rather slight. The predicted interaction of factor A and factor C
(Fig. 8b)) suggests a decrease of MS with increasing values of factor
C, which is in good analogy with literature [46] and our SQUID
data (Fig. 5c)). Formation of byproducts with hypostoichiometric
Table 7
Analysis of variance (ANOVA) for the representative model of saturation magnetization in the studied range of parameters.
Source
SS
d.f.
MS
F-value
P
Model
Residual
lack of fit
pure error
Total
5195.69
861.90
296.54
565.36
6057.59
10
17
12
5
27
519.57
50.70
24.71
113.07
10.25
o0.0001
0.22
0.9856
R2 ¼0.91; C.V¼10.72%; SS ¼ sum of squares; d.f. ¼degrees of freedom; MS¼ mean
square.
MS (Am2 kg 1)¼13.43 þ3.19A þ0.94B 2.66C þ0.48D 0.16AB 7.44C2
(3)
The analysis of variance (ANOVA) is displayed in Table 8.
88
H.-C. Roth et al. / Journal of Magnetism and Magnetic Materials 377 (2015) 81–89
Table 9
Confirmation of the models with data of the validation experiments.
V001
Predicted
95% PIlow
95% PIhigh
Experimental
V002
V003
MS (Am2 kg 1)
dp (nm)
MS (Am2 kg 1)
dp (nm)
MS (Am2 kg 1)
dp (nm)
84.23
67.61
100.86
80.53
16.6
13.8
19.4
15.8
79.19
62.98
95.39
73.34
15.6
12.9
18.3
16.3
59.50
43.33
75.66
74.50
11.0
8.3
13.8
13.3
PIlow ¼ lower boundary of prediction interval; PIhigh ¼ upper boundary of prediction interval.
Fig. 8. Contour plots of factor interaction a) AB, b) AC and c) AD for saturation magnetization and d) factor interaction AB for mean particle diameters.
addition of base, with respect to the total amount of iron ions,
results in decreasing MS with lower values of factor D (Fig. 8c)). At
high values of factor A, an optimum value of 1.4 is predicted for
factor D. This effect might be explained by the decrease of mean
particle size with an increase of the relative supersaturation of the
synthesis solution [46]. The correlation in Fig. 6 suggests that
smaller particles lead to decreasing values of MS. In the co-precipitation process, formation of byproducts is favored at pH o 8
and therefore leads to a decrease in MS. These two negative effects
of factor D in reaction pathways seem to have their minimum
influence on MS at a value of D¼1.4.
Our model suggests an increase in dp with increasing values of
factor A (Fig. 8d)) and sustains the data received from powder XRD
and literature [16,32]. The contour plot in Fig. 8d) indicates a trend
to bigger particles with increasing values of factor B. Powder XRD
analysis of our samples (Fig. 1b)) supports this indication. An
explanation for this effect might be provided by the nucleation
pathways according to Lamer (1950) [49]. The solubility of the iron
salts improves [66] while the pH decreases with increasing temperatures [67]. Thus, the relative supersaturation of the reaction
medium is reduced [41]. Furthermore the critical nucleus size increases with temperature according to thermodynamic equilibrium
[41]. Nuclei that are smaller than the critical nucleus size tend to
undergo Ostwald ripening and favor the growth of bigger particles
[68]. The burst of nucleation at high temperatures therefore leads to
a smaller amount of bigger crystals, facilitating the process of crystal
growth. Summarizing the results of the models, maximum values of
MS can be achieved at the highest temperatures, the highest iron
salt concentrations, the lowest ratios of Fe3 þ /Fe2 þ within the range
and levels of investigated parameters and a value of 1.4 for the introduced normality factor D.
H.-C. Roth et al. / Journal of Magnetism and Magnetic Materials 377 (2015) 81–89
4. Conclusions
In this study the statistical method based on “design of experiments” (DoE) was used to plan a reaction setup for the coprecipitation process of defined iron oxide nanoparticles. The focus lies on the influence of reaction conditions regarding size and
saturation magnetization of the product. Iron oxide nanoparticles
with mean particle diameters from 3 to 17 nm and saturation
magnetizations from 16.7 to 89.19 Am2 kg 1 were synthesized and
fully characterized by powder XRD, Raman- and Mössbauer
spectroscopy. The results distinctly show that magnetite is the
only iron oxide species for the majority of reaction conditions.
Samples prepared at hypostoichiometric ratios of hydroxide ions
with respect to iron ions in combination with a high
Fe3 þ /Fe2 þ -ratio tend to lead to a mixture of lepidocrocite and
goethite.
Based on the vast number of experiments, the correlation of
particle size with saturation magnetization could be depicted.
Employing the software Design Expert 8, statistically representative models could be generated, which enable the prediction of particle size and saturation magnetization within the
studied range of synthesis parameters with adequate accuracy. The
validity of the models was confirmed with three independent
experiments with a confidence level4 95%.
Acknowledgements
The authors would like to gratefully thank Prof. Dr. T. Nilges for
his support with powder XRD and Dr. M. Hanzlik for performing a
share of the TEM measurements. Furthermore I would like to express my very great appreciation to Dr. P. Fraga and the TUM
Graduate School, Technische Universität München for proof
reading this work. Also I am particularly grateful for the financial
support of this work by the Federal Ministry of Education and
Research (Grant numbers 1340/68351/3/11 and 031A173A) and
Clariant.
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