INSTITUTE OF PHYSICS PUBLISHING
JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 36 (2003) R182–R197 PII: S0022-3727(03)37541-2
The preparation of magnetic
nanoparticles for applications in
Pedro Tartaj1, Mar´ ıa del Puerto Morales1,
Sabino Veintemillas-Verdaguer, Teresita Gonz´ alez-Carre˜ no and
Carlos J Serna
Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, 28049, Madrid, Spain
E-mail: email@example.com and firstname.lastname@example.org
Received 17 March 2003
Published 18 June 2003
Online at stacks.iop.org/JPhysD/36/R182
This review is focused on describing state-of-the-art synthetic routes for the
preparation of magnetic nanoparticles useful for biomedical applications.
In addition to this topic, we have also described in some detail some of the
possible applications of magnetic nanoparticles in the field of biomedicine
with special emphasis on showing the benefits of using nanoparticles.
Finally, we have addressed some relevant findings on the importance of
having well-defined synthetic routes to produce materials not only with
similar physical features but also with similar crystallochemical
Nanotechnology is beginning to allow scientists, engineers,
and physicians to work at the cellular and molecular levels to
produce major advances in the life sciences and healthcare.
Real applications of nanostructured materials in life sciences
are uncommon at the present time. However, the excellent
properties of these materials when compared with their bulk
counterparts provide a very promising future for their use in
this field [1–3].
dimensions located in the transition region between molecules
and microscopic (micron-size) structures.
molecules, they are so large that they provide access to realms
as materials, they are so small that they exhibit characteristics
that are not observed in larger (even 100nm) structures. It is
in this size regime that many recent advances have been made
in biology, physics, and chemistry . For example, when
the particle dimensions of semiconductor materials become
comparable to, or smaller than the Bohr radius, an increase
in the energy band gap is observed [5–8]. In noble metals,
1Authors to whom correspondence should be addressed.
the decrease in size below the electron mean free path (the
distance the electron travels between scattering collisions with
the lattice centres) gives rise to intense absorption in the
visible–near-UV region . Metal nanoparticles also exhibit
a broad range of fascinating mechanical behaviour such as
superplasticity . Ceramic materials composed of powders
with a particle size in the nanometric range are also receiving
attention because they may significantly enhance sintering
rates or dramatically lower sintering temperatures [11–14].
Also, ceramic matrix composites with dispersed nanoparticles
have better mechanical properties [10,15].
such as superparamagnetism, high field irreversibility, high
saturation field, extra anisotropy contributions or shifted loops
after field cooling. These phenomena arise from finite size
and surface effects that dominate the magnetic behaviour of
individual nanoparticles .
were the first to predict that a particle of ferromagnetic
materials), would consist of a single magnetic domain, i.e. a
particle that is a state of uniform magnetization at any field.
The magnetization behaviour of these particles above a certain
temperature, i.e. the blocking temperature, is identical to that
of atomic paramagnets (superparamagnetism) except that an
Frenkel and Dorfman 
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extremely large moment and thus, large susceptibilities are
Industrial applications of magnetic nanoparticles cover a
broad spectrum such as magnetic seals in motors, magnetic
inks for bank cheques, magnetic recording media and
biomedical applications such as magnetic resonance contrast
media and therapeutic agents in cancer treatment [19–22].
Each potential application requires the magnetic nanoparticles
to have different properties.
applications, the particles need to have a stable, switchable
magnetic state to represent bits of information, a state that is
not affected by temperature fluctuations.
For biomedical applications the use of particles that
present superparamagnetic behaviour at room temperature (no
remanence along with a rapidly changing magnetic state) is
preferred [23–25]. Furthermore, applications in biology and
medical diagnosis and therapy require the magnetic particles
to be stable in water at neutral pH and physiological salinity.
The colloidal stability of this fluid will depend first, on the
dimensions of the particles, which should be sufficiently small
so that precipitation due to gravitation forces can be avoided,
and second on the charge and surface chemistry, which give
rise to both, steric and coulombic repulsions . Additional
restrictions to the possible particles that could be used for
biomedical applications strongly depend on whether these
For in vivo applications the magnetic particles must be
coated with a biocompatible polymer during or after the
synthesis process to prevent the formation of large aggregates,
changes from the original structure and biodegradation when
exposed to the biological system.
allow binding of drugs by covalent attachment, adsorption
or entrapment on the particles [27, 28].
factors, which determine the biocompatibility and toxicity
of these materials, are the nature of the magnetically
responsive component, such as magnetite, iron, nickel, cobalt,
neodimium–iron–boron or samarium–cobalt and the final size
of the particles, their core and the coatings.
particles such as magnetite (Fe3O4) or its oxidized form
for biomedical applications. Highly magnetic materials such
as cobalt and nickel are toxic, susceptible to oxidation and
hence are of little interest [21, 29].
advantage of using particles of sizes smaller than 100nm
(so-called nanoparticles) is their higher effective surface areas
stability) and improved tissular diffusion .
advantage of using nanoparticles is that the magnetic dipole–
as r6(r is the particle radius) [31–33]. Therefore, for in vivo
of a non-toxic and non-immunogenic material, with particle
sizes small enough to remain in the circulation after injection
and to pass through the capillary systems of organs and
tissues avoiding vessel embolism.
high magnetization so that their movement in the blood can
be controlled with a magnetic field and so that they can be
immobilized close to the targeted pathologic tissue .
For in vitro applications the size restrictions are not so
severe as in in vivo applications.
For example, in data storage
The polymer will also
Moreover, the main
They must also have a
consisting of superparamagnetic nanocrystals dispersed in
submicron diamagnetic particles with long sedimentation
times in the absence of a magnetic field can be used.
The advantage of using diamagnetic matrixes is that the
superparamagnetic composites can be easily provided with
In almost all applications the preparation method of
the nanomaterials represents one of the most important
challenges that will determine the particle size and shape,
the size distribution, the surface chemistry of the particles
and consequently their magnetic properties.
ferromagnetic materials such as Fe3O4, SrFe12O19, Fe–C and
some alloys like SmCo5, have irregular particle shape when
obtained by grinding bulk materials but can have a spherical
shape when prepared by wet chemistry, plasma atomization
or from the aerosol and gas phases.
the mechanism of formation, spherical particles obtained in
solution can be amorphous or crystalline if they result from a
disordered or ordered aggregation of crystallites, respectively.
the degree of structural defects or impurities in the particle, as
well as the distribution of such defects within the particle and
therefore its magnetic behaviour [16,35].
Recently many attempts have been made to develop
processes and techniques that would yield ‘monodispersed
colloids’ consisting of uniform nanoparticles both in size
and shape [36–39]. In these systems, the entire uniform
physicochemical properties directly reflect the properties of
each constituent particle. Monodispersed colloids have been
exploited in fundamental research and as models in the
quantitative assessment of properties that depend on the
particle size and shape. In addition, it has become evident
that the quality and reproducibility of commercial products
can be more readily achieved by starting with well-defined
powders of known properties. In this way, these powders have
found application in photography, inks in high-speed printing,
ceramic, catalysis, and especially in medicine.
The first part of this review deals with the possible use of
emphasis on the advantage of using nanoparticles with respect
to microparticles. The second part is concerned with different
methods described in the bibliography capable of producing
these magnetic nanoparticles with very narrow particle size
distribution, mainly based on magnetite or maghemite iron
oxide nanoparticles [21,29]. Finally, we address some of the
most relevant synthesis effects on the structural and magnetic
properties of the magnetic nanoparticles.
Also, depending on
2. Biomedical applications
We can classify biomedical applications of magnetic
nanoparticles according to their application inside (in vivo) or
diagnostic applications (nuclear magnetic resonance (NMR)
imaging), while for in vitro applications the main use is in
diagnostic (separation/selection, and magnetorelaxometry).
2.1. In vivo applications
2.1.1. Therapeutic applications
used to raise the temperature of a region of the body
affected by malignancy or other growths. It is administered
at temperatures above 41–42˚C [40–43].
volume. The temperature increase required for hyperthermia
can be achieved, among other methods, by using fine iron
oxide magnetic particles .
which a magnetic material can be heated by the action of an
external alternating magnetic field are the loss processes that
materials with low electrical conductivity [45,46].
The advantage of magnetic hyperthermia is that allows
the heating to be restricted to the tumour area. Moreover,
the use of subdomain magnetic particles (nanometre-sized)
is preferred instead multidomain (micron-sized) particles
because nanoparticles absorb much more power at tolerable
AC magnetic fields [42, 47–49].
mentioned that the heating potential is strongly dependent
on the particle size and shape, and thus having well-defined
synthetic routes able to produce uniform particles is essential
for a rigorous control in temperature.
Hyperthermia is a therapeutic procedure
The physical principle for
Finally, it should be
Freeman et al  that fine iron particles could be transported
point in the body with the aid of a magnetic field (figure 1), the
to the organs or tissues altered by diseases has become an
attractive field of research [51,52].
The process of drug localization using magnetic delivery
systems is based on the competition between forces exerted
on the particles by blood compartment, and magnetic forces
generated from the magnet, i.e. applied field.
magnetic forces exceed the linear blood flow rates in arteries
Since the pioneering concept proposed by
Figure 1. Schematic representation of the magnetically driven
transport of drugs to a specific region. A catheter is inserted into an
arterial feed to the tumour and a magnetic stand is positioned over
the targeted site.
are retained at the target site and maybe internalized by
the endothelial cells of the target tissue .
application the use of nanoparticles favour the transport
through the capillary systems of organs and tissues avoiding
2.1.2. Diagnostic applications
technique for clinical diagnosis has prompted the need
for a new class of pharmaceuticals, so-called magneto-
pharmaceuticals.These drugs must be administered to a
patient in order to (1) enhance the image contrast between
normal and diseased tissue and/or (2) indicate the status of
organ functions or blood flow . A number of different
agents have been suggested as potential NMR contrast agents.
been paramagnetic. Superparamagnetic particles represent
an alternative class of NMR contrast agents that are usually
referred to as T2(transversal relaxation time) or T∗
agents as opposed to T1(longitudinal relaxation time) agents
such as paramagnetic Gadolinium(III) chelates .
The relaxation rate increase produced by magnetic
particles is a contribution of several complex mechanisms.
The particles possess very large magnetic moments in the
presence of a static magnetic field, and dipolar interactions
between the superparamagnetic cores and surrounding solvent
relaxation rates, especially for particles with diameters below
Commercial iron oxide nanoparticles of maghemite
(Endorem®and Resovit®) have been used as contrast agents
in NMR imaging for location and diagnosis of brain and car-
diac infarcts, liver lesions or tumours, where the magnetic
ferences in tissue composition and/or endocytotic uptake pro-
cesses . Especially promising results have been detected
in the improvement of sensitivity of detection and delineation
of pathological structures, such as primary and metastic brain
tumours, inflammation and ischemia . For this purpose,
proteins such as transferrin , peptides such as the mem-
brane traslocating tat peptide of the HIV tat protein [60,61],
and oligonucleotides of various sequences  have been at-
tached to aminated cross-linked iron oxide nanoparticles in
order to obtain specific NMR imaging agents .
The development of the NMR imaging
2.2. In vitro applications
2.2.1. Diagnostic applications
Separation and selection. At present, considerable attention is
being paid to solid-phase extraction (SPE) as a way to isolate
and preconcentrate desired components from a sample matrix.
SPE offers an excellent alternative to the conventional sample
concentration methods, such as liquid–liquid extraction .
The separation and preconcentration of the substance from
large volumes of solution can be highly time consuming when
using standard column SPE, and is in this field where the
use of magnetic or magnetizable adsorbents called magnetic
solid-phase extraction (MSPE) gains importance.
procedure the magnetic adsorbent is added to a solution or
suspension containing the target. This is adsorbed onto the
Figure 2. Schematic representation of the magnetically assisted
separation of substances. In this particular case a magnetic
nanosphere to which an antibody has been anchored is dispersed in a
liquid medium containing the antigen (substance to analyse).
magnetic adsorbent and then the adsorbent with the adsorbed
target is recovered from the suspension using an appropriate
magnetic separator (figure 2). For separation and selection the
advantage of using magnetic nanoparticles instead magnetic
microparticles is that we can prepare suspensions that are
field. The applicability of iron oxide magnetic nanoparticles
in MSPE is clearly evidenced by the fact that already exists in
the market companies (DYNAL Biotech) that commercialize
introduced as a method for the evaluation of immunoassays
. Magnetorelaxometry measures the magnetic viscosity,
i.e. the relaxation of the net magnetic moment of a system of
magnetic nanoparticles after removal of a magnetic field .
There are two different relaxation mechanisms.
the internal magnetization vector of a nanoparticle relaxes in
the direction of the easy axis inside the core; this is called
N´ eel relaxation . Second, particles accomplish rotational
diffusion in a carrier liquid, called Brownian relaxation
. N´ eel and Brownian relaxation can be distinguished
by their different relaxation times .
Brownian relaxation can take place only in liquids, whereas
N´ eel relaxation does not depend on the dispersion of the
nanoparticles. The fact that magnetorelaxometry depends
on the core size, the hydrodynamic size and the anisotropy
allows this technique to distinguish between free and bound
can be used as an analytical tool for the evaluation of
immunoassays . For this application the benefits of
reducing particle size to the nanometre-sized are similar to
those described for separation and selection applications.
Recently, magnetorelaxometry was
2.3. Future applications
have been used for internal radiotherapy . However, little
work has been done in the use of magnetic nanoparticles
in radiotherapy. One strategy under active investigation to
improve dose localization is that of administration of drugs,
metabolites, etc that have been labelled with radioactive
isotopes in a quantity sufficient to deactivate the tumour cells
.In this way, the use of surface-activated magnetic
nanoparticles could have tremendous impact in improving the
efficiency of the cancer treatments.
or artificial replacement parts. In this field special mention
deserves the pioneering work of Dailey et al  who have
reported the synthesis of a silicone based magnetic fluid for
use in eye surgery. Retinal detachment is a major cause of
vision loss in adults. It occurs when the retina separates
from the choroid, resulting in eventual death of the retina
and subsequent loss of vision. Dailey and co-workers have
developed an internal tamponade from modified silicone fluid
containing sterically stabilized 4–10nm sized metal particles,
3. Synthesis methods
One of the latest tendencies in materials science is to tailor-
make classical products with controlled properties for special
uses. Particular attention should be paid to the preparation
methods that allow the synthesis of particles nearly of uniform
a homogeneous solution under controlled conditions or by
controlling the particle growth in a process where a precursor
in aerosol or vapour form is decomposed. Examples of such
preparations include gold colloids, sulfur sols, metal oxides
and hydrous oxides [36–38,71,72].
In the case of magnetic nanoparticles for biomedical
applications we have classified the synthesis methods into
those that produce magnetic nanoparticles from solution
composites consisting of magnetic nanoparticles dispersed in
submicron-sized organic or inorganic matrixes that usually
have spherical shape. Finally, we have also described briefly
another group of methods that use size selection principles
to produce uniform nanoparticles starting from polydisperse
3.1. Magnetic nanoparticles
methods allow the preparation of magnetic nanoparticles with
a rigorous control in size and shape in a simple rather way
and thus are very appropriate for their use in biomedical
applications. Uniform particles are usually prepared via
homogeneous precipitation reactions, a process that involves
the separation of the nucleation and growth of the nuclei
. A schematic representation of the different mechanisms
proposed in the bibliography to explain the formation of
uniform particles is shown in figure 3.
In a homogeneous precipitation, a short single burst
of nucleation occurs when the concentration of constituent
species reaches critical supersaturation.
so obtained are allowed to grow uniformly by diffusion of
solutes from the solution to their surface until the final size is
Precipitation from solution.
In general these
Then, the nuclei
Figure 3. Mechanism of formation of uniform particles in solution:
curve I: single nucleation and uniform growth by diffusion (classical
model of LaMer and Dinegar); curve II: nucleation, growth and
aggregation of smaller subunits; curve III: multiple nucleation
events and Ostwald ripening growth.
attained. To achieve monodispersity, these two stages must
be separated and nucleation should be avoided during the
period of growth. This is the classical model proposed by
LaMer and Dinegar  first to explain the mechanism of
formation of sulfur colloids and also for a limited number
of cases (curve I of figure 3). However, uniform particles
have also been obtained after multiple nucleation events. The
uniformity of the final product is in this case achieved through
a self-sharpening growth process (Ostwald ripening, curve III
of figure 3) . In addition, uniform particles have also
been obtained as a result of aggregation of much smaller
figure 3) [75–77]. An artificial separation between nucleation
and growth processes may be achieved by seeding in which
foreign particles are introduced into the solution of monomers
below the critical supersaturation .
to obtain uniform iron-based nanoparticles in solution are
briefly described in the following sections: coprecipitation,
microemulsions, the polyol process and decomposition of
in solution of magnetite spherical particles in the nanometre
range. In the first, ferrous hydroxide suspensions are partially
oxidized with different oxidizing agents . For example,
spherical magnetite particles of narrow size distribution with
mean diameters between 30 and 100nm can be obtained from
a Fe(II) salt, a base and a mild oxidant (nitrate ions) .
The other method consists in ageing stoichiometric
mixtures of ferrous and ferric hydroxides in aqueous media,
yielding spherical magnetite particles homogeneous in size
. In addition, it has been shown that by adjusting the
pH and the ionic strength of the precipitation medium, it is
pH and the ionic strength in the medium increases . Both
parameters affect the chemical composition of the surface and
consequently, the electrostatic surface charge of the particles.
Under these conditions, magnetite particles are formed by
aggregation of primary particles formed within an Fe(OH)2
gel. This is an ordered aggregation that gives rise to spherical
Figure 4. Magnetic nanoparticles prepared in solution by:
(a) coprecipitation (maghemite). (b) Polyol process (Fe-based
alloy). Reprinted from . (c) Microemulsions (maghemite).
Reprinted from .
crystalline particles . The smallest particles can also be
generated after adding polyvinylalcohol (PVA) to the iron
salts . A typical microstructure of magnetic nanoparticles
produced by this method is shown in figure 4.
Modifications of this method allow for synthesis in the
presence of dextran or any other substance that renders the
magnetic nanoparticles biocompatible and thus make this
In fact, this is the most common method used to obtain
the commercial NMR contrast agents based on magnetic
nanoparticles. For example, nanosized magnetic particles are
into iron(II,III)-carbonate by adding equivalent amounts of
alkaline carbonate, followed by thermal oxidation.  The
size of the particles can be controlled by the thermal reaction
velocity and concentration of the iron salts.
diameters in the range of 20–100nm can be obtained by
timely separation of iron(II,III)-carbonate at temperatures of
5–10˚C and subsequent heating.
been removed, the particles can be stabilized with water-
soluble polysaccharide- or synthetic polymer derivatives.
Nanoparticles coated with a starch derivative have a molar
mass of 10kDa. As a result of the starch matrix, the magnetic
particles can retain their dispersion stability in the pH range
3–12 and also in high salt concentrations .
After surplus salts have
(i.e. reverse micelle solutions) are transparent, isotropic,
thermodynamically stable liquid media.
fine microdroplets of the aqueous phase are trapped within
assemblies of surfactant molecules dispersed in a continuous
oil phase. The surfactant-stabilized microcavities (typically in
the range of 10nm) provide a confinement effect that limits
particle nucleation, growth, and agglomeration . W/O
microemulsions have been shown to be an adequate, versatile,
and simple method to prepare nanosized particles [85–90] and
for both in vivo and in vitro applications.
Pileni and co-workers  prepared nanosized magnetic
particles with average sizes from 4 to 12nm and standard
deviation ranging from 0.2 to 0.3 using microemulsions.
A ferrous dodecyl sulfate, Fe(DS)2, micellar solution was
used to produce nanosized magnetic particles whose size is
controlled by the surfactant concentration and by temperature.
A typical microstructure of magnetic nanoparticles produced
by this method is shown in figure 4. Magnetite nanoparticles
around 4nm in diameter have been prepared by the controlled
hydrolysis with ammonium hydroxide of FeCl2 and FeCl3
aqueous solutions within the reverse micelle nanocavities
generated by using AOT as surfactant and heptane as the
continuous oil phase .
Carpenter and co-workers  prepared metallic iron
particles coated by a thin layer of gold via a microemulsion.
provides functionality, making these composites applicable
in biomedicine.The reverse micelle reaction is carried
out using cetyltrimethylammonium bromide (CTAB) as the
surfactant, octane as the oil phase, and aqueous reactants as
the water phase . The metal particles are formed inside
the reverse micelle by the reduction of a metal salt using
sodium borohydride.The sequential synthesis offered by
reverse micelles is utilized to first prepare an iron core by the
reduction of ferrous sulfate by sodium borohydride. After the
reaction has been allowed to go to completion, the micelles
within the reaction mixture are expanded to accommodate
the shell using a larger micelle containing additional sodium
borohydride. The shell is formed using an aqueous hydrogen
Water-in-oil (W/O) microemulsions
In these systems,
of uniform nanoparticles that could be used in biomedical
applications such as magnetic resonance imaging is the polyol
of dissolved metallic salts and direct metal precipitation from
a solution containing a polyol [36,38]. This process was first
used to prepare noble metals such as Ru, Pd, Pt, Au, and
others such as Co, Ni or Cu [95, 96]. Latterly, the process
A very promising technique for the preparation
has been extended to the synthesis of other materials such as
Fe-based alloys [97,98], which could be used for biomedical
In the polyol process, the liquid polyol acts as the solvent
as a complexing agent for the metallic cations. The metal
precursor can be highly or only slightly soluble in the polyol.
The solution is stirred and heated to a given temperature
reaching the boiling point of the polyol for less reducible
metals. By controlling the kinetic of the precipitation, non-
agglomerated metal particles with well-defined shape and size
can be obtained. A better control of the average size of the
with foreign particles (heterogeneous nucleation). In this way,
nucleation and growth steps can be completely separated and
uniform particles result.
Iron particles around 100nm can be obtained by
disproportionation of ferrous hydroxide in organic media
. Fe(II) chloride and sodium hydroxide reacts with
ethylene glycol (EG) or polyethylene glycol (PEG) and the
Furthermore, iron alloys can be obtained by coprecipitation
of Fe, Ni, and/or Co in EG and PEG. Monodispersed quasi-
spherical and non-agglomerated metallic particles with mean
size around 100nm have been obtained without seeding
(homogeneous nucleation) while particles between 50 and
100nm have been obtained using Pt as the nucleating agent
formed by agglomerates of Fe and Co primary particles
produced over different lengths of time, spherical FeNi
particles present good homogeneity as a result of concomitant
primary particles . A typical microstructure of magnetic
nanoparticles produced by the polyol process is shown in
Whereas FeCo particles are
High-temperature decomposition of organic precursors. The
surfactants has yielded markedly improved samples with good
size control, narrow size distribution and good crystallinity of
individual and dispersible magnetic iron oxide nanoparticles.
Biomedical applications like magnetic resonance imaging,
magnetic cell separation or magnetorelaxometry strongly
depend on particle size and thus magnetic nanoparticles
produced by this method could be potentially used for these
For example, Alivisatos and co-workers  have
demonstrated that injecting solutions of FeCup3 (Cup:
N-nitrosophenylhydroxylamine) in octylamine into long-
chain amines at 250–300˚C yields nanocrystals of maghemite.
These nanocrystals range from 4 to 10nm in diameter, are
crystalline, and are dispersable in organic solvents (figure 5).
Hyeon and co-workers  have also been able to prepare
monodisperse maghemite nanoparticles by a non-hydrolytic
synthetic method.For example, to prepare maghemite
nanoparticles of 13nm (figure 5), Fe(CO)5 was injected
into a solution containing surfactants and a mild oxidant
Very recently, Sun and Zeng  have been able to
prepare monodispersed magnetite nanoparticles with sizes
Figure 5. Maghemite nanoparticles prepared in solution by
decomposition at high temperature of organic precursors:
(a) FeCup3. Reprinted from . (b) Fe(CO)5. Reprinted
from . (c) Fe(III) acetylacetonate. Reprinted from .
from 3 to 20nm by the high-temperature (265˚C) reaction
of iron(III) acetylacetonate in phenyl ether in the presence of
alcohol, oleic acid, and oleylamine (figure 5). In particular,
magnetite nanoparticles around 4nm were obtained by the
thermal decomposition of the iron precursor but to obtain
diameters up to 20nm a seed-mediated growth method was
Other solution techniques.
methods for the production of magnetic nanoparticles that
could be mainly used for in vivo applications. Nature has
Here we describe a series of
developed a variety of protein components that function as
carriers or storage devices for metal components. Of these
systems, the iron-storage protein ferritin is probably the most
of a central core of hydrated iron(III) oxide encapsulated
with a multisubunit protein shell. As a result of the inner
diameter of the nanoreactors, Mann and co-workers have been
able to prepare magnetite  and magnetite/maghemite
nanoparticles  of about 6–7nm in diameter.
magnetite/maghemite particles were generated by oxidation
of apoferritin (empty ferritin) with trimethylamino-N-oxide,
which was loaded with various amounts of iron(II) ions.
Of special interest is the use of dendrimers as templating
hosts for the production of magnetic nanoparticles.
be possible to prepare in a single-step biocompatible magnetic
nanoparticles that could be used for in vivo applications.
Recently, iron ferrite nanoparticles have been prepared
using dendrimers as templating hosts . Carboxylated
oxide nanoparticles. Oxidation of Fe(II) at slightly elevated
under a wide range of temperatures and pHs.
Sonochemical-assisted synthesis has also been reported
as an adequate method for the production of magnetite
and maghemite nanoparticles [107–109]. In sonochemistry,
the acoustic cavitation, that is, the formation, growth, and
a transient localized hot spot, with an effective temperature of
5000K and a nanosecond lifetime . The cavitation is a
quenching process, and hence the composition of the particles
formed is identical to the composition of the vapour in the
bubbles, without phase separation.
Electrochemical methods have also been used for
the production of maghemite nanoparticles .
electrochemical synthesis of nanoparticles of γ-Fe2O3 was
performed in an organic medium.
controlled by the imposed current density, and the resulting
particles were stabilized as a colloidal suspension by the use
of cationic surfactants. The size distributions of the particles
were narrow, with the average sizes varying from 3 to 8nm.
The size was directly
3.1.2. Aerosol/vapour methods.
have been shown to be excellent techniques for the direct and
continuous production of well-defined magnetic nanoparticles
high-production rate can anticipate a promising future for the
preparation of magnetic nanoparticles useful in in vivo and
in vitro applications. The main difference between spray and
laser pyrolysis is the final state of the ultrafine particles. In
spray pyrolysis, the ultrafine particles are usually aggregated
into larger particles, while in laser pyrolysis the ultrafine
particles are less aggregated due to the shorter reaction time.
Spray and laser pyrolysis
obtained by spraying a solution into a series of reactors where
the aerosol droplets undergo evaporation of the solvent and
thermolysis of the precipitated particle at higher temperature
. This procedure gives rise to microporous solids, which
finally sinter to form dense particles.
This method represents a convenient procedure for
obtaining finely dispersed particles of predictable shape, size,
and variable composition. The resulting powders generally
consist of spherical particles, the final diameter of which can
be predetermined from that of the original droplets.
method offers certain advantages over other more commonly
used techniques (such as precipitation from homogenous
solution) as it is simple, rapid, and continuous. Recently, for
example has been used for the production of materials with
relevant properties, say mesoporous microspheres  and
phosphorescent nanoparticles .
Most of the pyrolysis based processes employed to
produce maghemite nanoparticles start with a Fe3+salt and
some organic compound that acts as the reducing agent. It
was shown that in this procedure Fe3+is partially reduced to a
with the formation of magnetite, which is finally oxidized
to maghemite. Without the presence of a reducing agent,
hematite is formed instead of maghemite .
In alcoholic solutions, uniform γ-Fe2O3particles can be
prepared with a wide variety of particle morphologies and
sizes, ranging from 5 to 60nm, depending on the nature of
the iron precursor salt . A detailed description of the
device used for the preparation of these particles can be found
in reference  and a schematic representation is given
in figure 6.The device essentially consists in an aerosol
droplet generator (atomizer, ultrasonic, etc), a furnace and
a particle recovery system. Dense aggregates with spherical
shape composed of γ-Fe2O3subunits with a mean diameter
of 6 and 60nm have been obtained using Fe(III) nitrate and
Fe(III) chloride solutions, respectively. On the other hand,
γ-Fe2O3obtained from acetylacetonate solutions resulted in
monodispersed particles of about 5nm in diameter while
maghemite particles derived from Fe(II) ammonium citrate
appeared as hollow spheres with a mean diameter of 300nm.
The latter consisted of small crystallites aggregated forming
a shell, the size of which varied between 10 and 40nm,
microstructure of magnetic nanoparticles produced by this
method is shown in figure 7.
Laser pyrolysis. Since the pioneering work of Cannon and
co-workers  on the continuous production of nanometric
powders by laser-induced processes, different powders such
Figure 6. Schematic representation of the spray pyrolysis device
used for the preparation of maghemite nanoparticles. This device
consists of an aerosol generator (atomizer or an ultrasonic bath), one
furnace and a particle recovery system.
as Si, SiC, Si3N4and a Si/C/N composite have been prepared
[118,119]. The method involves heating a flowing mixture
of gases with a continuous wave carbon dioxide laser, which
initiates and sustains a chemical reaction. Above a certain
pressure and laser power, a critical concentration of nuclei is
reached in the reaction zone, which leads to homogeneous
nucleation of particles that are further transported to a filter
by an inert gas. Three characteristics of this method must be
emphasized: (a) the small particle size, (b) the narrow particle
size distribution, and (c) the nearly absence of aggregation.
Pure, well-crystallized and uniform γ-Fe2O3nanoparti-
method (figure 7). Samples with particles of 3.5 and 5nm in
ration of the magnetic nanocrystals is shown in figure 8. In the
device shown in figure 8, a small reaction zone is defined by
the overlap between the vertical reactant gas stream and the
horizontal laser beam. The reaction zone is safely separated
from the chamber walls. This design provides an ideal envi-
ronment for the nucleation of small particles in the nanometre
range, with less contamination and narrower size distribution
than those prepared by more conventional thermal methods.
To obtain the γ-Fe2O3 nanoparticles Fe(CO)5 (iron
pentacarbonyl) was used as precursor. Due to the fact that this
precursor does not absorb the radiation at the laser wavelength
Figure 7. Magnetic nanoparticles of maghemite prepared by:
(a) Spray pyrolysis. (b) Laser pyrolysis. Reprinted from .
(10.60 ± 0.05µm), ethylene was used as absorbent as well
as the carrier to transport the carbonyl vapour to the reaction
(652Wcm−2) but simply absorbs the laser radiation heating
the iron pentacarbonyl, which is decomposed into iron and
carbon monoxide. In order to obtain iron oxide, air has to be
introduced into the system, either with the iron pentacarbonyl
vapour causing oxidation under the laser radiation or mixed
3.2. Magnetic composites
For separation processes i.e. in vitro applications we can
use composites consisting of superparamagnetic nanocrystals
dispersed in submicron diamagnetic matrixes that have long
sedimentation times in the absence of a magnetic field.
An advantage of using diamagnetic matrixes is that the
superparamagnetic composite can be easily provided with
functionality and biocompatibility. We now describe some
of the most promising methods for the production of
superparamagnetic composites that could be useful in the field
3.2.1. Deposition methods.
(or shells) on colloidal templates have been prepared by
selection of the experimental conditions, mainly the nature
of the precursors, temperature, and pH, this method can give
spherical composites. Using this technique submicrometre-
sized anionic polystyrene (PS) lattices have been coated with
Inorganic and hybrid coatings
Figure 8. Schematic representation of the Laser pyrolysis device
used for the preparation of maghemite nanoparticles around 5nm
Figure 9. Schematic illustration of the LBL electrostatic assembly of nanoparticles onto spherical colloidal templates. Nanoparticles are
adsorbed onto the polyelectrolyte because they have opposite charge density.
uniform layers of iron compounds [127, 128] by ageing, at
elevated temperature, dispersions of the polymer colloid in
the presence of aqueous solutions of ferric chloride, urea,
hydrochloric acid, and polyvinylpyrrolidone.
One of the most promising techniques for the production
of superparamagnetic composites is the layer-by-layer (LBL)
self-assembly method. This method was firstly developed
for the construction of ultrathin films [129,130] and further
developed by Caruso et al [131, 132] for the controlled
synthesis of novel nanocomposites core-shell materials and
hollow capsules. It consists in the stepwise adsorption of
charged polymers or nanocolloids and oppositely charged
polyelectrolytes onto flat surfaces or colloidal templates,
Using this strategy, colloidal particles have been coated
with alternating layers of polyelectrolytes, nanoparticles, and
proteins . Furthermore, Caruso et al have demonstrated
that submicrometre-sized hollow silica spheres  or
polymer capsules  can be obtained after removal of
the template from the solid-core multilayered-shell particles
either by calcination or by chemical extraction.
mention deserves their work in the preparation of iron
oxide superparamagnetic and monodisperse dense and hollow
applications (figure 10).
3.2.2. Encapsulation of magnetic nanoparticles in polymeric
Encapsulation of inorganic particles into organic
polymers endows particles with important properties that
bare uncoated particles lack .
particles enhance compatibility with organic ingredients,
reduce susceptibility to leaching, and protect particle surfaces
from oxidation. Consequently, encapsulation improves
dispersibility, chemical stability, and reduces toxicity .
Polymer-coated magnetite nanoparticles have been syn-
thesized by seed precipitation polymerization of methacrylic
acid and hydroxyethyl methacrylate in the presence of the
magnetite nanoparticles . Cross-linking of polymers has
also been reported an adequate method for the encapsula-
tion of magnetic nanoparticles. To prepare the composites
by this method, first, mechanical energy needs to be supplied
to create a dispersion of magnetite in the presence of aque-
ous albumin , chitosan , or PVA polymers .
More energy creates an emulsion of the magnetic particle sol
in cottonseed , mineral , or vegetable oil .
Polymer coatings on
latex, 0.3 microns in diameter, with up to 24wt% in magnetite
Recently, the preparation of superparamagnetic latex
via inverse emulsion polymerization has been reported
. A ‘double-hydrophilic’ diblock copolymer, present
during the precipitation of magnetic iron oxide, directs
nucleation, controls growth, and sterically stabilizes the
coated particles repeptize creating a ferrofluid-like dispersion.
Inverse emulsification of the ferrofluid into decane, aided
by small amounts of diblock copolymer emulsifier along
with ultrasonication, creates minidroplets (180nm) filled with
magnetic particles and monomer. Subsequent polymerization
generates magnetic latex.
A novel approach to prepare superparamagnetic poly-
meric nanoparticles by synthesis of the magnetite core and
by Chu and co-workers . Stable magnetic nanoparticle
dispersions with narrow size distribution were thus produced.
The microemulsion seed copolymerization of methacrylic
acid, hydroxyethylmethacrylate, andcross-linkerresultedina
stable hydrophilic polymeric shell around the nanoparticles.
Changing the monomer concentration and water/surfactant
ratio controls the particle size.
inorganic matrixes, in particular of silica, as dispersion media
of superparamagnetic nanocrystals has been reported to be an
Encapsulation of magnetic nanoparticles in
An appropriate tuning of the magnetic
is essentialfor the
In this way, the use of
potential useof the
Figure 10. TEM micrographs of uncoated PS particles (a) and PS
particles precoated with a three layer polyelectrolyte film and
[Fe3O4/PAH] (b), [Fe3O4/PAH]4(c), and [Fe3O4/PDADMAC]4(d).
PAH is a cationic polyelectrolyte (poly(allylamine hydrochloride))
and PDADMAC is also a cationic polyelectrolyte
(poly(diallyldimethylammonium chloride)). The deposited Fe3O4
nanoparticles can be seen existing as aggregates. The magnetite
loading on the particles increases with additional depositions of
Fe3O4and polycation. The scale bar corresponds to all four TEM
images shown. Reprinted from .
effective way to modulate the magnetic properties by a simple
heating process [143–145].
Another advantage of having a surface enriched in silica
is the presence of surface silanol groups that can easily react
with alcohols and silane coupling agents  to produce
dispersions that are not only stable in non-aqueous solvents
but also provide the ideal anchorage for covalent bounding of
ligands a difficult task. In addition, the silica surface confers
high stability to suspensions of the particles at high volume
fractions, changes in pH or electrolyte concentration .
Recently, we have been successful in preparing
with a high loading of magnetic material by aerosol pyrolysis
[148,149]. Silica coated γ-Fe2O3hollow spherical particles
with an average size of 150nm (figure 11) were prepared by
the aerosol pyrolysis of methanol solutions containing iron
ammonium citrate and tetraethoxysilane (TEOS) at a total
salt concentration of 0.25M .
possible formation mechanism of the silica coated magnetic
hollow spheres is shown in figure 11. During the first stage the
rapid evaporation of the methanol solvent favours the surface
precipitation (i.e. formation of hollow spheres) of components
. The low solubility of the iron ammonium citrate in
methanol when compared with that of TEOS promotes the
initial precipitation of the iron salt solid shell. During the
second stage the probable continuous shrinkage of this iron
salt solid shell facilitates the enrichment at the surface of
the silicon oxide precursor (TEOS). In the third stage, the
γ-Fe2O3hollow spheres. The formation of the γ-Fe2O3is
associated with the presence of carbonaceous species coming
from the decomposition of the methanol solvent and from
the iron ammonium citrate and TEOS. On the other hand,
the aerosol pyrolysis of iron nitrate and TEOS at a total salt
concentration of 1M produced silica coated γ-Fe2O3dense
An illustration of the
Figure 11. (a) TEM picture of the silica/iron oxide composites
prepared by aerosol pyrolysis of a mixture of iron ammonium citrate
and TEOS. (b) Details of a hollow spherical particle showing an
outer particle layer mainly constituted (according to TEM
mycroanalyses) by SiO2. (c) Illustration of the formation
mechanism of the silica coated γ-Fe2O3hollow particles. Reprinted
Figure 12. TEM micrographs of the silica/iron oxide composites
prepared by aerosol pyrolysis of a mixture of iron nitrate (20mol%)
and TEOS (a) and further heated in a conventional furnace for 2h at
900˚C (b), 1050˚C (c), and 1200˚C (d). Note in the sample heated at
1050˚C the presence of γ-Fe2O3(dark regions) nanoparticles
smaller than 20nm dispersed in a microspherical silica particle
(lighter regions). At this temperature, the enrichment of silica on
particle outerlayers is clearly observed. It is important to note that
similar microstructures to that shown in micrographs (b) and (c)
were observed for smaller and bigger particles. Note also the high
stability of the spherical magnetic composites (the particles lost
spherical shape only temperatures of 1200˚C as a consequence of a
sintering process). Reprinted from .
spherical particles with an average size of 250nm (figure 12).
The increase in salt concentration to a value of 1M favours the
formation of dense spherical particles. Sedimentation studies
of these particles have shown that are particularly useful for
separation applications .
A W/O microemulsion method has also been used for the
preparation of silica-coated iron oxide nanoparticles .
Three different non-ionic surfactants (Triton X-100, Igepal
CO-520, and Brij-97) have been used for the preparation
of microemulsions, and their effects on the particle size,
crystallinity, and the magnetic properties have been studied.
reaction of ferrous and ferric salts with inorganic bases.
have been used with each surfactant to observe whether the
basicity influences the crystallization process during particle
formation. All these systems show magnetic behaviour close
to that of superparamagnetic materials. By use of this method,
nanoparticles is formed by the base-catalysed hydrolysis and
the polymerization reaction of TEOS in the microemulsion. It
renders these particles a potential candidate for their use in
in vivo applications.
3.3. Size selection methods
Biomedical applications like magnetic resonance imaging,
magnetic cell separation or magnetorelaxometry utilize
the magnetic properties of the nanoparticles in magnetic
fluids. Furthermore, these applications also depend on the
hydrodynamic size. Therefore, in many cases only a small
portion of particles contributes to the desired effect.
relative amount of the particles with the desired properties can
be increased by the fractionation of magnetic fluids [66,151].
Common methods currently used for the fractionation of
magnetic fluids are centrifugation  and size-exclusion
chromatography . All these methods separate the
particles via non-magnetic properties like density or size.
Massart et al  have proposed a size sorting procedure
of nanoparticles.The positive charge of the maghemite
surface allows its dispersion in aqueous acidic solutions and
the production of dispersions stabilized through electrostatic
repulsions. By increasing the acid concentration (in the
range 0.1–0.5moll−1), interparticle repulsions are screened
and phase transitions are induced. Using this principle, these
authors describe a two-step size sorting process, in order to
obtain significant amounts of nanometric monosized particles
with diameters between typically 6 and 13nm. As the surface
of the latter is not modified by the size sorting process, usual
procedures are used to disperse them in several aqueous or
Preference should be given, however, to partitions based
on the properties of interest, in this case the magnetic
properties. So far, magnetic methods have been used
only for the separation of magnetic fluids, for example, to
remove aggregates by magnetic filtration .
the fractionation of magnetic nanoparticles by flow field–flow
fractionation was reported . Field–flow fractionation is
a family of analytical separation techniques , in which
the separation is carried out in a flow with a parabolic profile
running through a thin channel. An external field is applied
at a right angle to force the particles toward the so-called
accumulation wall .
4. Effect of synthesis on the magnetic properties
4.1. Particle size and structural effects
We now present some of our results that clearly manifest the
importance of controlling the particle size and the structure to
produce magnetic materials with a defined magnetic response
for a specific biomedical application. It should be taken into
account that size and structural effects are parameters that can
be controlled through the synthesis methods. On the other
hand, magnetite and maghemite are by far the most used
materials for biomedical application and therefore this study
is focused on these materials.
Magnetite has a cubic inverse spinel structure with
oxygen forming a fcc close packing and Fe cations occupying
interstitial tetrahedral sites and octahedral sites .
Maghemite has a structure similar to that of magnetite, only
differs in that all or most of the Fe is in the trivalent state
(figure 13). Cation vacancies compensate for the oxidation
of Fe(II) cations . Maghemite has a cubic unit cell in
which each cell contains 32 O ions, 211
vacancies. The cations are distributed over the 8 tetrahedral
and 16 octahedral sites, whereas the vacancies are confined
to the octahedral sites. Synthetic maghemite often displays
superstructure forms, which arises as a result of the cations
and the vacancy ordering. The extent of vacancy ordering is
related to both the crystallite size and the amount of iron(II) in
the structure or other impurities . All of these possible
arrangements in the maghemite are partially responsible for
the different magnetic behaviour manifested by maghemite
nanoparticles prepared by different synthetic routes .
The extentof vacancy
spectra of different maghemite samples  (figure 14).
Thus, in the samples prepared by solution techniques
(coprecipitation), the one with the largest particle size (14nm)
shows the infrared features of γ-Fe2O3crystallites, which are
at least partially ordered, as evidenced by the multiple lattice
absorption bands between 800 and 200cm−1. Meanwhile, in
the sample with the lowest particle size (5nm) a significant
reduction in the number of lattice absorption bands associated
3iron(III) ions and 21
Maghemite- γ γ γ γ-Fe2O3
t = Tetrahedral
o = Octahedral
Fe3+8 t [ Fe2+8Fe3+8]o O32
Fe3+8 t[ Fe3+5.32.7Fe3+8] o O32
Figure 13. Chemical formula for the magnetite/maghemite system.
The order of the vacancies in the octahedral positions of the
maghemite can lead to a tetragonal superstructure (unit-cell is three
times the cubic one).
Figure 14. Infrared spectra for magnetite and maghemite
nanoparticles prepared by different methods.
in the infrared spectra of two samples that have a similar
particle size (5nm) but have been prepared by two different
techniques (solution and pyrolysis). Particularly, the infrared
spectrum of the sample prepared by pyrolysis only displays
two broad maximum at around 600 and 450cm−1indicating
a random distribution of vacancies and therefore is expected
to behave differently in the presence of an applied magnetic
It has been shown that the degree of order in the
distribution of cation vacancies, inherent in the γ-Fe2O3
structure, of particles smaller than ∼100nm affects the
magnetic properties, suggesting that magnetic moments in
the interior of the particles can be significantly influenced
by canting effects . For nanometre γ-Fe2O3particles,
this effect could explain at least in part the reduction in
saturation magnetization found at very small sizes. In fact,
the existence of magnetically disordered layers around the
particles have been proposed by various researchers as the
particle size approaches the frontier of 10nm [162, 163].
The proposed effects are in many cases, however, obscured
by a wide distribution of particle sizes and shapes or by
magnetic interactions between particles. The effect of the
size and structural ordering on the magnetic properties of
γ-Fe2O3 nanoparticles (<20nm) has been carried out in
uniform samples prepared by coprecipitation from solution
and laser pyrolysis methods .
in figure 15.A progressive cation disorder that strongly
nanoparticles as the particle size decreases.
particles, where some vacancy order is observed, are of about
8nm in diameter. In general, when the particles are obtained
by pyrolysis, the saturation magnetization is smaller than for
samples prepared by precipitation from solution.
Direct information about the directions of the atomic
moments in nanoparticles can be obtained by M¨ ossbauer
spectroscopy. The M¨ ossbauer spectra registered at 5K in a
magnetic field of 4T applied parallel to the γ-radiation of
uniform nanoparticles smaller than 5 nm prepared by laser
pyrolysis (samples Laser1 and Laser2) and precipitation in
The results are shown
Figure 15. Saturation magnetization values of maghemite
nanoparticles as a function of particle size and the preparation
method (filled symbols: 298K, empty symbols: 5K).
solution (solution), are shown in figure 16 . The fitting
of the spectra of samples Laser1 and Laser2 results in a non-
zero relative area of lines 2 and 5, which are very slightly
reduced by the applied field. The main effect was in the line
broadening which affects the lines 1 and 6, suggesting that
the directions of the atomic moments are highly disordered
for the laser samples due to a high degree of canting and spin
frustration. In contrast, the spectrum of a maghemite sample
of similar particle size (between 3 and 5nm), prepared by
precipitation in the presence of oleic acid shows well resolved
A and B sites and can be fitted with two sextets. The area of
lines 2 and 5 correspond to average canting angles of about
20˚ and 33˚, much smaller than the canting observed with
samples Laser1 and Laser2. The effect of the preparation
spectra shown in figure 16 for sample Laser1, and especially
for sample Laser2. The fit of these spectra gives average
hyperfine fields slightly smaller than those of conventional
microcrystalline maghemite particles (about 52T), and the
fields is presumably also due to the increase in the internal
magnetic disorder .
4.2. Interaction effects
The wide variety of magnetic behaviour of nanostructured
materials is complicated by interparticle interactions, which
limits their possible application in biomedicine. For
Figure 16. M¨ ossbauer spectra at 5K in the presence of a magnetic
field of 4T applied parallel to the γ-radiation for maghemite
nanoparticles prepared by different methods and with different
degree of cationic disorder.
sufficiently dilute dispersions,
usually of a dipolar nature are negligible and the crossover to
the physical properties of the individual particles. However,
at higher densities (usually needed in practical applications)
interparticle interactions strongly affect the behaviour of the
cause frustration of the moments, which no longer align
themselves precisely with the particles’ easy axes at low T.
results. While this phenomenon has been studied extensively,
most work to date has focused on shifts of the blocking
freezing can be described as a true thermodynamic spin glass
We have examined the effect of interaction on the
encapsulated in spherical silica particles that could be used
for biomedical applications [149,167]. In particular, we have
and the standard relation for the temperature variation
of the reduced remanence (ratio between the remanence
magnetization and the saturation magnetization extrapolated
at 0K, Mr(0)/Ms(0)) .
reaches its cusp with the increase in volume packing fraction,
which was associated with the increase in the interparticle
interactions. On the other hand, the fact that Mr(0)/Ms(0)
values were in all cases below 0.5 was explained from the
effect of competition between interparticle interactions and
intraparticle anisotropy on the spin relaxation process, which
produces frustration [168–170].
In the ZFC experiments we
5. Final remarks
The search for new synthetic routes or the improvement of
established ones which are able to produce reliable magnetic
nanoparticles with the correct characteristics of improved
tissular diffusion, colloidal stability and biocompatibility
is in continuous development.
understanding and control of the biological reactions with the
magnetic nanoparticle, we may be able to control the rejection
and understanding of their interaction with the body may lead
to better biocompatible nanomagnets.
For example the application of magnetic liposomes (lipid
vesicles, containing submicron-sized magnetic nanoparticles
in their structure either in the lipid bilayer or in the aqueous
compartment) as ‘vehicles’ for targeted drug delivery appears
to be a promising technique . Liposomes can be used for
encapsulation of many biologically active substances, and can
prolong their therapeutic action by gradual release of the drug.
Magnetic components of the liposomes allow concentration
of the liposomes in the desired area of the patient’s organs by
of note. These authors have developed magnetic liposomes
derivatized with the hydrophilic polymer polyethylene glycol
(PEG) that may escape rapid uptake by cells of the endothelial
If we can gain sufficient
Drug and gene delivery will continue to impact
significantly on the practice of biomedicine.
drug-targeting will undoubtedly dramatically improve the
therapeutic potential of many water-insoluble and unstable
drugs. The development of drugs able to target selected cells
In this field the work of Bergemann and co-workers  is
worthy of note. These authors have succeeded in developing
groups were attached, thereby enabling simple and reversible
binding of ligands. The remarkable feature of ionically bound
systems is that the active low molecular weight substances can
desorb from the carriers after a defined time span and hence
diffuse from the vascular wall into the tissue.
The authors would like to thank K O’Grady for proof reading
the manuscript.This research was supported by CICYT
under projects MAT2000-1504 and MAT2002-04001-C02.
The financial support from the regional government of
Madrid under project CAM 07N/0057/2002 is also gratefully
acknowledged. PT acknowledges the financial support from
the Ramon y Cajal program.
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