Polydispersity of Samples
Polydispersity is the main problem encountered when working with nanoparticles. It can be solved, in some cases, by the choice of the synthesis process, or by size-sorting processes once the particles are synthesized.
In the case of ferric oxide particles, the average diameter is easily controlled through the experimental conditions of synthesis, but the system is always poly-dispersed. The particle size distribution is well described using a log-normal distribution of diameters (Fig. 3):
In usual products synthesized by a coprecipitation method, the polydispersity s ranges between 0.3 and 0.4. This corresponds to a rather wide distribution. Synthesis using micelles reduced polydispersities but never obtained monodisperse samples.’48- Centrifugation and magnetic separation can be alternative procedures.’49- A size-sorting process has been proposed to reduce significantly the polydispersity down to 0.15. It is based on the thermo-dynamic properties of colloidal dispersions (”Phase Behavior of Dispersions of Magnetic Nanoparticles”) and has already been used to obtain monodispersed emul-sions.’15- It is described in the case of positive or negative ferrite particles dispersed in water in Refs. ’49- and ’50-. Such dispersions are stabilized by the electrostatic repulsions between particles. These repulsions depend on the ionic strength in the aqueous solution and can be reduced by addition of an electrolyte in the medium. The screening of the repulsions induces a reversible phase separation between a liquid phase dense in colloids and a liquid phase poor in colloids. If both phases are separated and analyzed, it is found that the dense phase contains the bigger particles, and the light phase contains the smallest ones. Performing this process two or three times, it is possible to fractionate the size distribution and obtain almost monodispersed samples with a reasonable yield.
Fig. 3 Two examples of log-normal distribution of diameters.
Metallic particles are usually obtained with a very low polydispersity (Fig. 2) and size sorting is indeed unnecessary.
MAGNETIC PROPERTIES
Because of their colloidal size, the magnetic particles under consideration here and whose synthesis is described above have magnetic properties that are strongly modified with respect to the properties of bulk materials.
Bulk Ferromagnetic Materials
In ferromagnetic or ferrimagnetic materials, the order results in high magnetostatic energy.’3,51- To reduce this energy, the bulk material divides into domains,called magnetic monodomains, separated by the so-called ”Bloch walls.” Each monodomain has a permanent magnetization vector, which is oriented, in zero field, to minimize this magnetostatic energy (Fig. 4). In zero field, this magnetization vector has a given crystallographic direction, which is one of the so-called ”easy axes of magnetization.” In some materials, there are three easy axes of magnetization; in others, only there is only one axis. In the first case, it is told that the material has a cubic an-isotropy; in the second instance, it has an axial anisotropy. Moving the magnetic vector away from an easy axis of magnetization costs energy, which is called the energy of anisotropy (Ea). This energy depends on constants called the magnetocrystalline anisotropy constants (denoted K), which are a function of the material under consideration.
Fig. 4 Magnetic domains in zero field.
On the macroscopic point of view, the magnetization of a ferromagnetic (or a ferrimagnetic) material in zero field is equal to zero, and its magnetization curve (magnetization as a function of the applied magnetic field) is a shape characteristic of a ferromagnetic material with a hysteresis loop (Fig. 5a).
Magnetic Properties of Fine Particles
The diameter of the colloidal particles under consideration here are always smaller than the dimension of a magnetic domain. It means that each particle is a magnetic mono-domain and has a permanent magnetic moment, whose intensity m is proportional to the specific magnetization of the material constituting the grain (Ms), and to the volume of this grain (V):
Ms is usually lower than the magnetization of the bulk material for several reasons. The first is relevant for oxidized materials; for example, metallic particles’ specific magnetization, if submitted to oxidation, will fall down— and this change will be more dramatic as the particle surface increases. But even for particles stable with respect to oxidation, the local disorganization of the surface leads to a lowering of the specific magnetization.[7]
For 7-nm-diameter maghemite particles, a typical value of m is 5.4 x 10~20 A m2, which corresponds to about 6000 mB.[52]
The direction of this moment is fixed in the direction of an easy axis of magnetization. Nevertheless, the nature of the anisotropy (cubic one or uniaxial one) depends on the particles’ shape and size. The value of the energy of an-isotropy is also modified compared with the value of the bulk material. For an uniaxial anisotropy, it is given by:
where V is the volume of the monodomain, and Ka eff is the anisotropy constant of the material in the grain. This anisotropy constant depends now on the particle shape, particle size, and the interactions between grains. It is difficult to propose a calculation of such an energy, but experimental magnetization or Mossbauer measurements have allowed estimations for ferrite particles.[37]
For a given material and a given temperature, the energy of anisotropy decreases when the particle size decreases. Under a given diameter, it becomes the same order of magnitude as the entropic term kT: this means that the magnetization vector fluctuates around the easy axis of magnetization, with a characteristic relaxation time (Neel relaxation time) such as t = t0 exp(Ea/kT) (t0 is on the order of 10~10 sec). This phenomenon is called superparamagnetism (by comparison with the paramagnetic behavior of isolated magnetic moments, and by opposition to the ferromagnetic behavior of the bulk material) and the particle is called a ”soft dipole.” For a given temperature, according to the nature of the material, the diameter below which superparamagnetism is observed differs. For example, at room temperature, 5-nm-diameter maghemite particles have a superparamagnetic behavior, although cobalt ferrite particles have a ferromagnetic behavior. But please note that the colloids under consideration here are always polydispersed in size and, at a given temperature, an assembly of such colloids presents a rather large distribution of relaxation times. Some studies have tried to relate the anisotropy of cobalt ferrite grains to the particle size.’53,54- A complete description of the magnetic properties of nanoparticles needs to take into account surface effects: the surface disordered spins fluctuate and hinder the dynamics of the magnetic moment associated with a particle. Surface anisotropy can be more important than the volume.’55-
Fig. 5 (a) Scheme of the magnetization curve of a ferromagnetic (or ferrimagnetic) material. (b) Real magnetization curve of a superparamagnetic material.
On a macroscopic point of view, the shape of the magnetization curve of a diluted assembly of super-paramagnetic grains is well described by the Langevin formalism (Fig. 5b):
The polydispersity has to be taken into account and can modify the shape of the curve because of its high influence on m.
COLLOIDAL DISPERSION OF MAGNETIC NANOPARTICLES
As mentioned earlier, because of their colloidal dimensions, magnetic nanoparticles can be dispersed in a liquid carrier, and a stable colloidal dispersion, usually called ”magnetic fluid” or ”ferrofluid,” can be obtained."6-1 Such dispersions conjugate the properties of usual colloidal dispersions and the magnetic properties of the nano-particles dispersed. Indeed, oily magnetic fluids have found many commercialized applications (special seals and bearings, moving coils speaker, inertia dampers, etc.)’56-and many other conceptual ones (captors, magnetic ink, magnetic levitation, magneto-optical devices, etc.).’57-
Processes for the Dispersion of Magnetic Colloidal Particles in Liquid Carriers
Oily carriers
Organic solvents are often needed for commercialized applications. That is the reason why most of the particle synthesis processes involve a step during which a surfactant is added to the mixture, to adsorb on particles and to provide them an affinity for the oily media.’58,59- The surfactant avoids aggregation of particles in the oily liquid carrier, and the resulting product is a stable colloidal dispersion of magnetic particles. Surfactants are, for applications, commercial products. Oleic acid is often used because it is one of the best surfactants for dispersing metal oxide particles in hydrocarbon media. But it cannot be used for dispersion of particles in aromatic oils or chlorinated solvents. In fact, the choice of a surfactant is not a trial-and-error work.’10,60,61- It is always a single-chain surfactant and the chemical nature of the chain is a function of the nature of the liquid carrier. For example, dispersion in aromatic oils is possible with surfactants having an aromatic cycle in their tail. The choice of the polar head is determined by the nature of the particle surface. Oleic acid is a good surfactant for ferric oxide particles because the carboxylic acid group is a good chelating agent of Fe species.’62- But even when the affinity of the surfactant for the surface is strong, it has to be kept in mind that desorption can occur (e.g., when diluting the colloidal dispersion with the liquid carrier). This is a serious limitation for applications as for theoretical studies.
Polymeric species, again introduced during the synthesis of particles, are sometimes described as stabilizers, in the case of metallic particles.’39,40- In some other cases, they are grafted as macrosurfactants on the particles after synthesis.
Anyway, the result is that, at the present time, it is possible to obtain dispersions of magnetic nanoparticles in a wide variety of media: alkane, aromatic solvents, chlo-rated solvents, ketones, phtalates, and commercial oils derived from silicon oils, resins, etc. Some dispersions are commercialized; others are laboratory products.
Aqueous solvents
Aqueous solvents are also used for the dispersion of ferrite particles, usually for fundamental studies or bio-medical applications.’64- In this case, the dispersions are stabilized, thanks to particle surface charges. Indeed, a metal oxide surface in water has a specific acid-base behavior, which leads to anionic or cationic surface charges according to the value of the pH, which are called ”structural charges”.’8- When particles have a sufficient number of structural charges, electrostatic repulsions can stabilize their dispersion in water or in a brine solution. Unfortunately, for the magnetic ferric oxides constituting the magnetic particles under consideration (cobalt ferrite, maghemite, etc.), particles have a sufficient amount of surface charges only for strongly alkaline media (pH> 11) or strongly acidic ones (pH<3).’9- As an example, it has been found that 7-nm-diameter maghemite particles have 80 structural charges at pH 2, 25 at pH 3, and only 8 at pH 4.
Such a pH range is not suitable for applications, but can be modified by adsorption of small organic molecules (e.g., citrate species). The latter provide to the surface their own acid-base behavior and ensure negative surface charges for particles for any pH higher than 3.[9,65- Moreover, it has been found that dispersions of citrate-coated particles were astonishingly stable in brine solution for electrostatically stabilized systems, indicating that adsorption of citrate leads to additional short-range repulsions of steric origin.[66] To modify the pH stability range of their dispersions, the particles can also be coated by silica or by molecules such as dimercaptosuccinic acid. This last molecule is of particular interest as it allows a further grafting of biological species through thiol bridges.[67]
The number of structural charges is not, in fact, the relevant parameter to explain the stability of electrostatically stabilized aqueous colloidal dispersions. As a matter of fact, the nature of the counterions of particles (charge and size) is of great importance because these counterions will condense on the charged surface, leading to an ”effective surface” charge, inferior to the structural one and is the relevant parameter to quantify the electrostatic repulsions.[68] Highly charged and small counterions have to be avoided to obtain stable dispersions. That is the reason why tetramethylammonium has often been used in the case of dispersions of negatively charged ferrite particles, and nitrate anions in the case of positively charged particles.
