Ferrofluids

Fig1. Ferrofluid monolayer at low area fraction.

Fig2. Ferrofluid monolayer at high area fraction.

What are Ferrofluids?

Dipolar magnetic fluids (also known as ferrofluids or ferrocolloids), are colloidal suspensions of ferromagnetic nanoparticles (typical sizes 10-20nm), usually stabilised by steric coatings (in non electrolyte carrier liquids) or by electrical double layers (in aqueous solutions). Sterical coatings are usualy made of a stabilizing dispersing agent (surfactant) which prevents particle agglomeration even when a strong magnetic field gradient is applied to the ferrofluid. The surfactant must be matched to the carrier type and must overcome the attractive van der Waals and magnetic forces between the particles. A typical ferrofluid may contain by volume 5% magnetic solid, 10% surfactant and 85% carrier.

Due to their size, ferrofluid particles can be considered as magnetic single-domains with a permanent magnetic moment $|\mathbf {m} |=m$ proportional to their volume $\pi \sigma _{m}^{3}/6$, where $\sigma _{m}$ is the diameter of the magnetic core of the particle.

To know more about the basics of ferrofluids, see for instance the ferrofluids in the Wikipedia.

Synthesis of ferrofluids

The idea of making a liquid with magnetic properties seems to date back to the 1779 when Gowan Knight tried to make a magnetic fluid by introducing iron filings into water. Unfortunately, the iron filings sedimented very quickly. In the XX century the issue was retaken by F. Bitter (1932), and W.C.Elmore (1938), but the particles they obtained were quite large and not fully stable. It seems that Stephen Papell Solomon (US Patent 3215572 ) working for NASA in the 60´s was the first to develop an easy and effective way of preparing such colloidal systems. The idea was to be able to use these particles to control the flux of fuel in a zero gravity environment. Since then, many synthesis have been developed to produce ferrofluid particles in both non-polar and polar solvents, increase their stability, improve the control over their size and degree of polidispersity, and produce particles with different materials and shapes. For recent reviews about the subject see (Lu2007) and (Tourinho1998).

You can also prepare your own ferrofluids and have fun at home! See for instance the educational article of Berger et al. (Berger1999), as well as (1), (2), (3), (4), (5), (6).

Why are Ferrofluids interesting?

Ferrofluids are interesting for a two fold reason:

• Ferrofluids are systems exhibing anisotropic interactions leading to a very reach phase behaviour, as well as very interesting rheological and magnetic properties. Thus ferrofluids are a paradigma of physical systems with anisotropic interactions.

• The singular properties of ferrofluids in external magnetic fields have found application in many areas, ranging from engineering, to biomedical applications (Popplewell1984,Rosensweig1985, Odenbach2002, Alexiou2003,Hilger2004, Scherer2005). Just to mention a few examples:
  • Magnetic Seals for instance in vaccum pumps and ferrofluid bearings.
  • Car dampers, nanoactuators, loudspeakers, adaptive optics (liquid mirrors), biologically inspired robots.
  • Cancer treatment, cell separation, ultrasensitive analysis, MRI.
  • Art.

See also as an example the links (1), (2) ...

Aggregating structures formed by Ferrofluids

Even in the absence of external fields, ferrofluids have a very complex microstructure, which is caused by the combination of interparticle interactions specific to magnetic fluids (see for instance figures 1 and 2). Ferrofluid particles are known to self-assemble into a variety of magnetic equilibrium structures which depend on several factors such as: system geometry, magnetic interactions, particle polydispersity, presence or absence of external fields, etc.

The number of probable cluster topologies in magnetic fluids is high: drops with high magnetic phase concentration (micron size), branched and fractal clusters (hundreds of nanometers in size), or chain- and ring-like structures (tens of nanometers). Signs of clustering process in ferrofluids at zero field are known for more than 40 years (Hess1966). Nonetheless, despite the large amount of clues obtained in subsequent studies (Shen2001, Donselaar1999, Cebula1983, Gazeau2002), a direct experimental proof of the existence of clusters like chains, rings, etc. has been elusive for many years, specially for those cases were dipole-dipole interactions were relatively week, like in magnetite nanoparticles ($Fe_{3}O_{4}$). Thus, due to the lack of conclusive experiments, the understanding of how dipole-dipole interactions influence the clustering process and determine the subsequent microstructure and phase behaviour of ferrofluids has become a challenge. In bulk ferrofluids, those aspects have been studied in detail through theoretical (Gennes1970, Jordan1973, Osipov1996, Zubarev1995, Tavares1997, Tavares1999, Roij1996, Tlusty2000, Morozov2002, Mendelev2004, Ivanov2004) and simulation (Weis1993, Levesque1994, Jund1995, Camp2000, Pshenichnikov2000, Wang2002, Wang2003, Holm2006) works. Comprehensive reviews on these subject for bulk systems are also available, see (Teixeira2000, Cabuil2000, Huke2004, Holm2005).

Ferrofluid Monolayers

The phase behaviour and microstructure of ferrofluid systems in reduced dimensions is not necessarily equivalent to that of 3D systems. In addition, thin-films and monolayers, have become recently a more successful experimental scenario to assert the existence of the clustering process (Klokkenburg2006, Butter2003, Puntes2001, Wen1999). In the experiments of Philipse and co-workers(Butter2003, Klokkenburg2006), images obtained by cryogenic transmission electron microscopy (cyro-TEM) give ample evidence of the existence of chain- and ring-like structures in ferrofluid monolayers, where all particles are trapped in one plane, but their magnetic moments are free to fluctuate in 3D (q2D monolayers).

In recent years, several theoretical and computational works have been devoted to the study of ferrofluids in monolayers and thin-films. The thermodynamics, and magnetisation properties of quasi-two-dimensional (q2D) systems have been studied by Lomba et al. (Lomba2000), and Gao et al. (Gao1997). Weis and co-workers (see (Weis2002b, Weis2003), and references therein), have performed Monte Carlo simulations of monolayers and systems of finite thickness involving dipolar interactions. They have shown that q2D dipolar systems, alone or in combination with other interactions, present a rich variety of structures, phases and phase transitions. In a recent q2D Monte Carlo study on dipolar hard spheres (DHS), Tavares et al. (Tavares2006) have reported the structure of the fluid to be well described by an ideal mixture of self-assembling clusters at low and intermediate densities. Very recently, Duncan-Camp (Duncan2006) have studied the kinetics of aggregation in monolayers using stochastic dynamics simulations. The results obtained in that work suggest that the conditions for defect-driven condensation (Tlusty2000) could be met by kinetic trapping, giving rise to a metastable phase transition between isotropic fluid phases. The structure formation and magnetic properties of polydisperse ferrofluids in monolayers have been also recently addressed by theory and Monte Carlo simulations (Morimoto2003, Aoshima2004, Kristof2005).

Current Research

Despite the progress obtained in previous studies, the understanding of the phase behaviour and microstructure formation of ferrofluids in constrained geometries is only partial. The understanding of such features is of paramount importance in order to know better those systems and reduce the large amount of times devoted to trial-error in order to improve or design new applications based on ferrofluids.

Our current interest focuses on the peculiarities of the aggregation processes in both quasi-two dimensional (monolayers) and bulk ferrofluid systems. We make use of a combination of density functional theory, and molecular dynamics (MD) simulations. The microstructure formation and phase behaviour are studied thoroughly through a comparison of the theoretical, and computational results. The active areas of research about ferrofluids in our group at this moment are:

• Ferrofluid monolayers: monodisperse particles.
• Ferrofluid monolayers: bidisperse particles.
• Structure factors of ferrofluids in the low-density low-aggregating limit.

Scientists

• Joan Josep Cerdà
• Christian Holm
• Sofia Kantorovich

Collaborators

• Group of Prof. Dr. Alexey Ivanov. Department of Mathematical Physics, The Urals State University, Ekaterinburg, Russia.

• Ben Erné from the group of Prof. A. Philipse at Van 't Hoff Laboratory for Physical and Colloid Chemistry.

Publications

• Zuowei Wang, Christian Holm, Hanns Walter Müller.
  Boundary condition effects in the simulation study of equilibrium properties of magnetic dipolar fluids.
  The Journal of Chemical Physics 119:379, 2003.
  [PDF] (175 KB) [DOI]
• Zuowei Wang, Christian Holm, Hanns Walter Müller.
  Computer simulation study of equilibrium properties of magnetic dipolar fluids.
  Magnetohydrodynamics 39(1):59–64, 2003.
  
• Zuowei Wang, Christian Holm.
  Structure and magnetization properties of polydispersed ferrofluids: A molecular dynamics study.
  Physical Review E 68(4):041401, 2003.
  [PDF] (419 KB) [DOI]
• J. P. Huang, Z. W. Wang, C. Holm.
  Computer simulations of the structure of colloidal ferrofluids.
  Physical Review E 71(6):061203, 2005.
  [PDF] (1.1 MB) [DOI]
• J. P. Huang, Z. Wang, C. Holm.
  Structure and magnetic properties of mono- and bi- dispersed ferrofluids as revealed by simulations.
  Journal of Magnetism and Magnetic Materials 289:234, 2005.
  [PDF] (113 KB) [DOI]
• Christian Holm, Jean-Jacque Weis.
  The Structure of Ferrofluids: A Status Report.
  Current Opinion in Colloid & Interface Science 10(3):133–140, 2005.
  [PDF] (166 KB) [DOI]
• Christian Holm, Alexey Ivanov, Sofia Kantorovich, Elena Pyanzina, Evgeniy Reznikov.
  Equilibrium properties of a bidisperse ferrofluid with chain aggregates: theory and computer simulations.
  Journal of Physics: Condensed Matter 18(38):S2737–S2756, 2006.
  [PDF] (1.0 MB) [DOI]
• Christian Holm, Alexey Ivanov, Sofia Kantorovich, Elena Pyanzina.
  Polydispersity influence upon magnetic properties of aggregated ferrofluids.
  Zeitschrift für Physikalische Chemie 220:105–115, 2006.
  [PDF] (261 KB) [DOI]
• Alexey O. Ivanov, Sofia S. Kantorovich, Evgeniy N. Reznikov, Christian Holm, Alexander F. Pshenichnikov, Alexander V. Lebedev, Alexandros Chremos, Philip J. Camp.
  Magnetic properties of polydisperse ferrofluids: A critical comparison between experiment, theory and computer simulation.
  Physical Review E 75(6):061405, 2007.
  [PDF] (339 KB) [DOI]
• Juan J. Cerdà, Sofia Kantorovich, Christian Holm.
  Aggregate formation in ferrofluid monolayers: simulations and theory.
  Journal of Physics: Condensed Matter 20(20):204125, 2008.
  [PDF] (342 KB) [DOI]
• Juan J. Cerdà, Sofia Kantorovich, Christian Holm.
  Effects of polidispersity in ferrofluid monolayers.
  unknown year.
  (coming soon)
  
• Sofia Kantorovich, Juan J. Cerdà, Christian Holm.
  Microstructure analyisis of monodisperse ferrofluid monolayers: theory and simulation.
  Physical Chemistry Chemical Physics 10(14):1883–1895, 2008.
  [PDF] (1.3 MB) [DOI]

Links

• Talk in Zurich ICIAM07, about ferrofluid monolayers. (1.84 MB)
• Poster about ferrofluid monolayers. (2 MB)

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--Jcerda 15:11, 29 April 2008 (CEST)