# Ferrofluids

**Ferrofluids** under construction

## 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 proportional to their volume , where 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 40´s. Nonetheless, it seems that was Stephen Papell Solomon (US Patent 3215572 ) working for NASA in the 60´s the first to develop an easy and effective way of preparing such colloidal systems. You can also prepare your own ferrofluids at home

## 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 (Rosensweig1985, Odenbach2002, Alexiou2003,Hilger2004, Scherer2005). Just to mention a few examples:

## 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 (). 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 in the aggregation processes in ferrofluids in both quasi-two dimensional systems (monolayers) and bulk 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

## Collaborators

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

## Publications

## Links

- Posters, presentations & co (file does not exist!)

## References

[Alexiou2003] Alexiou Ch, Jurgons R, Schmid R, Bergmann C, Henke J, Huenges E, and Parak F , J. Drug Target, (11), 139, (2003).

[Aoshima2004] Aoshima M, Satoh A, J. Coll. Int. Sci., (280), 83, (2004).

[Butter2003] Butter K, Bomans PH, Frederik PM, Vroege GJ, Philipse AP, J. Phys.: Condens. Matter, (15), S1451, (2003).

[Cabuil2000] Cabuil V, Curr. Opin. Colloid Interface Sci., (5), 44, (2000).

[Camp2000] Camp PJ, Patey GN, Phys. Rev. E, (62), 5403, (2000).

[Cebula1983] Cebula DJ, Charles SW, and Popplewell J, J. Physique, (44), 207, (1983).

[Donselaar1999] Donselaar LN, Frederik PM, Bomans PH, Buining PA, Humbel BM, and Philipse AP, J. Magn. Magn. Matter, (201), 58, (1999).

[Duncan2006] Duncan PD, Camp PJ, Phys. Rev. Lett., (97), 107202, (2006).

[Gao1997] Gao GT, Zeng XC, and Wang W., J. Chem. Phys., (106), 3311, (1997).

[Gazeau2002] Gazeau F, Dubois E, Bacri JC, Boue F, Cebers A, and Perzynski R, Phys. Rev. E, (65), 031403, (2002).

[Gennes1970] de Gennes PG, and Pincus PA, Phys. Kondens. Matter.,(11), 189, (1970).

[Hess1966] Hess PH, and Parker PH, J. Appl. Polym. Sci. (10), 1915, (1966).

[Hilger2004] Hilger I, Andr\"a W, Hergt R, Hiergeist R, and Kaiser W A, Inorganic Materials, Recent Advances ed D Bahadur, S Vitta, and O. Prakash (2004, New Delhi: Narosa Publishing House).

[Holm2005] Holm C, Weis JJ, Curr. Op. Coll. Int. Sci., (10), 133, (2005).

[Holm2006] Holm C, Ivanov A, Kantorovich S, Pyanzina E, Reznikov E, J. Phys.: Condens. Matter, ( 18), S2737, (2006).

[Huke2004] Juke B, and L\"ucke M, Rep. Prog. Phys., ( 67), 1731, (2004).

[Ivanov2004] Ivanov AO, Wang Z., and C. Holm, Phys. Rev. E, ( 69), 031206, (2004).

[Jund1995] Jund P, Kim SG, Tománek, and Hetherington J, Phys. Rev. Lett., (74), 3049, (1995).

[Pshenichnikov2000] Pshenichnikov AF, and Mekhonoshin V, J. Magn. Magn. Mater, (213), 357, (2000).

[Jordan1973] Jordan PC, Mol. Phys., (25), 961, (1973).

[Klokkenburg2006] Klokkenburg M, Dullens RPA, Kegel WK, Erné) BH, Philipse AP, Phys. Rev. Lett., (96), 037203, (2006).

[Kristof2005] Krist\'{o)f T, Szalai I, Phys. Rev. E, (72), 041105, (2005).

[Levesque1994] Levesque D, Weis JJ, Phys. Rev. E, (49), 5131, (1994).

[Lomba2000] Lomba E, Lado F, Weis JJ, Phys. Rev. E, (61), 3838, (2000).

[Mendelev2004] Mendelev VS, and Ivanov AO, Phys. Rev. E, (70), 051502, (2004).

[Morozov2002] Morozov KI, and Shliomis MI, 2002, Ferrofluids, Magnetically Controllable Fluids and Their Applications), Lect. Notes Phys., Springer, Berlin, 2002. Ed. Odenbach S.

[Morimoto2003] Morimoto H, Maekawa T, Matsumoto Y, Phys. Rev. E (68), 061505, (2003).

[Odenbach2002] Odenbach S (Ed.), Ferrofluids, Magnetically Controllable Fluids and Their Applications, Lect. Notes Phys., Springer, New York, 2002.

[Osipov1996] Osipov MA, Teixeira PIC, and Telo da Gama MM, Phys. Rev. E, (54), 2597, (1996).

[Puntes2001] Puntes VF, Krishnan KM, and Alivisatos AP, Science (291), 2115, (2001).

[Roij1996] van Roij R, Phys. Rev. Lett., (76), 3348, (1996).

[Rosensweig1985] Rosensweig RE, Ferrohydrodynamics (Cambridge University Press, Cambridge, 1985).

[Scherer2005] Scherer C, Figueiredo AM, Brazilian J. of Phys., (35), 718, (2005).

[Shen2001] Shen L, Stachowiak A, Fateen SK, Laibinis PE, and Hatton TA, Langmuir, (17), 288, 2001.

[Tavares1997] Tavares JM, Telo da Gama MM, and Osipov MA, Phys. Rev. E, (56), R6252, (1997).

[Tavares1999] Tavares JM, Weis JJ, and Telo da Gama MM, Phys. Rev. E, (59), 4388, (1999).

[Tavares2006] Tavares JM, Weis JJ, Telo da Gama MM, Phys. Rev. E, (73) 041507, (2006).

[Teixeira2000] Teixeira PIC, Tavares JM, and Telo da Gama MM, J. Phys.: Condens. Matter, (12), R411, (2000).

[Tlusty2000] Tlusty T, Safran SA, Science (290), 1328, (2000).

[Wang2002] Wang Z, Holm C, and Müller HW, Phys. Rev. E, (66), 021405, (2002).

[Wang2003] Wang Z, Holm C, Phys. Rev. E, (68), 041401, (2003).

[Weis1993] Weis JJ, Levesque D, Phys. Rev. Lett., (71), 2729, (1993).

[Weis2002b] Weis JJ, Tavares JM, and Telo da Gama MM, J. Phys.: Condens. Matter, (14), 9171, (2002).

[Weis2003] Weis JJ, J. Phys.: Condens. Matter, (15), S1471, (2003).

[Wen1999] Wen W, Pál KF, Zheng DW, and Tu KN, Phys. Rev. E, (59), R4758, (1999).

[Zubarev1995] Zubarev AY, and Iskakova LY, J. Exp. Theor. Phys., (80), 857, (1995).