Xerrada a Aachen l'any 2007 sobre ferrofluid monolayers.

1. STRUCTURE FORMATION IN FERROFLUID MONOLAYERS: theory and computer simulations. S. Kantorovich ， C. Holm, J.J. Cerdà Ural State University, Ekaterinburg Max-Plank Institute for Polymer Research

2. Ferrofluids Ferrofluid: stable colloidal suspension of sub-domain magnetic particles in a liquid carrier. The particles, which have an average size of about 10 nm, are coated with 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.

4. OVERVIEW DF Theory Check the degree of correctness of the theoretical formalism. Analyze the process of microstructure formation, and phase behavior: gain physical insight. MD Simulations

7. Computer Simulations Simulation results N=1000  =4.99

8. Computer Simulations

9. Computer Simulations 1 unit = 10 nm

10. Computer Simulations 1 unit = 10 nm

12. Theoretical Model: Equilibrium Surface Fractions.  -  Lagrange multiplier to be found from the mass balance equation 

13. Microstructure analysis: 2 nd Virial coefficients 3.48 11.86 108.62 4.15  10 3 B 2 33 3.73 28.95 580.50 3.72  10 4 1.10 3.80 35.50 1.40  10 3 2 . 02 2 . 59 3 . 28 4 .0 7 B 2 22 B 2 23  Q2D: 3 D dipoles , but 2 D sample 3 D dipoles& sample 2 D dipoles& sample Quasi 2D geometry changes the ferrofluid microstructure effective interactions are weaker

14. Microstructure analysis: tracking clusters… The eye (distance criterion) can be misleading Entropy criterion  1 r 12  2

15. Microstructure analysis: branched structures vs chains&rings

16. Microstructure analysis: Neighbours.  =2.59  =3.28 Theory Simulations  =3.28  =3.28  =3.28  =0.05  =0.15  =0.01  =2.59  =3.28  =2.59  =3.28

17. Microstructure analysis: Neighbours.  =4.07  =4.99 Theory Simulations  =4.99  =4.99  =4.99  =0.05  =0.15  =0.01  =4.07  =4.99  =4.07  =4.99

18. Microstructure analysis: cluster size. Theory (Excluded Area) Theory (No Excluded Area) Simulations  =1.54  =2.02  =1.54  =2.02

19. Theory (Excluded Area) Theory (No Excluded Area) Simulations  =2.59  =3.28  =2.59  =3.28 Microstructure analysis: cluster size.

20. Theory (Excluded Area) Theory (No Excluded Area) Simulations  =4.02 Microstructure analysis: cluster size.

21. The cut-off of the dipolar interaction (intra, and inter-cluster) could be the in a large extend the cause of the mismatch between theory and simulations at large values of the dipolar coupling constant λ . NEXT REFINEMENT Microstructure analysis: cluster size.