Xerrada a Aachen l'any 2007 sobre ferrofluids

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Xerrada a Aachen l'any 2007 sobre ferrofluid monolayers.

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Xerrada a Aachen l'any 2007 sobre ferrofluids

  1. 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. 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.
  3. 3. Ferrofluid Monolayers <ul><li>Absence of real space experi-mental information in 3D. </li></ul><ul><li>Recent direct-observation of chain and ring formation in monolayers. Direct comparison to experiments is feasible. </li></ul><ul><li>Quasi-two dimensional systems can exhibit a behavior different from 2D or 3D systems. </li></ul>
  4. 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
  5. 5. Modelization of the ferrofluid monolayer Quasi-two dimensional system <ul><li>Position particles: 2D. </li></ul><ul><li>Dipoles: free 3D rotation. </li></ul><ul><li>Single magnetic domain. </li></ul>Short range interaction Surfactant layer, oleic acid (2 nm) Magnetic core, Fe 3 O 4 U s (r 12 ) r 12 σ m /2 σ /2 WCA Potential k B T ≈ σ
  6. 6.   = 1.54 ... 4.99   = 0.01 ... 0.25 Range parameters Modelization of the ferrofluid monolayer Long-range interaction Control Parameters <ul><li>Area fraction, Φ . </li></ul><ul><li>Dipolar Coupling, λ </li></ul>U dd (1,2) - Point dipoles at the CM of particles.  1  2  1  2 r 12
  7. 7. Computer Simulations Simulation results N=1000  =4.99
  8. 8. Computer Simulations
  9. 9. Computer Simulations 1 unit = 10 nm
  10. 10. Computer Simulations 1 unit = 10 nm
  11. 11. Theoretical Model: Density Functional Approach. <ul><ul><li>Present Limitations </li></ul></ul>- Monodisperse system. - Intra-cluster: only nearest neighbors interactions. - Chains and rings. - No inter-cluster interactions. Excluded Area Interactions - Excluded area: partially. 2  2  
  12. 12. Theoretical Model: Equilibrium Surface Fractions.  -  Lagrange multiplier to be found from the mass balance equation 
  13. 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. 14. Microstructure analysis: tracking clusters… The eye (distance criterion) can be misleading Entropy criterion  1 r 12  2
  15. 15. Microstructure analysis: branched structures vs chains&rings
  16. 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. 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. 18. Microstructure analysis: cluster size. Theory (Excluded Area) Theory (No Excluded Area) Simulations  =1.54  =2.02  =1.54  =2.02
  19. 19. Theory (Excluded Area) Theory (No Excluded Area) Simulations  =2.59  =3.28  =2.59  =3.28 Microstructure analysis: cluster size.
  20. 20. Theory (Excluded Area) Theory (No Excluded Area) Simulations  =4.02 Microstructure analysis: cluster size.
  21. 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.

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