Abstract

An oscillatory-like relaxation process in which there are two valleys in the T-t curve is observed when light is transmitted through binary ferrofluids composed of both ferrimagnetic CoFe2O4 nanoparticles and paramagnetic p-MgFe2O4 nanoparticles in the presence of a high magnetic field and through pure (single) CoFe2O4 ferrofluids in a low magnetic field. This relaxation behavior is explained using a model of a bidispersed system based on both chained and unchained particles. In such a bidispersed system, the variation of the transmitted light results mainly from the motion of the chains, with the polarized unchained particles’ gas producing the modulation effect. The oscillatory-like relaxation phenomenon depends on the features of both the chained and unchained particle systems. If either the particle volume fraction of chained particles or of unchained particles is very low, or the degree of polarization of the unchained particles gas is very weak, a simple nonlinear relaxation process, giving only a valley in the T-t curve, will appear for the transmitted light. For pure CoFe2O4 ferrofluids, the number of chained and unchained particles does not remain constant under different values of the magnetic field. According to the analysis of the relaxation behavior of transmitted light, it is known that binary ferrofluids based on strong magnetic CoFe2O4 particles and weak magnetic p-MgFe2O4 particles can be much closer to the theoretical bidispersed system than single ferrofluids containing only strong magnetic particles.

© 2011 Optical Society of America

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  1. B. Huke and M. Lücke, “Magnetic properties of colloidal suspensions of interacting magnetic particles,” Rep. Prog. Phys. 67, 1731–1768 (2004).
    [CrossRef]
  2. S. H. L. Klapp, “Dipolar fluids under external perturbations,” J. Phys. 17, R525–R550 (2005).
    [CrossRef]
  3. B. H. Erné, K. Butter, B. W. M. Kuipers, and G. J. Vroege, “Rotational diffusion in iron ferrofluids,” Langmuir 19, 8218–8225 (2003).
    [CrossRef]
  4. M. Rasa, “Improved formulas for magneto-optical effects in ferrofluids,” J. Magn. Magn. Mater. 201, 170–173(1999).
    [CrossRef]
  5. J. Li, B. G. Zhao, Y. Q. Lin, X. Y. Qiu, and X. J. Ma, “Transmission of light in ionic ferrofluids, J. Appl. Phys. 92, 1128–1131(2002).
    [CrossRef]
  6. J. Li, X. D. Liu, Y. Q. Lin, X. Y. Qiu, and X. J. Ma, “Field-induced transmission of light in ionic ferrofluids of tunable viscosity,” J. Phys. D 37, 3357–3360 (2004).
    [CrossRef]
  7. J. Li, Y. Huang, X. D. Liu, Y. Q. Lin, Q. Li, and R. L. Gao, “Coordinated chain motion resulting in intensity variation of light transmitted through ferrofluids film,” Phys. Lett. A 372, 6952–6955 (2008).
    [CrossRef]
  8. J. Li, Y. Q. Lin, X. D. Liu, B. C. Wen, T. Z. Zhang, Q. M. Zhang, and H. Miao, “The modulation of coupling in the relaxation behavior of light transmitted through binary ferrofluids,” Opt. Commun. 283, 1182–1187 (2010).
    [CrossRef]
  9. S. Kantorovich and A. O. Ivanov, “Formation of chain aggregates in magnetic fluids: an influence of polydispersity,” J. Magn. Magn. Mater. 252, 244–246 (2002).
    [CrossRef]
  10. A. O. Ivanov and S. S. Kantorovich, “Chain aggregate structure and magnetic birefringence in polydisperse ferrofluids,” Phys. Rev. E 70, 021401 (2004).
    [CrossRef]
  11. S. S. Kantorovich, “Chain aggregate structure in polydisperse ferrofluids: different application,” J. Magn. Magn. Mater. 289, 203–206 (2005).
    [CrossRef]
  12. Z. Wang and C. Holm, “Structure and magnetic properties of polydisperse ferrofluids: a molecular dynamics study,” Phys. Rev. E 68, 041401 (2003).
    [CrossRef]
  13. J. P. Huang, Z. W. Wang, and C. Holm, “Computer simulations of the structure of colloidal ferrofluids,” Phys. Rev. E 71, 061203 (2005).
    [CrossRef]
  14. C. Holm, A. Ivanov, S. Kantorovich, E. Pyanzina, and E. Reznikov, “Equilibrium properties of a bidisperse ferrofluid with chain aggregates: theory and computer simulations,” J. Phys. 18, S2737 (2006).
    [CrossRef]
  15. G. M. Range and S. H. L. Klapp, “Demixing in simple dipolar mixtures: integral equation versus density functional results,” Phys. Rev. E 70, 031201 (2004).
    [CrossRef]
  16. G. M. Range and S. H. L. Klapp, “Phase behavior of bidisperse ferrocolloids,” Phys. Rev. E 70, 061407 (2004).
    [CrossRef]
  17. G. M. Range and S. H. L. Klapp, “Density-functional study of model bidisperse ferrocolloids in an external field,” J. Chem. Phys. 122, 224902 (2005).
    [CrossRef] [PubMed]
  18. S. N. Han, J. Li, R. L. Gao, T. Z. Zhang, and B. C. Wen, “Study of magnetisation behaviours for binary ionic ferrofluids,” J. Exp. Nanosci. 4, 9–19 (2009).
    [CrossRef]
  19. T.-Z. Zhang, J. Li, H. Miao, Q-M. Zhang, J. Fu, and B.-C. Wen, “Enhancement of the field modulation of light transmission through films of binary ferrofluids,” Phys. Rev. E 82, 021403 (2010).
    [CrossRef]
  20. Z. Wang, C. Holm, and H. W. Müller, “Molecular dynamics study on the equilibrium magnetization properties and structure of ferrofluids,” Phys. Rev. E 66, 021405(2002).
    [CrossRef]
  21. A. R. Wang, J. Li, and R. L. Gao, “The structural force arising from magnetic interactions in polydisperse ferrofluids,” Appl. Phys. Lett. 94, 212501 (2009).
    [CrossRef]
  22. J. J. Miles, R. W. Chantrell, and M. R. Parker, “Model of magnetic-field-induced ordering in dispersions of fine paramagnetic particles,” J. Appl. Phys. 57, 4271–4273(1985).
    [CrossRef]
  23. F. A. Tourinho, R. Fanck, and R. Massart, “Aqueous ferrofluid based on manganese and cobalt ferrites,” J. Mater. Sci. 25, 3249–3254 (1990).
    [CrossRef]
  24. J. Li, X. D. Liu, Y. Q. Lin, Y. Huang, and L. Bai, “Relaxation behavior measuring of transmitted light through ferrofluids film,” Appl. Phys. B 82, 81–84 (2006).
    [CrossRef]
  25. H.-E. Horng, C.-Y. Hong, S. L. Lee, C. H. Ho, S. Y. Yang, and H. C. Yang, “Magnetochromatics resulted from optical grating of magnetic fluid film subjected to perpendicular magnetic fields,” J. Appl. Phys. 88, 5904–5908 (2000).
    [CrossRef]

2010

J. Li, Y. Q. Lin, X. D. Liu, B. C. Wen, T. Z. Zhang, Q. M. Zhang, and H. Miao, “The modulation of coupling in the relaxation behavior of light transmitted through binary ferrofluids,” Opt. Commun. 283, 1182–1187 (2010).
[CrossRef]

T.-Z. Zhang, J. Li, H. Miao, Q-M. Zhang, J. Fu, and B.-C. Wen, “Enhancement of the field modulation of light transmission through films of binary ferrofluids,” Phys. Rev. E 82, 021403 (2010).
[CrossRef]

2009

A. R. Wang, J. Li, and R. L. Gao, “The structural force arising from magnetic interactions in polydisperse ferrofluids,” Appl. Phys. Lett. 94, 212501 (2009).
[CrossRef]

S. N. Han, J. Li, R. L. Gao, T. Z. Zhang, and B. C. Wen, “Study of magnetisation behaviours for binary ionic ferrofluids,” J. Exp. Nanosci. 4, 9–19 (2009).
[CrossRef]

2008

J. Li, Y. Huang, X. D. Liu, Y. Q. Lin, Q. Li, and R. L. Gao, “Coordinated chain motion resulting in intensity variation of light transmitted through ferrofluids film,” Phys. Lett. A 372, 6952–6955 (2008).
[CrossRef]

2006

C. Holm, A. Ivanov, S. Kantorovich, E. Pyanzina, and E. Reznikov, “Equilibrium properties of a bidisperse ferrofluid with chain aggregates: theory and computer simulations,” J. Phys. 18, S2737 (2006).
[CrossRef]

J. Li, X. D. Liu, Y. Q. Lin, Y. Huang, and L. Bai, “Relaxation behavior measuring of transmitted light through ferrofluids film,” Appl. Phys. B 82, 81–84 (2006).
[CrossRef]

2005

G. M. Range and S. H. L. Klapp, “Density-functional study of model bidisperse ferrocolloids in an external field,” J. Chem. Phys. 122, 224902 (2005).
[CrossRef] [PubMed]

S. S. Kantorovich, “Chain aggregate structure in polydisperse ferrofluids: different application,” J. Magn. Magn. Mater. 289, 203–206 (2005).
[CrossRef]

J. P. Huang, Z. W. Wang, and C. Holm, “Computer simulations of the structure of colloidal ferrofluids,” Phys. Rev. E 71, 061203 (2005).
[CrossRef]

S. H. L. Klapp, “Dipolar fluids under external perturbations,” J. Phys. 17, R525–R550 (2005).
[CrossRef]

2004

B. Huke and M. Lücke, “Magnetic properties of colloidal suspensions of interacting magnetic particles,” Rep. Prog. Phys. 67, 1731–1768 (2004).
[CrossRef]

J. Li, X. D. Liu, Y. Q. Lin, X. Y. Qiu, and X. J. Ma, “Field-induced transmission of light in ionic ferrofluids of tunable viscosity,” J. Phys. D 37, 3357–3360 (2004).
[CrossRef]

A. O. Ivanov and S. S. Kantorovich, “Chain aggregate structure and magnetic birefringence in polydisperse ferrofluids,” Phys. Rev. E 70, 021401 (2004).
[CrossRef]

G. M. Range and S. H. L. Klapp, “Demixing in simple dipolar mixtures: integral equation versus density functional results,” Phys. Rev. E 70, 031201 (2004).
[CrossRef]

G. M. Range and S. H. L. Klapp, “Phase behavior of bidisperse ferrocolloids,” Phys. Rev. E 70, 061407 (2004).
[CrossRef]

2003

Z. Wang and C. Holm, “Structure and magnetic properties of polydisperse ferrofluids: a molecular dynamics study,” Phys. Rev. E 68, 041401 (2003).
[CrossRef]

B. H. Erné, K. Butter, B. W. M. Kuipers, and G. J. Vroege, “Rotational diffusion in iron ferrofluids,” Langmuir 19, 8218–8225 (2003).
[CrossRef]

2002

J. Li, B. G. Zhao, Y. Q. Lin, X. Y. Qiu, and X. J. Ma, “Transmission of light in ionic ferrofluids, J. Appl. Phys. 92, 1128–1131(2002).
[CrossRef]

S. Kantorovich and A. O. Ivanov, “Formation of chain aggregates in magnetic fluids: an influence of polydispersity,” J. Magn. Magn. Mater. 252, 244–246 (2002).
[CrossRef]

Z. Wang, C. Holm, and H. W. Müller, “Molecular dynamics study on the equilibrium magnetization properties and structure of ferrofluids,” Phys. Rev. E 66, 021405(2002).
[CrossRef]

2000

H.-E. Horng, C.-Y. Hong, S. L. Lee, C. H. Ho, S. Y. Yang, and H. C. Yang, “Magnetochromatics resulted from optical grating of magnetic fluid film subjected to perpendicular magnetic fields,” J. Appl. Phys. 88, 5904–5908 (2000).
[CrossRef]

1999

M. Rasa, “Improved formulas for magneto-optical effects in ferrofluids,” J. Magn. Magn. Mater. 201, 170–173(1999).
[CrossRef]

1990

F. A. Tourinho, R. Fanck, and R. Massart, “Aqueous ferrofluid based on manganese and cobalt ferrites,” J. Mater. Sci. 25, 3249–3254 (1990).
[CrossRef]

1985

J. J. Miles, R. W. Chantrell, and M. R. Parker, “Model of magnetic-field-induced ordering in dispersions of fine paramagnetic particles,” J. Appl. Phys. 57, 4271–4273(1985).
[CrossRef]

Bai, L.

J. Li, X. D. Liu, Y. Q. Lin, Y. Huang, and L. Bai, “Relaxation behavior measuring of transmitted light through ferrofluids film,” Appl. Phys. B 82, 81–84 (2006).
[CrossRef]

Butter, K.

B. H. Erné, K. Butter, B. W. M. Kuipers, and G. J. Vroege, “Rotational diffusion in iron ferrofluids,” Langmuir 19, 8218–8225 (2003).
[CrossRef]

Chantrell, R. W.

J. J. Miles, R. W. Chantrell, and M. R. Parker, “Model of magnetic-field-induced ordering in dispersions of fine paramagnetic particles,” J. Appl. Phys. 57, 4271–4273(1985).
[CrossRef]

Erné, B. H.

B. H. Erné, K. Butter, B. W. M. Kuipers, and G. J. Vroege, “Rotational diffusion in iron ferrofluids,” Langmuir 19, 8218–8225 (2003).
[CrossRef]

Fanck, R.

F. A. Tourinho, R. Fanck, and R. Massart, “Aqueous ferrofluid based on manganese and cobalt ferrites,” J. Mater. Sci. 25, 3249–3254 (1990).
[CrossRef]

Fu, J.

T.-Z. Zhang, J. Li, H. Miao, Q-M. Zhang, J. Fu, and B.-C. Wen, “Enhancement of the field modulation of light transmission through films of binary ferrofluids,” Phys. Rev. E 82, 021403 (2010).
[CrossRef]

Gao, R. L.

S. N. Han, J. Li, R. L. Gao, T. Z. Zhang, and B. C. Wen, “Study of magnetisation behaviours for binary ionic ferrofluids,” J. Exp. Nanosci. 4, 9–19 (2009).
[CrossRef]

A. R. Wang, J. Li, and R. L. Gao, “The structural force arising from magnetic interactions in polydisperse ferrofluids,” Appl. Phys. Lett. 94, 212501 (2009).
[CrossRef]

J. Li, Y. Huang, X. D. Liu, Y. Q. Lin, Q. Li, and R. L. Gao, “Coordinated chain motion resulting in intensity variation of light transmitted through ferrofluids film,” Phys. Lett. A 372, 6952–6955 (2008).
[CrossRef]

Han, S. N.

S. N. Han, J. Li, R. L. Gao, T. Z. Zhang, and B. C. Wen, “Study of magnetisation behaviours for binary ionic ferrofluids,” J. Exp. Nanosci. 4, 9–19 (2009).
[CrossRef]

Ho, C. H.

H.-E. Horng, C.-Y. Hong, S. L. Lee, C. H. Ho, S. Y. Yang, and H. C. Yang, “Magnetochromatics resulted from optical grating of magnetic fluid film subjected to perpendicular magnetic fields,” J. Appl. Phys. 88, 5904–5908 (2000).
[CrossRef]

Holm, C.

C. Holm, A. Ivanov, S. Kantorovich, E. Pyanzina, and E. Reznikov, “Equilibrium properties of a bidisperse ferrofluid with chain aggregates: theory and computer simulations,” J. Phys. 18, S2737 (2006).
[CrossRef]

J. P. Huang, Z. W. Wang, and C. Holm, “Computer simulations of the structure of colloidal ferrofluids,” Phys. Rev. E 71, 061203 (2005).
[CrossRef]

Z. Wang and C. Holm, “Structure and magnetic properties of polydisperse ferrofluids: a molecular dynamics study,” Phys. Rev. E 68, 041401 (2003).
[CrossRef]

Z. Wang, C. Holm, and H. W. Müller, “Molecular dynamics study on the equilibrium magnetization properties and structure of ferrofluids,” Phys. Rev. E 66, 021405(2002).
[CrossRef]

Hong, C.-Y.

H.-E. Horng, C.-Y. Hong, S. L. Lee, C. H. Ho, S. Y. Yang, and H. C. Yang, “Magnetochromatics resulted from optical grating of magnetic fluid film subjected to perpendicular magnetic fields,” J. Appl. Phys. 88, 5904–5908 (2000).
[CrossRef]

Horng, H.-E.

H.-E. Horng, C.-Y. Hong, S. L. Lee, C. H. Ho, S. Y. Yang, and H. C. Yang, “Magnetochromatics resulted from optical grating of magnetic fluid film subjected to perpendicular magnetic fields,” J. Appl. Phys. 88, 5904–5908 (2000).
[CrossRef]

Huang, J. P.

J. P. Huang, Z. W. Wang, and C. Holm, “Computer simulations of the structure of colloidal ferrofluids,” Phys. Rev. E 71, 061203 (2005).
[CrossRef]

Huang, Y.

J. Li, Y. Huang, X. D. Liu, Y. Q. Lin, Q. Li, and R. L. Gao, “Coordinated chain motion resulting in intensity variation of light transmitted through ferrofluids film,” Phys. Lett. A 372, 6952–6955 (2008).
[CrossRef]

J. Li, X. D. Liu, Y. Q. Lin, Y. Huang, and L. Bai, “Relaxation behavior measuring of transmitted light through ferrofluids film,” Appl. Phys. B 82, 81–84 (2006).
[CrossRef]

Huke, B.

B. Huke and M. Lücke, “Magnetic properties of colloidal suspensions of interacting magnetic particles,” Rep. Prog. Phys. 67, 1731–1768 (2004).
[CrossRef]

Ivanov, A.

C. Holm, A. Ivanov, S. Kantorovich, E. Pyanzina, and E. Reznikov, “Equilibrium properties of a bidisperse ferrofluid with chain aggregates: theory and computer simulations,” J. Phys. 18, S2737 (2006).
[CrossRef]

Ivanov, A. O.

A. O. Ivanov and S. S. Kantorovich, “Chain aggregate structure and magnetic birefringence in polydisperse ferrofluids,” Phys. Rev. E 70, 021401 (2004).
[CrossRef]

S. Kantorovich and A. O. Ivanov, “Formation of chain aggregates in magnetic fluids: an influence of polydispersity,” J. Magn. Magn. Mater. 252, 244–246 (2002).
[CrossRef]

Kantorovich, S.

C. Holm, A. Ivanov, S. Kantorovich, E. Pyanzina, and E. Reznikov, “Equilibrium properties of a bidisperse ferrofluid with chain aggregates: theory and computer simulations,” J. Phys. 18, S2737 (2006).
[CrossRef]

S. Kantorovich and A. O. Ivanov, “Formation of chain aggregates in magnetic fluids: an influence of polydispersity,” J. Magn. Magn. Mater. 252, 244–246 (2002).
[CrossRef]

Kantorovich, S. S.

S. S. Kantorovich, “Chain aggregate structure in polydisperse ferrofluids: different application,” J. Magn. Magn. Mater. 289, 203–206 (2005).
[CrossRef]

A. O. Ivanov and S. S. Kantorovich, “Chain aggregate structure and magnetic birefringence in polydisperse ferrofluids,” Phys. Rev. E 70, 021401 (2004).
[CrossRef]

Klapp, S. H. L.

S. H. L. Klapp, “Dipolar fluids under external perturbations,” J. Phys. 17, R525–R550 (2005).
[CrossRef]

G. M. Range and S. H. L. Klapp, “Density-functional study of model bidisperse ferrocolloids in an external field,” J. Chem. Phys. 122, 224902 (2005).
[CrossRef] [PubMed]

G. M. Range and S. H. L. Klapp, “Demixing in simple dipolar mixtures: integral equation versus density functional results,” Phys. Rev. E 70, 031201 (2004).
[CrossRef]

G. M. Range and S. H. L. Klapp, “Phase behavior of bidisperse ferrocolloids,” Phys. Rev. E 70, 061407 (2004).
[CrossRef]

Kuipers, B. W. M.

B. H. Erné, K. Butter, B. W. M. Kuipers, and G. J. Vroege, “Rotational diffusion in iron ferrofluids,” Langmuir 19, 8218–8225 (2003).
[CrossRef]

Lee, S. L.

H.-E. Horng, C.-Y. Hong, S. L. Lee, C. H. Ho, S. Y. Yang, and H. C. Yang, “Magnetochromatics resulted from optical grating of magnetic fluid film subjected to perpendicular magnetic fields,” J. Appl. Phys. 88, 5904–5908 (2000).
[CrossRef]

Li, J.

J. Li, Y. Q. Lin, X. D. Liu, B. C. Wen, T. Z. Zhang, Q. M. Zhang, and H. Miao, “The modulation of coupling in the relaxation behavior of light transmitted through binary ferrofluids,” Opt. Commun. 283, 1182–1187 (2010).
[CrossRef]

T.-Z. Zhang, J. Li, H. Miao, Q-M. Zhang, J. Fu, and B.-C. Wen, “Enhancement of the field modulation of light transmission through films of binary ferrofluids,” Phys. Rev. E 82, 021403 (2010).
[CrossRef]

S. N. Han, J. Li, R. L. Gao, T. Z. Zhang, and B. C. Wen, “Study of magnetisation behaviours for binary ionic ferrofluids,” J. Exp. Nanosci. 4, 9–19 (2009).
[CrossRef]

A. R. Wang, J. Li, and R. L. Gao, “The structural force arising from magnetic interactions in polydisperse ferrofluids,” Appl. Phys. Lett. 94, 212501 (2009).
[CrossRef]

J. Li, Y. Huang, X. D. Liu, Y. Q. Lin, Q. Li, and R. L. Gao, “Coordinated chain motion resulting in intensity variation of light transmitted through ferrofluids film,” Phys. Lett. A 372, 6952–6955 (2008).
[CrossRef]

J. Li, X. D. Liu, Y. Q. Lin, Y. Huang, and L. Bai, “Relaxation behavior measuring of transmitted light through ferrofluids film,” Appl. Phys. B 82, 81–84 (2006).
[CrossRef]

J. Li, X. D. Liu, Y. Q. Lin, X. Y. Qiu, and X. J. Ma, “Field-induced transmission of light in ionic ferrofluids of tunable viscosity,” J. Phys. D 37, 3357–3360 (2004).
[CrossRef]

J. Li, B. G. Zhao, Y. Q. Lin, X. Y. Qiu, and X. J. Ma, “Transmission of light in ionic ferrofluids, J. Appl. Phys. 92, 1128–1131(2002).
[CrossRef]

Li, Q.

J. Li, Y. Huang, X. D. Liu, Y. Q. Lin, Q. Li, and R. L. Gao, “Coordinated chain motion resulting in intensity variation of light transmitted through ferrofluids film,” Phys. Lett. A 372, 6952–6955 (2008).
[CrossRef]

Lin, Y. Q.

J. Li, Y. Q. Lin, X. D. Liu, B. C. Wen, T. Z. Zhang, Q. M. Zhang, and H. Miao, “The modulation of coupling in the relaxation behavior of light transmitted through binary ferrofluids,” Opt. Commun. 283, 1182–1187 (2010).
[CrossRef]

J. Li, Y. Huang, X. D. Liu, Y. Q. Lin, Q. Li, and R. L. Gao, “Coordinated chain motion resulting in intensity variation of light transmitted through ferrofluids film,” Phys. Lett. A 372, 6952–6955 (2008).
[CrossRef]

J. Li, X. D. Liu, Y. Q. Lin, Y. Huang, and L. Bai, “Relaxation behavior measuring of transmitted light through ferrofluids film,” Appl. Phys. B 82, 81–84 (2006).
[CrossRef]

J. Li, X. D. Liu, Y. Q. Lin, X. Y. Qiu, and X. J. Ma, “Field-induced transmission of light in ionic ferrofluids of tunable viscosity,” J. Phys. D 37, 3357–3360 (2004).
[CrossRef]

J. Li, B. G. Zhao, Y. Q. Lin, X. Y. Qiu, and X. J. Ma, “Transmission of light in ionic ferrofluids, J. Appl. Phys. 92, 1128–1131(2002).
[CrossRef]

Liu, X. D.

J. Li, Y. Q. Lin, X. D. Liu, B. C. Wen, T. Z. Zhang, Q. M. Zhang, and H. Miao, “The modulation of coupling in the relaxation behavior of light transmitted through binary ferrofluids,” Opt. Commun. 283, 1182–1187 (2010).
[CrossRef]

J. Li, Y. Huang, X. D. Liu, Y. Q. Lin, Q. Li, and R. L. Gao, “Coordinated chain motion resulting in intensity variation of light transmitted through ferrofluids film,” Phys. Lett. A 372, 6952–6955 (2008).
[CrossRef]

J. Li, X. D. Liu, Y. Q. Lin, Y. Huang, and L. Bai, “Relaxation behavior measuring of transmitted light through ferrofluids film,” Appl. Phys. B 82, 81–84 (2006).
[CrossRef]

J. Li, X. D. Liu, Y. Q. Lin, X. Y. Qiu, and X. J. Ma, “Field-induced transmission of light in ionic ferrofluids of tunable viscosity,” J. Phys. D 37, 3357–3360 (2004).
[CrossRef]

Lücke, M.

B. Huke and M. Lücke, “Magnetic properties of colloidal suspensions of interacting magnetic particles,” Rep. Prog. Phys. 67, 1731–1768 (2004).
[CrossRef]

Ma, X. J.

J. Li, X. D. Liu, Y. Q. Lin, X. Y. Qiu, and X. J. Ma, “Field-induced transmission of light in ionic ferrofluids of tunable viscosity,” J. Phys. D 37, 3357–3360 (2004).
[CrossRef]

J. Li, B. G. Zhao, Y. Q. Lin, X. Y. Qiu, and X. J. Ma, “Transmission of light in ionic ferrofluids, J. Appl. Phys. 92, 1128–1131(2002).
[CrossRef]

Massart, R.

F. A. Tourinho, R. Fanck, and R. Massart, “Aqueous ferrofluid based on manganese and cobalt ferrites,” J. Mater. Sci. 25, 3249–3254 (1990).
[CrossRef]

Miao, H.

J. Li, Y. Q. Lin, X. D. Liu, B. C. Wen, T. Z. Zhang, Q. M. Zhang, and H. Miao, “The modulation of coupling in the relaxation behavior of light transmitted through binary ferrofluids,” Opt. Commun. 283, 1182–1187 (2010).
[CrossRef]

T.-Z. Zhang, J. Li, H. Miao, Q-M. Zhang, J. Fu, and B.-C. Wen, “Enhancement of the field modulation of light transmission through films of binary ferrofluids,” Phys. Rev. E 82, 021403 (2010).
[CrossRef]

Miles, J. J.

J. J. Miles, R. W. Chantrell, and M. R. Parker, “Model of magnetic-field-induced ordering in dispersions of fine paramagnetic particles,” J. Appl. Phys. 57, 4271–4273(1985).
[CrossRef]

Müller, H. W.

Z. Wang, C. Holm, and H. W. Müller, “Molecular dynamics study on the equilibrium magnetization properties and structure of ferrofluids,” Phys. Rev. E 66, 021405(2002).
[CrossRef]

Parker, M. R.

J. J. Miles, R. W. Chantrell, and M. R. Parker, “Model of magnetic-field-induced ordering in dispersions of fine paramagnetic particles,” J. Appl. Phys. 57, 4271–4273(1985).
[CrossRef]

Pyanzina, E.

C. Holm, A. Ivanov, S. Kantorovich, E. Pyanzina, and E. Reznikov, “Equilibrium properties of a bidisperse ferrofluid with chain aggregates: theory and computer simulations,” J. Phys. 18, S2737 (2006).
[CrossRef]

Qiu, X. Y.

J. Li, X. D. Liu, Y. Q. Lin, X. Y. Qiu, and X. J. Ma, “Field-induced transmission of light in ionic ferrofluids of tunable viscosity,” J. Phys. D 37, 3357–3360 (2004).
[CrossRef]

J. Li, B. G. Zhao, Y. Q. Lin, X. Y. Qiu, and X. J. Ma, “Transmission of light in ionic ferrofluids, J. Appl. Phys. 92, 1128–1131(2002).
[CrossRef]

Range, G. M.

G. M. Range and S. H. L. Klapp, “Density-functional study of model bidisperse ferrocolloids in an external field,” J. Chem. Phys. 122, 224902 (2005).
[CrossRef] [PubMed]

G. M. Range and S. H. L. Klapp, “Phase behavior of bidisperse ferrocolloids,” Phys. Rev. E 70, 061407 (2004).
[CrossRef]

G. M. Range and S. H. L. Klapp, “Demixing in simple dipolar mixtures: integral equation versus density functional results,” Phys. Rev. E 70, 031201 (2004).
[CrossRef]

Rasa, M.

M. Rasa, “Improved formulas for magneto-optical effects in ferrofluids,” J. Magn. Magn. Mater. 201, 170–173(1999).
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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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J. Li, Y. Q. Lin, X. D. Liu, B. C. Wen, T. Z. Zhang, Q. M. Zhang, and H. Miao, “The modulation of coupling in the relaxation behavior of light transmitted through binary ferrofluids,” Opt. Commun. 283, 1182–1187 (2010).
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[CrossRef]

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[CrossRef]

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[CrossRef]

T.-Z. Zhang, J. Li, H. Miao, Q-M. Zhang, J. Fu, and B.-C. Wen, “Enhancement of the field modulation of light transmission through films of binary ferrofluids,” Phys. Rev. E 82, 021403 (2010).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

T - t curve for CoFe 2 O 4 ionic ferrofluids with particle volume fraction ϕ = 0.2 % in an applied magnetic field B = 500 G . The magnetic field is applied at t = 0 .

Fig. 2
Fig. 2

Magnetization curves of CoFe 2 O 4 nanoparticles and p - MgFe 2 O 4 nanoparticles.

Fig. 3
Fig. 3

In different values of the magnetic field, the T - t curve of (a)  CoFe 2 O 4 ferrofluids with ϕ = 0.6 % and (b)  CoFe 2 O 4 p - MgFe 2 O 4 binary ferrofluids with ϕ A B = 0.6 % ( ϕ A = ϕ B = 0.3 % ) and p - MgFe 2 O 4 ferrofluid with ϕ = 0.6 % in the inset (f.v., first valley; s.v., second valley).

Fig. 4
Fig. 4

General graph of a T - t curve of oscillatory-like relaxation.

Fig. 5
Fig. 5

Scheme showing the microstructure transition and the relaxation behavior of the transmitted light in the model of a bidispersed system consisting of both chained particles and unchained particles. Both the applied magnetic field and the optical path are along the z direction. Circles with arrows represent chained particles, and dots represent unchained particles.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

T = ( I / I 0 ) / ( I / I 0 ) = I / I ,
ϕ A B = V A + V B V A + V B + V C = ϕ A + ϕ B ϕ A = V A V A + V B + V C , ϕ B = V B V A + V B + V C ,
λ i j = μ 0 m i m j 2 π r i j 3 k B T * , i , j = A , B ,
T A B = I A B ' / I 0 I A B / I 0 = T A T B ( 1 + I B / I A T A + I B / I A · T B ) , T A = I A / I A , T B = I B / I B ,
T A B = T A ( 1 + I B / I A ) T A / T B + I B / I A T A ( ( I B / I A ) 1 + 1 ) .
T A B = T B ( 1 + I B / I A ) 1 + I B / I A · T B / T A T B ( 1 + I B / I A ) ,

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