Theory of the dynamic magnetic susceptibility of ferrofluids

The dynamic magnetic response of a ferrofluid to a weak ac magnetic field is studied using statistical mechanical theory and Brownian dynamics simulations, taking account of dipole-dipole interactions between the constituent ferromagnetic colloidal particles, and the presence of a range of particle sizes. The effects of interactions and polydispersity on the frequency dispersion are shown to be substantial: the amplitude of the response can be about twice that of a noninteracting system; the frequency for peak power loss can be reduced by about one half; and polydispersity effects can even change the qualitative appearance of the susceptibility spectrum.

Figure 1

Results for monodisperse ferrofluids with $\lambda =1$: (a) $\chi \left(\omega \right)$ for a system with $\phi =0.314$; (b) ${\omega }_0$; (c) $a$; (d) $b$. The dotted-dashed red lines are from Debye theory, the dashed green lines are from MMF theory, and the solid blue lines are from MW theory. The points are from BD simulations [15]. In (a), solid symbols are the real part, and open symbols are the imaginary part.

Figure 2

$\chi \left(\omega \right)$ for a bidisperse ferrofluid (system A in Table 1): (a) ${\chi }_{\mathrm{L}}=0.80$; (b) ${\chi }_{\mathrm{L}}=1.60$; (c) ${\chi }_{\mathrm{L}}=2.40$; (d) ${\chi }_{\mathrm{L}}=3.20$. The dotted-dashed red lines are from Debye theory, the dashed green lines are from MMF theory, and the solid blue lines are from MW theory. The points are from BD simulations: solid symbols are the real part; open symbols are the imaginary part.

Figure 3

$\mathrm{\Delta }\varphi$ for a bidisperse ferrofluid (system A in Table 1): (a) ${\chi }_{\mathrm{L}}=0.80$; (b) ${\chi }_{\mathrm{L}}=1.60$; (c) ${\chi }_{\mathrm{L}}=2.40$; (d) ${\chi }_{\mathrm{L}}=3.20$. The dotted-dashed red lines are from Debye theory, the dashed green lines are from MMF theory, and the solid blue lines are from MW theory. The points are from BD simulations.

Figure 4

Cole-Cole plot for a bidisperse ferrofluid (system A in Table 1): (a) ${\chi }_{\mathrm{L}}=0.80$; (b) ${\chi }_{\mathrm{L}}=1.60$; (c) ${\chi }_{\mathrm{L}}=2.40$; (d) ${\chi }_{\mathrm{L}}=3.20$. The dotted-dashed red lines are from Debye theory, the dashed green lines are from MMF theory, and the solid blue lines are from MW theory. The points are from BD simulations.

Figure 5

Magnetic susceptibility spectrum for a bidisperse ferrofluid (system B in Table 1): (a) real part; (b) imaginary part; (c) phase lag; (d) Cole-Cole plot. The dotted-dashed red lines are from Debye theory, the dashed green lines are from MMF theory, and the solid blue lines are from MW theory. The points are from BD simulations: open symbols are for a noninteracting (NI) system; solid symbols are for an interacting system. In (a) and (b), dotted red lines show the individual small-particle (high-frequency) and large-particle (low-frequency) contributions to the Debye theory.