Magnetic-field-induced optical anisotropy in ferrofluids: A time-dependent light-scattering investigation

We report an experimental investigation of time dependent anisotropic light scattering by an aqueous suspension of tetramethyl ammonium hydroxide coated ${\mathrm{Fe}}_3{\mathrm{O}}_4$ nanoparticles $(\sim 6\mathrm{nm})$ under the ON-OFF transient of an external dc magnetic field. The study employs the synchronized recording and measurement of the two magnetic-field-induced light-scattering patterns produced by two identical orthogonal He-Ne laser beams passing through the ferrofluid sample and propagating parallel and perpendicular to the applied field, respectively. From these patterns, we extract the time dependence of the induced optical anisotropy, which provides a measure of the characteristic time scale and kinematic response for field-induced structure formation in the sample. We propose that the time evolution of the scattering patterns, which is very fast at short times and significantly slower at long times, can be explained using a model based on a two-stage chain formation and coarsening processes.

Figure 1

(Color online) (a) Schematic of the experimental setup for synchronously recording the time-dependent light scattering patterns produced by two orthogonal light beams through a ferrofluid sample placed in a uniform magnetic field. (b) The 3D geometry of the experiment. The scattered intensity on each screen $I\left(\vec{h}\right)$ or $I\left({\vec{h}}^{\prime }\right)$ is a function of the corresponding scattering vector $\vec{h}$ or ${\vec{h}}^{\prime }$, where $\vec{h}=(h_x,h_y)=h(\cos \alpha ,\sin \alpha )$ and ${\vec{h}}^{\prime }=(h_x^{\prime },h_y^{\prime })=h^{\prime }(\cos {\alpha }^{\prime },\sin {\alpha }^{\prime })$.

Figure 2

(Color online) Light scattering patterns from a ${\mathrm{Fe}}_3{\mathrm{O}}_4$ ferrofluid sample and the corresponding surface plots of the scattered intensity at representative instants of time for incident light propagating perpendicular to the applied field (i.e., on the ${\vec{k}}_i\perp \vec{B}$ screen). The sample had no prior history in the magnetic field. The magnetic field was turned on at $t=0$, and kept at a steady dc value of $400\mathrm{G}$ throughout the entire experiment.

Figure 3

(Color online) Light scattering patterns from a ${\mathrm{Fe}}_3{\mathrm{O}}_4$ ferrofluid sample and the corresponding surface plots of the scattered intensity at representative instants of time for incident light propagating parallel to the applied field (i.e., on the ${\vec{k}}_i\parallel \vec{B}$ screen). The sample had no prior history in the magnetic field. The magnetic field was turned on at $t=0$, and kept at a steady dc value of $400\mathrm{G}$ throughout the entire experiment

Figure 4

(Color online) (a) The angular dependence of the scattered intensity on the ${\vec{k}}_i\perp \vec{B}$ screen, at $t=30\mathrm{s}$ for various values of the scattering vector h; from top curve to bottom curve: $h=20\mathrm{mm}$, $h=40\mathrm{mm}$, $h=60\mathrm{mm}$, $h=80\mathrm{mm}$, $h=100\mathrm{mm}$. (b) The angular dependence of the scattered intensity on the ${\vec{k}}_i\perp \vec{B}$ screen for a scattering vector $h=60\mathrm{mm}$ at several instants of time; from top curve to bottom curve: $t=60\min$, $t=30\min$, $t=60\mathrm{s}$, $t=30\mathrm{s}$, $t=20\mathrm{s}$, $t=10\mathrm{s}$, $t=0\mathrm{s}$.

Figure 5

(Color online) The time dependence of the scattering anisotropy parameter $A$ defined in Eq. (4), corresponding to several values of the scattering vector $h$. From top curve to bottom curve: $h=100\mathrm{mm}$, $h=80\mathrm{mm}$, $h=60\mathrm{mm}$, $h=40\mathrm{mm}$, and $h=20\mathrm{mm}$. One can identify a very fast evolution shortly after the application of the magnetic field (see the inset), and a significantly slower process at longer times.

Figure 6

(Color online) The normalized intensity of the forward scattered light $(h=0)$ for the ${\vec{k}}_i\parallel \vec{B}$ direction as a function of time at several values of the applied magnetic field.

Figure 7

(Color online) The dependence of the characteristic time ${\tau }_0$ to zero forward scattered intensity in the ${\vec{k}}_i\parallel \vec{B}$ direction on the magnitude of the applied magnetic field. The best fit line reveals an approximate inverse dependence of ${\tau }_0$ with B. The inset shows a blow up of the normalized forward scattered intensity at short times.

Figure 8

Schematic of the proposed nanoparticles aggregation patterns as viewed by a light beam propagating along the field lines $({\vec{k}}_i\parallel \vec{B})$ and perpendicular to the field lines $({\vec{k}}_i\perp \vec{B})$. A rough time correspondence with the patterns in Figs. 2, 3 is included.