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Schematic representation of (a) the experimental optical microscopy setup and set of Helmholtz coils used to observe the one-dimensional rotation of a single Janus particle and (b) the concept underlying the one-dimensional rotation of a magnetic microsphere, where the particle rotates around a chosen and fixed axis determined by the orientation of the applied magnetic field.
(a) Bright field microscopy images of one-dimensional Brownian rotation of a single diameter microsphere magnetized through the equator and rotating around a 1.0 mT fixed axis that is parallel to the optical axis (perpendicular to the imaging plane). The images are shown for every 100th frame (2.2 s intervals) at a frame rate of 45 frames per second, where the image size is approximately . The bright spot in the image is caused by transmitted light passing through the noncoated hemisphere of the microsphere that does not have a thin nickel film (a similar particle is shown in a real-time video online). (b) Angular orientation in time for the particle shown in part (a) and (c) the resulting angular step displacement probability distribution function: circles are experimental values and the line is a Gaussian fit (enhanced online). [URL: http://dx.doi.org/10.1063/1.3485296.1]10.1063/1.3485296.1
Microscopy images of a four particle aggregate with (a) no applied magnetic field and (b) with a 1.0 mT field applied along the optical axis (in the direction perpendicular to the imaging plane), where the scale bar is . Schematic illustrations of the same aggregate oriented on the glass-fluid interface with (c) and (e) “field off” (gravitational forces determine the axis of free rotation) and (d) and (f) “field on” (magnetic forces determine the axis of free rotation). (g) Probability distribution function for the aggregate shown in (a) and (b), where the open circles denote data for “field on,” the closed circles denote data for “field off,” and the lines are Gaussian fits. The widths of the Gaussian fits are 0.98° and 2.0°, which give diffusion coefficients of and , respectively, using the described probability distribution equation.
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