Dipole moments of gyricon balls

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Abstract

Gyricon balls consist of two hemispheres of different colors and different electrical properties. When immersed in a liquid and exposed to a uniform electrical field, they rotate so that the ball is aligned along the polar axis. The dipole moment of the ball is modeled in terms of a uniform surface charge distribution on each hemisphere, and the predicted motion is obtained from a balance of electrical and viscous torques. The motion shows a long and variable initial decay, followed by a relatively rapid turning and then a long final delay. Measurements of the rotation between parallel electrodes lead to a dipole moment and surface charge density for the balls, with typical bipolar surface charge densities in the range of 0.1–0.3μC/m2.

Introduction

“Electric paper” is the name given to a novel class of electronic display which offers many of the advantages of paper including thinness, light weight, minimal power consumption, non-volatile memory, and mechanical flexibility. A leading candidate for electric paper displays is the gyricon [1], which consists of an array of hemispherically bichromal balls, in a thin, transparent sheet. A microscope photograph of a gyricon display is shown in Fig. 1. The photograph shows the border between a white and a black section of the image, as seen from the display side of the sheet. The left side of the image shows a large number of balls, most of which present their white hemisphere to the viewer. On the right, the balls have rotated to present their black side. The rotation of the balls is controlled by applying a voltage of either positive or negative polarity across the sheet that contains the balls. Typically, the color reversal is complete in a few tens of milliseconds.

Although the figure does not show it, each of the balls is contained in its own spherical cavity, which is slightly larger than the ball. The cavity is formed by casting the balls in an elastomer, and then swelling the elastomer by adding solvent, which then seeps into the cavities [1].

Color reversal usually involves both rotation and translation of the balls in the cavity. These two types of motion could be caused by an independent combination of monopolar and dipolar charge distributions on the balls, but they could also be caused by viscous interactions with the adjacent cavity walls with either a simple monopole or dipole. The difference is very important for design of the balls and cavities, since rotation may be very slow or incomplete if the translation brings the ball close to the wall very quickly. At the same time, a close approach to the wall helps to stabilize the image and prevent it from becoming blurred by shaking or external electric fields. Thus, knowledge of the charge state on the balls is crucial in designing a display which operates quickly and reliably.

The purpose of the work described here was to determine the dipole response of a gyricon ball, and to provide a method for measuring its dipole moment. This cannot be done directly in the display, because each ball is enclosed by a cavity which is only 10–40% larger than the ball itself. Viscous effects will cause the translation and rotation of the ball to become intertwined so that, for example, even a pure monopole will tend to “roll” down one side of the cavity, thus behaving as if it had a dipole.

An isolated ball far from any walls will not show this effect, so that its dipole moment can be measured independently. Some experiments have been carried out on a freely falling ball [2] but electric field levels were not as high as those that occur in the gyricon display. These fields may easily exceed 1V/μm, corresponding to tens of thousands of volts if the apparatus is on the order of centimeters. Thus, a simple scaling of the geometry poses practical problems in duplicating the field conditions in the display itself.

This paper describes a third approach to determination of the monopole and dipole moments of the gyricon ball. The ball is confined between two wide horizontal electrodes that are separated by only a few ball diameters. This allows the use of relatively low voltages, but does not invoke the viscous coupling between rotation and translation that is inherent in the presence of side walls.

Section snippets

Electrical torque

The gyricon relies on the difference in electrical properties of the two sides of the ball to generate an electrostatic torque in the presence of an applied electric field. This torque is given in terms of the dipole moment of the ball asτ=p×E,where p is the dipole moment and E is the applied field. In both the gyricon display and in the experiments reported here, the electric field is assumed to be uniform in the vertical direction, so the vector torque equation reduces to a scalar formτ=pEsin

Apparatus and methods

In the experiment, bichromal balls were placed between two horizontal electrodes in an insulating liquid, and a voltage applied. The balls moved in response to the voltage, rotating as they crossed the gap from one electrode to the other. The liquid used in these experiments was Isopar L with a mass density of 0.767mg/m3, and a dynamic viscosity of 1.62mPa s.

Bipolar charge distribution

The rotation rate is not uniform because the torque depends on the angle between the electric field and the dipole moment, which is rotating with the ball. Initially, the dipole is aligned, the torque is weak and the angular velocity is low. As the ball rotates, the angular velocity increases to a broad maximum when it is halfway around, and then slows again as it aligns in the opposite direction.

This initial delay gives no information on the dipole moment, so we chose to measure the time

Discussion

These results show that gyricon balls possess a dipole moment that causes them to turn in an electric field regardless of viscous-induced torques related to the monopole. The rotation observed in the experiments is fast enough to turn the balls in about 50ms, which is on the order of switching times observed in gyricon displays. Thus, it appears that the basic operating mode of the gyricon is the permanent dipole moment of the bichromal balls.

This does not preclude the existence of rotation

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