DRUMHEAD VIBRATIONS OF A
THIN LIQUID CRYSTAL FILM

An experiment to measure the surface tension of a free-standing liquid crystal film.

In this experiment a thin film of liquid crystal is vibrated by applying a rapidly alternating voltage. The film responds with more or less vibration (resembling that of a drumhead), depending on its mass, surface tension, and the frequency of the driving voltage. The vibrations of a circular membrane, whether a drumhead or a thin liquid crystal film, are described by the Bessel function. Knowing the mass of the film, the zeros of the Bessel function determine the frequencies at which the film will resonate. By measuring the resonant frequencies of the film, its surface tension can then be calculated, usually to an accuracy of a few percent.

Due to the dielectric properties of liquid crystals, an external electric field will induce a polarization, which tends to pull the film into the field. This is effected by placing a metal pin very near (about 10mm) beneath the film and applying a voltage to it. The metal plate holding the film is at ground so the field produced has a strong gradient, exerting a force on the liquid crystal film. Oscillation of the pin's voltage will then vibrate the film at the same frequency.

Vibrations of the film's surface are detected by bouncing a laser off it and measuring variations in the position of the reflected beam (see figure). The incoming beam is focussed so it makes a small spot on the film at a point which is likely to undergo large changes in slope (for example, not the film's center). The reflected beam is then directed to a split photodetector. Subtracting the intensities from each side of the detector yields a strong signal (about 1mV) that oscillates with the film. The magnitude of the oscillation is recorded along with the driving frequency. A typical spectrum of vibration amplitude vs. driving frequency is shown at the bottom of the page.

The film's mass is calculated from its known density, the film area (p /4 cm²), and a measurement of its thickness. The film's thickness is obtained from an estimate of the thickness of a layer and a measurement of its optical reflectivity, which can accurately give the number of molecular layers. Measuring the optical reflectivity involves the use of another laser beam reflected from the film.

The film's local environment is carefully controlled within the sealed can seen in the apparatus photo. The film plate is surrounded laterally by a current-heated wall, holding the film at its operating temperature. Since the surface tension of the liquid crystal depends critically on its phase, the temperature must be controlled and a separate measurement of the film plate is taken by a thermocouple. The vibrational response of the film is also sensitive to the gas surrounding it. To prevent damping of the oscillation by coupling to the gas, the pressure in the can is reduced to a few hundred millitorr in a helium environment.

Current work with the drumhead apparatus involves tracking a resonance peak as the film's temperature is slowly changed, giving a relationship between temperature and surface tension.