An impedance-measurement setup optimized for measuring relaxations of glass-forming liquids

An electronics system has been assembled to measure frequency-dependent response functions of glass-forming liquids in the extremely viscous state approaching the glass transition. We determine response functions such as dielectric permittivity and shear and bulk moduli by measuring electrical impedances of liquid-filled transducers, and this technique requires frequency generators capable of producing signals that are reproducible over the span of several days or even several weeks. To this end, we have constructed a frequency generator that produces low-frequency (1 mHz-100 Hz) sinusoidal signals with voltages that are reproducible within 10 ppm. Two factors that partly account for this precision are that signals originate from voltages stored in a look-up table and that only coil-less filters are used in this unit, which significantly reduces fluctuations of output caused by changes of temperatures of circuits. This generator also includes a special triggering facility that makes it possible to measure up to 512 voltages per cycle that are spaced apart at uniform phase intervals. Fourier transformations of such data yield precise determinations of complex amplitudes of voltages and currents applied to a transducer, which ultimately allows us to determine electrical impedances of transducers with a reproducibility error that is only a few parts per hundred thousand. This equipment is used in tandem with a commercial LCR meter and/or impedance analyzer that give(s) impedance measurements at higher frequencies, up to 1 MHz. The experimental setup allows measurements of the transducer impedance over nine decades of frequency within a single run.