Transient studies with the EQCM

Potential or current step transients seem to be more appropriate for kinetic studies since the initial and boundary conditions of the experiment are better defined unlike linear scan or cyclic voltammetry where time and potential are convoluted. The time resolution of the EQCM is limited in this case by the measurement of the resonant frequency. There are different methods to measure the crystal resonance frequency. In the simplest approach, the Miller oscillator or similar circuit tuned to one of the crystal resonance frequencies may be used and the frequency can be measured directly with a frequency meter [18]. This simple experimental device can be easily built, but has a poor resolution which is inversely proportional to the measurement time for instance for an accuracy of 1 Hz, a gate time of 1 second is needed, and for 0.1 Hz the measurement lasts as long as 10 seconds minimum to achieve the same accuracy. An advantage of the Miller oscillator is that the crystal electrode is grounded and can be used as the working electrode with a hard ground potentiostat with no conflict between the high ac circuit and the dc electrochemical circuit. 

Modern frequency meters allow fast measurements with good resolution, i.e., 60 ms (Philips PM6654) or 100 ms (HP5384) for 0.1 Hz resolution. The ultimate resolution of the QCM is limited, however, to miliseconds by the time required in equilibrating the crystal with the deposited mass, which is determined by the operating frequency and the quality factor of the QCM [3]. 

In order to increase the resolution, a heterodyne circuit may be used, which consists of two oscillators the quartz crystal microbalance and a second reference crystal. The frequency difference in the kilohertz range can be measured with a universal counter and the same resolution and gate time discussed above are valid however if the period of the differential wave is measured, the accuracy can be highly increased and a 1 Hz resolution is easily attainable for a 1 ms gate time. This approach has been used by Sheng-li Chen et al. [19] to measure the kinetics of silver oxide formation on polycrystalline silver. These authors reported a resolution of 0.1 Hz in 1 ms which corresponds to 0.44 ng cm 2 in the mass sensitivity. 

Bruckenstein [2] introduced a digital oscillator which comprised two TTL inverters with a positive feedback through the crystal. The circuit is very stable and can be interfaced directly with TTL or CMOS logic obtain- 

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