Crystal impedance measurements

In the event that the film is not rigid, the EQCM response is a function of both the film mass and its rheological characteristics. Application of the Sauerbrey equation under these circumstances is inappropriate it underestimates the mass change, to an extent that is dependent on the viscoelastic properties of the film. Under these circumstances, there are two questions to be addressed first, how does one diagnose film (non-)rigidity and, second, how does one interpret responses from a non-rigid film The answers to both questions can be found from crystal impedance measurements. This is a technique in which one determines the admittance (or impedance) of the loaded crystal as a function of frequency in the vicinity of resonance. Effectively, one determines the shape (width and height) and position (on the frequency axis) of the resonance, rather than just its position (as in the simple EQCM technique). 

Bund A, Schwitzgebel G (2000) Investigations on metal depositions and dissolutions with an improved EQCMB based on quartz crystal impedance measurements. Electrochim Acta 45 3703—3710... 

Repeated visual examination and impedence measurements indicated no degradation of the electrode over the course of the experiments (3 weeks). During this time, the selected electrodes were stored in the inert-atmosphere glove box in which the electrochemical experiments were performed. No electrode pretreatment procedures were used and the crystals were not recleaved. 

The crystal impedance is capacitive at frequencies below the fundamental wave and inductive at frequencies above the resonance. This information is useful if the resonance frequency of a crystal is unknown. A brief frequency sweep is carried out until the phase comparator changes over and thus marks the resonance. For AT quartzes we know that the lowest usable frequency is the fundamental wave. The anharmonics are slightly above that. This information is not only important for the beginning, but also in the rare case that the instrument loses track of the fundamental wave. Once the frequency spectrum of the crystal is determined, the instrument must track the shift in resonance frequency, constantly carry out frequency measurements and then convert them into thickness. 

More recently the treatment was extended to piezoelectric devices in contact with viscoelastic media (i.e., liquids and polymers). It was then realised that if the deposited mass was not rigidly coupled to the oscillating quartz crystal, separation of inertial mass and energy losses was not possible with the measurement of the resonant frequency alone. Quartz crystal impedance in the acoustic frequencies was introduced in order to study mass and viscoelastic changes and a full electrical characterization of the crystal behaviour near resonance was employed. 

Hillman et al. measured the quartz crystal impedance to determine changes in rigidity, swelling and ionic exchange in conducting polymer films [57, 58] and have also used dynamic quartz crystal impedance of modified electrodes during film growth and redox conversion [57] by qualitative analysis of the acoustic admittance-frequency peak width. 

Figure 13.7 shows a set of crystal impedance spectra as a function of time (coverage) during electroprecipitation of a PVF film. These measurements were made using a network analyzer in reflectance mode, as described previously [41]. For the long deposition times employed here, the film is relatively thick. Furthermore, there is appreciable solvent incorporation. These two factors mean that there will be considerable shear deformation of the film as a result of crystal oscillation. 

Through the combination of SPR with a - poten-tiostat, SPR can be measured in-situ during an electrochemical experiment (electrochemical surface plasmon resonace, ESPR). Respective setups are nowadays commercially available. Voltammetric methods, coupled to SPR, are advantageously utilized for investigations of - conducting polymers, thin film formation under influence of electric fields or potential variation, as well as - electropolymerization, or for development of -> biosensors and - modified electrodes. Further in-situ techniques, successfully used with SPR, include electrochemical - impedance measurements and -+ electrochemical quartz crystal microbalance. 

Depending upon the products, there might be very narrow margins to that exercise and the endpoint temperatures, velocities of cooling, and rewarming need to be known very accurately by previous laboratory determinations such as differential thermal analysis (DTA) or differential scanning calorimetry (DSC), low temperature electric impedance measurements, velocity of crystallization in the supercooled state, etc. 

Sabot, A and S. Krause (2002). Simultaneous quartz crystal microbalance impedance and electrochemical impedance measurements investigation into the degradation of thin polymer films. Analytical Chemistry 7 (14), 3304-3311. 

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