5D-3 More Accurate Simulation of Quartz Crystal Microbalance (QCM) Response to Viscoelastic Loading

The applications of QCMs were extended to liquids last years in the context of growing interest in monitoring biological systems that exhibit viscoelastic behavior. A special formula derived in 1985 by Kanazawa and Gordon [1] for the change in oscillation frequency of the crystal due to liquid loading is still widely in use because of its established applicability to aqueous systems. Our studies of monitoring the blood coagulation process [2] and the desirable extraction of related viscoelastic properties from the electrical admittance curves vs. frequency of QCM suggested re-examining the model and its issues. In one-dimensional approach, the frequency dependent electrical admittance Y of a QCM loaded by any viscoelastic stack is written down in terms of static capacity, piezoelectric coupling factor K², and the ratio of acoustic impedances Z_L of load and Z_Q of quartz, respectively. According to that model, at given quartz data real and imaginary part of complex acoustic impedance of load Z_L can be determined separately from resonant and antiresonant frequencies (maximum and minimum of |Y|). For the usual case of small frequency changes under the influence of both piezoelectricity and liquid loading, explicit expressions were derived for the resonant and the antiresonant frequencies, and inversely, for real and imaginary part of acoustic load impedance Z_L. These expressions yield also formula [1] as a particular case Deviations of resonant frequency shift from formula [1] have been confirmed experimentally by viscosity measurements of a set of water-glycerol mixtures using QCM and a standard method as a reference. The derived expressions show that under certain conditions of viscoelastic loading the resonant and antiresonant frequencies can shift even with opposite sign.