An extended Butterworth-Van Dyke model for quartz crystal microbalance applications in viscoelastic fluid media

An extended Butterworth-Van Dyke (EBVD) model with frequency-independent pa rameters for the characterization of a resonant compound formed by a quartz crystal in contact with a finite viscoelastic layer contacting a semi-infi nite viscoelastic. medium is extracted by analysis of the lumped element mo del. The formulation of the EBVD model is compared with the complete expres sion of the electrical admittance of the loaded quartz derived from the tra nsmission line model (TLM). Relative deviations between them do not exceed 3% around 1% bandwidth near resonance. An extended Martin & Granstaff's mod el and an explicit expression for the frequency shift that supposes an exte nsion of Kanazawa's model for viscoelastic media are obtained. An analysis of the errors associated with the extraction of shear parameters of the coa ting for different materials prove that, to obtain an error less than 5% in the shear parameters determination, the viscoelastic contribution, defined as the relative error in the thickness computed from the frequency shift b y Sauerbrey equation, must be greater than a limit that depends on Q, which is defined as the ratio of the shear storage modulus (G ') to shear loss m odulus (G "). In the materials studied, polymers in the transition range or in the rubbery state with Q = 1 and 10, the viscoelastic contribution must be higher than 15% and 50%, respectively, for a 5% limit error in the shea r parameters extraction. A criterion for a practical determination of the a ppropriate viscoelastic regimes is indicated.