Physical description of a viscoelastically loaded AT-cut quartz resonator

Abstract

In this work, the electrical admittance of this plane-parallel resonator loaded on one face with a viscoelastic medium is described directly in terms of the physical properties of the system. This description is based on the detailed matrix equations for the piezoelectric quartz and includes the piezoelectric effect of the quartz transducer and the shear modulus and viscosity of the overlayer. This physically based analysis has proven invaluable in relating the admittance behavior directly to the materials’ properties. Initial comparisons of the theory with experimental data are given, including the appearance of even harmonics as described by Benes [E. Benes, J. Appl. Phys. 56, 608 (1984)] for the asymmetrically loaded resonator. Additionally, measurements on a series of perfluoropolyether fluids of differing molecular weights indicate that they cannot be described as simple viscous liquids in the MHz range. The assignment of a frequency-dependent viscosity with a relaxation time proportional to the molecular weight resolves some of the discrepancies. Because this study relates the complete admittance spectrum of the loaded resonator to the overlayer material properties, it opens the possibility of studying more than just the changes in resonant frequency. A detailed analysis of the resonance spectrum using an impedance analyzer would provide data which can be fit to the material’s properties and would be particularly helpful with viscoelastic media.

Thermophysical Properties of Penetrants in Polymers via a Piezoelectric Quartz Crystal Microbalance

“…The oscillation of quartz crystals in liquids is contrary to the belief that the viscous losses to the liquid would suppress the oscillation of the crystals (Reed et al, 1990). When the quartz crystals oscillate in a liquid medium, the frequency is found to be dependent on the viscosity and density of the liquid in contact with the crystal,…”

Effect of a Non-Newtonian Load on SignatureS2for Quartz Crystal Microbalance Measurements

“…From 10% to 70%, it increased by 10% in every 20∼25 minutes [41]. At the fundamental frequency, 5 MHz, an AT-cut piezoelectric crystal was excited at the 3rd, 5th, 7th, 9th, and 11th overtones (15,25,35,45, and 55 MHz in order) and Δ and Δ were measured. After the initial measurement in air, 10 mM Tris buffer with 100 mM NaCL and pH 7.4 was injected for the initial stabilization of the QCM signals.…”

“…An early description of the viscoelastically coupled QCM resonator gave an example of measured changes in the frequency and resistance of the liquid-loaded QCM [2,15]. The Sandia group provided a complete description of the QCM's theoretical and experimental responses [16,17], with results for water-glycerol mixtures [16] and water and waterglycerol mixtures [17].…”

A wireless low-range pressure sensor based on P(VDF-TrFE) piezoelectric resonance

“…The piezoelectric behavior can be characterized by the equivalent circuit of the Butterworth-Van Dyke (BVD) model [17][18][19][20][21][22][23][24][25][26] in Figure 2. C 1 , L 1 and R 1 known as the "the mechanical arm", describe the mechanical vibrations resulting from the piezoelectric effect with a finite quality factor.…”