Theoretical analysis of the piezoelectric crystal/liquid interface for liquid-phase-based sensor applications

A general theory of the interaction of acoustic waves at the interface between a piezoelectric crystal and a viscous conductive liquid is developed. This analysis includes mass loading, viscous entrainment and acousto-ionic interaction between the electric field associated with the acoustic waves and the ions and dipoles in the solution. A detailed description of the acousto-ionic interaction is given. The appropriate boundary conditions at the interfaces are defined. General exact numerical solutions for the crystal/liquid interaction problem are proposed. For certain crystal orientations and shear horizontal surface waves, analytical closed form expressions for the change in wave velocity (thus the device frequency shift) and the attenuation in terms of material (liquid and crystal) parameters are obtained using the Green\u27s function formulation and an analytical expression for the effective permittivity function. For RBW devices, the reflection coefficients (amplitude, energy and phase shift) are obtained in terms of liquid parameters. The response and sensitivity of actual devices are discussed in terms of the number of reflections. A perturbation theory is used to obtain analytical expressions for the velocity change and attenuation for the case of dilute conductive solutions for acoustic plate modes (APM). The piezoelectric crystals that are studied include Cadmium Sulfide, $\alpha$-quartz and Lithium Niobate. The liquids investigated are viscous and/or conductive solutions. The effects of liquid properties such as conductivity, permittivity, viscosity, and density on the wave propagation (device frequency shift and/or energy loss) are studied to determine the characteristics of sensor devices. The effects of liquid shear relaxation time and dielectric relaxation are found to set a detection limit on the range of measurable viscosity and conductivity respectively. In general, a trade-off must be made among sensitivity, detection range and device loss. The developed theories which compare well with existing experimental data can be used effectively in the design and analysis of acoustic wave device sensors for liquid environments. (Abstract shortened with permission of author.