Love Wave Sensor Based on PMMA/ZnO/Glass Structure for Liquids Sensing ^†

Abstract

PMMA/ZnO/glass structure was investigated to enhance Love mode sensor sentivities. The phase velocities and the attenuation of the acoustic wave propagating along the PMMA/30° tilted c-axis ZnO/glass structure contacting a viscous non-conductive liquid were calculated for different PMMA (Polymethyl methacrylate) and ZnO guiding layer thicknesses, added mass thicknesses, and liquid viscosity and density. The sensor velocity and attenuation sensitivities were also calculated for different environmental parameters. The resulted sensitivities to liquid viscosity and added mass were optimized by adjusting the ZnO and PMMA guiding layer thickness corresponding to a sensitivity peak. The present analysis is of importance in manufacturing and applications of the PMMA-ZnO-glass structure Love wave sensors for the detection of liquids properties, such as viscosity, density and mass anchored to the sensor surface.

1. Introduction

The propagation of Love modes along 30° tilted c-axis ZnO/glass-based structures has been modeled and analysed aimed to the design of a sensor able to operate in liquid environment [1]. The sensor velocity and attenuation sensitivities to the changes of liquid viscosity and mass loading were calculated for different ZnO layer thicknesses and the peak sensitivity was achieved at the ZnO thickness to/wavelength ratio h/λ = 0.05, with electromechanical coupling coefficient is K² around 0.2% for substrate-transducer-piezolectric film (STF) configuration. K² is highest at h/λ = 0.3 but the sensitivies will be reduced significantly. Ideally, the sensor should have higher sensitivities and K².

The shear velocity of guiding layer must be lower than the substrate to satisfy the condition of existence of love wave. The higher ratio of shear wave velocity, or density, or both between substrate and the guiding layer material, the higher the maximum sensitivity [2]. Polymer material such as polymethyl-methacrylate (PMMA) has been used for Love wave guiding layer due to its low mass density and shear velocity [3]. However, it has high acoustic damping loss due to viscoelastic properties of PMMA. Double guiding layer of PMMA and elastic material such as SiO2 was reported to improve sensitivities without excessive increase in propagation loss [4]. Harding and Du used SiO2 and PMMA as double guiding layer with Quartz piezoelectric substrate. They achieved the highest mass loading sensitivity of 52 m²·kg⁻¹, which is higher than SiO2 (38 m²·kg⁻¹) and PMMA (31 m²·kg⁻¹) single guiding layer mass loading sensitivities.

In this paper, we theoretically investigate the performances of a PMMA/30° tilted c-axis ZnO/glass Love wave sensor for liquid sensings. The organization of the present article begins with wave equations of Love wave when a viscous Newtonian liquid is introduced in contacts with the guiding layer free surface, and a complex wave velocity is defined for the four layers system(substrate-guiding layer 1-guiding layer 2-liquid). The velocity and attenuation sensitivities to viscosity and to an added mass are then calculated in a viscous liquid environment. The aim of the present theoretical calculations is to investigate the influence of the addition of PMMA layer on ZnO/Glass Love wave sensor to obtain a high sensistivity, high K² love wave sensor.

2. Love Wave Sensors in PMMA-ZnO-Glass Layered Structures for Application in Liquid Environments: Statement of the Problem and Basic Equations

The 30° tilted ZnO coordinate system and the PMMA/ZnO/glass layered structure here studied are illustrated in Figure 1a,b. The substrate, that occupies the half-space x₂ > 0, is assumed to be an isotropic dielectric elastic medium, glass; the guiding layer 1 is assumed to be a ZnO film with the c-axis tilted 30°. The ZnO layer was considered isotropic but its elastic constants were considered numerically equal to the stiffened elastic constants of the 30° tilted piezoelectric counterpart; the guiding layer 2 PMMA is in contact with the viscous liquid half-space. The wave propagation direction is x₁ and no variation of the displacement components in the x₃ direction is assumed. The x₂ = 0 plane is the interface between the substrate and guiding layer 1, the x₂ = −h_gl1 and x₂ = −h_gl2 planes are the guiding layer 1-guiding layer 2 and guiding layer 2-liquid interfaces.

The equations of motion for the four media are the following:

$${\rho }_{sub}\frac{{\partial }^2{u}_3^{sub}}{\partial t^2}=c_{44}^{sub}\left(\frac{{\partial }^2}{\partial x_1^2}+\frac{{\partial }^2}{\partial x_2^2}\right)u_3^{sub}\mathrm{for}{\mathrm{x}}_2\text{ > }0$$

(1)

$${\rho }_{gl1}\frac{{\partial }^2{u}_3^{gl1}}{\partial t^2}=\overline{c_{44}^{gl1}}\left(\frac{{\partial }^2}{\partial x_1^2}+\frac{{\partial }^2}{\partial x_2^2}\right)u_3^{gl1}\mathrm{for}0\text{ < }{\mathrm{x}}_2\text{ <}-\mathrm{h}{\mathrm{gl}}_1$$

(2)

$${\rho }_{gl2}\frac{{\partial }^2{u}_3^{am}}{\partial t^2}=c_{44}^{gl2}\left(\frac{{\partial }^2}{\partial x_1^2}+\frac{{\partial }^2}{\partial x_2^2}\right)u_3^{gl2}\mathrm{for}-\mathrm{h}{\mathrm{gl}}_1\text{ < }{\mathrm{x}}_2\text{ <}-\mathrm{h}{\mathrm{gl}}_2$$

(3)

$$\frac{\partial v_3}{\partial t}=\frac{}{{\rho }_l}\left(\frac{{\partial }^2}{\partial x_1^2}+\frac{{\partial }^2}{\partial x_2^2}\right)v_3\mathrm{for}{\mathrm{x}}_2\text{ <}-(\mathrm{h}{\mathrm{gl}}_1+\mathrm{h}{\mathrm{gl}}_2)$$

(4)

The assumed solutions to the Equations (1)–(4) are the following:

$$\begin{gathered} u_3^{substrate}=\left[U_{sub}^0·e^{-q{x}_2}\right]·e^{j\left(k{x}_1-\omega t\right)} \\ {u}_3^{gl1}=\left[U_{gl1}^1·cos\left(b{x}_2\right)+U_{gl1}^2·\sin \left(b{x}_2\right)\right]·e^{j\left(k{x}_1-\omega t\right)} \\ {u}_3^{gl2}=\left[U_{gl2}^1·cos\left(p{x}_2\right)+U_{gl2}^2·\sin \left(p{x}_2\right)\right]·e^{j\left(k{x}_1-\omega t\right)} \\ {u}_3^{liquid}=\left[U_{liq}^1·e^{{\mathsf{\lambda }}_1{x}_2}\right]·e^{j\left(k{x}_1-\omega t\right)} \end{gathered}$$

The particle displacements and the traction components of stress must be continuous across the substrate/guiding layer, guiding layer/mass layer, and mass layer/liquid interfaces. The continuity conditions are a set of linear homogeneous algebraic equations whose coefficients are function of the wave phase velocity V_ph: a non trivial solution exists if the determinant of the coefficients vanishes; an optimized procedure was used to find a velocity value that drive the size of the determinant as close to zero as possible. The determinant is:

where H = h_gl1 + h_gl2, $q^2=k^2-k_s^2$, $b^2=k_{gl1}^2-k^2,$ $p^2=k_{gl2}^2-k^2,and{\lambda }_1^2=k^2-j\mathsf{\omega }\left({\rho }_l⁄\mathsf{\eta }\right).$

$$k=2\frac{\mathit{\pi }}{\lambda },ks=\left(2\frac{\mathit{\pi }}{\lambda }\right)\left(\frac{Vph}{Vs}\right),kgl1=\left(2\frac{\mathit{\pi }}{\lambda }\right)\left(\frac{Vph}{Vgl1}\right),kgl2=\left(2\frac{\mathit{\pi }}{\lambda }\right)\left(\frac{Vph}{Vgl2}\right)$$

V_s, V_gl1, V_gl2 are shear velocity in substrate, guiding layer 1 and guiding layer 2 respectively. To account viscoelastic properties of PMMA as guiding layer 2, it has complex shear modulus and complex shear velocity.

3. Viscosity Sensitivity of the Liquid-PMMA-ZnO-Glass Structure

Complex phase velocities V_ph were obtained by solving the the determinant of matrix equal to 0 using Levenberg-Marquard-Fletcher method in a Matlab routine. The viscous liquid was supposed to be a mixture of water and glycerol: the fraction of glycerol by volume ranged from 0 (only water) to 0.8 (80% glycerol, 20% water) and the $\sqrt{{\rho }_l·\eta }$ ranged from 1 to 10.59 kg·m⁻²s^0.5. The real and imaginary parts of the phase velocity (V_r and V_i) of the L₁ mode were calculated for different guiding layer thicknesses and for different water/glycerol mixtures. The propagation loss (α) is calculated by α = 2·π·log(e)·V_i/V_r. Figure 2a,b show the real velocity and propagation loss of the L₁ mode velocity as a function of the PMMA guiding layer thickness for different water/glycerol mixture. The thickness of ZnO is fixed at 0.5 μm and λ = 10 μm, supposing h/λ of ZnO 0.05.

The calculated data clearly show that, while the percentage of glycerol in water increases, the wave velocity decreases respect to the velocity along the bare substrate in pure water, and the attenuation increases. Calculations were repeated for different thicknesses of ZnO from 0.5 μm to 3 μm, supposing h/λ of ZnO from 0.05 to 0.3.

The attenuation and velocity relative changes vs. $\sqrt{\rho ·\eta }$ were linearly fitted, for each ZnO and PMMA thicknesses, and the slopes, i.e., the phase attenuation sensitivities $S_{\sqrt{\rho ·\eta }}^{v_{ph}}=\left(\raisebox{1ex}{$v_{ph}$}\!\left/ \!\raisebox{-1ex}{$v_{hp}^{water}$}\right.\right)/\sqrt{\rho ·\eta },$ $S_{\sqrt{\rho ·\eta }}^{att}$ = α/$\sqrt{\rho ·\eta }$, were plotted vs. the total thicknes; the calculated sensitivities dispersion curves are shown in Figure 3a,b.

The calculated sensitivities are significantly increasing when PMMA layers are added onto ZnO layer, with the optimum PMMA thickness of around 0.85 μm. Additional advantage of using PMMA layer is that the sensitivities are less dependant on ZnO thickness so that thicker ZnO can be used to obtain higher K².

4. Mass Sensitivity of the Liquid-PMMA-ZnO-Glass Structure

Figure 4a,b show the calculated relative change of phase velocity when a mass loaded onto the sensor. The data show an order increase of velocity change for PMMA/ZnO double guiding layer. Similarly to viscosity sensitivities, the mass loading sensitivities for PMMA/ZnO double guiding layer are less dependant on ZnO thickness. The mass loading sensitivities were calculated from the slope of the graphs. They are 55 m²_·kg⁻¹ for 0.5 μm and 29 m²_·kg⁻¹ for 3 μm ZnO layer only. For PMMA/ZnO double guiding layer with 0.85 um PMMA, the mass loading sensitivities are 683 m²_·kg⁻¹ for 0.5 μm and 553 m²_·kg⁻¹ for 3 μm ZnO layer.

5. Conclusions

The theoretical sensitivity of Love wave sensors, based on PMMA/ZnO/Glass structure, to the properties of a liquid environment, and to a mass deposited from a viscous Newtonian liquid phase is derived. The calculation of the real and imaginary parts of the phase velocity allowed the estimation of both the phase velocity and attenuation sensitivities to the liquid viscosity and density, and to a mass loaded onto guiding layer surface for different ZnO and PMMA thickness. It resulted that the sensitivities are increasing by adding PMMA layer on ZnO layer. Moreover, the sensitivies of PMMA/ZNO double guiding layer are less dependent on ZnO thickness.