Thickness shear mode acoustic wave sensor in liquid and the frequency interference between laterally coupled channels

THICKNESS SHEAR-MODE ACOUSTIC WAVE SENSOR IN LIQUID AND THE FREQUENCY INTERFERENCE BETWEEN LATERALLY COUPLED CHANNELS LU FENG NATIONAL UNIVERISTY OF SINGAPORE 2004 THICKNESS SHEAR-MODE ACOUSTIC WAVE SENSOR IN LIQUID AND THE FREQUENCY INTERFERENCE BETWEEN LATERALLY COUPLED CHANNELS BY LU FENG (B.Eng.,M.Eng XJTU) DEPARTMENT OF MECHANICAL ENGINEERING A TIESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2004 Acknowledgements Acknowledgements I would like to express my deepest gratitude to my supervisors, Associate Professor Lim Siak Piang, and Associate Professor Lee Heow Pueh I would like to thank their invaluable guidance, continuous encouragement and great patient throughout my study Their influence on me is beyond this thesis and will benefit me in my whole life I would also like to thank Dr Lu Pin for his encouragement and continuous discussion His advices and suggestions always give me fresh idea on the research And many thanks are conveyed for Dr Su Xiao-Di and Mr Wang Guang-Yu from Institute of Materials Research and Engineering (IMRE) for their help on preparing the experimental samples during the work The author also want to express his thanks for Ms Amy Chee Sui Cheng, Ms Priscilla Lee Siow Har and Mr Ahmad Bin Kasa fro their logistic support during his work I am grateful to the National University of Singapore for the research financial support during my study in the university Special thanks for my families for their endless encouragement i Table of Contents Table of Contents Acknowledgements………………………………………………………………….(i) Table of Contents ………………………………………………………………… (ii) Summary ……………………………………………………………………… (viii) List of Tables ……………………………………………………………………….(x) List of Figures ……………………………………………………………………(xiii) Notation…….……………………………………………………………………(xxiii) Chapter Introduction ………………………………………………………… (1) 1.1 Background…………………………………………………………… (1) 1.2 Development of Quartz Crystal Microbalance………………………… (4) 1.2.1 Single Quartz Crystal Microbalance……………………………….(4) 1.2.2 Development of Multi-Channel Quartz Crystal Microbalances… (9) 1.3 Objectives and Organization of the Thesis ………………………….…(11) 1.3.1 Objectives…………………………………………………… ….(11) 1.3.2 Organization of the Thesis…………………………………… …(12) Chapter Overview of the Piezoelectric Quart Crystal Resonator……………(15) 2.1 Introduction…………………………………………………………….(15) 2.2 Piezoelectric Quartz Crystal Resonator……………… …………… (15) ii Table of Contents 2.2.1 Properties of Quartz Crystal…………………………………… (17) 2.2.2 Wave Equations for Piezoelectric Quartz Crystal Materials… (19) 2.3 Operational Principle of Quart Crystal Microbalance………………….(23) 2.4 Electrical Analogue Approaches for Quartz Crystal Microbalance……(27) 2.4.1 Transmission-Line Model (TLM) for QCM…………………… (27) 2.4.2 Electrical Equivalent Circuit Model…………………………… (30) Chapter Quartz Crystal Microbalance Operated in Liquid with Slip Interfacial Model………………………………………… (33) 3.1 Introduction…………………………………………………………… (33) 3.2 One-Dimensional Mechanical Model of QCM in Liquid………………(35) 3.2.1 Piezoelectric Element Equations………………………………… (35) 3.2.2 One-Dimensional Equations of Quartz Crystal Microbalance… (36) 3.2.3 Shear Wave Equations of Viscoelastic Liquid………………… (41) 3.2.4 Non-Slip Interfacial Model between Solid and Liquid………… (43) 3.2.5 Slip Model on the QCM with Viscoelastic Liquid Loading…… (45) 3.3 Electrical Impedance of the Compounded QCM……………………….(50) 3.3.1 Impedance of QCM with Mechanical Slip Model…………….….(50) 3.3.2 Unperturbed Quartz Crystal Resonator Zero Attraction Strength Assumption ………………………………………………………(52) 3.3.3 Continuous Displacement Assumption -Infinite Attraction Strength Assumption……………………………………………………….(53) iii Table of Contents 3.4 Performance of the QCM with Viscoelastic Liquid Loading………… (53) 3.4.1 QCM Model for Numerical Analysis ……………………………(53) 3.4.2 QCM with Elastic Mass Absorption Layer………………………(56) 3.4.3 Performance of QCM in the Liquid………………………………(59) 3.5 Summary…………………………………………………………… (65) Chapter Detecting the Contact Interface Properties by Quartz Crystal Microbalance……………………………………………………… (66) 4.1 Introduction …………………………………………………………….(66) 4.2 Interfacial Slip Parameter of QCM in Viscoelastic liquid…………… (67) 4.2.1 Explicit Expression of the Slip Parameter……………………… (67) 4.2.2 Study of the Contact Condition for the QCM in Liquid………….(68) 4.2.3 Discussion on Solid-Liquid Interfacial Slip Parameter………… (73) 4.2.4 Relation of Attraction Strength G * / δ and Slip Length b …… (77) 4.3 Detecting the Interfacial Properties With QCM……………………… (79) 4.4 Experimental Section ………………………………………………… (83) 4.4.1 Apparatus and Setups…………………………………………… (83) 4.4.2 Parameters Fitting for QCM in the Air………………………… (85) 4.4.3 Results in Liquid and Slip Interface Treatment………………… (91) 4.5 Summary……………………………………………………………… (98) Chapter Quart Crystal Microbalance with Mass Partially Attached on the Electrode Surface…………………………………………………….(100) iv Table of Contents 5.1 Introduction ………………………………………………………… (100) 5.2 One-Dimensional Mindlin’s Equation for QCM…………………… (102) 5.2.1 Thickness Shear and Thickness Flexure Coupling Equations… (103) 5.2.2 Solutions of Decoupled Thickness Shear mode Vibration….… (106) 5.3 Numerical Analysis of Partial Mass Absorption on QCM Surface… (113) 5.3.1 Mass Absorption Covering Whole Electrode Area………….… (113) 5.3.2 QCM with Mass Absorption Partially on Electrode Surface….…(116) 5.3.3 Effect of Position of the Absorption on Electrode Surface…… (120) 5.4 Experiment Study on Position Sensitivity of QCM………………… (123) 5.4.1 Quartz Crystal Microbalance Sample ………………………… (123) 5.4.2 Position Sensitivity of Electrode Width and Thickness……… (125) 5.5 Summary…………………………………………………………….…(129) Chapter Two-dimensional Analysis of Energy Trapping Effect for Bi-mesa QCM………………………………………………………… ……….(130) 6.1 Introduction ………………………………………………………… (130) 6.2 Finite Element Modeling with Two-Dimensional Mindlin’s Quartz Plate Element ……………………………………………………………… (131) 6.2.1 Two-Dimensional Mindlin’s Equation for AT-cut Quartz Plate………………………………………………………….…(131) 6.2.2 Finite Element Equations for Quartz Plate Element………… (134) 6.2.3 Energy Trapping Factor of Thickness Shearing Mode ……… (139) 6.3 Conventional AT-cut Quartz Resonator with Electrode Plated……… (141) v Table of Contents 6.4 Energy Trapping Effect with Mesa Design………………………… (149) 6.4.1 Single-Mesa for Quartz Resonator……………………………(151) 6.4.2 Bi-mesa Design for Quartz Resonator……………………… (155) 6.5 Summary………………………………………………………………(156) Chapter Interference Analysis of the Laterally Coupled Quartz Crystal Microbalances Array……………………………………………… (158) 7.1 Introduction ………………………………………………………… (159) 7.2 Overview of Multi-channel Quartz Crystal Microbalance……………(159) 7.2.1 Design of the Multi-channel Quartz Crystal Microbalance…… (159) 7.2.2 Electrical Equivalent Circuit for the Laterally Coupled QCMs (164) 7.3 FEM Analysis of the Lateral Coupled Quartz Crystal Microbalances (169) 7.3.1 Simulation of the Single Quartz Crystal Microbalance…………(169) 7.3.2 Analysis of the Detuned Coupled QCMs Pair………………… (175) 7.3.3 Analysis of Symmetrical Designed QCM Channels……………(178) 7.3.4 Investigation on the Effect of the QCM Pair Layout on AT-cut Quartz Plate…………………………………………………… (184) 7.4 Experimental Evaluation…………………………………………… (187) 7.4.1 Electrical Characteristics of Lateral Coupled Resonators…….(187) 7.4.2 Effect of the Interval Distance and Thickness of Electrode… (191) 7.5 Summary………………………………………………………………(195) Chapter Conclusions and Recommendations……………………………… (196) vi Table of Contents 8.1 Conclusions……………………………………………………………(196) 8.2 Recommendations for Future Works………………………………….(201) Bibliography ……………………………………………………………………(203) Appendix A: Properties of AT-Cut Quartz Crystal …………… …………(216) Appendix B: Publications Relating to This Thesis…………………………….(217) vii Summary Summary A thickness shear-mode acoustic wave sensor is extended to be operated in viscous liquid environment The interfacial slip is one of the major controversies in this case In this thesis, a mechanical slip interface model between the liquid and the acoustic device is proposed Continuous displacement and stress assumptions on the contact interface are replaced by the motion equations of the contact molecular layers The proposed model involved interactive strength of the contact layer, contact molecular size and viscosity of the liquid on the formula From numerical simulation results, it is found that the slip modeling proposed can be a mechanism to explain recent reported experimental results, which have shown that frequency shift could be increased in some conditions Based on the mechanical slip interface model, the displacement slip parameter α and the single friction model value s proposed by recent analysis can be expressed empirically in terms of the complex interactive strength and liquid viscosity With the experimental value of the slip parameter reported in literature, it is shown that the real part of the interactive strength contributes significantly to distinguish different interface conditions for these two types of sensors reported in literature Three thickness shear mode acoustic wave sensors, which are coated with different biomonolayer, are fabricated to evaluate the slip modeling of the interface Frequency shifts of these three QCMs with liquid loading deviate from the theoretical results evaluated from continuous interface assumption significantly The frequency shift viii Bibliography Bruckenstein S and Shay M (1985) Experimental Aspects of the Use of the Quartz Crystal Microbalance in Solution Electrochimica Acta Vol 30 pp:1295-1300 Bruckenstein S., Fensore A., Li Z F and Hillman A R (1995) Dual Quartz Crystal Microbalance Compension Using A Submerged Reference Crystal Effect of Surface Roughness and Liquid Properties Journal of Electroanal Chemistry Vol.370 pp:189-195 Buttry D A (1991) 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a New Kind of Dual Modulated QCM Biosensor Biosensors and Bioelectronics Vol.12 No.12 pp:1219-1225 215 Appendix A Appendices A: Properties of the AT-cut quartz crystal AT-cut quartz crystal is cut with an angle 35.25o to the z-axis Its properties can be obtained from mother quartz crystal by rotation transforming Density : ρ q = 2675 kg/m3 y z {T } = [C E ]{S } − [e]T {E} x {D} = [e]{S } + [∈]{E} With stress and strain vector as [T ] = {σ xx , σ yy , σ zz ,τ xy ,τ yz ,τ xz }T [S ] = {ε xx , ε yy , ε zz , γ xy , γ yz , γ xz }T [C ] E − 3.66 0 ⎤ ⎡86.74 27.15 − 8.25 ⎢ 102.83 − 7.42 9.92 ⎥ ⎢ ⎥ ⎢ 129.77 5.70 ⎥ =⎢ ⎥ × 10 N / m 68.81 2.53 ⎥ ⎢ ⎢ 38.61 ⎥ ⎢ ⎥ 29.01⎥ ⎢ ⎣ ⎦ 0 ⎤ ⎡ 0.171 ⎢− 0.0187 0 ⎥ ⎢ ⎥ ⎢ − 0.152 0 ⎥ [e] = ⎢ ⎥ C/m − 0.0761 0.067 ⎥ ⎢ ⎢ 0.067 0 ⎥ ⎢ ⎥ 0.067 − 0.095⎥ ⎢ ⎣ ⎦ 0 ⎤ ⎡39.21 ⎢ [∈] = ⎢ 40.42 0.68 ⎥C / V m ⎥ ⎢ 0.68 39.82⎥ ⎣ ⎦ 216 Appendix B Publication relating to this study Appendices B: Publication relating to this study F Lu H P Lee and S P Lim Experimentally fitting the attraction strength of interface by the response of the thickness shear-mode acoustic wave sensor Journal of Physics D: Applied Physics 2005 (In Press) F Lu, H.P Lee P Lu and S P Lim Finite Element Analysis of Frequency Interference Analysis of Lateral Coupled Quartz Crystal Microbalances Sensors and Actuators Vol.119 pp:90-99 2005 F Lu, H.P Lee P Lu and S P Lim Energy Trapping Analysis for Bi-Stepped Mesa Quartz Crystal Microbalance Using the Finite Element Method Smart Materials and Structures Vol.112 pp:203-210 2004 F Lu, H.P Lee and S P Lim A Quartz Crystal Microbalance with Rigid Mass Partially Attached on Electrical Surface Sensors and Actuators: A Vol.112 pp:203-210 2004 F Lu, H.P Lee and S P Lim Detecting Solid-Liquid Interface Properties with Mechanical Slip Modeling for Quartz Crystal Microbalance(QCM) Operating in Liquid Journal of Physics: D Applied Physics Vol 37 2004 pp:898-906 F Lu, H.P Lee and S P Lim Finite Element Modeling and Analysis of Multi- Channel Quartz Crystal Microbalance International Conference IEEE 2003 Sensors Proceedings of IEEE , Volume: , 22-24 Oct 2003 Toronto Canada 2003 F Lu, H.P Lee and S P Lim Modeling and Analysis of Micro Piezoelectric Power Generators for Micro-Electromechanical Systems Applications Smart Materials and Structures Vol 13 2004 pp: 57-63 F Lu, H.P Lee and S P Lim Mechanical Description of Interfacial Slips for Quartz Crystal Microbalance With Viscoelastic Liquid Loading Smart Materials and Structures Vol 12 2003 PP: 881-888 217 Appendix B Publication relating to this study Zhaoxin Yuan, Guangyu Wang, Feng Lu, Pin Lu, Xiaodi Su Mass Sensitivity Analysis of Quartz Crystal Microbalance with Ring-Shaped Electrode(s) (Submitted) 218 .. .THICKNESS SHEAR- MODE ACOUSTIC WAVE SENSOR IN LIQUID AND THE FREQUENCY INTERFERENCE BETWEEN LATERALLY COUPLED CHANNELS BY LU FENG (B.Eng.,M.Eng XJTU) DEPARTMENT OF MECHANICAL ENGINEERING A... environment, the interference between the channels would be more complicated Beside the thickness shear mode, the longitudinal wave is also generated by QCM in liquid The longitudinal wave propagates and. .. mode in liquid including the electrode, sensing film and infinite liquid medium Kanazawa [1997] gave the review discussion on the correlations between the mechanical motion of the quartz and over-layer