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All-polymer flexural plate wave devices for sensing and actuation Berring, John 2013

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i    All-Polymer Flexural Plate Wave Devices for Sensing and Actuation  by  John Berring  B.Sc., Simon Fraser University, 2011  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  Master of Applied Science  in  THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Electrical and Computer Engineering)  The University Of British Columbia (Vancouver) December 2013  ? John Berring, 2013    i  Abstract Polymer based flexural plate wave (FPW) chemical sensors are unique among guided acoustic devices in that they are comprised of components with similar elastic moduli.  As a result, they can be very sensitive to stiffness and stress variations in an applied sensing layer. This property may be leveraged to detect the presence of an analyte or to interrogate the mechanical properties of the applied polymer. In this work, polyvinylidene fluoride (PVDF) based, polyethylene dioxythiophene polystyrene sulfonate (PEDOT:PSS) coated  FPW devices are fabricated and tested with the purpose of developing an all-polymer VOC sensor. The sensors are coated in polyvinyl acetate (PVAc) and polystyrene (PS) sensing layers and exposed to varying concentrations of toluene during testing. The PS coated sensors show a sensitivity of -80 cm2/g to -200 cm2/g while the PVAc coated devices demonstrate a sensitivity of -240 cm2/g to -490 cm2/g. A performance model is proposed which seeks to describe the sensing layer mechanical properties as a function of analyte vapour concentration in order to predict the sensor resonant frequency. The predictions of this model are compared with experimental results and design modifications are proposed. Along with this, soft material mechanical characterisation is investigated with the purpose of developing a tool for measuring composite resin properties during cure.  Finally, it is proposed that these devices may be used to drive acoustic streaming in microfluidic systems. To test the concept, droplets of fluid are applied to the device substrates and acoustically driven flow rates are measured.         ii  Preface This dissertation is based primarily on volatile organic compound sensing and microfluidic actuation experimental data collected and analyzed by the author. Experimental results and analysis are detailed in Chapter 5 while a novel model for sensing layer performance, similarly developed by the author, is presented in Chapter 3. Fabrication of the devices under investigation and, unless noted otherwise, the test apparatus, was also carried out by the author.  Much of this work could not have been completed without the contributions of researchers Christoph Sielmann, Suresha Mahadeva, Johnny Chen, and Robert Busch. The fabrication procedure detailed in Chapter 4 was designed primarily by Robert during his thesis work [1]. Christoph built upon this work to develop the current sensor operation and design. This includes the design of the sensor test platform, sampling and excitation method, and the humidity generation system. His main contributions are detailed in Sections 1.4, 1.6, 2.2.1, and 2.2.3.1. Section 5.1 details work which was carried out in conjunction with Chistroph, included here to provide background for Section 5.2. Finally, Suresha has contributed by characterising PVDF properties through FTIR and piezoelectric constant measurement, while Johnny constructed the screen printing apparatus described in Section 4.6 under my supervision. A version of Chapter 5.2 was published in Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS & EUROSENSORS XXVII), 2013 Transducers & Eurosensors XXVII [J. Berring, C. Sielmann, B. Stoeber, and K. Walus, ?VOC detection using an all polymer flexural plate wave sensor,? in 2013 Transducers Eurosensors XXVII: The 17th International Conference on Solid-State Sensors, Actuators and Microsystems] [2]. For this publication, the author carried out all testing and analysis and was the main contributor to the manuscript.        iii  Table of Contents Abstract ............................................................................................................................................................. i Preface ............................................................................................................................................................. ii Table of Contents ............................................................................................................................................ iii List of Tables ................................................................................................................................................. vii List of Figures ............................................................................................................................................... viii List of Symbols .............................................................................................................................................. xii 1 Introduction ................................................................................................................................................... 1 1.1 Motivation .............................................................................................................................................. 2 1.1.1 VOC Sensing .................................................................................................................................. 2 1.1.2 Resin Cure Characterisation............................................................................................................ 3 1.1.3 Acoustic Wave Microfluidic Manipulation .................................................................................... 3 1.2 Piezoelectric Guided Acoustic Wave Micro-Devices ............................................................................ 3 1.2.1 Overview ......................................................................................................................................... 3 1.2.2 Acoustic Wave Sensors ................................................................................................................... 4 1.2.3 Acoustic Wave Microfluidic Actuators .......................................................................................... 6 1.3 Flexural Plate Waves for Sensing .......................................................................................................... 7 1.4 Piezoelectricity and Piezoelectric PVDF ............................................................................................. 10 1.5 Transducers .......................................................................................................................................... 14 1.6 VOC Sensing Layer and Polymer-Solvent Solutions .......................................................................... 14 1.6.1 Overview ....................................................................................................................................... 14 1.6.2 Flory-Huggins Solution Theory .................................................................................................... 15 1.6.3 Modified Flory-Huggins Solution Theory .................................................................................... 18 1.6.4 Partition Coefficient ...................................................................................................................... 19 1.7 Flexural Plate Wave Driven Acoustic Streaming ................................................................................ 20 1.8 Objectives ............................................................................................................................................ 23 2 Experimental Methods ................................................................................................................................ 25 iv  2.1 Material Characterisation ..................................................................................................................... 25 2.1.1 Stress Strain Analysis and Piezoelectric Constant Measurement ................................................. 25 2.1.2 Differential Scanning Calorimetry ................................................................................................ 26 2.1.4 Laser Doppler Vibrometry ............................................................................................................ 27 2.1.5 Thin Film Stress Measurement ..................................................................................................... 27 2.2 Gas Sensing and Thin Film Characterisation ....................................................................................... 28 2.2.1 Signal Generation and Extraction ................................................................................................. 28 2.2.3 Sample Vapour Generation ........................................................................................................... 29 2.2.3.1 Water Vapour Generation ...................................................................................................... 30 2.2.3.2 Toluene Generation ................................................................................................................ 30 2.3 Acoustic Microfluidics ......................................................................................................................... 31 3 Design and Theory ...................................................................................................................................... 33 3.1 Overview .............................................................................................................................................. 33 3.2 Substrate ............................................................................................................................................... 33 3.2.1 Mechanical Properties and Geometry ........................................................................................... 33 3.2.1.1 Substrate Thickness ............................................................................................................... 34 3.2.1.2 Substrate Stress ...................................................................................................................... 35 3.2.2 Electrical Properties ...................................................................................................................... 36 3.2.3 Crystallinity................................................................................................................................... 36 3.3 Transducers and Backplane ................................................................................................................. 38 3.4 Polymer Sensing Layer ........................................................................................................................ 38 3.4.1 Polymer Film Thickness, Mass, and Elasticity ............................................................................. 39 3.4.2 Polymer Film Stress ...................................................................................................................... 42 3.4.3 Influence of Stiffness and Stress ................................................................................................... 45 3.4.4 Sources of Uncertainty .................................................................................................................. 46 3.5 Polymer Reference Layer .................................................................................................................... 48 4 Fabrication .................................................................................................................................................. 50 v  4.1 Overview .............................................................................................................................................. 50 4.2 Stretching ............................................................................................................................................. 51 4.3 Poling ................................................................................................................................................... 52 4.4 Framing ................................................................................................................................................ 57 4.5 Microinkjet Printing ............................................................................................................................. 57 4.6 Screen Printing ..................................................................................................................................... 59 4.7 Solvent Casting .................................................................................................................................... 60 5 Experimental Results and Discussion ......................................................................................................... 61 5.1 Humidity Sensing................................................................................................................................. 61 5.1.1 Overview ....................................................................................................................................... 61 5.1.2 Results and Discussion ................................................................................................................. 62 5.2 VOC Sensing ....................................................................................................................................... 63 5.2.1 Overview ....................................................................................................................................... 63 5.2.2 Results and Discussion ................................................................................................................. 63 5.3 Epoxy Curing Characterisation ............................................................................................................ 68 5.3.1 Overview ....................................................................................................................................... 68 5.3.2 Results and Discussion ................................................................................................................. 69 5.4 Acoustic Microfluidics ......................................................................................................................... 70 5.4.1 Overview ....................................................................................................................................... 70 5.4.2 Results and Discussion ................................................................................................................. 72 6 Conclusions ................................................................................................................................................. 78 6.1 Design and Fabrication ........................................................................................................................ 78 6.2 Modelling and Understanding .............................................................................................................. 79 6.3 Performance Testing ............................................................................................................................ 81 6.4 Future Work ......................................................................................................................................... 82 References ...................................................................................................................................................... 84 Appendix ........................................................................................................................................................ 89 vi  A.1 Glass Transition Temperature of a Polymer Solvent System ............................................................. 89 A.3 Influence of PEDOT:PSS Backplane on Sensor Resonant Frequency ............................................... 90 A.4 FH Model Implementation .................................................................................................................. 91 A.5 Electromechanical Coupling Coefficient ............................................................................................ 93                  vii  List of Tables  Table 1: Sensitivity, applications, operating frequency and schematic of the most popular acoustic modes. . 5 Table 2: Key properties of PVDF, obtained from [2], [4] ............................................................................. 13 Table 3: Polymer-solvent interaction parameter values for PVAc and PS [49]............................................. 17 Table 4: Reference channel barrier polymers and deposition details............................................................. 48 Table 5: Characteristics of sensors used during this investigation ................................................................ 64 Table 6: Sample frequencies and out of plane velocities. .............................................................................. 73 Table 7: Estimated uncertainty for various sensor properties ........................................................................ 47 Table 8: Predicted minimum detectable thickness, Young?s modulus, stress and density changes in an applied curing film. ........................................................................................................................ 71              viii  List of Figures  Figure 1: A PVDF FPW device, anchored in a steel frame ............................................................................. 2 Figure 2: The zeroth order symmetric (S0) and anti-symmetric (A0) FPW modes of oscillation .................... 7 Figure 3: A schematic of the composite plate structure. .................................................................................. 8 Figure 4: PVDF monomer molecular diagram. ............................................................................................. 12 Figure 5: A diagram of alpha phase (left) and beta phase (right) PVDF. ...................................................... 13 Figure 6: A diagram of the main transducer used during the investigation. Acoustic waves are generated at the centre, transmitting IDT and received at the outer IDTs. Wires are affixed to the contact pads with carbon glue. ............................................................................................................................ 14 Figure 7: A diagram showing the purpose of the sensing layer model .......................................................... 15 Figure 8: Solvent volume fraction as a function of solvent vapour concentration, predicted by FH solution theory (above GTT) and modified FH solution theory (below GTT). ........................................... 19 Figure 9: A diagram of SAW driven acoustic streaming (left) and FPW driven acoustic streaming (right).  The high velocity surface acoustic wave refracts into the fluid at the angle              , where Vf is the speed of sound in the fluid (1484 m/s in water) and Vph is the phase velocity of the wave. For waves with velocities smaller than Vf, acoustic power remains in the substrate.  As a result, flow is driven by disturbances in the viscous boundary layer. ............................................ 21 Figure 10: A diagram of a basic differential scanning calorimeter curve. Data from an untreated McMaster Carr PVDF sample heated to from 20 to 200 degrees and back. .................................................... 26 Figure 11: Thin film stress test setup.  Deflection of a PET film is measured and used to calculate stress of a solvent cast film .............................................................................................................................. 28 Figure 12: A diagram of the test setup used to measure sensor performance. ............................................... 28 Figure 13: An image of the sensor test setup. ................................................................................................ 29 Figure 14: Frequency response of a sensor coated in PVAc, exposed to building compressed air for 27 hours.  The large frequency shifts are attributed to humidity and temperature variations in the stream. ............................................................................................................................................ 30 Figure 15: An image of the Owlstone humidity generation system used. ..................................................... 30 Figure 16: A diagram of the toluene vapour generation setup. ...................................................................... 31 Figure 17: Test setup for investigating FPW driven acoustic streaming ....................................................... 32 Figure 18: A screenshot of the time domain performance of a thin-film device oscillating at 76 kHz. ........ 35 Figure 19: The resonant frequency of a 20 ?m sensor as a function of substrate tension, compared with predicted frequency. ....................................................................................................................... 36 ix  Figure 20: DSC scans of films from three different suppliers. The difference in melting peak area indicates a different in total crystallinity.  Note that the P.P. and Solef curves overlap during cooling. ...... 38 Figure 21: The measured and predicted percent change in thickness, density, and Young?s modulus of PVA exposed to varying degrees of humidity. Measured data obtained from [89] and [88]. ................. 42 Figure 22: A diagram of stress in the substrate and sensing layer during solvent casting and exposure to an analyte. A: A polymer solvent solution is applied to the substrate. Substrate stress is the only contribution to total tension. B: The polymer-solvent solution dries and contracts, causing an increase in tension in the sensing layer. C: The sensor is exposed to a solvent and the polymer film expands, reducing internal thin film stress. ............................................................................ 43 Figure 23: Images of substrate deflection during as a result of residual stress in an evaporating PS-xylene solution (visible in the first frame). 1 to 8 correspond to the chronological order of images taken over a 40 hour period. ..................................................................................................................... 44 Figure 24: Plots showing internal stress in films deposited via solvent casting.  Multiple thicknesses were used to confirm that stress was not varying as a function of thickness [90]................................... 45 Figure 25: PVA coated humidity sensor model predictions given sensitivity to polymer mass, stiffness and stress changes. ................................................................................................................................ 46 Figure 26: The predicted resonant frequency shift of a PVAc coated sensor along with the upper and lower bounds of the prediction given uncertainty in PVDF thickness, PVDF stress, and PVAc thickness. ........................................................................................................................................................ 47 Figure 27: Frequency response of sensors coated in barrier polymers .......................................................... 49 Figure 27: Main fabrication steps. (1-2) Stretch PVDF, (3) Pole PVDF, (4) Frame PVDF, (5) Print PEDOT, (6-7) Apply sensing layer/electrodes .............................................................................................. 50 Figure 28: Images of (a): manual and (b): automatic drawing devices. ......................................................... 51 Figure 29: Measured beta content of manually and automatically stretched films. ....................................... 52 Figure 30: Diagrams of contact poling (left) and corona poling (right)......................................................... 53 Figure 31: The d33 piezoelectric constant of PVDF films drawn and poled at 80, 100, and 120 degrees. ..... 54 Figure 32: DSC scans of raw, stretched, and poled McMaster Carr PVDF films. ........................................ 55 Figure 33: Time to dielectric breakdown as a function of field during contact poling. The grey area represents the region over which field intensity is sufficient to polarize PVDF at 80 degrees over half an hour. .................................................................................................................................... 56 Figure 34: An image of the printed IDT pattern ............................................................................................ 58 Figure 35: Screen printing apparatus (a) and the mask used to generate the IDT patterns (b). ..................... 59 Figure 36: Images of screen printed sensors. ................................................................................................. 60 x  Figure 37: PVA-Water vapour sensing results.  Left: Resonant frequency of a sensor coated in 3 PVA layers at different dew points and given a constant ambient temperature of 22 degrees.  Right: Frequency as a function of dew point for a 20 ?m sensor. ............................................................. 62 Figure 38: Resonant frequency and toluene concentration as a function of time .......................................... 65 Figure 39: Percentage shift of resonant frequency as a function of toluene concentration. Data from a 22 ?m thick sensor coated in 2 to 3 ?m thick PS (white points) and to 3 ?m thick PVAc (black points) 66 Figure 40: Resonant frequency shift as a function of toluene concentration. Left: PVAc sensing layer. (1) 1.8 ?m thick PVAc (2) 2.8 ?m thick PVAc (3) 3.2 ?m thick PVAc. Right: PS sensing layer. (4) 1.9 ?m thick PS (5) 1 ?m thick PS.   Data is tracked by solid lines, which correspond to constant stress models and dashed lines, which correspond to models with linearly decreasing stress. ...... 67 Figure 41: Frequency shift as a function of toluene concentration given a PVAc sensing layer.  The solid black line describes predicted frequency given a small glass transition region and a high rubbery elastic modulus of PVAc.  The solid grey line (beneath the black at low concentrations) describes the predicted performance given a large glass transition region and low rubbery elastic modulus. ........................................................................................................................................................ 68 Figure 42: Frequency response of a sensor successively coated in two layers of epoxy. .............................. 70 Figure 43: A diagram showing the fluid manipulation setup investigated.  A flexural plate wave is excited towards a droplet placed on the same substrate.  This drives flow within the droplet and, at high enough power, droplet movement. ................................................................................................. 71 Figure 44: A diagram of the droplet during actuation.  Important parameters such as wavelength, wave velocity, wave amplitude, and substrate thickness are labelled...................................................... 72 Figure 45: Example plots of LDV results. Left: the average out of plane wave velocity as a function of frequency. Right: A 2 dimensional plot of the LDV map. ............................................................. 73 Figure 46: Out of plane velocity as a function of driving voltage for the samples tested. ............................. 74 Figure 47: An image of a 2 mm droplet on the back of a sensor prior to actuation. ...................................... 75 Figure 48: Polystyrene sphere velocity as a function of radial frequency and wave amplitude squared. Measurements are obtained from three samples and compared with the maximum near boundary layer flow velocity predicted by the model discussed in Section 1.8. Model predictions are made assuming a constant frequency of 159 kHz. As such, predicted streaming velocity curves trend with a square of acoustic ampitude................................................................................................. 76 Figure 49: LDV images showing an acoustic wave propagating through an unloaded sensor (right) and a sensor with a droplet on the substrate (left) .................................................................................... 76 xi  Figure 50: A plot showing the relative average displacement amplitude of FPWs in an unloaded sensor and a sensor loaded with a 3 mm diameter droplet.  The relatively similar rate of attenuation shown by the two curves suggests that there is little energy radiated into the fluid. ...................................... 77 Figure 51: An example of the elastic modulus of a material under constant load at and increasing time or temperature [83]. ............................................................................................................................ 89 Figure 52: An example of a modulus-frequency curve of a material under constant load. ........................... 90 Figure 54: Sensor resonant frequency during PEDOT backplane casting (left) and during humidity cycling (right) .............................................................................................................................................. 90                  xii  List of Symbols   Wavenumber   Mass loading solution decay factor     Permittivity     Viscous loading decay factor ?  Acoustic wavelength    Chemical potential   Viscosity ? Density      Substrate stress, x-direction    Volume fraction solvent    Volume fraction polymer       Glass transition concentration    Polymer solvent interaction parameter    Radial frequency    Sensing layer surface area     Acoustic wave instantaneous position dPVDF  PVDF substrate thickness d  Sensing layer thickness dP Piezoelectric coefficient     Converse piezoelectric constant D   Stiffness     Electric displacement    Young?s modulus     Modified Young?s modulus     Electric field    Enthalpy    Gibb?s free energy xiii  GTT  Glass transition temperature    Bulk modulus L  Substrate length    Mass density    Linear inertia     Molecular weight between crosslinks or entanglements Mw   Molecular weight    Frequency    Rotational inertia     Solvent molecule count     Polymer monomer unit count    Fluid pressure     Solvent partial pressure    Entropy     Linearized mass sensitivity     Tension     Temperature Tg  Glass transition temperature tf  Film thickness     Polymer test substrate thickness    Fluid flow velocity     Poisson?s ratio      Phase velocity     Solution volume       Swelling    x-axis unit vector (wave propogation direction) x  distance in the x direction    z-axis unit vector (perpendicular to wave propagation) xiv     Distance in the z direction     Neutral plane of a beam   1  1 Introduction Sensors are an integral yet mostly invisible component of our modern existence. We rely on them daily to take objective measurements of our physical world and provide useful information.  From the microphones and accelerometers in our handheld devices to the particulate matter detectors monitoring the air we breathe, these tools are ubiquitous and indispensible. Current sensor research generally focuses on one of three areas: improving performance, reducing cost of fabrication, and developing new detection mechanisms.  In an effort to design highly sensitive, highly selective, robust and inexpensive devices, engineers and scientists have investigated a great variety of natural phenomena which may be leveraged to convert information from a physical to a digital state.  One such mechanism is the piezoelectric generation and detection of acoustic waves.  This process has been used in the detection of a wide variety of physical, chemical, and biological quantities. An application for such sensors is the measurement of volatile organic compounds (VOCs) for environmental monitoring. This work details the design, modeling, and testing of an all-polymer, flexural plate wave device for VOC detection, material characterisation, and microfluidic manipulation.  Composed of polyvinylidene fluoride (PVDF) and conductive polyethylene dioxythiophene polystyrene sulfonate (PEDOT:PSS), the device is compliant, chemically robust, and inexpensive to fabricate.  An image of a sample device is given in Figure 1.  Given its unique substrate, it may be configured to detect sensing layer stiffness and stress changes, along with mass.  This property is investigated as a method for improving VOC detection sensitivity and resolution.  Similarly, it is employed to characterise the mechanical properties of polymer films.  A key aspect of such a device is the interaction between the analyte, the sensing layer, and the detection mechanism.  For VOC detection and materials characterisation, the sensor is coated in a polymer film which is exposed to an analyte or allowed to cure.  The change in physical properties of this layer drives a shift in the sensor output.  Understanding this mechanism is necessary for developing a well characterized device.  As such, a model for sensing layer properties during analyte absorption is presented.  The predictions of this model are compared with VOC sensing and polymer characterisation results. Finally, in an effort to develop a fluid based acoustic sensing and mixing platform, acoustically driven microfluidic manipulation was investigated.  Flexural plate wave (FPW) devices were designed to drive acoustic streaming in water droplets.  Tests were carried out using laser Doppler vibrometry and optical microscopy.  The results are compared with previously developed acoustic streaming theory. 2   Figure 1: A PVDF FPW device, anchored in a steel frame 1.1 Motivation Polyvinylidene fluoride (PVDF) has shown potential as a low cost piezoelectric acoustic sensor substrate.  Past research has demonstrated that it is possible to fabricate an all-polymer flexural plate wave (FPW) device using PVDF and conductive polymer electrodes [3], [4].  Recent work has shown that, due to the softness of the substrate, such a device could be used as a combination mass loading, stress and stiffness sensitive detector [5]. These added dimensions of data could potentially lead to higher detection sensitivity and selectivity.  Such a device would be beneficial for the fields of environmental monitoring and composite resin development. In the former, inexpensive, disposable, selective and sensitive VOC measurement devices are required to expand and improve upon current air quality monitoring networks. In the latter, a sensor capable of detecting resin mechanical properties during cure could significantly contribute to the development of novel composites. Finally, the chemically robust, biocompatible nature of PVDF could allow for the development of a disposable biosensor.  With the demonstration of both sensing and acoustically driven microfluidic manipulation, a PVDF based biochemical micro-laboratory or lab on a chip (LOC) could also be designed. Further motivation and background for each of these applications is discussed below. 1.1.1 VOC Sensing  One of the ultimate goals of this project is to develop a high resolution, selective, VOC sensing system for environmental monitoring.  Current methods of organics detection require that air samples be taken and shipped to a lab for analysis.  This is a time consuming, expensive process so a real time detection system would improve the monitoring ability of environmental research and protection groups. A key milestone in the project is the development of a VOC detection device capable of sensing analyte concentrations less than 1 ppm [6]. It is proposed that this can be achieved by leveraging the high stiffness and stress sensitivity of the polymer FPW devices. To this end, a sensor was configured for VOC detection and tested through exposure to varying concentrations of toluene. 3  1.1.2 Resin Cure Characterisation An inexpensive stress and stiffness sensitive detector could also be invaluable as a soft-material characterisation tool.  During the development of novel composites, it is vital that the resin curing process is fully understood.  A polymer FPW stress and stiffness sensor would allow the simple mechanical  characterisation of a thermoset as it cures. The difficulty associated with fully characterising a resin is best demonstrated in a recent Journal of Composite Materials publication by Khoun et al. [7]. During this investigation, the thermal, chemorheological, and thermomechanical properties of an epoxy resin were obtained in order to develop a model capable of predicting elasticity, viscosity, shrinkage, and degree of cure as a function of time and temperature. Thermal gravimetric analysis was used to obtain thermal stability before differential scanning calorimetry (DSC) was used to obtain cure rate as a function of temperature.  After this, a rheometer was used to measure viscosity and shrinkage as a function of cure progression.  Finally, elastic modulus and the coefficient of thermal expansion were measured as a function of glass transition temperature using dynamic mechanical analysis (DMA). The methods discussed here are commonly used during composites research [8]?[10]. While effective, they demand expensive scientific equipment and the destruction of multiple samples.  As such, a simple, inexpensive, non-destructive thermomechanical resin characterisation tool would be highly valued in this industry. A nondestructive tool for characterising resin properties over a long period of time would be similarly useful.  1.1.3 Acoustic Wave Microfluidic Manipulation Polymer based acoustic sensors could be particularly useful as disposable biomedical diagnostic and detection tools.  Along with detection and measurement of biological samples, they could also be leveraged for pumping, mixing and separating fluids. As detailed in past investigations [11]?[13], flexural plate wave devices can be used to drive acoustic streaming in microfluidic systems. If microfluidic pumping, droplet translation, or mixing could be demonstrated with an all-polymer flexural plate wave device, then it would open up new opportunities involving the design of disposable micro-laboratories. 1.2 Piezoelectric Guided Acoustic Wave Micro-Devices  1.2.1 Overview Piezoelectric guided acoustic wave devices are sensors and actuators which use mechanical oscillations in elastic solids to interrogate or influence the local environment.  At their most basic, they are comprised of a piezoelectric transducer which converts electrical energy to mechanical energy, and a bounded propagation 4  medium which confines the acoustic wave and enables interaction with the surroundings via the two surfaces.  Both sensors and actuators may also be comprised of one or more transducers while sensors will often include a sensing layer affixed to the propagation medium. During operation, an oscillating electrical signal is applied to the input transducer.  This induces a changing electric field within the piezoelectric element of the transducer.  A periodic displacement is created which radiates away from the transducer, through the propagation medium.  When a device is configured for sensing, the wave travels through a region composed, in part, of a layer sensitive to an external physical or chemical quantity.  The presence of the external analyte causes a physical change in the sensing layer which alters the velocity, frequency, phase or amplitude of the acoustic wave.  This change is then detected at the input transducer or a second, receiving transducer. By comparison, a device configured for actuation is designed such that the acoustic wave can be used to manipulate adjacent fluid or drive a secondary micromechanical device [14], [15]. While both applications rely on the same fundamental principles, the design and development of sensors and actuators are sufficiently different that they merit independent discussions.  The next two sections provide a more detailed, separate, overview of acoustic sensors and actuators.   1.2.2 Acoustic Wave Sensors Acoustic wave microsensors were first seriously investigated in the late 1950?s with the development of a Thickness Shear Mode (TSM) Resonator, commonly known as a Quartz Crystal Microbalance (QCM) [16]. Modern Surface Acoustic Waves (SAW) sensors were developed to their current state in the late 60s [17], while Flexural Plate Wave (FPW) devices were first demonstrated in 1989 [18], [19].  They are commonly composed of a ceramic piezoelectric substrate such as barium titanate, lead titanate, quartz and lead zirconate titanate, aluminum or copper conductive transducers, and a polymer based sensing layer. Initially, these devices were designed to detect metallic mass loading during metal deposition processes [20].  It wasn?t until the late 70?s that acoustic wave devices were used as chemical vapour sensors [21].   From this period to the present, research of this topic has grown, being driven by the need to create progressively more sensitive and selective physical, chemical and biological microdetectors.  The expansion of the field has been facilitated by the development of modern integrated circuit fabrication techniques and the creation of the microelectromechanical systems (MEMS) industry.  This has not only reduced the cost of sensor manufacture, but has also allowed the creation of smaller, more sensitive devices. 5  Presently, acoustic sensors are used in fields as diverse as environmental monitoring [22], pharmaceutical research [23], and national defence [24].  Since the development of the first acoustic device, a wide variety of sensor geometries and propagation modes have been investigated including microstring  [25],  bulk acoustic wave  [26], and Love mode sensors [27].  However, the three most investigated modes remain TSM, SAW, and FPW.    These devices are commonly configured as mass or viscosity detectors, depending on the application.  Mass, or gravimetric, detection involves detecting mass loading change in a sensing layer by measuring changes in acoustic wave frequency velocity and phase.  Viscosity sensing involves measuring the change in acoustic wave frequency, velocity, phase, or amplitude to obtain information about the viscosity of an adjacent fluid.  It is difficult to directly rank the different sensor configurations and propagation modes without having a full understanding of the application specifications.  However, it is possible to broadly compare the strengths of each main detector type, as shown in Table 1. Here, the sensitivity, applications, and operating frequency range are compared for each mode. Diagrams showing sensor geometry and particle motion are included as well. Table 1: Sensitivity, applications, operating frequency and schematic of the most popular acoustic modes.  Characteristic TSM SAW FPW Mass Sensitivity STSM=-2/?? SSAW=-K/?? SFPW=-1/2?d Mass Sensing Applications Film thickness, chemical sensor (liquid and gas)[28] Particle detector, chemical sensor (liquid and gas) [29] Film thickness, chemical sensor (gas) [29] Viscosity Sensing Applications Polymer mechanical characteristics, fluid viscosity [30] Polymer transitions, film resonance, vapour sensing [31] Polymer transitions, vapour sensing, gels [19] Operating Frequency 106-107 Hz 107-109 Hz 105-108 Hz Diagram    6  A sensor design is judged primarily on its sensitivity, selectivity and resolution.  Resolution refers to the minimum detectable mass change of a specific analyte and is dependant strongly on sensing layer characteristics.  Selectivity is the degree to which a sensor is able to detect a single compound from a group of many similar chemicals.  This figure of merit is similarly dependant on sensing layer characteristics and is not easily compared.  Sensitivity is a measurement of the relative change in output signal of a device given a change in analyte concentration.  Linearized mass sensitivity is given by Equation 1.         .       (1) This defines sensitivity as the change in acoustic wave frequency, ?f [Hz], normalized by the resonant frequency of the device, fo [Hz], and divided by the change in mass loading, m [g/cm2].  The estimated mass sensitivities of each propagation mode can be obtained by describing sensor resonant frequency and frequency shift as a function of its physical characteristics (see Section 1.3 for more detail).  These functions are given in Table 1.  Here, ? refers to density of the substrate, ? refers to wavelength of the acoustic wave, Jn is a scaling factor, K is a scaling factor related to the Poisson ratio of the substrate, and d is the thickness of the substrate. The three design types can be categorized into two groups based on their sensitivity: those devices which show a sensitivity inversely proportional to wavelength and those which show sensitivity inversely proportional to substrate thickness.  FPW devices fall into the latter category.  This is an important property for these devices as it means that sensitivity can be controlled with the substrate thickness and that it is unrelated to frequency. As such, a high sensitivity, low frequency FPW device could be built which requires no expensive RF electronics support.    As will discussed in Section 5.4, a low frequency FPW would also suffer less attenuation than an otherwise identical high frequency device because attenuation in polymers is reduced at lower frequencies.  1.2.3 Acoustic Wave Microfluidic Actuators Acoustic wave microfluidic actuators are guided acoustic wave devices used to induce pumping, mixing, jetting, and atomisation of fluids.  The interaction between fluids and vibratory motion has been studied since Rayleigh and Faraday observed acoustically driven air flow in the late 19th century [32], [33]. While the field has been active in the intervening years, it has recently found new popularity in microfluidics research [13].  The development of increasingly smaller microfluidic devices is inhibited, in part, by viscous forces restricting the movement and mixing of liquid on a small scale. These forces may be overcome by using high power, short wavelength oscillations to drive rotational and linear steady state 7  flow.  This phenomenon is generally known as acoustic streaming and is being leveraged in the development of microscale lab-on-a-chip [34], fluid sensing [35], and drug delivery devices [36]. While the mathematical description of acoustic streaming varies depending on acoustic wave power, mode, and scale, the general mechanism remains the same.  High frequency acoustic waves drive oscillations in adjacent fluid which, due to viscous losses, lead to low velocity rotational or continuous flow.  A thorough review of the various mathematical models describing this is outside of the scope of this work and can be found in [13].    1.3 Flexural Plate Waves for Sensing Flexural plate waves are oscillations in an acoustically thin, homogeneous elastic plate. They are a subset of Lamb waves which occur in plates that are substantially thinner than the acoustic wavelength.  These oscillations show particle motion in the transverse and longitudinal direction.  Figure 2: The zeroth order symmetric (S0) and anti-symmetric (A0) FPW modes of oscillation An image of the two fundamental oscillation modes is shown in Figure 2: the zeroth order antisymmetric mode, indicated by A0, and the zeroth order symmetric mode, indicated by S0. These two modes will always show the greatest amplitude with the A0 wave dwarfing the S0 wave by an average of 3 orders of magnitude. Given the soft piezoelectric substrate and low d/? value, all but the fundamental modes are quickly attenuated during operation.  As such, only the zeroth order anti-symmetric mode is used for detection.  The motion of a particle in a plate displaced by this wave is given by,                           ,       (2) 8  where ax and az are complex displacement amplitude, in the x and z direction, ? is radial frequency, ? is wavelength,         is the wavenumber, and ? is attenuation coefficient. For the purpose of sensing, we are interested in the radial frequency and phase velocity, vp, of the acoustic wave.  A closed form approximation of these values can be calculated using Kirchoff?s plate theory.  As detailed in [37], the motion of a multi-layer thin plate under tension can be described by summing the forces acting on it in the z-plane,                                              (3)  Here, T is tension [N/m],  D is stiffness [Nm],  H is rotational inertia [kg], and M is linear inertia [kg/m2].  A schematic of the multi-layer plate is shown in Figure 3. It has a thickness of d, spanning N layers with individual properties.  The approximation is valid given that there is no deflection or force acting in y and that uz is independent of z.  Figure 3: A schematic of the composite plate structure. The constant of the first term in  Equation 3, T, is obtained through integration of in-plane stress, ?S,x, present in the propagation medium over its thickness,                   .      (4)  As a practical sensor is often composed of multiple materials under different amounts of stress, this operation will involve the summation of  tension terms from each layer. Stiffness is given by the integration of biaxial Young?s modulus, E?=E/(1-?p2), where ?p is Poisson?s ratio and E is Young?s modulus, and relative thickness squared,                       .     (5) z0 refers to the neutral plane of the plate structure.  This is a plane which has an internal stress that is not affected by bending. In the absence of external stress from another source, it separates the portions of the beam under compression and tension during bending. In a homogeneous beam, this point exists midway between the top and bottom. For a multilayered structure, as dealt with here, z0 is given by 9                                          .      (6) Similar to tension, the stiffness value of a multilayer structure is calculated via a summation of integrals.  Given a constant Young?s modulus over each layer, Equation 5 becomes                                   .   (7) Rotary inertia creates resistance to rotation in the plate.  It is defined as the integration of density, ?, and thickness squared,                      .     (8) Finally, linear inertia is given by the integration of density over the thickness of the pate,               .      (9) Equation 3 is solved by assuming that uz undergoes harmonic, undamped motion.  It has four solutions, two of which correspond to travelling waves.  The radial frequency for these solutions is               .       (10) Given the small value of rotary inertia, relative to linear inertia, the H term may be eliminated, simplifying the relationship [37].  Re-arranging for phase velocity, vph, results in,               .      (11) This relationship describes the fundamental mechanism of acoustic sensing.  As the mass density, stiffness, or tension of the multilayer substrate shift, the frequency and velocity of the FPW will change according to the phase velocity equation.    Most FPW devices are configured for gravimetric sensing.  A polymer sensing layer which absorbs a vapour analyte is applied to the substrate. In the presence of the analyte, the sensing layer gains mass according to the concentration of the analyte, increasing the value of M. During this process, the total tension and stiffness of the sensor may change; however, given a relatively stiff and thick substrate, these changes will be minor and can usually be ignored.  In such a case, the detection sensitivity can be described by the FPW function in Table 1. As discussed in [5], a device constructed with a substrate with a Young?s modulus similar to that of the sensing layer will not necessarily show a sensitivity inversely proportional to density and thickness.  10  Instead, the frequency will shift in accordance with mass, stiffness and tension changes within the sensing layer, leading to a more complex relationship for sensitivity.   A function for overall linearized sensitivity of a polymer acoustic sensor was derived in [38] by summing the effect of each property variation on resonant frequency,                                                 ,   (12) where SM, SD, and ST are mass sensitivity, stiffness sensitivity, and tension sensitivity, respectively. In order to relate stiffness and stress changes to the more commonly measured value, mass loading, a constant, s3d [m3/kg], was introduced by Sielmann to describe sensing layer swelling as a function of mass loading. Assuming that the Young?s modulus of the sensing layer remains constant and identical to that of the substrate during dissolution, Equation 12 may be differentiated to produce                                                                              (13) where             , the stiffness of a uniform beam or plate, Epoly is the Young?s modulus of the uniform beam, and T0 is initial substrate tension, defined by Equation 4.  This equation has two important properties for our application.  First is the differing polarity of one term.  Given the above two assumptions, a polymer absorbing an analyte will show an increased mass, stiffness, and tension.  The result will be that the stiffness term may act to cancel the effects of the two remaining terms.  However, if the geometry and material properties of the device are chosen correctly, it could be tailored to be selectively sensitive to one of the three terms.  This is the second important property of the relationship. Given the absence of substrate tension in the first term and the differing dependence on d0 and Epoly in the remaining two, it is theoretically possible to selectively design and tension the sensor to act primarily as a mass, stiffness, or stress detector.    In the following investigation, Equation 13 is used to guide design decisions and serve as a starting point for further performance model development. 1.4 Piezoelectricity and Piezoelectric PVDF Piezoelectric materials are solid, crystalline substances which, when compressed, generate an internal electric field.  The field is created generally as a result of asymmetry in the atomic unit cell.  In most non-centre symmetric materials, electrostatic dipoles will form within each cell of the crystal structure.  These may be uniformly oriented by heating the material and applying a high intensity electric field.  The result is an array of identically oriented atomic scale dipoles.  When these dipoles are deformed, the average electric 11  field strength within the material they make up changes. If the material is coated in a perfectly conductive element, this will cause a net flow of charge.  If it is completely insulating, a potential difference will remain as long as the deforming stress is applied.  The converse occurs when an external field is applied.  The field applies force to the dipoles and the material expands or contracts as a result. A mathematical description of these actions is given by,                          (14)                       ,     (15) where ? is the strain matrix, s is the compliance matrix [1/Pa],   is the stress tensor [Pa], dp is the direct piezoelectric constant matrix  [N/C], Ef is the electric field tensor [V/m], De is the electric displacement matrix [C/m2],  dpt is the converse piezoelectric constant matrix [C/N], and   is the permittivity of the material [F/m].  The superscript E and   refer to the fact that s and d were determined under constant electric field and stress, respectively.   A fully expanded version of Equation    is given in by,                                                                                             .  (16) This describes the electric displacement caused by the converse piezoelectric effect in 3 dimensions, where dimensions 1, 2, 3 correspond to x, y, z, respectively.  Note that Voigt notation has been used to describe the stress tensor.  Therefore   1=   11,   4=   23,   5=   13, etc.   The 5 possible converse piezoelectric constants are included in the expanded relationship.  Each refers to a different set of relative stresses and dimensions. For example,  1 stress will generate an electric displacement over a perpendicular plane with a strength that is dictated by d31. The piezoelectric constant of a material provides a gauge for its ability to produce charge or actuate in the presence of an applied field.  Examining its definition can provide further insight to the source of the piezoelectric effect.  The converse piezoelectric constant is the amount of electric displacement produced per unit stress.  Given that the electric displacement is the summation of electric field multiplied by permittivity and polarization, P, dP is described by, 12                                 .    (17) A stress applied to a material with a permanent polarization, in the presence of an electric field will generate charge through a changing permittivity, field, and polarization.  For stiff piezoelectric ceramics or inorganic crystals, the first two terms contribute little to the overall change in displacement current and may be ignored.  This is not the case for polymer piezoelectrics, however.  As discussed in [39], due to the semi-amorphous, soft nature of these materials, the change in average polarization only accounts for a portion of the excess charge.  Charge accumulation also occurs due to deformation of the internal electric field and permittivity of the dielectric.  This means that non-ferroelectric or amorphous polymers may demonstrate piezoelectric properties [40], [41].  These materials, along with semi-crystalline ferroelectrics, can show piezoelectric behavior as a result of embedded space charge or surface charge becoming reoriented under stress. While amorphous materials such as polyvinyl chloride, polyacrylonitrile, and polyvinyl acetate have demonstrated piezoelectric constants as high as 5 pC/N, semi-crystalline, ferroelectric polymers such as polyvinylidene fluoride (PVDF) show constants as high as 30 pC/N [41].  This high piezoelectric coefficient makes PVDF a popular material for sensing applications.  Past research has included the development of PVDF based biosensors [42], [43], non-destructive testing transducers [44], and acoustic chemical sensors [45]. For this application, the material was chosen due to its piezoelectric characteristics, its chemical robustness, and its relatively low cost of manufacture.  Highly piezoelectric PVDF was first identified in 1969 [46] and is the only commercially available piezoelectric polymer.  As shown in Figure 3, a single monomer of this material consists of two sets of fluorine and hydrogen affixed to a carbon backbone.  Figure 4: PVDF monomer molecular diagram. The polymer is semi-crystalline, consisting of five crystal phases, ?, ?, ?, ?, and ?, interspersed by amorphous regions [47]. ? and ? are the most common and well studied of the five.  The former occurs naturally in the greatest fraction while the latter shows the greatest average polarization per unit cell [48]. Images of the two phases are shown in Figure 5. 13   Figure 5: A diagram of alpha phase (left) and beta phase (right) PVDF. Alpha phase PVDF shows a very small average polarization.  When H and F atoms are aligned, as in the ?-phase crystal, the resulting high electronegativity gradient leads to a large polarization. Poling a film with high ? content will align the hydrogen-flourine dipoles and create a highly piezoelectric material.  PVDF film is manufactured through extrusion or solvent casting [49].  Different processing conditions will result in different properties [50]; however, in general, commercially available film consists primarily of alpha phase crystal and amorphous regions.  As is discussed in the Fabrication Section, stretching and annealing will convert the crystalline regions to ?-phase.  McMaster Carr PVDF film which was used in the development of this sensor was extruded externally. Key properties of the material used are given in Table 2. Table 2: Key properties of PVDF, obtained from [3], [5] Property Symbol Value Units Density ? 1780 kg/m3 Young's Modulus E 2.5 GPa Poisson?s ratio  0.35  Converse Piezoelectric Constant d31 13.7 pC/N d32 1.95 pC/N d33 -30 pC/N d24 -19.6 pC/N d15 -19.9 pC/N  ?11 6.6   Relative Permittivity ? 22 8.2    ? 33 7.4  Electromechanical Coupling Coef. k33 0.11  Melting Point Tm 175 oC Curie Temperature Tc 125-175 oC 14  1.5 Transducers Piezoelectric transducers convert electrical energy into mechanical energy to allow the direct coupling of a signal to an acoustic device. They achieve this by selectively exposing regions of the piezoelectric substrate to varying electric field intensity.  The transmitting and receiving electrodes of this sensor consist of periodic fingers of opposing polarity known together as interdigitated transducers (IDTs).  Developed in 1965, IDTs are the earliest electrode geometry to allow direct coupling of Lamb waves into a piezoelectric substrate [51].  Figure 6 shows a diagram of the transducer design used in this device. 400 ?m centre-to-centre finger spacing was used for this investigation, leading to an 800 ?m acoustic wavelength.  Figure 6: A diagram of the main transducer used during the investigation. Acoustic waves are generated at the centre, transmitting IDT and received at the outer IDTs. Wires are affixed to the contact pads with carbon glue. Beneath each IDT set, on the opposite side of the substrate, a conductive ground plane is also applied. Its purpose is to concentrate electric field through the substrate [5].  During operation, changing potential between fingers and the ground plane induces expansion and contraction in the x and z dimensions through the d31 and d33 piezoelectric constants. Given that the plane of zero stress in the piezoelectric-backplane-sensing layer structure is offset from the centre of the piezoelectric material, these strains will cause bending about each finger [37].       1.6 VOC Sensing Layer and Polymer-Solvent Solutions 1.6.1 Overview A guided acoustic sensor designed to selectively detect an analyte requires a sensing layer which has physical properties that will change predictably in the presence of that analyte.  For the detection of volatile organic compounds, polymers are chosen which will dissolve in the presence of small quantities of VOC vapour. During sorption, these polymer films swell, soften and gain mass, leading to a change in sensor Receiving IDT Receiving IDT Transmitting IDT Contact Pads 15  resonant frequency. In order to predict the response of a sensor to a certain concentration of analyte, the nature of these changes must be understood. Optimally, empirical data should be relied upon to develop a sensing model for each polymer-solvent combination.  However, as it is impractical to test all possible material pairs, a theoretical model must be used to identify the best candidates and predict their performance.  Such a model must be able to relate changing mechanical properties of a film to the external concentration of a solvent vapour.   A diagram showing the purpose of this model is shown in Figure 7. It should use solvent vapour concentration, environmental conditions and sensing layer characteristics to predict sensing layer thickness, density, Young?s modulus, and stress. These values can then be used to calculate sensor mass loading, tension, and stiffness using Equations 4 to 9. Equation 11 can then be used to calculate sensor phase velocity, frequency and phase.  Figure 7: A diagram showing the purpose of the sensing layer model. Phase velocity, frequency, and phase are predicted by the FPW Wave Velocity Equation (Equation 11). Sensing layer thickness, density, Young?s modulus, and stress are calculated using the sensing layer model, solvent vapour concentration, environmental conditions and sensing layer characteristics such as pure polymer density and Young?s modulus.   1.6.2 Flory-Huggins Solution Theory Flory-Huggins (FH) solution theory was chosen as a starting point for this model.  It describes the thermodynamics of polymer-solvent solutions and can be used to determine the volume fraction of a polymer and solvent as a function of external solvent concentration.  Given knowledge of the physical properties of the two materials in their pure form, this information can be used to estimate the density, thickness, Young?s modulus, and stress of a film absorbing an analyte. 16  Derived first by J.P. Flory in [52], FH solution theory describes the change in free energy of a polymer-solvent mixture based on statistical thermodynamics. During the combination of these two components, entropy of the system, S [J/K], changes due to the increase in the number of possible orientations for the polymer and solvent molecules.  Simultaneously, the enthalpy of the mixture, H [J],  changes due to electrostatic, polar, and Van der Waals interactions between the two reactants.  The resulting change in Gibb?s Free energy, G[J], is given by the equation,                  (18) where Te is temperature. FH solution theory interprets solvent molecules and polymer segments as constant volume spheres which occupy lattice sites in a three dimensional matrix. Assuming that these molecules mix randomly, that they do not react with one another, and that molecules of a given type are identical, then it is possible to estimate the entropy of the system by summing the number of polymer chain configurations. A full derivation can be found in [52].  The resulting relationship for change of entropy is,                      .     (19) Here, k is Boltzmann?s constant, N1 is the number of solvent molecules, N2 is the number of monomer units,   , is volume fraction of solvent and   is volume fraction of polymer.  Enthalpy change,             ,      (20) is calculated by the energy change per polymer-solvent interaction multiplied by the estimated number of interactions. In Equation 20,   is the polymer-solvent interaction parameter. The term      describes the average change in energy caused by the movement of one solvent molecule into the polymer.   Combining the two terms and converting molecular counts N1 and N2 to moles n1 and n2 nets the relationship,                            ,     (21) a common form of the Flory-Huggins equation.  In order for this relationship to be of use, the change in free energy of the system must be related to that of the solvent being absorbed.  Differentiating the free energy with respect to moles of solvent yields the change in chemical potential energy of the solvent during mixing,                          (22) Differentiating the right hand side of equation 19 similarly, noting that  is a function of n1, and converting remaining   terms to (1-   , results in,                                   .    (23) 17  Here, x is the number of segments per polymer chain.  For large values of x, this term may be ignored [52]. Chemical potential change of the ambient solvent may also be described assuming that it may be interpreted as an ideal gas,                    .      (24) Here P1 is the partial pressure of the analyte vapour while P10 is its saturation pressure.  Equating Equation 23 with Equation 24 results in,                         .     (25) This relationship shows       as a function of volume fraction of a polymer,   , as a function of the ambient concentration of a solvent and the polymer-solvent interaction parameter,    In Section 3.4, it will be used, with  Equation 26, to relate gas analyte concentration to volume fraction solvent and polymer. These will then be used to determine mass density, thickness, Young?s modulus and stress of the sensing layer.    plays a key role in the modeling of the polymer sensing layer as it dictates the degree to which the polymer will absorb an analyte.  A high interaction parameter corresponds to an insoluble polymer-solvent combination.  In general, a compound with a    value less than 0.5 for a certain polymer is a ?good? solvent [53]. As dictated by the FH equation, the better the solvent, the smaller the concentration required to induce a constant change in polymer and solvent volume fractions. Values for a set of common VOCs and two polymers investigated in this work are given in Table 3.  These values have been obtained by exposing samples to different concentrations of analyte, measuring a change in their physical properties and using a variation of Equation 23 to calculate   [54] .  A range of values are reported for some combinations as the parameter may change as a function of temperature, polymer molecular weight, and polymer hydrolysation [55]. Table 3: Polymer-solvent interaction parameter values for PVAc and PS [56].    Polymer-Solvent Interaction Parameter Poly(vinyl acetate) Polystyrene Ethanol 0.47 1.80 to 0.43 Butyl acetate 0.51 0.466 Water 2.5 4.4 to 3.1 Chloroform -0.17 to -0.09 0.52 to 0.17 Benzene 0.30 to 0.26 0.40 to 0.26 Acetone 0.31 to 0.39 0.81 to 1.1 Toluene 0.56 to 0.40 0.42 to 0.31 18   This model accurately describes the behavior of polymers above their glass transition temperature, Tg.  Below this temperature, polymers are said to be glassy while above, they are rubbery.  A polymer-solvent system in the latter state acts more like a liquid solution while that in the former acts more like a solid.  It may be driven from glassy to rubbery, either through heating or through the addition of solvent.  Adding solvent increases chain mobility and causes the glass transition temperature to fall.  If enough is added, Tg can fall past the temperature of the polymer, thereby causing a transition from one state to the other. During operation of the sensor, it is possible for the polymer sensing layer to be in a glassy or rubbery state.  In fact, given the rapid change in mechanical behavior which occurs near the glass transition temperature, it may be beneficial to design a sensing layer which operates near Tg. To explore this possibility and to properly model the behavior of the sensing layer, a modified Flory-Huggins model is used to describe polymer volume fraction below the glass transition temperature.   1.6.3 Modified Flory-Huggins Solution Theory As a greater quantity of solvent is absorbed by a glassy polymer, it may be driven into a rubbery state.  This transformation is accompanied by a change in sorption properties.  While in the rubbery state, the quantity of solvent in the mixture may be described by FH solution theory, the same approach significantly underestimates the volume of solvent in the same polymer in a glassy state [57].  To put it another way, at low analyte vapour concentrations, FH solution theory will underestimate the amount of solvent present in the polymer sensing layer. It is believed that microvoids allow excess penetrate to be absorbed. This mechanism is likened to Langmuir mode adsorption and has been described by a number of different models [57]?[59]. Due to the relatively high elastic modulus of the solid in this state, solvent sorption by a glassy polymer is not accompanied by the expansion seen in rubbery materials.  As such, Langmuir hole filling is the main cause of solvent uptake in this state and polymer swelling is very limited. Leibler and Sekimoto developed a model which accurately captures this behavior and relates it to the elasticity and volume fraction of the polymer [57]. Their modified FH equation relates the activity of the solvent to polymer volume fraction, polymer-solvent interaction parameter, solvent volume fraction,   , polymer bulk elastic modulus, K, and the polymer volume fraction at glass transition,        ,                                             .    (26) The glass transition volume fraction is the concentration of polymer at which the GTT is room temperature.  This can be calculated by taking the weighted average of the GTT of each component in the polymer-19  solvent mixture as a function of solvent concentration [60] (See Appendix-Section A.1).  Using data from a study on VOC sorption in amorphous polymers [61], the glass transition polymer volume for toluene in PS and PVAc at 25 oC is 0.83 and 0.90 respectively. Equation 23 is valid below the glass transition concentration and is used in conjunction with the Flory-Huggins equation to describe solvent and polymer volume fraction as a function of ambient vapour concentration.  Figure 8 shows the predicted volume fraction of toluene in a PS-toluene mixture as a function of vapour partial pressure.  At lower solvent concentrations, Equation 26 is used to predict solvent-polymer properties while at higher concentrations, the Equation 25 is used.    Figure 8: Solvent volume fraction as a function of solvent vapour concentration, predicted by FH solution theory (above GTT) and modified FH solution theory (below GTT). The fourth order polynomial fit function is used in the full sensor performance model (see Appendix- Section A.4 for further details).  The predicted polymer and solvent volume fractions are used to describe sensing layer thickness, density, elasticity and stress as a function of analyte concentration. 1.6.4 Partition Coefficient As most prior investigations of acoustic sensor detection layer sensitivity have been concerned primarily with mass density, the majority have used the partition coefficient, Kp, to model the same phenomenon [3], [5].  The partition coefficient,         ,      (27) 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8 Solvent Volume Fraction ?1 Solvent Vapor Pressure (P/Po) Flory-Huggins Leibler-Sekimoto  Poly. (Combination) 20  is a ratio which describes the concentration of a solvent in a polymer, Cs, per unit concentration of that solvent in the gas phase, Cg. While Kp values have been determined for a large number of polymer-solvent combinations under many different conditions [62], they only allow the calculation of average sensing layer density change.  Under certain conditions, an FPW device composed of a polymer substrate is highly sensitive to detection layer expansion, softening, and stress relaxation.  FH solution theory allows the prediction of these properties with only one empirical parameter.  1.7 Flexural Plate Wave Driven Acoustic Streaming Flexural plate wave driven microfluidic transport was first demonstrated by Moroney et al. in 1991 [12].  Prior to this, primarily standing waves and compressive oscillators were investigated as acoustic sources. In this work, it was demonstrated that Lamb waves, confined to a thin membrane, could induce continuous flow near the substrate, parallel to the direction of acoustic propagation.  An analytic model for the fluid motion was also presented. The topic was investigated with the goal of developing solid state micropumps for mixing, transport and cooling [63][11]. Follow up research from the same group involved the design of FPW devices for microfilteration [64] as well as the modelling of acoustically driven flow [65], [66].  In all cases, the flexural plate wave pumps were composed of a 4 ?m to 10 ?m thick zinc oxide and silicon nitride substrate and aluminum IDTs driving a 100 ?m wavelength acoustic disturbance.  The resulting in-plane wave velocity was in the low hundreds of meters per second and frequency of oscillation between 1 and 10 MHz.  In comparison to SAW devices fabricated during the same time period, these values are quite low. As a result, the maximum measured FPW driven flow velocity is often in the low hundreds of micrometers per second while that of current SAW devices can be as fast as a few meters per second [13].  This is due, in part, to the different mechanisms which drive streaming above each guided wave. When propagating in fluid, high velocity SAWs will refract away from the solid-fluid interface at an angle determined by the velocity of sound in the two different media.  These waves will attenuate in the fluid, causing fluid displacement.  Lower velocity FPWs will refract to a much smaller degree or not at all.  Those waves which travel at velocities lower than the speed of sound within the adjacent fluid will remain in the guiding medium.  Fluid flow in this case, is believed to be caused by evanescent waves causing displacement at the interface layer.  A comparison of the two different wave modes acting on a droplet is shown in Figure 9.   21  Figure 9: A diagram of SAW driven acoustic streaming (left) and FPW driven acoustic streaming (right).  The high velocity surface acoustic wave refracts into the fluid at the angle              , where Vf is the speed of sound in the fluid (1484 m/s in water) and Vph is the phase velocity of the wave. For waves with velocities smaller than Vf, acoustic power remains in the substrate.  As a result, flow is driven by disturbances in the viscous boundary layer. An analytic approximation of FPW driven streaming is detailed in [11]. As the governing equations which describe the streaming phenomenon are nonlinear, some form of approximation is required to obtain a closed form solution for flow.  In this case, successive approximation is used to obtain a first order solution for the Navier-Stokes (NS) equations.  The first order solution is used to calculate a second order approximation and, using the Longuet-Higgin?s equation, an estimation for average mass transport velocity [11].  The resulting relationship describes fluid flow rate, in the direction of the acoustic wave, as a function of distance from the substrate. The derivation, presented in [11], begins with the NS equations,                                            (28) a relationship for conservation of mass,                      (29) and a function describing the relationship between pressure and density,                      (30) Here    is fluid density,   is the fluid velocity vector, P is pressure,    is bulk viscosity,   is shear viscosity, cF is the speed of sound in the fluid and R represents relaxation effects in the fluid.  As per the method of successive approximation, velocity, pressure and density are decomposed into linear, quadratic, cubic and higher order components.    High velocity (Vph>Vf) SAW causing acoustic streaming in a droplet. Low velocity (Vph<Vf) FPW causing acoustic streaming in a droplet. 22                                                              (31)                               Two first order solutions are obtained given semi-infinite boundary conditions.  At the interface between the fluid and the substrate, a no-slip condition is imposed,                                    .    (32) Here, ? is radial frequency, a is out-of-plane acoustic wave amplitude, and ? is a decay factor. The solutions describe an evanescent wave (the mass loading solution), and an oscillating evanescent wave (viscous solution).  For sensing and fluid streaming, the most important aspect of these waves is the depth which they extend into the fluid.  For the mass loading solution, this is approximated by     [m], while for the viscous layer solution, it is approximated by      [m], where                   , and          ,     (33) In Equation 33, Vp  [m/s] is phase velocity of the acoustic wave, and Vf  [m/s] is the speed of sound in the adjacent fluid. ? and ?v are the decay factors for the first order mass loading and viscous solutions, respectively. Their inverse describes the practical limits of the mass-loading boundary layer and the viscous boundary layer.  The latter is important for streaming as the viscous solution is the cause of steady state flow. Fluid flow parallel to the substrate surface is generated within this boundary layer and reaches a maximum velocity near     . The mass transport velocity at the edge of the boundary layer is derived by obtaining the second order solution for Equation 28 given boundary conditions described by Equation 32.  An approximate solution for this problem was developed by Longuet-Higgens to calculate the drift velocity of water beneath ocean waves [67].  The application of this method to the current system is described in [11].   The maximum velocity of this flow is given by Uxlim.                                                   (34) Flow at the viscous boundary layer will drive slow streaming in the bulk fluid; however, for this work, it is used only as an estimate for maximum flow rate observable near the surface of the substrate. A more descriptive approximation for the relationship between acoustic amplitude and flow rate is given by Moroney et al.  in [68].  The second order solution for fluid motion varies as a square of the first order 23  solution. Squaring an approximation for the first order solution,               where V is the out-of-plane wave velocity, results in a function with a frequency doubled component and a DC component,                                       This DC component corresponds to the predicted drift velocity and varies as a function of acoustic wave amplitude squared, a relationship that has been confirmed with experimental observations [11], [68]. This approach was chosen as it has been used successfully to predict FPW driven fluid flow given a driving wave of similar frequency, phase velocity, and amplitude as that investigated here [11]. An alternative model for Uxlim is given by Manor et al. [69], was also considered. They present a general relationship for viscous boundary layer flow driven by a travelling SAW or Lamb wave in a substrate which is parallel to the fluid. The derivation is significantly different than that presented by Moroney et al. as it does not rely on the Longuet-Higgens equation, which is derived assuming drift flow driven by free surface waves, not oscillations from a solid substrate1.  Given an identical situation to that described above, the drift velocity in parallel with the substrate is approximated by,                     ,     (35) where V is velocity amplitude of the FPW. This approximation assumes that particle motion in the wave is retrograde and that the wave itself does not attenuate due to energy lost in the fluid.  Both Equation 34 and 35 will be compared with acoustic streaming experimental results. 1.8 Objectives The primary goal of this project is to design a highly sensitive, all-polymer acoustic sensor for VOC detection.  Building upon the development of a PVDF FPW device demonstrated in [5], this investigation was carried out with the purpose of meeting the following objectives:   1. Demonstrate VOC detection using polymer FPW sensor, characterize sensor performance. Humidity detection using an all-polymer FPW device has been demonstrated in past work [5]. A key goal of the investigation will be to build upon this work and demonstrate the detection of a volatile organic compound. This objective is addressed in Chapter 3 and Chapter 4 with a                                                      1 The key difference between these situations is the treatment of instantaneous stress acting on the fluid at the boundary layer. In the case of free surface waves, surface particles are not subjected to horizontal stress during oscillation. The opposite is true for fluid at an oscillating solid boundary. In this case, due to the no slip boundary condition, particles experience both vertical and horizontal stress. 24  discussion of the design and fabrication of the sensors and Chapter 5 with the presentation of the testing results.  2. Develop a model for sensing layer absorption of analyte, validate with test results. In previous work [70], the resonant frequency of the sensor was described by Equation 11, where tension, mass density, and stiffness are described using fitted linear functions. An important goal of this work was to develop a model which required no fit parameters and few empirical constants to predict the behavior of a sensor.  This objective is addressed in Chapter 3, with the introduction of a performance model, and Chapter 5, with its comparison to experimental results  3. Modify sensor design and fabrication to improve sensitivity. The practical sensitivity of the current sensor design is insufficient to compete with existing devices [5]. As such, one goal of this work will be to modify the design and fabrication to improve detection. This includes working to change sensor geometry, substrate materials, and sensing layer. This objective is addressed in Chapter 3 and Chapter 4.  4. Improve fabrication yield by investigating novel inkjet printing or conductive polymer deposition techniques. Sensor prototype fabrication has been carried out primarily using micro-inkjet printing. This has allowed new transducer designs to be easily manufactured and tested. The process can be time consuming, however, and results in a low sensor yield due to the poor droplet deposition precision. As such, one goal of this project was to investigate new methods which would allow higher yield and volume sensor manufacturing.  This objective is addressed in Chapter 4 with the discussion of screen printing for sensor fabrication.  5. Identify and investigate novel applications. The unique sensing characteristics and fabrication method associated with the all-polymer FPW device make it potentially useful in a wide range of detection and actuation applications. A portion of this investigation was therefor dedicated to identifying novel applications. Cure characterisation using FPWs is addressed in Section 5.3 while an all-polymer FPW acoustic manipulator is presented in Section 5.4. 25  2 Experimental Methods In this chapter, the equipment and methods used to characterize and test the sensor are described. It is separated into two broad categories: Material Characterisation and Gas and Thin Film Sensing. The first details the methods used to interrogate the properties of each component of the sensor while the second describes how sensor and device performance was tested.  2.1 Material Characterisation 2.1.1 Stress Strain Analysis and Piezoelectric Constant Measurement A Bose Uniaxial Stress-Strain tensionmeter was used to characterize thin polymer films.  The tool applies a known displacement or force to samples while measuring the opposite.  Both tensile and compressive stresses can be applied through forces ranging from -20 N to +20 N with a resolution of 0.001 N.  By analysing the resulting deformation caused by the application of a force over a known area, material properties such as elastic modulus and loss modulus can be determined.  During this project, this tool was used to determine the material properties of polymer samples and to measure the piezoelectric constant of processed PVDF.   Stress-strain analysis was carried out on a range of PVDF samples in order to obtain an accurate measurement of their elastic modulus throughout the fabrication process.  10 ?m to 75 ?m thick samples were cut to 1 cm by 6 cm dimensions.  These were then mounted in the uniaxial tensiometer.  A slow linear force ramp was applied to each one ranging from 0 to 0.5 N and the resulting displacement was measured.  The displacement and stress were then used to calculate tensile Young?s modulus.   Piezoelectric constant was measured by applying a compressive force to a sample over a known area and measuring the resulting charge accumulation using a Kistler 5015A Charge Meter and Keithley 2635A Sourcemeter.  The constant was calculated using Equation 13.  Doing so required that the sample was able to freely deform and that it maintain zero electric field strength during compression.  These requirements were satisfied by affixing electrodes over the compression paddles such that the surface area over which stress was applied was completely conductive and by electrically connecting these pads to a low input impedance charge amplifier.   Sample films were aligned such that stress was uniformly applied along the 3rd axis.  Charge build up was measured over the plane perpendicular to the 3rd axis and so the piezoelectric constant recorded was d33. 26  2.1.2 Differential Scanning Calorimetry Differential scanning calorimetry is a materials characterisation method which can be used to investigate phase transitions, heat capacity, and crystallinity of a material.  It involves heating a solid or liquid sample and measuring the heat required to change its temperature.  This is compared with the response of a well characterised material such as water and a heat flow curve is generated.  An example curve is given in  Figure 10.  Here, phase transitions are indicated by heat flow peaks.  In this case, the upper peak corresponds to melting and the lower to solidification; however, depending on their shape and location, they may also represent vaporization, sublimation, decomposition, and various forms of crystallization.  Figure 10: A diagram of a basic differential scanning calorimeter curve. Data from an untreated McMaster Carr PVDF sample heated to from 20 to 200 degrees and back. During this project, DSC was used to obtain the crystallinity of polycrystalline PVDF.  The amount of heat required to induce a phase transition in a material is directly related to its percentage crystallinity. A single crystalline substance will require more heat during melting and so, will have a larger phase transition peak.  The percentage crystallinity is calculated by dividing the difference between the heat of melting, Hm [J/g], and the heat of crystallization, Hc [J/g], by the heat of melting for a pure crystal of that material.                                   (36) Each of these terms is found by integrating over the corresponding peaks, highlighted in grey. Samples were heated from room temperature, past their melting temperature to 300 oC and back to 22 oC at a rate of 5 oC/min.   DSC was also used to determine the Curie temperature and the effect of processing on the crystallinity and melting point of PVDF.     2.1.3 Fourier Transform Infrared Spectroscopy   Fourier transform infrared spectroscopy (FTIR) is a method of investigating the structure and configuration 27  of organic samples by exciting molecular scale oscillations in the material with infrared light and measuring the frequencies which are absorbed or re-emitted.  During this investigation, FTIR was used to measure the relative quantity of the different PVDF crystalline phases. Thin PVDF samples were exposed to IR light with wavenumber from 600 cm-1 to 1500 cm-1 and the intensity of transmitted radiation was recorded as a function of wavelength.  For this material, the 763 cm-1 and 840 cm-1 bands will be absorbed by alpha and beta crystalline material, respectively. Comparing the relative amount of IR radiation absorbed over these wavenumbers, as described in [23], will provide an estimate for the quantity of each crystal phase in a material. 2.1.4 Laser Doppler Vibrometry A laser Doppler vibrometer (LDV) relies on the Doppler shift of a laser reflected from an oscillating surface to measure the velocity and frequency of that oscillation.  A beam of light is generated and split, with half the beam being sent to an oscillating sample and half being redirected to be used as a reference.  The reflected beam from the sample is recombined with the reference beam and directed to a photo-detector.  Displacement of the sample induces frequency and phase shifts in the reflected beam.  Upon recombination, these phase shifts become evident as changes in intensity due to constructive and destructive interference. Velocity, displacement, and frequency of the oscillating sample surface can be calculated from the intensity of the two combined beams.    In this work, an Polytec PSV-400 Scanning Vibrometer was used to investigate FPW oscillations in the PVDF substrate. Samples were excited by 300-800 Vpk-pk, 250 kHz to 500 kHz bandwidth pulses, centered at 250 kHz, or a by single frequency sinusoidal signal. These input signals induced plate waves with amplitudes up to 10 nm.  LDV scans covered an area of 1 cm2. Frequency and wavelength data was used to characterize sensor performance prior to electronic testing.  Amplitude data was used to obtain measurements for acoustic decay and to confirm acoustic streaming results.  2.1.5 Thin Film Stress Measurement During solvent casting of the polymer sensing layer, internal stress will build up due to film shrinkage.  The magnitude of this stress was measured using a KSV Attension contact angle measurement tool.  Various polymer solvent solutions were cast on a polyethylene terephthalate (PET) film with known mechanical properties.  During solvent evaporation, rising internal stress caused these films to deflect.  The deflection was photographed every 1 to 10 minutes over a period of 24 to 48 hours and the images were processed to extract displacement data.   28  The magnitude of internal stress in the applied films was estimated by measuring the induced curvature of the substrate film,                                             (37) where Es is the Young?s modulus of the substrate, ts is the substrate thickness, tf is the film thickness, R is the radius of curvature of the substrate-film combination, L is the length of the substrate and ? is the angle of deflection [72]. A diagram of the setup and deflecting substrate are shown in Figure 11. Tests were carried out at room temperature and pressure and samples were allowed to evaporate for 24 to 48 hours.  Images were processed using ImageJ.   Figure 11: Thin film stress test setup.  Deflection of a PET film is measured and used to calculate stress of a solvent cast film  2.2 Gas Sensing and Thin Film Characterisation 2.2.1 Signal Generation and Extraction Signals used for sensor testing were created using an Agilent 33220A Arbitrary Waveform Generator and amplified to 150 Vpk-pk using a Bose piezoamplifier. Two signal forms were used during the investigation, a pulse train of single frequency sinusoids and a pulse train of custom chirps.  Pulses are used due to electrostatic coupling between the input and output transducers.  Applying a continuous wave excitation to the transmitting IDTs would induce a nearly identical signal at the receiving IDTs as a result of electrical coupling. Applying a pulse ensures that the much slower, much more attenuated acoustic signal will arrive at the receiving IDTs after the electrostatically induced signal has ceased.   50X Gain AmplifierPVDF Sensor50X 10x10X Gain AmplifierAnalogconditioningDSP Resonance Frequency Figure 12: A diagram of the test setup used to measure sensor performance. 29  The acoustic wave generated at the transmitting IDT is converted back to an electrical signal at two receiving transducers.  Each of these transducers is connected to an AD8253 high impedance instrumentation amplifier.  Here, the signals are amplified by a factor of 10 before being sampled by a 16-bit, 168 MHz, Delta Sigma AD9262 ADC.  A Blackfin 506F DSP samples the digitized signals at 50 MHz and the data is averaged 1000 to 5000 times a second.  Data packets are sent to a laptop running Labview at a rate of 8 packets per second. The Labview program then calculates, displays and saves the frequency, phase, amplitude and velocity of each acoustic pulse. A diagram and an image of the data acquisition setup are shown in Figure 12 and Figure 13, respectively.     Figure 13: An image of the sensor test setup. During testing, a sensor is exposed to a certain concentration of analyte and the signal is allowed to settle for at least 30 minutes before data for that concentration is logged. 2.2.3 Sample Vapour Generation Sensor performance is tested by exposing the devices to a known concentration of reactant vapour.  Two systems were used to achieve this: an Owlstone OVG-4 Gas Calibration Generator for humidity creation and control and a custom made toluene vapour generator. In both cases, compressed air was initially obtained through the lab distribution system.  However, long term exposure tests demonstrated that this air showed strong temperature, humidity, or particulate matter variation.  The result, shown in Figure 14, was that the resonant frequency of a device exposed to this source could swing dramatically over 27 hours.  To reduce this source of noise, dry, compressed synthetic air was purchased and used during all tests discussed here. FilterA/DDSPAmplifierSensor30   Figure 14: Frequency response of a sensor coated in PVAc, exposed to building compressed air for 27 hours.  The large frequency shifts are attributed to humidity and temperature variations in the stream.   2.2.3.1 Water Vapour Generation Water was used as the first vapour based test analyte.  Varying concentrations of vapour were generated using the Owlstone OVG-4 unit, shown in Figure 15, by sending a controlled stream of air through an external bubbler at room temperature and mixing the resulting saturated air with varying amounts of dry air.  By changing the ratio of dry air to saturated air, the average concentration of water vapour could be controlled.  A humidity sensor was mounted after the sample test chamber to monitor water concentration.  Samples were exposed to 10% to 70% relative humidity (RH) at room temperature during testing.  Figure 15: An image of the Owlstone humidity generation system used. During testing, vapour concentration is measured via an attached humidity sensor.  It is reported in dewpoint [?C] or relative humidity [%].   2.2.3.2 Toluene Generation Toluene vapour was generated in a similar way as water vapour.  However, a custom built system was used instead of the Owlstone vapour generator due to the limited concentration of VOCs which it could produce.  The custom setup consists of a compressed air tank, two mass flow controllers (MFCs), and two toluene 31  bubblers held at different temperatures. Air controlled by MFC1 is pumped through a two stage toluene bubbler before being mixed with dry air controlled by MFC2.  Figure 16: A diagram of the toluene vapour generation setup. The two stage bubbler was chosen to ensure that the toluene laden air mixed with the dry air in a completely saturated state.  Pumping gas through the first bubbler causes it to become nearly saturated with toluene vapour at an elevated temperature.  Passing the stream through a second bubbler at room temperature brings the gas below its dew point, causing condensation and ensuring that it is completely saturated.  During testing, the bubblers were maintained at the correct temperatures using hotplates and volume flow rates ranged between 200 ml/min and 500 ml/min.  When adjusting the ratio of dry to saturated air, the flow rate of each stream was adjusted such that the total flow rate remained constant.  This was done to ensure that the pressure inside the test chamber did not deviate strongly from concentration point to concentration point. Such a deviation would induce stress on the sensor substrate and cause an unwanted resonant frequency shift. 2.3 Acoustic Microfluidics Acoustic streaming performance was investigated using laser Doppler vibrometry and video of polystyrene bead flow.  Samples were mounted beneath a Polytec MSA:400 laser Doppler vibrometer and parallel to a high resolution camera, as shown in Figure 17.  Droplets were applied to the front (IDT coated) or back (backplane coated) of the devices which were oscillated at a range of frequencies. 32   Figure 17: Test setup for investigating FPW driven acoustic streaming Periodic chirp and continuous sine wave excitations were applied to the samples during testing. 10 kHz-200 kHz signals were produced by an arbitrary waveform generator before being amplified and stepped up to amplitudes of 100-800 Vpk-pk. 1-5 mm diameter droplets were applied to the back of the substrate of each sample during testing.  0.5 ?m to 3 ?m polystyrene beads were added to the fluid at concentrations ranging from 0.005% to 0.2% and videos were recorded at  2 to  20 magnifications under fluorescent illumination. In a separate configuration, the camera was mounted above the droplet and polystyrene bead displacement at the surface of the substrate was recorded. Video from this test was analysed using ImageJ [73] and the average bead velocity was calculated.           33  3 Design and Theory 3.1 Overview This chapter details the sensor design and associated theory. It is organized by the main components of the acoustic device: Substrate, Transducers and Backplane, Polymer Sensing Layer and Polymer Reference Layer. In each section, a link between performance and the physical characteristics of the component is detailed.   Design modifications are also discussed.  During this project, significant changes were made to the sensor design.  Unlike those devices detailed in earlier work [3], [70], [1], current sensors are fabricated using a thin, untensioned substrate, coated with a polymer sensing layer for the detection of volatile organics.  The motivation and details of these modifications are presented in this section.  Along with this, a model for the sensing layer response is described. 3.2 Substrate The substrate facilitates the generation of acoustic waves and their propagation through the sensing layer. It is composed of 9 ?m to 25 ?m thick extruded, stretched, and poled PVDF.  The electrical, mechanical and chemical properties of the processed film play an integral role in overall sensor performance.  During this project, three main modifications were made to the substrate design.  First, thick 25 ?m to 75 ?m PVDF films, as used in [5] and [1], were replaced by thinner 9 ?m to 25 ?m films.  Second, the films were framed with 0 MPa to 30 MPa of tension, rather than above 30 MPa. Finally, a single film supplier was selected for future work.  The motivations for these changes are discussed along with design details.  3.2.1 Mechanical Properties and Geometry As the substrate makes up 50 to 90 percent of the material through which the acoustic wave propagates, its properties play a key role in determining signal characteristics.  Resonant frequency, sensitivity, and amplitude are all strongly dictated by substrate geometry, elasticity, density and stress.  The relationship between the substrate and resonant frequency is described by Equation 11.  Approximating the composite structure of the beam by a single uniform material reveals a simplified relationship for the frequency dependence on each physical property,                         .      (38) 34  A similar approximation is used to derive Equation 13, FPW mass loading sensitivity given a constant and uniform Young?s modulus and stress.  As discussed by Sielmann [5], the function demonstrates the strong sensitivity of a soft FPW acoustic device to changes in sensing layer stiffness and stress. It also illustrates the strong frequency dependence on substrate thickness and stress.  Described fully in [38], a device with a very thick substrate will act as a gravimetric sensor.  This is evident by the presence of higher order d0 terms in the stiffness and stress sensitivity functions.  Conversely, a very thin device will be strongly sensitive to stress and stiffness variations.  Substrate stress similarly has a strong effect on sensitivity.  Reducing its value allows stiffness and stress changes in the sensing layer to have a relatively larger influence on the velocity of the travelling wave.   In general, reducing substrate thickness and stress leads to an increase in sensitivity. A model developed by Sielmann [5], also demonstrates that reducing these two values would significantly reduce acoustic wave attenuation. As such, reducing thickness and stress and confirming their effect on sensitivity was a key goal of this investigation.   3.2.1.1 Substrate Thickness Substrate thickness was reduced primarily by fabricating devices using thinner raw PVDF film. As detailed in Section 4.0, sensors were fabricated using 25 ?m, 75 ?m, and 100 ?m thick films.  After stretching the sensors were fabricated with thicknesses from 9 ?m to 50 ?m.  As expected, reducing thickness leads to a reduction in average resonant frequency, from up to 250 kHz to 76 kHz.  The lowest frequency reached is still somewhat higher than the predicted minimum.  This discrepancy is attributed to substrate stress and is discussed below. A screenshot showing the performance of the lowest frequency sensor is given in Figure 18.  This device was fabricated on a 9 ?m substrate and excited with a 300 Vpk-pk chirp centered near 80 kHz. While it shows a low frequency and comparatively little attenuation, it also shows small output amplitude compared with those devices fabricated using thicker substrates. As shown in Figure 18, output signal amplitude is 8 mV after amplification by a factor of 10. In comparison, thick film sensors showed output amplitudes ranging from 50 mV to 140 mV under the same conditions. 35   Figure 18: A screenshot of the time domain performance of a thin-film device oscillating at 76 kHz. Due to the low amplitude of these devices, the application of a sensing layer causes the received signal to be completely suppressed during operation.  As such, they were used primarily during the investigation into microfluidic manipulation (Section 5.4).  3.2.1.2 Substrate Stress Substrate stress reduction was achieved by framing un-tensioned PVDF film prior to printing.  Based on measurements taken in [1], this should have caused a 30 MPa reduction in stress.  Given a 20 ?m thick device, resonant frequency should drop from 200 kHz to 50 kHz.  This was not the case.  Framed samples showed resonant frequencies ranging from 100 kHz to 170 kHz.    In an effort to determine the source of the phenomenon, a sample was mounted in a Bose, stress-strain analyser and exposed to a range of forces.  The resonant frequency at each step was measured and compared with predicted values. A plot of this comparison is shown in Figure 19.  Similar to results from thin film sensors, measured frequency was significantly higher than expected.  36   Figure 19: The resonant frequency of a 20 ?m sensor as a function of substrate tension, compared with predicted frequency. This discrepancy has been attributed to residual stress in the substrate, accumulated either during stretching and poling or as a result of contraction in the solvent cast backplane or electrodes.  When calculating the predicted performance of a device, this residual stress is obtained by measuring the resonant frequency of an uncoated sensor and solving  Equation 11 for substrate stress.   3.2.2 Electrical Properties In order for the substrate to function properly as a guiding medium for acoustic waves it must be insulating and it must show a high electromechanical coupling coefficient.  Low conductance is necessary not just to prevent IDT shorting but also to allow poling at high voltages. Dielectric breakdown limits the upper intensity of electric field exposed to the sample.  While there are multiple different common breakdown mechanisms, in general, a high dielectric constant is required to prevent shorting during poling. PVDF films show relative dielectric constants ranging from 7-8.5.  Electromechanical coupling coefficient is the ratio of electrical energy applied to the IDTs to the mechanical energy generated in the substrate.  Most piezoelectric PVDF films are reported to show coupling coefficients ranging from 0.1 to 0.15.  This is quite low in comparison with those coefficients demonstrated by stiffer materials such as PZT [74].  As a result, acoustic wave amplitudes are much lower in PVDF.  3.2.3 Crystallinity A complete description of piezoelectricity in PVDF still eludes researchers [46], [47], [49].  However, while the relative importance of space charges and polarized crystalline regions is under debate, it is clear 30 50 70 90 110 130 150 170 190 210 0 2 4 6 8 10 Frequency (kHz) Substrate Stress (MPa) Measured Data Theoretical 37  that certain material properties lead to greater piezoelectric constants.  As detailed in Section 1.5, a high ?-phase content will net a higher total polarization.   This has been investigated in detail and the link between processing conditions and ?-phase content has been demonstrated.     Total crystallinity is another important factor which determines sensor performance.  PVDF is composed of both crystalline and amorphous regions.  The greater the percentage of ordered content, the larger total polarization induced during poling [75]. Film microstructure is determined during manufacturing.  Crystallinity is determined by casting and extrusion conditions (temperature, pressure, extrusion rate) [50], [71]. However, unlike ?- and ?-phase content, total crystallinity is not reported as a film property when purchased.  Manufacturing conditions are similarly unavailable.  As such, film from different supplies, and even different batches from the same supplier, have shown significantly different degrees of crystallinity and resulting piezeoelectric constants.   This issue was addressed in an effort to identify causes of differences in performance between thick and thin film devices.  As discussed in Section 4.1, raw film with a thickness greater than 75 ?m was supplied by a redistributor, McMaster Carr, from an unknown manufacturer.  This film was used to manufacture 18 ?m to 25 ?m thick sensors which consistently produced large amplitude acoustic and electrical responses.  In order to fabricate thinner devices, 25 ?m films were obtained in sample sheets from Solef and Professional Plastics (PP). Sensors fabricated with film from these suppliers showed little to no piezoelectric response.  According to the data sheets provided by the suppliers, they were more or less chemically identical to the film sold by McMaster Carr. To determine the cause of poor performance in the thinner film samples, the microstructure of PVDF from each supplier was investigated.    FTIR scans revealed that the devices had ?- to ?-phase content ratios similar to functioning devices. This suggests that any difference in piezoelectric content between the film types should not be attributed to a lack of ?-content. DSC scans, on the other hand, showed a large discrepancy between samples.  As illustrated in Figure 20, those obtained from McMaster Carr showed melting peaks up to 1.5 times greater than those obtained from Solef and PP.  This indicates a significant difference in total crystallinity2. In accordance with these results, only McMaster Carr film was used for further work.                                                      2 This conclusion is further supported by the relative transparency of the films.  While the McMaster Carr samples were opaque, indicating a polycrystalline structure, the Solef and PP samples were transparent, indicating either a highly crystalline or highly amorphous structure. 38   Figure 20: DSC scans of films from three different suppliers. The difference in melting peak area indicates a different in total crystallinity.  Note that the P.P. and Solef curves overlap during cooling. 3.3 Transducers and Backplane Signals are converted between the electrical and mechanical energy domains through the sending and receiving transducers.  These consist of conducting IDTs and a backplane. The geometry of these two components dictates the mode, wavelength, and amplitude of the acoustic signal generated. Finger pitch determines wavelength, relative polarity determines mode and direction, and, as detailed in [5], finger count will determine acoustic power. The three-IDT design presented in Figure 6 is currently in use.  Fingers are spaced by 400 ?m, centre-to-centre, and separate backplanes are added beneath each electrode as detailed in [1], and [4]. Both electrodes and backplane are composed of PEDOT:PSS. This conductive polymer was chosen due to its high conductivity, good chemical and thermal stability, and its ability to cure without UV exposure.  Silver ink was also explored as a potential candidate, however, the large number of prototype sensors printed necessitates the use of an inexpensive fluid and so a low cost polymer was chosen. Clevios HP1000 PEDOT:PSS was sourced for this purpose.  It offers conductivity up to 1000 S/cm and has demonstrated conductivity of 700 S/cm when used for this application [76]. 3.4 Polymer Sensing Layer The sensing layer is a 1 ?m to 15 ?m thick polymer film which is solvent cast to the backside of the sensor.  Its purpose is to selectively absorb gaseous analytes, thereby perturbing the state of the substrate bound flexural plate wave. Understanding the response of the sensing layer to the presence of different vapours is an important step to designing a highly sensitive and selective device.  In this investigation, FH solution -0.6 -0.4 -0.2 -1E-15 0.2 0.4 0.6 0.8 1 100 120 140 160 Heat Flow (W/g) Temperature (Celcius)  McMaster PVDF Solef P.P. 39  theory was used to develop a model for sensing layer mechanical parameters as a function of analyte concentration.  The purpose of the model is three-fold: first, to provide a better understanding of how polymer characteristics affect sensor response, second, to allow the easy comparison of new detection layers prior to testing, and third, to act as a preliminary predictive model for performance. As discussed in Section 1.0, the response of the sensor is dependent on polymer mass loading, stiffness, and tension.  These terms are related to thickness, density, Young?s modulus, and stress.  As the analyte is absorbed, the polymer swells, gains mass, softens, and endures a rise in tensile stress.  The degree to which each one of these qualities changes is dependent on the properties of the polymer and solvent. Using FH solution theory and the empirical polymer-solvent interaction parameter, the concentration of analyte and polymer volume fraction are linked.  Volume fraction is then used to predict the aforementioned mechanical properties. Relationships for thickness, mass, and elasticity were developed first and those for stress were created following experiments which demonstrated their necessity.  As such, they will be presented separately here. 3.4.1 Polymer Film Thickness, Mass, and Elasticity Film thickness may be simply calculated given the assumption that film expansion occurs in only one dimension,                (39) Here, d0 is initial thickness [m],  while d is thickness [m] at a given polymer volume fraction [77].  This relationship assumes that the polymer acts as a Hookean elastic material.  Film density,       [kg/m3], is calculated with the knowledge that, as the polymer expands, the volume density lost by the polymer is gained by the solvent [78], [79],                                 (40) where      [kg/m3] is the density of the pure polymer,  Mw [kg/mol] is the molecular weight of the solvent, and        [mol/m3] the inverse of the solvent?s molar volume inside the film,                        (41) Here, V1 [m3/mol] is the molar volume of the pure solvent.   Estimating the change in Young?s modulus is less trivial. Given the polymers and analyte chosen for this investigation, solvent absorption drives the sensing layers from a glassy state, through glass transition, to a rubbery state. In future design iterations, a sensing layer will be chosen to operate in only one of these 40  regions; however, all three were investigated with the purpose of identifying the most sensitive operating mode. To support this investigation, three models were identified to estimate the Young?s modulus of the sensing layer in each state.  In the glassy state, elastic modulus of an amorphous lightly or un-crosslinked polymer is defined primarily by Van der Walls forces which bind adjacent chains together [80]. As a polymer swells with increased solvent concentration, the strength of these bonds will be reduced and the elastic modulus will fall in a roughly linear manner.   The influence of solvent on the mechanical properties of an amorphous polymer is similar to that of the influence of increasing temperature [81],[82], and so, a model for elasticity as a function of thermal expansion was used [83], [84],               .      (42) Here, Te [K] is the ambient temperature and ?e is a thermal expansion coefficient. During operation, Te remains constant while the glass transition temperature decreases.  The value of Tg is estimated using a volume fraction weighted average of the glass transition temperatures of each component in the mixture (see Appendix-Section A.1).  When the glass transition temperature becomes equivalent to the ambient temperature, the Van der Waals bonds constraining inter-chain movement will disappear, forcing the polymer into a viscoelastic state [84].  This is accompanied by a rapid change in viscoelectric behavior, which is commonly described using the Williams-Landel-Ferry (WLF) relationship [61],[84],[85]. Based on the principal of time-temperature superposition (see Appendix-Section A.2), it describes the shift in instantaneous elastic or viscous behavior of a polymer given a changing ambient temperature [85].  Given a known elastic modulus at an initial ambient and glass transition temperature, the WLF equation is used to predict Young?s modulus as a function of solvent induced GTT shifts,                                       .     (43) The known elastic modulus is the value predicted by Equation 42 just before the glass transition temperature. Constants c1 and c2 are empirically determined and obtained from [85] and [84] for this investigation. These values determine the slope of the modulus-concentration plot and so, should be measured directly in future design iterations.  Far above the glass transition temperature, the Van der Waals bonds have completely melted and polymer chains move more freely. According to statistical rubber elasticity theory, elasticity of a rubbery polymer is 41  inversely related to the molecular weight between crosslinks or entanglements, Mc, and directly related to the density of the polymer, ?pol, and temperature, T [86], [87],            .      (44) For a polymer film, expanding in one dimension on a rigid surface, this value will scale linearly with volume fraction of polymer [88],                  (45) For this investigation these relationships will be used to describe polymer elasticity at greater than 100 oC over the GTT, where Equation 43 is no longer valid [85]. As shown by past experimental results however, the glass transition region does not have discrete, well defined boundaries [89] and so elastic behavior may be approximated by equations Equation 44 and Equation 45 when the polymer is less than 100 oC over the GTT.  For future design iterations, direct measurement of polymer elasticity as a function of analyte concentration should be used to determine when this transition takes place. A large motivation for the development of this model has been the lack of past experimental work on the detailed mechanical properties of various polymers in the presence of solvents. As such, model validation was carried out using data from two investigations into the mechanical properties of a PVA-water mixture [90] and [89], rather than a polymer-VOC mixture.  The data sets were chosen as they were the most complete that could be found and were previously used to confirm sensor performance, when configured for humidity detection [70]. Figure 20 compares the mechanical data obtained from [90] and [89]  with results predicted by the model presented above.  As humidity rises, the PVA expands and softens.  Counter intuitively, its average density falls. Given the fast expansion of the film though, the total mass loading increases over the entire range.  Near 60% humidity, the glass transition concentration is reached and the elastic properties of the polymer change dramatically.  This is echoed in the experimental data; however, the transition between glass and rubber elasticity is likely much smoother in practise.  Further experimental data will be required to properly predict this transition. 42   Figure 21: The measured and predicted percent change in thickness, density, and Young?s modulus of PVA exposed to varying degrees of humidity. Measured data obtained from [90] and [89].  The predictive ability of the three curves shown in Figure 21 serves as validation for their use to describe sensing layer properties. Unless otherwise stated, Equations 39 to 45 are used to model sensor frequency response. 3.4.2 Polymer Film Stress Following an investigation into the performance of PVA as a sensing layer [70], discrepancies between results and model predictions led to an investigation of stress variation in the polymer. This investigation involved the development of a model for sensing layer stress as a function of polymer volume fraction and the measurement of residual stress in two solvent cast sensing layers. In Section 5.2, the influence of stress variation on predicted sensor resonant frequency shift is compared with toluene sensing results. Specifically, it is proposed that deviation between predicted and measured sensor performance can be attributed, in part, to stress variation in the sensing layer.  This section provides the background and theory to understand this hypothesis. Tension is given by the integration of stress over the thickness of the substrate and sensing layer.  Assuming a uniform distribution of force over both and isotropic mechanical characteristics, the quantity becomes a summation of thickness-stress terms,                                        (46) where Spvdf is stress in the substrate, Sres is residual stress in the sensing layer, and Sswelling is stress that occurs during absorption. This relationship details the sources of static and varying tension in the device. A Thickness Young?s Modulus Density 43  diagram of these forces is given in Figure 22.  An uncoated, tensioned sensor has only positive stress acting on its substrate.  During solvent casting of the sensing layer, residual stress builds up due to contraction of the polymer in a semi-gelled state.  When the sensing layer is exposed to an analyte, it will swell, resulting in a reduction of residual stress.    Figure 22: A diagram of stress in the substrate and sensing layer during solvent casting and exposure to an analyte. A: A polymer solvent solution is applied to the substrate. Substrate stress is the only contribution to total tension. B: The polymer-solvent solution dries and contracts, causing an increase in tension in the sensing layer. C: The sensor is exposed to a solvent and the polymer film expands, reducing internal thin film stress. As described in [88], stress induced by swelling may be estimated by calculating the average force required to cause the expansion,                                                       (47) Here, the swelling stress is approximated by multiplying the in-plane expansion of the film by the Young?s modulus.  This approximation assumes that stress is uniformly distributed through the film and acting only in-plane, that the film is significantly thinner than the substrate, and that edge effects can be ignored.  The final condition is important as it demands that the sensing layer extend well beyond the active region of the sensor.  Predicting residual stress is significantly more complex.  Residual stress occurs in solvent cast films due, primarily, to shrinkage during solvent evaporation.  The process is generally described using the glass transition temperature as a reference.  When saturated with a good solvent, the glass transition temperature of a polymer is far below room temperature and polymer chains are able to reorganize relatively freely.  During evaporation, the solvent volume shrinks and these chains are able to reduce the stress of contraction by moving around in the mixture. This will occur until solidification, defined as the point at which the glass transition temperature of the polymer rises past room temperature.  Solvent may still evaporate after this T PVDF-PositiveA.T PVDF-PositiveT poly-PositiveT PVDF-PositiveT poly-NegativeB.C.Solvent EvaporationSolvent Absorption44  point; however, the voids it leaves will no longer be filled by mobile polymer chains.  As such, shrinkage stress will build up in the film.   The source of this stress was identified first by Croll [91], who developed a relationship to predict its magnitude,                                    (48) where    is the volume fraction of solvent in the mixture at solidification and     is the volume fraction of solvent left when the mixture is completely dry.  The volume of both may be evaluated via DSC and are affected primarily by the quality of solvent.  A larger quantity of a poor solvent is required to drive an identical shift in glass transition temperature.  As a result, a greater volume of solvent will be left at solidification and more stress will develop.  Interestingly, while evaporation rate and temperature change also play a role in residual stress build-up [92], film thickness and initial solvent concentration do not [91].   Newer and more thorough models for residual stress creation in solvent cast film currently exist [93].  However, due to the difficulty of verifying their accuracy for our application, empirical results were used to predict residual film stress. PVAc-Tolune and PS-Xylene mixtures were tested using the method described in Section 2.1.5.    Figure 23: Images of substrate deflection during as a result of residual stress in an evaporating PS-xylene solution (visible in the first frame). 1 to 8 correspond to the chronological order of images taken over a 40 hour period. ? 45  A set of images showing the results from these internal stress investigations is shown in Figure 23.  They show the evaporation of xylene from a polystyrene film. The resulting residual stress, along with that which develops inside PVAc-toluene films is shown in Figure 23.  In order to confirm that fluid mass was not affecting film contraction, measurements were repeated with identical films on a digital scale.  The solution was found to lose a majority of its mass less than 10 minutes into the casting process. PVAc films demonstrated residual stress values of 0.45 MPa while PS films showed stress values of 2.3 MPa.  These values are quite close to those obtained in similar experimentation [94].  Given that both depositions took place under identical conditions using good solvents, the dissimilar values can be attributed to a difference in Young?s modulus. As shown in Equation 48, the residual stress in a solvent cast film is linearly related to the elasticity of that film.  A stiffer material will therefore show a greater residual stress, assuming that identical solvents and casting conditions are used.  Figure 24: Plots showing internal stress in films deposited via solvent casting.  Multiple thicknesses were used to confirm that stress was not varying as a function of thickness [91]. Measured residual stress was used in conjunction with Equation 47 to provide a prediction for stress variation in a VOC sensing performance model.  Results and discussion of this experiment are presented in Section 5.2.  The effect of residual stress from conductive PEDOT:PSS films was also investigated and found to be negligible (Appendix-Section A.3) 3.4.3 Influence of Stiffness and Stress With the inclusion of sensing layer stiffness and stress, predicted frequency shift behavior varies dramatically.  As discussed in [38], switching from purely gravimetric detection to mass and swelling detection can lead to a change in sensitivity polarity.  When Young?s modulus softening is included in the calculation, this may still be the case, depending on substrate stress and elasticity. If the polymer transitions 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 10 20 30 40 Stress (MPa) Time (hr) PVAc-Toluene PVAc-Toluene PS-Xylene PS-Xylene 46  through the GTT, the effect of sensing layer stress on the device performance will reduce dramatically, leading to a steep drop in resonant frequency. With the addition of swelling driven stress, frequency is predicted to shift in a strongly negative direction.  This suggests that an extremely high sensitivity device could be fabricated through the detection of stress variation.  However, doing so would require a substrate which has zero internal stress, and a sensing layer which is uniformly thick, much wider and longer than the active acoustic area, and much thinner than the substrate.   A device with all of these requirements has yet to be fabricated and so the stress sensitivity of current devices is lower than predicted.   Figure 25 shows the predicted frequency response of a 20 ?m thick, 800 ?m wavelength humidity sensor under 10 MPa of stress and with a 2 ?m PVA film.  The three curves correspond to FPW sensing models including the effect of mass only, mass and stiffness, and mass, stiffness, and stress combined.  Even with a substrate stress of 10 MPa, the model which includes sensing layer tension demonstrates a much stronger response.  The models are compared with experiment in the Section 5.2.  Figure 25: PVA coated humidity sensor model predictions given sensitivity to polymer mass, stiffness and stress changes. 3.4.4 Sources of Uncertainty Given that the model is in early stages of development, it has not been fully verified using well characterised materials and components. Optimally, important variables and constants should be measured directly, and if possible, in situ.  At this stage in the investigation, such direct measurements are not possible for a number of important characteristics: sensing layer elasticity, substrate stress, and the 47  polymer-solvent interaction parameter. The uncertainty associated with these variables significantly reduces model precision.  In addition to these unmeasured values, there are characteristics which are measured or calculated but with high uncertainty.  They are: initial sensing layer thickness and substrate thickness. The estimated uncertainty for each of these values (with PVAc as an example sensing layer) is listed in Table 7 Table 7: Estimated uncertainty for various sensor properties Property Value Uncertainty Sources PVDF Young?s Modulus (Pa) 2.9E+09 5.0E+07 Meas.-Section 2.1.1  PVDF Thickness (m) 2.2E-05 1.0E-06 Meas.-Caliper PVDF Stress (Pa) 2.5E+07 2.0E+06 Calc.-Section 3.2.1.2  PVAc Young?s Modulus (Pa) 3.0E+08 3.0E+07 [95], Calc. PVAc Thickness (m) 5.0E-06 5.0E-07 Calc.-Section 4.7 PVAc Stress (Pa) 5.0E+05 2.0E+05 Meas.-Section 2.1.5  The influences of the three variables which drive the greatest variation in performance are shown in Figure 26.  Measurement uncertainty in PVDF thickness, PVDF stress, and PVAc thickness can independently lead to up to ?3% variation in sensor frequency.   Figure 26: The predicted resonant frequency shift of a PVAc coated sensor along with the upper and lower bounds of the prediction given uncertainty in PVDF thickness, PVDF stress, and PVAc thickness. In future design iterations, geometric uncertainty could be reduced by using a profilometer to measure the substrate and sensing layer thickness with greater precision. Directly measuring substrate stress is more 48  challenging, however and requires a greater understanding of what drives tension changes in the substrate.  Future investigations should address this issue in detail in an effort to reduce model precision.  3.5 Polymer Reference Layer  During either gas sensing or thin film characterisation, a reference channel is required to compensate the effect of environmental changes on the signal.  The reference channel is embedded on the same substrate and is coated in an inert polymer.  Acoustic waves propagate through this polymer and show a frequency shift which is dependent only on external perturbations which affect the substrate.  The resulting reference signal is subtracted from the sensing signal, thereby eliminating the effect of disturbances which affect both.    An ideal reference layer must be chemically stable, non-porous, acoustically thin, and completely unresponsive to the analyte being tested.  This final requirement was investigated during early humidity sensing experiments.  A series of polymers which do not absorb water, shown in Table 4, were identified and investigated as potential reference barriers.  Each is completely insoluble in water and has the ability to be deposited in a very thin film. Table 4: Reference channel barrier polymers and deposition details Barrier  Solvent Deposition Method Polyvinyl Acetate Toluene Solvent Casting Polystyrene Xylene Solvent Casting Polyvinyl Flouride THF Solvent Casting Parylene C - Vapor Deposition  Polymer reference layer tests were carried out using low tension, 20 ?m thick sensors.  Coated devices were exposed to a range of concentrations of humidity and the resulting frequency shifts were measured.   49   Figure 27: Frequency response of sensors coated in barrier polymers The PEDOT only sensor demonstrated the largest deviation from ?dry? resonant frequency.  This is expected as PEDOT is a hygroscopic material [96].  It was similarly expected that the PS sample not show a frequency shift in the presence of water vapour.  Given that the remaining two barriers are considered insoluble in water, it was assumed that the fabrication method used led to porous or cracked films.   For future water vapour testing, PS was used as the reference polymer. This continued until it was discovered that sensing layer stress variation could effecting substrate stress and the resonant frequency of the device.  At this point, single channel sensors were used.  A method of decoupling sensing layer and substrate stress variations from the reference channel signal is still under investigation.     -8 -7 -6 -5 -4 -3 -2 -1 0 1 -15 -10 -5 0 5 10 15 20 Frequency Shift (%)  Dew Point (?C) Polystyrene Polyvinylidene Flouride Parylene C No Barrier-PEDOT Only 50  4 Fabrication 4.1 Overview The fabrication process can broadly be separated into three stages: PVDF preparation, electrode printing, and sensing layer application.  The first involves converting primarily ?-phase PVDF film into primarily ?-phase, piezoelectric. This is done by drawing the film before poling, applying a strong electric field, to increase its average polarization.  Electrode printing involves patterning the substrate with at least two sets of interdigitated transducers, following the application of a support frame.  Micro-inkjet and screen printing are both used to achieve this.  Finally, the sensing layer is applied via solvent or drop casting.  This is the process of depositing a thin film from a polymer-solvent solution.      Figure 27: Main fabrication steps. (1-2) Stretch PVDF, (3) Pole PVDF, (4) Frame PVDF, (5) Print PEDOT, (6-7) Apply sensing layer/electrodes The full process is shown in Figure 27.  It was primarily developed by Gabriel Man [97] and Robert Busch [1] during successive investigations.  Here, the steps will be detailed along with modification and additions made to the original fabrication procedure.  While each step was slightly modified to account for sensor design changes, poling and printing were modified most significantly.  The former was adjusted to allow the fabrication of thin film sensors while the latter, to increase the overall fabrication yield. 51  4.2 Stretching Stretching raw film prior to poling serves two purposes: it drives the conversion of ?-phase PVDF to ?-phase and reduces substrate thickness in the process. The process of ?- to ?-phase conversion has been covered in many past investigations [48], [98]?[100], and while there are ample empirical models for the effects of fabricating under different conditions, a detailed description of the polymer microstructure during stretching still eludes researchers.  In general, however, it is known that drawing a PVDF film at a high temperature will cause semi-crystalline spherulites to deform, leading to the reorganization of random, ?-phase regions, to ?-phase.  The ?-phase regions may then be oriented to increase the piezoelectric response of the film.   Drawing is carried out using a manual or an automatic stretching apparatus.  The former consists of a vice with attached film clamps while the latter is a custom made device which rolls half of the film about an aluminum drum with the second half anchored. Both are used during fabrication, thought the manual device, more often.    Figure 28: Images of (a): manual and (b): automatic drawing devices. Stretching is carried out at 80 to 90 ?C and at a rate of 1 cm/min.  15 cm by 10 cm films are anchored into the apparatus and placed in an oven.  They are brought to the stretching temperature over 30 minutes and then stretched over 12 minutes.  Films are drawn to  4.5 their original length and then allowed to cool while under tension.   These fabrication conditions are based on past investigations and independent research into film quality. Drawing temperature was chosen due to research indicating that maximum beta content percentage is achieved near 80 degrees [98], [101].  Similarly, draw ratio was chosen as  4 to  5 stretch had been demonstrated to lead to the greatest beta content over a wide range of temperatures [98], [101], [49]. Film Film Motor 52  In order to confirm these results, an investigation was carried out to determine the effect of temperature on manually stretched, 75 ?m films.  A plot showing the results of this investigation is shown in Figure 28 (FTIR measurements were obtained by Suresha Mahadeva).  6 samples were stretched at 3 different temperatures and their resulting beta content was measured via Fourier transform infrared spectroscopy.  As previously reported, the highest beta content was measured near 80 degrees.  Below this temperature films would break or show significant crazing during stretching. These results are in general agreement with the known underlying theory of stretching driven alpha to beta phase conversion.  At lower temperatures, a greater amount of stress is imposed on the film during drawing and alpha to beta phase conversion occurs with a higher efficiency.  Figure 29: Measured beta content of manually and automatically stretched films. 4.3 Poling Following drawing, samples are poled at a high temperature and under tension.   Stretched films are heated to between 80 and 90 degrees Celcius and a 50 MV/m to 150 MV/m field is applied for 30 minutes before cooling under tension and at the high potential.  One of two poling methods was used during fabrication: contact poling or corona poling.     Contact poling is the application of a high intensity field over an object using metal electrodes.  In this case, round, magnetic electrodes are placed on either side of the film and a DC voltage of 0.5 kV to 10 kV is applied to one. Corona poling involves the application of a high intensity field using charged oxygen and nitrogen molecules.  A needle is suspended above the film and held at a high potential.  Near the tip of the needle, where the field intensity is greatest, breakdown occurs in the surrounding air.  Ions are created which migrate to the surface of the film. These ions are then distributed evenly over a sample using a charged metal grid at a potential between ground and 10 kV.  If the backside of the film is held at ground 20 25 30 35 40 45 50 55 60 80 100 120 140 Beta Content (%) Drawing Temperature (C) 53  using a large electrode, a field develops between the charged ions and ground plate. The upper potential of this field is limited only by the grid potential. Diagrams of these two methods are shown in Figure 30.  Figure 30: Diagrams of contact poling (left) and corona poling (right).   Both methods were used during fabrication, contact poling, with the manual drawing apparatus, and corona poling, with the automated; however, contact poling was used most often as it consistently produced higher performing sensors.  The automated corona poling apparatus was designed in an effort to increase yield by reducing dielectric breakdown during fabrication and by increasing the total surface area of piezoelectric material. Active surface area was increased by designing the apparatus such that a large portion of the stretched film is exposed to charged ions.  Breakdown reduction was achieved as a result of the current limiting nature of the charged ion film.  During poling, certain forms of localized breakdown can lead to the creation of a conduction pathway through the film which has a reduced resistance.  If the initial charge transfer does not lead to a reduced potential over the sample, then conduction current will rise with the falling resistance of the film.  Unlike the conductive electrodes of the contact apparatus, the charged ion sheet of the corona apparatus does not support in-plane conduction.  As a result, when localized breakdown occurs, a small quantity of charge is shuttled across the film and the surrounding area suffers a reduction in potential, thereby limiting the leakage current and preventing a global breakdown. In practise, the corona apparatus functioned as expected; however, its optimization is an ongoing process being lead by Suresha Mahadeva [102], and so, contact poling characterisation and improvement was the focus of this investigation. In an effort to fabricate thinner films of a higher piezoelectric constant, a number of short investigations into contact poling processing characteristics were carried out. Initial attempts to fabricate thin film sensors (d < 20 ?m) were met with only minor success.  Samples showed high beta content but a low amplitude output signal. Along with this, thin film samples often suffered dielectric breakdown during fabrication.  As such, a project was undertaken to investigate poling in detail and improve yield 54   First, to confirm results presented in earlier investigations, piezoelectric constant was measured in films fabricated at three poling temperatures. Following this, and in conjunction with the supplier quality study discussed in 3.2, the influence of stretching and poling on total crystallinity was investigated.  Finally, a study on dielectric breakdown was carried out with the purpose of reducing the chance of membrane failure during poling.    As shown in Figure 31, piezoelectric constant tests revealed that contact poling between 80 and 100 ?C results in average d33 constants ranging from 14 pC/N to 30 pC/N.  The maximum measured constant is in agreement with past research on the topic.  Similarly, its occurrence in films stretched and poled at 80 ?C agrees with previous investigations into contact and corona poling of PVDF [40], [99], [102].   Figure 31: The d33 piezoelectric constant of PVDF films drawn and poled at 80, 100, and 120 degrees. Following confirmation of a sufficient piezoelectric constant, the effect of stretching and poling on overall crystallinity was investigated.  As total film crystallinity is directly related to piezoelectric constant, it is important to understand how each fabrication step is altering film microstructure.  To this end, four McMaster Carr PVDF samples were stretched and poled and samples from each step were analysed using differential scanning calorimetry.  Figure 32 shows the results from the scans.  Upwards facing peaks correspond with melting while downwards facing peaks correspond with solidification.  0 5 10 15 20 25 30 35 40 45 50 60 80 100 120 140 Piezoelectric Constant (pC/N) Drawing and Poling Temperature (?C) 55    Figure 32: DSC scans of raw, stretched, and poled McMaster Carr PVDF films. The largest difference between the samples is the relative height of the raw PVDF and all other processed films.  This is evidence of a drop in total crystallinity during stretching, a phenomenon which has been observed previously [103] and is an indication that there is potential room for overall improvement in sensor crystalline content.  During poling however, no such drop in peak area is observed. The offset solidification point observed in the corona poled films may be indicative of a larger beta content or increased polarization  [99], however, this has yet to be confirmed. The important key of this investigation is that, while stretching may reduce crystalline content, poling has a much less significant effect. During stretching and poling, dielectric breakdown is the primary failure mode experienced by films under 75 ?m thick. It occurred as a result of non-uniform film thickness, particulate matter between the metal electrodes, and unwanted film compression.  The last factor becomes more difficult to control when poling thinner films.  For very thin samples, compression induced by the electrodes would often lead to a significant drop in the potential required to reach the breakdown field intensity of the film.  Similarly, when poling with lower voltages, small variations in potential set point could be enough to induce current flow between the electrodes.   To further understand this failure mode, the practical time to breakdown of stretched samples at different field strengths was measured. Three films were stretched and contact poled at a variety of high potentials.  The time to breakdown of each film was measured.  The results are shown in Figure 33. -0.6 -0.4 -0.2 -1E-15 0.2 0.4 0.6 0.8 1 60 80 100 120 140 160 180 200 Heat Flow (W/g) Temperature (?C) Unprocessed Stretched Stretched and Poled (Contact) Stretched and Poled (Corona) 56   Figure 33: Time to dielectric breakdown as a function of field during contact poling. The grey area represents the region over which field intensity is sufficient to polarize PVDF at 80 degrees over half an hour. Unsurprisingly, time to breakdown (BD) drops sharply after a certain field strength.  In this case, the point at which the BD asymptote occurs is not the breakdown potential of the PVDF.  Rather, it is the practical potential given the poling set up and lab environment.  As indicated by the limit of the greyed out region, the practical breakdown field is only 30 to 40 MV/m greater than the minimum required poling field [101].  For a 10 ?m thick film, this corresponds to a deviation of 300 to 400 V, assuming perfectly parallel electrodes and a precisely measured, uncompressed film thickness. Given that higher field strength will net a greater polarization percentage and so it is desirable to pole closer to the breakdown voltage of the film, this buffer was deemed insufficient.   To reduce the chance of breakdown, improve yield, and improve polarized content, three modifications were made to the poling process.  First, thinner samples were stretched and poled in stacks of three.  By increasing the overall thickness of the composite sample, poling potential could be raised with confidence that small deviations were less likely to cause breakdowns.  Second, silicone oil was applied between electrodes and the sample.  This high dielectric constant fluid fills small voids and divots in the film, increasing potential required to cause breakdown in the thinned region. Finally, to reduce fringe field intensity near the edge of the contact electrodes, the ground electrode was replaced with a large metal plate such that the edges of each conductor no longer aligned.   These changes have lead to a drop in the occurrence of breakdown while their effect on piezoelectric constant has yet to be determined. 1 10 100 1000 0 50 100 150 200 250 300 350 Time to BD (s) Field (MV/m) 57  4.4 Framing Following stretching and poling, films are supported using 4 cm x 4 cm machined steel or 3D printed plastic frames.  These rigid structures provide support and maintain constant tension in the substrate.  One of two methods is used to affix them to the film, depending on whether the sensor substrate is to be under high or low stress.     Early in the development of these devices, high stress, ?pre-tensioned? sensors were fabricated in an effort to detect SAW or high frequency FPW waves [1].  Currently, devices with 20 to 60 MPa of stress are fabricated to explore the effect of tension on sensitivity and the performance of primarily gravimetric detectors.  Frames are applied to the substrates of these devices while the film is still affixed to the vice.  With the material under stress, two frames are placed on either surface and clamped into place with a temporary metal support structure.  Eight holes are then cut in the film and eighth inch bolts are inserted through the two frames and substrate prior to the application of Loctite and nuts.  The film is then cut out from the vice and trimmed to fit the frame.  During this process, it is important to ensure that the full area of each frame surface is in contact with the film and each nut is firmly tightened.  If this is not the case, the film will slip out from the frame and contract, leading to a reduction in tension.   For this investigation, un-tensioned sensors were primarily fabricated.  Frames are applied to the substrates of these devices as described above, after being cut from the vice and allowed to relax.  This last step is especially important as, if the film is not sufficiently relaxed when framed, it can re-tension over a period of a few days [104].  As such, stretched and poled PVDF was allowed to contract under no tension for 24 hours before framing.  4.5 Microinkjet Printing Microinkjet printing was used to pattern conductive polymer interdigitated transducers.  The choice of inkjet printing over common microfabrication techniques such as vapour deposition was driven by the need to print prototype transducer designs quickly at low cost given a substrate with a very low working temperature.   Once an IDT design was chosen, fabrication was carried out via screen printing, which allows greater production volume at a similarly low expense.   The ink used during printing is comprised of  94.7 % Clevios PEDOT:PSS, 5% DMSO, and 0.3% Triton X-1000.  DMSO is added to increase conductance while the surfactant, Triton, is added to increase ink adhesion to the hydrophobic PVDF substrate [97]. After mixing the three ink components, the solution is put through a 5 ?m porous filter and loaded into the printing reservoir.  58   Printing takes place at room temperature and pressure.  Using a humidifier, humidity near the printing stage is kept above 30% to prevent unwanted ink drying at the nozzle.  During printing, a 40 ?m piezoelectrically actuated nozzle dispenses picoliter scale droplets at a rate of about 20 per second.  The application of a single set of two or three transducer patterns occurs in three, staggered layers [97].  To increase electrode conductivity, the same pattern is often printed up to five times, in succession.  The minimum step size used during printing is 2.5 ?m while, due to droplet spreading, the minimum feature size is 100 ?m.    An image of a printed interdigitated transducer is given in Figure 34. Transducer fingers of opposite polarity are separated by a centre-to-centre finger spacing of 400 ?m, which leads to the generation of 800 ?m acoustic waves.  Figure 34: An image of the printed IDT pattern The two greatest difficulties faced during printing were nozzle clogging and shorting between transducers. The first occurs as a result of ink drying at the nozzle or particle agglomeration leading to clogging, while the second occurs due to unwanted droplet spreading.  Together, these two problems caused the vast majority of sensor failures.   Both problems could theoretically be reduced with strict environmental controls.  However, slowing evaporation at the nozzle requires a cool, humid environment, while increasing droplet evaporation during on the substrate to reduce spreading requires a warm, dry environment.  These two conditions are difficult 59  to achieve as the nozzle and substrate must be positioned within a few millimeters of each other.  In lieu of environmental control a camera was mounted on the printer to allow continuous monitoring of the print quality.  During fabrication, any deviation from the intended design or flow stoppage could be detected and the nozzle cleaned or repositioned.   4.6 Screen Printing To facilitate higher volume sensor production, a screen printing apparatus was designed and constructed. This work primarily carried out by Johnny Chen [105]. The apparatus consists of a 50.8 cm   61 cm steel frame in which a 420 count polyester mesh is suspended under 20 to 30 N of tension. The mesh is coated in a patterned emulsion which acts as a physical mask during ink application.  Beneath the frame is a sample stage, constructed to apply tension to films while ink is being applied.   An image of the apparatus in shown in Figure 35 along with a diagram of the mask used to pattern the emulsion. Emulsion patterning was carried out by Willox Graphic Supplies, Vancouver Canada through UV exposure and etching. The mask was designed using CleWin4 and is composed of 3 sets of 4 IDT designs. Each has a different minimum line width ranging from 25 ?m to 100 ?m.  Figure 35: Screen printing apparatus (a) and the mask used to generate the IDT patterns (b). In comparison to that used for  printing, very high viscosity ink is required for silk screen patterning. Due to supplier problems, custom high viscosity screen printing PEDOT could not be obtained for this investigation.  In order to achieve the necessary rheological properties from inkjet printing ink, a number of thickening methods were investigated.  First, silica powder was added to the solution in various concentrations.  While this lead to a stark rise in viscosity, it also resulted in agglomeration and a reduction in conductivity.  Following this, carbon powder was combined with the PEDOT. However, it lead to mesh clogging when used.  Finally, timed evaporation was used to reduce the water content of the ink. 60  Using a hotplate maintained at 90 ?C for 30 minutes, a sample of Clevios PEDOT:PSS was evaporated until only 22.7% of its original mass remained. This gel was used for printing optimization and the fabrication of a number of sample devices. Images of completed sensors, taken by Johnny Chen, are shown in Figure 36.  While there are areas of uneven ink distribution caused by bubbles or the shape of the mesh itself, IDT conductance is sufficiently high to produce functioning sensors. As such, screen printing was used to fabricate thin and thick substrate devices during the investigation.  A detailed description of the screen printing apparatus design, construction and optimization can be found in [105].   Figure 36: Images of screen printed sensors. 4.7 Solvent Casting Following IDT patterning, a conductive backplane is applied beneath each transducer. 1 to 5 ?L of PEDOT:PSS solution is spread out beneath the IDTs and allowed to dry for at least two hours. Deposition of the thin film sensing layer is then carried out using the same technique. Polymer pellets or powder are weighed and mixed with a casting solvent to create a 2% to 8% polymer solution.  In most cases, the solvent chosen is that which is being detected by the sensor: toluene for PVAc and water for PVA for example. However, a second solvent may be used to tailor the residual stress of the sensing layer.  The solution is deposited over the backside of the substrate such that it fully covers the transmitting and receiving IDTs in one contiguous film.  Assuming a uniform height distribution, the thickness of the film,                  ,      (49) may be calculated using the mass concentration of the solution, C [kg/kg] , solution volume, Vs [m3], solvent density, ?s [kg/m3], polymer density, ?pol [kg/m3], and deposition surface area, A [m2]. After drop casting, the solution is allowed to dry for at least 24 hours at room temperature and pressure.  Electrical contacts are connected in a similar way. Copper tape is applied to the printed PEDOT:PSS pads and carbon glue is used to affix 30 AWG wires to each input.  61  5 Experimental Results and Discussion In this chapter, sensor performance test results are detailed and discussed.  Four applications are investigated: humidity sensing, VOC sensing, resin curing characterisation, and droplet manipulation. The first involves coating the FPW device in a thin polymer film and exposing it to varying concentrations of humidity.  The resonant frequency of the sensor is measured as the film absorbs the solvent and the data is used to determine how film physical properties change with solvent concentration.  For this application, multiple layers of PVA were applied to the sensor and exposed to varying concentrations of water vapour.   This work was carried out in conjunction with Christoph Sielmann and so the results will only be explained in brief so as to provide context for further experiments.   VOC sensing was investigated by coating the device in polyvinyl acetate and polystyrene before exposing it to varying concentrations of toluene vapour.  Frequency shift results were then compared with those predicted by the analytic model presented in Sections 1.4 and 3.4.  Unlike the fit model used to determine polymer mechanical characteristics, this model was developed to act in a predictive manner such that vapour concentration could be deduced from resonant frequency data.  Its performance is compared with experimental results and modifications are made to increase its accuracy. Resin curing characterisation is similar to thin film polymer-solvent characterisation.  A gel consisting of a resin and hardener was applied to the back of a sensor.  Overtime, it cured and became solid, leading to stiffening, tensioning, and volumetric shrinkage.  The resulting change in frequency was used to determine rate of cure, elasticity, contraction, and density.  This application differs from the two previous as, in this case, the frequency of the sensor is monitored during a chemical process, rather than being recorded after the process has settled.  This allows the reaction to be studied as it occurs.   Finally, microfluidic manipulation involves inducing flow and mixing within droplets applied to the FPW substrate. Samples were mounted beneath a camera and LDV and flow was recorded within polystyrene sphere laden droplets.  Flow rate was measured along with acoustic wave amplitude inside and outside the droplet.  The results are compared with an acoustic streaming model described in Section 1.8. 5.1 Humidity Sensing 5.1.1 Overview Initial sensor performance characterisation tests were carried out using water vapour and a polyvinyl alcohol sensing layer.  In an effort to repeat results described in [5] and demonstrate vapour sensing, a lightly tensioned 18 ?m thick sensor, coated in 2 ?m to 6 ?m of Sigma-Aldrich PVA was exposed to a 62  range of water vapour concentrations.  PVA and water were chosen due to the high partition coefficient, ~20000, and low polymer-solvent interaction parameter of the combination.  While the purpose of the project is to develop a volatile organic compound detector, PVA is significantly more soluble in water than most polymers in the volatiles of interest at STP. As such, it was used to characterise the performance of the early, low sensitivity devices. 5.1.2 Results and Discussion Figure 36 shows the results of initial vapour exposure tests.  The plot on the left illustrates the frequency shift of the sensor as a function of time at different dew points. Settling time between setpoints can be attributed to the time it takes for the analyte to diffuse through the film. Resonant frequency was sampled at least 20 minutes after each humidity level shift.  Frequency data, as a function of dewpoint is given in Figure 36   (right) for three different thicknesses of PVA.    Figure 37: PVA-Water vapour sensing results.  Left: Resonant frequency of a sensor coated in 3 PVA layers at different dew points and given a constant ambient temperature of 22 degrees.  Right: Frequency as a function of dew point for a 20 ?m sensor. The most notable property of these plots is their increasing curvature with film thickness.  This is a strong deviation from the predicted behavior of a mass and stiffness sensitive FPW device.  As discussed in Section 1.3, such a device should show a decreasing mass sensitivity with increasing thickness.  In this case, the opposite is evident at high humidity.  This is a demonstration of sensitivity to elasticity or stress variation in the sensing layer.   Following these experiments, thin film material characterisation was investigated. In work primarily carried out by Christoph Sielmann, the frequency response of a solvent exposed sensor was used to determine the mechanical properties of a PVA sensing layer [70]. By fitting Equation 11 to frequency shift data, assuming density, Young?s modulus, thickness, and stress varied linearly with solvent concentration, 1.45 1.55 1.65 1.75 1.85 1.95 -10 0 10 20 Resonant Frequency(105) Dew Point (?C) 3 Layers - 5.5 ?m 2 Layers - 4 ?m 1 Layer - 2 ?m 63  estimates for each value at different solvent densities were obtained. These characteristics were compared with measured properties of previous research.  This work served as a demonstration of basic sensor functionality while also showing the need for a more comprehensive polymer sensing layer model.  Similar to initial results, shown in Figure 37, the sensitivity of these tested devices increased with increasing film thickness at high solvent concentrations. The behavior could be modelled using linear functions for each mechanical characteristic; however, it predicted strong changes in elasticity and internal stress, neither of which were accounted for in the previous sensing layer model. As a result, these tests served as motivation for the creation of a more detailed sensing layer model which did not rely on fit parameters (described in Section 3.4). 5.2 VOC Sensing 5.2.1 Overview Following the successful demonstration of humidity sensing, VOC detection was investigated. A polymer FPW device was configured for toluene detection and characterised. In this section, its performance is presented and compared with that predicted by the FPW sensing layer model described in Section 3.4.  The influence of sensing layer elasticity and stress variation are then discussed. 5.2.2 Results and Discussion A 22 ?m thick, 800 ?m wavelength device was fabricated for testing.  The sensor was coated in a polystyrene and polyvinyl acetate sensing layer. Framed samples were mounted in the test apparatus described in Section 2.2 with the sensing layer exposed to incoming gas.  A single channel was used during testing and so, to account for environmental effects, temperature and time of day was logged with each data point. Similarly, as the concentration of toluene vapour was varied, total flow rate was kept constant to ensure that the chamber pressure did not change. The model used to predict sensor response is described in Section 3.4. Using FH solution theory and polymer-solvent coefficients for PVAc-toluene and PS-toluene, the polymer volume fraction of each sensing layer is calculated as a function of analyte vapour concentration. Equations 38 through 42 are then used to calculate thin film thickness, mass, Young?s modulus, and stress. Three versions of the model are presented to demonstrate the influence of sensing layer elasticity and stress variation on device performance. First, sensor performance is predicted assuming constant sensing layer stress.  Frequency shift, in this case, is dominated by mass loading and a reduction in elastic modulus.  Second, the model is fit to experimental data given sensing layer stress which increases linearly with solvent concentration. Initial sensing layer stress and slope (Pa/ppm) are fit to each data set using a least mean squares algorithm.  64  This is done to determine the degree of stress variation required to account for deviation between the constant stress model and the results.  Finally, sensing layer stress is predicted using the residual stress data and relationship for polymer stress as a function of volume fraction shown in Section 3.4.2. Measured, calculated, and referenced constants used in the model are shown in Table 5. Table 5: Characteristics of sensors used during this investigation Property Value Source PVDF Density  1780 kg/m3 [106] PVDF Young?s Modulus  2.9 GPa Meas.-Section 2.1.1 PVDF Thickness  22 ?m Meas.-Caliper PVDF Stress  25 MPa Calc.-Section 3.2.1.2  PVAc Density 1190 kg/m3 [95] PVAc Young?s Modulus  0.3 GPa [64], Calc. PVAc Thickness 2.0 ?m to 3.2 ?m Calc.-Section 4.7 PVAc Stress  0.5 MPa Meas.-Section 2.1.5 PS Density 1060 kg/m3 [107] PS Young's Modulus  3.0 GPa [64], Calc. PS Thickness  1.0 ?m to 1.9 ?m Calc.-Section 4.7 PS Stress (Pa) 5.00E+06 Meas.-Section 2.1.5  Samples were exposed to 6 toluene concentration set points per test.  At each setpoint, amplitude, phase, and frequency were allowed to settle for half an hour before a measurement was taken.  As shown in Figure 38, between test points, there are significant, asymmetric frequency jumps.  These artifacts occur due to MFC resets which take place during large flow rate changes.  Figure 38: Resonant frequency and toluene concentration as a function of time 65  The percentage shift of resonant frequency as a function of toluene concentration is shown in Figure 39 for a sensor coated in 1.8 ?m, 2.1 ?m and 3.2 ?m PVAc (blue) and 1 ?m and 1.9 ?m PS (red).  In both cases, the frequency decreases with increasing toluene vapor concentration, suggesting a primarily mass and stress sensitive device.  In the glassy region, the mass sensitivity of the PS coated sensors ranged from -80 cm2/g to -200 cm2/g while that of the PVAc coated sensors ranged from -240 cm2/g to -490 cm2/g.  At higher concentrations, this increases by a factor of 2 to 30. This increase is likely due to a drop in sensing layer stiffness as it passes through the glass transition concentration or an increase in swelling induced stress during absorption. The maximum resolution of each design can be calculated using the analyte concentration sensitivity.  PVAc coated devices showed a maximum sensitivity of 0.8 Hz/ppm while PS coated devices showed a maximum of 0.4 Hz/ppm.  Assuming an average noise of 90 Hz [5] and a required signal to noise ratio of 3, a minimum of 340 ppm and 680 ppm is required to produce a detectable signal in the PVAc and PS sensors, respectively.    Figure 39: Percentage shift of resonant frequency as a function of toluene concentration. Data from a 22 ?m thick sensor coated in 2 to 3 ?m thick PS (white points) and to 3 ?m thick PVAc (black points) Figure 40 shows resonant frequency as a function of toluene concentration along with two performance models.  The solid lines correspond to predicted sensor performance given constant substrate and sensing layer tension values. Device frequency was predicted according to the model described in Section 1.3 and 3.4, using material characteristics detailed in Table 6.   This model was designed to predict frequency shift 66  as a function of vapour concentration and vice versa.  As such, all substrate and sensing layer physical properties must be known prior to vapour exposure.  Density, elastic modulus, and thickness of both materials were measured or calculated during the construction of the device. Directly measuring substrate and sensing layer stress is not possible, however.  Substrate stress was therefore calculated by measuring the resonant frequency of an uncoated sensor and using Equation 11 to determine total tension in the substrate.  Sensing layer stress was obtained the same way, following solvent casting.  Dashed lines in Figure 40 correspond to model results given a sensing layer stress which varies linearly with solvent concentration. Equation 11 was fit to the data assuming sensing film swelling drove an decrease in total stress as it expanded.   Figure 40: Resonant frequency shift as a function of toluene concentration. Left: PVAc sensing layer. (1) 1.8 ?m thick PVAc (2) 2.8 ?m thick PVAc (3) 3.2 ?m thick PVAc. Right: PS sensing layer. (4) 1.9 ?m thick PS (5) 1 ?m thick PS.   Data is tracked by solid lines, which correspond to constant stress models and dashed lines, which correspond to models with linearly decreasing stress. Figure 40 (left) shows sensor response given three different PVAc coatings.  At low concentrations, the drop in frequency is primarily driven by mass loading. Between 10,000 ppm and 15,000 ppm, the model predicts that the glass transition concentration will be reached in the film.  As a result, the elastic modulus should fall dramatically, leading to a drop in film stiffness and a drop in frequency. A similar change in behavior is shown in experimental results with frequency dropping fast as a function of toluene concentration above 15,000 ppm.  Unlike data set (2) and (3), data set (1) deviates from the model considerably. Fitting the model assuming a linear variation in stress (dashed lines) reveals a decrease of 1.4 kPa/ppm in the sensing layer. Apart from this deviation, the ability of the constant stress model to predict resonant frequency suggests that the devices are primarily sensitive to mass and stiffness variation. Moreover, it suggests that the polymer transition from glassy to rubbery has a significant effect on the resonant frequency of the device. 67  Figure 40 (right) compares PS data and model results.   The constant stress model and experimental data agree in a similar manner shown by the PVAc results. Following the transition from glassy to rubbery elasticity, the resonant frequency of the device drops dramatically.  In this case, there is less deviation between the predicted and measured results. The strong agreement between the modelled and measured results suggest that changing sensing layer stress does not play a significant role in determining device response. Instead, mass and elasticity change are the dominant drivers of resonant frequency.   In an attempt to account for the discrepancy between modelled and measured PVAc results, swelling driven stress was included in the model for FPW resonant frequency as a function of solvent concentration.  Equation 47 describes the predicted in-plane stress as a function of Young?s modulus and volume fraction polymer. Incorporating this effect in the existing model results in a strong downward shift in frequency driven by polymer expansion. In the glassy region, for example, the stress rate of change is 2.1 kPa/ppm, about double that which is predicted by the fit function. This is plotted in Figure 41 with data set (1) which deviated the most from the constant stress model.       Figure 41: Frequency shift as a function of toluene concentration given a PVAc sensing layer.  The solid black line describes predicted frequency given a small glass transition region and a high rubbery elastic modulus of PVAc.  The solid grey line (beneath the black at low concentrations) describes the predicted performance given a large glass transition region and low rubbery elastic modulus. Here, two separate curves are plotted to illustrate the potential effect of the glass transition temperature.  When in the glassy state, the sensing layer expands and remains relatively elastic, resulting in a dramatic drop in frequency. Above the glass transition temperature, Young?s modulus will drop between 1 and 3 orders of magnitude as the polymer transitions to a rubbery material.  This transition is described by Equation 40.  In the rubbery state, the modulus is described by Equation 45.  As empirical data is required to determine exactly when the material exits the transition region and enters the rubbery region, Figure 40 68  shows the results assuming a very large transition region (grey line) and a very small transition region (black line).  These modelling results demonstrate a key characteristic of soft FPW devices.  Given a device which is primarily sensitive to stress variation, a large reduction of sensing layer Young?s modulus, caused by a transition from glass to rubbery behavior, will reduce overall sensitivity.  Comparatively, a device which is sensitive to mass and stiffness variation will show an increased sensitivity as a result of this transition.  The results also suggest that the current model overestimates the influence of stress variation on the resonant frequency of the device. It is possible that this is due to non-idealities of the sensors tested. Specifically, the model assumes a sensing layer film which is significantly thinner than the substrate and which does not influence the internal stress of the PVDF.  These devices were fabricated prior to the development of this model and so the aforementioned requirements are not entirely satisfied. It is also likely that localized stress variation in the film could have a strong effect on the overall sensitivity.  During fabrication, the devices are connected electrically using carbon glue. As the material dries and stiffens, it may be inducing tensile stress on the substrate.  In summary, VOC detection was demonstrated using toluene as an analyte and PS and PVAc as sensing layers. A model for sensing layer mass loading, thickness, and Young?s modulus as a function of solvent concentration was then used to predict sensor response. Predicted and measured frequency response showed strong agreement over 4 out of 5 experimental data sets. In an attempt to account for the deviation between predicted and measured results from data set (1), swelling driven sensing layer stress variation was included in the performance model. The resulting prediction overestimated device sensitivity, suggesting stress change did not play a significant role in the VOC detector frequency response. 5.3 Epoxy Curing Characterisation 5.3.1 Overview Fibre reinforced plastics are composed of two materials: a woven structure and a support matrix.  The woven structure is a high tensile strength fibre such as carbon, graphite, fibreglass, or Kevlar, while the support matrix is a thermoset or a thermoplastic.  A thermoset is a liquid which, when mixed with a catalyst, forms a solid through the non-reversible reaction while thermoplastics are materials that can be melted and cooled repeatedly to form a desired shape.  The former category is primarily used in high performance reinforced plastics and is the focus of this investigation. [7] While the strength of a composite material is determined mainly by the reinforcing fibre, the support resin will dictate its working temperature, impact resistance, durability, chemical resistance, and thermal 69  mechanical properties. These will be affected by the chemical composition of the resin and the processing parameters of the curing process.  As such, understanding the thermal and mechanical properties of a curing polyester resin is a key goal in composites research. Measuring these properties during crosslinking is no straightforward task; however, and a range of expensive laboratory procedures are currently used to characterise new resins. It is proposed that the unique sensing properties of the FPW device will allow the simple interrogation of resins during curing.  Given a 20 ?m thick PVDF acoustic sensor coated in a 10 ?m film with an elasticity and density similar to the substrate, it is predicted that a 1-2% deviation in film density, elasticity, stress, or thickness could be detected (See Appendix-Section A.4). This potential high resolution served as justification for initial experiments. 5.3.2 Results and Discussion The general sensing mechanism was tested using a Bondit B-45 epoxy.  Between 25 and 50 ?L of the resin, applied with a spatula, was spread over an 18 ?m sensor which was being driven by a chirp centered near 150 kHz.  The resulting frequency shift was then measured as the epoxy cured.  When crosslinking had completed, a second layer was added and the experiment repeated.  The results are shown in Figure 42.   At t = 0, the uncoated sensor shows an output frequency of about 150 kHz.  Soon after, the resin is applied resulting in a ~5 kHz mass driven drop in frequency.  Over the next two hours, the frequency rises as the epoxy stiffens.   Figure 42: Frequency response of a sensor successively coated in two layers of epoxy. 70  When the experiment is repeated, a larger mass is added, resulting in a larger initial frequency drop and follow-up stiffness driven rise.  These results serve as a demonstration of sensitivity to stiffness changes in curing films.   The predicted resolution of this device can be found by determining the thickness, Young?s modulus, stress, and density changes required to induce a resonant frequency shift 3 times greater than the background noise of 90 Hz.  These minimum detectable changes are shown in Table 7 for a 20 ?m thick sensor under 25 MPa of substrate stress. For simplicity, the calculations assume that the final film modulus and density are equivalent to that of PVA. The calculations demonstrate that, even for a moderately tensioned, thick substrate sensor, the minimum detectable variation for each property of interest can be quite low. Table 7: Predicted minimum detectable thickness, Young?s modulus, stress and density changes in an applied curing film.  Substrate Applied Film Minimum Detectable Values Thickness (m) 2.0E-05 1.0E-05 6.7E-08 Elastic Modulus (Pa) 2.9E+09 2.9E+09 4.0E+07 Stress (Pa) 2.5E+10 0 2.9E+05 Density (kg/m3) 1.78E+03 1190 15 5.4 Acoustic Microfluidics 5.4.1 Overview Droplets of varying sizes were applied to these 800 ?m wavelength devices and the resulting flow caused during actuation was recorded.  The purpose of the investigation was to confirm the ability of these devices to drive acoustic streaming, compare the results with an approximated model for FPW driven creeping flow, and determine whether polymer FPW acoustic devices could be configured to act as microfluidic pumps. A diagram of the setup is shown in Figure 43.  FPW waves are generated at a transducer and propagate into the droplet at its base.  Depending on the amplitude and frequency of the acoustic wave, fluid flow, vibration, translation, jetting, or atomisation could be induced in the droplet. 71   Figure 43: A diagram showing the fluid manipulation setup investigated.  A flexural plate wave is excited towards a droplet placed on the same substrate.  This drives flow within the droplet and, at high enough power, droplet movement. Important properties of the wave-droplet system are shown in Figure 44.  Based on past sensor performance data, the estimated maximum wave amplitude, out of plane velocity, and phase velocity are 20 nm, 18mm/s, and 130 m/s, respectively.  These variables have a strong effect on the magnitude and direction of power transferred to the fluid.  Given a wavelength of 800 ?m and an unloaded resonant frequency of about 150 kHz, the mass loading boundary layer in the fluid will extend to about 130 ?m while the viscous boundary layer will extend to about 1.3 ?m. These terms are important as they confirm the validity of the acoustic streaming model boundary conditions.  Near boundary layer flow in the droplet is approximated by assuming the fluid is semi-infinite.  For this to be true, the droplet surface near the centre needs to be sufficiently far away from the limits of the first order flow velocity.  These are approximated by the mass loading and viscous boundary layers which, for a 1 mm thick droplet, are sufficiently distant from the upper boundary.  Figure 44: A diagram of the droplet during actuation.  Important parameters such as wavelength, wave velocity, wave amplitude, and substrate thickness are labelled. 72  Given the wave and fluid characteristics described above, it is predicted that during testing, near boundary layer viscous flow will be induced in the direction of the acoustic wave travel.  This is based largely on similar work carried out by White and Moroney [11], [12], in which they present the model described in Section 1.7.  A key, relevant result of this work is the development of Equation 34, a function which approximates the maximum x-velocity of steady state, near boundary flow induced by a travelling acoustic wave in an adjacent substrate.  It is obtained by taking the limit of the function describing Uxlim as a function of distance from the substrate and describes the motion of fluid well above the viscous boundary layer yet below the mass loading layer.  Well above this point, the influence of the oscillating surface is significantly reduced and the approximations made in obtaining this model are no longer valid.  When flow within the bulk droplet is calculated, the near boundary flow solutions are used as lower boundary conditions. In accordance Moroney?s work, measured flow velocity near the substrate of the device is compared with the maximum average mass transport velocity described by Equation 31.   5.4.2 Results and Discussion Prior to microfluidic testing, each sample was interrogated using a laser Doppler vibrometer, as explained in Section 2.3. The goal of these tests was to confirm operation, determine resonant frequency, and measure the maximum operational amplitude of each device.  Resonant frequency was determined using a 350 Vpk-pk, 0 to 200 kHz bandwidth chirp to excite the samples.  During this excitation, the out of plane velocity of a 2 mm by 2 mm section of the substrate over a range of frequencies was measured.  Example results are shown in Figure 45.  Figure 45: Example plots of LDV results. Left: the average out of plane wave velocity as a function of frequency. Right: A 2 dimensional plot of the LDV map. Device performance data is shown in Table 7.  With the resonant frequency of each functioning sample identified, the devices were interrogated using a continuous sine wave excitation.  73  Table 6: Sample frequencies and out of plane velocities. Sensors excited at 350 Vpk-pk Sample Thickness Resonant Freq.  Out of Plane Vel. 1 20 ?m - - 2 18 ?m 130 kHz 60 ?m /s 3 10 ?m 105 kHz 100 ?m /s 4 10 ?m 100 kHz 55 ?m /s 5 20 ?m 140 kHz 45 ?m /s 6 10 ?m 98 kHz 110 ?m /s 7 25 ?m 150 kHz 0.4 ?m /s 8 20 ?m 141 kHz 350 ?m /s 9 20 ?m 141 kHz 350 ?m /s  This was done to identify the operating voltage range of the devices and develop an empirical relationship between input signal and the out of plane velocity or amplitude. Those devices which showed the greatest out of plane velocity were used for further testing. During droplet flow imaging, the empirical voltage-velocity relationship was used to predict the wave amplitude and power of the unloaded devices. The upper input voltage operating limit was imposed by dielectric breakdown.  Given the geometry of the electrodes and the measured DC breakdown field of about 100 MV/m, the predicted maximum input voltage was 2 kV to 4 kV. Initial testing revealed that, even when an AC signal was applied, on average, breakdown occurred at 800 V.  At lower input voltages, the devices which showed the greatest out of plane velocity were sample 2 and 8. During fluid flow imaging, the sample 2 failed due to dielectric breakdown.  It was repaired and re-interrogated using the LDV prior to undergoing further testing.  The LDV results of these three samples are shown in Figure 46.   74   Figure 46: Out of plane velocity as a function of driving voltage for the samples tested. Following LDV characterisation, fluid flow testing was carried out.  Droplets of water ranging from 1 mm to 3 mm in diameter were applied to the back of each device, adjacent to the input transmitting IDTs.  Special care was taken to prevent the fluid from touching the backplane or any other conductive region of the samples.  This was done to eliminate the possibility of electrophoretic flow interfering with acoustically driven flow.   During testing, 0.5 ?m to 3 ?m polystyrene spheres were injected into each droplet and their horizontal movement was recorded. An image of a 2 mm droplet on a sample is given in Figure 47.  Fluid was illuminated using a fluorescent lamp.  To increase the uniformity of light intensity and reduce droplet evaporation rate, semi-opaque, PVDF film was mounted around the droplet to disperse light and absorb heat.  Figure 47: An image of a 2 mm droplet on the back of a sensor prior to actuation. 0 5 10 15 20 25 0 200 400 600 Out of Plane Velocity (mm/s) Driving Voltage (Vpk-pk) Sample 2A- 159 kHz Sample 2B - 168 kHz Sample 8 - 168 kHz 75  A continuous sinusoidal signal with a 300 Vpk-pk to 800 Vpk-pk amplitude was used to excite droplets. When power was applied, polystyrene spheres closest to the substrate were generally observed to move away from the input transducers, in the direction of FPW movement. Concurrently, spheres in the center and near the surface of the droplet moved in the opposite direction.  Velocity measurements were taken at the substrate surface, near the centre of each droplet.  The results of these measurements are shown in Figure 48.  Logarithmic streaming velocity in ?m/s is plotted against the log of wave amplitude squared times radial frequency.  Along with this, the predicted maximum mass transport velocity, calculated via the Longuet-Higgens relationship and through Manor?s approximation, is plotted.  Over the range of acoustic power investigated, there is marginal agreement between both models and the results. While both models tend to overestimate predicted velocity, measured velocity trends roughly with acoustic amplitude squared.  This breaks down significantly at lower velocities.  It is likely that, at these low flow rates, unaccounted for mechanical and thermal noise drives the polystyrene spheres to higher velocities. At higher acoustic power, the lower than predicted fluid velocity observed may be a result of polystyrene spheres not being fully exposed to the near boundary viscous layer flow field.     Figure 48: Polystyrene sphere velocity as a function of radial frequency and wave amplitude squared. Measurements are obtained from three samples and compared with the maximum near boundary layer flow velocity predicted by the model discussed in Section 1.8. Model predictions are made assuming a constant frequency of 159 kHz. As such, predicted streaming velocity curves trend with a square of acoustic ampitude 0.1 0.5 5.0 50.0 5E-12 5E-11 5E-10 Streaming Velocity(?m/s) ?A2 (rad nm2) Sample 2A - 159 kHz Sample 2B - 159 kHz Sample 8 - 168 kHz Ulim (Longuet-Higgins) Ulim (Manor) 76  During testing, a number of samples were flipped over such that the acoustic behavior of the sensor could be measured during actuation. This was done to determine the amplitude and attenuation of the FPW inside the droplet. The results are shown in Figure 50.  Figure 49: LDV images showing an acoustic wave propagating through an unloaded sensor (right) and a sensor with a droplet on the substrate (left) Figure 49 shows a comparison of the loaded and unloaded device acoustic response in 2-D. With a droplet applied to the back of the substrate, acoustic wave amplitude is reduced along with in-plane group and phase velocity. The changing in-plane velocity causes refraction and acoustic focussing to occur about the droplet. Figure 50 shows a plot of average acoustic wave amplitude compared with average amplitude underneath the centre of the droplet, demonstrating the relatively small increase in attenuation caused by the fluid. At high wave velocities, a large portion of acoustic energy is radiated into the fluid, causing significantly increased wave attenuation [13].   The model for maximum flow velocity requires that damping driven by radiation be negligible [11]. Amplitude data was used to confirm this requirement.  Unloaded samples show an average decay of  25 dB/cm while sample loaded with a 3 mm diameter drop show 27 dB/cm.  The similar results suggest that little energy is being radiated away from the substrate.  This is consistent with the model for near boundary streaming used here which assumes FPW power loss is small enough that decay can be neglected. 77   Figure 50: A plot showing the relative average displacement amplitude of FPWs in an unloaded sensor and a sensor loaded with a 3 mm diameter droplet.  The relatively similar rate of attenuation shown by the two curves suggests that there is little energy radiated into the fluid. In summary, all-polymer flexural plate wave devices for fluid manipulation were fabricated and tested. Using an input voltage of 800 Vpk-pk, flow velocities of up to 9 ?m/s were driven in water droplets placed on the sample substrates. Predictions made by two models for near boundary layer viscous streaming were compared with experimental results and marginal agreement between modelled and measured flow velocity was observed.   Throughout experimentation, the low wave velocity and frequency of the samples produced proved to be a significant barrier. In order to overcome these limitations, high voltage input signals were used to drive large amplitude oscillations. This approach was limited, however as the samples often experienced dielectric breakdown during operation. For future designs to produce a useful amount of acoustic power, higher frequency designs will have to be investigated.             -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 0 1 2 3 Displacement (nm) Distance (mm) Unloaded ? Loaded Sample 78  6 Conclusions The unique stiffness and stress sensitivity of polymer based flexural plate wave devices makes them promising candidates for high resolution chemical sensors and soft material characterization tools. Previously, the basic operation of a PVDF flexural pate wave sensor was demonstrated using humidity detection.  The performance of the device was confirmed using a model which described resonant frequency as a function of analyte mass loading in the sensing layer.  Building upon this work, all-polymer FPW devices were fabricated and used to demonstrate VOC sensing, cure-characterisation, and microfluidic manipulation.  Along with this, a model for VOC sensing by a polymer based FPW device was developed and compared with experimental results.   In order to achieve these goals, advances were made in the understanding, design, and fabrication of all-polymer FPW devices. These advances are summarized below along with modeling and test results. 6.1 Design and Fabrication Thin Film, Low Stress Sensors: As discussed in [5], a thinner sensor significantly increases stiffness and stress sensitivity. During the investigation, a transition was made from 20 to 30 ?m thick devices to 9 to 15 ?m thick devices.  The thinnest sensor fabricated and successfully tested showed a resonant frequency of 76 kHz but a reduced output amplitude. These devices were used primarily in microfluidic manipulation tests. Sensors with substrates under little or no stress were similarly shown to have an increased stiffness and stress sensitivity. Low stress sensors were fabricated with resonant frequencies varying from 100 kHz to 150 kHz.  This about double the predicted frequency, a discrepancy which was attributed to residual stress in the substreate. PVDF Crystallinity and Performance: Initially, three separate suppliers provided varying thicknesses of unprocessed PVDF film for fabrication: McMaster Carr, Professional Plastics, and Solef.  During the investigation into thinner substrates, it was discovered that PP and Solef films consistently produced poorly performing devices. Using DSC, it was discovered that these two films showed significantly lower average total crystallinity. The low piezoelectric constant and low acoustic amplitude was attributed to this characterised and McMaster Carr films were used during future investigations. Reference Layers: An investigation was carried out into the performance of a variety of reference layers for humidity detection. Solvent cast PS, PVDF, and PVAc were compared along with vapour deposited Parylene C. Each material was applied to an acoustic sensor and the device was exposed to a range of 79  humidities. The frequency shift of the coated sensors was then compared to that of one coated only in PEDOT, a hygroscopic polymer. All materials were expected to be impermeable to water vapour and so the resonant frequency shift of the device was predicted to be negligible.  This was not the case however, as all but the PS coated sensor showed a response which varied with humidity concentration. Polystyrene was therefore used as a barrier for future tests until it was discovered that the internal stress of the sensing layer could be affecting the reference layer signal. Stretching and Poling:  The influence of stretching and poling temperature on piezoelectric constant and beta content was investigated.  As suggested in previous investigations, it was confirmed that the optimal fabricating temperature was near 80 oC. Dielectric breakdown was then investigated with the purpose of increasing thin film sensor yield. Time to breakdown was measured as a function of applied electric field and compared with the minimum required poling intensity. It was discovered that, for thin films, a small variation in field intensity or sample thickness could easily lead to dielectric breakdown.  Thus, the poling setup was modified to accommodate thinner PVDF substrates.  Thin film samples are now poled in groups of three with silicone oil separating each film and the electrodes.  Screen Printing: A screen printing apparatus for the application of PEDOT:PSS electrodes to a PVDF substrate was designed, built, and tested.  Substrate hydophobicity, ink viscosity, ink surface tension, and ink conductivity were identified as the key variables which would lead to a successful print.  Conductive screen printing ink was developed through the evaporation of low viscosity inkjet printing ink. While shorting still occurs during fabrication, this apparatus significantly reduces overall manufacturing time and increases yield. 6.2 Modelling and Understanding In an effort to better understand and predict sensor performance, a model was developed to describe sensing layer physical properties as a function of analyte concentration. It was created to analyze sensor performance and serve as a design tool. As it does not rely heavily on empirical sensor performance data, it can be used to investigate the effect of design changes prior to device fabrication. This is particularly useful for the task of identifying appropriate sensing layers for different analytes. Given the lack of relevant polymer-solvent solution physical data available, it is difficult to predict polymer mechanical properties as a function of solvent concentration without manufacturing and testing a device. The model solves this problem and allows the simple comparison of a range of sensing layer designs. Using Flory-Huggins solution theory and a modified version developed by Leibler and Sekimoto, the concentration, in volume fraction, of a solvent in a glassy or rubbery amorphous polymer was predicted as a function of the solvent vapour concentration. The volume fraction solvent and polymer were then used to 80  predict sensing layer density, thickness, Young?s modulus and stress.  Using PVA-water absorption data from previous research, the predictive ability of the model was validated for density, thickness and Young?s modulus.  It is well known that as solvent concentration increases, the mass increase of a polymer-solvent system can be approximated as a linear function of solvent vapour concentration.  This property is fundamental to the operation of most acoustic chemical sensors. Over a wide range of analyte concentrations, however, nonlinearly increasing thickness and decreasing density makes sensing layer mass vs. analyte vapour pressure difficult to predict.  As shown by the PVA-water data and model, the Flory-Huggins and Leibler-Sekimoto model captures this swelling and density change behavior below, near, and above the glass transition temperature of the polymer, leading to an accurate estimate of mass loading. Volume fraction polymer is similarly used to predict changes in sensing layer elastic modulus. Unlike the thickness or density, the elastic behavior of a polymer system changes dramatically as the mixture transitions from a glassy to a rubbery state. This behavior was therefore described with three relationships for Young?s modulus as a function of volume fraction polymer. While it?s in the glassy regime, the polymer modulus will fall roughly linearly with volume fraction. This is shown by the PVA data and predicted by the model. In the glass transition region, it falls exponentially by 1 to 3 orders of magnitude before returning a roughly linear drop in the rubbery region. For a device which is sensitive to stiffness, this behavior is incredibly important.  Depending on the relative mass, stiffness, and stress sensitivity of a device, the change in GTT can lead to a stark rise or drop in its resonant frequency while operating in the transition region.  The FH and LS models are used to demonstrate this potential for high stiffness sensitivity.  To create a complete understanding of sensing layer behavior, volume fraction polymer and solvent were also used to approximate in-plane swelling driven stress. The model suggested that a lightly tensioned sensor would show extreme sensitivity to sensing layer stress while the polymer was in the glassy state. Above the glass transition temperature, the device would be less sensitive due to the reduction in film Young?s modulus.  While the model has yet to be validated experimentally, it was used to demonstrate the potential effect of sensing layer stress on device frequency during detection.   In summary, the expanded sensing layer model was used to predict the performance of a chemical vapour sensor over a wide range of frequencies.  It was shown that, for a stiffness and stress sensitive device, the glass transition temperature of the sensing layer has a strong impact on frequency response. In order to leverage this sensitivity, a polymer must be chosen which is near its glass transition temperature during operation. The model also predicts the rate of vapour driven density change and swelling over a wide range 81  of analyte concentrations and glass transition temperatures.  This showed that, for a constant solvent vapour concentration, a rubbery sensing layer will gain mass, and swell to a much greater extent than a glassy one. This model was compared with toluene detection results given PVAc and PS coated sensors. Assuming a constant sensing layer stress and a substrate stress of about 25 MPa, the model accurately predicts sensor frequency as a function of solvent concentration.  Specifically, it is able to predict the downturn in frequency driven by the changing glass transition temperature of the sensing layers.  The addition of predicted sensing layer stress variation results in a significant overestimation of frequency drop as a function of solvent concentration in comparison to measured results. This is likely a result of localized substrate tensioning caused by carbon glue contacts, and non-uniform sensing layer thickness.  It is also possible that, due to the dual sorption mechanisms which occur in glassy polymers, calculating film swelling using polymer volume fraction may lead to an overestimation of film thickness and therefore, stress magnitude. 6.3 Performance Testing A set of 9 ?m to 25 ?m thick, low tension PVDF flexural plate wave devices were fabricated and characterized.  Their performance as VOC sensors, soft material characterisation devices, and microfluidic manipulators was interrogated and compared with analytical models.  Following the demonstration of humidity detection using PVA as a sensing layer, the devices were configured to detect toluene. This involved fabricating lower tension sensors with 1 ?m to 3 ?m thick PVAc and PS sensing layers. Testing was carried out by exposing samples to a wide range of toluene vapour concentrations and measuring the frequency response. Polystyrene and poylyvinyl acetate coated devices showed a sensitivity of -80 cm2/g to -200 cm2/g and -240 cm2/g to -490 cm2/g, respectively. These responses correspond with a minimum detectable concentration of 340 ppm to 680 ppm toluene.  Frequency vs. concentration curves showed two distinct regions of sensitivity. At low concentrations, frequency fell linearly with toluene presence while, at high concentrations, it drops off with a constantly increasing slope. As confirmed by the performance model, this behavior is attributed to the transition of the polymer sensing layer from a glassy state to a rubbery state, resulting in a greater amount of solvent absorption and a significant drop in elastic modulus. The unique stress and stiffness sensitivity of the devices was also leveraged to demonstrate the mechanical characterisation of a curing epoxy.  A sensor was coated in multiple layers of a commercial epoxy and the frequency response of the device was measured as the epoxy cured.  The frequency drops with the addition of the material and then rises as it stiffens.  It is proposed that this sensing mechanism could be used to interrogate novel resins and composites as they cure. 82  Finally, acoustic streaming was investigated using a set of PVDF FPW devices. In an effort to develop a combination fluid sensing, mixing, and pumping platform for disposable biosensing applications, all-polymer acoustic microfluidic manipulation devices were fabricated and tested.  Devices were shown to be capable of producing out-of-plane wave velocities of up to 20 mm/s at a resonant frequency of 110 kHz to 170 kHz. Near this operating point, a near boundary viscous flow velocity of up to 9 ?m/s could be induced. While this work demonstrated that these devices could be used to cause acoustically driven flow, it also showed that significantly more acoustic power will be required to generate a useful flow velocity. Achieving this acoustic power will require designing a device which oscillates at a higher frequency or out-of-plane amplitude. 6.4 Future Work With the successful demonstration of VOC sensing, the primary goal of this project now shifts to increasing device sensitivity.  To begin competing with existing VOC detectors, a minimum resolution of less than 1 ppm is required. For toluene detection, this means achieving at least a 300  improvement in sensitivity. This may be achieved through a combination of sensor design modifications. First, as detailed thoroughly in [5], thinning the sensor substrate will increase sensitivity.  While a reduction in film thickness was achieved during this investigation, it was accompanied by a reduction in signal strength. Prior to the fabrication of thinner devices, the electromechanical coupling coefficient, k, should be characterized as a function of substrate thickness to confirm that it acts as predicted by theory. Similarly, both d33 and d31 coefficients should be measured as a function of thickness. Once the source of the signal strength reduction has been identified, work can continue to produce a significantly thinner sensor. Given the lack of commercially available PVDF film thinner than 25 ?m, this work should focus on the spraying or casting of sub-micron piezoelectric film. Second, substrate tension should similarly be reduced to increase sensitivity to polymer stiffness and stress variations.  This should entail an investigation into the possible sources of residual stress in the substrate. While the influence of the sensing layer and backplane has been ruled out, it is possible that stress induced by the carbon contacts may be affecting the acoustic signal. Third, experimental and modelling work has shown that the sensing layer glass transition region may be leveraged to produce a highly sensitive stiffness variation device. In order to use this region to detect low concentrations of solvent, the device must be operating at or near the glass transition temperature of the sensing layer. This may be achieved by operating at a raised temperature or through the addition of plasticizers to the sensing polymer, causing a decrease in its GTT. 83  Fourth, the use of rubbery polymers for sensing should be investigated. As the high elastic modulus of the glassy polymers tested restricted film expansion at low concentrations, a less elastic, rubbery film may lead to greater absorption and solvent driven film expansion at low concentrations. Fifth, stress induced by polymer film swelling should be measured and compared with the current model.  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Dual, ?Mechanical characterization of PEDOT:PSS thin films,? Synth. Met., vol. 159, no. 5?6, pp. 473?479, Mar. 2009. [97] G. Man, ?Towards all-polymer surface acoustic wave chemical sensors for air quality monitoring,? 2009. [98] V. Sencadas, R. Gregorio, and S. Lanceros-M?ndez, ?? to ? Phase Transformation and Microestructural Changes of PVDF Films Induced by Uniaxial Stretch,? J. Macromol. Sci. Part B, vol. 48, no. 3, pp. 514?525, 2009. [99] V. Sencadas, S. Lanceros-M?ndez, and J. F. Mano, ?Characterization of poled and non-poled ?-PVDF films using thermal analysis techniques,? Dec. 2004. [100] ?FTIR studies of b-phase crystal formation in stretched PVDF films.? [Online]. Available: http://www.academia.edu/3469135/FTIR_studies_of_b-phase_crystal_formation_in_stretched_PVDF_films. [Accessed: 06-Aug-2013]. [101] Y. Huan, Y. Liu, and Y. Yang, ?Simultaneous stretching and static electric field poling of poly(vinylidene fluoride-hexafluoropropylene) copolymer films,? Polym. Eng. Sci., vol. 47, no. 10, pp. 1630?1633, 2007. [102] S. K. Mahadeva, J. Berring, K. Walus, and B. Stoeber, ?Effect of poling time and grid voltage on phase transition and piezoelectricity of poly(vinyledene fluoride) thin films using corona poling,? J. Phys. Appl. Phys., vol. 46, no. 28, p. 285305, Jul. 2013. [103] S. Lanceros-M?ndez, J. F. Mano, A. M. Costa, and V. H. Schmidt, ?FTIR and DSC Studies of Mechanically Deformed ?-VDF Films,? 2001. [104] A. M. Vinogradov, V. Hugo Schmidt, G. F. Tuthill, and G. W. Bohannan, ?Damping and electromechanical energy losses in the piezoelectric polymer PVDF,? Mech. Mater., vol. 36, no. 10, pp. 1007?1016, Oct. 2004. [105] J. Chen, ?Screen Printing Processes for Flexible Sensor Device Fabrication,? University of British Columbia, EECE 597 Technical Report, Feb. 2013. [106] ?McMaster-Carr.? [Online]. Available: http://www.mcmaster.com/#pvdf-film/=po65li. [Accessed: 05-Dec-2013]. [107] ?Polystyrene average Mw 35,000 | Sigma-Aldrich.? [Online]. Available: http://www.sigmaaldrich.com/catalog/product/aldrich/331651?lang=en&region=CA. [Accessed: 05-Dec-2013].  89  Appendix A.1 Glass Transition Temperature of a Polymer Solvent System As detailed in [61], the glass transition temperature of a polymer and plasticizer mixture may be approximated with a weighted average of the GTTs of each component,                                      .      Here Tg1 and Tg2 are the glass transition temperatures of solvent and polymer, ?1 and ?2 are the thermal expansion coefficients of the solvent and polymer, and TgAv is the glass transition temperature of the mixture. Using data from a study on VOC sorption in amorphous polymers [61], the glass transition polymer volume for toluene in PS and PVAc at 22 Co is 0.83 and 0.90 respectively. A.2 Time Temperature Superposition and the WLF Equation Over time, a polymer under constant load will show reduced elasticity and viscosity due to relaxation within the material. A diagram of one such curve is shown in Figure 51, here, a material is subjected to a tensile force over a range of time periods. Increasing the temperature of the material increases the relaxation rate, causing a decrease in elasticity.  Time-temperature superposition is the concept that the influence of increasing time and temperature on polymer viscoelesticity is identical.   Figure 51: An example of the elastic modulus of a material under constant load at and increasing time or temperature [84]. As such, it is possible to calculate the elastic modulus-time or viscosity-time curve of a material at a range of temperatures given data taken at only one temperature. An example of this is shown in Figure 51. Elasticity of a material is measured over a wide range of frequencies at T0. If it were to be repeated at two higher temperatures, the resulting modulus curve could be calculated through a linear shift related to the difference between the new temperature and the glass transition. 90   Figure 52: An example of a modulus-frequency curve of a material under constant load. The WLF equation is used to describe the shift in viscosity or elasticity of a material caused by changing temperatures in the glass transition region. For the application in question, the elastic modulus of the material is only required at one frequency, ~150 kHz. The whole modulus-frequency curve is not required for the polymers of interest, only a single data point.  The WLF equation can then be used to shift this value according to changes in temperature or glass transition temperature. A.3 Influence of PEDOT:PSS Backplane on Sensor Resonant Frequency The influence of stiffness residual stress caused by the casting of PEDOT was investigated. A layer of PEDOT:PSS was solvent cast on the back of an otherwise clean sensor and allowed to solidify while the sensor was operated. The change in frequency was then monitored.  Large increases in frequency would have indicated significant stiffening and none were observed.  Following this, the sensor was exposed to humidity cycling to investigate the possibility of residual stress influencing the resonant frequency of the sensor.  Figure 54: Sensor resonant frequency during PEDOT backplane casting (left) and during humidity cycling (right) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.61.11.151.21.251.31.35x 105Time (hr)Freq (Hz)Freq (Hz)91  A.4 FH Model Implementation The polynomial fit used to describe PS volume fraction as a function of tolune vapour pressure is,                                                                       (51) where Press is the vapour pressure of the solvent.  It is used to calculate the volume fraction of polymer in the sensing layer which is then used to calculate sensing layer thickness, density, elasticity, and stress.  An example of this is given in the script below.  This function takes sensor and substrate physical characteristics, solvent vapour pressure, and sensor operating frequency at 0 ppm  solvent concentration and produces a prediction for sensor resonant frequency up to solvent saturation. function PSHumfitSinglePointConstSet2 PlotFit   function [xdata1,ydata1,xdata2,ydata2,xdata3,ydata3,xdata4,ydata4]=loadData %%%Load Data%%%% .... %%%Frequency and solvent concentration data is loaded%%%  xdata1=TolRes5(1,1:1);ydata1=TolRes5(2,1:1);xdata2=TolRes6(1,1:1);ydata2=TolRes6(2,1:1); xdata3=TolRes7(1,1:1);ydata3=TolRes7(2,1:1);xdata4=TolRes1(1,:);ydata4=TolRes1(2,:);   function PlotFit(estimates) [xdata1,ydata1,xdata2,ydata2,xdata3,ydata3,xdata4,ydata4]=loadData; xdata=xdata1; ydata=ydata1; T=22.9; %Temperature of gas stream Pamb=101325; %Ambient Pressure in Pa P=133.3224*10^(6.95464-(1344.8/(T+219.482))); % Saturation vapour pressure in Pa ConcMT=P./Pamb; %Mole fraction of toluene ConcPPMT=ConcMT*10^6; Pamb=101325; %Ambient PRessure Tamb=273.15+22.8; %Ambient Temperature R = 8.314;           %J/K/mol Mw = 92;           %g/mol SolVol=5e-6; %litres of solution cast Conc=0.02; %Concentration of solution Area=0.00724*0.011; %Casting area TolDen=861; %Density of casting solution (xylene) T=22.9; %Temperature of gas stream Pamb=101325; %Ambient Pressure in Pa Ptol=133.3224*10^(6.95464-(1344.8/(T+219.482))); % Saturation vapour pressure in Pa PVDF.density = 1780;     %kg/m^3 PVDF.PR = 0.35;          %Poisson ratio PVDF.YM = 2.9e9;         %Pa PVDF.d = 22e-6;          %Thickness, m PVDF.m = PVDF.density * PVDF.d; PS.densityBase = 1190;       %kg/m^3 PS.PR = 0.3;           %Poisson ratio PS.YM = 286e6;          %Pa 92  PS.dBase = Conc*SolVol*889/(Area*PS.densityBase*1000) %Initial thickness of PS sensing layer lambda = 800e-6;        %Wavelength of IDTs, m PS.S = 5000000; %Est. Residual stress in the sensing layer   humlist=linspace(0, 100); for i = 1:length(humlist)     Press = humlist(i);     PS.density = PS.densityBase; %Initial PS density     Qpol=1/(0.5728*(Press / 100)^4 + 2.0263*(Press / 100)^3 - 2.167*(Press / 100)^2  + 0.7*(Press / 100)^1 +  1.1144); %Inverse of Volume fraction polymer, calculated by FH and modified FH fit     PS.d=PS.dBase*(0.5728*(Press / 100)^4 + 2.0263*(Press / 100)^3 - 2.167*(Press / 100)^2  + 0.7*(Press / 100)^1 +  1.1144); %Thickness, calculated by volume fraction polymer multiplied by initial thickness     Qpol2=1/(9.9648*(Press / 100)^6 - 25.075*(Press / 100)^5 + 24.207*(Press / 100)^4 - 10.771*(Press / 100)^3 + 2.3348*(Press / 100)^2 + 0.077*(Press / 100)+  0.002 );     %FH model alone for comparison     Qsolv=1-Qpol; %Solvent volume fraction     c1=Qsolv/(.000106*(1-Qsolv));     rhoFilm=(PS.density+c1*Mw/1000)/(1+Qsolv/(1-Qsolv)) ; %film density     PS.m=rhoFilm*PS.d;   %Mass density of film     Swell=1/Qpol;     [ E, TgAv] = PolElasticMod(Qsolv, 3e9); %Elastic modulus of film     YoungTest(i)=E;     TgTest(i)=TgAv;     PS.YM=E;     if i<2         %Stress in the substrate is calculated using the resonant         %frequency of the unexpeosed sensor.         [rho] = psolveInverse( PVDF, PS, lambda, ydata );         PVDF.S = rho;     else     end     [v(i) f(i)] = psolve( PVDF, PS, lambda ); %Resonant frequency is calculated using Equation 11 end figure(1) plot( humlist*3.3540e+004/100, f,'-k', 'LineWidth',2, 'linesmoothing', 'on'  ); hold all % Plotting function for frequency data is called. TolConcPS   function [ E, TgAv] = PolElasticMod(Qsolv, E0) Tg1=-156+273.15; %Glass transition of polymer Tg2=105+273.15; %Glas transition of solvent A1=1.067e-3; %Thermal expansion coefficient of polymer A2=6.15e-4; %thermal expansion coeffieicnt of solvent TgAv=(A2*(1-Qsolv)*Tg2+A1*Qsolv*Tg1)/(A2*(1-Qsolv)+A1*Qsolv); %Average glass transition. if TgAv<(23+273.15)     %Young's modulus as a function of GTT, as approximated by WLF equation     E=E0*(1-.1)*exp(-7.3*(23+273.15-TgAv)/(36+(23+273.15-TgAv))); else     %Young's modulus in a glassy state. 93      E=E0*(1-0.3*(23+273)/TgAv);      end   The function below, written by Chrsitoph Sielman, uses the closed form solutions of equations 4 to 11 to calculate sensor frequency and wave velocity as a function of substrate and sensing layer density, thickness, Young?s modulus, and stress.  %Solve for phase velocity and frequency based on input substrate and %sensing layer  function [v, f] = psolve( subst, sens, lambda )     %Stress term     T = subst.S * subst.d + sens.S * sens.d;      %Stiffness term     B = 2 * pi / lambda;     EprimeSubst = subst.YM / (1 - subst.PR ^ 2);     EprimeSens = sens.YM / (1 - sens.PR ^ 2);     h0 = 0;     h1 = sens.d;     h2 = sens.d + subst.d;     x0 = ( EprimeSens * ( h1 ^ 2 - h0 ^ 2 ) + EprimeSubst * ( h2 ^ 2 - h1 ^ 2 ) ) / ( 2 * ( EprimeSens * ( h1 - h0 ) + EprimeSubst * ( h2 - h1 ) ) );     D = 1/3 * ( EprimeSens * ( ( h1 - x0 ) ^ 3 - ( h0 - x0 ) ^ 3 ) + EprimeSubst * ( ( h2 - x0 ) ^ 3 - ( h1 - x0 ) ^ 3 ) );      %Mass term     M = subst.m + sens.m;      %Final velocity and frequency calculation     v = sqrt( ( T + B ^ 2 * D ) ./ M );     f = v / lambda; end  A.5 Electromechanical Coupling Coefficient Electromechanical coupling coefficient is the ratio of electrical energy applied to the IDTs to the mechanical energy generated in the substrate.  The coefficient, k, is given by,          ,      (50)  Where S is an element of the compliance matrix of the material and ? is the permittivity of the material under stress. This term is used in Section 5.4 to describe acoustic wave amplitude as a function of input voltage.  Most piezoelectric PVDF film is reported to show coupling coefficients ranging from 0.1 to 0.15.  94  This is quite low in comparison with those coefficients demonstrated by stiffer materials such as PZT.  As a result, acoustic wave amplitudes are much lower in PVDF.  

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