Quartz Crystal Microbalance 1 Biosensor Bio Recognition Element Transducer Signal Output Enzymes; Electrochemical Antibodies; Requires: Optical Receptors; Simple read out and data interpretation; Requires: Whole Sample cells... Easy to use; Immobilization Quick response. 2 Quartz resonators with front and back electrodes http://en.wikipedia.org/wiki/Image:Quartz_resonators_with_front_and_back_electrodes.jpg 3 Theory Thin quartz disk with electrodes plated on it Piezoelectric An oscillating electric field applied across the device -> acoustic wave propagates through the crystal Thickness of the device is a multiple of a half- wavelength of the acoustic wave -> minimum impedance Deposition of thin film -> decrease the frequency (mass of the film) 4 Piezoelectric effect Pressure -> electricity Mechanical strain/stress variation -> separate the center of gravity of the positive charges from the center of gravity of the negative charges -> dipole moment -> Polarization change Generated voltage between two electrodes Insulating materials -> charges on the surface Depend on the symmetry of the distributions of the positive and negative charges -> material 5 Single-crystal 32 classes 11 -> center of symmetry -> nonpolar ->symmetric ionic displacements -> no net change in dipole moment Quartz 6 Converse effect Electric filed -> strain mechanically One-to-one correspondence Decays due to the charge dissipation Increase with applied force -> drops to zero when force remains constant Pressure removed -> negative voltage -> decays to zero 7 Resonant oscillation Electric and mechanical oscillations are close to the fundamental frequency of the crystal Depend on: thickness, chemical structure, shape, density, shear modulus of the quartz, mass, physical properties of the adjacent mediums (density, viscosity of air/liquid). 8 Resonant frequency Sauerbrey: changes in the resonant frequency relates to the mass: 2 Δf = −2Δmnf0 /ηq ρ q ρq η q are the density and viscosity of the quartz (2.648g/cm3 and 2.947*10-11 g/cm s) f0: basic oscillator frequency of the quartz Δm: material adsorbed on the surface per unit area n: Overtone number 9 Corrections Thick overlayer -> nonlinear relation between Δ f and Δ m Liquid -> shear motion on the surface generates motion in the liquid near the interface -> liquid density and viscosity 10 Typical setup 4-6 MHz fundamental resonant frequency Resolution down to 1Hz Water cooling tubes, oscillation source, frequency sensing equipment, measurement and recording device 11 Classification BAW (Bulk acoustic wave): thickness-shear mode (TSM) Small quartz crystal disk: 10-15mm diameter 0.1-0.2 mm thickness Resonance frequency: 6-20MHz 2 For a 10 MHz crystal, detection limit: 0.1 ng/mm Sensitivity is limited by the mass of the whole crystal 12 Classification (cont.) SAW (Surface acoustic wave) Acoustic energy confined to the surface Wave propagates along the solid medium surface Rayleigh wave Displacement of the particles near the surface has: longitudinal component and a shear vertical component 13 SAW IDT (interdigital transducer) electrode Time-varying voltage -> synchronously varying deformation of the piezoelectric substrate -> propagating surface wave SAW -> alternating voltage in another IDT (receiver) Delay line: two IDTs and a propagation path (sensitive area) Environmental change -> resonance frequency change 14 SAW High frequencies up to GHz range Sensitivity increases as the square of the fundamental frequency -> higher sensitivity potential Dual delay configuration -> sensing delay line coated with reactive film -> measure frequency difference (in the order of KHz) Reference measurement: compensate fluctuations 10-100 ppb concentration level Selectivity of 1000:1 Mass detection limit: in the range of 0.05 pg/mm2 15 Biosensing Single/Multi-step binding Ag immobilization -> Ab attachment -> mass increase -> frequency decrease Two crystals (reference/indicator) Ratio in blank solution Ratio in test solution 16 Virus Reusable 18 times 17 Microorganism Long-term stability: 10 weeks RT or 4 degree C Reused 12 times 18 Environmental Analysis Parathion antibody -> specific detection of pesticide at parts per billion levels 19 Drinking water screening Antibodies -> E. coli. 20 Food Analysis Ab -> Salmoella 21 E.coli 22 Listeria Less than 15 min As sensitive as ELISA 23 Commercial sources Mass changes up to approximately 100ug Minimum detectable mass change: 1ng/cm2 24 Challenges Reproducible immobilization of the biological materials on the crystal surface Reusability of the crystal 25 Energy Trapping The electrodes at the front and the back of the crystal usually are key-hole shaped, thereby making the resonator thicker in the center than at the rim. This confines the displacement field to the center of the crystal by a mechanism called energy trapping. The crystal turns into an acoustic lens and the wave is focused to the center of the crystal. Energy trapping is necessary in order to be able to mount the crystal at the edge without excessive damping. Energy trapping slightly distorts the otherwise planar wave fronts. 26 Amplitude of Motion The amplitude of lateral displacement rarely exceeds a nanometer. 4 u = dQU 0 (nπ ) 2 el u0 the amplitude of lateral displacement n the overtone order, d the piezoelectric strain coefficient, Q the quality factor, Uel the amplitude of electrical driving. Due to the small amplitude, stress and strain usually are proportional to each other. The QCM operates in the range of linear acoustics. 27 Equivalent Circuits - electromechanical analogy a graphical representation of the resonator’s properties and their shifts upon loading forces -> voltages speeds -> currents ratio of force and speed -> mechanical impedance speed means the time derivative of a displacement, not the speed of sound 28 Electro-acoustic analogy stresses (rather than forces) -> voltages The ratio of stress and speed at the crystal surface -> load impedance, ZL 29 Equivalent circuit. C0 is the electrical (parallel) capacitance across the electrodes. L1 is the motional inductance (proportional to the mass). C1 is the motional capacitance (inversely proportional to the stiffness) R1 is the motional resistance (quantifying dissipative losses). A is the effective area of the crystal ZL the load impedance. 30 Small-Load Approximation When the frequency shift is much smaller than the frequency itself Δf i = Z l f f πZ q ff is the frequency of the fundamental. Zq is the acoustic impedance of material The small-load approximation is central to the interpretation of QCM-data. It holds for arbitrary samples and can be applied in an average sense. Assume that the sample is a complex material, such as a cell culture. If the average stress-to-speed ratio of the sample at the crystal surface (the load impedance, ZL) can be calculated -> a quantitative analysis of the QCM experiment. 31 More general relation The limits of the small-load approximation : the frequency shift is large when the overtone-dependence of Δf and Δ(w/2) is analyzed in detail in order to derive the viscoelastic properties of the sample. Δf Z l = −iZ q tan(π ) f f Must be solved numerically. The small-load approximation is the first order solution of a perturbation analysis. 32 Nonlinear function of strain The definition of the load impedance implicitly assumes that stress and speed are proportional and that the ratio therefore is independent of speed. when the crystal is operated in liquids and in air - >linear acoustics However, when the crystal is in contact with a rough surface -> stress is a nonlinear function of strain (and speed) because the stress is transmitted across a finite number of rather small load-bearing asperities. The stress at the points of contact is high 33 Non-linear acoustics Generalization of the small-load equation. If the stress, σ(t), is periodic in time and synchronous with the crystal oscillation: Δf 1 2 = σ t cos ωt () ( )t f f πZ q ωu0 Angular brackets denote a time average and σ(t) is the (small) stress exerted by the external surface. The function σ(t) may or may not be harmonic. 34 Viscoelastic Modeling For a number of experimental configurations, there are explicit expressions relating the shifts of frequency and bandwidth to the sample properties. Assumptions The resonator and all cover layers are laterally homogeneous and infinite. The distortion of the crystal is given by a transverse plain wave with the wave-vector perpendicular to the surface normal (thickness-shear mode). There are neither compressional waves nor flexural contributions to the displacement pattern. There are no nodal lines in the plane of the resonator. All stresses are proportional to strain. Linear viscoelasticity holds. Piezoelectric stiffening may be ignored. 35 Probing near the surface QCM only probes the region close to the crystal surface. The shear wave evanescently decays into the liquid. In water the penetration depth is about 250 nm at 5 MHz. Surface roughness, nano-bubbles at the surface, slip, and compressional waves can interfere with the measurement of viscosity. Also, the viscosity determined at MHz frequencies sometimes differs from the low-frequency viscosity. 36 Interpretation of the Sauerbrey Thickness The QCM always measures an areal mass density, never a geometric thickness. The conversion from areal mass density to thickness usually requires the physical density as an independent input. It is difficult to infer the viscoelastic correction factor from QCM data. Complex samples are often laterally heterogeneous. Complex samples often have fuzzy interfaces. 37 References http://www.youtube.com/watch?v=QnCvEGpZ0Tc http://www.thinksrs.com/products/QCM200.htm http://en.wikipedia.org/wiki/Quartz_crystal_microbalance Sensors in Biomedical Applications – Fundamentals, Technology and Applications Gabor Harsanyi, CRC press, 2000, ISBN 1-56676-885-3. Biosensors and their applications Edited by Victor C. Yang and That T. Ngo, 2000, Kluwer Academic/Plenum Publishers, New York, ISBN 0-36-46087-4 38.