Quartz Crystal Microbalance 1
Biosensor Transducer Bio Recognition Element Signal Output Electrochemical Enzymes; Requires: Antibodies; Optical Receptors; Simple read out and Whole data interpretation; Requires: cells... Sample 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: Δ = − Δ η ρ 2 f 2 mnf / 0 q q � ρ q η q are the density and viscosity of the quartz (2.648g/cm 3 and 2.947*10 -11 g/cm s) � f0: basic oscillator frequency of the quartz � Δ m: 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 � For a 10 MHz crystal, detection limit: 0.1 ng/mm 2 � 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/mm 2 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/cm 2 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 π 0 el 2 ( n ) u 0 the amplitude of lateral displacement � n the overtone order, � d the piezoelectric strain coefficient, � Q the quality factor, � U el 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, Z L 29
Equivalent circuit. C 0 is the electrical (parallel) capacitance across the electrodes. � L 1 is the motional inductance (proportional to the mass). � C 1 is the motional capacitance (inversely proportional to the � stiffness) R 1 is the motional resistance (quantifying dissipative losses). � A is the effective area of the crystal � Z L the load impedance. � 30
Small-Load Approximation � When the frequency shift is much smaller than the frequency itself Δ f i = Z π l f Z f q � f f is the frequency of the fundamental. � Z q 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, Z L ) 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 Δ f and Δ ( w /2) is analyzed in detail in order to derive the viscoelastic properties of the sample. Δ f = − π Z iZ tan( ) l q 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: Δ ( ) ( ) t f 1 2 = σ ω t cos t π ω f Z u f q 0 � 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
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