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Quartz Crystal Microbalance

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BiosensorBio Recognition Element

Enzymes; Antibodies; Receptors; Whole cells...

Electrochemical

Optical

Transducer

Signal Output

Requires: Sample Immobilization

Requires:

Simple read out and data interpretation;

Easy to use;

Quick response.

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Quartz resonators with front and back electrodes

http://en.wikipedia.org/wiki/Image:Quartz_resonators_with_front_and_back_electrodes.jpg

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Theory

Thin quartz disk with electrodes plated on itPiezoelectricAn oscillating electric field applied across the device -> acoustic wave propagates through the crystalThickness of the device is a multiple of a half-wavelength of the acoustic wave -> minimum impedanceDeposition of thin film -> decrease the frequency (mass of the film)

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Piezoelectric effect

Pressure -> electricityMechanical strain/stress variation -> separate the center of gravity of the positive charges from the center of gravity of the negative charges -> dipole moment -> Polarization changeGenerated voltage between two electrodesInsulating materials -> charges on the surfaceDepend on the symmetry of the distributions of the positive and negative charges -> material

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Single-crystal

32 classes11 -> center of symmetry -> nonpolar ->symmetric ionic displacements -> no net change in dipole moment

Quartz

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Converse effect

Electric filed -> strain mechanicallyOne-to-one correspondenceDecays due to the charge dissipationIncrease with applied force -> drops to zero when force remains constantPressure removed -> negative voltage -> decays to zero

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Resonant oscillation

Electric and mechanical oscillations are close to the fundamental frequency of the crystalDepend on: thickness, chemical structure, shape, density, shear modulus of the quartz, mass, physical properties of the adjacent mediums (density, viscosity of air/liquid).

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Resonant frequency

Sauerbrey: changes in the resonant frequency relates to the mass:

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 quartzΔm: material adsorbed on the surface per unit arean: Overtone number

qqmnff ρη/2 20Δ−=Δ

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Corrections

Thick overlayer -> nonlinear relation between Δ f and Δ mLiquid -> shear motion on the surface generates motion in the liquid near the interface -> liquid density and viscosity

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Typical setup

4-6 MHz fundamental resonant frequencyResolution down to 1HzWater cooling tubes, oscillation source, frequency sensing equipment, measurement and recording device

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Classification

BAW (Bulk acoustic wave): thickness-shear mode (TSM)

Small quartz crystal disk: 10-15mm diameter0.1-0.2 mm thicknessResonance frequency: 6-20MHzFor a 10 MHz crystal, detection limit: 0.1 ng/mm2

Sensitivity is limited by the mass of the whole crystal

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Classification (cont.)

SAW (Surface acoustic wave)Acoustic energy confined to the surfaceWave propagates along the solid medium surfaceRayleigh wave

Displacement of the particles near the surface has: longitudinal component and a shear vertical component

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SAW

IDT (interdigital transducer) electrodeTime-varying voltage -> synchronously varying deformation of the piezoelectric substrate -> propagating surface waveSAW -> alternating voltage in another IDT (receiver)Delay line: two IDTs and a propagation path (sensitive area)Environmental change -> resonance frequency change

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SAW

High frequencies up to GHz rangeSensitivity increases as the square of the fundamental frequency -> higher sensitivity potentialDual delay configuration -> sensing delay line coated with reactive film -> measure frequency difference (in the order of KHz)Reference measurement: compensate fluctuations10-100 ppb concentration levelSelectivity of 1000:1Mass detection limit: in the range of 0.05 pg/mm2

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Biosensing

Single/Multi-step bindingAg immobilization -> Ab attachment -> mass increase -> frequency decreaseTwo crystals (reference/indicator)

Ratio in blank solutionRatio in test solution

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Virus

Reusable 18 times

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Microorganism

Long-term stability: 10 weeksRT or 4 degree CReused 12 times

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Environmental Analysis

Parathion antibody -> specific detection of pesticide at parts per

billion levels

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Drinking water screening

Antibodies -> E. coli.

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Food Analysis

Ab -> Salmoella

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E.coli

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Listeria

Less than 15 minAs sensitive as ELISA

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Commercial sources

Mass changes up to approximately 100ugMinimum detectable mass change: 1ng/cm2

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Challenges

Reproducible immobilization of the biological materials on the crystal surfaceReusability of the crystal

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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.

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Amplitude of Motion

The amplitude of lateral displacement rarely exceeds a nanometer.

u0 the amplitude of lateral displacementn 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.

eldQUn

u 20 )(4π

=

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Equivalent Circuits - electromechanical analogy

a graphical representation of the resonator’s properties and their shifts upon loadingforces -> voltages speeds -> currents ratio of force and speed -> mechanical impedancespeed means the time derivative of a displacement, not the speed of sound

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Electro-acoustic analogy

stresses (rather than forces) -> voltages The ratio of stress and speed at the crystal surface -> load impedance, ZL

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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 crystalZL the load impedance.

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Small-Load Approximation

When the frequency shift is much smaller than the frequency itself

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.

lqf

ZZi

ff

π=

Δ

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More general relation

The limits of the small-load approximation :the frequency shift is largewhen the overtone-dependence of Δf and Δ(w/2) is analyzed in detail in order to derive the viscoelastic properties of the sample.

Must be solved numerically. The small-load approximation is the first order solution of a perturbation analysis.

)tan(f

ql ffiZZ Δ

−= π

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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 acousticsHowever, 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

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Non-linear acoustics

Generalization of the small-load equation. If the stress, σ(t), is periodic in time and synchronous with the crystal oscillation:

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.

( ) ( )t

qf

ttuZf

f ωσωπ

cos21

0

=Δ

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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.

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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.

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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.

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References

http://www.youtube.com/watch?v=QnCvEGpZ0Tchttp://www.thinksrs.com/products/QCM200.htmhttp://en.wikipedia.org/wiki/Quartz_crystal_microbalanceSensors in Biomedical Applications – Fundamentals, Technology and ApplicationsGabor Harsanyi, CRC press, 2000, ISBN 1-56676-885-3. Biosensors and their applicationsEdited by Victor C. Yang and That T. Ngo, 2000, KluwerAcademic/Plenum Publishers, New York, ISBN 0-36-46087-4