Quartz Crystal Microbalance 1 Biosensor Transducer Bio - - PowerPoint PPT Presentation

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Quartz Crystal Microbalance

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Biosensor

Bio 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 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)

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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

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Single-crystal

• 32 classes
• 11 -> center of symmetry -> nonpolar ->symmetric ionic

displacements -> no net change in dipole moment

• Quartz

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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

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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).

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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 quartz Δm: material adsorbed on the surface per unit area n: Overtone number

q q

mnf f ρ η / 2

2

Δ − = Δ

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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

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Typical setup

4-6 MHz fundamental resonant frequency Resolution down to 1Hz Water 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 diameter 0.1-0.2 mm thickness Resonance frequency: 6-20MHz For 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 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

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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

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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

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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

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Virus

• Reusable 18 times

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Microorganism

• Long-term stability: 10 weeks
• RT or 4 degree C
• Reused 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 min
• As sensitive as ELISA

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Commercial sources

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

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Challenges

Reproducible immobilization of the biological

materials on the crystal surface

Reusability 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 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.

el

dQU n u

2

) ( 4 π =

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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

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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 crystal
• ZL 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.

l q f

Z Z i f f π = Δ

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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.

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

perturbation analysis.

) tan(

f q l

f f iZ Z 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 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

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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

q f

t t u Z f f ω σ ω π cos 2 1 = 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=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