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Gravimetric Sensing

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The Quartz Crystal Microbalance in Soft Matter Research

Part of the book series: Soft and Biological Matter ((SOBIMA))

Abstract

The advanced QCMs provide information beyond gravimetry, but that is not to say that gravimetry was obsolete. Gravimetry is based on the Sauerbrey equation, derived in this chapter from the small load approximation. Strategies are discussed to improve the limit of detection. At least as important as sensitivity is specificity, meaning the ability to distinguish between different analytes. Specificity is achieved with receptor layers.

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Author information

Authors and Affiliations

  1. Institute of Physical Chemistry, Clausthal University of Technology, Clausthal-Zellerfeld, Germany

    Diethelm Johannsmann

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  1. Diethelm Johannsmann
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Correspondence to Diethelm Johannsmann .

Glossary

Variable

Definition (Comments)

C

Mass-sensitivity constant

d

Thickness of a layer

f

Frequency

f

As an index: film

f̃ r

Resonance frequency

f 0

Resonance frequency at the fundamental (f 0 = Z q /(2m q ) = Z q /(2ρ q d q ))

G q

Shear modulus of AT-cut quartz (G q  ≈ 29 × 109 Pa, often called µ q in the literature.)

m

Mass per unit area

n

Overtone order

q

As an index: quartz resonator

Q

Q-factor (Q = 1/D = f r /(2Γ))

ref

As an index: reference state of a crystal in the absence of a load

S

As an index: Surface

t

Time

û

(Tangential) displacement

v̂

Velocity (v̂ = iωû)

Z̃ L

Load impedance

Z q

Acoustic wave impedance of AT-cut quartz (Z q  = 8.8 × 106 kg m−2 s−1)

Γ

Imaginary part of a resonance frequency (Half-bandwidth at half-height of a resonance)

δ

As a prefix: uncertainty, scatter

Δ

As a prefix: A shift induced by the presence of the sample

ε

A small quantity (in Taylor expansions)

ρ

Density

ρ q

Density of crystalline quartz (ρ q  = 2.65 g/cm3)

\( {\hat{\sigma }} \)

(Tangential) stress (also called traction when exerted at a surface)

ω

Angular frequency

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Johannsmann, D. (2015). Gravimetric Sensing. In: The Quartz Crystal Microbalance in Soft Matter Research. Soft and Biological Matter. Springer, Cham. https://doi.org/10.1007/978-3-319-07836-6_8

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