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Combined Instruments

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The Quartz Crystal Microbalance in Soft Matter Research

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

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Abstract

The QCM is often combined with other techniques of interface analysis. In some cases, doing that in situ is straight-forward. An example is the electrochemical QCM (EQCM). The combination with optical reflectometry is particularly interesting because the data analysis proceeds along similar lines, but still often leads to an effective optical thickness, which is lower than the Sauerbrey thickness.

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Notes

  1. 1.

    A mantra of the book is “Measure a frequency if you can”. There is a corresponding wisdom in astronomy (and even optics) which says: “Measure an angle if you can”. The positions of the stars count as angles and so does their color because color turns into an angle after a diffraction grating. The apparent brightness of a star cannot be turned into an angle and the measurement of a star’s distance therefore is a difficult matter. It is about as difficult has measuring a resonator’s effective area (proportional to the peak conductance). Of course the apparent brightness can be measured, but it cannot be measured with the same ease and precision as the star’s position in the sky and its color. Now to SPR spectroscopy: Film thickness turns into an angle (the coupling angle) when probed with an SPR spectrometer. SPR spectroscopy is a scheme to turn the parameter of interest into an angle.

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Authors and Affiliations

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

    Diethelm Johannsmann

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Glossary

Variable

Definition (Comments)

a

Contact radius

amb

As an index: ambient medium

A

Effective area of the resonator plate

c

Speed of propagation, speed of light

d f

Film thickness

f

Frequency

f

As an index: film

f 0

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

\( \tilde{G} \)

Shear modulus (\( \tilde{G} = G^{{\prime }} + {\text{i}}G^{{\prime \prime }} \))

G*

Effective shear modulus (Eq. 11.2.12)

k pl

Wavenumber of surface plasmon

k x

x-component of the wavenumber of the incident beam

liq

As an index: liquid (mostly the ambient medium)

n

Overtone order

\( \tilde{n} \)

Refractive index

pl

As an index: plasmon

Q

Quality factor

R(θ)

A reflectivity curve. (In SPR spectroscopy, R is the reflected intensity; θ is the angle of incidence.)

sub

As an index: substrate (mostly a metal film)

z

Spatial coordinate along the surface normal

\( \tilde{Z} \)

Acoustic wave 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

Δ

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

\( {\tilde{\varepsilon}} \)

Dielectric constant optical frequencies (\( {\tilde{\varepsilon } = }\tilde{n}^{2} \))

η

Viscosity

κ P

Spring constant of a contact with a particle

λ

Wavelength

Λ

Wavelength of a corrugation grating (Eq. 16.2.1)

θ

Angle of incidence

ρ

Density

ω

Angular frequency

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Johannsmann, D. (2015). Combined Instruments. 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_16

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