Quartz crystal microbalance (QCM) · how it worksHow a crystal
weighs a molecule.
A quartz crystal microbalance (QCM) is a mass sensor that weighs nanograms by listening to a vibrating quartz crystal: whatever sticks to its surface lowers its resonant frequency. Six experiments take you from a slice of quartz to a protein film: change the thickness, add molecules, pour a liquid, soften a polymer, warm the room. Every number is computed with the physics of real AT-cut quartz.
Click the liquid to release antigens →
Experiment 01 · The QCM sensor: an AT-cut quartz crystalA slice of quartz
that sings.
At the heart of every quartz crystal microbalance is a thin disc of quartz, cut at a precise angle (the AT cut) and coated with two gold electrodes. Quartz is piezoelectric: an alternating voltage makes it shear, the two faces sliding in opposite directions like the pages of a book.
The plate resonates when its thickness holds exactly half a wavelength of that shear wave. Thinner plate, shorter wave, higher note. It can also ring at the overtones: three, five, seven half-waves across the same thickness.
Halve the thickness and watch the frequency double. Then press “Why not n = 2?”: the faces move together, no charge reaches the electrodes, and the crystal stays silent. That is why a QCM only ever reports odd overtones: n = 1, 3, 5, 7, 9 on a 5 MHz openQCM crystal.
Experiment 02 · QCM resonance, frequency and dissipationMany ways to listen.
A resonance is a peak: the crystal answers strongly at one frequency and hardly at all a little away from it. Its position, fr, tells us about mass. Its width, the half-bandwidth Γ, tells us how much energy is lost, which we call dissipation, D. Reading both is what QCM-D, the quartz crystal microbalance with dissipation monitoring, adds to a plain QCM.
You can find the peak by sweeping a band of frequencies and recording the answer, the way openQCM Q-1 and NEXT do, like a small network analyser (they record gain and phase; the figure shows the conductance). You can kick the crystal and time how fast it falls silent: the ring-down. Or you can let the crystal drive itself: put it in the feedback loop of an amplifier and it oscillates at its own resonance, which a counter then measures. That is the oscillator, the way openQCM Wi2, SpaceBug, TWIN and the Holder work. All of them read the same physics, each with its own trade-offs.
Run a sweep in air, then in water. The peak drops, shifts and becomes about thirty times wider. In the ring-down, the same water makes the crystal fall silent thirty times sooner. In the oscillator, water raises the crystal’s resistance thirtyfold: the loop must have the gain to keep it ringing.
| Method | Reads | Used in |
|---|---|---|
| Frequency sweepscalar or vector network analysis | f and D, on any overtone | openQCM Q-1, NEXT |
| OscillatorPierce, Colpitts, Miller, bridge | f; D only with gain control | openQCM Wi2, SpaceBug, TWIN, Holder |
| Ring-downdrive, switch off, fit the decay | f and D from τ | several commercial QCM-D |
| Phase-locked looptracks the zero-phase point | f and resistance, continuously | lab and process monitors |
| Impedance analyserfull spectrum, equivalent-circuit fit | R, L, C of the crystal | reference lab method |
Experiment 03 · Mass and the Sauerbrey equationAdd a nanogram,
hear it drop.
Anything that sticks to the crystal and moves with it makes the plate effectively thicker, so the note goes down. In 1959 Günter Sauerbrey showed that for a thin, rigid film the shift is simply proportional to the mass per unit area: the Sauerbrey equation, the basis of every QCM mass measurement.
The proportionality constant depends only on the crystal: 56.6 Hz for every microgram per square centimetre at 5 MHz, four times more at 10 MHz. A layer of proteins, a few nanometres thin, already moves the frequency by ten hertz or more, well above the noise of a good instrument.
Add 1 nm of gold: the peak moves but keeps its width, because a rigid film adds mass and no losses. Add a protein layer: a hydrated protein layer also widens the peak a little (see experiment 05). Add a lipid bilayer: although it forms in water, a supported bilayer behaves as a rigid film and barely widens the peak (ΔD below 0.5 × 10⁻⁶). Switch to a 10 MHz crystal and add the same layer again: the step is four times larger. The trace at the bottom is what you would see on screen during an experiment.
Experiment 04 · QCM in liquids: Kanazawa–GordonA wave that dies
in a quarter of a micron.
Put water on the crystal and the frequency drops by hundreds of hertz, even though nothing has stuck to it. The oscillating surface drags a thin film of liquid along, and the shear wave it launches dies away within a few hundred nanometres: the penetration depth δ.
Kanazawa and Gordon worked out the shift in 1985: it depends on the product of density and viscosity of the liquid. This is why a liquid measurement always starts from a stable baseline in the liquid itself, and why it also raises the dissipation.
Go from water to 80% glycerol: the wave reaches further into the liquid, the peak moves further to the left and becomes wider. Raise the overtone and the wave becomes shorter: higher overtones look closer to the surface.
Experiment 05 · Soft films and QCM-DWhen the film
wobbles.
Sauerbrey assumes the film moves as one rigid piece. Polymers, hydrogels and many biomolecular layers do not: they are soft, so the top of the film lags behind the bottom. The film then stores and loses energy, and each overtone sees it differently.
Two signs give it away: the overtones no longer agree (Δf/n spreads apart) and the dissipation rises. Which way they spread depends on the medium. In air a soft film looks heavier at the higher overtones. Under water, where QCM-D is usually done, it is the other way round: Δf/n becomes less negative at higher overtones and Sauerbrey underestimates the mass, the “missing mass” of soft films. Reading several overtones together is how QCM-D (quartz crystal microbalance with dissipation monitoring) tells a soft film from a rigid one, and how models such as Voigt recover its thickness, stiffness and viscosity.
Start rigid: all overtones sit on the Sauerbrey line. Now lower the stiffness and make the film thicker. Under water the overtones fan out above the line and the dissipation bars grow; switch to air and the same film fans out below it. Push further and the film reaches its own resonance: the overtones jump, and no Sauerbrey-like reading is possible.
Experiment 06 · Temperature and frequency driftThe crystal also
feels the weather.
The AT cut was chosen because its frequency barely changes with temperature near room temperature: the curve is an almost flat S. Almost. A few tenths of a part per million per degree is still a hertz or two per degree on a 5 MHz crystal; a few degrees of drift is the same order as a protein layer.
Liquids make it worse: water's viscosity falls by about 2% per degree, so the Kanazawa shift moves by about 1%, some 7 to 8 Hz per degree at 5 MHz. That is why openQCM NEXT holds the measurement chamber at a set temperature with a Peltier stage.
Move the room by one degree and compare the drift with a protein layer. Then switch on thermal control and see the band of uncertainty shrink.
Your turn
From the bench
to your data.
Free download · PDF
The QCM-D fundamentals guide.
The physics of this page in five pages you can keep: Sauerbrey, dissipation, overtones, the working constants of openQCM sensors and a table to choose the right model. Leave your email and the download link appears right here.