QCM-D, the quartz crystal microbalance with dissipation monitoring, reads two numbers from a vibrating quartz crystal instead of one. The frequency shift Δf tells you how much mass has settled on the sensor. The dissipation shift ΔD tells you how that mass behaves: whether it is a rigid layer that moves with the crystal, or a soft, hydrated film that absorbs part of the vibration. Read on several overtones, the two together describe films that a plain QCM cannot weigh correctly: proteins, polymers, hydrogels, lipid layers, cells.
What dissipation is
A quartz crystal resonates like a bell: it answers strongly at one frequency and hardly at all a little away from it. The position of that resonance peak follows the mass on the crystal. Its width follows the energy lost in every cycle of oscillation. Dissipation is that loss, written as the inverse of the quality factor:
D = 1/Q = Edissipated / (2π · Estored) = 2Γ / fr
Here Γ is the half-bandwidth of the resonance and fr its frequency. D is dimensionless and small, so it is usually given in units of 10⁻⁶. A clean crystal in air loses very little energy and has a sharp, narrow peak. In water the peak becomes about thirty times wider, and a soft film widens it further.
Reading Δf and ΔD together
The pair Δf, ΔD is what makes QCM-D useful. Three typical situations:
- Rigid film. A thin metal layer, or a supported lipid bilayer, moves as one piece with the crystal. Δf/n is the same on every overtone and ΔD stays low (below about 0.5 × 10⁻⁶ for a lipid bilayer). The Sauerbrey equation applies: Δm = −Δf/(n · Cf), with Cf = 56.6 Hz·cm²/µg at 5 MHz.
- Soft, viscoelastic film. Polymers, hydrogels and many hydrated protein layers lag behind the crystal surface. ΔD rises and the overtones no longer agree: Δf/n spreads apart. Under water, Sauerbrey then underestimates the mass, the “missing mass” of soft films, and a viscoelastic model such as Voigt is needed to recover thickness, shear modulus and viscosity.
- Liquid alone. Changing the liquid on the crystal shifts both frequency and bandwidth even though nothing is bound: the Kanazawa–Gordon relation links the shift to the square root of the density–viscosity product of the liquid. This is why a QCM-D experiment starts from a stable baseline in the measuring liquid.
A simple check before any modelling: if Δf/n overlaps on all overtones and ΔD stays close to zero while the frequency falls, treat the film as rigid. If not, it is viscoelastic and the overtones are your data, not noise.
Why QCM-D uses several overtones
An AT-cut crystal can only be driven at its odd overtones: n = 1, 3, 5, 7, 9 (on a 5 MHz openQCM crystal: 5, 15, 25, 35 and 45 MHz). Each overtone probes the sample at a different frequency, and the shear wave it launches into a liquid dies away within a different distance: higher overtones see closer to the surface, lower overtones see deeper into the film and the liquid above it. Comparing frequency and dissipation across overtones tells you whether a film is homogeneous, whether its surface behaves differently from its bulk, and gives a viscoelastic model enough equations to solve for its unknowns.
How dissipation is measured
There are three common ways to read the frequency and the losses of a quartz crystal:
- Frequency sweep (network analysis): the instrument steps a sinusoidal excitation across the resonance, records the response and reconstructs the whole peak, then extracts its position and width. Works on any overtone. Used by openQCM Q-1 and openQCM NEXT.
- Ring-down: the crystal is driven, the drive is switched off and the decay time τ of the free oscillation is fitted; D = 1/(π f τ). Used by several commercial QCM-D instruments.
- Oscillator: the crystal sits in the feedback loop of an amplifier and oscillates at its own resonance, which a counter reads. Excellent for frequency; dissipation only with additional gain control. Used by openQCM Wi2, SpaceBug, TWIN and the Holder.
On openQCM Q-1 and NEXT the width of each resonance is taken at a cut-off level calibrated for each overtone, rather than at the textbook −3 dB point, because peak amplitude falls at higher overtones and the −3 dB level approaches the noise floor. The resulting instrumental dissipation Dn(inst) differs in absolute value from the −3 dB definition, while its changes ΔDn faithfully track real changes in energy loss. The method, and how to map it to literature values, is explained in how openQCM Q-1 and NEXT measure dissipation across multiple harmonics.
openQCM QCM-D instruments
- openQCM NEXT: multi-harmonic QCM-D. Frequency and dissipation on every overtone from the 1st to the 9th in each cycle (about 9 s for all overtones), a ~50 µl measuring cell held to ±0.01 °C by a Peltier stage, open hardware, firmware and software.
- openQCM Q-1: benchtop QCM with dissipation monitoring. It sweeps one selected overtone at a time, up to the 9th, and can take the EQCM module for electrochemistry.
- openQCM Wi2: compact, USB-powered QCM for frequency monitoring, when dissipation is not needed.
The side-by-side comparison lists modes, overtones, thermal control and modules for each instrument.
Practical tips for QCM-D measurements
- Hold the temperature. Water’s viscosity falls by about 2% per degree, which moves the liquid-loaded frequency by some 7 to 8 Hz per degree at 5 MHz: the same order as a protein layer.
- Start from a stable baseline in the same liquid you will measure in, and change one thing at a time.
- With viscous samples, widen the sweep so that it captures the whole, broadened peak, increase the number of points, and rely first on the fundamental and the 3rd overtone, where the signal is strongest.
- Report the overtones you used and plot Δf/n, so that rigid and soft behaviour can be told apart by the reader.
From QCM-D data to film properties
The free QCM calculator runs in your browser with four models: Sauerbrey, Kanazawa–Gordon, Voigt–Voinova and a multi-overtone Voigt inverse fit that turns Δf and ΔD on several overtones into thickness, shear modulus and viscosity. To see the physics move, the six interactive experiments of how a quartz crystal microbalance works include resonance, liquids and soft films; the QCM-D fundamentals guide condenses them into five pages. For applications, browse the peer-reviewed papers that used openQCM.