How to Analyze Quartz Crystal Microbalance with Dissipation (QCMD) Data?

Quartz crystal microbalance with dissipation monitoring (QCMD) is a powerful tool for studying soft matter at interfaces by measuring the resonance frequency (∆f) and dissipation (∆D). QCMD allows users to assess the mass, organization, viscoelastic properties, and dynamics of materials adsorbed on sensor surfaces. To interpret the QCMD data correctly, selecting the right model for a specific experimental scenario is essential. Here is a concise summary of what can be achieved using QCMD and the appropriate models for various cases.

Mass Measurement (Sauerbrey Equation):

QCMD can measure the mass of rigid, thin films deposited on the sensor surface when the dissipation (∆D) is negligible (e.g., -ΔΓ_n/Δf_n << 0.5 (where ΔΓ_n = ∆D_nf_n/2 for a 5 MHz crystal); Figure 1), which implies a stiff, non-viscoelastic film. The Sauerbrey equation is applied in such cases:

Here, Δm is the mass per unit area (ng/cm²), f₀ is the fundamental resonance frequency of the sensor (typically 5 MHz), Z_q = 8.8 x 10⁶ kgm^-2s^-1 and is the shear-wave impedance of the quartz plate, Δf_n is the measured frequency shift (Hz), and n is the overtone number.

Figure 1. Illustration of polyelectrolytes of opposite charge (in blue and light brown color) adsorbed on a silica coated QCMD sensor.

The Sauerbrey equation assumes that the film is rigid (no energy dissipation), leading to a linear relationship between the frequency shift and mass. This model works well for systems like thin metallic layers or stiff polymers. It fails when the film is viscoelastic, leading to significant energy dissipation.

QCMD Applications in Homogeneous/ Non-Homogeneous and Rigid/ Non-Rigid Systems

Polymer films and brushes

QCMD is frequently used for studying thin polymer films and brushes, particularly when probing their viscoelastic properties. The canonical viscoelastic model is generally applied to interpret the data for thin, laterally homogeneous films, such as polymer films and polymer brushes​. In such cases, the model assumes a sharp cutoff between the film and the bulk liquid, and that the viscosity of the film is much larger than that of the surrounding solvent.

Structured adsorbates

When dealing with laterally heterogeneous samples, such as adsorbed particles or structured adsorbates (e.g., viruses, proteins) or their interactions, QCMD helps determine their size, rigidity and contact stiffness. For these cases, the finite element method (FEM) is used to solve fluid dynamics problems (e.g. Stokes equation), modeling the oscillatory flow and adsorbate shapes based on the domains of complex viscosity.

Another method to retrieve adsorbate size and coverage from QCMD measurements is to use the acoustic ratio (ΔΓ_n/(-Δf_n); Figure 2), which relates to adsorbate ability to dissipate acoustic energy. This can be explained more in detail when taking the Stokes relation into account, where the friction parameter is directly related to the radius of a hypothetical sphere diffusing in a volume at the same speed as the object of interest. When the particle coverage is increasing, the acoustic ratio decreases linearly. At low adsorbate coverages, it is possible to distinguish between the coverage and height contributions in the measurement.

Figure 2. Acoustic ratio (-ΔΓ_n/(-Δf_n) plotted against -Δf/n. Sizes and coverages of, e.g., liposomes and virus particles, may be determined from such profiling (representation of theoretical model of size and coverage with acoustic ratio).

These approaches have been successfully applied to systems like liposomes, lipid assemblies, ferritin, viral particles​, etc.

Porous and rough surfaces

For rough or porous materials, QCMD helps quantify the effect of surface structures on fluid interactions, such as adsorption or surface roughness, and its influence on liquid entrapment. Roughness models using the Brinkman equation are often applied to porous structures, where the height and the width of the cavities are on the same order. In addition, they are often based on the fact that the frequency and dissipation shifts depend on the liquid viscosity.

Conclusion:

BioNavis QCMD instruments (100, 110 and 400), equipped with advanced software, provide detailed insights into the mass, mechanical properties, and dynamics of materials at interfaces. The selection of the appropriate analysis tools (e.g., Sauerbrey, canonical viscoelastic, FEM or model-free acoustic ratio) depends on the type of material being studied (rigid, viscoelastic, structured, etc.) and the nature of the shifts observed in frequency and dissipation.

This text was inspired by the review article:
Johansmann and Reviakine  in Nature Review Methods Primers 4, 63 (2024).

https://www.nature.com/articles/s43586-024-00340-4

Learn more about the measurement principle of QCMD instruments in the technology section: https://bionavis.com/technology/qcmd/