Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation

Abstract

A simulation based on the frequency‐domain lattice Boltzmann method (FreqD‐LBM) is employed to predict the shifts of resonance frequency, Δf, and half bandwidth, ΔΓ, of a quartz crystal microbalance with dissipation monitoring (QCM‐D) induced by the adsorption of rigid spheres to the resonator surface. The comparison with the experimental values of Δf and ΔΓ allows to estimate the stiffness of the contacts between the spheres and the resonator surface. The contact stiffness is of interest in contact mechanics, but also in sensing because it depends on the properties of thin films situated between the resonator surface and the sphere. The simulation differs from previous implementations of FreqD‐LBM insofar, as the material inside the particles is not included in the FreqD‐LBM algorithm. Rather, the particle surface is configured to be an oscillating boundary. The amplitude of the particles' motions (displacement and rotation) is governed by the force balance at the surface of the particle. Because the contact stiffness enters this balance, it can be derived from experimental values of Δf and ΔΓ. The simulation reproduces experiments by the Krakow group. For sufficiently small spheres, a contact stiffness can be derived from the comparison of the simulation with the experiment.

Anisotropic Particle Deposition Kinetics from Quartz Crystal Microbalance Measurements: Beyond the Sphere Paradigm

“…Although quantitatively different, in all cases, the frequency and bandwidth shifts can be approximated by linear functions of the deposition time. This facilitates a precise calculation of the complex impedance ΔZ* in the limit of low particle coverage considering that it is defined as the ratio of the tangential stress (i.e., the force per the surface area of the sensor) to the surface velocity 55,75…”

“…Although quantitatively different, in all cases, the frequency and bandwidth shifts can be approximated by linear functions of the deposition time. This facilitates a precise calculation of the complex impedance Δ Z* in the limit of low particle coverage considering that it is defined as the ratio of the tangential stress (i.e., the force per the surface area of the sensor) to the surface velocity , normalΔ Z * = normalΔ F i * normalΔ S V i * − 1 where Δ F i * is the excess complex force transferred to the sensor because of the particles present in its vicinity (but not necessarily adsorbed), Δ S is the surface area of the sensor, and V i * is the sensor complex velocity.…”

“…It should be mentioned that, in a general case, the impedance depends upon the particle size, shape, orientation, sensor topography (roughness), oscillation frequency, etc., which renders its ab initio theoretical calculation a complicated task, even for spherical particles. − However, the impedance can be experimentally determined using the above QCM kinetic data, taking advantage of the following definitions ,, normalΔ f = prefix− f normalF π Z normalQ Im ( Δ Z * ) normalΔ D ̅ = prefix− f normalF π Z normalQ Re ( Δ Z * ) where Z Q is the acoustic impedance of quartz equal to 8.8 × 10 6 kg m –2 s –1 .…”

“…One can suppose that the obtained results can be used as useful reference data for estimating the range of applicability of recent hydrodynamic theories of QCM sensor impedance in the case of a heterogeneous, particle-like load. − …”

Exploring Metal Electroplating for Energy Storage by Quartz Crystal Microbalance: a review

“…So far, an encouraging study in which both analytical and numerical solutions agree in the description of the frequency and dissipation response of the QCM with rigid particles disconnected to but in the vicinity of the sensor has been presented. [145] Looking ahead, further demonstrations of unified results from the various analytical and numerical modeling approaches, such as FEM, LBM, and hydrodynamic spectroscopy, will come and their validation with experiment will be demonstrated, although more efforts are needed.…”