Particle Adsorption Using a Quartz Crystal Microbalance with Dissipation by Applying a Kelvin–Voigt-Based Viscoelastic Model and the Gauss–Newton Method

Abstract

The use of a quartz crystal microbalance with dissipation (QCM-D) to study the adsorption of particles larger than 100 nm, such as liposomes, viruses, and nano/micro-plastics, remains challenging owing to the lack of appropriate models for data evaluation. This study presents a method for quantifying the adsorption of negatively charged polystyrene latex (100 nm–1 μm) at the solid–liquid interface. The validity of a viscoelastic model based on Kelvin–Voigt theory was assessed, and the model was used to evaluate particle adsorption data obtained from QCM-D measurements. The Gauss–Newton method was used to fit the data; the values obtained were larger than results from atomic force microscopy, indicating that the viscoelastic model combined with the Gauss–Newton method can quantify the adsorption of large polystyrene particles and the surrounding water around them. We suggested that QCM-D, in combination with an appropriate viscoelastic model, is applicable to estimate adsorption at the solid–liquid interface even for soft particles larger than 1 μm, which are out of the range of applications to the hydrodynamics model. Furthermore, we successfully showed that the recorded dissipation reflects the viscoelastic properties of the layer. The viscoelastic model allowed quantification of the rheological properties of the layer. The ratio of the viscous and elastic contributions was characterized by using loss tangent (tan δ) values that were extracted from the experimental data by applying the viscoelastic model. These values were lower for the adsorption of the negatively charged polystyrene particles on a positive surface than on a negative surface. This suggests that tan δ reflects the strength of the contact between the particle and substrate.