A Two-Phase Model for Adsorption from Solution Using Quartz Crystal Microbalance with Dissipation

Quartz crystal microbalance with dissipation (QCM-D) conveniently monitors mass and mechanical property changes of thin films on solid substrates with exquisite resolution. QCM-D is frequently used to measure dissolved solute/sol adsorption isotherms and kinetics. Unfortunately, currently available methodologies to interpret QCM-D data treat the adlayer as a homogeneous medium, which does not adequately describe solution-adsorption physics. Tethering of the adsorbate to the solid surface is not explicitly recognized, and the liquid solvent is included in the adsorbate mass, which is especially in error for low coverages. Consequently, the areal mass of adsorbate (i.e., solute adsorption) is overestimated. Further, friction is not considered between the bound adsorbate and the free solvent flowing in the adlayer. To overcome these deficiencies, we develop a two-phase (2P) continuum model that self-consistently determines adsorbate and liquid-solvent contributions and includes friction between the attached adsorbate and flowing liquid solvent. We then compare the proposed 2P model to those of Sauerbrey for a rigid adlayer and Voinova et al. for a viscoelastic-liquid adlayer. Effects of 2P-adlayer properties are examined on QCM-D-measured frequency and dissipation shifts, including adsorbate volume fraction and elasticity, adlayer thickness, and overtone number, thereby guiding data interpretation. We demonstrate that distinguishing between adsorbate adsorption and homogeneous-film adsorption is critical; failing to do so leads to incorrect adlayer mass and physical properties.