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.