Modified Sauerbrey equation: a facile method to quantitatively probe the conformation of isolated molecules at solid-liquid interfaces.

Despite the increasingly popular application of the quartz crystal microbalance (QCM) technique in monitoring phenomena taking place at solid-liquid interfaces, ranging from changes in mass to changes in conformation, a simple, direct relationship between QCM signal and surface mass remains elusive. In this paper, we report that the proportional relationship between the QCM signal and the surface mass arises from the linear relationship between the viscosity of the layer adsorbed at the solid-liquid interface and the surface coverage, as well as a small viscosity shift. The proportionality coefficient depends on the intrinsic viscosity of adsorbates, solvent density, and quartz crystal thickness. The intrinsic viscosity is dominated by the conformation of the entire molecular chain and the adsorption blob for end-grafted and physisorbed molecules, respectively. Using this modified Sauerbrey equation, the phenomena relating to the conformation of discrete chains at the solid-liquid interfaces can be semi-quantitatively described.