Probing Colloid–Substratum Contact Stiffness by Acoustic Sensing in a Liquid Phase

Abstract

In a quartz crystal microbalance, particles adhering to a sensor crystal are perturbed around their equilibrium positions via thickness-shear vibrations at the crystal's fundamental frequency and overtones. The amount of adsorbed molecular mass is measured as a shift in resonance frequency. In inertial loading, frequency shifts are negative and proportional to the adsorbed mass, in contrast with "elastic loading", where particles adhere via small contact points. Elastic loading in air yields positive frequency shifts according to a coupled resonance model. We explore here the novel application of a coupled resonance model for colloidal particle adhesion in a liquid phase theoretically and demonstrate its applicability experimentally. Particles with different radii and in the absence and presence of ligand-receptor binding showed evidence of coupled resonance. By plotting the frequency shifts versus the quartz crystal microbalance with dissipation overtone number, frequencies of zero-crossing could be inferred, indicative of adhesive bond stiffness. As a novelty of the model, it points to a circular relation between bandwidth versus frequency shift, with radii indicative of bond stiffness. The model indicates that bond stiffness for bare silica particles adhering on a crystal surface is determined by attractive Lifshitz-van der Waals and ionic-strength-dependent, repulsive electrostatic forces. In the presence of ligand-receptor interactions, softer interfaces develop that yield stiffer bonds due to increased contact areas. In analogy with molecular vibrations, the radii of adhering particles strongly affect the resonance frequencies, while bond stiffness depends on environmental parameters to a larger degree than for molecular adsorption.