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.

Interpreting Deposition Behavior of Polydisperse Surface-Modified Nanoparticles Using QCM-D and Sand-Packed Columns

“…At the lowest IS (0.3 mM CaCl 2 ), Si-NCs capped with C 11 are monodispersed (d p *97 nm), and in terms of frequency shifts, all the overtones (n = 3, 5, 7, 9, 11, 13) exhibit ''negative'' responses, in agreement with inertial (i.e., Sauerbrey) loading (Olsson et al, 2012). As the IS increases to 1.5 mM CaCl 2 , the Si-NCs experience aggregation and the suspensions become more polydisperse (d p = 481 -224 nm).…”

“…Firmly coupled particles decrease the crystal resonance frequency as per conventional mass-loading theory (i.e., inertial loading); whereas weakly coupled particles possess a resonance of their own that, depending on the bond stiffness, might increase the crystal resonance frequency (i.e., elastic loading) (Pomorska et al, 2010). The latter case has been shown to occur when micron-sized particles are deposited on a QCM sensor (Berglin et al, 2008;Fatisson et al, 2009;Olsson et al, 2012), and in some instances, a transition from inertial loading (negative frequency shifts) at low overtones to elastic loading (positive frequency shifts) at high overtones can be observed along with a maximum in the dissipation factor (DD n ) (Pomorska et al, 2010;Olsson et al, 2012). In Figure 5a and b, we have plotted the frequency and dissipation response, at different overtones (n) for Si-NCs capped with C 11 in CaCl 2 .…”

“…Df (13) p0). Conversely, positive frequency shifts at high overtones (n) are a clear indication of a ''coupled resonance'' type response, which is linked to the bond strength between particles and collector, but cannot be interpreted as deposited mass (Pomorska et al, 2010;Olsson et al, 2012).…”

“…This can be explained by the fact that for particles approaching sizes resulting in a ''coupled resonance'' response, the bond strength (i.e., stiffness) influences the magnitude of the negative frequency shift. A stronger bond (e.g., by reduced electrostatic repulsion or Ca 2 + bridging) reduces the frequency shifts per attached particle (Pomorska et al, 2010;Olsson et al, 2012). At 3 mM CaCl 2 , the particle size becomes large enough (d p = 930 -671 nm) to result in the typical ''coupled resonance'' response.…”

Probing biomechanical properties with a centrifugal force quartz crystal microbalance

“…Without mention of the actual physics of the coupling, we observe that the finite element simulation, as well as the experimental data, follows a simple mechanical model based on coupled oscillators 31,32 . The arrangement of this mass-springdashpot mechanical model is shown in Fig.…”