Effects of Multiple-Bond Ruptures in Force Spectroscopy Measurements of Interactions between Fullerene C_(60) Molecules in Water

Abstract

Interactions between fullerene C_(60) molecules in water were measured by force spectroscopy. Fullerene molecules were covalently connected to bifunctional water-soluble poly(ethylene glycol) (PEG) linkers and subsequently tethered to the substrate and to the tip of the atomic force microscope to facilitate single molecule detection and avoid spurious surface effects. The distributions of rupture forces for substrates prepared with different incubation times of C_(60)-PEG-NH_2 exhibit high rupture forces that cannot be explained by the theoretical distribution of single molecule binding. Moreover, the relative amplitude of the high force peak in the histogram increases with incubation time. These observations are explained by attributing the measured high forces to the rupture of multiple bonds between fullerene molecules. Force spectroscopy data analysis based on the most probable forces gives significantly different dissociation rates for samples that exhibit different amplitudes of the high force peak. An approximate analytical model that considers ruptures of two bonds that are simultaneously loaded by tethers with different lengths is proposed. This model successfully fits the distributions of the rupture forces using the same set of kinetic parameters for samples prepared with different grafting densities. It is proposed that this model can be used as a common tool to analyze the probability distributions of rupture forces that contain peaks or shoulders on the high force side of the distribution.