Effects of Multiple-Bond Ruptures in Force Spectroscopy Measurements of Interactions between Fullerene C₆₀ Molecules in Water

Abstract

Interactions between fullerene C60 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 C60-PEG-NH2 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.

Mechanical Rupture of Mono- and Bivalent Transition Metal Complexes in Experiment and Theory

“…At the moment of bond breakage, the force is distributed over both bonds, leading to higher forces than for the single-bond case (in between one and two times of the The Journal of Physical Chemistry C Article single-bond rupture force). 45,46 Therefore, the second maxima may also be due to simultaneous bond rupture.…”

Distributions of Parameters and Features of Multiple Bond Ruptures in Force Spectroscopy by Atomic Force Microscopy

“…Using the high force asymptotic of the FJC model and assuming the same Kuhn length a for both chains and also neglecting difference in the attachment points, we can write the total force sensed by AFM probe as 16 where F K is the characteristic thermal force of polymeric tether,…”

“…26 However, detailed kinetic models indicate that for two bonds that are subjected to equal pulling forces the total most probable rupture force is lower than the sum of two individual most probable forces measured in single-molecule experiments. 14,27,28 Moreover, if forces on two bonds are not equal, the resulting most probable rupture force becomes even lower. 16,29 In this article, we use an analytical model 16 that does not make an assumption that the forces applied to separate bonds are equal.…”

Charge-Transfer Complexes Studied by Dynamic Force Spectroscopy

“…In some cases, a long tail of the distribution towards higher forces was observed (Figure 4). This tail has been attributed to diverse causes such as heterogeneity of chemical bonds [30] or simultaneous ruptures of more than one complex [31,32]. A plot of the most probable rupture force vs. the most probable loading rate at each retracting speed is shown in Figure 5.…”