Establishing the presence or absence of nanoscale compositional heterogeneity with nanoscale resolution is becoming instrumental for the development of many fields of science. Force versus distance measurements and parameters directly or indirectly derived from these profiles can be potentially employed for this purpose with sophisticated instruments such as the atomic force microscope (AFM). On the other hand, standards are necessary to reproducibly and conclusively support hypothesis from experimental data and these standards are still emerging. Here, we define a set of standards for providing data originating from atomic force measurements to be employed to compare between sample properties, parameters, or, more generally, compositional heterogeneity. We show that reporting the mean and standard deviation only might lead to inconsistent conclusions. The fundamental principle behind our investigation deals with the very definition of reproducibility and repeatability in terms of accuracy and precision, and we establish general criteria to ensure that these hold without the need of restricting assumptions.

Advances in quantification of nanoscale forces are mainly focused on repulsive forces, the sample's stiffness, and related parameters such as deformation. The reactivity and chemistry of the surface however depends on longer range forces that are prevalent in ambient conditions and control functional surfaces. Suitable models and appropriate parametrization of this range, however, are still emerging. Here, we define and employ metrics to parametrize long-range forces and experimental observables in dynamic atomic force microscopy and force measurements in a general way even when suitable physical models are lacking. We find that plateaus in the attractive part of the force that can be of more than 1 nm in range are a general characteristic of surfaces exposed to the ambient environment. These plateaus can be identified directly from force measurements or indirectly from computationally low-cost parameters that we define here. We further demonstrate that the defined metrics can be employed for rapid discrimination between sharp (less than 10 nm in radius) and blunt tips. Thus, our results exemplify the potential use of metrics to quantify phenomena that can lead to useful relationships without the restrictions of assumptions imposed by modeling the underlying physics.

Despite the current interest in the scientific community in exploiting divergent surface properties of graphitic carbon allotropes, conclusive differentiation remains elusive even when dealing with parameters as fundamental as adhesion. Here, we set out to provide conclusive experimental evidence on the time evolution of the surface properties of highly oriented pyrolytic graphite (HOPG), graphene monolayer (GML) and multiwalled carbon nanotubes (MWCNTs) as we expose these materials to airborne contaminants, by providing (1) statistically significant results based on large datasets consisting of thousands of force measurements, and (2) errors sufficiently self-consistent to treat the comparison between datasets in atomic force microscopy (AFM) measurements. We first consider HOPG as a model system and then employ our results to draw conclusions from the GML and MWCNT samples. We find that the surface properties of aged HOPG are indistinguishable from those of aged GML and MWCNT, while being distinct from those of cleaved HOPG. Herein, we provide a sufficient body of evidence to disregard any divergence in surface properties for multidimensional sp (2) carbon allotropes that undergo similar aging processes.

No abstract

No abstract