Quantifying Effective van der Waals Interactions Across Two-Dimensional Material Interfaces

Abstract Van der Waals (vdW) interactions play a central role in determining the properties and functionality of two-dimensional (2D) materials and their heterostructures. However, quantitative nanoscale characterization of these interactions remains challenging. Here, we introduce a universal multifrequency atomic force microscopy (AFM) framework for quantitative mapping of effective vdW interaction landscapes and the extraction of effective Hamaker constants with Ångström-scale vertical resolution. Using graphene, graphene oxide, hexagonal boron nitride, molybdenum disulfide, and highly oriented pyrolytic graphite as model systems, we systematically investigate the influence of layer number, substrate, defects, step edges, surface roughness, and functionalization on local vdW interactions. The measurements reveal pronounced spatial variations and nonadditive behavior, demonstrating that effective Hamaker constants can be enhanced or suppressed by nanoscale structural and interfacial features. This work provides a rapid and versatile approach for nanoscale characterization of vdW interactions and offers new opportunities for engineering interfacial forces in 2D materials and van der Waals heterostructures.