Necessity of two-dimensional visualization of validity in the nanomechanical mapping of atomic force microscopy for sulphur cross-linked rubberElectronic supplementary information (ESI) available: A conversion of force-distance curve to force-deformation curve. See DOI: 10.1039/c8ra06669h

The importance of the two-dimensional (2D) visualization of validity for nanomechanical mapping in atomic force microscopy (AFM) for sulphur cross-linked rubber is emphasized for accurately interpreting the nanoscale physical properties on the surface of the soft material. The " R -factor," evaluated to be the difference between the experimental and theoretical force-deformation curves, was considered to be the reliability index of the AFM analysis for all data points on the sample surface. A small R -factor corresponds to high accuracy. The advantage of the R -factor mapping method is demonstrated using nanomechanical mapping data of the inhomogeneous isoprene rubber network by the Johnson-Kendall-Roberts and the Derjaguin, Muller, and Toporov contact mechanics models. The 2D R -factor mapping clearly and correctly supported the roles of sulphur cross-linking reagents to control the network morphology of vulcanizates. Additionally, the blanket effect, which is induced by the rubber layer on the hard part and influences experimental force-deformation curves, is firstly proposed in this study. Nanomechanical mapping with 2D reliability indexes is expected to contribute to an advance in AFM studies on soft matter such as rubber materials, leading to a more accurate understanding of the structural characteristics of the rubber networks. Thus, this validity confirmation method is necessary for developing rubber science and technology. The two-dimensional visualization of validity for nanomechanical mapping in atomic force microscopy for sulphur cross-linked rubber is emphasized for accurately interpreting the nanoscale physical properties on the surface of the soft material.