Finite element modeling of indenter-sample contact during force imaging of filled rubber by atomic force microscopy

Finite element analysis (FEA) models were developed to study the interaction between atomic force microscope (AFM) tips and filled rubber compounds during nano-indentation. The filled systems were represented by simple models consisting of one or two discrete hard domains in a rubber matrix in order to study how such a hard domain at or near the location of an indentation measurement affected the force-distance response. Parameters studied included domain size and shape, lateral position and depth from the indentation location, effect of sample thickness, and the ability to measure modulus variation across "rubber-particle" interfaces. The analyses showed the degree to which the underlying and adjacent sample regions influenced the force-distance response at a given location. The results identified several limitations of force imaging as a characterization technique for filled systems and suggested a basis for the development of more complex FEA models.