Model for mechanical properties nanoprobes

Researchers may use several different instruments to determine chemical and mechanical properties of materials with nanometer-scale vertical, and occa sionally, lateral, resolution. Three such instruments are the depth-sensing indenter, the atomic force microscope, and the surface forces apparatus. U ntil now, these methods were individually modeled, and an analysis of their mechanical response was never done in a general way. In this article, we s how that these instruments can be treated as a class-a class that we call m echanical properties nanoprobes (MPNs)-that can be described by a single un iversal linear model. Using this model, we solved both the quasistatic and dynamic response as a function of excitation frequency and complex complian ce using an electrical analog for the mechanical system. Earlier work did n ot find correct solutions for the amplitude and phase, did not examine the influence of finite stiffness in the head of the MPN, and overlooked the di fference between a partial and full derivative and its influence on quasist atically acquired farce curves. The equations here will allow scientists to correctly interpret their results concerning elastic and anelastic materia ls response, especially for low-modulus, high-damping samples such as polym ers.