Model for mechanical properties nanoprobes

Abstract

Researchers may use several different instruments to determine chemical and mechanical properties of materials with nanometer-scale vertical, and occasionally, lateral, resolution. Three such instruments are the depth-sensing indenter, the atomic force microscope, and the surface forces apparatus. Until now, these methods were individually modeled, and an analysis of their mechanical response was never done in a general way. In this article, we show that these instruments can be treated as a class—a class that we call mechanical properties nanoprobes (MPNs)—that can be described by a single universal linear model. Using this model, we solved both the quasistatic and dynamic response as a function of excitation frequency and complex compliance using an electrical analog for the mechanical system. Earlier work did not 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 difference between a partial and full derivative and its influence on quasistatically acquired force curves. The equations here will allow scientists to correctly interpret their results concerning elastic and anelastic materials response, especially for low-modulus, high-damping samples such as polymers.