Atomic Force Microscopy Model Research Articles

Vanishing Cantilever Calibration Error with Magic Ratio Atomic Force Microscopy

AbstractAn analysis is presented of the error propagation through a simplified contact model for atomic force microscopy (AFM) static force spectroscopy, one that is meant to be intuitive and pedagogically informative rather than maximally realistic. It is shown that an important dimensionless ratio appears in several critical locations in the closed form error equation, and that under common calibration methods there exists a ``magic'' ratio where an important class of systematic calibration errors cancel out completely. This argument is extended to more complex contact models and the presence of a magic ratio is demonstrated using real data. A method is shown to identify and operate at optimal conditions in commercial AFMs. Targeting this magic ratio provides a simple, comprehensive guideline for cantilever selection, system calibration, and imaging parameter selection.

Computer simulations of the mechanical response of brushes on the surface of cancerous epithelial cells.

We report a model for atomic force microscopy by means of computer simulations of molecular brushes on surfaces of biological interest such as normal and cancerous cervical epithelial cells. Our model predicts that the force needed to produce a given indentation on brushes that can move on the surface of the cell (called “liquid” brushes) is the same as that required for brushes whose ends are fixed on the cell’s surface (called “solid” brushes), as long as the tip of the microscope covers the entire area of the brush. Additionally, we find that cancerous cells are softer than normal ones, in agreement with various experiments. Moreover, soft brushes are found to display larger resistance to compression than stiff ones. This phenomenon is the consequence of the larger equilibrium length of the soft brushes and the cooperative association of solvent molecules trapped within the brushes, which leads to an increase in the osmotic pressure. Our results show that a careful characterization of the brushes on epithelial cells is indispensable when determining the mechanical response of cancerous cells.

A Note on the Two-Spring Tomlinson Model

In this note, quasistatic solutions of a two-mass-two-spring Tomlinson model for atomic force microscopy are derived, and are compared with the corresponding results of the single-spring Tomlinson model. It is clarified that the solutions of the two models are equivalent provided that the effective spring constant is correctly defined. It is also shown that modeling the onset of stick-slip motion in terms of the criteria defined by explicit tip and cantilever stiffness is the most convenient to investigate the effects of the tip-flexibility on the stick-slip motion.