Error analysis in calculation and interpretation of AFM tip-surface interaction forces

This review addresses some possible errors in calculation and interpretation of AFM tip-surface interaction forces. These usually ignored errors can affect the accuracy and correctness of the interpretation results obtained from measured interaction forces, thus hindering the application of AFM technology in related fields of colloid and interface science. Based on comprehensive analysis and assessment, three important aspects in the existing literature that may introduce significant errors in calculation and interpretation of AFM tip-surface interaction forces have been identified, and corresponding reasonable suggestions have been proposed. (1) The frequently used over-approximated electrostatic force formulas can cause great errors in the electrostatic force and the fitting of surface potential and surface charge density. Therefore, adequate electrostatic force calculation methods, like linear superposition approximation (LSA) or exact numerical solutions, should be used. (2) The over-approximated AFM tip-surface interaction models (spherical tip and flat tip-flat surface interaction models (s-f and f-f)) will lead to large errors in the electrostatic force and van der Waals force, and the subsequently fitted surface potential, surface charge density, and Hamaker constant. Therefore, the conical tip with spherical end and the conical tip with flat circular end-flat surface interaction models (cs-f and cf-f) rather than the over-approximated models (s-f and f-f) should be applied. Besides, it is recommended to use cf-f instead of cs-f to measure the interaction forces for more accuracy. (3) The inaccurately obtained (usually by SEM image) AFM tip geometry parameters (radius and half angle) have significant impacts on the fitting results of surface potential, surface charge density, and Hamaker constant. More accurate AFM tip geometry parameters and reasonable assessment of errors in calculation and interpretation are necessary.