Dr. Jeffery J. Weimer
Chemistry/Chemical & Materials Engineering, The University of Alabama in Huntsville
The Uncertainty Budget of the Hamaker Constant When Fitting Theoretical Force-Distance Curves in Atomic Force Microscopy
DATE: Friday, February 3, 2017
TIME: 3:00 p.m. – 4:00 p.m.
PLACE: Shelby Center 218
The Hamaker constant A defines forces between macroscopic bodies in colloidal systems. The atomic force microscope, widely applied to image surfaces at atomic resolutions, measures the appropriate force-distance data. While curve fitting for A is routine, methods to define the resulting confidence in A are all but ignored. The uncertainty budget analysis handles this issue.
The starting point of the talk summarizes the formulations behind uncertainty analysis and propagation. The model system for consideration is a colloidal sphere approaching from a distance above flat surface plate. A general expression is derived for the overall relative uncertainty (variance) on A. The expression has three groups of factors. The first is the relative uncertainties of system parameters. They include relative measurement uncertainties (NIST Type A) and relative calibration uncertainties (NIST Type B). The second group are sensitivity factors. They are partial derivatives of the equations for force with regard to system parameter, and they scale the response of the overall uncertainty budget expression accordingly. The third group is a set of weighting parameters that scale the relative contribution of each force term in the overall uncertainty budget.
Case studies are taken for perfect theoretical systems, perfect measurement systems, and real measurement systems. The results are systems of equations that define the contributions of uncertainties in distance, sphere radius, and other fitting terms to the overall uncertainty budget. Applications are shown with empirical estimates made at one point as well as results when curve fitting. The outcome is an as-yet-unrealized, systematic report of the confidence that we can expect from doing curve fits to measured force-distance data in order to bring rigorous comparative analysis of the value of A from different systems to a proper science.
Refreshments will be served at 2:30 p.m. in SC 201 suite landing.
