Measuring the elastic modulus of polymers using the atomic force microscope

Testing a new method of nanoindentation using the atomic force microscope (AFM) was the purpose of this research. Nanoindentation is a useful technique to study the properties of materials on the sub-micron scale. The AFM has been used as a nanoindenter previously; however several parameters needed to obtain accurate results, including tip radius and cantilever sensitivity, can be difficult to determine. To solve this problem, a new method to determine the elastic modulus of a material using the atomic force microscope (AFM) has been proposed by Tang et al. This method models the cantilever and the sample as two springs in a series. The ratio of the cantilever spring constant (k) to diameter of the tip (2a) is treated in the model as one parameter (α=k/2a). The value of a, along with the cantilever sensitivity, are determined on two reference samples with known mechanical properties and then used to find the elastic modulus of an unknown sample. To determine the reliability and accuracy of this technique, it was tested on several polymers. Traditional depth-sensing nanoindentation was preformed for comparison. The elastic modulus values from the AFM were shown to be statistically similar to the nanoindenter results for three of the five samples tested.

VALIDATION OF A 'DISPLACEMENT TOMOGRAPHY' INVERSION METHOD FOR MODELING SHEET INTRUSIONS

The study of volcano deformation data can provide information on magma processes and help assess the potential for future eruptions. In employing inverse deformation modeling on these data, we attempt to characterize the geometry, location and volume/pressure change of a deformation source. Techniques currently used to model sheet intrusions (e.g., dikes and sills) often require significant a priori assumptions about source geometry and can require testing a large number of parameters. Moreover, surface deformations are a non-linear function of the source geometry and location. This requires the use of Monte Carlo inversion techniques which leads to long computation times. Recently, ‘displacement tomography’ models have been used to characterize magma reservoirs by inverting source deformation data for volume changes using a grid of point sources in the subsurface. The computations involved in these models are less intensive as no assumptions are made on the source geometry and location, and the relationship between the point sources and the surface deformation is linear. In this project, seeking a less computationally intensive technique for fracture sources, we tested if this displacement tomography method for reservoirs could be used for sheet intrusions. We began by simulating the opening of three synthetic dikes of known geometry and location using an established deformation model for fracture sources. We then sought to reproduce the displacements and volume changes undergone by the fractures using the sources employed in the tomography methodology. Results of this validation indicate the volumetric point sources are not appropriate for locating fracture sources, however they may provide useful qualitative information on volume changes occurring in the surrounding rock, and therefore indirectly indicate the source location.