## Date of Award

12-2017

## Degree Type

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Chemical Engineering

## Committee Chair

Stephen P. Beaudoin

## Committee Co-Chair

David S. Corti

## Committee Member 1

Michael T. Harris

## Committee Member 2

Ronald G. Reifenberger

## Abstract

The Hamaker constant, A, is a very important parameter used to quantify the strength of the van der Waals (vdW) attractive interaction among particles and between particles and surfaces. Consequently, an accurate measurement of A is of fundamental importance to a wide range of research and manufacturing fields. Therefore, this dissertation primarily focuses on the development and application of a new method to determine Hamaker constants of solid materials using an atomic force microscope (AFM). While the direct contact or pull-off method is typically employed during an AFM force measurement, this contact-technique is highly dependent upon material properties that are difficult to quantify precisely, such as surface roughness, contact separation distance, and surface deformation. Thus, the method presented in this work utilizes the approach-to-contact regime of an AFM force experiment which should be less dependent upon these surface effects. First, a previous “jump-into-contact” quasi-static method for determining A from AFM measurements is corrected and extended to include various AFM tip-surface force models of interest. Then, to test the efficacy of the “jump-into-contact” quasi-static model, a dynamic model of the tip motion is developed. For finite AFM cantilever-surface approach speeds, a true “jump” point, or limit of stability, is found not to appear and the quasi-static model fails to represent the dynamic tip behavior. Therefore, the proposed method is “quasi-dynamic” in nature rather than quasi-static. This was achieved by determining the well-defined deflection at first contact “dc” instead of the jump-into-contact distance. An apparent Hamaker constant “Aapp” is then calculated from this dc value and a corresponding quasi-static-based equation. The resulting value of Aapp depends on the cantilever’s approach speed and the sampling resolution of the AFM. Since Aapp approaches the “true” value of A only in the quasi-static and continuous sampling limits, a double extrapolation procedure is initially suggested to obtain an estimate of the Hamaker constant of the solid surface. The accuracy of this procedure is tested using simulated AFM data and is shown to yield an accurate, self-consistent estimate of the Hamaker constant. Experimental verification is provided for both the dynamic model and this new quasidynamic method. By analyzing the dynamics of cantilevers with different mechanical properties, guidelines for the selection of a given cantilever for an AFM measurement are presented. A new dimensionless parameter is introduced to guide cantilever selection and AFM operating conditions. The value of quantifies how close a given experiment is to its quasi-static limit for a chosen cantilever-surface approach speed. For sufficiently small values of (i.e. a cantilever that effectively behaves “quasi-statically”) simulated data indicate that Aapp will be within ~1% or less of the inputted value of the Hamaker constant. Hence, with the new method, Hamaker constants may now be reliably estimated using a single measurement taken with an appropriately chosen cantilever and a slow, yet practical, approach speed. This is confirmed by the very good agreement found between the experimental AFM results obtained using this new method and previously reported predictions of Hamaker constants for amorphous silica, polystyrene, and α- Al2O3 substrates obtained using the Lifshitz method. However, due to the nanometer length scale of the cantilever tip, visually approximating its geometric features can yield significant error in the estimate of A. Thus, an additional modification was made to the quasi-dynamic method using a simple sphere-plate model which allows one to represent all of the system’s geometric features with just one parameter: the tip’s radius of curvature. The effective radius of the tip “Reff” is determined from a “calibration” step, in which the dc is measured for a substrate with a known Hamaker constant. Hence, no visual fitting of the tip shape is required and all geometric uncertainties of the tip are accounted for within the calibrated tip radius. After Reff has been determined, estimates of A for any other surface of interest can now be determined using this effective sphere model. An additional experimental study was conducted to validate this modification and, again, the results are in good agreement with predictions from the Lifshitz approximation. Then, the modified quasi-dynamic model was employed to study the strength of the adhesive interaction between TNT and several swab materials which are used as explosive detection devices at security checkpoints. This information is crucial for the development and improvement of next-generation swab detection protocols to further advance this field.

The final two studies presented in this dissertation investigate inherent noise that is present in an AFM adhesion experiment. First, a modification to the dynamic model is presented which includes naturally-occurring, thermal fluctuations of the cantilever during its approach to contact with the surface. The analysis indicates that the impact of thermal noise on the accuracy of measured dc and thus the A predicted by the quasi-dynamic method will be minimal. Finally, a statistical analysis tool called the bootstrap is employed to determine the error associated with a previously developed adhesion simulation technique which utilizes topographical maps of the substrate to represent inherent surface roughness.

## Recommended Citation

Fronczak, Sean G., "A New Method for Determining Hamaker Constants of Solids Based on the Dynamic Approach Behavior of an Atomic Force Microscope" (2017). *Open Access Dissertations*. 1548.

https://docs.lib.purdue.edu/open_access_dissertations/1548