MODELING SCATTERED INTENSITIES FOR MULTIPLE PARTICLE TIRM USING MIE THEORY A Thesis by ADAM L. ALLEN Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE August 2006 Major Subject: Biomedical Engineering MODELING SCATTERED INTENSITIES FOR MULTIPLE PARTICLE TIRM USING MIE THEORY A Thesis by ADAM L. ALLEN Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Approved by: Chair of Committee, Kenith Meissner Committee Members, Michael A. Bevan Gerard L. Coté Head of Department, Gerard L. Coté August 2006 Major Subject: Biomedical Engineering iii ABSTRACT Modeling Scattered Intensities for Multiple Particle TIRM Using Mie Theory. (August 2006) Adam L. Allen, B.S., Texas A&M University Chair of Advisory Committee: Dr. Kenith Meissner Single particle TIRM experiments measure particle-surface separation distance by tracking scattered intensities. The scattered light is generated by an evanescent wave interacting with a levitating microsphere. The exponential decay of the evanescent wave, normal to the surface, results in scattered intensities that vary with separation distance. Measurement of the separation distance allows us to calculate the total potential energy profile acting on the particles. These experiments have been shown to exhibit nanometer spatial resolution and the ability to detect potentials on the order of kT with no external treatment of the particle. We find that the separation distance is a function of the decay of the evanescent wave and the size of the sphere. Different sizes of spheres, located the same distance from the surface, exhibit varying scattered intensity distributions. Single particles have been studied extensively but multiple particle experiments are needed for studies of more complex systems and surfaces. Increasing the number of colloidal particles in a TIRM experiment greatly increases the complexity of the system. Calculation of separation distances and potentials over a large group of microspheres requires that the spheres display a uniform stuck-particle intensity distribution. But, for large numbers of particles, this is not the case. In some instances, stuck-particle intensities can vary more than an order of magnitude. iv This research involves creating a mathematical model to study scattered intensity distributions for a large size range of polystyrene microspheres. The model is based on basic Mie theory. We compare the theoretically simulated results to the experimentally obtained results and find that scattered intensity variations in multiple particle TIRM experiments are attributed to particle polydispersity (particle size variation). This is a very important result because we know that if we can maintain a relatively uniform particle size distribution, then we will see a relatively uniform stuck-particle intensity distribution. The model can then be used to select a size range of microspheres that will exhibit a more uniform distribution so as to increase the sensitivity and feasibility of multiple particle TIRM. v TABLE OF CONTENTS Page ABSTRACT........................................................................................................................iii TABLE OF CONTENTS.....................................................................................................v LIST OF FIGURES ............................................................................................................vi INTRODUCTION ...............................................................................................................1 PROBLEM: SCATTERED INTENSITY VARIATIONS IN TIRM.................................3 Total internal reflection microscopy (TIRM) ..............................................3 Evanescent wave generation ........................................................................3 Single particle TIRM....................................................................................5 Mapping potential energies..........................................................................6 Multiple particle TIRM ................................................................................7 Diffusing polloidal probe microscopy (DCPM) ..........................................8 SOLUTION: MIE THEORY............................................................................................11 History of Mie theory.................................................................................11 Assumptions in Mie theory ........................................................................12 Angular scattered intensities ......................................................................12 Common difficulties with Mie theory........................................................15 Size effects .................................................................................................17 MATLAB code for Mie theory..................................................................21 SUMMARY AND CONCLUSIONS ................................................................................25 Simulation parameters................................................................................25 Experimental methods................................................................................27 Results and discussion - 1m polystyrene particles...................................29 Results and discussion - 4m polystyrene particles...................................32 Results and discussion - 6m polystyrene particles...................................35 Summary and conclusion ...........................................................................36 Future work ................................................................................................38 REFERENCES ..................................................................................................................39 APPENDIX A MATLAB CODE FOR MODELING.......................................................41 VITA..................................................................................................................................52 vi LIST OF FIGURES FIGURE Page 1. Evanescent wave generation with refractive indices, m1>m2 ......................4 2. Basic set up for TIRM..................................................................................6 3. Brownian motion continuously affects the levitating particle .....................7 4. DCPM set up and results............................................................................10 5. Angular scattering polar plot......................................................................14 6. Description of morphology dependent modes ...........................................17 7. Qsca for polystyrene spheres in air..............................................................18 8. Qsca for polystyrene spheres in water .........................................................19 9. Qsca for polystyrene spheres in various mediums.......................................20 10. 1m polystyrene - Scattered intensity and size distribution vs. radius ......29 11. 1m polystyrene – Intensity vs. particle frequency ...................................29 12. 4m polystyrene - Scattered intensity and size distribution vs. radius ......32 13. 4m polystyrene – Intensity vs. particle frequency ...................................32 14. Isca for 4m polystyrene – Zoomed in ........................................................33 15. Effects of changing value of median diameter for 4m polystyrene .........34 16. 6m polystyrene - Scattered intensity and size distribution vs. radius ......35 17. 6m polystyrene – Intensity vs. particle frequency ...................................35 1 INTRODUCTION A novel technique, called total internal reflection microscopy (TIRM), has been developed that can measure distances as small as a nanometer. TIRM is special because it provides a very sensitive, non-intrusive and instantaneous1 ability to measure these extremely small distances. In TIRM we track the intensity of light scattered by a very small sphere. Changes in this scattered intensity represent a change in distance between the sphere and a transparent plate. This allows for us to physically observe, in real-time, the changes in scattered intensity; as a result, using a microscope, we can see these differences in distance. This is true even though we can measure distances that are approximately 20,000 times smaller than the width of human hair. TIRM is also useful because we can use these measured distances to calculate the total sum of forces, or potential energies, acting on the sphere. Since we can detect very small changes in distance and we use this information to calculate the forces acting on the sphere, we can detect forces with unprecedented sensitivity. It has been shown that 1 TIRM is able to detect forces on the order of kBT . There are many interesting chemical and biomedical applications because of the extreme sensitivity. Dr. Bevan’s group at Texas A&M University is interested in using this technology to map the potential profiles of patterned surface. Instead of using single sphere, this technique makes use of a large number of small spheres to track changes in distance. If these spheres are spread out over a patterned surface, we measure the surface variations. Then, using these measured distances, we can calculate the potential energy variations across