UNIVERSITY OF KENTUCKY College of Engineering www.uky.edu

1. Numerical Simulations Results Conclusions Directed Melting and Movement of Nanosized Gold Particles via Surface Plasmon Resonance E. Hawes, J.T. Hastings, C. Crofcheck and M.P. Mengüç College of Engineering, University of Kentucky, Lexington, KY, University of Kentucky, Lexington, KY 40506 UNIVERSITY OF KENTUCKY College of Engineering www.uky.edu RADIATIVE TRANSFER LABORATORY Department of Mechanical Engineering www.uky.edu/rtl Introduction a) Particle separation: As particles separate, there is a minor shift in absorption magnitude (1X) that correlates to distance. b) For the horizontal configuration: The primary Peak occurs at 535 nm, with a secondary peak at 505 nm. The variation between the absorption of all the gold particles is due to mesh related-error, but is all within the same magnitude. c) Vertical Configuration: The primary peak occurs at 545 nm, with a secondary Peak at 505 nm. The particles in a vertical configuration absorbs more than the horizontal configuration.The particles closest to the surface absorb the most energy, although the difference is negligible. d) Pyramidal Configuration: The peak absorption occurs 535 nm, with a secondary peaks appear to occur at 505 and 610 nm. e) Particle Size with Probe: The results show that as a particle size increases in 10 nm increments, the absorption in the particle increase by almost and order of magnitude. Although not shown in a figure, additional simulations have shown that an AFM probe touching a particle greatly increases the absorption (4X), and shifts the peak resonance wavelength from 290 nm to 450 nm. This resonance shift is less (350 nm) when the probe is at a distance from the particles. As the probe moves away from a particle, there is an exponential decrease in the particle’s absorption. f) The presence of other particles suppresses particle absorption by a magnitude of 1X, and shifts the resonance wavelength from 450 nm to 525-550 nm. The degree of the shift is dependent on the proximity of the particles to the probe. The alignment of the particles with respect to the incident field changes the magnitude of absorption. Research into understanding and manipulating materials at the nanoscale is critical to the future of directed self assembly. In order to achieve this goal, we must first understand the complex effects of the unique properties that direct nanoscale particles. Our group is interested in using the surface plasmon resonance (SPR) and an atomic force microscope to selectively move and manipulate nanoscale particles (Figure 1). To achieve this end, we have conducted various three dimensional numerical simulations, presented below (Figure 2). The numerical results showed that these particles can be locally excited at their surface plasmon resonance (SPR), and that these resonances change due to the size and spacing of the particles, as well as the introduction of an AFM tip. Results for different geometrical configurations are presented. The numerical simulations used gold particles on a glass substrate. The particles ranged in size from 10-50 nm. Simulations involving a probe (AFM tip) modeled the probe as silicon. Each material was defined by a wavelength dependent index of refraction. The results were computed for wavelengths from 200-700 nm at intervals of 5 nm, although only relevant wavelengths are shown in the results. The particular study conducted is a step in a much larger project. By understanding the interactions of particle spacing, particle agglomerates and an AFM probe, we hope to use these properties to locally heat and direct nanosized particles. Figure 3: Particle Separation; the relative absorption of 20 nm gold particles separated by 0, 5 and 10 nm. Figure 4: Horizontal Configuration; the relative absorption of three adjacent 20 nm gold particles on a surface Figure 5: Vertical Configuration; the relative absorption of three adjacent 20 nm gold particles stacked on a surface Figure 6: Pyramidal Configuration; the relative absorption of six adjacent 20 nm gold particles arranged in a pyramid on a surface Simulations Solving heat transfer at this size scale calls for the solution of Maxwell’s equations (ME). ME solves the electric field and propagation of energy for every point in the system. Conceptual properties associated with the electric field can then be extrapolated; one can determine properties such as intensity, absorption and scattering. These in turn are then used to predict the behavior of the nanoparticles in various systems. Due to the complex calculations involved with solving ME analytically, we used a finite element method. The numerical simulations were conducted with the commercial program Comsol. We have defined ‘relative absorption’ in our simulations as the integrated intensity of the nanoparticle relative to incident energy. This is the same definition used to describe the enhancement of the electric field on the metal surface, at resonance, is described by (Raether): This equation essentially describes the difference in intensity between the incident and absorbed electric field. This resonance enhancement is derived from the Poynting vector, which (in resonance) is (Raether): Accuracy Various studies have been conducted to determine the accuracy of COMSOL’s Multiphysics programming (Ford, Hanke).Uncertainty and error, for models that are appropriately designed, are primarily a result of the mesh size. One study conducted says that the error in computing is less than 5% if the largest element size within the mesh is 1/8 of the incident wavelength.14 For our calculations, we used a DELL PC which had a 4 GHz CPU and 2.0 GB memory. COMSOL can use up to 60% of available memory when operating with the Windows XP system. This essentially indicates that one can simulate models using a maximum mesh of 105 elements: more than that and the model will not run. Figure 3 Figure 4 Figure 5 Figure 6 Figure 7a: The relative absorption of gold particles of 10, 20, 30, 40 and 50 nm particles separated from a silicon probe by 10 nm Figure 7b: A cross section of a 10 nm particle, from one of the simulations in 7a, showing the intensity throughout particle, versus wavelength Figure 8a: The relative absorption of 20 nm gold particles in the plus configuration. Figure 8b: The effect of the excited particles on the surface that they are resting on. 7(b) 7(a) Figure 2 a-g show the various three dimensional configurations simulated. The accompanying numerical results are shown under ‘Results.’ The simulations show a) Particle Separation: how absorption changes when particles are close or far. b) Horizontal Configuration: the absorption of three adjacent particles c) Vertical Configuration: the absorption of three adjacent particles stacked above a surface d) Pyramidal Configuration: the absorption of six particles in a pyramid e) Particle Size with Probe: how absorption changes for various sized particles in the presence of a silicon probe f) ‘Plus Configuration’: how absorption changes for particles in a ‘t’ shape in the presence of a silicon probe • (b) 8(a) 8(b) (c) (d) This research is leading us to a better understanding of nanoscale radiation transfer processes as applied to future directed self-assembly processes. The experimental results provide information about the ease of manipulating particles, as well as fundamental information regarding the effect of heat on the forces acting at the nanoscale. References -Menguc, M.P, M. Francoeur and E. Hawes, 2006. Nanoscale Radiation Review, upcoming. -Hawes, E., C. Crofcheck, J.T. Hasting, M.P.M Menguc, 2006. Spectrally selective heating of nanosized particles by surface plasmon resonance , Journal of Quantitative Spectroscopy and Radiative Transfer, upcoming. -Raether, H., 1988. Surface Plasmons on Smooth and Rough Surfaces and on gratings, 1988, New York, Springer-Verlag. -Ford, G.W. and W.H. Weber, 1984. Electromagnetic Interactions of Molecules with Metal Surfaces, Physics Report, Vol. 113, No. 4, pp. 197-287. -Hanke, M. 2004. Benchmarking FEMLAB 3.0a. Parallel and Scientific Computing Institute, Report No. 2004:01. Acknowledgments This work is partially sponsored by a National Science Foundation grant (NSF-NER #CMMI-0609137), and by the University of Kentucky. (e) (f)