Nanoparticle Optics Lab Part II Light Scattering Theory

Nanoparticle Optics Lab Part II Light Scattering

Theory • A collimated light source is the most basic tool for nanoparticle work. Often called a Tyndall beam. Named after the 19 th century scientist John Tyndall who studied light scattering in detail. • HOTS: Higher Order Tyndall Spectra

Theory: Scattering Angle • How is the angle measured? • Zero is the forward direction, the direction of the undeviated rays • 180° is backward, rays scattered directly back into the source. • Note that in the diagram to the right the scattering angles are 129 ° (180° – 51°) and 139 ° (180° – 42°), respectively.

Theory: Scattering Plane • the scattering plane is defined by the two rays involved, the source-particle ray and the particle-observer ray • The scattering plane is determined by observation, it is not fixed in space. • For example, if the observer moves, the scattering plane will move with the observer • The scattering plane is useful to define the direction of polarization of light (parallel and perpendicular)

Theory: Rayleigh Scattering (electric dipole) vertical source polarization horizontal source polarization

Theory: Rayleigh Scattering (electric dipole) unpolarized source Note that 90° scattering is polarized perpendicular to the scattering plane.

Theory: Mie Absorption and Scattering by a Sphere (exact solution) • Gustav Mie (1908) motivation: The colors of colloidal gold. • Multipole expansion (EM modes of a sphere) – – electric dipole magnetic dipole, electric quadrupole magnetic quadrupole, electric octupole etc. • If d < λ/20 then only the first term (dipole) is needed. In this limiting case, Mie’s theory reduces to Rayleigh’s theory small particle limit: Mie Rayleigh

Objective • Learn about the scattering plane and the polarization of Rayleigh scattering. • Learn about Mie scattering and the angular dependence of scattering. • Observe HOTS and angular scattering for monodisperse sols.

Procedure: Rayleigh Scattering • Shine Tyndall beam through colloidal silica without polarizer. • Observe beam from top and side of jar. • Use polarized lens to check polarity of light scattering from silica in jar.

Procedure: Rayleigh Scattering • Place polarizer between Tyndall beam and jar. • Observe light intensity from side of jar. • Note difference in scattering intensity between parallel and perpendicular polarized source.

Procedure: HOTS • Replace jar of colloidal silica with colloidal sulfur. • With source polarized perpendicular, observe different colors of HOTS spectra. • Rank particle size in the two jars by counting the number of times a certain color repeats when moving 180 degrees around the jar. • Larger particles cause more repetitions. • Use one eye and look for an easy color to see such as red.

Procedure: Scattering Angle • Using the procedure for colloidal sulfur, rank three polystyrene samples in order of size. • Put one polystyrene sample in the path of the 543. 5 nm He. Ne laser. • Prop one side of the sample container on a slide to point the back surface reflection of the container away from the laser. • Line up laser beam emitted from sample container with iris. • Use crossed polarizers to adjust laser beam intensity.

Procedure: Scattering Angle • Find points of minimum scattering intensity. • Use one eye to line up sight in the middle of the bottle at angle of minimum intensity. • Record angles for each bottle.

Results: Rayleigh Scattering • With unpolarized source, light scattered at 90 degrees from the source was polarized perpendicular. • With source polarized perpendicular, light scattered at 90 degrees was polarized perpendicular. Moving 180 degrees around the bottle produced changes in intensity with a minimum at 90 degrees.

Results: HOTS • Observed different number of color repetitions for colloidal sulfur. • For polystyrene observed one, five, and three repetitions for bottles D, E, and F respectively.

Results: Scattering Angle • Saw different numbers of scattering intensity minimums for bottles D, E, and F. • Observed one, five, and two minimums for bottles D, E, and F respectively. This led us to believe the largest particles were in bottle E, and the smallest were in D. • Different observers recorded slightly different angles of minimums.

Analysis • Table lists averages of measured angles of minimum intensity from three observers. • Angles were compared to Mie Plot data to estimate diameter of polystyrene.

Analysis • Graph shows best fit to observed data. • Minimums above 160 degrees and below 20 degrees were not taken into account.

Questions • Size estimated for particles is: 350 nm, 1160 nm, and 750 nm for bottles D, E, and F respectively. • Polydispersed sol will cause light from different wavelengths to overlap in HOTS. Colors will be less distinct. • A way to improve this experiment would be to use a light detector to measure the scattered intensity at different angles. Human error would be reduced.