Nanoparticle Optics LabPart II

Light Scattering

Theory

• A collimated light source is the most basic tool for nanoparticle work. Often called a Tyndall beam. Named after the 19th 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 sourcepolarization

horizontal source polarization

unpolarized source

Note that 90° scatteringis polarized perpendicular to the scattering plane.

Theory: Rayleigh Scattering (electric dipole)

Theory: MieAbsorption 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 HeNe 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.

Bottle Angles of Minimum Intensity (degrees)D 98E 49 64 80 97 142F 70 105

Analysis

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

Mie Plot Data

-3

-2

-1

0

1

2

3

4

5

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

Angle (degrees)

log

(In

ten

sity

)

350 nm

1160 nm

750 nm

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.