Light Scattering Chris Sorensen Department of Physics Kansas State University Manhattan, KS 66506-2601 email@example.com
Light Scattering It’s how we see the world. Every non-luminous thing we see, we see via light scattering. Reflection is a special form of light scattering. Non Invasive Probe of Aerosol Systems Colloid Science Biophysics Condensed Matter Physics Aerosol Science Atmospheric Visibility Earth’s Radiation Budget Problems Becoming More Complex
Laser Light Scattering Typically “VU” scattering incident polarization vertical, no polarizer on detector, i.e., unpolarized.
Rayleigh ScatteringScattering from Small Particles What do we mean by “small”? ---small compared to . (Only two length scales, R and ).
Rayleigh Scattering (2) Since R<<, the point sub volumes within particle see the same incident phase are all essentially the same distance from the detector Thus they scatter in phase to the detector (regardless of angle). Total scattering amplitude Total scattered intensity
Rayleigh Scattering (3)Unit Analysis Cross section units: area = (length)2. But so far we have σ ~ V2 = (length)6
Rayleigh Scattering (3b)Unit Analysis Cross section units: area = (length)2 . But so far we have So there must be another length scale involved—the only other length scale is . So
Blue sky and red sunset. Consequences of Rayleigh Scattering (1)
Consequences of Rayleigh Scattering (2) • Isotropic scattering
Consequences of Rayleigh Scattering (3)The Tyndall Effect The increased scattering as a system coarsens, e.g., precipitates. Is N N V2/4 Hence Is Vparticle.
Single Slit Diffraction Patterns a = slit width, = light wavelength
The scattering wave vector, q. Theory leads to q = (4π/λ)sin(θ/2) Much more useful than the scattering angle, θ.
Rayleigh-Debye-Gans Theory [3u-3 (sin u-u cosu)]2 Where u = qR (a nice dimensionless variable!) Simply the square of the Fourier Transform of a sphere. Good when = 2kR|m-1|<1 where m is the particle refractive index and is the phase shift parameter.
RDG • RDG is equal to Rayleigh when scattering angle is small in the “Forward Lobe” • RDG contains Porod’s Law when qR>1 I q-4
Inverse q Note that since q = (4π/λ)sin(θ/2), inverse q has units of length. Inverse q is the “length scale of the scattering experiment”.
Crossovers and Length Scales. On log-log plots one finds in general that I(q) vs. q crosses over from one slope to another (i.e., from one power law to another) when q passes through a length scale of the scatterer as demonstrate here.
How big are the water drops in the fog? Why is the edge of the halo red?
e.g., if (green), kR=1 implies R=0.08 (Dia=0.16 ). Mie Scattering for Spheres m=1.33 Various kR = (2π/λ)R
Patterns in Mie Scattering(normalized to I(0))Sorensen and Fischbach, Opt. Commun. 173, 145 (2000).
The Mie Ripples Δθ = λ/diameter Useful for large, single particles or very narrow size distribution
Fractal Aggregate Rg = Radius of Gyration a root-mean-square radius N=monomers/aggregate N ~ RgD D = Fractal dimension
Fractal Aggregate Scattering Notation: Dm=Df=D No ripples because surface is “soft”.
Guinier Analysis When Thus Regardless of shape Regardless of refractive index Plot I(0)/I(q) vs. q2 Slope = Rg2/3 (Recall the Zimm plot of biophysics)
Classic Zimm Plot cellulose nitrate fraction in acetone (Benoit, Holtzer, and Doty, JPC58, 635 (1954).
Premixed CH4/O2 Flame Soot Gangopadhyay et al. Appl. Optics 30, 4859 (1991).
Shearing 1 min after the onset of aggregation. Shear rate: 2.3 sec-1. Gel time: 50 ± 10 min.