Light Scattering. Chris Sorensen Department of Physics Kansas State University Manhattan, KS 66506-2601 [email protected] 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.
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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
Condensed Matter Physics
Earth’s Radiation Budget
Problems Becoming More Complex
Typically “VU” scattering
incident polarization vertical,
no polarizer on detector, i.e.,
What do we mean by “small”?
---small compared to .
(Only two length scales, R and ).
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
Cross section units: area = (length)2.
But so far we have
σ ~ V2 = (length)6
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
The increased scattering as a system coarsens, e.g., precipitates.
Is N N V2/4
Hence Is Vparticle.
a = slit width, = light wavelength
Theory leads to
q = (4π/λ)sin(θ/2)
Much more useful than the scattering angle, θ.
[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
where m is the particle refractive index and
is the phase shift parameter.
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”.
Why is the edge of the halo red?
Δθ = λ/diameter
Useful for large, single particles or very narrow size distribution
Rg = Radius of Gyration a root-mean-square radius
N ~ RgD
D = Fractal dimension
No ripples because surface is “soft”.
Regardless of shape
Regardless of refractive index
Plot I(0)/I(q) vs. q2
Slope = Rg2/3
(Recall the Zimm plot of biophysics)
cellulose nitrate fraction in acetone (Benoit, Holtzer, and Doty, JPC58, 635 (1954).
Gangopadhyay et al. Appl. Optics 30, 4859 (1991).
Light Scattering by Small Particles, H.C. van de Hulst, Wiley, New York (1957).
The Scattering of Light and Other Electromagnetic Radiation, M. Kerker, Academic, New York (1969).
Absorption and Scattering of Light by Small Particles, C.E. Bohren and D.R. Huffman, Wiley, New York (1983).
"Optical Structure Factor Measurements of Soot Particles in a Premixed Flame," Appl. Optics 30, 4859 (1991) S. Gangopadhyay, I. Elminyawi and C.M. Sorensen.
"Light Scattering Measurements of Monomer Size, Monomers per Aggregate and Fractal Dimension for Soot Aggregates in Flames," Appl. Optics 31, 6547 (1992) C.M. Sorensen, J. Cai and N. Lu.
"Test of Static Structure Factors for Describing Light Scattering from Fractal Soot Aggregates," Langmuir 8, 2064 (1992) C.M. Sorensen, J. Cai and N. Lu.
"Comparison of Size and Morphology of Soot Aggregates as Determined by Light Scattering and Electron Microscope Analysis," Langmuir 9, 2861 (1993) J. Cai, N. Lu and C.M. Sorensen.
"Depolarized Light Scattering from Fractal Soot Aggregates," N. Lu and C.M. Sorensen, Phys. Rev. E50, 3109 (1994).
"Scattering and Absorption of Light by Particles and Aggregates," C.M. Sorensen, in Handbook of Surface and Colloidal Chemistry, Ed. K.S. Birdi, CRC Press, Boca Raton, 1997; p. 533-558.
"Light Scattering Study of Fractal Cluster Aggregation Near the Free Molecular Regime," C. Oh and C.M. Sorensen, J. Aerosol Sci. 28, 937 (1997).
"Structure Factor Scaling in Aggregating Systems," H. Huang, C. Oh, and C.M. Sorensen, Phys. Rev. E57, 875 (1998).
"Aerogelation in a Flame Soot Aerosol," C.M. Sorensen, W.B. Hagemann, T.J. Rush, H. Huang, and C. Oh, Phys. Rev. Lett. 80, 1782 (1998).
"Scaling Description of the Structure Factor of Fractal Soot Composites," C.M. Sorensen, C. Oh, P.W. Schmidt and T. Rieker, Phys. Rev. E58, 4666 (1998).
"Scaling Approach for the Structure Factor of a Generalized System of Scatterers," C. Oh and C.M. Sorensen, J. Nanopart. Res. 1, 369 (1999).
"Patterns in Mie Scattering," C.M. Sorensen and D.F. Fischbach, Opt. Commun. 173, 145 (2000).
"Guinier Analysis for Homogeneous Dielectric Spheres of Arbitrary Size," C.M. Sorensen and D. Shi, Optics Commun. 178, 31 (2000).
"Light Scattering from Fractal Aggregates. A Review," C.M. Sorensen, Aerosol Sci. Tech. 35, 648 (2001).
"Patterns in the Ripple Structure in Mie Scattering," C.M. Sorensen and D. Shi, J. Opt. Soc. Am. 19, 122 (2002).
“Experimental Test of the Rayleigh-Debye-Gans Theory for Light Scattering by Fractal Aggregates,” G.M. Wang and C.M. Sorensen, Applied Optics 41, 4645 (2002).
“Scattering and Adsorption of Light by Particles and Aggregates,” in Handbook of Surface and Colloidal Chemistry, ed. by K.S. Birdi, CRC Press, Boca Raton, 2003, p. 623.
"Observation of Soot Superaggregates with a Fractal Dimension of 2.6 in Laminar Acetylene/Air Diffusion Flames," C.M. Sorensen, W. Kim, D. Fry, A. Chakrabarti, Langmuir 19, 7560-7563 (2003).
"Universal Occurrence of Soot Aggregates with a Fractal Dimension of 2.6 in Heavily Sooting Laminar Diffusion Flames," W. Kim, C.M. Sorensen, A. Chakrabarti, Langmuir 20, 3969-3973 (2004).
"Structure Factor Scaling in Colloidal Phase Separation," J.J. Cerda, T. Sintes, C.M. Sorensen and A. Chakrabarti, Phys. Rev. E 70, 051405 (2004).
"Aggregates, Superaggregates and Gel-Like Networks in Laminar Diffusion Flames," W.G. Kim, C.M. Sorensen, D. Fry and Amit Chakrabarti, J. Aerosol Science (accepted).
“Patterns in Mie Scattering: Evolution when Normalized by the Rayleigh Cross Section,” M.J. Berg, C.M. Sorensen, and A. Chakrabarti, Applied Optics, accepted.
“Multiple Scattering Effects on Optical Structure Factor Measurements,” T. Mokhtari, C.M. Sorensen and A. Chakrabarti, Applied Optics, accepted.