Light scattering
Download
1 / 54

Light Scattering - PowerPoint PPT Presentation


  • 336 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Light Scattering' - donar


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Light scattering
Light Scattering

Chris Sorensen

Department of Physics

Kansas State University

Manhattan, KS 66506-2601

[email protected]


Light scattering1
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
Laser Light Scattering

Typically “VU” scattering

incident polarization vertical,

no polarizer on detector, i.e.,

unpolarized.



Rayleigh scattering scattering from small particles
Rayleigh ScatteringScattering from Small Particles

What do we mean by “small”?

---small compared to .

(Only two length scales, R and ).


Rayleigh scattering 2
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
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
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


Consequences of rayleigh scattering 1

Blue sky and red sunset.

Consequences of Rayleigh Scattering (1)




Consequences of rayleigh scattering 3 the tyndall effect
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

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
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 plotted vs theta
RDGPlotted vs theta


Rdg plotted vs qr
RDGPlotted vs. qR


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

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.


Forward scattering from 9.6 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.m polystyrene microspheres in water.


How big are the water drops in the fog? 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.

Why is the edge of the halo red?


Lunar halo
Lunar halo 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.


Mie scattering for a sphere
Mie Scattering for a Sphere 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.


Mie scattering for spheres m 1 33 various kr 2 r

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
Patterns in Mie Scattering (Dia=0.16 ).(normalized to I(0))Sorensen and Fischbach, Opt. Commun. 173, 145 (2000).


Quasi universality with
Quasi Universality with (Dia=0.16 ).



The mie ripples

The Mie Ripples (Dia=0.16 ).

Δθ = λ/diameter

Useful for large, single particles or very narrow size distribution


Forward scattering from large 10 particles
Forward scattering from large (10 (Dia=0.16 ).μ) particles




Fractal aggregate
Fractal Aggregate (Dia=0.16 ).

Rg = Radius of Gyration a root-mean-square radius

N=monomers/aggregate

N ~ RgD

D = Fractal dimension


Fractal Aggregate Scattering (Dia=0.16 ).

Notation: Dm=Df=D

No ripples because surface is “soft”.


Guinier analysis
Guinier Analysis (Dia=0.16 ).

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
Classic Zimm Plot (Dia=0.16 ).

cellulose nitrate fraction in acetone (Benoit, Holtzer, and Doty, JPC58, 635 (1954).


Premixed ch 4 o 2 flame soot
Premixed CH (Dia=0.16 ).4/O2 Flame Soot

Gangopadhyay et al. Appl. Optics 30, 4859 (1991).


Kim, Sorensen and Chakrabarti, Langmuir (Dia=0.16 ).20, 3969 (2004).



Baby bomb
Baby Bomb (Dia=0.16 ).




General Features of Fractal Aggregate Structure Factor 2.3 sec-1. Gel time: 50 ± 10 min.


Remember q logarithmic
Remember 2.3 sec-1. Gel time: 50 ± 10 min.qlogarithmic


Bibliography
Bibliography 2.3 sec-1. Gel time: 50 ± 10 min.

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).


"Size Distribution Effect on the Power Law Regime of the Structure Factor of Fractal Aggregates," C.M. Sorensen and G.M. Wang, Phys. Rev. E60, 7143 (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.


ad