Transcript Optical Properties of Aerosols

Optical Properties of Aerosols
ENVR 416
Aerosol Technology
LA on a smoggy day
LA on a clear day
1
Topics
•Definitions
• Extinction
• Scattering
• Visibility
2
Introduction
• Aerosol scattering is responsible for many atmospheric events
- sunsets
- halos around the sun or moon
- rainbows
- white (extensive scattering from the surface) and black
(complete scattering where light cannot penetrate) clouds
- visibility degradation from pollution
• Aerosol light scattering is also a powerful method used by
instruments that measure aerosol size and concentration
- these instruments are sensitive and do not manipulate particles
3
Light Scattering Regimes
Dp < 0.05 µm  described by molecular scattering…aka
“Rayleigh Scattering”
Dp > 100 µm  described by geometric optics (diffracted,
reflected, refracted rays)
0.05 µm < Dp < 100 µm  Dp on the order of λ, described by
“Mie Theory”
NOTE: All scattering can be derived via Mie Theory, developed
by Gustav Mie in 1908 using Maxwell’s theory of
Electromagnetic Radiation. Limiting cases such as
Dp << λ and Dp >> λ allow for simplifications to be made.
4
Definitions
c = speed of light = 3x1010 cm/s = f*λ
For visible light, λ = 400-700 nm
m = refractive index  relates the change in velocity that light
experiences upon going from one medium to another
(a material related property)
m = c/vp = speed of light in a vaccum/speed of light in a material, p
5
Index of Refraction
6
Index of Refraction
m  m 1  ai   m  m ai
'
'
scattering
'
absorption
Scattering portion measured with Snell’s Law:
m1' sin  2

'
m2 sin 1
1
2
m2'
m1'
7
Index of Refraction
Absorption often measured via spectrophotemtry
A
4a

m  m 1  ai   m  m ai
'
'
'
Bulk absorption
A0
A0
For electrically conductive material
For most aerosol particles
8
Relative Index of Refraction (mr)
Used to describe a two phase system, i.e. a particle in air
mp
Vm
mr 

mm V p
m 1
m 1
mr  m
For air
For vacuum
For aerosol particles in air
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Intensity of Light
Light arriving at a surface:
radiant _ power
I
unit _ area
scattered light
W
m2
detector
Incident light
10
Intensity of Light
Light from a point source:
radiant _ power
I
solid _ angle
W
sr
A
4
A
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Size Parameter (α)

d


- Added to simplify light scattering equations
- Makes α = ratio of particle size to wavelength of radiation
  6
For dp on the order of mm
12
Electromagnetic Theory
Light possesses wave/particle duality
 we will treat it as the electric wave component of EM radiation
 Light can be:
1) unpolarized (sunlight)
2) parallel polarized
3) perpendicular polarized
13
Topics
•Definitions
• Extinction
• Scattering
• Visibility
14
Extinction
Definition: the attenuation of light along an axis resulting from scattering and/or
absorption
Particles
Extinction is dependent upon the chemical composition of particles as
well as particle size, shape, orientation and number.
Light
Extinction is also dependent upon the polarization and frequency of the
incident beam.
15
Extinction
Mathematically, how do we quantify the results of extinction?
dI
d 2
  IN
Qe
dL
4
dI
d 2
I I  0 N 4 Qe dL
0
I
I0
I
L
I
d 2
ln   N
Qe L
I0
4
I
e
I0
N
d 2
4
Qe L
Lambert-Beer Law
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Extinction
I
e
I0
N
d 2
4
Qe L
Lambert-Beer Law
For a monodisperse aerosol:
# concentration
e  N
d 2
4
Represents fractional loss in intensity per unit length
Qe
Extinction efficiency
Extinction coefficient (L-1)
Particle area
17
Extinction
Extinction Efficiency
Qe
radiant power scattered and absorbed by a particle
Qe 
radiant power geometrica lly incident on a particle
• Represents the relative ability of a particle to remove light from a beam compared with
blocking or interception by the projected area of the particle
• Does not have to approach 1… in fact:
0  Qe  5
Qe  QA  QS
For polydisperse aerosols:
e  
i
Ni di2 Qe i
4
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Example Problem
If:
I
 0.5 d p  0.7 mm
I0
L  2km Qe  2
What is: a) Number concentration in #/m3
b) Mass concentration in mg/m3 ?
N
I
e
I0
d 2
4
Qe L
Lambert-Beer Law
 ln 0.5
  e  3.466 x10  4 m -1  3.85x10 -13 m 2 N 2
2000 m
N  4.5 x108
particles
m3
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Example Problem
particles
4.5 x108
m3


  0.7 x10 6 m 3  1000 kg  109 mg 
mg





80
.
8

3

 m3  kg 
6
m


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Extinction
Recall:
Qe is f ( scattering , absorption, shape, d p ,  )
Therefore, there is no single equation to calculate
8  d 
Qe   
3  
4
Qe
for all dp
2
 m 1 
 2
 for d p  0.05mm
m 2
2

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Extinction
For dp > 4mm
Qe  2
“Extinction Paradox”
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Extinction Paradox
Based on the condition that extinction must be observed at long relative distances
dobs >>
10d 2

For coffee cup  100 km
(rarely observed condition)
10d 2

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Beers Law (Mass Concentration)
Cm  N p
d 3
6
Cm
N 3
d
p
6
I
 e  e L  e
I0

3CmQe L
2 pd
d 2
Cm  d 2 


e  N
Qe  3
d
4
4 

p
6
3CmQe
e 
2 p d
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Topics
•Definitions
• Extinction
• Scattering
• Visibility
25
Scattering
• Responsible for optical effects caused by aerosols
• Basis for many aerosol measuring instruments
• Important for visibility and radiation balance
Think of an aerosol particle as a light source with its own angular distribution of
light intensity
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Scattering
Physical basis
• The scattering of EM radiation by any system is related to the heterogeneity of that
system (the physics remains the same)
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Scattering
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Scattering
Two cases
In this case, the whole particle “sees” the same E-field
and scatters in phase
dp << 
(Rayleigh)
In this case, the E-field is not the same for the entire particle
and a complex interference pattern of scattered wavelets will result
dp ~ 
(Mie)
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Scattering
Rayleigh Region: dp<< 
 4 Nd p 6 m 2  1
2

Is 
1

cos
 Ii
4 2
2
8 r m  2
Unpolarized light
 4 Ndp 6 m 2  1
2

Is,2 
cos
 Ii
4 2
2
8 r m  2
Parallel to scattering plane
 4 Nd p 6 m 2  1
Is,1 
Ii
4 2
2
8 r m  2
Perpendicular to scattering plane
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 4 Ndp 6 m 2  1

Is, || 
cos 2 Ii
4 2
2
8 r m  2
Perpendicular Polarization
dp = 0.02 mm
Parallel Polarization
Intensity
 = 650 nm
Perpendicular Polarization
dp = 0.002 mm
Parallel Polarization
www.philiplaven.com
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Mie Scattering
Size Parameter
k=2
k = 10
k = f2L(ө,m,dp)
f||(ө,m,dp)
Mie Regime
Particle size
f||, fL
k = 10
k=
d p

k = 0.8
k = 0.8
Rayleigh Regime
W.C. Hinds, Aerosol Technology: Properties, Behavior and Measurement of Airborne Particles, John Wiley
and Sons, 1982
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Mie Equations
• At a distance r in the direction Ө from a spherical particle the
intensity of scattered light is:
I(ө) =
I 0 2  f ( , m, d p )   f ( , m, d p )|| 
Unpolarized light
8 r
2 2
IL(ө) =
I 0 2 f ( , m, d p ) 
I║(Ө) =
I 0 2 f ( , m, d p )||
4 2 r 2
4 r
2 2
Perpendicularly polarized
Parallel polarized
where f is a function of Ө, m and dp
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Mie Web Calculators
http://omlc.ogi.edu/calc/mie_calc.html
34
Incident light = 532nm
Dp = 0.7mm
k = 4.13
Dp = 0.2mm
m = 1.33
90º
m = 1.33
k = 1.18
Unpolarized
90º
Parallel
Perpendicular
180º
0º
270º
180º
0º
270º
http://omlc.ogi.edu/calc/mie_calc.html
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Mie Region dp ~ λ
Mars picture from Pathfinder
http://www.weatherstock.com/cloudcat.html
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Microchemistry: time dependence of and acid-base
reaction in a single optically levitated microdroplet
M. Trunk, J. Popp, M. Lankers, W. Kiefer
Institut fur Physikalische Chemie Der Universitat Wurzburg
Wurzburg, Germany
Chem. Phys. Lett. 264(1997) 233-237
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Experimental
• Optical levitation and Raman spectroscopy combined to study the
following acid-base reaction:
 NH4C10H9O2(s)
NH3(g) +
Capric Acid
• The appearance and position of MDRs in the Raman spectrum are
monitored to determine change in droplet size due to processes such as
evaporation and reaction.
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Experimental Schematic
Droplet generation chamber
nebulizer
Levitated droplet
Photodiode
lens
lens
mirror
t=0
lens
Observation chamber
argon-ion laser
  514.53 nm
lens
Quartz plate
spectrograph
mirror
mirror
mirror
Interference
filter
converter
Spectrum Accumulation time ~ 1 sec
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Optical Levitation
• The gravitational force exerted on a particle is balanced by photon
pressure produced by a vertically directed laser beam
Fg
Prad
E

c
where Prad is the radiative pressure, ΦE is the
energy flux, and c is the speed of light
Say for example, we have a particle with dp = 10 mm
Fg = mg = 5.14x10-12 N
Flaser
Fg/A = 163.6 Pa = Prad
ΦE = 4.91x1010 Jm-2s-1
Given  = 514.5nm, we need 3.88x1019 photons/sec to maintain levitation
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Morphology Dependent Resonance
• 355 nm light from Nd:YAG laser aligned with droplet edge optimizes coupling
into a MDR
• Internally reflected light can circulate around circumference of the droplet on
order of 10ns, provided an integral number of wavelengths circulate in the
droplet
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Results
• Peaks that appear in the
bulk case also
appear after reaction between
ammonia and the particle,
indicating formation of the
ammonium salt in or around
particle
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Raman Intensity (arb. Units)
C-H Stretching Region
Wavenumber (cm-1)
43
Laser Power Required for Levitation
• Negative peaks correspond
to MDRs
Experimental
Theoretical
Post-Reaction time
NH3(g) insertion
• After the reaction, the particle
size remains constant, and
the required laser power for
levitation will also remain
constant
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Wave number (cm-1)
NH3(g) insertion
Time (s)
• This plot shows the movement of MDR #2 as a function of time
• From 0-200 s, evaporation occurs. When NH3 is introduced, the MDR moves to
larger wavenumbers, indicating droplet growth via reaction
• After ~210 s, the MDR remains stationary, indicating droplet size change has
ceased, and formation of ammonium salt has occurred at the surface
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Topics
•Definitions
• Extinction
• Scattering
• Visibility
46
Visibility
http://www.dailymail.co.uk/news/worldnews/article-1215443/Australia-dust-storm-sweepseastern-coast.html
47
Visibility
Visible range  how far one can see in a given direction
Limited by:
1) Visual acuity
2) Contrast
Aerosol particles with 0.1 mm < dp < 1 mm reduce contrast by scattering light
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Object luminance
Contrast
B0  B '
C0 
B ' Background luminance
Inherent contrast
Luminance  luminous intensity per unit solid angle per unit area of surface
Units: lumens/m2•sr, cd/m2
r2
r
Total area =
4r 2
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Typical Contrast Values
Sky near the horizon:
Clear day  104 cd/m2
Overcast night  10-4 cd/m2
B0  B '
C0 
B'
White paper:
If B0  B'
Sunlight  25,000 cd/m2
Overcast night  0.03 cd/m2
C0  0
If B0  B'
C0  0
C0  1
For black object against
white background
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What makes distant objects lighter (lower contrast)?
Aerosol particles!
Inherent contrast  contrast that would exist w/o aerosol interference
CR = apparent contrast  contrast that results when aerosol particles (scatterers) are
present
BR  BR '
CR 
BR '
C R  C0
In the limit of no aerosol
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Koschmieder’s Law
Luminance Loss
(scattering + absorption)
Luminance Gain
(sunlight)
BR
L
dB
B Ba   e B  0 dx
0
 B  BR '   e L
e
CR   0
 BR ' 
C R  C 0 e  e L
52
Perfect viewing
53
Threshold of Brightness Contrast (ε)
C R  C 0 e  e L
  C0 e L
e v
54
SIZE-RESOLVED MEASUREMENTS OF LIGHT
SCATTERING BY AMBIENT PARTICLES IN THE
SOUTHWESTERN U.S.A
WARREN H. WHITE and EDWARD S. MACIAS
Chemistry Department, Washington University, St Louis, MO 63130, U.S.A
ROBERT C. NININGER
Aerovironment Inc., Monrovia, CA 91016, U.S.A
and
DAVID SCHORRAN
Desert Research Institute, Reno, NV 89506. USA
.4tmospheric
Environment, Vol. 28. No 5, pp. 909 -921. 1994
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• Goal  to look at extinction contribution from coarse particles
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