optical properties of aerosols

1LA on a smoggy day LA on a clear day

Optical Properties of Aerosols

ENVR 416Aerosol Technology

2

Topics

•Definitions

• Extinction

• Scattering

• Visibility

3

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

4

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 asDp << λ and Dp >> λ allow for simplifications to be made.

5

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

6

Index of Refraction

7

Index of Refraction

aimmaimm ''' 1

scattering absorption

Scattering portion measured with Snell’s Law:

1 2

'1m

'2m

1

2'2

'1

sinsin

mm

8

Index of Refraction

Absorption often measured via spectrophotemtry

aA 4

Bulk absorption

aimmaimm ''' 1

0A0A

For electrically conductive material

For most aerosol particles

9

Relative Index of Refraction (mr)

Used to describe a two phase system, i.e. a particle in air

p

m

m

pr V

Vmm

m

1m For air

1m For vacuum

mmr For aerosol particles in air

10

Intensity of Light

areaunitpowerradiantI

__

2m

W

detector

Incident light

scattered light

Light arriving at a surface:

11

Intensity of Light

Light from a point source:

anglesolidpowerradiantI

__

srW

A

4A

12

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

13

Electromagnetic TheoryLight 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

14

Topics

•Definitions

• Extinction

• Scattering

• Visibility

15

Extinction

Definition: the attenuation of light along an axis resulting from scattering and/or absorption

ParticlesExtinction is dependent upon the chemical composition of particles as well as particle size, shape, orientation and number.

LightExtinction is also dependent upon the polarization and frequency of theincident beam.

16

Extinction

Mathematically, how do we quantify the results of extinction?

I0 I

eQdIN

dLdI

4

2

I

I

L

edLQdNIdI

0 0

2

4

LQdNII

e4ln

2

0

LQdN eeII 4

0

2

Lambert-Beer Law

17

ExtinctionLQdN ee

II 4

0

2

Lambert-Beer Law

For a monodisperse aerosol:

ee QdN4

2

Extinction coefficient (L-1)Particle area

Extinction efficiency

# concentration

Represents fractional loss in intensity per unit length

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Extinction

particle aon incident lly geometricapower radiant particle aby absorbed and scatteredpower radiant

eQ

Extinction Efficiency eQ

• 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:

50 eQ

SAe QQQ For polydisperse aerosols:

i

ieiie

QdN4

2

19

Example Problem

If: 5.00

II md p m7.0 kmL 2 2eQ

What is: a) Number concentration in #/m3

b) Mass concentration in mg/m3 ?

LQdN eeII 4

0

2 Lambert-Beer Law

2m 3.85x10m 10466.3m 20005.0ln 213-1-4 Nxe

38 particles 105.4

mxN

20

Example Problem

3

9

3

36

38

mg 8.80

kgg 10

mkg 1000

6m 107.0particles 105.4 mm

xm

x

21

Extinction

),,,,( is pe dshapeabsorptionscatteringfQ

Recall:

Therefore, there is no single equation to calculate eQ for all dp

mmmdQe m

05.0dfor

21

38

p

2

2

24

22

Extinction

For dp > 4mm 2eQ “Extinction Paradox”

23

Extinction Paradox

Based on the condition that extinction must be observed at long relative distances

210d

For coffee cup 100 km(rarely observed condition)dobs >>

210d

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Beers Law (Mass Concentration)

6

3dNC pm

p

m

dCN

6

3

46

4

2

3

2 ddCQdN

p

mee

dQC

p

eme

23

dLQC

L p

em

e eeII 2

3

0

25

Topics

•Definitions

• Extinction

• Scattering

• Visibility

26

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 oflight intensity

27

Scattering

Physical basis

• The scattering of EM radiation by any system is related to the heterogeneity of that system (the physics remains the same)

28

Scattering

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ScatteringTwo cases

In this case, the whole particle “sees” the same E-fieldand scatters in phase

dp << (Rayleigh)

dp ~ (Mie)

In this case, the E-field is not the same for the entire particleand a complex interference pattern of scattered wavelets will result

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ScatteringRayleigh Region: dp<<

i2

2

2

24

6p

4

s Icos12m1m

r8Nd

I

i2

2

2

24

6p

4

s,2 Icos2m1m

r8Nd

I

i2

2

24

6p

4

1s, I2m1m

r8Nd

I

Unpolarized light

Parallel to scattering plane

Perpendicular to scattering plane

31www.philiplaven.com

Inte

nsity

= 650 nm

dp = 0.02 mm

dp = 0.002 mm

Parallel Polarization

Perpendicular Polarization

Parallel Polarization

Perpendicular Polarization

i2

2

2

24

6p

4

||s, Icos2m1m

r8Nd

I

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Mie Scattering

W.C. Hinds, Aerosol Technology: Properties, Behavior and Measurement of Airborne Particles, John Wiley and Sons, 1982

k = 10

k = 2

k = 0.8

k = 10

k = 2

k = 0.8

Rayleigh Regime

Mie Regime

Particle sizek =

pd

f||(ө,m,dp)

fL(ө,m,dp)

f ||, f

LSize Parameter

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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) =

IL(ө) =

I║(Ө) =

22

20

4),,(

rdmfI p

22

||2

0

8),,(),,(

rdmfdmfI pp

22||

20

4),,(

rdmfI p

Unpolarized light

Perpendicularly polarized

Parallel polarized

where f is a function of Ө, m and dp

34

Mie Web Calculators

http://omlc.ogi.edu/calc/mie_calc.html

35

http://omlc.ogi.edu/calc/mie_calc.html

Dp = 0.2mmm = 1.33

90º

Dp = 0.7mm

m = 1.33

Incident light = 532nm

Parallel

Unpolarized

Perpendicular

90º

0º180º

270º

0º180º

270º

k = 4.13 k = 1.18

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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 WurzburgWurzburg, 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:

NH3(g) + NH4C10H9O2(s)

• 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.

Capric Acid

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Experimental Schematic

converter

mirror

mirror

mirror

mirrorspectrograph

Quartz plate

lenslens

lensargon-ion laser

lens

Interferencefilter

514.53 nm

Levitated dropletPhotodiode

t = 0

Spectrum Accumulation time ~ 1 sec

Droplet generation chamber

nebulizer

Observation chamber

40

Optical Levitation

• The gravitational force exerted on a particle is balanced by photon pressure produced by a vertically directed laser beam

Fg

Flaser

cP Erad

where Prad is the radiative pressure, ΦE is theenergy 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

Fg/A = 163.6 Pa = Prad

ΦE = 4.91x1010 Jm-2s-1

Given = 514.5nm, we need 3.88x1019 photons/sec to maintain levitation

41

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

42

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

43

C-H Stretching Region

Wavenumber (cm-1)

Ram

an In

tens

ity (a

rb. U

nits

)

44

Laser Power Required for Levitation

Experimental

Theoretical

• Negative peaks correspond to MDRs

Post-Reaction time

• After the reaction, the particle size remains constant, and the required laser power for levitation will also remain constant

NH3(g) insertion

45

Time (s)

Wav

e nu

mbe

r (cm

-1)

• 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

NH3(g) insertion

46

Topics

•Definitions

• Extinction

• Scattering

• Visibility

47

Visibility

http://www.dailymail.co.uk/news/worldnews/article-1215443/Australia-dust-storm-sweeps-eastern-coast.html

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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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Contrast

''0

0 BBBC

Inherent contrast

Object luminance

Background luminance

Luminance luminous intensity per unit solid angle per unit area of surface

Units: lumens/m2•sr, cd/m2

r

r2

Total area = 24 r

50

Typical Contrast Values

Sky near the horizon:

Clear day 104 cd/m2

Overcast night 10-4 cd/m2

White paper:

Sunlight 25,000 cd/m2

Overcast night 0.03 cd/m2

''0

0 BBBC

If '0 BB

00 C

If '0 BB 00 C

10 C For black object against white background

51

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

''

R

RRR B

BBC 0CCR In the limit of no aerosol

52

Koschmieder’s Law

Luminance Loss(scattering + absorption)

Luminance Gain (sunlight)

RB

B

L

ea

dxBB

dB

0 0

L

R

RR

eeBBBC

''0 L

ReeCC 0

53

Perfect viewing

54

Threshold of Brightness Contrast (ε)

LR

eeCC 0veLeC 0

55

SIZE-RESOLVED MEASUREMENTS OF LIGHT SCATTERING BY AMBIENT PARTICLES IN THE

SOUTHWESTERN U.S.AWARREN H. WHITE and EDWARD S. MACIAS

Chemistry Department, Washington University, St Louis, MO 63130, U.S.A

ROBERT C. NININGERAerovironment Inc., Monrovia, CA 91016, U.S.A

andDAVID SCHORRAN

Desert Research Institute, Reno, NV 89506. USA

.4tmospheric Environment, Vol. 28. No 5, pp. 909 -921. 1994

56

• Goal to look at extinction contribution from coarse particles

57

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