Transcript TCDI - Aggie Research

Study of Vibrational Overtone Induced
Dissociation of Organic Acids From
Biomass Burning - Using Cavity Ring
Down Spectroscopic Techniques
Solomon Bililign,
Department of Physics
North Carolina Agricultural and Technical State University
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About UNC and NCA&T

Chartered in 1789, UNC was the first public university in the United
States and the only one to graduate students in the eighteenth
century. Today, UNC is a multi-campus university composed of all 16
of North Carolina's public institutions that grant baccalaureate
degrees, as well as the NC School of Science and Mathematics, the
nation's first public residential high school for gifted students.
North Carolina
Agricultural and Technical State University
NC Agricultural and Technical State
University
Description
North Carolina Agricultural & Technical State University is a public,
comprehensive, land-grant and "high research activity" university
committed to fulfilling its fundamental purposes through exemplary
undergraduate and graduate instruction, scholarly and creative
research, and effective public service. The University is accredited by
the Commission on Colleges of the Southern Association of Colleges
and Schools to award bachelor's, master's and doctoral degrees.
Since its inception as a land-grant university in 1891, North Carolina
A&T has had a rich tradition of leadership and achievement. Those
qualities are still evident today.
Carnegie Classification of Institutional Characterics
Basic Type
Doctoral-Research
Universities
Size and Setting
Medium four-year,
primarily residential
Enrollment Profile
Very high undergraduate
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FACTS ABOUT ISETCSC
Partner
Institutions
 North Carolina A&T State
University -Lead
 North Carolina State University
 University of Minnesota
 Fisk University-Tennessee
 California State University-Fresno
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 City University of New York
Nine
Academic
Departments
4
MISSION
Train students in NOAA scientific
areas and develop technology and
analysis techniques of global data
sets for improved understanding
of climate and environmental
change
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Aligned with the
NOAA Office of
Atmospheric Research
Thirty one
scientists and
engineers in
seven institutions
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&T
ISETCSC INTERDSICIPLINARY RESEARCH THRUSTS
TA-1 Departments
Physics
Chemistry
Oceanography
Electrical Engineering
Chemical Engineering
TA -II- Departments
Physics
Chemistry
Meteorology
Hydrology
Mathematics
Computational science
Environmental Science
Civil Engineering
c
Sun photometer
Thrust Area I
Sensor science
and technology
Thrust Area II
Global Observing
systems: numerical
and physical
research
CUNY
Scientific
Thrust Area III
Data
Environmental mining & Fusion
Distributed
Technology
architecture
Development
Fresno
1. Climate prediction
2. Pattern recognition for
seasonal hurricane
forecasts
Student field experience
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FISK
TA-III-Departments
Mathematics
Computer science
Physics
Electrical engineering
Alaska
Chesapeake Bay
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Thrust Area I
Sensor science,
Sensor technology
A-7
A-1 A-2 A-3 A-4 A-5
Sensor technology,
Eye safe Lidar, etc.
(CUNY)
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A-6
a) Cavity ring down spectroscopy
b) Negative ion proton transfer
mass spectroscopy
(Bililign, Fiddler)
Luminescent
Sensors (Assefa,
NCA&T).
A-8
RC(O)O2 + HO2
reaction branching ratios
(Hasson, Fresno State).
The Research Group
Fiddler
Begashaw
Cochran
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What is in the atmosphere?
 1950s: Atmosphere is 99.999% composed of N2, O2, CO2,
He, Ar, Ne. All are inert! (no chemistry). O3 in the
stratosphere. Trace CH4, N2O
 1960s: Recognized that reactive compounds in the
atmosphere were important even at extremely low levels.
 1970s: Regional air quality becomes a major research topic.
 1980s: Global atmospheric chemistry becomes a major
research topic.
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Agricultural and Technical State University
Emission Sources
Natural (Biogenic/Geogenic)
» Lightning (NOx) N2 NOx
» Volcanoes (SO2, aerosols)
» Oceans
» Vegetation
* Highly variable in space and time, influenced by
season, T, pH, nutrients…
FIRE
Anthropogenic
» Mobile sources
» Industry
» Power generation
» Agriculture
North Carolina
Agricultural and Technical State University
Source: Lecture notes
by
Christine Wiedinmyer
NCAR
Example: Emissions from fires
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Agricultural and Technical State University
Courtesy of Brian Magi, NOAA GFDL
What is emitted from fires?
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Agricultural and Technical State University
Urbanski et al., Wildland Fires and Air Pollution,
2009
Acids emitted in Biomass burning
Source: Veres, P., et al.
Journal of Mass
Spectrometry, 2008.
.
274(1-3): p. 48-55
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Global Emission Estimates:
Particles
Andreae and Rosenfeld, Earth Science Reviews, 2008
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Agricultural and Technical State University
Atmospheric Abundance
CH3OOH
H2
500
H2O2
Nitrogen
78%
Ethane
CO2
380
NH3
N2O
310
HCHO
HNO3
Ne
Oxygen
20%
H2O
Argon
1%
CO
He (5)
CH4 (1.8)
18
SO2
100
NOx
700
500
500
400
300
300
200
100
others
Ozon
30
ppm
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Agricultural and Technical State University
ppb
ppt
Image courtesy of Max-Planck-Institut für Meteorologie, Hamburg
14
7/21/2015
Biomass burning- Why
do we care?

Biomass burning is a significant source of atmospheric gases and particles

It occurs naturally in wildfires

It occurs when people clear forests for agriculture, cooking fuel.

Most abundant compounds emitted: water vapor, CO2, CO, and thousands of
additional compounds and aerosols.

Many of these compounds are poorly characterized due to analytical
challenges.

One poorly understood, but significant class of Volatile organic compounds
(VOC) present in biomass burning is gas-phase organic acids. They are
extremely difficult to measure because of their adsorptive nature.

Accurate measurement of optical properties( single scattering albedo) of
aerosols is crucial for quantifying the influence of aerosols on climate in
climate models and remote sensing applications
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Research activities related to
biomass burning in Bililign’s Group
 Negative Ion proton transfer mass spectrometry to Measure: a)
Acidities of gas-phase acids; b) Rate of H-transfer; c) Water cluster
characterization.
 Investigate vibrational overtone initiated photodissociation
processes that are significant sources of atmospheric radicals
using cavity ring down spectroscopy
 Measurement of the Henry's law coefficient and first order loss rate
of Isocyanic Acid in Water Solutions
 NEW work: measurement of optical properties of biomass aerosols
using cavity ring down spectroscopy
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16
Some Important Photolysis
Reactions
O2 + hn (l < 240 nm)  O + O
source of O3 in stratosphere
O3 + hn (l < 340 nm)  O2 + O(1D)
source of OH in troposphere
NO2 + hn (l < 420 nm)  NO + O(3P)
source of O3 in troposphere
CH2O + hn (l < 330 nm)  H + HCO
source of HOx, everywhere
H2O2 + hn (l < 360 nm)  OH + OH
source of OH in remote atm.
HONO + hn (l < 400 nm)  OH + NO
source of radicals in urban atm.
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17
Interest in OH Radical Formation
•Life time 10−9 seconds and a high reactivity
•The hydroxyl radical is often referred to as the "detergent" of
the troposphere and has an important role in eliminating some
Greenhouse gases dominant removal mechanism of for large
number of volatile organic compounds (VOCs)
•The rate of reaction with the hydroxyl radical often
determines lifetime of many pollutants.
•Major loss mechanism for methane
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THE DRIVING FORCE
The radiation from the Sun
drives several processes in
the atmosphere:
 Retention of short and
long-wave radiation.
 Photo-induced chemistry.
OH•
O3
O2
H2 O
NO
R
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R’•
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O2
R’OO•
NO2
R’O•
19
Atmospheric Photochemistry
 Ozone photolysis (λ<310nm)
 OH radical formation
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20
The Oxidative Power of the
Atmosphere
21
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Agricultural and Technical State University
+ OH•
Other products
Peractic acid:
+ OH•
•
K. A. Sahetchian, et al.,
Symp. Int. Combust. Proc.,
1992, 24, 637-643.
λ ≤ 698strong
nm
Relatively
Activation energy = vibrational overtone
168.0 ± 3.4 kJ/mol
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Direct Overtone Photolysis
 In polyatomic molecules the X-H stretching at considerably
higher frequency than other vibrational modes.
 They dominate the ground electronic vibrational overtone
spectrum-uncoupled from other vibrations
 These modes can have direct excitation from the ground
vibrational level to several excited levels (“overtone
transitions”).
 If the vibrational level accessed in this way lies above the
dissociation limit, dissociation is followed.
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VIBRATIONAL OVERTONE-INDUCED
PHOTODISSOCIATION
ν=5
E = hv
ν=4
ν=3
ν=2
ν=1
Figure adapted from a diagram by Mark M. Somoza
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24
Cavity Enhanced Spectroscopy
O’Keefe and Deacon 1988
• Light introduced and detected through a mirror.
• Light intensity inside of the optical cavity depends on a number of
factors, and can be much smaller or much larger than the incident
intensity
• Allows the measurement of absorption coefficient on an absolute
scale
• Effective or average path length may be very (very, very) long
Limited partly, but not exclusively, by mirror reflectivity
• So …. offers potential for very high sensitivity absorption (or
extinction) spectroscopy
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Agricultural and Technical State University
Beer’s Law (Lambert-Beer Law)
dz
I0
I
Light
Source
Detector
dI     I  dz
I

I0

dI
I
L
L
    dz
I ( z)  I 0 exp[   L ]
0
  Absorption (Extinction) Coefficient


 (cm-1) = NAbs (cm-3)  (cm2)
If  is known, N can be determined absolutely
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THEORY
I
z
Absorber [A]
LA
d
The detector receives a series of pulses separated by the
roundtrip time t = 2d/c with decreasing power from pulse
to pulse.
2 L
P0
After one pass through cavity: P1  T e
  is the absorption coefficient
 After each round trip the pulse power decreases by an
additional factor
R Exp (  2 L A )
2
T = 1− R− A << 1- Transmission is very small
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Agricultural and Technical State University
EBA
L-
THEORY
 After m rounds the power has decreased to:
Pm  (Re
Pm  P1 e
L A
)
2m
P1  [( 1  T  A ) e
2 m [ln R   L A ]
 P1 e
L A
]
2m
P1
 2 m [T  A  L A ]
If the detector time constant is large compared to the
pulse width it just detects the envelope of the pulse and
records an exponential decay with the decay time
d
c


1
With out a gas  = 0; The decay
T  A  LA
time will be lengthened to
d
0 
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c
T  A
EBA
L-
Cavity Ring-Down
Absorption (Extinction) Spectroscopy
1
Define:
RL 
1
d
LA

1
o

T  A  LA
d

T  A
d
c

LA
d
c
RL  1
1 
 

  [ A ] 
c    0 
Minimum detectable absorption is limited by the reflectivity R,
the unavoidable losses A of the resonator and accuracy of
measuring o and 1
1  R   
Minimum detectable absorption =


R= Reflectivity, L cavity length
L   o  min
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c
What is an Optical Cavity ?
“A region bounded by
two or more mirrors
that are aligned to
provide multiple
reflections of light
waves”
Triangular
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Bow-Tie
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30
Stable Optical Resonators
g2
R1 = R
R = mirror radius of curvature
d = mirror separation
“g parameter”
g 1,2 = 1 -
Unstable
d
R 1,2
Plane Mirrors
R=•
Stability condition
g1
0  g1g 2  1
Confocal
(d = R)
R
Spherical
(d = 2R)
2R
Unstable
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Agricultural and Technical State University
2
Gaussian Beams
Most optical beams propagating in free space are almost TEM,
field component lie in a plane perpendicular to the direction of
propagation
E z
 .E   t .E t 
0
z
The wave is propagating with a velocity = c. The major variation of the field
with z is a term of approximate form: exp(-ikz), with k = wn/c= 2pn/lo. Since
lo is quite small for optical frequencies, k is a large number.
If the beam has a finite diameter D the transverse divergence can be
approximated by Et/D ;So that the ratio of Ez/Et is very small.
Assuming a solution of the form E(x,y,z) = Eo (x,y,z) e-ikz and substituting
into the wave equation, and after some approximation
   2 ki
2
t
is the central equation for Gaussian beams
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
z
0
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Transverse Electric Modes (TEM)
TEM00
TEM10
 .E   t .E t 
 t   2 ki
2

z
TEM00
Longitudinal
TEMnm
Transverse
TEM11
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l (or n)
E z
z
0
0
TEM20
CONDITIONS
 mode matched Laser mode to the fundamental TEM00q resonator
mode..
 Mode of laser in resonance
With a mode of the cavity
 The relaxation time of the resonator must be longer than that of
excited molecules, i.e. R > 0.9999 and careful alignment.
 Due to the spectral bandwidth of the laser pulse many fundamental
resonator modes within the bandwidth dwR can be excited.
Therefore in order to resolve absorption lines the laser bandwidth
dwL should be smaller than the absorption width.
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EBA
L-
Resonances in Optical Cavities
Round trip phase shift =
2kd = n.2p
Note: k 2p/lw/c
Resonant
Non-resonant
Cavity Transmission
Free Spectral
Range (nq+1-nq )
T (n ) 
n 

Full Width Half Max

FSR

∆n
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(1  R )
2
2
2 2 pn d 
(1  R )  4 R sin 

 c 
c
FSR 
2d
c 1 R
2d p
R
Limitations on 0 (effective path length)
1
1.
Mirror Reflectivity
Best achievable is T ≈ 5 ppm
Strong function of l
2.
Cavity Length
3.
Rayleigh scattering

1 (1  R )

1
 0  
  Rayleigh  Mie 

 i 
c  L
RL
RL i

“Empty” =
Mirror + Rayleigh +
Mie
+ Interfering
Cavity Loss
Transmission Scattering
Scattering
Absorptions

Rayliegh  l-4 !
4.
Mie Scattering - Aerosol
Also scales steeply with l
Aerosol extinction can be
large!
5.
Interfering absorbers
1-2 specific to CRDS
3-5 common to any direct absorption measurement
but … particularly acute when
min < 10-8 cm-1
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RING-DOWN TIME
Number
density of
Absorption
absorber
1
1
coefficient
(molec•cm-3)
(cm-1)c  
I0
Intensity

0
11 1 
      N abs 
c  0 
Absorption
cross section
(cm2•molec)
Speed of light in air
I0/e
Without sample
With sample
Time
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Agricultural and Technical State University
37
Components of a CRD setup
Positionin
g mirrors
Optical cavity with two
highly reflective mirrors
(~99.995%)
Translated light intensity
into an electronic signal
Photomultiplier
Tube (PMT)
Telescope
Matches the
lasers pulse
38
and optical
cavity modes.
Optical
Isolator
This protects the
laser from back
reflection
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Dye Laser
Pulsed laser
source with
variable
wavelength
light.
Data
Acquisition
Determines
Tau values
EXPERIMENTAL SETUP
Iris
Nd:YAG
Lens 1
Lens 2
Turning
Mirror
Pressure
Transducer
Sample Flow
Purge Flow
Collimator
Optical
Fiber
PMT
Pin
Hole
Dye Laser
HeNe Laser
Silver
Turning
Mirrors
Polarizer
Waveplate
Ring-down Cavity
Purge Flow
PC
Fitting
Zinc
Lamp
Copper Tubing
Mirror Mount
and Bellows
Turning
Mirror
Teflon Tubing
Phototube
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Bandpass
Filter
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University
UV Cell
Detector
Exhaust
Flow system
Bubbler
Inline
Filter
MFM
Sample
Ring-down Cell
N2
MFM
UV Cell
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40
CRDS SETUP
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CONTROL AND DATA ANALYSIS
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INSTRUMENT SPECIFICATIONS
 Ring-down cavity length: 91 cm
 Typical ring-down times at 620 nm: ~100 μs
 Dye laser wavelength accurate to ±0.02 nm
against HITRAN
 The minimum detectable extinction coefficient
from taking the limit at τ approaches τ0
αmin~3.5*10-9 cm-1•Hz-1/2
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CALIBRATION AND COMPARISON WITH WATER
Averaged CRDS Spectra
HITRAN
-24
0.8
2
Absorption Cross Section (cm /molecule)
1.0x10
0.6
0.4
0.2
0.0
629.0
629.2
629.4
629.6
629.8
630.0
Wavelength (nm)
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44
Quantifying Photolysis Processes
Photolysis reaction:
AB + hn  A + B
Photolysis rates:
Photolysis frequency (s-1)
J=
l F(l) (l)f(l) dl
(other names: photo-dissociation rate coefficient, J-value)
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CALCULATION OF PHOTOLYSIS
COEFFICIENTS
J (s-1) = l F(l) (l)f(l) dl
F(l) = spectral actinic flux, quanta cm-2 s-1 nm-1
 probability of photon near molecule.
(l)absorption cross section, cm2 molec-1
 probability that photon is absorbed.
f(l)photodissociation quantum yield, molec quanta-1
 probability that absorbed photon causes dissociation.
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Difficult: must measure absolute change in n (products)
and I (photons absorbed)
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Spectral Irradiance, L
Typical light ray striking a thin layer of air in
the atmosphere adapted from Madronich, 1987..
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Actinic flux
solar zenith angle
Watts m-2
p
p 2p
2p 2
E 
  L ( ,  ) cos  sin  d  d 
0 0
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F 
  L ( ,  ) sin  d  d 
0 0
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ABSORPTION CROSS SECTION
J = ∫[σ(λ)•Φ(λ)•I(λ)]dλ

Data was collected by flowing diluted and undiluted
acetic acid sample, which varied the concentration.

The number density of monomeric acetic acid in the
UV cell (nUV,M) was calculated from the UV absorbance
(A) in each experiment, the known equilibrium
constant for dimerization (Keq), and the known
absorbance cross sections for acetic acid monomer
and dimer at 214 nm.
A  ( U V , M nU V , M   U V , D nU V , D )
nU V , M  
K eq 
PD
2
 7 . 1  10
PNorth
M Carolina
9
 UV ,M
2 U V , D K eq
2

 U V , M  4 A  U V , D K eq
2
2  U V , D K eq
 7705 
exp 

 T 
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ABSORPTION CROSS SECTION
J = ∫[σ(λ)•Φ(λ)•I(λ)]dλ

Dilution was taken into account…
Faux/2
Fsamp+Fdil; nin
nUV
Faux/2
nRD
n R D , M  nU V , M 

Fsam p  Fdil  ( F purge / 2)
and the cross section was determined.
RL
n R D , M c air

Fsam p  Fdil  F purge
1
1 
 

 0 
The
dimer cross section was assumed to be zero.
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RESPONSE OF THE RING-DOWN CAVITY FOR
THE DILUTED AND UNDILUTED ACTIC ACID
RUNS
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CALCULATED CROSS SECTION FOR ACETIC
ACID MONOMER
10-Point
Rectangular
Smoothed Mean
± 1σ
Mean ± 1σ
Mean
Maximum cross section:
1.84×10-24 cm2•molecule-1
10Integrated cross section:
Point
(5.23±0.73)×10-24 cm2•moleculeSmooth
1•nm
ed
(1.38±0.19)×10-22 cm2•moleculeMean
1•cm
-1
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COMPARISON WITH OTHER SYSTEMS
Molecule
Integrated Cross
Section
(×10-22 cm2
•molecule-1•cm-1)
References
C2H4O2
1.38 ± 0.19
this work
HNO3
2.57 ± 0.24
Brown, et al. 2000
CH3OOH
2.1 ± 1.3
Homitsky, et al. 2004
H2SO4
2.38 ± 0.57
Feierabend, et al.
2006
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CONCLUSION
 An ultra sensitive CRDS instrument with pressure and
temperature monitoring capabilities was built.
 The instrument was used to measure the fourth O-H
overtone absorption cross sections for the acetic acid
monomer.
 The results for the monomer are similar to what has been
previously reported for other systems.
 This measurement aids in quantifying the contribution of
overtone induced processes for the fate of the acetic
acid in the atmosphere.
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Solution Compositions
Peracetic Acid Mixture
+
Hydrogen peroxide
Peracetic acid
(AcOOH, 9%)
+ H 2O
Acetic acid
Water(AcOH)
(H2O)
Aqueous Hydrogen Peroxide
+ H 2O
Hydrogen peroxide
(5%)
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Agricultural and Technical State University
Water
(95%)
RESPONSE OF THE RING-DOWN CAVITY FOR
THE DILUTED AND UNDILUTED PERACTIC
ACID RUNS
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Peracetic Acid Mixture and Aqueous
Hydrogen Peroxide
All of the peaks
in this region can
be attributed to
water.
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Agricultural and Technical State University
I. Begashaw,
et al.,Aqueous Hydrogen Peroxide
Peracetic Acid Mixture
and
J. Phys. Chem. A
2011, 115, 753-761,
S. Brown, et al., J. Phys. Chem. A, 2000, 104, 4976-4983, 10.1021/jp000439d.
10.1021/jp1087338.
Missing
feature
Expected absorption from H2O2 not present.
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Further Work for Increasing Sensitivity
 Increase the limits of detection
 Increase the cavity length, causing longer ring-down
times
 Switch the bath gas from N2 to He (decreases Rayleigh
scattering)
 Isolate peracetic acid
 Oxidizing hydrogen peroxide into oxygen
 Increasing the pH so that acetic acid is mostly
deprotonated and kept from entering the gas phase
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Increasing the Cavity Length
Iris
Nd:YAG
Polarizer
Lens 1
Pin
Hole
Lens 2
Turning
Mirror
Dye Laser
HeNe Laser
Silver
Turning Collimator
Mirrors
Fitting
Pressure
Transducer
Optical
Fiber
PMT
Waveplate
Wavemeter
Purge Flow
Ring-down Cavity
Purge Flow
PC
Zinc
Lamp
Copper Tubing
Teflon Tubing
Mirror Mount
and Bellows
Turning
Mirror
Sample
Flow
Phototube
Detector
UV Cell
Bandpass Filter
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Agricultural and Technical State University
Exhaust
Resulting Increased Sensitivity
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Agricultural and Technical State University
Improved Measurement of the Peracetic Acid Mixture
AcOH
?
Absorption “shelf”
missing absorption or scattering
Broadband
Causes:
HO
1. Scattering by particles (Mie)Filter was used 2
2. Scattering by gasses (Rayleigh)
The isolation of peracetic acid from other
Gas density only changed by 0.5% (decreased)
constituents is clearly needed.
3. Incomplete mixing of gases with different refractive
indices
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Agricultural and Technical State University
Isolation of Peracetic Acid
+
Hydrogen peroxide
Water(H2O2, 6%)
(H2O)
+ H 2O
Acetic acid
(AcOH)
→ O2(g)
+ SO42– →
H2O2 + Ce4+ + SO42–
AcOOH + Ce4+
Peracetic acid
(AcOOH, 32%)
+ Ce3+ + H2SO4
Expected end point: light blue solution (due to ferroin indicator)
Actual product: yellow liquid with a white precipitate
• Reaction too slow to be practical (>5 hrs)
• Strange precipitate, unknown reaction product
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Another isolation scheme is needed
NEW work: measurement of optical
properties of biomass aerosols
using cavity ring down
Spectroscopy
Sujeeta Singh, Marc Fiddler
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Radiative Forcing
Incoming solar ~340 W m-2
1827 – Fourier recognizes atmospheric heat
trapping
1860 – Tyndall measures infrared spectra
1896 – Arrhenius estimates doubling of CO2
would increase global temperatures by 5-6 oC
Changes since 1750:
long-lived gases ~ 3 W m-2
ozone ~ 0.4 W m-2
aerosols and clouds ~ -1 W m-2
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Agricultural and Technical State University
IPCC, 2007
Many different types of aerosols
 Size distributions
 Composition (size-dependent)
Aerosol Extinction
Extinction:
Single particle scattering Albedo:
 ext   scat   abs
w 
 scat
 ext
Need to determine aerosol
 optical properties:
(l) = optical depth
wo = single scattering albedo
P(Q) = phase function or g = asymmetry factor
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Measurement of optical properties:
Extinction
Beer’s Law
I
I0
Extinction Coefficient
p Nd p Q e
2
 exp(  e L )
 e  NA p Q e 
(monodisperse aerosols)
Extinction Efficiency
Qe 
4
radiant power scattered and absorbed by a particle
radiant power geometrica
L North
= path
length,
Carolina
lly incident
on the particle
N = number of particles per volume
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Figure 3. instrumentation for handling aerosols Spindler, C.; Riziq, A. A.; Rudich, Y. (2007). Aerosol
Sci. Technol.,41, 1011
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Nephelometer: Measuring light
scattering
The nephelometer is an instrument that measures aerosol light
scattering. It detects scattering properties by measuring light scattered
by the aerosol and subtracting light scattered by the gas, the walls of
the instrument
and the background noise in the detector.
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NEW AEROSOL RESEARCH FACILITY
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Mie Scattering Theory
For spherical particles, given:
Complex index of refraction: n = m + ik
Size parameter:
 = 2pr / l
Can compute:
Extinction efficiency
Qe(, n)
x
pr2
Scattering efficiency
Qs(, n)
x
pr2
Phase function
or asymmetry factor
P(Q, , n)
g(, n)
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Mie Scattering with CRDS
A. Pettersson et al. (2004),J. Aerosol Sci., 35, 995-1011
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Thank you
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