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![Page 1: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/1.jpg)
Aerosol Self Nucleation• SO2 nucleation Experiment
(over the web) at the UNC smog chamber facility in Pittsboro
• Homogeneous Nucleation Theory
• Some examples
• Global Calculation of nucleated particles from SO2 going into the atmosphere/year???
![Page 2: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/2.jpg)
Aerosol Self Nucleation• Why are we interested?
Contribute to natural aerosol concentrations
global warming implications health implications serve as sites for the sorption of other gas
phase compounds-toxic
• Usually they are very small pyrene (gas) .0007 m
viruses .002 -.06 m
if condensationnuclei start asclusters of 3-8 .001- .005 m molecules
![Page 3: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/3.jpg)
If gases are coming together to form particles or clusters
• free energy of the system
• surface tension
• level of gas saturation
• amount of cluster growth
• vapor pressure of the gas molecules
![Page 4: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/4.jpg)
Free energy and surface tension
• What is surface tension if a liquid has a meniscus surface we could define a
force per unit length, t , that the liquid surface moves from the flat surface of the liquid
t x l = force
force x distance = work if the distance is dy work = t x l x dy
dy x l has the units of area
work/area = t = surface tension
the free energy of the meniscus moving from position a to b or dy:
G = H -TS ; H = work + heat
G = t x A + heat -TS
![Page 5: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/5.jpg)
Free energy and surface tension
• G = t x dA + heat -TS
• often the free energy of just the surface is given as:
GS = t x A
• for a spherical liquid nuclei or small cluster
GS = 4r2 x t
• for gas molecules forming a small cluster where
Nl gas molecules -> oooo
• the change in total free energy is the change in going from a pure vapor to a system that contains particle embryos
• GT = Gembryo system - Ggas vapor
![Page 6: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/6.jpg)
Free energy and surface tension
• GT = Gembryo system - Ggas vapor
• let g = chemical potential of the remaining gas, l the liquid or embryo system; NT will be the total number of starting gas molecules; after embryo formation the Ng = # of gas molecules, so,
Ng = NT - Nl
where Nl the number of liquid embryo molecules
GT = g Ng + l Nl+ 4r2 x t
- NT g
Substituting NT = Ng + Nl
GT = Nl {l - g} + 4r2 x t
![Page 7: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/7.jpg)
Free energy and surface tension• GT = Nl {l - g} + 4r2 x t
• the number of molecules in a liquid cluster, Nl , is the volume of the cluster divided by the volume of one molecule, vl
• where Nl = 4/3 r 3 / vl
GT = 4/3 r 3 / vl {l - g} + 4r2 x t
the Gibbs Duhem equation describes the change in chemical potential with vapor pressure
d = v dp; since vg>>> vl
d {l - g} = vg dP
{l - g} = - kT ln P/Po
![Page 8: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/8.jpg)
dU = SdT+ TdS -Vdp-pdV+
For a closed system which only does pressure volume work
subtracting
0 = SdT -Vdp+
At constant temperature, one obtains the Gibbs-Duhem Equation for gases
i
k
iinpVTSU
1
ii
k
i i ii
k
dn n d
1 1
i
k
iidnpdVTdSdU
1
n di ii
k
1
d {2- 1} = vg dP
![Page 9: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/9.jpg)
Free energy and and saturation {l - g} = - kT ln P/Po
define P/Po as the saturation ratio S GT = 4/3 r 3 / vl {l - g} + 4r2 x t
GT = -4/3 r 3 / vl {kT ln S}+ 4r2 t
A plot of GT vs particle diameter for different saturation ratios >1,shows it to go thru a maximum and then fall; this max is called the critical diameter (or radius rc)
differentiating and solving for rc
rc= 2t vl/(kT ln S);
ln S = 2t Mw/(RT rc); molar units (Kelvin equation) what happens to vapor pressure over a particle as r decreases and why??
ln P/Po = 2t Mw/(RT rc);
![Page 10: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/10.jpg)
An expression for cluster #, Nl If we go back to
GT = -4/3 r3c
/ vl {kT ln S}+ 4r2 t
and take the derivative with respect to r again, and set this equal to zero, one gets:
4r2c
/ vl {kT ln S}= 8r t
mulyiplying both sides by r/3 we get something that looks like the cluster # Nl where Nl = 4/3 r 3 / vl
since rc= 2t vl /(kT ln S)
substituting we obtain a valve for Nl , the number of molecules in a cluster with a radius of rc and as function of saturation
Nv
3 2 3
3 l
2
3 ( )kT lnS
![Page 11: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/11.jpg)
Estimate cluster rc and the cluster #, Nl
substituting molar values in the Nl expression one obtains:
rc = 2t Mw/(RTln S );
critical #s (Nl) and rc for 3 organics
saturation ratio2 3 4 5
acetone (# Nl) 265 67 33 21 (rc in nm) 2.0 1.3 1.0 .8
benzene (# Nl) 706 177 88 56 (rc in nm) 3.0 1.8 1.5 1.3
styrene (# Nl) 1647 413 202 132 (rc in nm) 4.2 2.7 2.1 1.8
NM wt
R T Sl
32 3 2
3 2 3
( ln )
![Page 12: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/12.jpg)
A Flow reactor study-pinene + O3 nucleated
particles
![Page 13: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/13.jpg)
y = 0.1125e100.92x
R2 = 0.9508
0.10
1.00
10.00
100.00
1000.00
10000.00
100000.00
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14Reacted -pinene conc. (ppmV)
Parti
cle
conc
. (#/
cm3 )
Exp. 1Exp. 2Exp. 3Exp. 4allExpon. (all)
A Flow reactor study-pinene + O3 nucleated
particles
![Page 14: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/14.jpg)
Nvt
l 3 2 23
3 1
3( )kT lnS
1. Assume the number of nuclei/cc formed is proportional to 1/Nl
Nl =number of molecules in a cluster
-pinene seed products that form are proportional to their saturation ratio
nucle i / cc ( )kT lnS 3
![Page 15: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/15.jpg)
0.1
1
10
100
1000
10000
100000
0 2 4 6 8 10 12
Saturation rato
prt
icle
s/c
c
Plot of 1/Nl vs S
![Page 16: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/16.jpg)
-pinene and O3 data vs. model
0.00.10.20.3
0.40.50.60.7
7.0 7.5 8.0 8.5 9.0
time hours (EST)
pp
mV
A-pinene data
O3 data
O3 model
a-pinene model
Do “high” saturation ratios of the products really occur??
Mar 11, 1996: model particle products
0.0
0.2
0.4
0.6
0.8
7.5 8.0 8.5 9.0
Hours (EST)
ppm
V
seed 1
diacid
pinacid
pinald
oxypinald
pinalic
oxypinacid
![Page 17: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/17.jpg)
CHOOO
CH3
O
OO
Criegee2
Criegee1
O
OO
-pinene
O3
COOHCOOH
pinic acid
+ other
products
O
pinonic acid
CHOO
COOH
+ CO, HO2, OH
COOHO
norpinonaldehyde
norpinonic
acid
Mechanism
![Page 18: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/18.jpg)
Gas phase pinonaldehdye
OO
mg
/m3
Time in hours EST
![Page 19: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/19.jpg)
Particle phase pinonic acid
model
pinonic acid data
norpinonic acid
OH
pinonic acid
O=o
![Page 20: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/20.jpg)
If we can calculate the saturated
vapor pressure, Po ??
We can compare it to the partial pressure of compounds predicted or measured in the gas phase and
estimate a P/Po
ln ( ) . (ln )]PTT
TT
o b b 19 1 8 5
Where Po is in atmospheres
![Page 21: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/21.jpg)
Boiling points can be estimated based on chemical structure (Joback, 1984)
Tb= 198 + Tb
T (oK)
-CH3 = 23.58 K-Cl = 38.13-NH2 = 73.23
C=O = 76.75CbenzH- = 26.73
Joback obs (K) (K)
acetonitrile 347 355acetone 322 329benzene 358 353amino benzene 435 457benzoic acid 532 522toluene 386 384pentane 314 309methyl amine 295 267trichlorethylene 361 360phenanthrene 598 613
![Page 22: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/22.jpg)
Time (min) Sat ratio
Time vs Sat ratio
0.00
3.00
6.00
9.00
0.00 2.00 4.00 6.00 8.00
time in min
P/P
o
![Page 23: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/23.jpg)
A a remote–web nucleation experiment at the smog chamber
Do rural concentrations of SO2 nucleate in sunlight??
![Page 24: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/24.jpg)
The Chamber had two sides
Or Darkness
Formaldehyde
SO2
300 m3 chamber
Teflon Film walls
NO &NO2
![Page 25: Aerosol Self Nucleation SO 2 nucleation Experiment (over the web) at the UNC smog chamber facility in Pittsboro Homogeneous Nucleation Theory Some examples.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649eca5503460f94bd8647/html5/thumbnails/25.jpg)
Adding SO2 to the Chamber
• SO2 ppmtank x volume from tank =
SO2 ppmchamber x chamber volume
• Tank flow is 5 l/min; so how long do we leave the tank on to get 0.02 ppm SO2 in the chamber, if the tank is 1000 ppm????