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???

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

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

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

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

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

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

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

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);

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

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 )

A Flow reactor study-pinene + O3 nucleated

particles

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

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

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

-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

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

Gas phase pinonaldehdye

OO

mg

/m3

Time in hours EST

Particle phase pinonic acid

model

pinonic acid data

norpinonic acid

OH

pinonic acid

O=o

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

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

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

A a remote–web nucleation experiment at the smog chamber

Do rural concentrations of SO2 nucleate in sunlight??

The Chamber had two sides

Or Darkness

Formaldehyde

SO2

300 m3 chamber

Teflon Film walls

NO &NO2

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????