Nucleation: Formation of Stable Condensed Phase

Homogeneous – Homomolecular H2O(g) H2O(l)

Homogeneous – Heteromolecular nH2O(g) + mH2SO4(g) (H2O)n(H2SO4)m

Heterogeneous HomomolecularnH2O(g) + Xs/l (H2O)nXs/l

Not relevant to atmosphere

Appears to be important in atmosphere

Certainly happens (clouds)

New Particle Formation in Atlanta

Kinetics of Cluster Formation

i i+1 i+2i-2 i-1i-3

Formation Rate of Cluster i:ki-1N1Ni-1 + kri+1Ni+1

kri+1

Loss Rate of Cluster i: kiN1Ni + kriNi

dNi/dt = ki-1N1Ni-1 + kri+1Ni+1 - kiN1Ni - kr

iNi

Because N1 >>Ni dNi/dt = kfi-1Ni-1 + kr

i+1Ni+1 - kfiNi - kr

iNi

Describes time rate of change of cluster i as system adjusts to some initial perturbation and approaches steady state

Steady State Cluster Flux

dNi/dt = kfi-1Ni-1 + kr

i+1Ni+1 - kfiNi - kr

iNi = 0

At steady state, the concentration of cluster i no longer changes with time.

But, there is a steady state flux of molecules from one cluster to another as the system approaches equilibrium

kfi-1Ni-1 - kr

iNi = kfiNi - kr

i+1Ni+1 = J

J describes the net rate of formation of any cluster size and hence, for S > 1, it is the nucleation rate

Question

What is J, once equilibrium has been achieved?

Does it make sense to calculate a nucleation rate by assuming the cluster distribution is at equilibrium?

Which is larger, kfi or kf

i+1?

Forward and Reverse Rate Constants

Forward Rate Constant: “reaction” of monomer with cluster i

A + Ai Ai+1

From kinetic theory: Rate proportional to collision frequency

1/

21/ 1ii iZ N N

1/

21/ 1i

fi ik N

1/

22 4i A ir r

Reverse Rate Constant: evaporation from cluster i

More challenging, but should only depend on T and ri

Connect to Kelvin Equation

Thermodynamics of Cluster Formation

*iG

*

2

lnl

iR kT S

Recall Kelvin Equation Derivation• Obtained from examining free energy change associated with increasing size of arbitrary particle

3

2 44 ln

3i

i il

RG R kT S

Ri*

S<1

S>1

Gi*A Ai**iG

Critical Radii and Numbers

*

2

lnl

iR kT S

S=2 dynes cm-

1

vlx102

3 cm3 molec-

1

Ri* Ang

i*

H2O 72 3 15 482

Acetone

23 12.3 20 265

Ethanol 22 9.7 15 147

Binary Nucleation

iG

*iG

is now a surface

is now a saddle point where na* and nb* are such that* * 0

b a

i i

a bn n

G G

n n

H2SO4-H2O

New Particle Formation in the Atmosphere

Observed in continental and marine boundary layers, forested regions, polluted urban areas, and cloud outflow

Tend to occur over 100’s of km, with a frequency of 5 –40% of days.

Events tend to be in morning to midday suggesting a photochemical process with possible influence from boundary layer dynamics

Wide-spread phenomenon

Regional and frequent

Photochemical in nature

Impacts of New Particle Formation

Formation events tend to increase aerosol number concentrations by factors of 2-10.

Newly formed particles (<10nm) tend to grow into accumulation mode particles (100 nm) at a rate of 1-20 nm/hr (fast).

Accumulation mode particles act as cloud condensation nuclei such that new particle formation may impact cloud cover and direct scattering of solar radiation.

Nuclei vs Measured New Particles

A typical stable nuclei will have a radius <~ 1nm

Size measurements are limited to particles with r > 3nm

Thus significant post-nucleation growth will have occurred before measurement

What formed the nuclei? What contributed to growth?

When Will New Particle Formation Be Observed?

Formation of stable clusters

Rapid growth of nuclei to observable size with slow loss of nucleated particles

condensational growth to observable sizes

coagulation loss

monomer

condensation sink

i*

Existing Aerosol Limits Observation of New Particle

FormationNucleation Rate will scale with N1

12 2 4het

dNP L k OH SO k H SO

dt 2

2 4 sshet

k OH SOH SO

k

khetAvailable surface area

Net production of observable new particles

Pobs = Condensational Growth Rate – Coagulation Sink

Area of nuclei relative to area of preexisting aerosol important for Pobs>0

The “McMurry” NumberWhen coagulation of nuclei with preexisting aerosol dominates their condensational growth, new particle formation will not be observed even though nucleation may be occurring.

1

1 1 1 1 11 1

44 4

j j

jj

j j j

NA A A

L f jN N N N

nuclei j coagulation loss rate

condensational growth rate (jj+1)

L: McMurry number

L = 1: equal # condensing vapor molecules lost to preexisting aerosols as contribute to nuclei growth

QuestionsWhen should new particle formation be observed, when L>1 or L<1?

L>1 not observed; L<1 observed

How do we interpret the <10nm particles that appear when L>1?

What are the key players to nucleation and growth?

H2SO4-NH3-H2O: Binary or Ternary nucleation

H2SO4-Organic acid complexes:

Location dependent? Zhang, et al. 2004

Mass Spectrometer to Measure New Particle Composition

What’s in those new particles?

Mass spectrometry of new particles suggests H2SO4 and NH3 are most important constituents. No organics were observed.

Hygroscopicity and Volatility Apparatus

size select

humidify or volatilize

resize

If hygroscopic: will grow with humidification

If volatile: will shrink with heat

These new particles should take up water like ASHygroscopicity of New Particles

Consistent with GF for small ammoniated sulfates measured in lab

Volatility measurements also suggest no significant organic component.

OC volatile @~ 100oCSulfates involatile