Nucleation: Formation of Stable Condensed Phase
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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