1. Homogeneous nucleation: freezing of supercooled water Exponential dependence arises from energy term
T dependence from this term

2. Evaluating “threshold” conditions
if we have a certain volume Vd of supercooled water, say that of a cloud droplet or a raindrop, at what temperature should we expect it to freeze?
First, note that only a single nucleation event suffices to cause the entire volume of the drop, regardless of size, to freeze.
The relevant variable is therefore the nucleation frequency ωi = Vd Ji (T ), the product of liquid volume and nucleation rate, not Ji (T ) alone.
A larger liquid volume, Vd , implies that a smaller volumetric rate, Ji (T ), is needed to get the same freezing effect; equivalently, the chance of finding one critical ice embryo in a large volume is greater than that in a small volume of supercooled water.
The choice of a “significant” nucleation rate, and an estimate of threshold conditions, thus depends on the volume of supercooled liquid, as well as the temperature.
A nucleation frequency of ωi = 1 s−1 is often chosen as a reasonable criterion for homogeneous freezing

3. Threshold conditions and rates
Once the threshold condition has been met the drops don’t all freeze at once. The process is visualized as stochastic (non-deterministic)
Consider N0 drops, each with identical volume Vd at the temperature T
All begin unfrozen at t=0; how many have frozen at time t?
The

4. Threshold temperature
How do we expect TF to change with cooling rate gc?

5. Threshold temperature depends on drop size, cooling rate
What cloud regime is this process active in?

6. -56 ˚C
6 – 12 km
-24 ˚C
2 – 6 km
2 ˚C
0 – 2 km

7. Heterogeneous freezing -40 C
-40°C: This temperature marks the “lower limit”, temperature wise, for supercooled water.
Heterogeneous
freezing
Fletcher 1962
-40 C
Compare curves:

8. Freezing of haze droplets
Haze droplets are smaller than cloud droplets
And contain solute
What is the effect on freezing?
dotted lines are solutions
(proportional to pure water curve, assuming Raoult’s Law)
where solution curves cross the ICE line, there is an equilibrium (ice and solution have same vapor pressures)
MELTING POINT DEPRESSION
pure water
pure ice (solid line)
Notice the DTm points follow the ICE line

9. Freezing of haze droplets
Trace out all the temperatures that give the melting point depressions as a function of solution composition
Then instead of vapor pressure if ice [in equilibrium with the solution], make y axis vapor pressure of ice DIVIDED BY the vapor pressure of pure (supercooled) water at the same T
 A WATER ACTIVITY
Relative humidity

10. What conditions allow haze to freeze?
We have to supercool solution drops MORE than pure water drops
OR, we can view this differently:
At low temperatures, we don’t have to supersaturate with respect to water (ie form a conventional cloud) before freezing can occur: we just need to dilute the haze enough to support freezing according to “Koop’s curve”
So in a rising parcel, RHw rises and haze particle dilutes, then freezes when it crosses the Koop line
pure water
Relative humidity
What cloud regime is this process active in?

11. Koop et al. (2000) concept
Koop et al. found that [threshold] freezing occurred when the water activity was “offset” by a constant amount Daw = (dark line; applies to drops of ~microns diam)
So, since we know Tm(aw), the freezing temperature of solutions is
Tf = Tm(aw – Daw)
Apparently this is independent of particle composition!
Daw = 0.305
that is, haze particles should dilute to similar RHw and then freeze, regardless of what the solutes are – but size matters
[For chosen threshold]

12. Biomass burning aerosol
Lab data from CSU group
Biomass burning aerosol

13. More lab tests at low temperature
Arizona Test Dust
SOA-coated ATD
[Koehler, 2008]

14. Effective freezing temperature parameterization
Alternative treatment due to Sassen and Dodd (1988) and DeMott (2002)
Focuses on T depression instead of shifts in aw
DThf = l DTm
l = 1.7 was suggested by Sassen & Dodd; DeMott found it varied 1.2 – 2.2

15. Homogeneous freezing of solution droplets (haze particles) occurs in cirrus clouds
Koop et al. (2000) showed how relation between melting and homogeneous freezing temperatures (T50%) collapse to reveal relation with water activity. Schematic depiction given here.
Effective freezing temperature parameterization relates homogeneous freezing temperature depression (below pure water) to constant factor on melting temperature. lhom ≈2, but varies to some extent for different solutes.
3 hypothetical solution droplets
melting
melting
freezing
freezing
Dawhom ~ 0.33
Thfo
lhomDTm
Nucleation rate Jhf or freezing Thf are proportional to Dawhom = aw – aw,ice. Underpinning may be via similar solute and pressure impacts on H-bonding network (Baker and Baker, 2004)
Archuleta et al. (2005) relate Dawhom and l parameterizations (reproduced under Creative Commons license of Atmos. Chem. Phys.)

16. Other mechanisms? What happens out here, warmer than ~-40 C?
Arizona Test Dust
What happens out here, warmer than ~-40 C?
(do we have to form drops first?)

17. Homogeneous nucleation of ice by sublimation
Formation of ice by vapor molecules going directly to the ice phase—very similar to homogeneous nucleation of water from the vapor.
Consider hexagonal embryo
Can immediately write down
p = ambient vapor pressure
ps = equilibrium vapor pressure over solid
This type of nucleation not likely to produce ice particles in the Earth’s atmosphere
T < -60°C RHice ~ 150%
Mother-of-pearl clouds in stratosphere?
0.025Jm-2
homogeneous freezing favored over deposition
0.100Jm-2

18. Heterogeneous nucleation mechanisms

19. Summary of ice nucleation regimes
0.6
Homogeneous freezing
Condensation/immersion freezing
heterogeneous freezing regime
Haze (deliquescent)
Contact-freezing
Ice supersaturation (Sice – 1)
0.3
Deposition nucleation
water saturation 25 50
Supercooling (°C)

20. Ice nucleation mechanisms (another view)
T = -35 ˚C
T < -35 ˚C
T > -35 ˚C
Ice nuclei cause freezing by condensation-, immersion-, or contact freezing
All drops freeze
(or evaporate)
DROPS
RHw = 100%
Homogeneous freezing of hygroscopic particles
f(T, RH)
IN active in this regime may initiate ice formation before homogeneous freezing can occur – may inhibit ice formation
Ice nuclei cause freezing by deposition freezing
HAZE or DRY PARTICLES

21. Heterogeneous Nucleation of Ice
Suspect presence of foreign particle may aid nucleation of ice by allowing ice to form at higher temperatures compared to homogeneous nucleation of freezing –and at lower humidities compared to formation of ice by homogeneous nucleation from the vapor.
Nucleation on a planar substrate
Nucleation by deposition
vapor
solid
From force balance,
contact angle
If large; contact angle is large
large curvature

22. “Similar” substrates cause a strain in the ice.
Both ice and substrate have lattice structure so must examine microscopic properties of the nucleation process.
Ice
Fletcher 1962
Substrate
Dislocation occurs if ice retains its lattice structure right down to the surface of the substrate, or:
Ice lattice will deform elastically to coherently join the lattice of the substrate—this results in a strain in the ice lattice.
Dislocations normally occur when substrate has a considerably different lattice structure than ice.
“Similar” substrates cause a strain in the ice.
Dislocation – increases increases contact angle
Strain – raises
What is the best nucleating substrate?

23. In general a combination of strain and dislocation will exist.
small increase in µs
ice
substrate
Young 1983
increase in σcs
In general a combination of strain and dislocation will exist.
So µs increased due to strain and σcs increased due to dislocations

24. Why is σcs increased due to dislocations?= O H+
Why is σcs increased due to dislocations?
H2O – polar molecule
Interfacial energy σcs is minimized when H+ - O- dipole aligns with the local field at the surface of the substrate. _ +
arises due to ionic nature of nucleating material
Misalignment results in electrical ‘torque’