Different heterogeneous routes of the formation of atmospheric ice

Anatoli Bogdan

Institute of Physical Chemistry, University of Innsbruck Austria

andDepartment of Physics, University of Helsinki

Finland

Contents Introduction - ice in the atmosphere Heterogeneous formation of ice - contact freezing - immersion freezing - classical notions of heterogeneous freezing - a new hypotheses of heterogeneous freezing

What are high-altitude cirrus clouds?

- sub-visible cirrus (SVC) clouds with optical depth<0.03

- thin cirrus clouds with optical depth < 0.3

(From Winker and Trepte, GRL, 25, 3351-3354 (1998).)

SVC cloud in tropical tropopause region at about 17 km

Short information about SVC clouds Location of the SVC clouds: - globally widespread near the tropopause regionTemperature range: - between 210 and 185 KFormation: - freezing diluted H2SO4/H2O aerosol dropletsOrigin of aerosol droplets in the upper troposphere: - in situ gas-to-particles conversion - deposition processes from the lower stratosphere (Minnis, P. et al., Science, 259, 1411-1415 (1993); McCormick, M. P., et al.,

Nature, 373, 399-404 (1995)) Observed size of aerosol droplets: - depending on background or volcanic conditions diameter can be in the range of about 0.2 – 3 m (Hofmann & Rosen, Science, 222, 325-327 (1983).

Composition of aerosol droplets: - < 30 – 35 wt % H2SO4

Why are SVC clouds important for the climate?

- they reflect and scatter incoming solar radiation (cooling effect)

- they trap outgoing terrestrial infrared radiation (warming effect)

- they supply surface for heterogeneous loss of ozone that is an important greenhouse gas at high altitudes (cooling effect)

Both radiative properties and the rate of ozone loss depend on the microphysics of SVC clouds

Microphysical characteristics of SVC clouds

- Small ice water content (IWC) : 10-4 – 10-6 g/m3

- Small effective ice diameter : < 20 – 30 m

- Small ice particle density : < 1 cm-3

- Different shape (habits) of ice crystals

Polar stratospheric clouds (PSCs)

Formation of ice in the atmosphere

Nucleation occurs in the interior of a uniform pure substance (vapor of liquid), by a process called

homogeneous nucleation. The creation of a nucleus implies the formation of an interface at

the boundaries of a new phase.

Heterogeneous freezing in the atmosphere

Nucleation induced by a foreign insoluble particle (nuclei) is called by hetergogeous nucleation.

Fumed silica (SiO2) is fractal object

- SiO2 is widely encountered in meteoritic smoke particles (MSPs) and combustion origin

Fumed silica (SiO2) can be considered as a representative of atmospheric ice nuclei

Using of fumed silica in heterogeneous freezing measurements of aqueous droplets

Weight (g) of H2SO4 in diluted H2SO4/H2O drops as a function of size (0.2 - 2 mand composition (10 – 25 wt % H2SO4)

Weight of H2SO4 is in the range 5*10-16 – 1.2*10-12 g

Initial thickness of an over-layer of initial composition of 38 wt % H2SO4

Different routes of the formation of ice in the atmosphere

Contact freezing occurs when a super-cooled drop comes in "contact" with an ice nuclei

Immersion freezing occurs when an ice nuclei is inside of a super-cooled drop

When an ice crystal falls through super-cooled droplets then

accretion or riming occurs, i.e.,

super-cooled drops freeze onto ice crystal.The resultant particle

is often referred to as graupel

When an ice crystal falls through other ice crystals then aggregation occurs which produce a snowflake

1.4 Some useful thermodynamic properties

Entropy, thermodynamically defined as dT

dqS rev , is a thermodynamic property showing a direction of any spontaneous changes

occurring in nature. When a system is in thermal equilibrium with its surrounding and there is an exchange of heat dq between the system and the surrounding then for any spontaneous changes

T

dqdS

. (1.28)

This expression is called the Clausius inequality. If the system is isolated then dq = 0 and the Clausius inequality implies that

0dS , (1.29) i.e., in the isolated system entropy cannot decrease when a spontaneous processes takes place.

A system can exchange a heat with its surrounding either when volume is constant or when pressure is constant. When heat is transferred to a system at constant volume then, in the absent of any non-expansion work (for example, chemical reactions), we have dqv = dE, and consequently the Clausius inequality reads as

0T

dEdS (1.30)

or

dE – T dS ≤ 0. (1.31) The last expression allows us to define a new thermodynamic property called the Helmholtz energy

A = E – TS. (1.32) Eqs. (1.31) and (1.32) show that, at constant T and V, the criteria of the spontaneous change is

dAT,V ≤ 0, i.e., the system tends towards a lower Helmholtz energy.

When a heat is transferred to a system at constant pressure, and there is no non-expansion work, then dqp = dH, and the Clausius inequality can be written as

0T

dHdS (1.33)

or

dH – T dS ≤ 0 . (1.34) This expression allows us to introduce the Gibbs energy (sometimes called also free energy)

G = H –TS. (1.35) Eqs. (1.34) and (1.35) show that, at constant T and p, the criteria of the spontaneous change is

dGT,p ≤ 0, i.e., a system tends towards a lower Gibbs energy. Since in the atmosphere, the different phisyco-chemical processes occur rather at constant pressure than at constant volume, below we will deal mainly with the Gibbs energy.

The Gibbs energy of solids and liquids is almost independent of pressure, Fig.3. However, in the case of gases (both real and perfect) the Gibbs energy is a strong function of pressure. Indeed, an infinitesimal change in the properties of H = E + pV, T, and S result in that the Eq. (1.35) can be written as

dG = [(T dS – p dV) + p dV + V dp] – T dS – S dT = V dp – S dT. (1.36) (Here we used the expression dE = TdS – p dV.) The Eq. (1.36) shows that a change in G is proportional to a change in p and T, i.e., the Gibbs energy may the best regarded as a function of p and T. At constant temperature, dT = 0, integration of (1.36) gives

G(pfinal) = G(pinitial) + f

i

p

p

Vdp . (1.37)

It is seen from Fig. 3 that for solids or liquids, the change in volume with pressure is small, so V can be treated as a constant and the integral can be considered approximately as ≈ V∆p. Since at normal pressure the value of V∆p is small, we can suppose that the Gibbs energies of solids and liquids are independent of pressure. But in the case of gases, when the volume varies markedly with pressure and the molar volume of the gas is large, the integral cannot be neglected. For the perfect gas, substituting V = nRT/p into the integral, we get

G(pf) = G(pi) + nRT f

i

p

p p

dp = G(pi) + nRT ln

i

f

p

p. (1.38)

In physical chemistry, the initial pressure is taken as pi = p° =1 bar, which is called standard pressure. The (1.38) allows relating the Gibbs energy at any given pressure p with its standard Gibbs energy G° (Gibbs energy at the standard pressure 1 bar, Fig. 4) by the expression

G(p) = G° + nRT ln p

p (1.39)

The molar Gibbs energy is called the chemical potential μ. For the perfect gas it is expressed as

Gm = μ = μ° + RT ln p

p, (1.40)

where μ° is the standard chemical potential of the perfect gas (i.e., the chemical potential at the standard pressure 1 bar). The chemical potential expresses a capacity of a substance to bring about phase and chemical changes.

Phase equilibrium: Two systems are in equilibrium if they fulfill the conditions of chemical equilibrium

μ1 = μ2 , (1.44) thermal equilibrium

T1 = T2 , (1.45)

and mechanical equilibrium

p1 = p2. (1.46) If one of the system possesses a curved surface then the mechanical equilibrium expressed by the Laplace equation

p1 – p2 = 2γ/r, where p1 and p2 are pressures of the two phases, γ surface tension of the system with curved surface, and r radius of curvature. For example, two phases will be in the unstable equilibrium at the moment of the formation of a critical embryo of a new phase within a mother phase. The unstable means that the new phase will grow infinitely when the radius of the embryo slightly exceeds the critical embryo.

As temperature decreases, ice is formed in a super-cooled water droplet when the pressure of ice becomes less than the pressure of water, i.e., when a super-saturation with respect to ice appears.

This brings about a change in Gibbs free energy per unit volume, Gv, between the water and ice phase. This change in free energy is balanced by the energy gain to create a new volume (negative change), and the energy cost due to creation of a new interface (positive change). When the overall free energy change, ΔG is negative, nucleation is favored.

If a formed ice nucleus is too small (known as an unstable nucleus or "embryo"), the energy that would be released by forming its volume (negative change) is not enough to create its surface (positive change) then nucleation does not proceed. The formed nucleus should reach some critical size (or radius), in order to be stable and the growth of the ice phase proceeds.

In the classic theory, for a spherical ice cluster we cam write for the overall Gibbs energy change

where the first term is negative and the second one positive.

The Gibbs free energy needed to form the ice cluster of critical radius can be found from the conditions

The Gibbs free energy change needed to form the ice cluster of critical radius is

where Gv is a change in free energy per unit volume.

and the critical radius

Large supercooling favors the freezing of water. We can relate ΔG to supercooling ΔT = T – To, where = 273.15 K, and find r* and ΔG * as a function of ΔT

               and

                         The larger the supercooling ΔT = T – To, the smaller the critical radius and the less energy needed to form it.

Heterogeneous nucleation

Heterogeneous nucleation occurs much more often than homogeneous nucleation. The free energy needed for heterogeneous nucleation is equal to the product of homogeneous nucleation and a function of contact angle :

                                        where                              

                        

The barrier energy needed for heterogeneous nucleation is reduced, and less super-cooling is needed.

In nature freezing usually occurs below the maximum heterogeneous freezing temperature (which is melting temperature of ice, 273.15 K) but above the homogeneous freezing temperature which is about 233 K.

Water in between these two temperatures is said to be in super-cooled state.

A new hypotheses of heterogeneous freezing