Mechanisms of Supercooling and Supersaturation

[Red_CCF]

I have a couple of questions:

The homogeneous freezing temperature of water is listed at -42C. However, from the equations formulated to find critical radius here, I did not see any factors which restricts the homogeneous nucleation temperature to a certain value. How is the homogeneous nucleation temperature defined? I can see how the probability of a nuclei of critical radius increases with decreasing temperatures. However, in the absence of heterogeneous nucleation sites, would a block of water left at say -20C never freeze, or would it eventually freeze after a very long time? Microscopically how is a solid nucleus formed?

In the same Wikipedia article, I did not understand this statement:

Supercooling brings about supersaturation, the driving force for nucleation. Supersaturation occurs when the pressure in the newly formed solid is less than the liquid pressure

what is meant by solid and liquid pressure, and since they are different, can phase change be considered isobaric?

How is supersaturation achieved? I think one way is to lower the temperature of some water vapour inside an enclosed container with no nucleation sites. Is it possible to generate a supersaturated system by evaporation, such that water continue to evaporate even when P > P_sat(T_system)?

Similar to the above question, if I have liquid water in equilibrium with its vapour (P_vapour = P_sat(T)) inside an closed system with no nucleation sites at temperature T, if I lower the temperature, does the system supersaturate, or does vapour begin condensing?

Thank you

 

[Valerie Park]

for your help!The homogeneous nucleation temperature is usually defined as the temperature at which the probability of a nucleus of critical radius is great enough to allow for spontaneous freezing. The probability increases with decreasing temperatures, so it is usually assumed that the homogeneous nucleation temperature is -42C. However, this is just an approximation and the exact temperature could be different depending on the conditions.Solid pressure is the pressure exerted by the solid material that forms the nucleus of a crystal. It is the pressure inside the solid at the time of nucleation. Liquid pressure is the pressure exerted by the liquid material that surrounds the solid nucleus. It is the pressure of the liquid at the time of nucleation. Phase change can be considered isobaric if the pressure in the newly formed solid is equal to the liquid pressure. Supersaturation is achieved by cooling a gas or liquid below its saturation temperature. When the temperature is lowered, the vapor pressure drops below the atmospheric pressure, creating a supersaturated state. It is also possible to generate a supersaturated system by evaporation, as long as the pressure stays below the saturation vapor pressure at the given temperature. If you lower the temperature of liquid water in equilibrium with its vapor, the vapor pressure will drop below the atmospheric pressure, resulting in supersaturation. If there are no nucleation sites present, the water will remain in a supersaturated state until a nucleus forms, at which point it will begin to condense.