The homogeneous nucleation in supercooled water. An examination using statistics and irreversible thermodynamics

According to the rate constant of crystallization, the lifetime of a droplet of supercooled liquid is τ = 15 s at 237 K. The rate constant J strongly depends on the temperature T. The experimental results can be reproduced by the phenomenological Arrhenius equation. The plot lnJ vs. 1/T shows an ascending straight line. The slope gives the activation energy Ea = − 2.65 · 10− 18 J at 237 K. In contrast to chemical kinetics, the activation energy is negative, Ea < 0. It must be given off to the surroundings, otherwise neither nucleation nor crystallization of a droplet of supercooled water is possible. Hence the critical germ is nothing else than the transition state of crystallization of a water droplet, and the activation energy equals the enthalpy of nucleation Ea = ΔHN < 0. In combination with the enthalpy of crystallization ΔHl = − 7.4 · 10− 21 J of one H2O molecule at 237 K the number N = 3.6 · 102 of molecules can be determined, which are engaged in the formation of the critical germ and the transition state, respectively.