The Planck–Benzinger thermal work function in the condensation of water vapor

Abstract Based on the Planck–Benzinger thermal work function using Chun's method, the innate temperature‐invariant enthalpy at 0 K, Δ H 0 ( T 0 ), for the condensation of water vapor as well as the dimer, trimer, tetramer, and pentamer form in the vapor phase, was determined to be 0.447 kcal mol −1 for vapor, 1.127 for the dimer, 0.555 for the trimer, 0.236 for the tetramer, and 0.079 kcal mol −1 for the pentamer using Δ G ( T ) data reported by Kell et al. in 1968 and Kell and McLaurin in 1969. These results suggest that the predominant dimeric form is the most stable of these n ‐mers. Using Nemethy and Scheraga's 1962 data for the Helmholtz free energy of liquid water, the value of Δ H 0 ( T 0 ) was determined to be 1.21 kcal mol −1 . This is very close to the value for the energy of the hydrogen bond E H of 1.32 kcal mol −1 reported by Nemethy and Scheraga, using statistical thermodynamics. It seems clear that very little energy is required for interconversion between the hypothetical supercooled water vapor and glassy water at 0 K. A hypothetical supercooled water vapor at 0 K is apparently almost as highly associated as glassy water at that temperature, suggesting a dynamic equilibrium between vapor and liquid. This water vapor condensation is highly similar in its thermodynamic behavior to that of sequence‐specific pairwise (dipeptide) hydrophobic interaction, except that the negative Gibbs free energy change minimum at 〈 T s 〉, the thermal setpoint for vapor condensation, where TΔS = 0, occurs at a considerably lower temperature, 270 K (below 0°C) compared with ∼350 K. The temperature of condensation 〈 T cond 〉 at which Δ G ( T ) = 0, where water vapor begins to condense, was found to be 383 K. In the case of a sequence‐specific pairwise hydrophobic interaction, the melting temperature, 〈 T m 〉, where Δ G ( T m ) = 0 was found to be 460 K. Only between two temperature limits, 〈 T h 〉 = 99 K and 〈 T cond 〉 = 383 K, where Δ G ( T cond ) = 0, is the net chemical driving force favorable for polymorphism of glassy water and hypothetical supercooled water vapor. Analysis of the water vapor condensation process based on the Planck–Benzinger thermal work function confirms that a thermodynamic molecular switch occurs at 10 K, wherein a change of sign in [Δ C p ( T )] cond leads to a true negative minimum in the Gibbs free energy of vapor condensation, and hence a maximum in the related equilibrium constant, K cond . © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006