Hydrophobic hydration processes. General thermodynamic model by thermal equivalent dilution determinations

The "hydrophobic hydration processes" can be satisfactorily interpreted on the basis of a common molecular model for water, consisting of two types of clusters, namely W(I) and W(II) accompanied by free molecules W(III). The principle of thermal equivalent dilution (TED) is the potent tool (Ergodic Hypothesis) employed to monitor the water equilibrium and to determine the number xi(w) of water molecules W(III) involved in each process. The hydrophobic hydration processes can be subdivided into two Classes: Class A includes those processes for which the transformation A(-xi(w)W(I)-->xi(w)W(II)+xi(w)W(III)+cavity) takes place with the formation of a cavity, by expulsion of xi(w) water molecules W(III) whereas Class B includes those processes for which the opposite transformation B(-xi(w)W(II)-xi(w)W(III)-->xi(w)W(I)-cavity) takes place with reduction of the cavity, by condensation of xi(w) water molecules W(III). The number xi(w) depends on the size of the reactants and measures the extent of the change in volume of the cavity. Disaggregating the thermodynamic functions DeltaH(app) and DeltaS(app) as the functions of T (or lnT) and xi(w) has enabled the separation of the thermodynamic functions into work and thermal components. The work functions DeltaG(Work), DeltaH(Work) and DeltaS(Work) only refer specifically to the hydrophobic effects of cavity formation or cavity reduction, respectively. The constant self-consistent unitary (xi(w)=1) work functions obtained from both large and small molecules indicate that the same unitary reaction is taking place, independent from the reactant size. The thermal functions DeltaH(Th) and DeltaS(Th) refer exclusively to the passage of state of water W(III). Essential mathematical algorithms are presented in the appendices.