Quantum chemical analysis of thermodynamics of the two-dimensional cluster formation at the air/water interface

The thermodynamics of the two-dimensional cluster formation of normal fatty alcohols (n = 8-16) and that of 2-methylhexadecanolat in the air/water interface is quantum chemically analyzed. The calculation provides reasonable values for the thermodynamic characteristics for the formation of alcohol clusters (m = 2-7) with various structures at the air/water interface. The calculated values of enthalpy ΔH_m^cl, entropy ΔS_m^cl, and Gibbs energy ΔG_m^cl for the formation of a definite cluster structure can be satisfactory represented by a linear dependence on the number of CH₂ groups in the alcohol molecule. The absolute terms and coefficients of these equations can be characterized in form of the dependencies on the number of bonds formed between the alkyl groups (one to four bonds) and the contributions to the interactions from hydrogen bonds and lone pairs of oxygen atoms. The enthalpy and entropy of the cluster formation can be estimated from the molecular geometry of the clusters (relative positions of methylene and hydroxyl groups), the number of carbon atoms in the monomer and the number of molecules in the cluster. Reliable estimates predict plane clusters with tetragonal or hexagonal structure, and linear clusters with an arbitrary number of CH₂ groups and an arbitrary (up to infinite) number of monomers in the cluster. The calculations show that stable tetramers are formed by n-decanol, whereas n-dodecanol and the higher homologues cannot only form tetramers but also infinite clusters. These results are in agreement with the existence of a first-order phase transition in the experimental surface pressure-area isotherms of n-dodecanol, n-tetradecanol, n-hexadecanol, and 2-methylhexadecanol monolayers that does not occur in n-decanol monolayers. The thermodynamic model which assumes equilibrium between the oligomers and clusters within the monolayer agrees well with the experimental results, and suggests that in the fluid state the monolayers are comprised of monomers and oligomers (dimers to tetramers), the aggregation degree of which increases with the increase of the alkyl chain length. The data obtained by the thermodynamic model agree qualitatively, and also quantitatively (especially for Gibbs energy) with the quantum chemical calculations.