Quantum Chemical Analysis of Thermodynamics of the Two-Dimensional Cluster Formation at the Air/Water Interface

Abstract

The thermodynamics of the two-dimensional cluster formation of normal fatty alcohols (n ) 8-16) andthat 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 ∆H m cl , entropy ∆S m cl , and Gibbs energy ∆G m cl for the formation of a definite cluster structure can be satisfactory represented by a linear dependence on the number of CH 2 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 CH 2 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.

Theoretical description of 2D-cluster formation of nonionic surfactants at the air/water interface

“…Correspondingly, they are termed as hydrogen-hydrogen (СН···НС) interactions. Investigations [104,187,196] proved that it is possible to distinguish six interaction types depending on the mutual orientation of the surfactant molecules in the cluster (see Fig. 5).…”

“…In the study [187], we showed that PM3 describes the interactions between the alkyl chains most appropriately despite the fact that its atom-atomic potentials somewhat overestimate the attraction forces [57]. Now, there are a number of new parametrizations of this method, e.g., PM6 and PM7 capable of a better description of noncovalent interactions [72].…”

“…Theoretical background for such scheme is the pairwise additivity of the intermolecular interactions and the fact that their force decreases much stronger than Coulombic interactions [21]. As the calculations [104,187,196] showed, the clusterization enthalpy, entropy, and Gibbs' energy depend significantly on the mutual orientation of the hydrocarbon chains of interacting molecules. This is proved by anisotropy of these interactions revealed in study [197].…”

“…Assuming that adjacent atoms contribute to the maximal increment in the energy of the intermolecular interaction, we demonstrated in refs. [32,104,149,196,[198][199][200][201] that the interaction between two next-neighbor surfactant molecules can be expanded into the sum of increments contributed by the pairwise interactions between the nextneighbor methylene units and between the next-neighbor functional groups. The structure of the hydrocarbon substituents is like as the terminal interacting atoms of the methylene units are hydrogen atoms.…”

Aggregation and re-organization of normal fatty alcohols at the air/water interface

“…For the cluster formation of n-alcohols at the air/water interface the quantum chemical studies of the entropy and enthalpy of cluster formation in the minimum potential energy points were performed earlier [11,12]. In the present paper the growth and re-organization of two-dimensional clusters of n-alcohols are theoretically investigated.…”