Reasonable values of the thermodynamic characteristics for the cluster formation of odd alcohols at the air/water interface are obtained by the quantum chemical PM3 approximation. The calculated values of enthalpy
Δ
, entropy Δ
and Gibbs energy Δ
for the formation of clusters of a given structure depend linearly
on the number of CH2 groups in the odd alcohol molecule. The additive approach, proposed in a recent
paper, was further developed to extend the results of the calculations of the thermodynamic properties of
small associates (2 to 7 alcohol molecules) to infinite clusters of odd and even homologues. Hydrogen O···H
bonds, O···O interactions between the oxygen lone pairs, and four types of H···H interaction are taken into
account, and the thermodynamic characteristics of the formation of linear, rhombic, rectangular, etc. clusters
are calculated. Depending on the cluster type, the dependence of the Gibbs free energy on the alkyl chain
length can be either the same for all homologous alcohols or can be different for the even and odd homologues.
The most stable associates are clusters possessing rhombic or dodecahedral structures and linear clusters
possessing one H···H bond per each methylene group. The former type exhibits a monotonic dependence of
the thermodynamic parameters on the number of methylene groups, whereas for the latter type this dependence
is stepwise. The results of the quantum chemical calculations agree well with the results obtained on the
basis of a thermodynamic model that assumes equilibrium between oligomers and clusters within the monolayer.
The experimental Π−A isotherms, indicating the existence of a first-order phase transition, and the microscopic
morphology of the condensed-phase domains of tridecanol monolayers support the results of the quantum
chemical and thermodynamic calculations.

Within the framework of PM3 molecular orbital approximation the thermodynamic function characteristics for the formation and geometrical structure of monomers, dimers, trimers, and tetramers of nondissociated n-carboxylic acids C(n)H(2n+1)COOH with n = 5-15 are calculated. It is shown that spontaneous aggregation of homologous fatty acids for the homologues with carbon atoms numbers n > or = 13 at the air/water interface can take place, leading to the formation of infinite plane rectangular clusters, whereas for the homologues with n < 11 spontaneous decomposition of large aggregates is energetically preferable. At the same time, the formation of trimers is more probable for the lower homologues (8 < n < 13). These results agree well both with the experimental data reported by various authors and with thermodynamic models developed earlier for soluble and insoluble monolayers. The slopes of the regressions calculated for the dependencies of the thermodynamic parameters on the alkyl chain length for all the clusters considered are all equal to each other. This fact indicates that the contributions of the CH2 groups to the thermodynamic characteristics of alcohols and acids are the same, and the differences in the formation of clusters by these substances should be attributed only to the differences in the structure and interactions of relevant functional groups. Therefore, it enables one to describe both acids and alcohols within the framework of the developed method, and it makes it possible to extend the proposed approach onto other classes of amphiphilic compounds.

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.

A generalized Volmer's equation is derived for a multicomponent Langmuir monolayer. This general equation is then used to derive the equations of state for the monolayer of a single amphiphile considering the twodimensional (2D) main phase transition. A theory developed recently (J. Phys. Chem. 1996, 100, 15478) is extended to incorporate the important case that the area per one amphiphile molecule within the aggregate differs from that characteristic for the nonaggregated amphiphile. The general equation derived involves four parameters, two of which refer to the state of the gaseous monolayer whereas the other two parameters express the 2D aggregation constant and the difference between the area per one amphiphile molecule within the aggregate and the area per one nonaggregated molecule. The experimental Π-A isotherms for Langmuir monolayers of various amphiphiles, either measured by the authors or referred to elsewhere, agree well with the proposed model for physically reliable values of model parameters.

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