Quantum Chemical Analysis of the Thermodynamics of 2D Cluster Formation of Odd n-Alcohols at the Air/Water Interface

Quantum chemical assessment of the molecular area corresponding to the onset of the LE-LC phase transition for amphiphilic 2D monolayers at the air/water interface

An approach for the assessment of the area per surfactant molecule in a monolayer at the onset of the LE-LC phase transition (A_c) is proposed based on the quantum chemical approach and a thermodynamic model for amphiphilic monolayers, which takes into account the nonideality of the mixing entropy. The values of the Gibbs' clusterization energy for small surfactant associates, as well as the geometric parameters of the monolayer unit cells, were used, previously calculated using the semiempirical PM3 method for eight classes of amphiphilic compounds: saturated and ethoxylated alcohols, saturated and unsaturated cis-carboxylic acids, α-hydroxylic and α-aminoacids, N-acyl-substituted alanine and dialkyl-substituted melamine. The obtained A_c values are in satisfactory agreement with the available experimental data. This allows using the proposed approach for prognostic purposes in the cases where there are no corresponding π-A isotherms for necessary surfactants, but there are calculated thermodynamic and structural parameters of its clusterization.

Contribution of Different Molecules and Moieties to the Surface Tension in Aqueous Surfactant Solutions. II: Role of the Size and Charge Sign of the Counterions

Understanding the role of the counterion species in surfactant solutions is a complicated task, made harder by the fact that, experimentally, it is not possible to vary independently bulk and surface quantities. Here, we perform molecular dynamics simulations at constant surface coverage of the liquid/vapor interface of lithium, sodium, potassium, rubidium, and cesium dodecyl sulfate aqueous solutions. We investigate the effect of counterion type and charge sign on the surface tension of the solution, analyzing the contribution of different species and moieties to the lateral pressure profile. The observed trends are qualitatively compatible with the Hofmeister series, with the notable exception of sodium. We point out a possible shortcoming of what is at the moment, in our experience, the most realistic nonpolarizable force field (CHARMM36) that includes the parametrization for the whole series of alkali counterions. In the artificial system where the counterion and surfactant charges are inverted in sign, the counterions become considerably harder. This charge inversion changes considerably the surface tension contributions of the counterions, surfactant headgroups, and water molecules, stressing the key role of the hardness of the counterions in this respect. However, the hydration free energy gain of the counterions, occurring upon charge inversion, is compensated by the concomitant free energy loss of the headgroups and water molecules, leading to a negligible change in the surface tension of the entire system.

Theoretical Description of Mixed Film Formation at the Air/Water Interface: Carboxylic Acids-Alcohols

The thermodynamic parameters of formation and clusterization of aliphatic alcohols C _n H_2n+1OH and carboxylic acids C _n H_2n+1COOH (n = 6-16) are calculated using the quantum-chemical semiempirical PM3 method. Four types of dimers are constructed in two directions of the spread monolayer comprising the most energetically advantageous monomer structures. The hydrophobic chains of alcohol and carboxylic acid molecules in the regarded dimers are found to be tilted within 12° to the normal of the spread monolayer. The structures of the mixed and pure surfactant dimers are the basis for the mixed alcohol-carboxylic acid monolayers of the following types: two dimensional (2D) film 1 with single distribution of the individual component in the other one, when the molecules of the first component do not interact with each other but are completely surrounded by the molecules of the second component; 2D film 2 with domain structure, when the film consists of "islands" of the individual components. The dependences of the clusterization Gibbs' energy per one monolayer molecule on the molar fraction of the components for the mixed 2D films 1 formed by surfactants with equal alkyl chain length are found to be limited from top to bottom by the corresponding dependences for pure components. This indicates the absence of synergetic interaction between the hydrophilic head groups of carboxylic acids and alcohols and conforms to the available experimental data. The formation of the described types of mixed films is competitive. The preferential formation of 2D films 1 with single distribution of the first component among the molecules of the second one is possible when the length of the carboxylic acid hydrocarbon chain is longer by Δn = 1-2 methylene units than that of the corresponding alcohol alkyl chain. According to the fractionally linear law, the highest possible content of the carboxylic acids in such 2D films 1 depends on the Δn value and does not exceed 33.3%.

Quantum chemical clarification of the alkyl chain length threshold of nonionic surfactants for monolayer formation at the air/water interface

A theoretical basis is introduced for the experimental fact that for various surfactant classes the alkyl chain length threshold varies for the formation of condensed monolayers.

Quantum chemical analysis of thermodynamics of 2D cluster formation of alkanes at the water/vapor interface in the presence of aliphatic alcohols

Using the quantum chemical semi-empirical PM3 method it is shown that aliphatic alcohols favor the spontaneous clusterization of vaporous alkanes at the water surface due to the change of adsorption from the barrier to non-barrier mechanism. A theoretical model of the non-barrier mechanism for monolayer formation is developed. In the framework of this model alcohols (or any other surfactants) act as 'floats', which interact with alkane molecules of the vapor phase using their hydrophobic part, whereas the hydrophilic part is immersed into the water phase. This results in a significant increase of contact effectiveness of alkanes with the interface during the adsorption and film formation. The obtained results are in good agreement with the existing experimental data. To test the model the thermodynamic and structural parameters of formation and clusterization are calculated for vaporous alkanes C(n)H(2n+2) (n(CH3) = 6-16) at the water surface in the presence of aliphatic alcohols C(n)H(2n+1)OH (n(OH) = 8-16) at 298 K. It is shown that the values of clusterization enthalpy, entropy and Gibbs' energy per one monomer of the cluster depend on the chain lengths of corresponding alcohols and alkanes, the alcohol molar fraction in the monolayers formed, and the shift of the alkane molecules with respect to the alcohol molecules Δn. Two possible competitive structures of mixed 2D film alkane-alcohol are considered: 2D films 1 with single alcohol molecules enclosed by alkane molecules (the alcohols do not form domains) and 2D films 2 that contain alcohol domains enclosed by alkane molecules. The formation of the alkane films of the first type is nearly independent of the surfactant type present at the interface, but depends on their molar fraction in the monolayer formed and the chain length of the compounds participating in the clusterization, whereas for the formation of the films of the second type the interaction between the hydrophilic parts of the surfactant is essential and different for various types of amphiphilic compounds. The energetic preference of the film formation of both types depends significantly on the chain length of compounds. The surfactant concentration (in the range of X = 0-10%) exerts a slight influence on the process of film formation.

Quantum chemical approach in the description of the amphiphile clusterization at the air/liquid and liquid/liquid interfaces with phase nature accounting. I. Aliphatic normal alcohols at the air/water interface

A new model based on the quantum chemical approach is proposed to describe structural and thermodynamic parameters of clusterization for substituted alkanes at the air/liquid and liquid/liquid interfaces. The new model by the authors, unlike the previous one, proposes an explicit account of the liquid phase (phases) influence on the parameters of monomers, clusters and monolayers of substituted alkanes at the regarded interface. The calculations were carried out in the frameworks of the quantum chemical semiempirical PM3 method (Mopac 2012), using the COSMO procedure. The new model was tested in the calculations of the clusterization parameters of fatty alcohols under the standard conditions at the air/water interface. The enthalpy, Gibbs' energy and absolute entropy of formation for alcohol monomers alongside with clusterization parameters for the cluster series including the monolayer at air/water interface were calculated. In our calculations the sinkage of monomers, molecules in clusters and monolayers was varied from 1 up to 5 methylene groups. Thermodynamic parameters calculated using the proposed model for the alcohol monolayers are in a good agreement with the corresponding experimental data. However, the proposed model cannot define the most energetically preferable immersion of the monolayer molecules in the water phase.

Quantum-chemical analysis of hexagonal crystalline monolayers of ethoxylated nonionic surfactants at the air/water interface

In the framework of the quantum chemical semiempirical PM3 method the monolayers of the monoethoxylated normal alcohols CnH2n+1OCH2CH2OH with n = 6-16 (CnE1) at the air/water interface are described. The optimized structures of small clusters (dimers, trimers, tetramers, pentamers, hexamers and heptamers) comprising the hexagonal monolayer are obtained. For these aggregates thermodynamic parameters of formation and clusterization are calculated. The correlation dependencies of the clusterization enthalpy, entropy and Gibbs energy on the number of CHHC interactions and interactions between the functional groups realized in the cluster are obtained on the basis of calculated data. The calculated parameters of the hexagonal monolayer unit cell are: a = 4.02 Å; b = 7.94 Å, t = 4°, close to those for an aliphatic alcohol monolayer according to GIXD experiments: a = 5.0 Å; b = 7.5 Å, t = 0-9°. Spontaneous clusterization of monoethoxylated alcohols at the air/water interface under standard conditions is shown to be possible for molecules possessing more than 14 carbon atoms in the alkyl chain, in good agreement with the characteristics of the surface pressure-molecular area (π-A) isotherms. It is found that addition of the -O-CH2-CH2- unit to the hydrophilic part of aliphatic alcohols results in a shift of their spontaneous clusterization threshold to that of the compounds with hydrocarbon chains 3 methylene units longer. The temperature effect of CnE1 is assessed. It corresponds to the spontaneous clusterization temperature decrease of 10-20 K per two methylene units taken from the alkyl chain in agreement with experimental data. The comparison of clusterization Gibbs energy dependencies for small aggregates of CnE1 confirms the experimental fact that the crystalline monolayers are formed by preferential aggregation of trimers.

The quantum-chemical approach to calculations of thermodynamic and structural parameters of formation of fatty acid monolayers with hexagonal packing at the air/water interface

The structural parameters of fatty acid (with formula CnH2n+1COOH, n = 7-16) monolayers at the air/water interface were modeled within quantum-chemical semiempirical program complex Mopac 2012 (PM3 method). On the basis of quantum-chemical calculations it was shown that molecules in the highly ordered monolayer can be oriented at the angle ∼16° (tilted monolayer), or at the angle ∼0° to the normal to the air/water interface (untilted monolayer). The structural parameters of both tilted and untilted monolayers correspond well to the experimental data. The parameters of the unit cell of the modelled tilted monolayer are: a = 8.0-8.2 Å and b = 4.2-4.5 Å (with the corresponding experimental data 8.4-8.7 Å and 4.9-5.0 Å). For the modelled untilted monolayer these parameters are: a = 7.7-8.0 Å; b = 4.6 Å (with the corresponding experimental data 8.4 Å and 4.8-4.9 Å). Enthalpy, entropy and Gibbs' energy of clusterization were calculated for both structures. The correlation dependencies of the calculated parameters on the number of pair intermolecular CHHC interactions in the clusters and the pair interactions between functional groups were obtained. It was shown that the spontaneous clusterization of the fatty carboxylic acids at the air/water interface under standard conditions is energetically preferable for molecules which have 13 or more carbon atoms in the alkyl chain and this result also agrees with the corresponding experimental parameters.

On the inclusion of alkanes into the monolayer of aliphatic alcohols at the water/alkane vapor interface: a quantum chemical approach

In the framework of the quantum chemical semiempirical PM3 method thermodynamic and structural parameters of the formation and clusterization of aliphatic alcohols C(n)H(2n+1)OH (n(OH) = 8-16) at 298 K at the water/alkane vapor C(n)H(2n+2), (n(CH(3)) = 6-16) interface were calculated. The dependencies of enthalpy, entropy and Gibbs' energy of clusterization per one monomer molecule of 2D films on the alkyl chain length of corresponding alcohols and alkanes, the molar fraction of alkanes in the monolayers and the immersion degree of alcohol molecules into the water phase were shown to be linear or stepwise. The threshold of spontaneous clusterization of aliphatic alcohols at the water/alkane vapor interface was 10-11 carbon atoms at 298 K which is in line with experimental data at the air/water interface. It is shown that the presence of alkane vapor does not influence the process of alcohol monolayer formation. The structure of these monolayers is analogous to those obtained at the air/water interface in agreement with experimental data. The inclusion of alkane molecules into the amphiphilic monolayer at the water/alkane vapor interface is possible for amphiphiles with the spontaneous clusterization threshold at the air/water interface (n(s)(0)) of at least 16 methylene units in the alkyl chain, and it does not depend on the molar fraction of alkanes in the corresponding monolayer. The inclusion of alkanes from the vapor phase into the amphiphilic monolayer also requires that the difference between the alkyl chain lengths of alcohols and alkanes is not larger than n(s)(0) - 15 and n(s)(0) - 14 for the 2D film 1 and 2D film 2, respectively.

Superposition-additive approach in the description of thermodynamic parameters of formation and clusterization of substituted alkanes at the air/water interface

The superposition-additive approach developed previously was shown to be applicable for the calculations of the thermodynamic parameters of formation and atomization of conjugate systems, their dipole polarizability, molecular diamagnetic susceptibility, π-electronic ring currents, etc. In the present work, the applicability of this approach for the calculation of the thermodynamic parameters of formation and clusterization at the water/air interface of alkanes, fatty alcohols, thioalcohols, amines, nitriles, fatty acids (C(n)H(2n+1)X, X is the functional group) and cis-unsaturated carboxylic acids (C(n)H(2n-1)COOH) is studied. Using the proposed approach the thermodynamic quantities determined agree well with the available data, either calculated using the semiempirical (PM3) quantum chemical method, or obtained in experiments. In particular, for enthalpy and Gibbs' energy of the formation of substituted alkane monomers from the elementary substances, and their absolute entropy, the standard deviations of the values calculated according to the superposition-additive scheme with the mutual superimposition domain C(n-2)H(2n-4) (n is the number of carbon atoms in the alkyl chain) from the results of PM3 calculations for alkanes, alcohols, thioalcohols, amines, fatty acids, nitriles and cis-unsaturated carboxylic acids are respectively: 0.05, 0.004, 2.87, 0.02, 0.01, 0.77, and 0.01 kJ/mol for enthalpy; 2.32, 5.26, 4.49, 0.53, 1.22, 1.02, 5.30 J/(molK) for absolute entropy; 0.69, 1.56, 3.82, 0.15, 0.37, 0.69, 1.58 kJ/mol for Gibbs' energy, whereas the deviations from the experimental data are: 0.52, 5.75, 1.40, 1.00, 4.86 kJ/mol; 0.52, 0.63, 1.40, 6.11, 2.21 J/(molK); 2.52, 5.76, 1.58, 1.78, 4.86 kJ/mol, respectively (for nitriles and cis-unsaturated carboxylic acids experimental data are not available). The proposed approach provides also quite accurate estimates of enthalpy, entropy and Gibbs' energy of boiling and melting, critical temperatures and standard heat capacities for several classes of substituted alkanes. For the calculation of thermodynamic functions of clusterization of dimers, trimers and tetramers of fatty alcohols, thioalcohols, amines, carboxylic acids and cis-unsaturated carboxylic acids two superposition-additive schemes are proposed which ensure the correct superimposition of the molecular graphs, including intermolecular hydrogen-hydrogen interactions in the clusters. The calculations involve the thermodynamic parameters of clusterization obtained earlier by the PM3 method. It is shown that the proposed approach reproduces quite accurately the values calculated earlier and is applicable for the prediction of the thermodynamic parameters of the formation of surfactant monolayers.

Temperature effect on the monolayer formation of substituted alkanes at the air/water interface: a quantum chemical approach

An approach to calculation of the threshold temperature for spontaneous clusterization of substituted alkanes (amines, nitriles, alcohols, thioalcohols, saturated and unsaturated carboxylic acids, α-amino acids, carboxylic acid amides, and melamine derivatives) at the air/water interface with dependence on the alkyl chain length was developed. In the framework of this approach, four schemes for the description of the temperature dependencies of the thermodynamic parameters of clusterization of the concerned amphiphilic compounds were proposed. They use the data obtained previously in the framework of quantum chemical semiempirical PM3 method and differ from each other by the degree of their theoretical accuracy. It was shown that the threshold temperature for spontaneous clusterization of the regarded classes of substituted alkanes can be described using a fractionally linear function in dependence on the alkyl chain length. It was found that, in agreement with the presented experimental data, the effect of the alkyl chain elongation of the substituted alkanes by two methylene units correlates with the decrease of the subphase temperature (ΔT) by 10-20 K. The general shape of the obtained dependencies indicates that the difference in the ΔT values for the amphiphilic molecules decreases with increasing alkyl chain length. This implies that the contribution of the intermolecular CH···HC interactions between the alkyl chains of monolayer molecules should be a decisive factor.

Superposition-additive approach: thermodynamic parameters of clusterization of monosubstituted alkanes at the air/water interface

The applicability of the superposition-additive approach for the calculation of the thermodynamic parameters of formation and atomization of conjugate systems, their dipole electric polarisabilities, molecular diamagnetic susceptibilities, π-electron circular currents, as well as for the estimation of the thermodynamic parameters of substituted alkanes, was demonstrated earlier. Now the applicability of the superposition-additive approach for the description of clusterization of fatty alcohols, thioalcohols, amines, carboxylic acids at the air/water interface is studied. Two superposition-additive schemes are used that ensure the maximum superimposition of the graphs of the considered molecular structures including the intermolecular CH-HC interactions within the clusters. The thermodynamic parameters of clusterization are calculated for dimers, trimers and tetramers. The calculations are based on the values of enthalpy, entropy and Gibbs' energy of clusterization calculated earlier using the semiempirical quantum chemical PM3 method. It is shown that the proposed approach is capable of the reproduction with sufficiently enough accuracy of the values calculated previously.

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

The quantum-chemical semiempiric PM3 method is used to calculate the thermodynamic parameters of clusterization for the racemic α-amino acids C(n)H(2n+1)CHNH(2)COOH with n=5-15 at 278 and 298 K. Possible relative orientations of the monomers in the heterochiral clusters are considered. It is shown that, for the racemic mixtures of α-amino acids, the formation of heterochiral 2D films is most energetically preferable with the alternating (rather than "checkered") packing of the enantiomers with opposite specific rotation. The two enantiomeric forms of α-amino acids in the heterochiral 2D clusters are tilted with respect to the normal to the q direction at angles of φ(1)=20° and φ(2) = 33°, whereas the single enantiomeric forms are oriented at an angle of δ=9° with respect to the normal to the p direction. It is shown that the heterochiral 2D film based on the α-amino acid structures oriented at the angle φ(2)=33° with respect to the normal to the q direction possesses a rectangular unit cell with the geometric parameters a = 4.62 Å and b = 10.70 Å and the tilt angle of the alkyl chain of the molecule with respect to the interface t(2)=35°, which is in good agreement with the X-ray structural data a=4.80 Å, b=9.67 Å, and t(2)=37°. The parameters of the lattice structure of monolayers formed by amphiphilic amino acids are shown to be determined by the "a" type of the intermolecular H-H interactions, whereas the tilt angle of the molecules with respect to the interface depends on the volume and the structure of the functional groups involved in the hydrophilic part of the molecule. Spontaneous clusterization of the racemic form of α-amino acids at the air/water interface at 278 K takes place if the alkyl chain length is equal or higher than 12-13 carbon atoms, whereas for 298 K this clusterization threshold corresponds to 14 carbon atoms in the hydrocarbon chain. These values agree with the experimental data.

Quantum-chemical description of the thermodynamic characteristics of clusterization of melamine-type amphiphiles at the air/water interface

The semiempiric PM3 method is used to calculate the thermodynamic parameters of the formation of monomers, dimers, trimers, and tetramers of the amphiphilic melamine-type series of 2,4-di(n-alkylamino)-6-amino-1,3,5-triazine (2C(n)H(2n+1)-melamine) with n = 9-16. The most stable conformations are determined, which then are used to construct the clusters. The peculiar feature of these structures is the existence of a bend at one of the alkyl chains. Thus, the formation of infinite films becomes possible because of their spatial arrangement. From the calculation of the relative amount of various conformers in the mixture, it follows that, if the alkyl chain length is lower than 11-12 carbon atoms, the mixture is composed mainly of the monomers that do not contain any intramolecular interactions, whereas for higher alkyl chain lengths the monomers that involve such interactions prevail in the mixture. For all clusters thus considered, the thermodynamic parameters (enthalpies, entropies, and Gibbs' energies) of clusterization are calculated. It is shown that the dependencies of these parameters on the alkyl chain length either exhibit stepwise shape or are represented by the combination of a linear and stepwise function. This depends on the different number of hydrogen-hydrogen interactions in the structures considered. Five types of clusters that are capable of the formation of infinite 2D films are considered in detail. For each of these types, the dependencies of the clusterization enthalpy, entropy, and Gibbs' energy on the alkyl chain length in the constituting monomers are derived. Using these dependencies, it becomes possible to calculate these thermodynamic characteristics for clusters of any size, and also for infinite 2D films. It is shown that the spontaneous clusterization of 2C(n)H(2n+1)-melamine becomes possible if the alkyl chain length exceeds 9 carbon atoms.

Evaporation of sessile droplets of dilute aqueous solutions containing sodium n-alkylates from polymer surfaces: influences of alkyl length and concentration of solute

The evaporation of sessile droplets placed on polymer surfaces was studied by microscopic observation of the changes in shape of aqueous solution droplets in which the alkyl lengths and the initial concentrations of sodium n-alkylates were varied. Although the initial contact angles of the droplets were not significantly different, the evaporation process varied significantly with the alkyl length of the sodium n-alkylate employed. For the sodium dodecanoate (C 12), showing the highest surface activity, the concentration was found to have a significant effect on the evaporation process of the droplets. In the evaporation of water droplets, variations in the three distinct stages were caused by the different concentration of solutes distributed near or at the air/water interface. It is revealed that the concentration of droplet solute near the air/water interface requires not only solvent evaporation but also some affinity of the solute for the interface. The initial C 12 concentration-dependence of the evaporation of C 12 solution droplets is discussed with particular emphasis on the sudden spreading or sudden contraction of the contact area near the end of evaporation. It is suggested that the cluster formation by C 12 molecules at the air/liquid interface during the evaporation causes Marangoni instability in an evaporating droplet, and the clusters are expected to move dynamically, depending on the droplet concentration of C 12, from the droplet center to the contact line and vice versa, showing Marangoni flow along the air/water interface.

Molecular interactions in amphiphilic assemblies: theoretical perspective

In recent experimental studies, a number of morphological features have been revealed on amphiphilic assemblies that need consideration of the molecular chiral structure and the molecular polarity. Molecular chirality and polarity influence the intermolecular energy profile as a function of the distance and orientation between neighboring molecules in the condensed-phase aggregates of mono- and bilayers. After the experimental information is summarized, related microscopic theoretical works are presented. The molecular theory shows that the mesoscopic chiral shape of the condensed phase can be predicted from the molecular chiral structure studying the intermolecular energy profile. The theoretical insights have implications for related biological systems.

Progress in characterization of Langmuir monolayers by consideration of compressibility

Over decades, information about the rheological properties of the condensed monolayer phases has been obtained by introduction of a two-dimensional compressibility which is defined on the basis of the surface pressure-molecular area (Pi-A) features of the monolayer. Since the last decade, fundamental progress was attained in the experimental determination of the main characteristics of Langmuir monolayers in microscopic and molecular scale. Already smallest changes in the molecular structure of the amphiphile can result in changes in the molecular arrangement in the monolayer and thus, in changes of the main characteristics of the monolayer such as, the surface pressure-area per molecule (Pi-A) isotherms, the shape and texture of the condensed phase domains and the two-dimensional lattice structure. As the classical equations of state allowed only characterisation of the fluid (gaseous, liquid-expanded) state, thermodynamically based equations of state, which consider also the aggregation of the monolayer material to the condensed phase, have been developed. The present review focuses particularly to amphiphilic monolayers, the Pi-A isotherms of which indicate the existence of two condensed phases. For this case, the experimental results of the differences in the structure features and phase properties are discussed. The generalisation of the equation of state for Langmuir monolayers developed for the case that one, two or more phase transitions in the monolayer take place, is in agreement with the experimental results that the two-dimensional compressibility of the condensed phases undergoes a jump at the phase transition, whereas the compressibility is proportional to the surface pressure within one of the condensed phases. An example is presented which explains the procedure of the theoretical analysis of Pi-A isotherms indicating the existence of two condensed phases. An element of the procedure is the application of the general principle that the behaviour of any thermodynamic system is determined by the stability condition. An interesting anisotropy of the compressibility is revealed by GIXD studies of the S-phase of octadecanol monolayers. However, similar studies performed close to the LS-S-phase transition would result in a thermodynamically impossible negative compressibility. Close to this phase transition, the compressibility cannot be determined from the positions of the maxima because the monolayer is in a disordered state attributed to elastic distortions by fluctuations with the structure of the new phase in the surrounding matrix without destroying the quasi-long-range positional order.

Surface Pressure Isotherm for the Fluid State of Langmuir Monolayers

The equation of state for the monolayer comprised of the molecules of different sizes (water and biopolymers) is modified to describe the fluid (liquid-expanded and gaseous) state of the insoluble molecules monolayer. In contrast to the equation of state derived previously in ref 1, this equation does not involve either the Gibbs' adsorption equation or the differential equation for the chemical potential of the insoluble component, but it is based only on the equations for the chemical potential of the solvent in the bulk and in the surface layer. The results calculated from the proposed equations are in perfect agreement with the experimental Pi-A isotherms of the liquid-expanded state obtained for Langmuir monolayers of various types of amphiphilic compounds. The values of molecular areas of amphiphilic molecules estimated from the fitting of experimental data to the proposed equation are found to be quite similar to those measured in independent grazing incidence X-ray diffraction (GIXD) experiments.

Quantum Chemical Analysis of the Thermodynamics of 2D Cluster Formation of n-Carboxylic Acids at the Air/Water Interface

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.

Quantum Chemical Semiempirical Approach to the Structural and Thermodynamic Characteristics of Fluoroalkanols at the Air/Water Interface

In the framework of quantum chemical PM3 approximation, the geometrical structure and thermodynamic functions characteristics of the formation of monomers (n = 1-14, 34), dimers (n = 1-14, 34), and trimers and tetramers (n = 1-8) of fluoroalkanols with the composition C(n)F(2)(n+1)CH(2)CH(2)OH are calculated. It is shown that, in contrast to the fatty alcohols, which have a flat zigzag structure, the fluoroalkanol monomers are helical with an average backbone torsion angle equal to 162 degrees. For the minimum-energy structure of dimers, the self-organization of the molecules in a dimer was observed; that leads to an opposite alternation of the torsion angles corresponding to the matching atoms in the two molecules that form the dimer. This results in the fact that the most stable conformation of the dimer is the double helix. The lead (39.5 A) and diameter (7.3 A) of the double helix are determined from the calculations of C(34)F(69)CH(2)CH(2)OH dimers. Enthalpy, entropy, and Gibbs energy of the clusterization are shown to be linearly dependent on the length of the fluorinated chain. From the analysis of these thermodynamic quantities, it is concluded that dimerization of fluoroalkanols at the air/water interface takes place if the hydrocarbon link number exceeds 6, whereas for ordinary alcohols this characteristic number is 11. These calculated values agree with experimental data. The additive scheme for the evaluation of the clusterization free energies for arbitrary clusters is developed and applied to obtain the estimate of the Gibbs clusterization energy for infinitely large clusters.