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

A theoretical basis is provided for the experimental fact that for various surfactant classes the alkyl chain length threshold varies for the formation of condensed monolayers. The existence of the alkyl chain length threshold for a surfactant enabling the formation of monolayers is determined by the entropy increment to the Gibbs' energy, assessed by using the quantum chemical semiempiric method PM3. The value of the clusterization threshold is not stipulated by the surfactant solubility in water, rather by the electron-donor and electron-seeking properties of the head groups. These properties in turn impact the value of the solubility threshold for surfactants. The value of the clusterization threshold depends quadratically on the substituent constants, i.e. it is independent of whether the functional group is a donor or an acceptor of electrons. Rather it depends only on the donor or the acceptor 'force' of the substituent. The square-law dependence of the surface clusterization threshold of the amphiphile on the solubility threshold is evidenced.

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.

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.

A quantum chemical model for assessment of the temperature dependence in monolayer formation of amphiphiles at the air/water interface.

In the present study it is shown that parameters used in the framework of the model for the assessment of the threshold temperature of spontaneous clusterization of nonionic amphiphiles at the air/water interface (T(Cl)) are independent of the amphiphile type used in the developed schemes. The temperature dependence of the clusterization Gibbs' energies of alkyl amides, α-amino acids and 2-hydroxycarboxylic acids obtained in the framework of several schemes is listed. The exploited schemes differ from each other by the degree of their theoretical validity. The values of the clusterization threshold temperature for substituted alkanes can be described by a fractionally linear function versus the number of CH···HC interactions in the framework of the simplest scheme taking into account the found corrections and agree well with available experimental data.

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.

Thermodynamics of the clusterization process of trans-isomers of unsaturated fatty acids at the air/water interface.

In the frameworks of the quantum-chemical semiempirical PM3 method, the thermodynamic parameters of trans-isomers of unsaturated carboxylic acids at the air/water interface were studied. Systems with 18-26 carbon atoms in the alkyl chain and different positions of the double bond are considered. Using quantum-chemical semiempirical PM3 method enthalpy, Gibbs' energy of monomers' formation from the elementary compounds and absolute entropy of trans-unsaturated carboxylic acids are calculated. It has been shown that thermodynamic parameters mentioned above for isomers with the same number of carbon atoms in the hydrocarbon chain but different position of double bond are practically the same within the margin of error. For dimers, trimers, and tetramers of the four trans-unsaturated carboxylic acids, the thermodynamic parameters of clusterization were calculated. It is shown that the position of double bond does not significantly affect the values of thermodynamic parameters of formation and clusterization of carboxylic acids with equal alkyl chain lengths. The only exception is the case that the double bond is in the ω-position (extremely distanced from the carboxylic group). In this case, the number of intermolecular interactions between alkyl chains is changed. Spontaneous clusterization of trans- in the standard conditions is possible for molecules that possess more than 16-17 carbon atoms in the alkyl chain. These threshold values exceed the corresponding values that were calculated previously using the quantum-chemical PM3 method for saturated carboxylic acids (12-13 carbon atoms in the alkyl chain) and are a little bit smaller than the corresponding parameters for cis-unsaturated carboxylic acids (18-19 carbon atoms). These values agree with experimental parameters. Also, the calculated structural parameters of trans-unsaturated carboxylic acids' monolayer for the unit cell with a = 6.98 Å, b = 8.30 Å, and for the molecular tilt angle with 64.95° agree with the experimental parameters.

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 analysis of thermodynamics of two-dimensional cluster formation of alpha-amino acids at the air/water interface.

The semiempirical quantum-chemical PM3 method is used to calculate the thermodynamic parameters of clusterization of the S-form of alpha-amino acids with the general composition C(n)H(2n+1)CHNH(2)COOH (n = 5-15) at 278 and 298 K. It is shown that six stable conformations of monomers exist, for which the thermodynamic parameters (enthalpy and Gibbs' energy) of the formation and absolute entropy are calculated. The correlation dependencies of the calculated parameters on the alkyl chain length are found to be linear. The structures of the monomers are used to build larger clusters (dimers, tetramers, hexamers). For all small clusters (comprised of two to six molecules), the thermodynamic parameters of formation and clusterization are calculated. It is shown that for tetramers and hexamers the enthalpy, entropy, and Gibbs' energy of clusterization are linearly dependent on the alkyl chain length, whereas for the dimers these dependencies are stepwise. The thermodynamic characteristics of clusterization of associates tilted by angles of 9 and 30 degrees with respect to the normal to the interface are calculated. It is shown that the 30 degrees angle orientation is more energetically advantageous for this class of compounds. The geometric parameters of the unit cell characteristic for the infinite 2D film which corresponds to the most advantageous conformation of the monomer were calculated using the PM3 parametrization to be a = 4.57-4.71 A and b = 5.67-5.75 A, with the angle between the axes theta = 100-103 degrees . These values agree well with the available experimental data. Spontaneous clusterization of alpha-amino acids at the air/water interface at 278 K takes place if the alkyl chain length exceeds 11-12 carbon atoms, whereas for 298 K this clusterization threshold corresponds to 13-14 carbon atoms in the alkyl chain, also in agreement 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.

Thermodynamics of the clusterization process of cis isomers of unsaturated fatty acids at the air/water interface.

In the framework of the semiempirical PM3 method, the thermodynamic parameters of cis isomers of unsaturated carboxylic acids at the air/water interface are studied. The model systems used are unsaturated cis fatty acid of the composition Delta = 12-15 and omega = 6-11, where Delta and omega refer to the number of carbon atoms between the functional group and double bond, and that between the double bond and methyl group, respectively. For dimers, trimers, and tetramers of the four acid series, the thermodynamic parameters of clusterization are calculated. It is shown that the position of the double bond does not significantly affect the values of thermodynamic parameters of formation and clusterization of carboxylic acids for equal chain lengths (n = Delta + omega). The calculated results show that for cis unsaturated fatty acid with odd Delta values the spontaneous clusterization threshold corresponds to n = 17-18 carbon atoms in the alkyl chain, while for monounsaturated acids with even Delta values this threshold corresponds to n = 18-19 carbon atoms in the alkyl chain. These differences in the clusterization threshold between the acids with even and odd Delta values are attributed to the formation of additional intermolecular hydrogen bonds between the ketonic oxygen atom of one monomer and the hydrogen atom linked to the alpha-carbon atom of the second monomer for the acids with odd Delta values or between the hydroxyl oxygen atom of one monomer and hydrogen atom linked to the alpha-carbon atom of the second monomer for the acids with even Delta values. The results obtained in the study agree satisfactorily with our experimental data for cis unsaturated nervonic (Delta15, omega9) and erucic acids (Delta13, omega9), and published data for some fatty acids, namely cis-16-heptadecenoic (Delta16, omega1), cis-9-hexadecenoic (Delta7, omega9), cis-11-eicosenoic (Delta11, omega9) and cis-9-octadecenoic acid (Delta9, omega9).

Simplified method of the quantum chemical analysis for determination of thermodynamic parameters of 2D cluster formation of amphiphilic compounds at the air/water interface.

A simplified method is proposed to estimate the thermodynamic parameters of clusterization at the air/water interface for various classes of amphiphilic compounds with a single alkyl chain. The method is based on the calculation of thermodynamic characteristics only for one of the homologous series of dimers (n=6-16) governing the formation of infinite clusters. The method is used to calculate the thermodynamic parameters of clusterization for alcohols, thioalcohols, carboxylic acids and amines, and the dependencies of the Gibbs energy of clusterization on the alkyl chain length are evaluated. It is shown that the alkyl chain length, at which the spontaneous clusterization begins, as calculated using the proposed simplified method, is in fact the same as that calculated using the additive scheme developed earlier. The simplified method proposed was verified using alkylnitriles as example. In contrast to alcohols, thioalcohols and amines, infinite 'rhombic' clusters are formed rather than 'rectangular' clusters for this class of compounds. Spontaneous clusterization of nitriles is shown to start for alkyl chains containing 18-19 carbon atoms. This value agrees with that obtained from experimental data with 17-18 carbon atoms. The proposed simplified method introduces an exact and suitable tool for the estimation of thermodynamic parameters of the clusterization of amphiphilic compounds.

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.