Quantum Chemical Approach in the Description of the Amphiphile

Article pubs.acs.org/JPCB

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 Yuri B. Vysotsky,† Elena A. Belyaeva,*,‡ Elena S. Kartashynska,† Valentine B. Fainerman,§ and Natalia A. Smirnova‡ †

Donetsk National Technical University, 58 Artema Street, 83000 Donetsk, Ukraine Institute of Chemistry, Saint Petersburg State University, University Avenue, 26, Petrodvorets, Saint Petersburg, 198504, Russian Federation § Medical Physicochemical Centre, Donetsk Medical University, 16 Ilych Avenue, Donetsk 83003, Ukraine ‡

S Supporting Information *

ABSTRACT: 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.

1. INTRODUCTION The study of self-organization processes, which include the formation of monolayers (in particular on the water surface) and micelles are usually interesting for researchers from the two positions - theoretical and practical. From the theoretical point of view formation of such systems is important in the understanding of the formation particularities of the new two-dimensional phase (which can be applied further in the simulation of the formation of three-dimensional structures as well); in the study of molecular recognition processes, modeling of cell membranes processes. At the same time Langmuir monolayers can be transferred onto a solid substrate (Langmuir−Blodgett or Langmuir−Schaefer method), the resulting structures found practical applications in microelectronics and optics, in the production of the thin-film coatings with desired optical, adsorption and friction properties; also in biotechnology−in the creation of artificial biological membranes and biosensors.1−3 Surfactant monolayers at different interfaces (in particular the Langmuir monolayers at water surface) have been deeply and comprehensively investigated during the last century. Since the 90th of the twentieth century quantum chemical methods have © XXXX American Chemical Society

joined to the experimental ones, such as X-ray diffraction and Brewster angle spectroscopy enabling modeling the monolayer unit cells and calculation of their structural and thermodynamic parameters. But despite the great amount of the papers on this subject, the problem of the correct accounting of the liquid phase in description of the monolayers has not been solved yet neither in ab initio nor in semiempirical methods. Continuum models, which take into account the solvent (such as AMSOL and COSMO), give one the opportunity to calculate parameters of molecules just in a single phase, so these methods do not fit for parameters calculations of the systems which involve two phases, for example the air/water interface. That is why, for such systems, the supramolecular approach is usually used in the quantum chemical calculations to consider a number of water molecules around the surfactant ones. Because of this the problem of the mutual location of all molecules in the regarded system arises. Moreover, the greater number of water molecules that is Received: December 4, 2014 Revised: January 20, 2015

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DOI: 10.1021/jp512099x J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

restricted Hartree−Fock method was applied to the calculation of the wave function. The standard entropy and Gibbs energy were estimated from the calculated vibrational frequencies via the usual statistical thermodynamic equations.14 Optimization of the structural characteristics and calculation of the thermodynamic parameters of molecules in water were carried out within the conductor-like screening model (COSMO). COSMO and COSMO-RS models are widely presented nowadays in different program complexes for molecular modeling. It shows good results in calculating of the range of parameters (for example, adsorption constants,15 pKa values,16 and interfacial tension17). In this procedure the solvent is represented by an ideal conductor for which the total electrostatic potential due to solute and solvent wipes out on the solute boundary. On the basis of screening energies, surface areas, and screening surface charge densities calculated for the regarded compounds with a continuum solvation model like COSMO the intermolecular interactions in a liquid system can be described as pairwise interactions of surface segments. The effects of the finite dielectric constant ε are recovered by correction factor which gives opportunity to use this method with the error less than 2ε−1. That is why COSMO is very well suited for high dielectric constant solvents like water.14,18,19 In this paper we set the value of the dielectric constant ε equal to 78.3 as all calculations were carried out under the normal conditions. Results of the direct calculations were processed in the frameworks of the program package Microsoft Office Excel. Theoretical and Experimental Background of the Proposed Models. 1 X-ray diffraction data show that condensed monolayers at air/water interface are characterized by the crystalline lattice structure (see, for example, ref 20). 2 All molecules of the monolayer are in the maximum extended all-trans conformation. In case when one of the boundary phases is water hydrophilic part of surfactant is immersed in the water phase and the hydrophobic one is pushed out of water. As a result molecules of the monolayer are stretched (e.g., refs 21 and 22). 3 Molecules are immersed in the water phase on the same number of the methylene groups (usually 2−3 groups).23 4 The value of the angle between molecules of the monolayer and the normal to the interface for different classes of the surfactants is in the range 0−40°.12,13 5 Intermolecular interactions are pairwise additive. The force of the intermolecular interactions decreases significantly with the increasing of distance between interacting molecules; it is inversely proportional to the distance between molecules raised to the sixth power. So, in theoretical description of monolayers it is correct to consider only intermolecular interactions between the nearest molecules.20,21 Model 1. Using quantum chemical methods in description of the monolayers at interfaces faces a number of difficulties and the main one is absence of possibility to calculate structural and thermodynamic parameters of the molecules which are at the interface between two immiscible phases. It is possible to neglect one of the phases presuming that molecule completely belongs to the other phase. But in such case one needs to estimate neglected increments and in some way to consider the influence of the interface on the calculated parameters. Model 1 was developed to describe clusterization of the substituted alkanes at air/water

considered, the more complex this problem is in view of the rapidly increasing possible agglomeration number. In our previous studies,4−11 we considered the air/water interface in calculations of the structural and thermodynamic parameters for the film formation of substituted alkanes through its orienting and stretching effect. According to this model (see model 1) hydrophilic functional group of the molecule and several nearest methylene groups tend to immerse in water phase, and the rest part of the nonpolar hydrocarbon radical is ejected into the air phase; the number of methylene groups immersed in water is usually the same for molecules in the monolayer. So the interface orients and stretches the monolayer molecules. As a result, the surfactants form monolayers with the densest packing, when the surfactant molecules are maximally extended in all-trans conformation, occupy the minimum area, and orient at some angle (often 0−40°12,13) to the surface normal. Model 1 can describe correctly such high-ordered condensed monolayers.4−11 The results obtained within model 1 are in a good agreement with the available experimental data such as the threshold of the spontaneous clusterization, structural parameters of the monolayers (parameters of the unit cell, tilt angle of the monolayer molecules with respect to the interface), but in the same time this model needs some correction to consider the influence of the liquid phase not indirectly but at least in the frameworks of the continuum model. Essentially, model 1 needs such improvement to consider the parameters of surfactants molecules which are completely or partly ionized (for example, carboxylic acids in the alkaline medium and amines in the acidic medium), because in such case the neglection of the solvent impact will be too rude approximation. It would be interesting to determine what immersion of monolayer molecules in the liquid phase is energetically preferable.

2. METHODS Monolayers can be described as van der Waals molecules, so in order to calculate their parameters within quantum chemical methods one needs to take into account electron correlations. In the framework of nonempiric methods, the electron correlation is considered, but the use of such methods is attended by the significant time requests. Therefore, in the frameworks of the proposed approach intermolecular interactions should be considered via atom−atomic potentials. Calculations in the frameworks of semiempirical methods include approximate solution of the Schrö dinger equation and atom−atomic potentials. Different semiempirical methods are characterized by different potentials and they are parametrized using different physicochemical properties. Earlier6,7 we showed that the most adequate description of the intermolecular interactions between molecules of substituted alkanes in the monolayer and the most accurate results in calculation of parameters of the monolayer formation can be obtained within semiempiric PM3 method. Besides that PM3 method is parametrized with respect to the enthalpies of formation. So, optimization and calculations of the thermodynamic parameters (enthalpy, entropy and Gibbs’ energy) were carried out in the frameworks of the PM3 method (program complex Mopac 2012).14 The eigenvector-following algorithm used in the Mopac2000 package by default for the geometry optimization was found unsuitable for large clusters. So, modified Broyden−Fletcher−Goldfarb−Shanno (BFGS) procedure was used for optimization of the investigated structures and for calculation of their thermodynamic properties. The minimum points were identified as those for which the Hessian matrix does not contain negative eigenvalues. The B


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The Journal of Physical Chemistry B interface; within this model quantum chemical calculations were carried out for the structures in vacuum (it was decided that results obtained for the molecules and clusters in vacuum are close to the corresponding results obtained in air phase as dielectric permittivities for these two phases are also close). When constructing the cluster structures we consider that all molecules are extended in all-trans conformation, and immersed in water phase on the same number of the methylene groups (usually 2−3 groups)23 so that the “mattress”-like structure is formed on the water surface. Thereby, it was no direct accounting of the interaction between the monolayer molecules and the liquid phase molecules. It was shown7 that enthalpies of dimerization of fatty alcohols in water and in air are very similar, this fact allows to use model 1 correctly in the description of the structural and thermodynamic parameters of the un-ionized surfactants at the air/water interface. In the same time this model does not fit for description of clusterization of the ionized surfactant forms since it is impossible to neglect of the solvation effects in this case. In addition, as quantum chemical calculations were carried out only for the structures in the water and air phases, model 1 can be used only for the water/air interface. The second hindrance is the problem of consideration of the intermolecular interactions in the monolayer. Particularly, as it is mentioned above, description of the intermolecular interactions needs accounting of the electron correlation, so such calculations are impossible in the frameworks of the quantum mechanic methods and need significant computing resources and time expenses. However, modern quantum chemical methods include atom−atomic potentials, which implicitly consider electron correlation. This problem is solved in the best way in quantum chemical semiempirical PM3 method for the observed systems. Thus, optimizations of the cluster structures and calculations of the thermodynamic parameters of formation were carried out within PM3 method. Model 1 can be used in description of the solid high-ordered monolayers, but is not applicable to investigations of liquid and gaseous films. The monolayer translational symmetry needs to be considered in calculations that are another complex task. Fortunately, intermolecular interactions are pairwise additive. As the force of the intermolecular interaction is inversely proportional to the distance between interacting molecules raised to the sixth power, it is correct to consider only intermolecular interactions between the nearest molecules in theoretical description of the monolayer24,25 neglecting the translational symmetry. Intermolecular interactions between molecules of the substituted alkanes in the monolayers significantly depend on the mutual orientation of the interacting molecules. They can be identified by mutual disposition of the hydrogen atoms of the hydrocarbon chain and mutual disposition of the functional groups. Presuming that the nearest atoms make the maximum increment in energy of intermolecular interaction we showed4−12 that intermolecular interaction between two nearest molecules of the substituted alkanes can be resolved into increments of the interactions between the nearest methylene groups and the nearest functional groups (see Figure 1). We singled out several types of the pairwise CH···HC interactions depending on the mutual orientation of the interacting molecules. The most energetically preferable are ≪a≫ and ≪f≫ types of the interactions (see Figure 2),25 which are realized in the monolayers of the fatty alcohols at the air/water interface. As pairwise CH···HC interactions of the ≪a≫ and ≪f≫ types were

Figure 1. Illustration of the pairwise interactions between the nearest methylene groups (thick arrows) and the nearest functional groups (thin arrows).

Figure 2. Illustration of the ≪a≫ and ≪f≫ types of interactions.25

revealed to be isoenergetic,25 so in what follows, the interactions of both types were considered simultaneously and their number identified as κa. As a result the additive scheme was obtained, which allows calculating the thermodynamic clusterization parameters for the clusters of any dimensions including monolayer. Owing to the fact that the program package Mopac 2012 is capable of calculations of thermodynamic parameters at different temperatures, Model 1 also gives one the opportunity to obtain temperature dependencies of clusterization parameters. Procedure 1. To calculate structural and thermodynamic parameters of the clusterization of the substituted alkanes in the frameworks of model 1 one needs to follow the next sequence of actions: 1 Calculation of structural parameters of the most stable conformations of the regarded surfactant in the frameworks of the quantum chemical semiempirical PM3 method paying attention to the fact that the hydrocarbon chain must be maximally extended (all methyl groups must be in all-trans conformation). To determine mutual disposition of the hydrocarbon chain and functional group one should make conformational analysis. For this analysis one has to vary the value of the torsion angle between the plane of the hydrocarbon chain and the plane of the functional group from 0° to 360° with the step of 5°, for example. The enthalpy of formation of every structure should be calculated at various torsion angles in order to get dependence of the enthalpy of formation on the value of the angle. In the vicinity of the obtained minima one should make the additional optimization, after which the most energetically preferable structures are determined. C


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Figure 3. Graphical illustration of procedure of the changing of the angle to get dependence of the Gibbs’ energy of dimers formation on the value of angle between molecules of the monolayer and normal (ϕ < ϕ1 < ϕ2).

2

3

4

5

6

These structures are initial ones for construction of structures of the dimers, trimers, tetramers and larger clusters up to monolayer. Calculation of thermodynamic parameters (the enthalpy, Gibbs’ energy) of formation and the absolute entropy for the series of the most energetically preferable conformations C6 − C16. The angle between monolayer molecules and the normal to the interface was estimated applying the procedure described in2 (in the case of surfactants the angle varies from 0° to 45°). In order to determine the value of this angle we vertically shifted one molecule in dimer with respect to the other while the second molecule was fixed. The angle changes during this motion (see Figure 3), for each structure obtained in such a way that its Gibbs’ energy of formation was calculated. As a result we have obtained the dependence of the Gibbs’ energy of dimer formation on the value of molecular tilt angle to the normal to the interface, which enables us to obtain the most stable dimer structure. On the basis of the most energetically preferable structures of the monomers accounting for the value of the angle between molecules of the monolayer and normal to the interface, one should form structures of the dimers, trimers, tetramers and other small clusters, which are comprised in the monolayer. It is obvious that in all these structures monomers need to be located parallel to each other (functional groups in one direction, hydrocarbon chains in the other) as in real condensed monolayer. Then, obtained structures need optimization. This procedure should be carried out for the homologous series of structures C6−C16 as well. The next step is calculation of the thermodynamic parameters (enthalpy, Gibbs’ energy) of formation and the absolute entropy for the series of the small clusters optimized in the supermolecule approximation (as is described in the previous item). Parameters of the clusters within this approximation are calculated like parameters of the single molecule. Water molecules were not taken into account in this calculation. In order to calculate thermodynamic parameters (enthalpy, entropy, Gibbs’ energy) of clusterization at 298 K, ΔH°mcl, ΔS°mcl, and ΔG°mcl, one should use the formulas: ΔH°mcl = ΔH°298 − mΔH°298,mon, ΔS°mcl = S°298 − mS°298,mon, and ΔG°mcl = ΔH°mcl − TΔS°mcl. Here m is the number of monomers in the cluster, ΔH°298 is the enthalpy of formation of the cluster, kJ/mol; S°298 is the absolute entropy of the cluster, J/(mol·K); ΔH°298,mon is enthalpy of formation of the monomer, J/(mol·K);

S°298,mon is absolute entropy of the monomer, J/(mol· K); T is the absolute temperature, K. Conclusions about the structure of the unit cell for the regarded monolayer should be made on the basis of all calculated values of the clusterization Gibbs’ energy. 7 For the values of thermodynamic parameters calculated in item 6, one should obtain their correlation dependencies on the number of all pairwise interactions in the considered cluster. Using the estimated increments of all present pairwise interactions between the nearest molecules in the monolayer one can calculate thermodynamic parameters (enthalpy, entropy, Gibbs’ energy) of clusterization for the cluster of any dimension if the regarded cluster is a part of the investigated monolayer. 8 The dependencies obtained for clusters of various size in item 7 give opportunity to estimate thermodynamic parameters per one monomer for the infinite cluster (monolayer); the procedure is described in detail below. 9 The last step is calculation of the thermodynamic parameters of the monolayer formation for the investigated class of compounds. Then, one should compare the calculated structural and thermodynamic parameters with the corresponding experimental data. Model 2. The main task of model 2 is to account explicitly the influence of two adjacent phases on the parameters of amphiphile clusterization in the interface region between the phases (in this work we investigated the air/water interface). For solving this problem an extension of model 1 is needed. According to model 2, the influence of the phases on the calculated thermodynamic parameters is estimated by carrying out calculations in the both phases. The quantum chemical calculations and estimations of thermodynamic parameters are carried out separately for each of two phases, the nature of the phase being taken into account (e.g., the dielectric permeability of each of the phases can be estimated in frames of the continuum model COSMO).14 Procedure 2. 1 One needs to obtain the most stable conformations of monomers of the investigated class of compounds in both adjacent phases as described in item 1 of procedure 1. 2 Thermodynamic parameters (enthalpy, Gibbs’ energy) of formation and the absolute entropy for the series of the most energetically preferable conformations of C6−C16 need to be calculated. For the calculated values of thermodynamic parameters in each of the phases one should obtain the correlation dependencies of the parameters on the number of methylene groups in one molecule. D


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The Journal of Physical Chemistry B 3 After, for methylene groups and functional groups, the increments to the enthalpy, Gibbs’ energy of formation and the absolute entropy of monomers in the both phases are determined, the corresponding parameters of monomers at the air/water interface can be estimated. To calculate these parameters one needs to sum up all increments from methylene and functional groups taking into account to what phase the groups under consideration belong. 4 On the basis of the most energetically preferable structures of monomers accounting the value of the angle between monolayer molecules and the normal to the interface one should form structures of dimers, trimers, tetramers and other small clusters, which compose the monolayer. Then, the obtained structures need to be optimized (this procedure should be carried out for the homologous series of structures C6−C16 as well). 5 After that one needs to do quantum chemical calculations of thermodynamic parameters of formation for all optimized clusters. The values of the enthalpy, entropy, Gibbs’ energy of clusterization for all considered clusters should be calculated for the both adjacent phases (see item 6 of procedure 1). 6 Correlation dependencies of the calculated thermodynamic parameters of clusterization on the number of all pairwise interactions between the nearest molecules in the clusters should be obtained separately for the both phases. In such way all increments of the pairwise interactions of different types will be singled out (for each of two adjacent phases). The determination of all increments of pairwise interactions in enthalpy, entropy, and Gibbs’ energy of clusterization allows obtaining the corresponding thermodynamic parameters of clusterization for the clusters which are partly immersed in one phase and partly in the other. 7 Correlation dependencies for the calculated clusterization parameters obtained in item 7 should be converted into the corresponding dependencies, which give opportunity to calculate thermodynamic parameters per one monomer for the infinite cluster (monolayer) at air/liquid or liquid/ liquid interfaces (the procedure is described in details below); 8 All increments of pair interactions between methylene groups (CH···HC interactions) and pairwise interactions between functional groups in the two adjacent phases should be summed in order to calculate thermodynamic parameters of clusterization for the monolayer at air/liquid or liquid/liquid interface per one monomer. 9 Finally the comparison of the calculated structural and thermodynamic parameters of the monolayer with the corresponding experimental data should be made.

Figure 4. Geometric structure of monomers of fatty alcohol (R = hydrocarbon chain).26

further calculations only conformers with the angle 60° were under consideration. Analysis for the water phase has shown that the most energetically preferable monomer position for fatty alcohols is also characterized by the torsion angle C2−C1−O−H = 60°. Then for the series of monomers C6H13OH−C16H31OH, the thermodynamic parameters of their formation (enthalpy and Gibbs’ energy) and absolute entropy were calculated in the water and air phases. The results are shown in Table 1. The corrected values for enthalpy and Gibbs’ energy are presented in Tables 1 and 2 in brackets (the correction procedure is described in details below). For the enthalpy of formation and the absolute entropy calculated for monomers in the air and in the water phase correlation dependencies on the number of the methylene groups in the chain were obtained: ΔH °298,mon(air) = −(22.7 ± 0.1)nair − (199.9 ± 0.1) kJ/mol

(R = 0.99999, S = 0.01 kJ/mol, N = 11) (1)

S°298,mon(air) = (32.1 ± 0.1)nair + (208.7 ± 0.6) J/(mol ·K) (R = 0. 99999, S = 0.6 J/(mol ·K), N = 11)

(2)

ΔH °298,mon(water) = −(22.8 ± 0.1)n water − (212.5 ± 0.2) kJ/mol

(R = 1, S = 0.02 kJ/mol, N = 11)

(3)

S°298,mon(water) = (31.1 ± 0.1)n water + (217.8 ± 0.9) J/(mol ·K) (R = 0.99997, S = 0.8 J/(mol ·K), N = 11)

(4)

where nair and nwater are the numbers of the methylene groups in the air and water correspondingly; R is regression coefficient; S is standard deviation; N is sample amount. To obtain corresponding parameters of the molecule of the fatty alcohol which partly belongs to the air and partly to water phase one should use the next formulas:

3. RESULTS AND DISCUSSION In this paper, the proposed model 2 was tried to study clusterization of fatty alcohols (C6H13OH − C16H31OH) at the air/water interface. According to model 2 described above, first, thermodynamic parameters of monomer formation were calculated. Structural parameters of monomers of fatty alcohols in the air were estimated earlier,18 so there was no need to perform a special conformation analysis (item 1) for these monomers. Torsion angles are C2−C1−O−H = 60° and 300° (−60°) (see Figure 4), as the structures characterized by these angles are isoenergetic, in

ΔH °298,mon(air − water) = −(22.7 ± 0.1)nair − (22.8 ± 0.1) n water − (212.5 ± 0.2) kJ/mol

(5)

S°298,mon(air − water) = (32.1 ± 0.1)nair + (31.1 ± 0.1)n water + (217.8 ± 0.9) J/(mol ·K) E

(6) DOI: 10.1021/jp512099x J. Phys. Chem. B XXXX, XXX, XXX−XXX

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are presented in Table 2 (other levels of immersion are presented in Supporting Information, Table 2S). For correct calculation of the absolute entropy (and Gibbs’ energy of formation) one needs to account free rotation of methylene and hydroxyl groups. The direct quantum chemical calculations (and as a result the values of the absolute entropy calculated by the formula 6) do not consider the mentioned phenomenon, and the corrections were obtained as earlier,1−8 using the least-squares method. So, to calculate these corrections one should estimate the difference between the results of the direct quantum chemical calculations and the corresponding experimental values of the absolute entropy. Then the correlation dependence of this difference on the number of methylene groups in water (and consequently on their number in the air phase) should be analyzed. In this case, the free term characterizes the correction on the free rotation of the hydroxyl group and methylene groups in the water phase (the number of the methylene groups per an alcohol molecule in the water phase in each case has a fixed value from 1 up to 5); the slope characterizes correction on the free rotation of one methylene group in the air. As a result, the correction per one methylene group in the air for molecules of fatty alcohols is 7.2 J/mol·K (at any sinkage in water phase). Earlier these corrections were obtained for several other classes of substituted alkanes in the air; for normal fatty amines, thioalcohols, carboxylic acids the corrections are 7.1 J/(mol·K),9 7.0 J/(mol·K),8 6.1 J/(mol·K),4 7.3 J/(mol·K)11 correspondingly. The values of the absolute entropy and Gibbs’ energy of formation for the series of fatty alcohol monomers with account of the correction for the free rotation of methylene and hydroxyl groups are shown in Table 1 and Table 2 in brackets. From Table 1 one can see a good agreement between the experimental and calculated (with account of the free rotation correction) values of the absolute entropy in the air phase, the standard deviation being 3.95 J/ (mol·K). The standard deviation for the Gibbs’ energy of monomer formation in the water phase on the number of the carbon atoms in the chain is 0.3 kJ/mol and in the air phase −0.2 kJ/mol, and for the monomers that are at air/water interface (or partly immersed in water), this value is 0.2 kJ/mol. As we can see, the values of these standard deviations almost coincide, so model 2 is incapable to obtain the most energetically preferable sinkage of the monomer molecule. Small Clusters. The structures of small clusters (from dimers to nonamers) were constructed on the basis of the optimized monomer structure (see Figure 5). For each cluster series with the chain length from 6 to 16 carbon atoms, the optimization was carried out for both air and water medium. From Table 3, one can see that the formation of trimers and hexamers is characterized by the lower Gibbs’ energy than that of the dimers formation, so the formation of the monolayers with the hexagonal unit cell (see Figure 6) seems more likely than that with the oblique unit cell. Such results correspond well to the parameters calculated earlier within model 126 on one hand, and they are in a good agreement with the experimental data26−29 on other hand. The available experimental data30−35 show that amphiphils with a small functional group (when its crosssectional area is commensurable with that of the hydrocarbon chain)such as alcohols, carboxylic acids, amines, thioalcohols, amides of the carboxylic acids, and so on, usually form monolayers with the hexagonal unit cell. At the same time monolayers of the compounds with more voluminous functional

Table 1. Thermodynamic Parameters of Alcohol Monomers system C6H13OH C7H15OH C8H17OH C9H19OH C10H21OH C11H23OH C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH C6H13OH C7H15OH C8H17OH C9H19OH C10H21OH C11H23OH C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH C6H13OH C7H15OH C8H17OH C9H19OH C10H21OH C11H23OH C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH C6H13OH C7H15OH C8H17OH C9H19OH C10H21OH C11H23OH C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH

monomer (air)

monomer (water)

ΔH°298,mon, kJ/mol −349.6 −372.4 −395.2 −418.1 −440.9 −463.8 −486.6 −509.5 −532.3 −555.2 −578.0 S°298,mon, J/(mol·K) 401.0 (479.1) 403.9 433.3 (518.6) 435.7 465.4 (557.9) 468.4 496.8 (596.4) 497.2 529.1 (635.8) 530.1 561.8 (675.7) 559.3 594.4 (715.5) 591.0 625.2 (753.5) 621.8 658.7 (794.1) 654.3 689.7 (832.3) 684.6 721.2 (871.0) 716.0 ΔS°298,mon, J/(mol·K) −649.6 (−571.5) −646.7 −753.6 (−668.3) −751.2 −857.7 (−765.3) −854.8 −962.6 (−863.0) −962.2 −1066.6 (−959.8) −1065.5 −1170.1 (−1056.2) −1172.6 −1273.8 (−1152.7) −1277.1 −1379.2 (−1250.9) −1382.6 −1482.0 (−1346.5) −1486.4 −1587.3 (−1444.6) −1592.4 −1692.0 (−1542.2) −1697.2 ΔG°298,mon, kJ/mol −142.7 (−166.0) −156.8 −134.4 (−159.8) −148.5 −126.2 (−153.7) −140.5 −117.6 (−147.3) −131.3 −109.4 (−141.2) −123.4 −101.3 (−135.2) −114.3 −93.1 (−129.2) −106.0 −84.4 (−122.6) −97.4 −76.5 (−116.9) −89.3 −67.9 (−110.4) −80.6 −59.4 (−104.1) −72.2 −336.3 −359.0 −381.7 −404.5 −427.2 −449.9 −472.7 −495.4 −518.2 −540.9 −563.6

experiment (air)26 −336.4 −355.5 −381.2 −396.7 −418.4 −436.7 −460.4 −475.9 −501.8 −522.5 −543.1 479.2 518.5 557.7 597.0 636.2 675.2 714.7 753.9 793.2 832.4 871.7 −571.4 −668.4 −765.4 −862.4 −959.4 −1056.7 −1153.5 −1250.5 −1347.5 −1444.5 −1541.5 −166.1 −156.3 −153.1 −139.7 −132.5 −121.8 −116.7 −103.3 −100.3 −92.0 −83.7

When molecule sinkage in the water phase is one methylene group, then nwater = 1, when sinkage is two groups, then nwater = 2 and so on; nair = n − nwater, where n is the total number of the carbon atoms in the chain. In order to calculate entropy of the monomer formation one needs to subtract absolute entropies of the elements included in regarded compound from the absolute entropy of this compound. Gibbs’ energy was calculated according the wellknown formula ΔG°298,mon = ΔH°298,mon − TΔS°298,mon. As illustration thermodynamic parameters calculated for the molecules that immersed in water for the 3 methylene groups F


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The Journal of Physical Chemistry B Table 2. Thermodynamic Parameters of the Fatty Alcohol Monomers at the Air/Water Interface (nwater = 3) system

ΔH°298, J/mol

S°298, J/(mol·K)

ΔS°298, J/(mol·K)

ΔG°298, kJ/mol

C6H13OH C7H15OH C8H17OH C9H19OH C10H21OH C11H23OH C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH

−349.2 −371.9 −394.7 −417.4 −440.2 −462.9 −485.6 −508.4 −531.1 −553.8 −576.6

407.4 (500.7) 439.5 (540.0) 471.6 (579.2) 503.6 (618.5) 535.7 (657.7) 567.8 (697.0) 599.9 (736.2) 631.9 (775.5) 664.0 (814.7) 696.1 (854.0) 728.2 (893.2)

−643.2 (−549.9) −747.4 (−646.9) −851.6 (−743.9) −955.7 (−840.9) −1059.9 (−937.9) −1164.1 (−1034.9) −1268.3 (−1132.0) −1372.5 (−1229.0) −1476.7 (−1326.0) −1580.8 (−1423.0) −1685.0 (−1520.0)

−157.5 (−185.3) −149.2 (−179.2) −140.9 (−173.0) −132.6 (−166.8) −124.3 (−160.6) −116.0 (−154.5) −107.7 (−148.3) −99.4 (−142.1) −91.04 (−135.9) −82.7 (−129.8) −74.4 (−123.6)

Figure 5. Geometrical structures of small clusters of the fatty alcohol.

indicated as n1 − n6. The number of molecules in the cluster in one direction was indicated as q and in the other one as p (so, each cluster contains p × q monomers). The following correlation dependencies were obtained for the clusterization:

groups (hydroxycarboxylic acids, amino acids and their N-acyl substitutes) are usually characterized by the oblique unit cell. The correlation dependencies on the number of pairwise interactions were determined for the calculated thermodynamic parameters of clusterization in the air phase. The pairwise interactions between the nearest functional groups were also taken into account together with the number of pairwise CH··· HC interactions described above. In the preceding study26 it is shown that there are six types of pairwise interactions between hydroxyl groups in the hexagonal fatty alcohol monolayer, these interactions depending on the mutual orientation of the hydroxyl groups (see Figure 7). Here and later on these interactions are

ΔH °mCl (air) = − (9.8 ± 0.1)κa a − (17.5 ± 1.4) (n1a + n2 a) + (10.8 ± 0.8)(n4 a + n5a) + (5.2 ± 2.0)n6 a kJ/mol (R = 0.9998; S = 6.1 kJ/mol; N = 69) G

(5)


S°m,298(air), J/(mol·K)

640.1 690.1 742.6 794.1 848.3 896.7 950.6 1001. 8 1053.8 1106.0 1159.2

837.7 885.2 973.3 1023.6 1114.1 1171.3 1253.4 1312.9 1394.0 1464.1 1538.0

832.1 909.5 968.7 1048.9 1110.0 1192.4 1248.3 1337.9 1395.3 1475.5 1533.7

1007.7 1080.1 1174.6

ΔH°m,298(air), kJ/mol

−702.5 −756.0 −803.9 −857.3 −905.3 −958.6 −1006.6 −1060.0 −1108.0 −1161.3 −1209.3

−1093.7 −1187.7 −1259.6 −1353.5 −1425.5 −1519.4 −1591.4 −1685.4 −1757.3 −1851.3 −1923.2

−1095.8 −1173.2 −1261.7 −1339.7 −1427.7 −1505.0 −1593.6 −1670.9 −1759.6 −1836.9 −1925.6

−1475.1 −1590.1 −1700.0

system




C6H13OH C7H15OH C8H17OH

Cl

H

−129.9 −154.2 −174.0

−86.9 −96.2 −116.4 −125.6 −146.0 −155.2 −175.6 −184.7 −205.1 −214.2 −234.7

−84.8 −110.7 −114.6 −140.1 −143.9 −169.6 −173.3 −199.1 −202.9 −228.6 −232.4

−29.9 −38.0 −40.5 −48.4 −50.9 −58.7 −61.3 −69.1 −71.7 −79.5 −82.1

ΔH 298(air), kJ/mol

air phase

−596.3 −653.2 −687.1

−371.0 −390.43 −427.63 −441.56 −477.22 −492.95 −534.88 −537.76 −580.79 −593.60 −630.00

−365.3 −414.8 −423.0 −466.9 −473.2 −514.1 −529.9 −562.7 −582.0 −605.0 −625.6

−161.9 −176.5 −188.2 −199.5 −209.8 −226.9 −238.2 −248.6 −263.6 −273.3 −283.2

ΔSCl298(air), J/(mol·K)

47.8 40.5 30.8

23.7 20.1 11.0 5.9 −3.8 −8.3 −16.2 −24.4 −32.1 −37.3 −46.9

24.1 12.9 11.7 −1.0 −2.9 −16.4 −15.4 −31.4 −29.4 −48.4 −45.9

18.3 14.6 15.6 11.1 11. 7 8.9 9.7 5.0 6.9 1.9 2.3

ΔG 298(air), kJ/mol Cl

Dimers CC6H13OH C7H15OH C8H17OH C9H19OH C10H21OH C11H23OH C12H25OH C13H27OH C14H28OH C15H29OH C16H31OH Trimers 1 C6H13OH C7H15OH C8H17OH C9H19OH C10H21OH C11H23OH C12H25OH C13H27OH C14H28OH C15H29OH C16H31OH Trimers 2 C6H13OH C7H15OH C8H17OH C9H19OH C10H21OH C11H23OH C12H25OH C13H27OH C14H28OH C15H29OH C16H31OH Tetramers C6H13OH C7H15OH C8H17OH

system

−1518.3 −1633.6 −1744.5

−1125.5 −1203.1 −1291.7 −1369.2 −1457.8 −1535.4 −1623.9 −1701.8 −1790.4 −1867.9 −1956.1

−1128.8 −1223.2 −1294.7 −1389.5 −1461.2 −1555.6 −1627.5 −1722.2 −1793.5 −1888.1 −1948.0

−725.2 −779.2 −826.8 −880.8 −928.5 −982.4 −1030.2 −1084.1 −1131.8 −1185.5 −1233.9

ΔH°m,298(water), kJ/mol

1022.4 1089.4 1175.7

843.4 910.1 991.5 1053.3 1127.0 1195.8 1255.3 1334.9 1407.9 1478.8 1536.8

848.8 892.5 984.1 1026.6 1125.1 1165.6 1257.5 1296.3 1404.6 1448.2 1539.9

642.5 691.3 751.5 795.0 854.8 894.8 956.7 994.3 1060.9 1100.4 1169.2

S°m,298(water), J/(mol·K)

−120.1 −144.1 −163.6

−76.9 −85.9 −106.0 −115.0 −135.1 −144.1 −164.0 −173.5 −193.5 −202.5 −222.2

−80.1 −106.0 −109.0 −135.3 −138.6 −164.3 −167.7 −193.9 −196.6 −222.7 −214.1

−26.1 −34.4 −36.4 −44.7 −46.7 −54.9 −56.9 −65.2 −67.2 −75.2 −77.9

ΔHCl298(water), kJ/mol

water phase

−593.2 −653.4 −697.7

−368.3 −396.9 −413.6 −438.2 −463.3 −482.2 −517.7 −530.6 −554.9 −574.9 −611.3

−362.9 −414.6 −421.0 −464.9 −465.2 −512.4 −515.5 −569.2 −558.2 −605.5 −608.2

−165.3 −180.1 −185.2 −199.4 −205.4 −223.9 −225.4 −249.3 −247.6 −268.7 −262.9

ΔSCl298(water), J/(mol·K)

56.7 50. 44.3

32.9 32.4 17.2 15.5 3.0 −0.4 −9.8 −15.3 −28.2 −31.2 −40.0

28.0 17.5 16.4 3.3 0.1 −11.6 −14.1 −24.3 −30.2 −42.2 −32.8

23.1 19.3 18.8 14.8 14.5 11.8 10.2 9.1 6.6 4.8 0.4

ΔGCl298(water), kJ/mol

Table 3. Thermodynamic Parameters of Formation (ΔH°m,298 kJ/mol,) and Clusterization (ΔHCl298 kJ/mol, ΔSCl298, J/(mol·K), ΔGCl298 kJ/mol), the Absolute Entropies S°m,298, J/(mol·K) of Fatty Alcohols in the Air and in Water Medium

The Journal of Physical Chemistry B Article


S°m,298(air), J/(mol·K)

1248.3 1341.2 1416.9 1531.3 1584.0 1677.5

1261.4 1355.6 1478.1 1575.9 1705.6 1797.0 1912.5 2029.0 2134.8 2241.7 2361.7

1378.8 1481.2 1612.6 1715.4 1847.9 1953.1 2088.4 2198.1 2337.3 2441.0 2570.8

1788.3 1925.6 2090.2 2231.0 2389.8

−1816.3 −1927.2 −2042.5 −2153.4 −2268.8 −2379.7

−1852.8 −2001.5 −2139.3 −2287.9 −2425.8 −2574.4 −2712.4 −2860.9 −2998.9 −3147.5 −3285.5

−2250.3 −2433.0 −2602.7 −2785.5 −2955.3 −3138.1 −3308.1 −3490.7 −3660.8 −3843.5 −4013.5

−3010.8 −3251.4 −3483.1 −3724.1 −3955.9

system

C9H19OH C10H21OH C11H23OH C12H25OH C13H27OH C14H28OH



I

C6H13OH C7H15OH C8H17OH C9H19OH C10H21OH

−320.4 −379.5 −429.2 −488.3 −538.2

−232.5 −279.1 −312.2 −358.6 −392.1 −438.4 −472.0 −518.2 −551.9 −598.1 −631.8

−171.4 −206.6 −230.6 −265.6 −289.8 −324.7 −349.0 −383.9 −408.1 −443.1 −467.4

−199.4 −218.3 −242.7 −262.7 −287.1 −307.1

ΔHCl298(air), kJ/mol

air phase


Table 3. continued

−1419.7 −1540.9 −1633.2 −1743.7 −1842.8

−1027.2 −1118.7 −1180.0 −1265.6 −1326.6 −1417.7 −1478.0 −1553.2 −1614.8 −1697.2 −1756.5

−743.6 −810.9 −849.1 −908.3 −939.7 −1011.9 −1059.5 −1097.0 −1158.7 −1206.7 −1244.4

−739.0 −775.1 −830.3 −846.3 −916.8 −957.3


102.6 79.7 57.5 31.3 10.9

73.61 54.26 39.45 18.52 3.26 −15.93 −31.53 −55.39 −70.67 −92.38 −108.35

50.2 35.1 22.5 5.1 −9.7 −23.1 −33.2 −57.0 −62.9 −83.5 −96.5

21.9 12.7 4.7 −10.5 −13.9 −21.9

ΔGCl298(air), kJ/mol Tetramers C9H19OH C10H21OH C11H23OH C12H25OH C13H27OH CC14H28OH C15H29OH C16H31OH Pentamers C6H13OH C7H15OH C8H17OH C9H19OH C10H21OH C11H23OH C12H25OH C13H27OH C14H28OH C15H29OH C16H31OH Hexamers C6H13OH C7H15OH C8H17OH C9H19OH C10H21OH C11H23OH C12H25OH C13H27OH C14H28OH C15H29OH C16H31OH Octamers C6H13OH C7H15OH C8H17OH C9H19OH C10H21OH

system

−3082.7 −3323.0 −3554.4 −3795.6

−2295.8 −2480.3 −2650.1 −2829.6 −3000.5 −3176.1 −3350.9 −3526.5 −3696.5 −3876.4 −4046.4

−1904.9 −2054.0 −2191.8 −2341.6 −2478.7 −2628.3 −2766.4 −2915.6 −3053.7 −3203.3 −3341.0

−1860.4 −1971.5 −2087.2 −2198.3 −2314.1 −2425.3 −2540.6 −2652.5


1788.1 1922.3 2103.4 2255.2

1483.3 1560.1 1684.0 1808.2 1941.1 2081.2 2208.8 2338.6 2477.1 2602.1 2748.1

1270.1 1358.9 1490.3 1575.1 1699.9 1802.2 1940.9 2020.7 2177.4 2247.9 2383.3

1256.1 1357.1 1423.9 1519.6 1590.1 1680.8 1759.4 1852.4


−286.31 −343.90 −392.56 −451.01

−198.4 −245.9 −278.8 −321.2 −355.2 −393.5 −431.3 −469.8 −502.7 −545.5 −578.5

−157.1 −192.1 −215.7 −251.2 −274.3 −309.5 −333.6 −368.3 −392.2 −427.5 −451.0

−188.1 −207.9 −232.2 −251.9 −276.3 −296.1 −320.3 −340.5


water phase

−1443.0 −1563.2 −1643.5 −1722.2

−940.0 −1054.0 −1126.2 −1174.8 −1239.5 −1274.9 −1337.3 −1392.3 −1448.5 −1505.4 −1548.1

−749.3 −819.6 −851.5 −910.8 −950.6 −994.5 −1014.3 −1088.4 −1093.9 −1174.9 −1196.9

−732.5 −763.3 −813.5 −844.4 −897.2 −936.2 −978.9 −1011.8


143.7 121.9 97.2 62.2

81.7 68.2 56.9 28.9 14.2 −13.6 −32.8 −54.9 −71.0 −96.9 −117.1

66.2 52.2 38.1 20.2 9.0 −13.2 −31.1 −44.0 −66.3 −77.4 −94.3

30.2 19.5 10.2 −0.2 −8.9 −17.1 −28.5 −39.0


The Journal of Physical Chemistry B Article


Article

161.2 130.8 111.4 67.1 44.8

ΔS°mCl (air) = − (17.4 ± 0.2)κa a − (126.1 ± 3.2)n1a − (66.0 ± 1.9)(n2 a + n3a + n6 a) − (40.7 ± 1.9) (n4 a + n5a) J/(mol ·K) (R = 0.9999; S = 14.1 J/(mol · K); N = 69) −1660.7 −1786.3 −1916.3 −1996.4 −2119.0

ΔH°mCl

(6)

Using the formula ΔG°m = − TΔS°m , we have obtained the following dependence of the clusterization Gibbs’ energy on the number of methylene groups: Cl

Cl


−333.7 −401.6 −459.7 −527.8 −586.7 1974.3 2134.9 2298.9 2478.1 2651.9

ΔG°mCl (air) = − (4.6 ± 0.2)κa a + (20.1 ± 2.4)n1a


+ (19.7 ± 0.6)n3a + (22.9 ± 1.3)(n4 a + n5a) + (24.9 ± 2.5)n6 a kJ/mol

(7)

where κa is the number of pairwise CH···HC interactions; n1−n6 are the numbers of pairwise interactions between hydroxyl groups of each type depending on their mutual orientation (see Figure 5); index a indicates air phase. Then, for the parameters calculated for the liquid water phase the corresponding dependencies take the following form: ΔH °mCl (water) = −(9.4 ± 0.1)κa w − (16.2 ± 1.4)n1w + (15.3 ± 1.3)n5 w + (11.8 ± 1.6)n6 w kJ/mol

−3479.7 −3753.1 −4016.8 −4290.4 −4554.6


water phase




(R = 0.9997; S = 6.7 J/mol · K; N = 75)

(8)

Nonamers C6H13OH C7H15OH C8H17OH C9H19OH C10H21OH

− (106.4 ± 7.00)n6 w J/(mol ·K)

116.2 88.7 59.8 27.2 −1.5

(9)

ΔG°mCl (air) = − (4.9 ± 0.2)κa w + (22.5 ± 2.2)n1w + (3.8 ± 1.8)n2 w + (6.5 ± 1.5)n4 w + (53.9 ± 2.1)n5 w

−1682.1 −1814.7 −1926.9 −1997.1 −2099.3

+ (43.5 ± 3.7)n6 w kJ/mol

1926.9 2085.0 2261.9 2474.4 2662.4 −3411.7 −3682.9 −3950.1 −4208.2 −4472.0 C6H13OH C7H15OH C8H17OH C9H19OH C10H21OH

(10)

w

index indicates the water phase. From the dependencies 5−10 one can see that n3w in water phase is statistically insignificant (i.e., the increment in the Gibbs’ energy of clusterization is approximately 0), while in the air phase the n3a increment in the corresponding parameter is (19.7 ± 0.6) kJ/mol. Thus, formation of such interaction in the liquid water phase is more preferable than in the air phase. The increments from n1 and n2 in the air and water phases coincide within the error; the n4 interaction is more preferable in water phase, while n5 and n6 are less preferable in water. It should be mentioned that pairwise CH···HC interactions at the interface occur (in Figure 8, this interaction is indicated by the arrow) in case when clusters are immersed in the water phase on the even number of methylene groups (e.g., 2 or 4 methylene groups). Since the increments from one pairwise CH···HC interaction in the air and in the water phase are very close (see 5−10), the increment from one pairwise CH···HC interaction at the air/ water interface was calculated as arithmetical mean from the corresponding increments in the water and air phases. Then, thermodynamic parameters of clusterization for the clusters, which are at air/water interface, can be calculated using the formulas

−385.1 −452.1 −514.4 −567.9 −627.1

S°m,298(air), J/(mol·K) system

ΔHCl298(air), kJ/mol

(n1w + n5 w ) − (12.9 ± 5.9)n2 w − (21.7 ± 5.1)n4 w (R = 0.9999; S = 16.8J/(mol ·K); N = 75)


Table 3. continued

air phase


ΔGCl298(air), kJ/mol

system

ΔS°mCl (water) = −(15.1 ± 0.2)κa w − (129.7 ± 2.6)

J


Article


Figure 6. Scheme of formation of the monolayer fragment with the hexagonal unit cell.

ΔG°mCl (air − water) = −(4.6 ± 0.2)κa a − (4.9 ± 0.2)κa w − (4.7 ± 0.2)κa a − w + (22.5 ± 2.2) n1w + (3.8 ± 1.8)n2 w + (6.5 ± 1.5)n4 w + (53.9 ± 2.1)n5 w + (43.5 ± 3.7)n6 w kJ/mol

To calculate the clusterization thermodynamic parameters of fatty alcohol cluster of any dimension at the air/water interface (but only in case when this cluster is a fragment of the hexagonal monolayer shown above in Figure 6) one needs to obtain the numbers of pairwise interactions between the nearest methylene groups and between the nearest hydroxyl groups of each type in the considered cluster (see Figure 6); then these numbers should be inserted in the dependencies 11−13. The number of the pairwise interactions can be expressed by the following formulas:

Figure 7. Schematic illustration of six types of the pairwise interactions between functional groups in the fragment of the fatty alcohol monolayer26

n1w = (q − 1)

{ p +2 1 }

(14)

⎧ (q − 1)(p − 1) ⎫ ⎬ n w 2 = (q − 1)(p − 1) − ⎨ ⎩ ⎭ 2 ⎧ (q − 1)(p − 1) + 1 ⎫ ⎬ =⎨ ⎩ ⎭ 2

n w 3,6 = (p − 1)

ΔH °mCl (air − water) = −(9.8 ± 0.1)κa a − (9.4 ± 0.1)κa w − (9.6 ± 0.1)κa a − w − (16.2 ± 1.4) w

{ 2q },

n w 4,5 = (q − 1)

{ 2p }

(15)

(16)

Here and after {...} indicates the integer part of the number; q and p are the numbers of the molecules in the cluster in two directions (see Figure 7); ni is the number of pairwise interactions between the nearest hydroxyl groups (see Figure 3). Next, one should define the number of the pairwise CH···HC interactions in the air, water and straight on the interface  depending on the number of methylene groups immersed in the water phase. This number can be calculated like that • For the odd number of the methylene groups in water:

Figure 8. Illustration of the pairwise CH···HC interaction at the interface.

w

(13)

{ n − 2n } n−n +1 ){ } 2

Kaa = (n w1 + n w 4 + n w 6)

w

n1 + (15.3 ± 1.3)n5 + (11.8 ± 1.6)n6 kJ/mol (11)

+ (n w 3 + n w 5

ΔS°mCl (air − water) = −(17.4 ± 0.2)κa a − (16.3 ± 0.2)κa a − w − (15.1 ± 0.2)κa w

Kaw =

− (129.7 ± 2.6)(n1w + n5 w ) − (12.9 ± 5.9)n2 w

water

{ n 2 }(n + n n +1 +{ }(n 2 water

water

− (21.7 ± 5.1)n4 w − (106.4 ± 7.0)n6 w J/(mol ·K)

water

w 1

w 3 w 4

(17)

+ n w 5) + n w 6)

(18)

(12) K


Article


Table 4. Thermodynamic Parameters of Clusterization of Fatty Alcohols for the Series from Dimers to Nonamers (nwater = 3) alcohol

ΔHCl298, kJ/mol

ΔSCl298, J/(mol·K)

ΔGCl298, kJ/mol

ΔHCl298, kJ/mol

ΔSCl298, J/(mol·K)

ΔGCl298, kJ/mol


−35.3 −45.1 −45.1 −54.9 −54.9 −64.7

−162.2 −179.7 −179.7 −197.2 −197.2 −214.6

13.0 8.4 8.4 3.9 3.9 −0.7

Dimers C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH

−64.7 −74.5 −74.5 −84.3 −84.3

−214.6 −232.1 −232.1 −249.6 −249.6

−0.8 −5.3 −5.3 −9.9 −9.9


−80.6 −110.0 −110.0 −139.4 −139.4 −168.7

−388.0 −440.4 −440.4 −492.8 −492.8 −545.2

35.0 21.2 21.2 7.5 7.5 −6.3

Trimers 1 C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH

−168.7 −198.1 −198.1 −227.5 −227.5

−545.2 −597.6 −597.6 −650.0 −650.0

−6.3 −20.0 −20.0 −33.8 −33.8


−78.0 −87.8 −107.3 −117.1 −136.7 −146.5

−392.0 −409.4 −444.4 −461.8 −496.8 −514.2

38.8 34.3 25.1 20.5 11.3 6.8

Trimers 2 C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH

−166.1 −175.9 −195.4 −205.2 −224.8

−549.2 −566.6 −601.6 −619.0 −654.0

−2.4 −7.0 −16.2 −20.8 −29.9


−123.3 −152.7 −172.2 −201.6 −221.2 −250.5

−617.8 −670.2 −705.1 −757.5 −792.4 −844.8

60.8 47.1 37.9 24.1 15.0 1.2

Tetramers C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH

−270.1 −299.5 −319.1 −348.4 −368.0

−879.7 −932.1 −967.1 −1019.5 −1054.4

−8.0 −21.7 −30.9 −44.6 −53.8


−158.6 −197.8 −217.3 −256.5 −276.1 −315.2

−780.0 −849.8 −884.8 −954.6 −989.6 −1059.4

73.8 55.5 46.3 28.0 18.8 0.5

Pentamers C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH

−334.8 −374.0 −393.5 −432.7 −452.3

−1094.4 −1164.2 −1199.2 −1269.0 −1303.9

−8.7 −27.0 −36.2 −54.5 −63.7


−204.3 −253.3 −282.7 −331.6 −361.0 −409.9

−997.0 −1084.3 −1136.7 −1224.0 −1276.4 −1363.8

92.8 69.8 56.1 33.2 19.4 −3.5

Hexamers C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH

−439.3 −488.2 −517.6 −566.5 −595.9

−1416.2 −1503.5 −1555.9 −1643.2 −1695.6

−17.3 −40.2 −53.9 −76.9 −90.6


−288.8 −357.3 −406.3 −474.8 −523.7 −592.3

−1499.8 −1622.1 −1709.4 −1831.7 −1919.0 −2041.3

158.2 126.1 103.2 71.1 48.1 16.0

Octamers C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH

−641.19 −709.72 −758.66 −827.18 −876.13

−2128.58 −2250.83 −2338.16 −2460.42 −2547.75

−6.88 −38.97 −61.89 −93.98 −116.90


−334.5 −412.8 −471.6 −549.9 −608.6 −686.9

−1716.8 −1856.5 −1961.3 −2101.1 −2205.9 −2345.6

177.1 140.4 112.9 76.2 48.7 12.1

Nonamers C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH

−745.66 −823.97 −882.70 −961.0 −1019.8

−2450.37 −2590.09 −2694.89 −2834.6 −2939.4

−15.45 −52.12 −79.63 −116.3 −143.8

system

• For the even number of the methylene groups in water: L


Article


Table 5. Thermodynamic Parameters of Clusterization of the Fatty Alcohol Monolayer at Air/Water Interface Per Monomer (for Three Methylene Groups in Water) system

ΔHCl298∞/m, kJ/mol

ΔSCl298∞/m, J/(mol· K)

ΔGCl298∞/m, kJ/mol


−61.64 −76.32 −86.11 −100.80 −110.59 −125.27

−315.32 −341.52 −358.99 −385.18 −402.65 −428.85

32.33 25.45 20.87 13.99 9.40 2.53 w

water

w

water

w

4

5

=

{

n water − 1 w n 1+ 2

}

Kaa = n w1

−135.06 −149.74 −159.53 −174.21 −184.00

−446.31 −472.51 −489.98 −516.18 −533.64

−2.06 −8.93 −13.52 −20.39 −24.98

w

w a

n water 2

water

water

5

w 1

water

w

w

3

(23) water

5

+1

2

(n w 4 + n w 6 )

(20)

}

(24)

• For the even number of the methylene groups in water

(21)

{ n − n 2 − 1 } + (n + n ) { n − 2n } + (n + n ){ n − n 2 + 1 }

Kaa = n w1

After calculation of the number of pairwise interactions of all types the obtained results were substituted in eqs 11−13 and parameters of clusterization were calculated for all types of clusters considered in this paper. Parameters calculated for nwater = 3 are presented in Table 4 (these parameters for other nwater values are presented in the Supporting Information, Table 4S). As in case of the monomers the values of the thermodynamic parameters calculated for the clusters with different sinkage in the water phase (from 1 up to 5 methylene groups) coincide within the error. So, the proposed model 2 cannot estimate the influence of the immersion level of molecules in the water phase on the thermodynamic parameters of clusters and consequently on the monolayer formation. From Table 6, it is seen that trimers and hexamers structures formation is still the most preferable (they are characterized by the lowest values of the clusterization Gibbs’ energy). It proves ones more that monolayer formation goes via formation of the trimers, hexamers and more complex clusters of hexagonal structure.26 Large and Infinite Clusters. There is a fragment of the monolayer of fatty alcohols at air/water interface in Figure 5. Equations 11−21 allow calculating the number of pairwise interactions for the cluster of any dimension if its structure corresponds to the structure of the monolayer. To get thermodynamic parameters of the infinite cluster (monolayer) one needs to divide the number of pairwise interactions, which were calculated by 14 - 21, by the number of monomers in this cluster m = p·q and to calculate the limit of the obtained expressions at m tending to infinity. Then, the number of pairwise interactions between functional groups per one molecule in the cluster is n w1 − 60 ∞/m = 0.5

C12H25OH C13H27OH C14H29OH C15H31OH C16H33OH

3

{ }

(n w 3 + n w 4 + n w 5 + n w 6 )

ΔGCl298∞/m, kJ/mol

w

water

6

(19)

Kaw

ΔSCl298∞/m, J/(mol•K)

Kaa = (n w1 + n w 4 + n w 6)

w

3

ΔHCl298∞/m, kJ/mol

{ n − 2n } n−n +1 + (n + n ){ } 2 n n K ={ (n + n + n ) + { } 2

{ n − n 2 + 1 } + (n + n ) { n − 2n } + (n + n ){ n − n 2 + 1 }

Kaa = n w1

system

w

water

w

3

w

water

w

4

5

water

6

(25)

Kaw =

{n − n 2

water

−1

}n { n 2 } w 1

+ (n w 3 + n w 4 + n w 5 + n w 6 ) Kaa = n w1

water

(26) (27)

The parameters obtained by eqs 22−27 were substituted in eqs 11−13 in order to get thermodynamic parameters of clusterization per monomer for the infinite cluster. The results of this calculation are presented in Table 5. There are results only for nw = 3 in Table 5, as model 2 cannot show which level of immersion in the water phase is the most preferable for the molecules of the monolayer. Thermodynamic parameters obtained for the monolayers with other sinkage considered in this work coincide within the error of estimations mentioned earlier. Dependencies of the Gibbs’ energy of clusterization per one monomer on the number of carbon atoms in the chain for dimer, trimers, hexamers and infinite cluster at air/water interface are shown in Figure 9 (for three methylene groups in water). From Figure 9, one can see that the spontaneous clusterization of hexagonal monolayers of fatty alcohols takes place in the standard conditions when the length of hydrocarbon chains is 12 or more carbon atoms (i.e., from the dodecanol), and it agrees well with the available experimental data.6,7 Figure 9 shows that monolayer formation goes via formation of trimers1 and trimers 2, which form hexamers, then more complex clusters up to the monolayer. These data agree well with our previous calculations and experimental results. Processing of the experimental π−A isotherms of dodecanol, tridecanol, and tetradecanol shows that the aggregation number for dodecanol is equal to 2.3, while for tridecanol and tetradecanol it is 2.8 and 3.0 correspondingly.6,7

(22)

In the same way the number of the pairwise CH···HC interactions per one molecule in the cluster can be calculated: • For the odd number of the methylene groups in water M


Article


coefficient is equal to 0.96), while for model 2, it is 0.47 kJ/mol (correlation coefficient is equal to 0.97). The Gibbs’ energies of clusterization for the infinite cluster (monolayer) calculated using models 1 and 2, and the values estimated from the experimental data are shown in Table 6. The corrected values are given in the brackets. Equation 13 with account of the correlation coefficient becomes the following: ΔGCl 298 ∞/m(air − water)corr = −(0.7 ± 0.2)κa a − (0.8 ± 0.3)κa w − (0.8 ± 0.3)κa a − w + (3.6 ± 0.4)n1w + (0.6 ± 0.3)n2 w + (1.0 ± 1.5)n4 w + (8.6 ± 0.3)n5 w + (7.0 ± 0.6)n6 w kJ/mol

(28)

Using expression 27, we calculated the corrected values of the Gibbs’ energy of clusterization for all types of fatty alcohols clusters considered in this paper (the level of immersion was varied from 1 to 5 methylene groups in the water phase). The calculated dependencies of the Gibbs’ energy of clusterization (with formation of dimers, trimers 1, trimers 2, hexamers, and the monolayer) on the number of carbon atoms in the alkanol and the experimental values for the alkanol monolayer in water at 298 K are presented in Figure 10. The

Figure 9. Dependencies of the Gibbs’ energy of clusterization per one mole of alcohol monomers on the number of carbon atoms in the chain (n): 1, dimers; 2, trimer 2; 3, trimer 1; 4, hexamers; 5, monolayer. T = 298 K.

From Figure 9, it is seen that formation of dimers and trimers for dodecanol is equiprobable, while with the elongation of the chain (tetradecanol and following homologues) formation of trimers becomes more energetically favorable. The calculated thermodynamic parameters of the monolayers were compared with the corresponding experimental results. As for dodecanol the experimental values of Gibbs’ energy of clusterization were determined only at 283 K (−1.2 kJ/mol) and 288 K (−0.9 kJ/mol),6,7 so, Gibbs’ energy of clusterization at 298 K was obtained using extrapolation (−0.7 kJ/mol). The values of the Gibbs’ energy of clusterization for tridecanol and tetradecanol under standard conditions are −0.9 and −2.3 kJ/ mol correspondingly. Table 6 shows that the calculated values Table 6. Gibbs’ Energies of Clusterization for Monolayers of Fatty Alkanols C6−C16 in water at 298 K Calculated within Model 1, Model 2, and the Experimental Values ΔGCl298∞/m (air−water), kJ/mol system

model 1

model 2


24.5 (2.1) 17.6 (1.5) 13.0 (1.1) 6.2 (0.5) 1.6 (0.1) −5.3 (−0.5) −9.9 (−0.9) −16.8 (−1.4) −21.4 (−1.8) −28.2 (−2.4) −32.8 (−2.8)

32.3 (4.9) 25.5 (3.8) 20.9 (3.1) 14.0 (2.1) 9.40 (1.4) 2.5 (0.4) −2.1 (−0.3) −8.9 (−1.3) −13.5 (−2.0) −20.4 (−3.1) −25.0 (−3.8)

experiment6,7

Figure 10. Dependencies of the Gibbs’ energy of alcohol clusterization per one mole of monomers (calculated with an account of the correlation factor) on the number of carbon atoms in the chain: 1, dimers; 2, trimer 2; 3, trimer 1; 4, hexamers; 5, the monolayer.

Gibbs’ energy values are referred to one mole of monomers in the clusters. The calculated values are presented only for the case when three methylene groups are in the water phase (for the other levels of immersion the corresponding data coincide within the error). From Figure 10, one can see that the slope of the curves is different for clusters of various sizes while the parameters of the spontaneous clusterization stay the same; under standard conditions the spontaneous clusterization is possible for molecules of fatty alcohols containing 12 or more carbon atoms in the chain, and this result is in a good agreement with the experimental data.6,7

−0.7 −0.9 −2.3

somewhat exceed the corresponding experimental parameters. The calculated parameters were corrected using the correction coefficient, its value for model 1 being (0.1 ± 0.01) and for model 2 (0.15 ± 0.03). For estimations of the correction coefficient one needs to obtain the correlation dependence of Gibbs’ energy of clusterization from the direct quantum chemical calculation on the corresponding experimental values of the Gibbs’ energy. The slope of this dependence is the correction coefficient. After introduction of the correction coefficient, the standard deviation of clusterization Gibbs’ energy calculated using model 1 from the corresponding experimental data is 0.52 kJ/mol (the correlation

4. CONCLUSIONS The new model (model 2) of quantum chemical description of the clusterization of substituted alkanes at air/liquid and liquid/ liquid interfaces was proposed, which allows to account directly the influence of the liquid phase (phases) on the structural and thermodynamic parameters of the monolayers. The influence of N


Article


(5) Vysotsky, Yu. B.; Fomina, E. S.; Belyaeva, E. A.; Vollhardt, D.; Fainerman, V. B.; Miller, R. Quantum Chemical Analysis of the Thermodynamics of 2D Cluster Formation of Aliphatic Amides at the Air/Water Interface. J. Phys. Chem. C 2012, 116 (50), 26358−26376. (6) Vysotsky, Yu. B.; Bryantsev, V. S.; Fainerman, V. B. Thermodynamics of 2D Cluster Formation of Odd n-Alcohols at the Air/Water Interface. J. Phys. Chem., B 2002, 106, 11285−11294. (7) Vysotsky, Yu. B.; Bryantsev, V. S.; Fainerman, V. B.; Vollhardt, D.; Miller, R. Quantum Chemical Semi-empirical Approach to the Thermodynamic Characteristics of Oligomers and Large Aggregates of Alcohols at the Water/air Interface. Colloids Surf., A 2002, 209, 1−14. (8) Vysotsky, Yu. B.; Belyaeva, E. A.; Fainerman, V. B.; Vollhardt, D.; Miller, R. Quantum Chemical Analysis of Thermodynamics of 2D Cluster Formation of n-Thioalcohols at the Air/Water Interface. J. Phys. Chem., C 2007, 111, 5374−5381. (9) Vysotsky, Yu. B.; Belyaeva, E. A.; Fainerman, V. B.; Aksenenko, E. V.; Vollhardt, D.; Miller, R. Quantum Chemical Analysis of the Thermodynamics of 2-Dimensional Cluster Formation of Alkylamines at the Air/Water Interface. J. Phys. Chem. C 2007, 111, 15342−15349. (10) Vysotsky, Yu. B.; Belyaeva, E. A.; Fomina, E. S.; Vollhardt, D.; Fainerman, V. B.; Miller, R. 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. Phys. Chem. Chem. Phys. 2014, 16, 3187−3199. (11) Vysotsky, Yu. B.; Fomina, E. S.; Belyaeva, E. A.; Fainerman, V. B.; Vollhardt, D. On the Inclusion of Alkanes into the Monolayer of Aliphatic Alcohols at the Water/Vapor of Alkanes Interface. A quantum chemical approach. Phys. Chem. Chem. Phys. 2013, 15, 2159−2176. (12) Weissbuch, I. Separation of Enantiomers and Racemate Formation in Two-Dimensions Crystals at the Water Surface from Racemic α-amino Acid Amphiphiles: Design and Structure. J. Am. Chem. Soc. 1997, 119, 933−942. (13) Weinbach, S. P. Effect of Cosolvent on the Lateral Order of Spontaneously Formed Amphiphilic Amide Two-Dimensional Crystallites at the Air-Solution Interface. J. Am. Chem. Soc. 1993, 115, 11110− 11118. (14) Stewart, J. J. P. MOPAC 2012; Stewart Computational Chemistry: Colorado Springs, CO, 2012; http://OpenMOPAC.net. (15) Goss, K.-U. Predicting Adsorption of Organic Chemicals at the Air-Water Interface. J. Phys. Chem. A 2009, 113, 12256−12259. (16) Andersson, M. P.; Olsson, M. H. M.; Stipp, S. L. S. Predicting the pKa and Stability of Organic Acids and Bases at an Oil−Water Interface. Langmuir. 2014, 30, 6437−6445. (17) Andersson, M. P.; Bennetzen, M. V.; Klamt, A.; Stipp, S. L. S. First-Principles Prediction of Liquid/Liquid Interfacial Tension. J. Chem. Theory Comput. 2014, 10, 3401−3408. (18) Klamt, A. Conductor-like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena. J. Phys. Chem. 1995, 99, 2224−2235. (19) Anisimov, V. M.; Cavasotto, C. N. Hydration Free Energies Using Semiempirical Quantum Mechanical Hamiltonians and a Continuum Solvent Model with Multiple Atomic-Type Parameters. J. Phys. Chem. B 2011, 115, 7896−7905. (20) Dutta, P. Studies of Monolayers Using Synchrotron X-ray Diffraction. Curr. Opin. Solid Mater. Sci. 1997, 2, 557−562. (21) Weck, M.; Fink, R.; Ringsdorf, H. Molecular Recognition via Hydrogen Bonding at the Air−Water Interface: An Isotherm and Fourier Transform Infrared Reflection Spectroscopy Study. Langmuir 1997, 13 (13), 3515−3522. (22) Can, S. Z.; Mago, D. D.; Walker, R. A. Structure and Organization of Hexadecanol Isomers Adsorbed to the Air/Water Interface. Langmuir 2006, 22, 8043−8349. (23) Bell, G. R. Structure of a Monolayer of Hexadecyltrimethylammonium p-Tosylate at the Air−Water Interface. J. Am. Chem. Soc. 1997, 119, 10227−10228. (24) Dai, L. Intelligent Macromolecules for Smart Devices: from Materials Synthesis to Device Applications; Springer-Verlag: London, 2004. (25) Lee, Y. S. Self-assembly and Nanotechnology a Force Balance Approach; John Wiley & Sons, Inc.: New York, 2008; p 344

the liquid phase (phases) was considered in the frameworks of the COSMO procedure.14,15 Proposed model 2 was tried in quantum chemical calculations of the structural and thermodynamic parameters of fatty alcohol clusterization at the air/water interface. Enthalpy, entropy, and Gibbs’ energy were calculated for the series of the monomers and small clusters at air/water interface. It was shown that spontaneous clusterization takes place for compounds having 12 or more carbon atoms in the hydrocarbon chain under normal conditions with formation of the monolayer uniting hexagonal unit cells. Formation of the monolayer passes via next stages: formation of trimers, hexamers, and more complex clusters on the basis of the mentioned onesup to the infinite cluster (monolayer). All these results are in agreement with the experimental data.6,7 The use of model 2 results in somewhat better agreement between the calculated and experimental values comparatively to model 1. The standard deviation of the Gibbs’ energy of clusterization for the monolayer of the fatty alcohols calculated within model 1 from the corresponding experimental parameters is 0,52 kJ/mol (the correlation coefficient is equal to 0.96), and 0.47 kJ/mol for model 2 (the correlation coefficient is equal to 0.97). In the same time model 2 cannot estimate, which level of immersion of the hydrocarbon chain in water medium will be the most energetically preferable as the thermodynamic parameters calculated for the clusters with different levels of immersion coincide within the error of estimations. The proposed model 2 can be used further in calculations of the clusterization parameters of any surfactants (including ionic ones) at liquid/liquid and liquid/air interfaces.

■

ASSOCIATED CONTENT

S Supporting Information *

Tables with the thermodynamic parameters of clusters and monolayers formation for the level of molecules immersion from 1 up to 5 (except 3). This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*(E.A.B.) E-mail: [email protected] and [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank Saint-Petersburg State University for the financial support (RFBR Project No. 12.50.1192.2014 and No. 12.38.76.2012).

■

REFERENCES

(1) Kaganer, V. M.; Dutta, M. H. Structure and phase transition in Langmuir monolayers. Rev. Mod. Phys. 1999, 71 (3), 779−817. (2) Custelcean, R.; Jackson, J. E. Dihydrogen bonding: Structures, energetics, and dynamics. Chem. Rev. B 2001, 101 (7), 1963−1980. (3) Rodrigues, L.; van der Mei, H.; Banat, I. M.; Teixeira, J.; Oliveira, R. Inhibition of microbial adhesion to silicone rubber treated with biosurfactant from Streptococcus thermophilus A. FEMS Immunol Med. Microbiol. 2006, 46 (1), 107−112. (4) Vysotsky, Yu. B.; Muratov, D. V.; Boldyreva, F. L.; Fainerman, V. B.; Vollhardt, D.; Miller, R. Quantum Chemical Analysis of the Thermodynamics of 2D Cluster Formation of n-Carboxylic Acids at the Air/Water Interface. J. Phys. Chem. B 2006, 110, 4717−4730. O


Article

The Journal of Physical Chemistry B (26) Fomina, E. S.; Vysotsky, Yu. B.; Belyaeva, E. A.; Vollhardt, D.; Fainerman, V. B.; Miller, R. On Hexagonal Orientation of Fatty Alcohols in Monolayers at the Air/Water Interface: Quantum chemical Approach. J. Phys. Chem. C 2014, 118 (8), 4122−4130. (27) Daubert, T. E.; Danner, R. P.; Sibul, H. M.; Stebbins, C. C. Physical and thermodynamic properties of pure chemicals: Data Compilation, Part 1 − Part 5; Taylor & Francis: Philadelphia, PA, 1998; p 9860. (28) Lenne, P.-F.; Bonosi, F.; Renault, A.; Bellet-Amalric, E.; Legrand, J.-F.; Petit, J.-M.; Rieutord, F.; Berge, B. Growth of Two-Dimensional Solids in Alcohol Monolayers in the Presence of Soluble Amphiphilic Molecules. Langmuir 2000, 16, 2306−2310. (29) Kraack, H.; Ocko, B. M.; Pershan, P. S.; Sloutskin, E.; Tamam, L.; Deutsch, M. How many phases and phase transitions do exist in Gibbs adsorption layers at the air-water interface? Langmuir 2004, 20, 5386− 5395. (30) Majewski, J.; Popovitz-Biro, R.; Bouwman, W. G.; Kjaer, K.; AlsNielsen, J.; Lahav, M.; Leiserowitz, L. The Structural Properties of Uncompressed Crystalline Monolayers of Alcohols CnH2n+1OH (n = 13−31) on Water and Their Role as Ice Nucleators. Chem.Eur. J. 1995, 1, 304−311. (31) Shin, M. C.; Bohanon, T. M.; Mikrut, J. M.; Zschack, P.; Dutta, P. Pressure and pH Dependence of the Structure of a Fatty Acid Monolayer with Calcium Ions in the Subphase. J. Chem. Phys. 1992, 97, 1556−1559. (32) Wang, J.-L. Two-dimensional Structures of Crystalline Selfaggregates of Amphiphilic Alcohols at the Air-Water Interface as Studied by Grazing Incidence Synchrotron X-ray Diffraction and Lattice Energy Calculations. J. Am. Chem. Soc. 1994, 116, 1192−1204. (33) Nandi, N. Effect of Molecular Chirality on the Morphology of Biomimetic Langmuir Monolayers. Chem. Rev. 2003, 103, 4033−4075. (34) Vollhardt, D.; Siegel, S.; Cadenhead, D. A. Characteristic Features of Hydroxystearic Acid Monolayers at the Air/Water Interface. J. Phys. Chem. B 2004, 108, 17448−17456. (35) Weissbuch, I. Toward Stereochemical Control, Monitoring, and Understanding of Crystal Nucleation. Cryst. Growth Des. 2003, 3, 125− 150.

P


Quantum Chemical Approach in the Description of the Amphiphile

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