Quantum-Chemical Analysis of Thermodynamics of Two

J. Phys. Chem. B 2009, 113, 16557–16567

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Quantum-Chemical Analysis of Thermodynamics of Two-Dimensional Cluster Formation of r-Amino Acids at the Air/Water Interface Yu. B. Vysotsky,† E. S. Fomina,† E. A. Belyaeva,† E. V. Aksenenko,‡ D. Vollhardt,*,§ and R. Miller§ Donetsk National Technical UniVersity, 58 Artema Str., 83000 Donetsk, Ukraine, Institute of Colloid Chemistry and Chemistry of Water, 42 Vernadsky AVenue, 03680 KyiV (KieV), Ukraine, and Max Planck Institute of Colloids and Interfaces, D-14424 Potsdam/Golm, Germany ReceiVed: August 11, 2009; ReVised Manuscript ReceiVed: October 8, 2009

The semiempirical quantum-chemical PM3 method is used to calculate the thermodynamic parameters of clusterization of the S-form of R-amino acids with the general composition CnH2n+1CHNH2COOH (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° with respect to the normal to the interface are calculated. It is shown that the 30° 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 Å and b ) 5.67-5.75 Å, with the angle between the axes θ ) 100-103°. These values agree well with the available experimental data. Spontaneous clusterization of R-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. Introduction The total number of various R-amino acids found so far in natural substances already exceeds 100.1 Among these, the series of the R-amino acids with the general formula CnH2n+1CHNH2COOH with nonbranched alkyl chain structure is of particular interest. Along with the R-amino acids of more complicated structure, they represent the basic unit for the synthesis of protein molecules. These R-amino acids exhibit optical activity, so that they are prospective for the design of films and structures with predefined optical properties, and also for controlled crystallization of chiral compounds and resolution of enantiomers using respective condensed phases of Langmuir monolayer.2,3 Another possible application of R-amino acids is the production of solid membranes which could be used as chemical sensors.4 In this regard, the calculation of crystallization parameters of R-amino acids (also thermodynamic parameters) should be interesting both from the point of view of membrane biology and also for supramolecular chemistry as well as condensed state physics. In this Article, we present the study of structural and energetic characteristics of the clusterization process of R-amino acids CnH2n+1CHNH2COOH (n ) 5-15) at the air/water interface. * Corresponding author. E-mail: [email protected]. † Donetsk National Technical University. ‡ Institute of Colloid Chemistry and Chemistry of Water. § Max Planck Institute of Colloids and Interfaces.

Recent studies of morphology and 2D lattice structure of Langmuir monolayers have shown that dependent on the chemical structure of the amphiphile and the state of the monolayer the alkyl chains are different tilted to the plane of the surface.4,5 In our previous quantum-chemical studies of long chain alcohols, thioalcohols, amines, nitriles, and carboxylic acids,6-11 it was shown that the values of thermodynamic parameters calculated for the monolayers of these surfactants in which the alkyl chains are oriented at an angle of 9° with respect to the normal to the interface agree well with experimental data.12-16 However, it was experimentally shown17 that monolayers composed of amino acid molecules tilted 36° with respect to the normal to the interface can exist at 278 K. Therefore, the present study focuses attention on the calculation of structural and thermodynamic parameters of clusterization for R-amino acid monolayers with the molecules oriented at 9 and 30° with respect to the normal to the air/water interface at 278 and 298 K. Methods For calculations of the structural and energetic parameters of R-amino acid clusterization at the air/water interface described here, the Mopac2000 quantum-chemical software package18 was employed; the BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm was used in the framework of the PM3 parametrization. Among all semiempirical methods MINDO/3, MNDO, AM1, and PM3, the latter provides the most adequate description

10.1021/jp907751z  2009 American Chemical Society Published on Web 11/19/2009

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Figure 1. Torsion angles of the functional groups of R-amino acids.

Figure 3. Dependence of the monomer formation enthalpy of R-amino octanoic acid on the value of the angle γ.

Figure 2. Potential energy surface for the monomer of R-amino hexadecanoic acid.

of amphiphilic monolayers at the interface, because this method takes into account the hydrogen-hydrogen interactions between the alkyl chains. Also, the PM3 method is parametrized with respect to the formation heats19,20 and, therefore, is capable of the most correct reproduction of the thermodynamic values. Results and Discussion Monomers. In the first stage of the study, the conformational analysis of R-amino acid monomers was performed. All of the R-amino acids studied here comprise one carbon atom in asymmetric position; thus, these monomers exhibit chiral behavior. The thermodynamic characteristics of the enantiomers are almost equal to each other;21,22 therefore, only the R-amino acids of the S series (which are of major biological interest)23 were chosen for the conformational analysis. Also, it was shown24-27 that preferential homochiral aggregation of the enantiomers from the racemic mixtures is observed. The monomer potential energy dependence on the values of the two torsion angles R ) ∠C2-C1-C3-O1 and β ) ∠C2-C1-N-H1 corresponding to the carboxy and amino functional groups, respectively (see Figure 1), was calculated. These two torsion angles were varied in the range from 0 to 360° in steps of 15°. Figure 2 illustrates the potential energy dependence for the monomer of R-amino hexadecanoic acid on these torsion angles. Six minima on the potential surface are clearly seen. Additional optimization of the monomer structures in the vicinity of these minima confirmed that six stable

conformations exist which correspond to the (R, β) values (-81°, -55°); (-107°, 48°); (88°, -53°); (67°, 64°); (-160°, 160°); and (34°, 160°). Whereas the formation heats for all of these conformers are quite close to each other, the first one (R ) -81°, β ) -55°) is energetically most preferable and the last one (R ) 34°, β ) 160°) is less preferable. The dependence of the heat of formation on the torsion angle γ (∠C4-C2-C1-C3, see Figure 1) between the “head” of the molecule (the “head” comprises both functional groups) and the hydrophobic alkyl chain for the energetically most preferable conformation is shown in Figure 3. It is seen that three minima exist which correspond to γ values of 74, 166, and 295°. Despite the fact that the structure of monomers with γ ) 166° is energetically more advantageous, we have found (as explained below in more detail) that larger clusters are formed on the basis of the monomers with γ ) 74°. Figure 4 shows the geometric structures of six monomers constructed with γ ) 74°. It is seen that monomer 1 is stabilized due to the formation of the interactions between the two hydrogen atoms of the amino group and the carbonyl oxygen of the COOH group. Intermolecular interaction between one atom of the amino group and the hydroxyl oxygen takes place in monomer 2. Monomer 3 is stabilized due to the interaction between one of the hydrogen atoms of the amino group and the hydroxyl hydrogen of the COOH group, and to the intermolecular interaction of the carbonyl oxygen with the γ-hydrogen of the hydrophobic skeleton of the molecule. The stability of monomer 4 is based on the interactions of the hydroxyl oxygen atom with one hydrogen atom of the amino group and with the hydrogen atom of the alkyl chain. In monomers 5 and 6, interactions exist between the hydrogen atoms of the hydrocarbon skeleton and carbonyl oxygen or hydroxyl oxygen, respectively. Tables 1 and 2 list the calculated thermodynamic parameters (enthalpy and Gibbs’ energy of formation and absolute entropy) for all of these stable conformations of monomers at 278 and 298 K. It should be noted that experimental data regarding standard thermodynamic characteristics of the formation of R-amino acids with normal structure are very scarce. Most studied are amino acids which are involved in living organisms and ω-amino acids which are used in the production of synthetic fibres. Therefore, the calculated results can be compared only with the experimental data of S-alanine which is the first one among the studied amino acid series. From the standard heat of formation of the S-alanine crystalline form (-561.2 kJ/mol)28 and its sublimation heat (138.1 kJ/mol),28 the standard heat of formation of the

Thermodynamics of 2D Cluster Formation of R-Amino Acids

J. Phys. Chem. B, Vol. 113, No. 52, 2009 16559 0 S278,mon ) (30.25 ( 0.06) · n + (280.24 ( 0.57) [R ) 0.9998; S ) 2.35 J/(mol · K); N ) 90] (2) 0 ∆H298,mon ) -(22.56 ( 0.11) · n - (369.41 ( 1.08) [R ) 0.999; S ) 4.45 kJ/mol; N ) 90] (3) 0 S298,mon ) (31.60 ( 0.06) · n + (285.15 ( 0.59) [R ) 0.9998; S ) 2.41 J/(mol · K); N ) 90] (4)

Figure 4. Geometric structure of the of R-amino acid associates.

gaseous form of S-alanine is easily calculated to be -423.1 kJ/ mol. From the comparison of the enthalpy values calculated for S-alanine with the experimental value, it is seen that in the sequence from the first monomer to the sixth one the agreement becomes gradually worse. This confirms the fact that the first monomer is the most advantageous from the energetic point of 0 ) view. For the most preferable S-alanine structure, ∆H298,mon -423.0 kJ/mol. The calculated data summarized in Tables 1 and 2 were used to construct the correlation dependencies of the standard thermodynamic characteristics on the alkyl chain length of the amino acid. These dependencies are linear, similar to other classes of amphiphiles (alcohols, thioalcohols, carboxylic acids, and amines) studied by us earlier.6-11 The values of the slope of these dependencies, which characterize the contribution of the methylene groups involved in the alkyl chain, are confined to the ranges of -22.94 (-22.54) to -22.97 (-22.58) kJ/mol for enthalpy and 30.21 (31.57) to 30.28 (31.65) J/(mol · K) for entropy. Here and below, the first values listed correspond to 278 K, and the values in parentheses correspond to 298 K. The absolute term that characterizes the contribution of the hydrophilic part of the molecule was found to be -389.07 (-387.13) to -398.49 (-396.71) kJ/mol for enthalpy and 307.34 (313.53) to 313.08 (319.80) J/(mol · K) for entropy. As the values of the slopes and absolute terms of corresponding correlations are quite similar, it is possible to express these partial correlations in a general form: 0 ∆H278,mon ) -(22.96 ( 0.11) · n - (370.82 ( 1.08) [R ) 0.999; S ) 4.43 kJ/mol; N ) 90] (1)

where R is the regression coefficient, S is the standard deviation, and N is the sampling amount. The slope values in eqs 1-4 that characterize the contributions from the methylene groups agree well with the values calculated earlier for other classes of amphiphilic compounds.6-11 In particular, at 298 K, the slope value for the enthalpy of formation of amines, saturated carboxylic acids, and alcohols is -22.68 kJ/mol, for the absolute entropies, the values characteristic for these substances are 39.24, 38.38, and 38.61 J/(mol · K), respectively, and for the Gibbs’ energies, the values are 6.23, 6.52, and 6.44 kJ/mol, respectively. It can be concluded that for different classes of compounds the methylene groups contribute additively to the thermodynamic characteristics of monomers, and therefore, the correlation dependencies valid for different classes can be represented as a single dependence. Dimers, Tetramers, and Hexamers. The dimers were built from the monomer conformations obtained above. The structures of these entities on the basis of monomer 1 are illustrated in Figure 5. According to two possible relative orientations of the functional groups, namely, parallel and serial (schematically indicated by arrows in Figure 5a and b, respectively), the structures of dimers (and, subsequently, more complicated clusters) could be subdivided into two classes, characterized by parallel and serial relative orientation of the “heads”. As noted above, the dimers and other (larger) clusters were built on the basis of the monomers with γ ) 74°. The relative positions of monomers in the dimers were chosen to enable the formation of the “a” type of H-H interactions because, as shown,6,29 these configurations are energetically more preferable. Also, for the dimers with serial orientation, the monomers are inclined 9° to the normal to the interface, and for monomers with parallel orientation, this angle was taken to be 30°. This geometry is necessary for the subsequent formation of tetramers which act as unit cells of 2D infinite clusters. Table 3 summarizes the calculated thermodynamic parameters of clusterization of three conformations of the studied R-amino acids (which correspond to monomers 1, 3, and 6) on which the energetically most preferable structures of 2D films are built. Enthalpy, entropy, and Gibbs’ free energy of clusterization were calculated from the expressions Cl 0 Cl Cl 0 ∆HT,m ) ∆HT0 - mHT,mon ; ∆ST,m ) ∆ST,m - mST,mon ; Cl Cl Cl ) ∆HT,m - T∆ST,m ∆GT,m

where ∆HT0 and ST0 are the enthalpy and entropy of the clusters 0 0 and ST,mon are the enthalpy at a certain temperature T, HT,mon and entropy of the corresponding monomers at the same temperature T, and m is the number of monomers in a cluster. The dimers, tetramers, and hexamers are indicated with the same numbers as the initial monomers of which they are built. The structures of the hexamers that were built on the basis of the monomers with parallel and serial arrangement of the functional groups are denoted by “P” and “S”, respectively. Figure 6 illustrates three projections (views) of each of the hexamer types. It is seen that in these structures the monomer molecules are inclined by 30° with respect to the normal to one of the sides of the unit cell, whereas their inclination with respect to the

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TABLE 1: Thermodynamic Parameters of Formation of r-Amino Acid Monomers at 278 K molecule

monomer 1

monomer 2

C3H7NO2 C4H9NO2 C5H11NO2 C6H13NO2 C7H15NO2 C8H17NO2 C9H19NO2 C10H21NO2 C11H23NO2 C12H25NO2 C13H27NO2 C14H29NO2 C15H31NO2 C16H33NO2 C17H35NO2

-425.18 -443.47 -466.38 -489.36 -512.41 -535.47 -558.53 -581.61 -604.68 -627.75 -650.82 -673.90 -696.97 -720.05 -743.12

-423.37 -443.01 -465.99 -488.96 -512.01 -535.06 -558.12 -581.19 -604.26 -627.33 -650.40 -673.47 -696.55 -719.62 -742.70


-421.64 -525.40 -627.74 -730.05 -832.20 -934.50 -1037.21 -1139.99 -1242.76 -1345.58 -1448.78 -1551.80 -1654.89 -1758.75 -1861.79

-421.57 -525.52 -627.69 -729.80 -832.23 -934.50 -1037.31 -1139.61 -1242.72 -1345.00 -1448.31 -1551.79 -1654.94 -1758.02 -1861.03


-307.96 -297.40 -291.87 -286.41 -281.06 -275.68 -270.19 -264.69 -259.19 -253.68 -248.06 -242.49 -236.91 -231.11 -225.54

-306.17 -296.92 -291.49 -286.08 -280.65 -275.27 -269.75 -264.37 -258.78 -253.42 -247.77 -242.08 -236.47 -230.89 -225.33

monomer 3 0 , ∆H278,mon

kJ/mol -421.53 -440.40 -463.34 -486.31 -509.39 -532.43 -555.51 -578.58 -601.65 -624.72 -647.80 -670.87 -693.95 -717.02 -740.10

0 ∆S278,mon , J/(mol · K) -420.33 -524.79 -626.89 -729.09 -831.60 -933.83 -1036.72 -1138.79 -1242.61 -1345.41 -1448.61 -1550.92 -1654.39 -1757.27 -1861.78 0 ∆G278,mon , kJ/mol -304.68 -294.51 -289.07 -283.63 -278.20 -272.83 -267.30 -261.99 -256.21 -250.70 -245.08 -239.72 -234.03 -228.50 -222.53

normal to the other side of the cell is by 9°. It is seen from the data shown in Figure 3 that associates in which the molecules are inclined at 30° with respect to the normal to the interface are most advantageous from the energetic point of view. This is because the number of H-H interactions which are formed in these structures is larger than the number of such interactions that can arise in structures with an almost perpendicular orientation of molecules with respect to the interface. For all series of calculated thermodynamic parameters of clusterization (enthalpy, entropy, and Gibbs’ energy) the correlation dependencies on the number of intermolecular interactions Ka were built. The values of the slope which characterize the energetic contribution from the H-H interactions between the alkyl chains of the R-amino acid molecules were found to be in the range -9.83 (-9.86) to -10.42 (-10.45) kJ/mol for enthalpy, -19.64 (-19.73) to -24.89 (-24.98) J/(mol · K) for entropy, and -3.07 (-2.58) to -4.59 (-4.20) kJ/mol for Gibbs’ energy. The absolute term for the dimers, tetramers, and

monomer 4

monomer 5

monomer 6

-420.85 -440.35 -463.37 -486.32 -509.39 -532.43 -555.51 -578.57 -601.64 -624.71 -647.79 -670.86 -693.94 -717.01 -740.09

-415.20 -434.37 -457.10 -480.11 -503.13 -526.19 -549.25 -572.33 -595.40 -618.47 -641.55 -664.62 -687.69 -710.77 -733.84

-413.15 -432.27 -455.09 -478.09 -501.13 -524.19 -547.25 -570.32 -593.40 -616.47 -639.54 -662.62 -685.69 -708.77 -731.84

-423.74 -527.41 -629.69 -731.74 -833.96 -936.64 -1039.09 -1140.97 -1244.57 -1347.31 -1450.36 -1553.83 -1656.92 -1759.91 -1863.52

-418.96 -522.08 -623.48 -725.92 -828.10 -930.75 -1033.18 -1135.70 -1238.64 -1341.82 -1444.39 -1548.91 -1651.24 -1754.79 -1858.49

-415.56 -521.54 -623.68 -725.93 -828.17 -930.49 -1033.25 -1135.64 -1238.37 -1342.05 -1444.58 -1547.75 -1650.35 -1754.78 -1856.72

-303.05 -293.72 -288.31 -282.90 -277.55 -272.05 -266.64 -261.38 -255.65 -250.16 -244.59 -238.89 -233.31 -227.76 -222.03

-298.73 -289.23 -283.78 -278.30 -272.92 -267.44 -262.03 -256.60 -251.05 -245.44 -240.01 -234.02 -228.65 -222.94 -217.18

-297.62 -287.28 -281.71 -276.28 -270.90 -265.51 -260.01 -254.61 -249.13 -243.38 -237.95 -232.34 -226.89 -220.94 -215.68

hexamers (in the order of their enumeration in Figures 3 and 6) is -2.27 (-1.94), -19.49 (-19.32), -2.63 (-2.31), -18.95 (-18.77), -4.05 (-3.72), -10.34 (-10.07), -42.78 (-42.13), -34.55 (-33.81), -20.97 (-20.11), -47.60 (-46.34), and -74.79 (-73.79) kJ/mol for enthalpy, -94.72 (-93.54), -159.95 (-159.35), -106.94 (-105.82), -160.54 (-159.88), -106.87 (-105.77), -140.06 (-139.12), -471.89 (-469.64), -461.73 (-459.16), -429.76 (-426.81), -689.12 (-684.70), and -782.34 (-778.83) J/(mol · K) for entropy, and 24.06 (25.94), 24.97 (28.17), 27.10 (29.23), 25.68 (28.88), 25.66 (27.80), 28.59 (31.39), 88.41 (97.82), 93.81 (103.02), 98.50 (107.08), 143.98 (157.70), and 142.70 (158.30) kJ/mol for Gibbs’ energy. Note that the values listed above were calculated per one interaction between the monomers. From these data, it is easily seen that spontaneous clusterization of R-amino acids becomes only possible if the alkyl chain length is such that the negative contribution from the H-H interactions into the Gibbs’ clusterization energy is high enough


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TABLE 2: Thermodynamic Parameters of Formation of r-Amino Acid Monomers at 298 K molecule

monomer 1

monomer 2


-423.00 -440.90 -463.42 -486.01 -508.67 -531.33 -554.00 -576.68 -599.35 -622.04 -644.71 -667.39 -690.08 -712.76 -735.44

-421.20 -440.45 -463.03 -485.61 -508.26 -530.92 -553.59 -576.26 -598.94 -621.62 -644.29 -666.98 -689.66 -712.34 -735.02


-432.23 -537.85 -642.05 -746.22 -850.23 -954.40 -1058.97 -1163.62 -1268.26 -1372.93 -1478.00 -1582.89 -1687.84 -1793.58 -1898.48

-432.16 -537.97 -642.01 -745.97 -850.27 -954.40 -1059.08 -1163.25 -1268.22 -1372.36 -1477.54 -1582.89 -1687.90 -1792.84 -1897.72


-294.20 -280.62 -272.09 -263.63 -255.30 -246.91 -238.43 -229.92 -221.41 -212.90 -204.27 -195.69 -187.10 -178.28 -169.70

-292.41 -280.13 -271.72 -263.31 -254.88 -246.50 -237.98 -229.61 -221.01 -212.65 -203.99 -195.28 -186.66 -178.07 -169.50

monomer 3 0 , ∆H298,mon

kJ/mol -419.36 -437.83 -460.38 -482.96 -505.64 -528.29 -550.97 -573.64 -596.32 -619.01 -641.69 -664.37 -687.05 -709.73 -732.42

0 ∆S278,mon , J/(mol · K) -430.91 -537.23 -641.18 -745.25 -849.63 -953.72 -1058.47 -1162.41 -1268.09 -1372.75 -1477.82 -1581.99 -1687.33 -1792.08 -1898.45 0 ∆G298,mon , kJ/mol -290.95 -277.74 -269.31 -260.88 -252.45 -244.08 -235.55 -227.25 -218.43 -209.93 -201.30 -192.93 -184.23 -175.69 -166.68

to counterbalance the positive contribution caused by the interaction between the hydrophilic parts of the molecules. Also, the interactions between dimers with serial orientation of their “heads” result in a higher (by module) negative contribution to the enthalpy value than the interactions between dimers with

Figure 5. Relative orientations of monomers in the dimer: (a) parallel; (b) serial.

monomer 4

monomer 5

monomer 6

-418.68 -437.78 -460.40 -482.97 -505.64 -528.29 -550.97 -573.64 -596.32 -619.00 -641.68 -664.36 -687.04 -709.72 -732.41

-413.03 -431.79 -454.14 -475.88 -499.38 -522.05 -544.71 -567.39 -590.07 -612.75 -635.43 -658.11 -680.80 -703.48 -726.16

-410.97 -429.69 -452.12 -474.73 -497.38 -520.04 -542.72 -565.39 -588.07 -610.75 -633.43 -656.11 -678.79 -701.47 -724.15

-434.32 -539.85 -644.00 -747.90 -851.99 -956.53 -1060.85 -1164.59 -1270.06 -1374.66 -1479.58 -1584.91 -1689.86 -1794.72 -1900.20

-429.52 -534.50 -637.76 -739.18 -846.11 -950.63 -1054.93 -1159.31 -1264.12 -1369.16 -1473.59 -1579.98 -1684.18 -1789.59 -1895.15

-426.13 -533.96 -637.97 -742.08 -846.18 -950.37 -1054.99 -1159.24 -1263.84 -1369.39 -1473.78 -1578.82 -1683.28 -1789.57 -1893.38

-289.25 -276.90 -268.49 -260.09 -251.75 -243.24 -234.84 -226.59 -217.84 -209.35 -200.76 -192.05 -183.46 -174.89 -166.15

-285.03 -272.51 -264.08 -255.60 -247.24 -238.76 -230.35 -221.92 -213.36 -204.74 -196.30 -187.28 -178.91 -170.18 -161.41

-283.99 -270.57 -262.00 -253.59 -245.22 -236.83 -228.33 -219.93 -211.44 -202.67 -194.24 -185.62 -177.17 -168.18 -159.93

parallel orientation, whereas for the entropy the effect is just opposite: the lower (negative) contribution is brought by the interactions between dimers with parallel orientation. As the entropy contribution to the Gibbs’ energy is much more essential than the enthalpy factor, the parallel arrangement of the “heads” in dimers is more advantageous with respect to the Gibbs’ energy value. The regression slopes for the R-amino acids are quite close to those calculated earlier for alcohols, thioalcohols, cyanoalkanes, amines, and carboxylic acids: In these cases, the coefficients at 298 K, as calculated in refs 6-11, were in the range -10.07 to -10.36 kJ/mol for the clusterization enthalpy and in the range -22.87 to -26.89 J/(mol · K) for the entropy. The slopes of the calculated regression coefficients are quite similar for the partial correlations. Therefore, the partial correlations for all of the clusters considered can be generalized to one correlation:

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Cl ∆Hm,278 ) -(10.26 ( 0.04) · Ka - (18.14 ( 0.41) · n1,P - (17.41 ( 0.52) · n3,P - (7.37 ( 0.69) · n6,P - (2.35 ( 0.71) · n6,S [N ) 121; R ) 0.9999; S ) 3.01 kJ/mol] (5) Cl ∆Sm,278 ) -(21.62 ( 0.45) · Ka - (141.89 ( 4.55) · n1,P - (76.35 ( 4.91) · n1,S - (144.46 ( 6.25) · n3,P - (87.85 ( 6.48) · n3,S - (119.40 ( 6.25) · n6,P - (93.28 ( 6.48) · n6,S, [N ) 121; R ) 0.999; S ) 26.79 J/(mol · K)] (6) Cl ∆Hm,298 ) -(10.28 ( 0.04) · Ka - (17.98 ( 0.41) · n1,P - (17.20 ( 0.52) · n3,P - (7.22 ( 0.69) · n6,P - (2.18 ( 0.71) · n6,S, [N ) 121; R ) 0.9999; S ) 2.99kJ/mol] (7) Cl ∆Sm,298 ) -(21.72 ( 0.45) · Ka - (141.64 ( 4.53) · n1,P - (75.47 ( 4.89) · n1,S - (144.04 ( 6.22) · n3,P - (86.91 ( 6.44) · n3,S - (118.66 ( 6.22) · n6,P - (92.39 ( 6.44) · n6,S, [N ) 121; R ) 0.999; S ) 26.64 J/(mol · K)] (8)

where Ka is the number of H-H interactions, while ni,P and ni,S identify the existence of the interactions between the parallel (P) and serial (S) oriented functional “heads” in the structure, with i denoting the number of the dimer. If ni,P * 0 or ni,S * 0, then corresponding interactions exist (the number of interactions between the “heads” can exceed 1) in the system, while ni,P ) 0 or ni,S ) 0 indicate that this interaction is absent. The standard deviation for the enthalpy is 2.99 kJ/mol, which is quite the same as the value obtained in ref 26 for amines (3.01 kJ/mol). For the entropy, the deviation is 26.64 J/(mol · K), which is lower than that for alcohols (36.1 J/(mol · K)),6 amines (37.7 J/(mol · K)),27 and thioalcohols (29.58 J/(mol · K)),10 and somewhat higher than the value of 17.2 J/(mol · K) obtained for carboxylic acids.9

Figure 6. Geometric structures of hexamers.

Vysotsky et al. Large and Infinite Clusters. Next, we consider infinite clusters with unit cells of the corresponding tetramers which are built on the basis of the three most energetically advantageous conformations of monomers 1, 3, and 6. For structures with a finite number of monomers in the cluster (dimers, tetramers, and hexamers), it was shown above that the associates oriented by 30° with respect to the normal to the interface are more advantageous than those oriented by 9°. Therefore, in the following, we consider clusters formed by molecules oriented by 30° with respect to the normal to the interface; see Figure 6. The geometry of the unit cell of the infinite clusters of R-amino acids is shown in Figure 7. Note that the 2D unit cell parameters calculated using the semiempirical PM3 method (see Table 4) agree well with the grazing incidence X-ray diffraction (GIXD) experimental data:7 a ) 4.91 Å, b ) 5.25 Å, θ ) 112°, while the experimental tilt angle t between the molecular axis and the normal to the interface is ∼36°. It is seen from Figure 8 that the infinite clusters involve two types of intermolecular interactions between the hydrophilic parts of R-amino acid molecules, namely, between the -COOH and -NH2 groups and between two -COOH groups, which are formed for serial and parallel orientations of the functional groups in the cluster unit cell structure. Denoting by nCOOH-NH2 the number of interactions between the acid and amine group of the “heads” along the q direction and by nCOOH-COOH the number of interactions between the acid groups of the “heads” along the p direction, one can easily determine these numbers from Figure 8: nCOOH-NH2 ) p · (q - 1);

nCOOH-COOH ) q · (p - 1)

(9) while the number of intermolecular H-H interactions depends on the alkyl chain length as

{ n -2 2 } + q · (p - 1){ n +2 1 }

Ka ) p · (q - 1)

(10)

where n is the number of carbon atoms in the alkyl chain, and braces {...} denote the integer part of a number.



TABLE 3: Standard Thermodynamic Characteristics of Clusterization of Dimers, Tetramers, and Hexamers of r-Amino Acids, as Calculated in the PM3 Approximation molecule

Cl ∆H298,m , kJ/mol

Cl ∆S298,m , J/(mol · K)

Cl ∆S278,m , J/(mol · K)

Cl ∆G278,m , kJ/mol

C7H15NO2 C8H17NO2 C9H19NO2 C10H21NO2 C11H23NO2 C12H25NO2 C13H27NO2 C14H29NO2 C15H31NO2 C16H33NO2 C17H35NO2

-31.28 -33.41 -41.48 -43.71 -51.79 -54.09 -62.16 -64.56 -72.53 -73.90 -82.93

-155.27 -171.66 -184.24 -196.77 -211.77 -221.27 -237.00 -245.86 -262.81 -255.00 -286.03

Dimer 1, P (R ) -81°, β ) -55°) 14.99 -31.54 17.74 -33.66 13.42 -41.72 14.93 -43.94 11.32 -52.00 11.84 -54.30 8.47 -62.35 8.71 -64.73 5.78 -72.69 2.09 -74.06 2.31 -83.06

-156.18 -172.56 -185.07 -197.58 -212.50 -221.98 -237.65 -246.48 -263.36 -255.55 -286.49

11.87 14.31 9.73 10.99 7.08 7.41 3.72 3.79 0.53 -3.02 -3.42


-31.32 -36.85 -40.10 -46.77 -49.53 -57.08 -59.62 -67.46 -70.01 -77.85 -80.37

-185.27 -194.40 -216.02 -216.89 -238.43 -245.10 -254.91 -270.16 -279.13 -293.48 -304.93

Dimer 1, S (R ) -81°, β ) -55°) 23.89 -31.48 21.08 -36.99 24.27 -40.22 17.86 -46.89 21.52 -49.62 15.96 -57.17 16.34 -59.70 13.04 -67.53 13.17 -70.06 9.61 -77.89 10.50 -80.40

-185.81 -194.86 -216.42 -217.29 -238.74 -245.41 -255.19 -270.37 -279.32 -293.60 -305.04

20.18 17.18 19.95 13.52 16.75 11.05 11.25 7.64 7.59 3.73 4.40


-31.48 -34.01 -41.82 -44.36 -52.19 -54.74 -62.57 -65.12 -72.97 -75.53 -82.91

-168.27 -180.72 -193.12 -206.13 -217.66 -230.06 -244.14 -254.87 -267.75 -280.48 -284.60

Dimer 3, P (R ) 88°, β ) -53°) 18.66 -31.74 19.85 -34.25 15.73 -42.05 17.06 -44.58 12.68 -52.39 13.82 -54.93 10.18 -62.75 10.83 -65.30 6.82 -73.12 8.06 -75.66 1.90 -83.04

-169.15 -181.57 -193.92 -206.90 -218.37 -230.74 -244.75 -255.46 -268.28 -280.97 -285.07

15.28 16.23 11.86 12.94 8.32 9.21 5.29 5.72 1.47 2.45 -3.80


-30.59 -37.07 -39.30 -47.06 -49.36 -57.30 -59.71 -67.64 -70.09 -78.01 -80.48

-189.09 -205.85 -207.28 -232.01 -233.89 -254.75 -260.55 -279.18 -287.87 -304.14 -310.95

Dimer 3, S (R ) 88°, β ) -53°) 25.76 -30.76 24.27 -37.20 22.47 -39.43 22.08 -47.16 20.34 -49.47 18.62 -57.39 17.93 -59.80 15.56 -67.70 15.70 -70.14 12.62 -78.04 12.18 -80.52

-189.65 -206.30 -207.76 -232.38 -234.28 -255.04 -260.85 -279.38 -288.06 -304.25 -311.05

21.96 20.16 18.33 17.44 15.66 13.51 12.71 9.97 9.94 6.54 5.95


-33.24 -35.37 -43.42 -45.73 -53.71 -56.09 -64.04 -66.50 -74.42 -76.91 -84.81

-175.04 -185.09 -199.16 -211.43 -226.37 -236.49 -251.16 -261.65 -278.28 -285.05 -302.62

Dimer 6, P (R ) 34°, β ) 160°) 18.92 -33.48 19.78 -35.61 15.93 -43.63 17.28 -45.94 13.75 -53.89 14.38 -56.28 10.80 -64.21 11.47 -66.66 8.51 -74.55 8.03 -77.04 5.37 -84.91

-175.86 -185.92 -199.90 -212.17 -227.02 -237.13 -251.71 -262.19 -278.74 -285.50 -302.98

15.41 16.07 11.94 13.04 9.22 9.64 5.77 6.23 2.93 2.33 -0.68

C7H15NO2 C8H17NO2 C9H19NO2 C10H21NO2 C11H23NO2 C12H25NO2

-22.42 -27.44 -30.76 -37.46 -39.98 -47.84

-169.00 -178.08 -196.62 -205.19 -212.55 -230.68

Dimer 6, S (R ) 34°, β ) 160°) 27.94 -22.67 25.63 -27.66 27.84 -30.97 23.68 -37.67 23.36 -40.17 20.90 -48.02

-169.86 -178.85 -197.35 -205.89 -213.23 -231.29

24.55 22.06 23.89 19.57 19.10 16.28



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TABLE 3: Continued molecule


Cl ∆S298,m , J/(mol · K)

C13H27NO2 C14H29NO2 C15H31NO2 C16H33NO2 C17H35NO2

-50.34 -58.23 -60.76 -68.64 -71.13

-240.43 -258.95 -267.81 -280.35 -292.33


-131.16 -138.95 -162.20 -179.91 -202.12 -221.45 -243.27 -262.97 -285.06 -304.58 -326.83




Cl ∆S278,m , J/(mol · K)


-50.52 -58.38 -60.91 -68.76 -71.25

-241.04 -259.46 -268.32 -280.78 -292.75

16.49 13.75 13.69 9.29 10.14

-642.46 -650.06 -714.41 -731.18 -788.54 -816.83 -886.74 -893.54 -948.23 -970.74 -1029.00

Tetramer 1 (R ) -81°, β ) -55°) 60.30 -131.59 54.77 -139.39 50.70 -162.52 37.98 -180.25 32.86 -202.36 21.96 -221.70 20.97 -243.40 3.30 -263.10 -2.49 -285.13 -15.30 -304.61 -20.19 -326.79

-643.93 -651.61 -715.56 -732.39 -789.40 -817.65 -887.22 -893.99 -948.48 -970.82 -1028.85

47.42 41.76 36.40 23.35 17.09 5.60 3.24 -14.57 -21.45 -34.72 -40.77

-119.78 -135.06 -157.28 -176.15 -198.29 -217.75 -239.96 -259.46 -281.71 -301.21 -323.48

-629.98 -667.33 -711.15 -759.46 -794.42 -840.96 -880.47 -926.85 -968.25 -1009.41 -1047.99

Tetramer 3 (R ) 88°, β ) -53°) 67.95 -120.31 63.81 -135.50 54.64 -157.69 50.16 -176.49 38.45 -198.59 32.86 -217.99 22.42 -240.16 16.74 -259.59 6.83 -281.77 -0.41 -301.21 -11.18 -323.44

-631.78 -668.90 -712.56 -760.66 -795.47 -841.77 -881.14 -927.27 -968.51 -1009.43 -1047.86

55.32 50.46 40.40 34.97 22.56 16.02 4.80 -1.81 -12.52 -20.59 -32.14


-106.06 -119.29 -143.36 -159.82 -181.90 -201.97 -223.37 -242.89 -265.05 -284.49 -306.69

-595.42 -620.96 -699.82 -704.06 -762.77 -819.74 -847.93 -872.72 -931.13 -948.87 -1016.62

Tetramer 6 (R ) 34°, β ) 160°) 71.37 -106.71 65.76 -119.91 65.19 -143.84 49.99 -160.36 45.40 -182.34 42.31 -202.32 29.31 -223.72 17.18 -243.20 12.42 -265.30 -1.72 -284.68 -3.73 -306.79

-597.64 -623.11 -701.47 -705.90 -764.34 -820.94 -849.14 -873.77 -931.97 -949.55 -1017.04

59.44 53.31 51.17 35.88 30.14 25.90 12.34 -0.29 -6.21 -20.71 -24.06

C7H15NO C8H17NO2 C9H19NO2 C10H21NO2 C11H23NO2 C12H25NO2 C13H27NO2 C14H29NO2 C15H31NO2 C16H33NO2 C17H35NO2

-203.12 -240.67 -284.64 -312.39 -354.65 -385.08 -427.50 -458.03 -500.67 -531.08 -573.74

-1025.20 -1105.99 -1225.51 -1245.60 -1341.15 -1389.97 -1541.36 -1591.67 -1682.85 -1726.57 -1826.53

Hexamer 1, P (R ) -81°, β ) -55°) 102.39 -203.91 88.92 -245.96 80.56 -285.42 58.80 -315.02 45.02 -352.18 29.13 -387.28 31.82 -420.33 16.29 -460.05 0.82 -493.06 -16.56 -532.97 -29.43 -566.01

-1028.00 -1135.28 -1250.27 -1273.13 -1392.14 -1489.96 -1538.77 -1631.90 -1684.64 -1772.62 -1825.64

81.87 69.65 62.15 38.91 34.83 26.93 7.45 -6.38 -24.73 -40.18 -58.48

C7H15NO C8H17NO2 C9H19NO2 C10H21NO2 C11H23NO2 C12H25NO2 C13H27NO2 C14H29NO2 C15H31NO2 C16H33NO2 C17H35NO2

-211.74 -245.38 -285.09 -314.60 -352.11 -387.14 -420.31 -460.14 -493.24 -533.26 -566.39

-1102.15 -1133.24 -1249.10 -1271.66 -1391.87 -1489.54 -1538.68 -1632.19 -1685.22 -1773.66 -1827.00

Hexamer 1, S (R ) -81°, β ) -55°) 116.70 -205.79 92.33 -241.39 87.14 -285.08 64.36 -312.93 62.66 -355.04 56.74 -385.44 38.21 -427.63 26.25 -458.07 8.95 -500.58 -4.70 -530.94 -21.95 -573.46

-1070.05 -1108.53 -1227.08 -1247.51 -1342.55 -1391.17 -1541.83 -1591.85 -1682.62 -1726.07 -1825.53

91.68 66.78 56.05 33.87 18.19 1.30 0.99 -15.54 -32.81 -51.09 -65.96

21.31 18.94 19.05 14.91 15.98

To calculate the values per one monomer molecule, relevant for the infinite 2D cluster, one has to divide expressions 9 and

10 by the number of monomers in the cluster (m ) p · q) and calculate the limits of the resulting expressions at an infinite



TABLE 4: Unit Cell Parameters for 2D Infinite Clusters conformer

a, Å

tetramer 1 tetramer 2 tetramer 3 tetramer 4 tetramer 5 tetramer 6

4.57-4.71 4.82-4.87 4.61-4.88 4.80-4.85 4.75-4.83 4.59-4.67

C18H37NO2

b, Å Calculated Values 5.67-5.75 5.59-5.95 5.39-5.47 5.74-5.84 5.26-5.52 5.71-5.80 Experimental Values17 5.25

4.91

θ, deg

t, deg

100-103 90-93 103-106 88-91 100-103 100-105

30 30 30 30 30 30

112

36

TABLE 5: Values of the Coefficients for the Calculation of the Thermodynamic Characteristics per One Monomer Molecule in Infinite 2D Clusters Cl ∆ST,∞ /m, J/(mol · K)

Cl ∆HT,∞ /m, kJ/mol

type of infinite 2D cluster

U

V

U

V

U

V

-218.24 -232.31 -212.68

-4.25 -4.25 -4.25

42.54 47.17 49.40

T ) 298 K -21.72 -21.72 -21.72

-217.11 -230.95 -211.05

-3.81 -3.81 -3.81

47.32 51.62 53.49

infinite cluster 1 infinite cluster 3 infinite cluster 6

-10.26 -10.26 -10.26

T ) 278 K -18.14 -21.62 -17.41 -21.62 -9.72 -21.62

infinite cluster 1 infinite cluster 3 infinite cluster 6

-10.28 -10.28 -10.28

-17.98 -17.20 -9.40

number of molecules in the cluster. Therefore, for p ) ∞ and q ) ∞, eqs 9 and 10 become

nCOOH-NH2 ) 1,

nCOOH-COOH ) 1;

{ n -2 2 } + { n +2 1 } (11)

Ka )

Introducing eq 11 into the correlation equations for the enthalpy and entropy of clusterization (eqs 5-8), one obtains the expressions for the thermodynamic characteristics of clusterization per one monomer molecule in the infinite 2D films composed of the three most energetically advantageous conformations of R-amino acids: Cl ∆AT,∞ /m ) U ·

[{ n -2 2 } + { n +2 1 }] + V

Cl ∆GT,∞ /m, kJ/mol

(12)

where the slope U and the absolute term V for each thermoCl Cl Cl Cl (i.e., ∆HT,∞ , ∆ST,∞ , and ∆GT,∞ ), dynamic characteristic ∆AT,∞ temperature, and cluster type are listed in Table 5. The dependencies of the thermodynamic quantities per one R-amino acid molecule on the alkyl chain length are illustrated in Figures 9-11 for the infinite cluster 1 at 278 K. The solid lines show the dependencies calculated using eq 12 with the coefficients listed in Table 5, whereas the points correspond to the results of quantum-chemical calculations. From Figure 11, it is seen that spontaneous clusterization of the most energetically preferable conformation of R-amino acids should take place if the alkyl chain length exceeds 11-12 carbon atoms. This prediction agrees well with the experimental data.17 For infinite clusters formed on the basis of conformations 3 and 6, this spontaneous clusterization threshold corresponds to the alkyl chain length of 12 and 13 carbon atoms, respectively. In our earlier studies,6-11 the calculations were performed at 298 K. Therefore, similar calculations for R-amino acids were also performed at 298 K to compare the above data obtained for 278 K with previous results for other classes of compounds. The parameters of the correlation dependencies of the thermodynamic quantities are listed in Table 5. It follows from the calculated data that the increase of the temperature to 298 K

results in the increase of the clusterization threshold for all of the conformations of R-amino acids by two carbon atoms. In particular, at this temperature, the spontaneous clusterization threshold for cluster 1 is 13-14 carbon atoms, whereas the clusterization of alcohols becomes possible if the alkyl chain length exceeds 10-12 carbon atoms;8 for carboxylic acids11 and thioalcohols,12 this threshold value is 14-15, and for amines, the threshold is 18-19 carbon atoms in the alkyl chain.29 Conclusions To summarize, in the present study, the semiempirical PM3 method is employed to study the clusterization process thermodynamics of R-amino acids with the general composition CnH2n+1CHNH2COOH (n ) 5-15) at the air/water interface. Using the conformational analysis, it is shown that six energetically preferable conformations of the R-amino acid monomer exist. For these conformations, enthalpies and Gibbs’ energies of the monomer formation and absolute entropies of the monomers are calculated. It is shown that the thermodynamic parameters calculated for the most energetically advantageous monomer 1 agree well with the experimental data.28 The regression dependencies of the calculated thermodynamic parameters on the number of methylene groups are developed. The contributions of one CH2 group to the total entropy and enthalpy are shown to be quite equal to those calculated earlier for other classes of substituted alkanes.6-11 The geometrical structures of the dimers are constructed on the basis of these six conformations of monomers. It is shown that, in each of the six cases considered, two types of relative orientations of the functional groups in the dimer (“parallel” and “serial”, cf. Figure 5) can exist. For the dimers with “parallel” orientation, the spontaneous dimerization can occur at lower alkyl chain lengths than for the dimers with “serial” orientation. This can be ascribed to the fact that in the former case more intermolecular H-H interactions are formed, that determine the clusterization energetics. The three most energetically advantageous conformations of the dimers are determined, which are used as the basis to

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Vysotsky et al.

Figure 7. Structure of the unit cell of the infinite 2D cluster: (a) view along the a axis; (b) view along the b axis; (c) view along the molecular chain axis.

Figure 9. Dependence of the variation of clusterization enthalpy on the alkyl chain length; p and q are the numbers of monomer molecules which determine the size of the 2D cluster film.

Figure 8. Fragment of the geometric structure of the infinite 2D Cluster 1.

construct three tetramers and two hexamers. It is shown that the geometric parameters of the unit cells of 2D clusters (tetramers) built on the basis of the six conformations of the monomers agree well with the experimental data reported in ref 17.


J. Phys. Chem. B, Vol. 113, No. 52, 2009 16567 that the nature of intermolecular H-H interactions for different classes of compounds is the same. At this temperature, the spontaneous clusterization threshold for the most energetically advantageous infinite cluster 1 corresponds to a larger alkyl chain length (13-14 carbon atoms) than that at 278 K. References and Notes

Figure 10. Dependence of the variation of clusterization entropy on the alkyl chain length; p and q are the same as in Figure 9.

Figure 11. Dependence of the variation of clusterization Gibbs’ energy on the alkyl chain length; p and q are the same as in Figure 9.

For all of the structures mentioned above, the thermodynamic parameters of clusterization at 278 and 298 K are calculated. From these values obtained for the three most energetically advantageous conformations of R-amino acid clusters, the correlation dependencies of the clusterization thermodynamic parameters on the alkyl chain length are derived. These dependencies are used to calculate the thermodynamic characteristics of clusterization per one monomer for infinite monolayers with corresponding structure. It is shown that at 278 K the simultaneous formation of the monolayer on the basis of monomer 1 takes place if the alkyl chain length exceeds 11-12 carbon atoms, in agreement with the experimental data.17 For the conformations of the 2D films on the basis of monomers 3 and 6, this spontaneous clusterization threshold corresponds to the larger alkyl chain length with 12 and 13 carbon atoms, respectively. The parameters of correlation dependencies calculated for 298 K agree well with those calculated earlier for other classes of surfactants6-11 for the same temperature. This supports the view

(1) Barton, D., Ollis, W. D. ComprehensiVe Organic Chemistry; Pergamon Press: New York, 1982. (2) Weissbuch, I.; Leiseriwitz, L.; Lahav, M. Curr. Opin. Colloid Interface Sci. 2008, 13, 12. (3) Steed, J. W., Atwood, J. L. Supramolecular Chemistry; John Wiley & Sons, Ltd: New York, 2000. (4) Somasundaran, P. Encyclopedia of Surface and Colloid Science; Taylor & Francis: New York, 2006. (5) Kaganer, V. M.; Mo¨hwald, H.; Dutta, P. ReV. Mod. Phys. 1999, 71, 779. (6) Vysotsky, Yu. B.; Bryantsev, V. S.; Fainerman, V. B.; Vollhardt, D.; Miller, R. J. Phys. Chem. B 2002, 106, 121. (7) Vysotsky, Yu. B.; Bryantsev, V. S.; Fainerman, V. B.; Vollhardt, D. J. Phys. Chem. B 2002, 106, 11285. (8) Vysotsky, Yu. B.; Bryantsev, V. S.; Fainerman, V. B.; Vollhardt, D.; Miller, R. Colloids Surf., A 2002, 209, 1. (9) Vysotsky, Yu. B.; Bryantsev, V. S.; Fainerman, V. B.; Vollhardt, D.; Miller, R. Prog. Colloid Polym. Sci. 2002, 121, 72. (10) Vysotsky, Yu. B.; Muratov, D. V.; Boldyreva, F. L.; Fainerman, V. B.; Vollhardt, D.; Miller, R. J. Phys. Chem. B 2006, 110, 4717. (11) Vysotsky, Yu. B.; Belyaeva, E. A.; Fainerman, V. B.; Vollhardt, D.; Miller, R. J. Phys. Chem. C 2007, 111, 5374. (12) Nakahara, H.; Mo¨bius, D. J. Colloid Interface Sci. 1986, 114, 363. (13) Vogel, V.; Mo¨bius, D. J. Colloid Interface Sci. 1988, 126, 408. (14) Boyd, E. J. J. Phys. Chem. 1958, 62, 536. (15) Itaya, A.; Van der Auweraer, M.; De Schryver, F. C. Langmuir 1989, 5, 1123. (16) Wang, J.-L.; Leveiller, F.; Jacquemain, D.; Kjaer, K.; Als-Nielsen, J.; Lahav, M.; Leiserowitz, L. J. Am. Chem. Soc. 1994, 116, 1192. (17) Weissbuch, I.; Berfeld, M.; Bouwman, W.; Kjaer, K.; Als-Nielsen, J.; Lahav, M.; Leiserowitz, L. J. Am. Chem. Soc. 1997, 119, 933. (18) Stewart, J. J. MOPAC 2000.00 Manual; Fujitsu Limited: Tokyo, Japan, 1999. (19) Soloviov, M. E.; Soloviov, M. M. Computational Chemistry; SOLON-Press: Moscow, 2005 (in Russian). (20) Stone, A. J. The theory of intermolecular force; Clarendon Press: Oxford, U.K., 1996. (21) Sullivan, R.; Pyda, M.; Pak, J.; Wunderlich, B.; Thompson, J. R.; Pagni, R.; Pan, H.; Barnes, C.; Schwerdtfeger, P.; Compton, R. J. Phys. Chem. A 2003, 107, 6674. (22) Thirumoorthy, K.; Nandi, N.; Vollhardt, D. Colloids Surf., A 2006, 282, 222. (23) Hart, H., Craine, L. E., Hart, D. J. Organic chemistry; Houghton Mifflin Company: New York, 1999. (24) Weissbuch, I.; Kuzmenko, I.; Berfeld, M.; Leiserowitz, L.; Lahav, M. J. Phys. Org. Chem. 2000, 13, 426. (25) Kuzmenko, I.; Kjaer, K.; Als-Nielsen, J.; Lahav, M.; Leiserowitz, L. J. Am. Chem. Soc. 1999, 121, 2657. (26) Nandi, N., Thirumoorthy, K. Chirality in biological nanospace; 17th International Symposium of Surfactants in Solution, Berlin, 2008. (27) Hoffmann, F.; Stine, K. J.; Hu¨hnerfuss, H. J. Phys. Chem. B 2005, 109, 240. (28) Dean, J. Lange’s handbook of chemistry; McGraw-Hill, Inc.: New York, 1999. (29) Vysotsky, Yu. B.; Belyaeva, E. A.; Fainerman, V. B.; Aksenenko, E. V.; Vollhardt, D.; Miller, R. J. Phys. Chem. C 2007, 111, 15342.

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Quantum-Chemical Analysis of Thermodynamics of Two

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