Quantum-Chemical Analysis of Thermodynamics of Two-Dimensional

ARTICLE pubs.acs.org/JPCB

Quantum-Chemical Analysis of Thermodynamics of Two-Dimensional Cluster Formation of Racemic r-Amino Acids at the Air/Water Interface Yu. B. Vysotsky,† E. S. Fomina,† E. A. Belyaeva,† E. V. Aksenenko,‡ V. B. Fainerman,§ 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 § Donetsk Medical University, 16 Ilych Avenue, Donetsk 83003, Ukraine Max Planck Institute of Colloids and Interfaces, D-14424 Potsdam/Golm, Germany

)

‡

ABSTRACT: The quantum-chemical semiempiric PM3 method is used to calculate the thermodynamic parameters of clusterization for the racemic R-amino acids CnH2nþ1CHNH2COOH with n = 5-15 at 278 and 298 K. Possible relative orientations of the monomers in the heterochiral clusters are considered. It is shown that, for the racemic mixtures of R-amino acids, the formation of heterochiral 2D films is most energetically preferable with the alternating (rather than “checkered”) packing of the enantiomers with opposite specific rotation. The two enantiomeric forms of R-amino acids in the heterochiral 2D clusters are tilted with respect to the normal to the q direction at angles of j1 = 20 and j2 = 33, whereas the single enantiomeric forms are oriented at an angle of δ = 9 with respect to the normal to the p direction. It is shown that the heterochiral 2D film based on the R-amino acid structures oriented at the angle j2 = 33 with respect to the normal to the q direction possesses a rectangular unit cell with the geometric parameters a = 4.62 Å and b = 10.70 Å and the tilt angle of the alkyl chain of the molecule with respect to the interface t2 = 35, which is in good agreement with the X-ray structural data a = 4.80 Å, b = 9.67 Å, and t2 = 37. The parameters of the lattice structure of monolayers formed by amphiphilic amino acids are shown to be determined by the “a” type of the intermolecular H-H interactions, whereas the tilt angle of the molecules with respect to the interface depends on the volume and the structure of the functional groups involved in the hydrophilic part of the molecule. Spontaneous clusterization of the racemic form of R-amino acids at the air/water interface at 278 K takes place if the alkyl chain length is equal or higher than 12-13 carbon atoms, whereas for 298 K this clusterization threshold corresponds to 14 carbon atoms in the hydrocarbon chain. These values agree with the experimental data.

’ INTRODUCTION Chirality is operative in numerous biological systems at microscopic and macroscopic level.1-3 The omnipresence of chirality gives rise to the question about the role of chiral structures in biological systems. Chiral interfaces are of special interest not only for the understanding of biological assemblies but also for the potential application in material science. Recent experimental studies of biomimetic systems indicate that the chirality of particular amphiphilic monolayers can control the characteristics of the aggregated structures of monolayers.4,5 Chiral discrimination effects of biomimetic monolayers have been manifested in the form of different shapes of the surface pressure-area (π-A) isotherms, different handedness exhibited by condensed phase domains from different enantiomers, or external infrared reflection-absorption spectroscopy.6-14 Both homo- and heterochiral preference for chiral interaction has been r 2011 American Chemical Society

observed depending on the intermolecular interaction of the amphiphilic molecules.15-17 Recent comprehensive studies of the condensed phase domains of various amino acid amphiphiles, such as N-palmitoyl aspartic acid, N-palmitoyl- or N-stearoyl serine methyl ester, Npalmitoyl threonine and its diastereomer N-palmitoyl allo-threonine and their methyl esters, and N-palmitoyl or N-myristoyl alanine, have revealed a large morphological variety and differences in the two-dimensional lattice structure.5,15,18-21 The two enantiomeric forms of amino acid amphiphiles show curvatures in opposite directions. Usually, the domain shape of the 1:1 racemic mixtures is different from that of the enantiomeric forms but very often oppositely curved texture elements can be Received: November 10, 2010 Published: February 18, 2011 2264

dx.doi.org/10.1021/jp110730b | J. Phys. Chem. B 2011, 115, 2264–2281

The Journal of Physical Chemistry B

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Figure 1. Optimized geometric structures of S-monomers of R-amino acids.

observed within a single domain, suggesting at least elements of homochiral preference or chiral segregation. Accordingly, the chiral discrimination phenomena raise questions about how such slight differences in the molecular feature control the higher-length-scale structural characteristics and how to treat the intermolecular interaction. Therefore, first theoretical studies of the preference of homochiral or heterochiral interactions in racemic mixtures of the surfactants have been previously performed using the Monte Carlo22 and molecular dynamics23-26 methods. In our recent paper, 27 the clusterization of enantiomeric R-amino acids at the air/water interface was studied using the quantum-chemical PM3 method. The R-amino acids with an unbranched alkyl chain and the general formula CnH2nþ1CHNH2COOH (n = 5-15) have been chosen because of the fact that their monolayers have been studied rather scarcely from both the experimental28-31 and the theoretical point of view. In the present study, we focus on the determination of the structural and thermodynamic characteristics at the clusterization of racemic mixtures of R-amino acids at the air/water interface.

’ METHODS For the calculation of the structural and energetic parameters of the clusterization of racemic R-amino acids at the air-water interface, the Mopac2000 quantum-chemical software package32 was employed in the framework of the PM3 parametrization. This method is parametrized with respect to the formation heats33,34 and is capable of the account for the H-H interactions between the alkyl chains which govern the formation of surfactant films. Statistical processing of the calculated data was performed using the MS Excel software. ’ RESULTS AND DISCUSSION Monomers. The conformational analysis of the monomers of R-amino acids was made in our previous study.27 Six stable monomer conformations (monomers 1-6, see Figure 1, where the values of the torsion angle of the carboxyl group R = C2C1-C4-O1 and that of the amino group β = C2-C1-N-H1 are listed) were found to exist, among which monomer 1 with R = -81 and β = -55 is most preferable. This monomer has a torsion angle between the hydrophilic headgroup and the alkyl chain of the molecule γ = C3-C2-C1-C4 = 74. For the other conformers of the S-series, the torsion angles are listed in Figure 1. The values of the torsion angles of the R-enantiomers have the opposite sign from the S-enantiomers. Figure 2 illustrates the structure of the enantiomers of R-amino acids. Here, a schematic notation is introduced with the dextorotatory isomer shown by the green circle and denoted by R and the laevorotatory isomer shown by the orange circle and denoted by S; the

Figure 2. The structure of enentiomers of R-amino acids.

arrow indicates the direction from the nitrogen atom of the amino group to the oxygen atom in the OH unit of the carboxyl group. Dimers. The structures of the R-amino acid monomers listed above were used to compose the racemic dimers which involve the “a” type of the hydrogen-hydrogen interactions between the alkyl chains of the molecules. It was shown in ref 35 that these interactions are most energetically preferable. The structure of the alkyl chain of the molecules enables the creation of four dimer structures by two monomers which form the “a” type of hydrogen-hydrogen interactions. In this case, the angle which reflects the relative orientation of the hydrophilic head groups of the molecules is close to the multiple of 90. It is easy to show that 13 dimers with different relative orientations of the enantiomers can 2265

dx.doi.org/10.1021/jp110730b |J. Phys. Chem. B 2011, 115, 2264–2281


Figure 3. Types of relative arrangement of enantiomers in heterochiral dimers.

exist, which are listed in Figure 3. Among these dimers, five pairs of the structures exist which complement each other when the formation of large clusters is considered: dimer 1-dimer 5, dimer 2-dimer 6, dimer 3-dimer 8, dimer 4-dimer 7, and dimer 9-dimer 10. It should be noted that the dimers constructed in this way can have different tilt angles of their alkyl chains with respect to the air/water interface. Note that the quantum chemical calculation yields the tilt angles of the molecule with respect to the axes p and q of the unit cell, rather than the tilt angle of the molecules with respect to the interface. Figure 4 illustrates schematically the orientation of the R-amino acid molecule axis (CO) with respect to the interface plane (pOq). Here, the CO3 segment is perpendicular to the interface pOq and the CO1 and CO2 segments are perpendicular to the axes p and q, respectively. In Figure 4, t denotes the tilt angle of the molecule with respect to the normal to the interface and δ and j are the tilt angles of the molecule with respect to the normal within the O1OC plane and the O2OC plane, respectively. It follows from the theorem of the three perpendiculars that O3O2O and O3O1O are the right angles. Then, according to the right-angle triangles O3CO, O3CO1, O3CO2, O1CO, O2CO, O1OO3, and O2OO3 (here the first listed vertex of the triangle corresponds to the right angle), it is straightforward to show that sin j sin δ ¼ sin t, ¼ sin t, θ1 þ θ2 ¼ θ ð1Þ cos θ2 cos θ1 The solution of set 1 with respect to θ1, θ2, and t is ! sin j - ctg θ , θ2 ¼ θ - θ1 , θ1 ¼ arctg sin δ 3 sin θ sin δ t ¼ arcsin ð2Þ cos θ1 It was shown in our recent paper27 that an almost parallel (t = 9) orientation of the R-amino acid molecules in the cluster with respect to the normal to the interface is energetically less advantageous than the tilted orientation. Similar to the procedure adopted in our previous papers, to determine the t angle, first the dimer with the “a” H-H interaction type was constructed of two enantiomers, and applying the parallel shift to one molecule with respect to the other one, the dependence of the Gibbs’ energy on the j angle was tabulated. It has been shown that two of these

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Figure 4. Orientation of the R-amino acid molecule with respect to the air/water interface.

angles exist, j1 = 20 and j2 = 33, which correspond to the two values t1 = 22 and t2 = 35. Both of these orientations can be the basis for the arrangement of the monolayers, which results in the total of 156 different geometric structures of dimers. For all the types of racemic dimers based on all the monomer conformations with two possible tilt angles t, the thermodynamic parameters of dimerization were calculated at T = 278 K. Table 1 illustrates the influence of the relative positions of the monomers in a dimer on these parameters for the dimers based on the most energetically preferential monomers 1 and 2 for the hydrocarbon chain with 12 carbon atoms. Enthalpy, entropy, and Gibbs’ free energy of clusterization 0 0 Cl 0 were calculated as ΔHCl T,m = ΔHT - mHT,mon, ΔST,m = ST 0 Cl Cl Cl mST,mon, ΔGT,m = ΔHT,m - T 3 ΔST,m, respectively, where ΔH0T and S0T are the enthalpy and entropy of the corresponding clusters at temperature T; H0T,mon and S0T,mon are the enthalpy and entropy of the corresponding monomers at the same temperature, and m is the number of monomers in the cluster. From Table 1, it is seen that among the dimers based on monomer 1 (that with the tilt angle t1 = 22) dimer 1 is most energetically preferable. Note that the structures of dimers 2, 4, and 6 (those based on monomer 1 inclined at t2 = 35) and the structures of the dimers 4 and 12 (based on monomer 2) are sterically hindered. Therefore, the corresponding entries in Table 1 are void. Among the pairs of complementary dimers based on the two conformations of monomers 1 and 2, the pairs of dimer 1 and dimer 5 are most energetically preferable. Also, this pair of the dimers based on the monomer 2 structure with t1 = 22 is somewhat more preferable with respect to the Gibbs’ energy than the same pair based on the monomer 1 structure. Almost the same energy gain is obtained for the combination of dimers 1 and 5 and dimers 3 and 8 for monomer 1. However, below it is shown that in the tetramers this combination is less preferable than the combination of the pair consisting of dimers 9 and 10. This is because in the tetramers based on the pair of racemic dimers 9 and 10 two pairs of homochiral dimers are present with “parallel” relative orientation of the head groups, which leads to a higher energetic yield than that for the tetramers based on the pair of dimers 1 and 5 and dimers 3 and 8, in which only one such interaction is present, while the second (less energetically preferable) link is formed between the similar enantiomers with “serial” relative orientation of their head groups. It should be noted that for the homochiral dimers in 2266



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Table 1. Thermodynamic Parameters of Dimerization for the Racemic Dimers with Different Values of the Tilt Angle t of the Alkyl Chain with Respect to the Normal to the Interface t1 = 22 structure

ΔHCl 278,m,

kJ/mol

ΔSCl 278,m,

J/(mol 3 K)

t2 = 35 ΔGCl 278,m,

kJ/mol

ΔHCl 278,m,

kJ/mol

ΔSCl 278,m,

ΔGCl 278,m, kJ/mol

J/(mol 3 K)

Monomer 1 dimer 1

-62.12

-230.16

1.86

-54.76

-226.32

8.16

dimer 2 dimer 3

-59.41 -55.79

-239.49 -233.14

7.17 9.02

-45.00

-204.92

11.97

dimer 4

-54.75

-232.88

9.99 -40.88

-204.06

15.85

dimer 5

-50.23

-230.41

13.83

dimer 6

-42.30

-217.19

18.08

dimer 7

-53.93

-235.93

11.66

-53.94

-235.77

11.60

dimer 8

-56.63

-244.82

11.43

-48.78

-220.10

12.41

dimer 9

-53.12

-221.87

8.56

-55.66

-234.29

9.48

dimer 10 dimer 11

-45.43 -39.84

-229.58 -213.33

18.40 19.47

-45.10 -35.57

-223.51 -221.66

17.03 26.05

dimer 12

-54.70

-227.90

8.65

-54.70

-227.48

8.54

dimer 13

-60.60

-238.19

5.62

-54.71

-232.90

10.04

dimer 1

-62.25

-230.31

1.78

-54.94

-223.84

7.29

dimer 2

-57.68

-239.43

8.88

-58.59

-223.31

3.49

-50.12

-221.42

11.44

-40.41 -40.65

-208.96 -209.70

17.68 17.65

Monomer 2

dimer 3

-58.23

-241.99

9.04

dimer 4

-60.48

-249.30

8.83

dimer 5 dimer 6

-54.02 -40.22

-239.10 -234.65

12.46 25.01

dimer 7

-52.84

-256.53

18.48

-51.12

-227.09

12.01

dimer 8

-50.13

-259.20

21.92

-50.42

-220.89

10.99

dimer 9

-57.72

-236.21

7.94

-57.03

-227.55

6.23

dimer 10

-44.49

-241.06

22.52

-42.58

-231.29

21.72

dimer 11

-49.40

-232.06

15.12

-33.67

-225.71

29.08

dimer 12

-53.61

-217.03

6.73

dimer 13

-66.02

-248.47

3.05

-56.17

-238.97

10.27

the tetramer the δ angle (see Figure 4) is 9. This orientation of the enantiomers in the elementary cell of the racemic monolayer agrees with the experimental data.28 The formation of corresponding complementary pairs of dimers 3 and 8 and dimers 9 and 10 based on the monomer 2 structure is less preferential than that for the dimers based on monomer 1. The structures of dimers and tetramers most preferable with respect to the Gibbs’ energy based on monomer 1 with two possible tilt angles to the normal to the interface are shown in Figures 5 and 6. Consider next the dependence of thermodynamic parameters of dimerization for the chosen dimers 1 and 5 with t1 = 22 and dimers 9 and 10 with t2 = 35 on the geometric structure of monomers 1-6 and on the alkyl chain length. For all the series of dimers, for enthalpy, entropy, and Gibbs’ energy of dimerization of the racemic R-amino acids (except for the dimers with t1 = 22 based on monomer 5 with R = -160, β = 160 for which the structures are sterically hindered), the correlation dependencies on the number of H-H interactions Ka were calculated. The correlation coefficients are listed in Table 2, where the number in parentheses after the name of the dimer indicates the number of the monomer on which the dimer is based. From these data, it is seen that the larger (by absolute value) contributions to enthalpy and entropy are brought by the interactions between the hydrophilic parts of the molecules oriented at t1 = 22 (as in dimer 5)

and at t2 = 35 (as in dimer 10). However, when combined to yield the Gibbs’ energy, these enthalpy and entropy factors partly compensate each other, and the formation of dimer 1 (9) is more advantageous than the formation of dimer 5 (10). Also, dimer 5 (10), because of the repulsion between the likely charged oxygen atoms present in the carboxyl groups of the head groups, involves a smaller number of H-H interactions. The combination of these partial correlations into the total one yields: • for dimer 1 with t1 = 22: nþ1 0 ΔH278, dim ¼ - ð9:98 ( 0:09Þ 3 2 - ð3:40 ( 0:51Þ 3 ðn1, 1 þ n2, 1 þ n3, 1 þ n4, 1 Þ - ð7:52 ( 0:63Þ 3 n6, 1 ½N ¼ 109; R ¼ 0:9997; S ¼ 1:44 kJ=mol ð3Þ

nþ1 ¼ - ð24:28 ( 0:39Þ 3 2 - ð88:20 ( 2:26Þ 3 ðn1, 1 þ n2, 1 þ n3, 1 þ n4, 1 Þ - ð104:61 ( 2:82Þ 3 n6, 1 ½N ¼ 109; R ¼ 0:9996; S ¼ 6:43 J=ðmol 3 KÞ ð4Þ ΔS0278, dim

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Figure 5. Geometric structures of the associates of R-amino acids with racemic structure tilted by an angle of t1 = 22 with respect to the normal to the interface (for monomer 1 taken as an example).

ΔG0278, dim ¼ - ð3:18 ( 0:08Þ 3

nþ1 2

ΔS0278, dim ¼ - ð24:28 ( 0:39Þ 3

þ ð20:84 ( 0:45Þ 3 ðn1, 1 þ n2, 1 þ n3, 1 þ n4, 1 Þ þ ð21:28 ( 0:57Þ 3 n6, 1 ½N ¼ 109; R ¼ 0:9955; S ¼ 1:29 kJ=mol • for dimer 5 with t1 = 22: 0 ΔH278 , dim

- ð130:68 ( 2:32Þ 3 n1, 5 - ð145:39 ( 2:32Þ 3 n2, 5 - ð137:69 ( 1:87Þ 3 ðn3, 5 þ n4, 5 Þ - ð142:90 ( 2:44Þ 3 n6, 5 ½N ¼ 109; R ¼ 0:9996; S ¼ 6:43 J=ðmol 3 KÞ ð7Þ

ð5Þ

n-3 ¼ - ð9:98 ( 0:09Þ 3 2

ΔG0278, dim

- ð11:27 ( 0:52Þ 3 n1, 5 - ð15:30 ( 0:51Þ 3 n2, 5

n-3 ¼ - ð3:18 ( 0:08Þ 3 2

þ ð29:09 ( 0:47Þ 3 n1, 5 þ ð24:95 ( 0:47Þ 3 n2, 5 þ ð27:33 ( 0:37Þ 3 ðn3, 5 þ n4, 5 Þ

- ð10:77 ( 0:42Þ 3 ðn3, 5 þ n4, 5 Þ - ð12:16 ( 0:55Þ 3 n6, 5 ½N ¼ 109; R ¼ 0:9997; S ¼ 1:44 kJ=mol

n-3 2

þ ð27:39 ( 0:49Þ 3 n6, 5 ½N ¼ 109; R ¼ 0:9955; S ¼ 1:29 kJ=mol

ð6Þ 2268

ð8Þ



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Figure 6. Geometric structures of the associates of R-amino acids with racemic structure tilted by an angle of t2 = 35 with respect to the normal to the interface (for monomer 1 taken as an example).

• for dimer 9 with t2 = 35:

þ ð26:04 ( 0:39Þ 3 n5, 9 þ ð25:78 ( 0:39Þ 3 n6, 9 ;

n-1 0 ΔH278, dim ¼ - ð9:99 ( 0:09Þ 3 2 - ð6:15 ( 0:62Þ 3 n1, 9 - ð13:41 ( 0:62Þ 3 n2, 9 - ð6:22 ( 0:62Þ 3 n3, 9 - ð11:07 ( 0:62Þ 3 n4, 9 - ð7:67 ( 0:62Þ 3 n5, 9 - ð7:92 ( 0:62Þ 3 n6, 9

½N ¼ 126; R ¼ 0:9979; S ¼ 1:00 kJ=mol • for dimer 10 with t2 = 35: 0 ΔH278 , dim ¼ - ð9:99 ( 0:09Þ 3

n-4 2

- ð15:00 ( 0:57Þ 3 n1, 10 - ð12:36 ( 0:57Þ 3 n2, 10 - ð21:03 ( 0:55Þ 3 n3, 10 - ð21:21 ( 0:57Þ 3 n4, 10 - ð6:00 ( 0:57Þ 3 n5, 10 - ð11:74 ( 0:57Þ 3 n6, 10

½N ¼ 109; R ¼ 0:9996; S ¼ 1:58 kJ=mol ð9Þ n-1 0 ΔS278, dim ¼ - ð23:54 ( 0:34Þ 3 2 - ð115:41 ( 2:25Þ 3 n1, 9 - ð129:67 ( 2:25Þ 3 n2, 9 - ð114:96 ( 2:25Þ 3 n3, 9 - ð125:89 ( 2:25Þ 3 n4, 9 - ð121:31 ( 2:25Þ 3 n5, 9 - ð121:24 ( 2:25Þ 3 n6, 9 ½N ¼ 109; R ¼ 0:9997; S ¼ 5:74 J=ðmol 3 KÞ

ð11Þ

½N ¼ 109; R ¼ 0:9996; S ¼ 1:58 kJ=mol ΔS0278, dim ¼ - ð23:54 ( 0:34Þ 3

ð10Þ

n-4 2

ð12Þ

- ð147:02 ( 2:08Þ 3 n1, 10 - ð147:60 ( 2:08Þ 3 n2, 10 - ð163:73 ( 2:08Þ 3 n3, 10 - ð164:03 ( 2:08Þ 3 n4, 10 - ð128:21 ( 2:08Þ 3 n5, 10 - ð141:74 ( 2:08Þ 3 n6, 10

n-1 ¼ - ð3:44 ( 0:06Þ 3 2 þ ð25:96 ( 0:39Þ 3 n1, 9 þ ð22:63 ( 0:39Þ 3 n2, 9 þ ð25:73 ( 0:39Þ 3 n3, 9 þ ð23:92 ( 0:39Þ 3 n4, 9 ΔG0278, dim

½N ¼ 126; R ¼ 0:9997; S ¼ 5:74 J=ðmol 3 KÞ 2269

ð13Þ



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Table 2. Parameters of Correlation Equations for the Thermodynamic Characteristics of Dimerization of r-Amino Acids y = (a ( Δa) 3 Ka þ (b ( Δb) (Sampling Amount N = 11) t1 = 22 system

t2 = 35

(a ( Δa)

(b ( Δb)

system

(a ( Δa)

(b ( Δb)

ΔH0278,dim, kJ/mol dimer 1 (monomer 1)

-10.20 ( 0.27

-2.08 ( 1.48

dimer 9 (monomer 1)

-10.24 ( 0.14

-5.08 ( 0.65

dimer 5 (monomer 1) dimer 1 (monomer 2)

-9.71 ( 0.23 -10.20 ( 0.25

-12.34 ( 0.85 -2.12 ( 1.38


-9.19 ( 0.32 -10.19 ( 0.18

-17.39 ( 1.09 -12.56 ( 0.84 -14.52 ( 1.11

dimer 5 (monomer 2)

-9.60 ( 0.30

-16.25 ( 1.69

dimer 10 (monomer 2)

-9.27 ( 0.33

dimer 1 (monomer 3)

-10.21 ( 0.26

-2.07 ( 1.45

dimer 9 (monomer 3)

-10.23 ( 0.14

-5.20 ( 0.64

dimer 5 (monomer 3)

-10.17 ( 0.16

-9.67 ( 0.58


-9.90 ( 0.29

-21.29 ( 0.96

dimer 1 (monomer 4)

-10.11 ( 0.26

-3.10 ( 0.41

dimer 9 (monomer 4)

-10.05 ( 0.19

-10.81 ( 0.89

dimer 5 (monomer 4)

-10.12 ( 0.16

-9.96 ( 0.63


-10.85 ( 0.82

-18.62 ( 2.73

dimer 1 (monomer 5)

dimer 9 (monomer 5)

-10.21 ( 0.17

-6.74 ( 0.80


-10.12 ( 0.27

-6.79 ( 1.49


-9.37 ( 0.30 -10.23 ( 0.17

-7.87 ( 0.77 -6.89 ( 0.75

dimer 5 (monomer 6)

-10.09 ( 0.15

-11.66 ( 0.60


-9.66 ( 0.27

-12.73 ( 0.89

ΔS0278,dim, dimer 1 (monomer 1)

-24.73 ( 1.47

-86.63 ( 8.09

dimer 5 (monomer 1)

-25.70 ( 0.89

-126.70 ( 3.23

J/(mol 3 K) dimer 9 (monomer 1)

-23.90 ( 0.34

-114.02 ( 1.53


-20.95 ( 1.14

-154.80 ( 3.77

dimer 1 (monomer 2)

-25.06 ( 1.25

-82.70 ( 6.89

dimer 9 (monomer 2)

-24.56 ( 0.83

-125.31 ( 3.79

dimer 5 (monomer 2)

-23.85 ( 1.25

-146.87 ( 4.56


-20.82 ( 0.96

-155.76 ( 3.17

dimer 1 (monomer 3)

-24.56 ( 1.45

-87.02 ( 7.97

dimer 9 (monomer 3)

-23.31 ( 0.36

-115.96 ( 1.65


-25.01 ( 0.53 -23.18 ( 1.82

-133.85 ( 1.95 -94.21 ( 10.05


-23.24 ( 0.63 -25.37 ( 0.97

-164.62 ( 2.10 -118.06 ( 4.41

dimer 5 (monomer 4)

-24.56 ( 0.64

-136.47 ( 2.57


-26.10 ( 2.69

-156.35 ( 8.92

dimer 9 (monomer 5)

-23.88 ( 0.95

-119.86 ( 4.31

dimer 1 (monomer 5)


-20.71 ( 1.04

-136.73 ( 3.45

dimer 1 (monomer 6)

-23.11 ( 1.17

-110.78 ( 6.46

dimer 9 (monomer 6)

-24.18 ( 0.63

-118.52 ( 2.87

dimer 5 (monomer 6)

-24.60 ( 0.91

-141.72 ( 3.62


-24.00 ( 1.70

-140.37 ( 5.63

-3.60 ( 0.14 -3.37 ( 0.27

26.62 ( 0.65 25.65 ( 0.90

dimer 5 (monomer 5)

ΔG0278,dim, dimer 1 (monomer 1) dimer 5 (monomer 1)

-3.33 ( 0.16 -2.57 ( 0.25

22.01 ( 0.86 22.88 ( 0.92

kJ/mol dimer 9 (monomer 1) dimer 10 (monomer 1)

dimer 1 (monomer 2)

-3.32 ( 0.13

20.87 ( 0.74

dimer 9 (monomer 2)

-3.36 ( 0.03

22.28 ( 0.42

dimer 5 (monomer 2)

-3.06 ( 0.20

27.58 ( 0.73


-3.48 ( 0.17

28.79 ( 0.55 27.03 ( 0.76

dimer 1 (monomer 3)

-3.38 ( 0.16

22.11 ( 0.89

dimer 9 (monomer 3)

-3.75 ( 0.17

dimer 5 (monomer 3)

-3.21 ( 0.27

27.54 ( 0.98


-3.44 ( 0.18

24.47 ( 0.59

dimer 1 (monomer 4)

-3.67 ( 0.28

23.10 ( 1.55

dimer 9 (monomer 4)

-3.00 ( 0.11

22.01 ( 0.50

dimer 5 (monomer 4)

-3.29 ( 0.30

27.97 ( 1.20


-3.60 ( 0.18

24.84 ( 0.59


-3.57 ( 0.17 -3.61 ( 0.35

26.58 ( 0.79 30.14 ( 1.16

dimer 1 (monomer 5) dimer 5 (monomer 5) dimer 1 (monomer 6)

-3.69 ( 0.11

24.00 ( 0.59

dimer 9 (monomer 6)

-3.51 ( 0.16

26.06 ( 0.72

dimer 5 (monomer 6)

-3.26 ( 0.34

27.74 ( 1.36


-2.99 ( 0.36

26.29 ( 1.18

n-4 2 þ ð15:00 ( 0:57Þ 3 n1, 10 þ ð12:36 ( 0:57Þ 3 n2, 10 þ ð21:03 ( 0:55Þ 3 n3, 10 þ ð21:21 ( 0:57Þ 3 n4, 10 þ ð6:00 ( 0:57Þ 3 n5, 10 þ ð11:74 ( 0:57Þ 3 n6, 10 ΔG0278, dim ¼ - ð9:99 ( 0:09Þ 3

½N ¼ 109; R ¼ 0:9979; S ¼ 1:00 kJ=mol ð14Þ Here, n is the number of carbon atoms in the alkyl chain, braces {...} denote the integer part of the number, R is the regression coefficient, S is the standard deviation, and N is the sampling

amount. The values ni,1, ni,9 and ni,5, ni,10 identify the interactions between the functional groups of the head groups in the structure of the racemic dimers 1 or 9 and 5 or 10, respectively, where i denotes the monomer structure: the value 1 or 0 indicates the presence or absence of this interaction in the structure, respectively. Some conclusions could be drawn from the regression dependencies of the Gibbs’ energies eqs 5, 8, 11, and 14 of dimerization. In particular, the racemic dimers are more preferentially formed for their orientation at the tilt angle t1 = 22 with respect to the normal to the interface. In this case, spontaneous dimerization 2270



ARTICLE

Table 3. Standard Thermodynamic Characteristics of Racemic r-Amino Acids for the Clusterization of Dimers and Tetramers on the Basis of Monomer 1 with Molecular Chains Tilted by an Angle of 22 with Respect to the Normal to the Interface, as Calculated in the PM3 Approximation molecule

ΔHCl 298,m, kJ/mol

ΔSCl 298,m, J/(mol 3 K)

C7H15NO2

-24.92

-155.40

C8H17NO2

-32.85

C9H19NO2 C10H21NO2

ΔGCl 298,m, kJ/mol

ΔHCl 278,m, kJ/mol


ΔGCl 278,m, kJ/mol

dimer 14 21.39

-25.20

-156.33

18.26

-173.11

18.73

-33.10

-173.96

15.26

-35.17 -43.12

-183.38 -199.51

19.48 16.34

-35.41 -43.34

-184.23 -200.28

15.81 12.34

C11H23NO2

-45.54

-209.95

17.03

-45.76

-210.70

12.82

C12H25NO2

-53.45

-224.85

13.55

-53.66

-225.51

9.04

C13H27NO2

-55.94

-234.48

13.94

-56.12

-235.14

9.24

C14H29NO2

-63.83

-249.52

10.52

-63.99

-250.09

5.53

C15H31NO2

-66.35

-260.31

11.23

-66.50

-260.87

6.02

C16H33NO2

-74.22

-271.67

6.73

-74.37

-272.16

1.29

C17H35NO2

-76.71

-284.12

7.96

-76.85

-284.60

2.27

C7H15NO2

-31.32

-185.15

23.86

-31.48

-185.70

20.15

C8H17NO2

-36.86

-195.87

21.51

-36.99

-196.33

17.59

C9H19NO2

-40.12

-216.48

24.39

-40.23

-216.89

20.06

C10H21NO2

-46.76

-217.97

18.19

-46.88

-218.37

13.83

C11H23NO2

-49.53

-239.97

21.98

-49.61

-240.27

17.18

C12H25NO2

-57.08

-245.78

16.16

-57.18

-246.09

11.23

C13H27NO2

-59.62

-256.22

16.73

-59.70

-256.50

11.61

C14H29NO2 C15H31NO2

-67.47 -70.01

-271.21 -280.71

13.35 13.64

-67.53 -70.06

-271.42 -280.92

7.93 8.03

C16H33NO2

-77.86

-294.26

9.83

-77.89

-294.39

3.95

C17H35NO2

-80.40

-305.65

10.69

-80.43

-305.76

4.57

C7H15NO2

-30.99

-149.67

dimer 1 13.61

-31.26

-150.59

10.60

C8H17NO2

-33.55

-165.76

15.85

-33.80

-166.63

12.53

C9H19NO2 C10H21NO2

-41.33 -43.87

-178.88 -191.61

11.98 13.22

-41.56 -44.10

-179.70 -192.39

8.39 9.39

C11H23NO2

-51.56

-202.78

8.87

-51.77

-203.53

4.81

C12H25NO2

-54.25

-218.29

10.80

-54.45

-218.98

6.43

C13H27NO2

-61.94

-229.51

6.45

-62.12

-230.16

1.86

C14H29NO2

-64.63

-243.37

7.89

-64.80

-243.97

3.02

C15H31NO2

-72.32

-255.63

3.85

-72.48

-256.19

-1.26

C16H33NO2

-75.01

-266.25

4.33

-75.16

-266.76

-1.00

C17H35NO2

-82.71

-277.63

0.03

-82.85

-278.10

-5.53

C7H15NO2

-21.34

-148.26

dimer 5 22.84

-21.60

-149.13

19.86

C8H17NO2

-23.79

-156.54

22.86

-24.07

-157.52

19.72

C9H19NO2

-29.69

-173.70

22.08

-29.89

-174.44

18.60

C10H21NO2

-32.22

-173.24

19.41

-32.48

-174.15

15.94

C11H23NO2

-39.69

-200.29

20.00

-39.88

-200.98

15.99

C12H25NO2

-41.97

-213.83

21.75

-42.15

-214.45

17.46

C13H27NO2 C14H29NO2

-50.06 -51.33

-229.81 -227.15

18.43 16.36

-50.23 -51.50

-230.41 -227.73

13.83 11.81

C15H31NO2

-60.45

-256.30

15.93

-60.59

-256.81

10.80

C16H33NO2

-61.82

-252.39

13.39

-61.96

-252.88

8.34

C17H35NO2

-70.84

-279.93

12.57

-70.96

-280.34

6.97

C7H15NO2

-116.88

-578.23

-117.49

-580.32

43.84

C8H17NO2

-134.62

-631.10

-135.15

-632.98

40.82

dimer 15

tetramer 1 55.44 53.45 2271



ARTICLE

Table 3. Continued molecule

ΔHCl 298,m, kJ/mol


C9H19NO2

-155.87

-669.39

C10H21NO2 C11H23NO2

-175.83 -196.66

-718.18 -752.98

C12H25NO2

-217.39

C13H27NO2

-238.35

ΔGCl 298,m, kJ/mol

ΔHCl 278,m, kJ/mol


ΔGCl 278,m, kJ/mol

43.61

-156.34

-671.05

30.21

38.19 27.72

-176.26 -197.05

-719.71 -754.35

23.82 12.65

-802.32

21.70

-217.73

-803.45

5.63

-839.90

11.94

-238.63

-840.90

-4.86

C14H29NO2

-259.07

-884.16

4.41

-259.29

-884.93

-13.28

C15H31NO2

-280.12

-925.20

-4.41

-280.29

-925.81

-22.91

C16H33NO2

-300.84

-967.61

-12.49

-300.95

-967.98

-31.85

C17H35NO2

-321.87

-1007.85

-21.53

-321.94

-1008.06

-41.70

tetramer 5 C7H15NO2

-96.52

-591.35

79.71

-97.06

-593.18

67.85

C8H17NO2

-108.96

-616.74

74.83

-109.59

-618.94

62.47

C9H19NO2

-131.54

-677.32

70.31

-131.92

-678.68

56.75

C10H21NO2

-152.70

-721.80

62.39

-153.02

-722.91

47.95

C11H23NO2

-171.13

-751.53

52.82

-171.51

-752.85

37.78

C12H25NO2

-190.68

-769.61

38.66

-191.00

-770.67

23.25

C13H27NO2 C14H29NO2

-212.86 -232.34

-833.47 -876.33

35.51 28.80

-213.13 -232.54

-834.42 -877.04

18.84 11.28

C15H31NO2

-254.53

-916.16

18.49

-254.68

-916.74

0.17

C16H33NO2

-274.07

-954.61

10.40

-274.17

-954.94

-8.70

C17H35NO2

-296.16

-1002.90

2.70

-296.21

-1003.05

-17.37

becomes possible for R-amino acids with the alkyl chain length more than 12 carbon atoms in the alkyl chain for dimer 1 based on monomers 1-4, whereas this threshold is 14 carbon atoms for dimer 9 with t2 = 35 based on monomer 2. However, for dimers 5 and 10 (which are complementary to dimers 1 and 9, respectively), the situation is inverse, when the molecules in the dimer are tilted at t2 = 35 with respect to the normal to the interface, and thus more energetically advantageous. Therefore, in the following, the small clusters and infinite films based on the two most preferable monomers 1 and 2 are considered. Small Clusters of Heterochiral r-Amino Acids with t1 = 22. For the racemic tetramers 1 and 5, and also for the heterochiral dimers 1 and 5, and homochiral dimers 14 and 15 (constructed of the two conformations of monomers 1 and 2, see Figure 5) on which these tetramers are based, the thermodynamic parameters of formation and clusterization were calculated. Table 3 summarizes enthalpies, entropies, and Gibbs’ energies of clusterization of the structures for monomer 1 taken as an example. For all the series of the thermodynamic parameters so calculated, the correlation dependencies on the number of H-H interactions Ka formed in the structures were determined. In particular, for the clusters with t1 = 22 based on monomer 1, the values of the slope, which characterize the energetic yield from the H-H interactions between the alkyl chains of the R-amino acid molecules, vary within the ranges of -9.71 (-9.74) to -10.29 (-10.32) kJ/mol for enthalpy, of -20.44 (-20.53) to -25.70 (-25.80) J/(mol 3 K) for entropy, and of -2.57 (-2.05) to -4.42 (-4.01) kJ/mol for Gibbs’ energy. Here and in the following, the values without and within parentheses correspond to temperatures of 278 and 298 K, respectively. The absolute terms for the dimers and tetramers (in the order in which they are listed in Figure 4) are -3.92 (-3.60), -19.49 (-19.32),

-2.07 (-1.74), -12.34 (-12.05), -22.67 (-21.84), and -41.59 (-40.91) kJ/mol. For the entropy, these values are -106.10 (-104.98), -160.60 (-160.00), -86.63 (-85.48), -126.70 (-125.69), -396.59 (-393.68), and -486.40 (-484.02) J/(mol 3 K), and for the Gibbs’ energy 25.57 (27.69), 25.16 (28.36), 22.01 (23.73), 22.88 (25.41), 87.58 (95.48), and 93.63 (103.33) kJ/mol. For the associates based on monomer 2, the regression parameters are somewhat different from those listed above, whereas the general tendency is rather similar. Here, these values are not listed because the clusters based on monomer 2 are less energetically favorable with respect to the Gibbs’ clusterization energy than those based on monomer 1. From the data listed above and in Table 3, it is seen that the interactions between the hydrophilic head groups in the dimers are characterized as follows. Among the homochiral pairs, the higher (by absolute value) contribution to the enthalpy is brought by the dextrorotatory dimers with the “serial” orientation of the head groups in the dimer, whereas the contribution into the entropy values is lower (by absolute value) from the laevorotatory dimers with “parallel” relative orientation of the head groups. It was noted above that for the racemic dimers the formation of dimer 1 is more energetically advantageous than the formation of dimer 5. Also, comparing the values of the Gibbs’ clusterization energy of racemic dimers (with monomer 1 of R-amino tridecane acid, ΔGCl 278,m = -1.26 kJ/mol taken as an example) with their homochiral analogues with “parallel” and “perpendicular” orientations (ΔGCl 278,m = 0.53 and 7.59 kJ/mol, respectively, see ref 27), one can see that the formation of the racemic dimer 1 is more preferential than the formation of the homochiral dimer 14 or dimer 15. On the basis of the discussion above, one can make a conjecture about the possible process of the clusterization of R-amino acids from the racemic mixtures. First, the most 2272



ARTICLE

Table 4. Values of the Coefficients for the Calculation of the Thermodynamic Characteristics for Small Clusters with t1 = 22 (N = 55) small clusters based on monomer 1 (i = 1) parameter

ΔHCl 1,i(T),

kJ/mol

ΔSCl 1,i(T),

small clusters based on monomer 2 (i = 2) ΔHCl 1,i(T),

J/(mol 3 K)

kJ/mol

ΔSCl 1,i(T), J/(mol 3 K)

T = 278 K ci

-10.19 ( 0.05

-21.11 ( 0.66

-10.02 ( 0.06

-21.18 ( 0.69

di ei

-3.78 ( 0.51 -17.94 ( 0.49

-108.35 ( 6.47 -152.98 ( 6.19

-0.96 ( 0.62 -5.73 ( 0.58

-106.15 ( 6.62 -135.97 ( 6.31

fi

-1.61 ( 0.42

-75.82 ( 5.30

-2.29 ( 0.51

-73.68 ( 5.47

gi

-9.30 ( 0.41

-107.55 ( 5.24

-12.20 ( 0.51

-112.74 ( 5.56

ci

-10.22 ( 0.05

-21.20 ( 0.65

-10.0.5 ( 0.06

-21.27 ( 0.68

di

-3.50 ( 0.51

-107.41 ( 6.41

-0.71 ( 0.61

-105.27 ( 6.26 -135.29 ( 6.26

T = 298 K

ei

-17.81 ( 0.49

-152.52 ( 6.13

-5.73 ( 0.58

fi

-1.37 ( 0.41

-74.99 ( 5.25

-2.08 ( 0.51

-72.88 ( 5.42

gi

-9.15 ( 0.41

-107.04 ( 5.19

-12.07 ( 0.52

-112.25 ( 5.51

energetically preferable dimer 1 is formed, followed by its linking to tetramer 1, which in turn join together to form larger structures which could involve also less energetically advantageous interactions between the hydrophilic parts of the molecules, similar to those in dimer 5. The values of the slope of the correlation dependencies for the clusterization enthalpies and entropies listed above are quite similar to those obtained earlier for the enantiomeric pure R-amino acids and other classes of amphiphiles studied.35-40 Therefore, following the line of our previous studies, the partial correlations could be combined to general expressions for the thermodynamic parameters of clusterization to obtain ACl 1, i ðTÞ ¼ ci 3 Ka þ di 3 ni, 14 þ ei 3 ni, 15 þ fi 3 ni, 1 þ gi 3 ni, 5 ð15Þ where i = 1 or 2 denotes the monomer on which the corresponding clusters are based, ACl 1,i(T) stands for the thermodynamic characteristic of clusterization (enthalpy or entropy) of the clusters based on the ith monomer at temperature T, ci, di, ei, fi, and gi are the coefficients dependent on the particular thermodynamic characteristic, temperature, and structure of the monomer which forms the corresponding associate (see Table 4), Ka is the number of the H-H interactions formed in the cluster, and ni,14, ni,15, ni,1, and ni,5 are the identifiers of the interactions between the functional groups of the head groups in the structures of the homochiral dimers 14 and 15 and the racemic dimers 1 and 5, respectively. If interaction between the functional groups of the head groups exists in the structure of the cluster, the value of the corresponding identifier is equal to the number of the interactions of this type; if this interaction is absent, then this identifier is zero. In the correlation equations thus obtained, the multiple regression coefficients are close to unity (R = 0.9999). The standard deviations for enthalpy and entropy of clusterization for the racemic R-amino acids do not exceed those for the corresponding thermodynamic characteristics of the surfactant classes studied previously.35-40 Small Clusters of Heterochiral r-Amino Acids with t2 = 35. The values of the thermodynamic parameters of formation and clusterization for racemic R-amino acids with t2 = 35 (see Figure 6) are listed in Table 6 with monomer 1 taken an example. In this table, the clusterization parameters for dimer 10 and

tetramer 10 of R-amino heptanoic acid (C7H15NO2) are omitted, because in these structures the edge effects arise because of the small length of the monomeric alkyl chain. Similar to the case discussed above, the correlation dependencies of the enthalpy, entropy, and Gibbs’ energy of clusterization on the number of H-H interactions Ka formed in the structures were determined for the associates with t2 = 35. From these correlation dependencies calculated for the clusters based on monomer 1, the contribution from the intermolecular H-H interactions between the alkyl chains of R-amino acid molecules for enthalpy was found to vary between -9.19 (-9.05) and -10.24 (-10.26) kJ/mol, for entropy between -20.25 (-20.34) and -24.58 (-24.67) J/(mol 3 K), and for Gibbs’ energy of clusterization between 3.37 (-2.88) and -4.47 (-4.05) kJ/mol, where the values without and within the parentheses correspond to the temperatures 278 and 298 K, respectively. The contributions from the hydrophilic parts of the associates to enthalpy for the dimers and tetramers (in the order in which they are listed in Figure 4) were -2.10 (-1.77), -5.08 (-4.82), -17.39 (-17.30), -11.20 (-10.26), and -35.93 (-38.97) kJ/mol. Here and in the following, the first value of the thermodynamic parameter corresponds to both types of the homochiral dimers (16 and 17), because their structures are identical to each other. For the entropy, these values are -92.41 (-91.23), -114.02 (-113.04), -154.80 (-154.49), -369.44 (-366.18), and -447.79 (-444.95) J/(mol 3 K), and for the Gibbs’ energy 23.59 (25.43), 26.61 (28.86), 25.64 (28.73), 91.50 (98.86), and 88.96 (93.63) kJ/mol. Similar to the case considered above, the tendency of the regression parameters for the clusters based on monomer 2 is similar to that for the clusters based on monomer 1, and therefore, these parameters are omitted here. Also, similar to the clusters with t1 = 22 considered above, the absolute value of the contribution brought to enthalpy and entropy by the hydrophilic parts of the molecules involved in dimer 10 is higher than that arising from the interactions between the head groups in its complementary dimer 9. However, when the Gibbs’ energy value corresponding to the interactions between the hydrophilic head groups is calculated, these enthalpy and entropy factors compensate partly for each other, and the formation of dimer 9 turns out to be more preferential than 2273



ARTICLE

Table 5. Standard Thermodynamic Characteristics of Racemic r-Amino Acids for the Clusterization of Dimers and Tetramers on the Basis of Monomer 1 with Molecular Chains Tilted by an Angle of 35 with Respect to the Normal to the Interface, as Calculated in the PM3 Approximation molecule

ΔHCl 298,m, kJ/mol


C7H15NO2

-31.28

-155.46

C8H17NO2

-33.41

-172.27

C9H19NO2

-41.42

C10H21NO2 C11H23NO2

ΔGCl 298,m, kJ/mol

ΔHCl 278,m, kJ/mol


ΔGCl 278,m, kJ/mol

15.05

-31.54

-156.37

11.93

17.93

-33.66

-173.17

14.48

-183.64

13.31

-41.65

-184.47

9.63

-43.77 -51.71

-196.96 -208.59

14.93 10.44

-44.00 -51.92

-197.77 -209.32

10.98 6.27

C12H25NO2

-54.15

-221.76

11.93

-54.37

-222.47

7.48

C13H27NO2

-62.08

-235.00

7.95

-62.26

-235.64

3.25

C14H29NO2

-64.56

-245.71

8.66

-64.73

-246.32

3.74

C15H31NO2

-72.45

-260.94

5.30

-72.60

-261.48

0.09

C16H33NO2

-74.94

-270.13

5.56

-75.09

-270.65

0.15

C17H35NO2

-82.82

-284.20

1.87

-82.95

-284.65

-3.81

C7H15NO2 C8H17NO2

-24.71 -25.80

-158.46 -161.06

22.51 22.19

-24.94 -26.04

-159.23 -161.88

19.33 18.97

C9H19NO2

-34.88

-184.64

20.15

-35.07

-185.32

16.45

C10H21NO2

-36.26

-187.36

19.57

-36.47

-188.09

15.82

C11H23NO2

-45.18

-209.71

17.31

-45.35

-210.31

13.11

C12H25NO2

-46.60

-209.96

15.97

-46.79

-210.60

11.75

C13H27NO2

-55.51

-233.55

14.09

-55.66

-234.06

9.41

C14H29NO2

-56.96

-230.75

11.80

-57.12

-231.31

7.18

C15H31NO2 C16H33NO2

-65.86 -67.18

-257.82 -258.87

10.97 9.96

-65.98 -67.45

-258.24 -259.32

5.81 4.64

C17H35NO2

-76.22

-278.66

6.82

-76.32

-278.99

1.24

C8H17NO2

-26.18

-172.02

25.09

-26.41

-172.84

21.64

C9H19NO2

-28.52

-181.57

25.59

-28.75

-182.38

21.95

C10H21NO2

-33.62

-187.61

22.29

-33.82

-188.33

18.53

C11H23NO2

-36.25

-198.96

23.04

-36.46

-199.66

19.05

C12H25NO2

-42.65

-212.84

20.77

-42.86

-213.52

16.50

C13H27NO2 C14H29NO2

-44.93 -49.60

-222.91 -228.51

21.50 18.50

-45.10 -53.18

-223.51 -240.47

17.03 13.67

C15H31NO2

-54.75

-233.88

14.95

-54.90

-234.42

10.27

C16H33NO2

-63.23

-260.72

14.46

-63.38

-261.23

9.24

C17H35NO2

-64.68

-259.52

12.65

-64.82

-260.00

7.46

C7H15NO2

-108.83

-555.46

56.70

-109.50

-557.76

45.56

C8H17NO2

-115.68

-583.37

58.16

-116.36

-585.72

46.47

C9H19NO2 C10H21NO2

-149.89 -158.26

-649.93 -675.11

43.79 42.92

-150.44 -158.81

-651.85 -677.01

30.77 29.40

C11H23NO2

-191.30

-735.62

27.92

-191.74

-737.17

13.20

C12H25NO2

-199.04

-750.94

24.74

-199.51

-752.54

9.69

C13H27NO2

-232.62

-816.53

10.71

-232.94

-817.68

-5.63

C14H29NO2

-240.33

-834.30

8.29

-240.68

-835.53

-8.40

C15H31NO2

-274.17

-905.16

-4.44

-274.38

-905.93

-22.53

C16H33NO2

-281.92

-910.79

-10.51

-282.18

-911.68

-28.74

C17H35NO2

-315.77

-987.09

-21.62

-315.88

-987.46

-41.37

C8H17NO2

-118.03

-608.92

63.42

-118.66

-611.10

51.23

C9H19NO2

-138.45

-630.43

49.42

-130.70

-632.54

45.15

dimer 16 (dimer 17)

dimer 9

dimer 10

tetramer 9

tetramer 10

2274



ARTICLE

Table 5. Continued molecule

ΔHCl 298,m, kJ/mol


C10H21NO2 C11H23NO2

-154.09 -174.49

-698.60 -744.69

C12H25NO2

-191.15

C13H27NO2

-212.24

C14H29NO2

ΔGCl 298,m, kJ/mol

ΔHCl 278,m, kJ/mol


54.09 47.42

-154.60 -174.90

-700.36 -746.13

40.10 32.52

-765.85

37.07

-191.63

-767.45

21.72

-807.59

28.42

-212.56

-808.73

12.26

-232.54

-858.01

23.15

-232.88

-859.20

5.98

C15H31NO2

-250.92

-884.68

12.72

-251.20

-885.70

-4.98

C16H33NO2

-274.19

-939.11

5.66

-274.43

-939.90

-13.14

C17H35NO2

-292.67

-968.69

-4.00

-292.85

-969.29

-23.38

the formation of dimer 10. Therefore, similar to the case discussed above, the clusterization of R-amino acids should also take place via the preferential formation of the structures based on dimer 9 followed by their aggregation. Combining the partial correlations to the general one yields ACl 2, i ðTÞ ¼ ci 3 Ka þ di 3 ðni, 14 þ ni, 17 Þ þ ei 3 ni, 19 þ fi 3 ni, 10 ð16Þ where, similar to the notation used in eq 15, i = 1 or 2 denotes the monomer on which the corresponding clusters are based, ACl 2,i(T) stands for the thermodynamic characteristic of clusterization (enthalpy or entropy) of the clusters based on the ith monomer at temperature T, ci, di, ei, and fi are the coefficients dependent on the particular thermodynamic characteristic, temperature, and the structure of the monomer which forms the corresponding associate (see Table 6), and ni,16, ni,17, ni,9, and ni,10 are the identifiers of the interactions between the functional groups of the head groups in the structures of the homochiral dimers 16 and 17 and the racemic dimers 9 and 10, respectively. If interaction between the functional groups of the head groups exists in the structure of the cluster, the value of the corresponding identifier is equal to the number of the interactions of this type; if this interaction is absent, this identifier is zero. Similar to the case of associates with t1 = 22, the general correlation for the small clusters with t2 = 35 is characterized by the multiple regression coefficient almost equal to 1, and almost equal standard deviations of enthalpy and entropy. Large and Infinite Clusters. The structures of infinite 2D films which can be based on the two enantiomers of R-amino acids are illustrated by Figure 7. Here, in the clusters shown in Figure 7a, the corresponding enantiomers alternate in q direction, whereas, in the clusters shown in Figure 7b, they alternate in the p direction. In the cluster of Figure 7a, the molecules of the optical isomers are oriented within the OO2C plane at the angle j with respect to the normal to the q axis (cf. Figure 4). It was noted above that there exist two possible j values, 20 and 33, which determine two tilt angles of the molecules with respect to the normal to the interface, t1 = 22 and t2 = 35, respectively. In the cluster of Figure 7b, this angle j is formed between the R-amino acid molecules of the same chirality and the normal to the interface in the q direction. The third cluster type shown in Figure 7c is the so-called checkered structure, formed by alternation of the two enantiomers in both directions. In this case, the molecules of all clusters considered are inclined along the p direction within the OO1C plane at the angle δ = 9 with respect to the normal to the p axis in this plane; see Figure 4.

ΔGCl 278,m, kJ/mol

From the calculated thermodynamic parameters of the tetramers, it follows that the tetramer built by alternating packing of the optical isomers along the q direction is most energetically preferable. These isomers are inclined with respect to the normal to the q direction at the angles of j1 = 20 and j2 = 33; see Figure 7a. This orientation of the optical isomers with respect to the interface in the structure of the unit cell agrees with the experimental data.28 Therefore, in the following, we consider two types of clusters with alternating packing of the optical isomers and inclined relative positions that are determined by the two values of the angle t indicated above. It was already noted that, in this case, the structural elements of the infinite 2D cluster 1 shown in Figure 8 are the racemic dimers 1 and 5 tilted at the angle t1 = 22 with respect to the normal to the interface (cf. Figure 5), whereas the infinite 2D cluster 2 shown in Figure 9 is based on the complementary dimers 9 and 10 with t2 = 35 (cf. Figure 6). Using the PM3 parametrization, from the structures of the hexamers and octamers optimized, the geometric parameters of the unit cells for these two clusters were calculated to be a = 4.74 Å, b = 9.86 Å, and θ = 90 (Figure 10) and a = 4.62 Å, b = 10.70 Å, and θ = 90 (Figure 11) for the infinite 2D clusters 1 and 2, respectively. These values agree reasonably with the X-ray structure data:28 a = 4.80 Å, b = 9.67 Å, θ = 90, with the value of t ∼ 37. It should be noted that, in contrast to the racemic 2D clusters considered here, the homochiral 2D clusters of R-amino acids based on monomer 1, as shown earlier in ref 27, possess an oblique lattice with the parameters a = 4.64 Å, b = 5.71 Å, and θ = 102. In this case, the tilt angle between the molecular axis and the normal to the interface is t ∼ 31. These values obtained using the PM3 parametrization agree well with the experimental parameters of the unit cell for the homochiral monolayers of R-amino acids: a = 4.91 Å, b = 5.25 Å, θ = 112, with t ∼ 36.28 It is interesting to compare the geometric parameters of the monolayers of R-amino acids with those of carboxylic acids. The unit cell parameters of the carboxylic acid monolayers obtained by GIXD studies were found to be a = 4.90 Å, b = 8.42 Å, θ = 90, t = 9.41 The comparison of these values with those listed above shows that the b parameter of the unit cell of amphiphiles which possess a more “bulky” functional group is larger, and the molecules are more tilted (rather than almost perpendicular) with respect to the interface. It should be mentioned that, for the formation of intermolecular H-H interactions of the “a” type which are responsible for the spontaneous clusterization of the substituted alkanes, which possess bulky functional groups, the interacting molecules should be displaced relative to each other, 2275



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Table 6. Values of the Coefficients for the Calculation of the Thermodynamic Characteristics for Small Clusters with t2 = 35 (N = 53) small clusters based on monomer 1 (i = 1) parameter

ΔHCl 2,i(T),

kJ/mol

ΔSCl 2,i(T),

small clusters based on monomer 2 (i = 2) ΔHCl 2,i(T),

J/(mol 3 K)

kJ/mol

ΔSCl 2,i(T), J/(mol 3 K)

T = 278 K ci

-10.02 ( 0.09

-20.83 ( 0.71

-10.08 ( 0.14

-21.11 ( 0.66

di ei

-2.34 ( 0.68 -5.27 ( 0.65

-80.72 ( 5.45 -107.26 ( 5.15

4.72 ( 1.07 -8.33 ( 0.98

-108.35 ( 6.47 -152.98 ( 6.19

fi

-14.44 ( 0.61

-140.70 ( 4.83

-13.58 ( 0.96

-75.82 ( 5.30

ci

-10.06 ( 0.08

-20.75 ( 0.72

-10.08 ( 0.14

-21.13 ( 0.84

di

-1.97 ( 0.65

-81.21 ( 5.51

4.96 ( 1.06

-67.12 ( 6.52

ei

-5.39 ( 0.61

-108.24 ( 5.22

-8.10 ( 0.97

-114.25 ( 5.96

fi

-14.34 ( 0.57

-141.83 ( 4.89

-13.38 ( 0.95

-145.34 ( 5.85

T = 298 K

Figure 7. Structures of 2D film fragments.

Figure 9. Structure of the unit cell of the infinite 2D cluster 2 on the basis of monomer 1: (a) view along the a axis; (b) view along the b axis; (c) view along the molecular chain axis. Figure 8. Structure of the unit cell of the infinite 2D cluster 1 on the basis of monomer 1: (a) view along the a axis; (b) view along the b axis; (c) view along the molecular chain axis.

resulting, consequently, in an increased tilt of the molecules with respect to the normal to the interface. It should be noted that, in principle, it is possible to construct the unit cell of the racemic 2D cluster of R-amino acid with more close packing of the molecules than those described above.

Figure 12 illustrates two fragments of the R-amino acid monolayer based on monomer 1 with t2 = 35, where the fragment shown in Figure 12a involves the “a” type of the H-H interactions, whereas the fragment shown in Figure 12b is built with the formation of other types of H-H interactions. It is seen that the cluster shown in Figure 12b possesses the oblique lattice (θ = 111) with the geometric parameters a = 3.54 Å and b = 8.31 Å which are significantly smaller than those compared with the experimental data. This fact could be construed as the evidence of 2276



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Figure 10. Schematic fragment of the geometric structure of the infinite 2D cluster 1.

the fact that it is the “a” type of the H-H interactions between the hydrocarbon chains (cf. Figure 12a) that determines the geometric structure of the monolayer lattice. Thus, one can to some extent predict the parameters of the substituted alkane monolayer lattice on the basis of this conclusion prior to any quantum-chemical calculations. To do this, one should arrange the studied structures in a way that the hydrogen atoms of the interacting entities form the “a” types of H-H interactions and are separated from each other by ∼1.7 Å along each principal direction of the 2D cluster. It should be noted, however, that the tilt angle at which the molecules are inclined with respect to the interface can be reliably estimated using quantum-chemical calculations only. The infinite 2D cluster 1 is based on the racemic dimers 1 and 5 with the alkyl chains tilted at t1 = 22 with respect to the normal to the air/water interface. Figure 8 shows that this type of infinite cluster comprises four types of interactions between the hydrophobic parts of the R-amino acid molecules: interaction between the -COOH and -NH2 groups which is formed due to the serial arrangement of the functional groups in the dextrorotatory dimer 15, interaction between the two -COOH groups which is formed due to the parallel arrangement of the functional groups in the laevorotatory dimer 14, and two heterochiral interactions between the functional groups in dimer 1 and dimer 5, respectively (these interactions are shown by dashed lines in Figure 8).

Denoting the numbers of interactions between the laevorotatory and dextrorotatory homochiral head groups by n14 and n15, respectively, and the numbers of heterochiral interactions along the q direction as n1 and n5, respectively, it is straightforward to calculate these values from Figure 7 as q ðp - 1Þ, n14 ¼ n15 ¼ 2 3 q q-1 n1 ¼ p 3 , n5 ¼ p 3 ð17Þ 2 2 while the dependence of the number of H-H interactions on the number of carbon atoms in the alkyl chain n is q n q n-2 Ka ¼ ðp 1Þ þ ðp 1Þ 2 3 2 2 3 2 q nþ1 q-1 n-3 þp 3 þp 3 ð18Þ 2 2 2 2 where p and q are the numbers of the monomers in the p and q directions, respectively. To obtain the values per one monomer molecule for the 2D film, one should divide the expressions for eqs 17 and 18 by the number of monomers in the cluster m = p 3 q and calculate the limiting values of the resulting expressions at p f ¥, q f ¥. Then, for the infinite 2D cluster 1 which involves all types of 2277



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Figure 11. Schematic fragment of the geometric structure of the infinite 2D cluster 2.

Figure 12. The fragments of the 2D clusters with different packing of monomers: (a) 2D cluster with the “a” type of H-H interactions; (b) more close packed 2D cluster without any “a” type H-H interactions.

interactions between the functional groups, eqs 17 and 18 become 1 1 n1 ¼ n5 ¼ ; n14 ¼ n15 ¼ ; 2 2 1 n 1 n-2 1 nþ1 1 n-3 Ka ¼ 3 þ 3 þ 3 þ 3 2 2 2 2 2 2 2 2

The numbers of homochiral and heterochiral interactions between the head groups along the p and q directions, n16, n17 and n9, n10, respectively, can be calculated as q ðp - 1Þ, n16 ¼ n17 ¼ 2 3 q q-1 n9 ¼ p 3 , n10 ¼ p 3 ð20Þ 2 2 while for the dependence of the number of H-H interactions on the number of carbon atoms in the alkyl chain n, one obtains q nþ1 q nþ1 ðp - 1Þ þ ðp - 1Þ Ka ¼ 2 3 2 2 3 2 q n-1 q-1 n-4 þp 3 þp 3 ð21Þ 2 2 2 2 Then, for the infinite 2D cluster 2, eqs 20 and 21 become 1 n16 ¼ n17 ¼ n9 ¼ n10 ¼ ; 2 1 nþ1 1 nþ1 1 n-1 1 n-4 þ 3 þ 3 þ 3 Ka ¼ 3 2 2 2 2 2 2 2 2

ð19Þ The infinite 2D cluster 2 (see Figure 9) based on the racemic dimers 9 and 10 with t2 = 35 also comprises four types of interactions between the hydrophilic parts of the molecules: two homochiral interactions between the -COOH groups which are formed due to the parallel relative arrangement of the functional groups in the corresponding dimers and two heterochiral interactions that arise between the functional groups of dimers 9 and 10 (the interactions are shown by dashed lines in Figure 9).

ð22Þ Introducing eqs 19 and 22 into the correlation equations for the clusterization enthalpy and entropy eqs 15 and 16, respectively, one obtains the expressions for the thermodynamic characteristics of clusterization per one monomer for the two 2278



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Table 7. Values of the Coefficients for the Calculation of the Thermodynamic Characteristics per One Monomer Molecule in Infinite 2D Clusters ΔHCl,¥ (T)/m, kJ/mol i

ΔSCl,¥ (T)/m, J/(mol 3 K) i

ΔGCl,¥ (T)/m, kJ/mol i

type of infinite 2D cluster

Ui

infinite cluster 1

-10.19

-16.31

-21.11

-222.34

-4.32

45.50

infinite cluster 2

-10.06

-11.84

-20.75

-206.25

-4.29

45.50

infinite cluster 1

-10.22

-15.92

-21.20

-220.99

-3.90

49.93

infinite cluster 2

-10.02

-12.20

-20.83

-204.7

-3.81

48.80

infinite cluster 1

-10.02

-10.59

-21.18

-214.27

-4.14

48.98

infinite cluster 2

-10.06

-6.24

-21.03

-198.55

-4.21

48.96

infinite cluster 1

-10.05

-10.20

-21.27

-212.85

-3.71

53.23

infinite cluster 2

-10.08

-5.78

-21.13

-196.92

-3.79

52.90

Vi

Ui

Vi

Ui

Vi

Infinite 2D Cluster Based on Monomer 1, T = 278 K

T = 298 K

Infinite 2D Cluster Based on Monomer 2, T = 278 K

T = 298 K

Figure 13. Dependence of the variation of the 2D cluster 1 clusterization enthalpy on the alkyl chain length.

types of infinite 2D films (infinite 2D cluster 1 and 2D cluster 2) with different tilt angles with respect to the interface: 1 n 1 n-2 1 nþ1 Cl, ¥ A1, i ðTÞ=m ¼ U1, i 3 3 þ 3 þ 3 2 2 2 2 2 2 1 n-3 þ 3 ð23Þ þ V1, i 2 2 1 nþ1 1 nþ1 Cl, ¥ þ 3 A2, i ðTÞ=m ¼ U2, i 3 3 2 2 2 2 1 n-1 1 n-4 þ 3 ð24Þ þ 3 þ V 2, i 2 2 2 2 where the values of the coefficients U1,i, U2,i and V1,i, V2,i correspond to the particular thermodynamic characteristic, to the cluster type (2D cluster 1 and 2D cluster 2), to the structure of the monomer on which this cluster is based, and to temperature. These values are listed in Table 7. The dependencies of the variation of thermodynamic characteristics per one R-amino acid molecule on the alkyl chain length at 278 K for the clusters based on monomer 1 are shown in Figures 13-18. For the sake of clarity, the graphical

Figure 14. Dependence of the variation of the 2D cluster 1 clusterization entropy on the alkyl chain length.

dependencies for small clusters are shown only for the racemic structures of dimers 1 and 9, most energetically advantageous, and tetramers 1 and 9, with the tilt angles with respect to the normal to the interface of t1 = 22 and t2 = 35, respectively. The solid lines represent the dependencies calculated from eqs 23 and 24 with the coefficients listed in Table 7, whereas the points correspond to the data obtained by direct quantum-chemical calculations. It is seen that the values predicted from the additive scheme agree well with those calculated by PM3 parametrization. Note that the dependencies obtained for the tetramers and infinite clusters of the first type are linear, whereas these dependencies are stepwise for the structures of the second type. This is due to the specific “patterns” of numerical dependencies of the number of intermolecular interactions formed between the alkyl chains of the length n, cf. eqs 18, 19 and 21, 22. Figures 15 and 18 show that the energetic yields corresponding to the formation of the two types of racemic clusters based on monomer 1 (with t1 = 22 and t2 = 35) are almost equal to each other (to within the error of the quantum-chemical calculations), and the clusterization threshold corresponds to the alkyl chain length of 12-13 carbon atoms. At the same time, the spontaneous clusterization of monomer 2 to the infinite 2D cluster 1 with t1 = 22 2279



Figure 15. Dependence of the variation of the 2D cluster 1 clusterization Gibbs’ energy on the alkyl chain length.

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Figure 18. Dependence of the variation of the 2D cluster 2 clusterization Gibbs’ energy on the alkyl chain length.

threshold are in rather good agreement with the experimental data.28 Similar to our previous study,27 the thermodynamic clusterization parameters were also calculated for 298 K to compare these with those obtained for other classes of surfactants. It was found that for this temperature the racemic clusters of R-amino acids for both structures based on the most energetically preferable monomers considered above can be formed for the alkyl chain length by two carbon atoms higher than the clusterization threshold corresponding to a temperature of 278 K. A similar dependence was found earlier for the clusterization of homochiral R-amino acids.27

Figure 16. Dependence of the variation of the 2D cluster 2 clusterization enthalpy on the alkyl chain length.

Figure 17. Dependence of the variation of the 2D cluster 2 clusterization entropy on the alkyl chain length.

is less preferable with respect to the Gibbs’ energy than that to the 2D cluster 2 with t2 = 35 (for which the clusterization threshold is n = 13) and can occur at n = 14. Therefore, the formation of the 2D infinite cluster 2 from monomer 1 is almost as probable (to within the error of the calculated Gibbs’ energy values) as that from monomer 2. These values of the spontaneous clusterization

’ CONCLUSIONS The semiempiric quantum-chemical method PM3 is used to study the possible course of the clusterization of amphiphilic R-amino acids of normal structure from their racemic mixtures on the air/water interface. It is shown that the formation of heterochiral dimers 1 and 9 is energetically more advantageous than that of the corresponding dimers 5 and 10 or homochiral dimers, because dimers 1 and 9 involve more intermolecular H-H interactions. Therefore, the possible course of the clusterization of R-amino acids from racemic mixtures is the formation of dimer 1 or dimer 9, their subsequent linking to larger clusters, and, finally, the joining of these clusters to larger aggregates, which could also involve less energetically advantageous structures based on dimer 5 or 10. It is shown that, for the racemic mixtures of R-amino acids, the formation of heterochiral 2D films is most energetically preferable with the alternating (rather than “checkered”) packing of the enantiomers with opposite specific rotation. In this case, the laevorotatory and dextrorotatory enantiomers alternate along the q direction, whereas the alkyl chains of the enantiomers of similar specific rotation are arranged along the p direction. Two tilt angles of the R-amino acid molecules with respect to the normal to the interface are possible, t1 = 22 and t2 = 35, and the molecules are more inclined with respect to the q direction (the tilt angle with respect to the normal to the q direction of the 2D cluster is j1 = 20 and j2 = 33). At the same time, the enantiomers of similar specific rotation in both types of film are oriented at an angle of δ = 9 with respect to the normal to the p direction. 2280


The Journal of Physical Chemistry B For the conformations of monomers 1 and 2 of the R-amino acids, the thermodynamic parameters of clusterization for the structures of 2D cluster 1 and 2D cluster 2 (tilted at the angles t1 = 22 and t2 = 35 with respect to the normal to the interface, respectively) were calculated. It is shown that the formation of the structures based on monomers 1 and 2 with t2 = 35 results in almost the same energetic yields (within the calculation error), and the clusterization threshold at 278 K corresponds to the Ramino acid molecules with the alkyl chain length of n = 12-13 carbon atoms, which agrees with the experimental data.28 Also, the formation of the monolayers based on monomer 1 with t1 = 22 becomes possible for the alkyl chain length of 12 carbon atoms, whereas for monolayers based on monomer 2 the spontaneous clusterization threshold corresponds to 14 carbon atoms in the alkyl chain. For a temperature of 298 K, the spontaneous clusterization threshold corresponds to the alkyl chain by two carbon atoms longer than that for 278 K. As the clusterization thresholds for the homochiral (n = 1112)42 and for the racemic (n = 12-13) R-amino acids are quite close to each other, it remains rather unclear whether homochiral or heterochiral interactions are mainly responsible for the clusterization in the racemic monolayers of R-amino acids. It should also be noted that the process of the formation of racemic domains in the monolayer depends on the external factors of the experimental system. The geometric parameters of the unit cell for the 2D cluster 2 based on monomer 1 with the alkyl chain tilted at t2 = 35 with respect to the normal to the interface are a = 4.62 Å, b = 10.70 Å, and θ = 90, which agree well with the experimental data a = 4.80 Å, b = 9.67 Å, and θ = 90.28 It is shown that the structural parameters of the unit cell of the 2D clusters of substituted alkanes are determined by the “a” type of the H-H interactions, whereas the tilt of the monolayer molecules with respect to the interface depends on the volume and the structure of the functional groups involved in the hydrophilic part of the molecule.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ REFERENCES (1) Alberts, B.; Bray, D.; Lewis, J.; Raff, M.; Roberts, K.; Watson, J. D. Mol. Biol. Cell, 2nd ed.; Garland Publishing: New York, 1989. (2) Wenz, G. Angew. Chem., Int. Ed. 1994, 33, 803. (3) Ringsdorf, H.; Schlarb, B.; Venzmer, J. Angew. Chem., Int. Ed. 1988, 27, 113. (4) Vollhardt, D. Adv. Colloid Interface Sci. 1996, 64, 143. (5) Vollhardt, D. Encyclopedia of Surface and Colloid Science, 2nd ed.; Taylor & Francis: New York, 2006; Vol. 5, pp 4104-4118. (6) Arnett, E. M.; Harvey, N. G.; Rose, P. L. Acc. Chem. Res. 1989, 22, 131. (7) Harvey, N. G.; Mirajovsky, D.; Rose, P. L.; Verbiar, R.; Arnett, E. M. J. Am. Chem. Soc. 1989, 111, 1115. (8) Harvey, N. G.; Rose, P. L.; Mirajovsky, D.; Arnett, E. M. J. Am. Chem. Soc. 1990, 112, 3547. (9) Heath, J. G.; Arnett, E. M. J. Am. Chem. Soc. 1992, 114, 4500. (10) Stine, K. J.; Uang, J. Y-J.; Dingman, S. D. Langmuir 1993, 9, 2112. (11) Gericke, A.; H€uhnerfuss, H. Langmuir 1994, 10, 3782. (12) H€uhnerfuss, H.; Neumann, V.; Stine, K. J. Langmuir 1996, 12, 2561.

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(13) Hoffmann, F.; H€uhnerfuss, H.; Stine, K. J. Langmuir 1998, 14, 1525. (14) Hoffmann, F.; Stine, K. J.; H€uhnerfuss, H. J. Phys. Chem. B 2005, 109, 240. (15) Nandi, N.; Vollhardt, D. Chem. Rev. 2003, 103, 4033. (16) Nandi, N.; Vollhardt, D. J. Phys. Chem. B 2003, 107, 3464. (17) Nandi, N.; Vollhardt, D.; Brezesinski, G. J. Phys. Chem. B 2004, 108, 327. (18) Nandi, N.; Vollhardt, D. Thin Solid Films 2003, 433, 1221. (19) Vollhardt, D. Adv. Colloid Interface Sci. 1996, 64, 143. (20) Nandi, N.; Vollhardt, D. Colloids Surf., A 2001, 183-185, 67. (21) Nandi, N.; Vollhardt, D. Colloids Surf., A 2002, 198-200, 207. (22) Andelman, D.; Orland, H. J. Am. Chem. Soc. 1993, 115, 12322. (23) Nandi, N.; Bagchi, B. J. Am. Chem. Soc. 1996, 118, 11208. (24) Thirumoorthy, K.; Nandi, N.; Vollhardt, D. Colloids Surf. 2006, 282-283, 222. (25) Nandi, N.; Vollhardt, D. Colloids Surf. 2002, 198-200, 207. (26) Nandi, N.; Vollhardt, D. J. Phys. Chem. B 2002, 106, 10144. (27) Vysotsky, Yu. B.; Fomina, E. S.; Belyaeva, E. A.; Aksenenko, E. V.; Vollhardt, D.; Miller, R. J. Phys. Chem. B 2009, 113 (52), 16557. (28) Weissbuch, I.; Berfeld, M.; Bouwman, W.; Kjaer, K.; Als-Nielsen, J.; Lahav, M.; Leiserowitz, L. J. Am. Chem. Soc. 1997, 119 (5), 933. (29) Weissbuch, I.; Lieserowitz, L.; Lahav, M. Curr. Opin. Colloid Interface Sci. 2008, 13, 12. (30) Kuzmenko, I.; Rapaport, H.; Kjaer, K.; Als-Nielsen, J.; Weissbuch, I.; Leiserowitz, L. Chem. Rev. 2001, 101, 1659. (31) Steed, J. W., Atwood, J. L. Supramolecular Chemistry; John Wiley & Sons, Ltd: New York, 2000. (32) Stewart, J. J. MOPAC 2000.00 Manual; Fujitsu Limited: Tokyo, Japan, 1999. (33) Soloviov, M. E.; Soloviov, M. M. Computational Chemistry; SOLON-Press: Moscow, 2005 (in Russian). (34) Stone, A. J. The theory of intermolecular force; Clarendon Press: Oxford, U.K., 1996. (35) Vysotsky, Yu. B.; Bryantsev, V. S; Fainerman, V. B. J. Phys. Chem. B 2002, 106, 121. (36) Vysotsky, Yu. B.; Bryantsev, V. S.; Fainerman, V. B. J. Phys. Chem. B 2002, 106, 11285. (37) Vysotsky, Yu. B.; Bryantsev, V. S.; Fainerman, V. B.; Vollhardt, D.; Miller, R. Colloids Surf., A 2002, 209, 1. (38) Vysotsky, Y. B.; Bryantsev, V. S.; Fainerman, V. B. Prog. Colloid Polym. Sci. 2002, 121, 72. (39) Vysotsky, Yu. B.; Muratov, D. V.; Boldyreva, F. L.; Fainerman, V. B.; Vollhardt, D.; Miller, R. J. Phys. Chem. B 2006, 110, 4717. (40) Vysotsky, Yu. B.; Belyaeva, E. A.; Fainerman, V. B.; Vollhardt, D.; Miller, R. J. Phys. Chem. C 2007, 111, 5374. (41) Weidemann, G.; Brezesinski, G.; Vollhardt, D.; Bringezu, F.; de Meijere, K.; M€ohwald, H. J. Phys. Chem. B 1998, 102, 148. (42) Zhang, Y. J.; Song, Y.; Zhao, Y.; Li, T. J.; Jiang, L.; Zhu, D. Langmuir 2001, 17, 1317.

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Quantum-Chemical Analysis of Thermodynamics of Two-Dimensional

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