Quantum Chemical Analysis of the Thermodynamics of 2D Cluster

Article pubs.acs.org/JPCC

Quantum Chemical Analysis of the Thermodynamics of 2D Cluster Formation of Aliphatic Amides at the Air/Water Interface Yu. B. Vysotsky,† E. S. Fomina,† E. A. Belyaeva,† D. Vollhardt,‡,* V. B. Fainerman,§ and R. Miller‡ †

Donetsk National Technical University, 58 Artema Strasse, 83000 Donetsk, Ukraine Max Planck Institute of Colloids and Interfaces, D-14424 Potsdam/Golm, Germany § Donetsk Medical University, 16 Ilych Avenue, Donetsk 83003, Ukraine ‡

ABSTRACT: The semiempirical quantum chemical PM3 method is used to calculate the thermodynamic and structural parameters of formation and clusterization of aliphatic amides with the general composition CnH2n+1CONH2 (n = 6−16) at 293 and 298 K. Enthalpy, absolute entropy, and Gibbs’ energy of the formation for two stable conformations of monomers are calculated. The correlation dependencies of the calculated parameters on the alkyl chain length are found to be linear. The structures found for the monomers are used to build clusters (dimers, trimers, tetramers). The thermodynamic parameters of formation and clusterization for all cluster series are calculated. The obtained clusterzation parameters show stepwise dependencies on the alkyl chain length. It is demonstrated that the formation of two structurally different 2D films is possible. In the first film, the aliphatic amide molecules are oriented at the angles δ1 = 10° and φ1 = 20.5° to the normal to the sides of the unit cell, and in the second film, the values of these angles are δ2 = 23° and φ2 = 10°, respectively. The parameters of the unit cells of regarded monolayers are a1 = 4.74 Ǻ , b1 = 4.26 Ǻ , the angle between them θ1 = 89°, and a2 = 4.51 Ǻ , b2 = 4.74 Ǻ , θ2 = 84°, respectively. The values of θ, δ, and φ angles determine the tilt angle of alkylamide molecules with respect to the normal to the air/water interface, t1 = 25° and ,t2 = 23°. The dependencies of the thermodynamic parameters of monolayer clusterization on the alkyl chain length of amides indicate two different types: linear for 2D film 1 and stepwise for 2D film 2. The spontaneous clusterization threshold of aliphatic amides at the air/water interface is 14 carbon atoms in the alkyl chain at 293 K for 2D film 1 and 15 carbon atoms for 2D film 2. These values agree well with the available experimental data. It is shown that the thermodynamic parameters of formation and clusterization of aliphatic amides can be obtained in the framework of the superposition−additive approach as a sum of the corresponding parameters for carboxylic acids and amines after subtraction of those alcohols.

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INTRODUCTION It is known that the functional amide group can be a part of various biological compounds, such as polypeptides and proteins.1 For example, the amide group is an integral part of the general structure of sphingolipids. 2,3 Sphingolipids consisting of long-chain amino alcohols (sphingosine or dihydrosphingosine) linked by an amide bond to a fatty acid, and their metabolites are involved in many vital biological processes, including differentiation, cellular senescence, apoptosis, and proliferation.4 Special attention found the amphiphilic derivatives of ethanolamine not only because of their occurrence in a wide variety of animals, plants, and microbes5,6 but also because of their interesting biological, pharmaceutical, and medicinal properties.7−10 It should also be noted that amphiphilic amides can be the main component of soil wetting agents11 and “green” biodegradable polymers.12,13 Furthermore, artificial biomembranes14 and sensors15 have been developed on the basis of amphiphilic amides. Correspondingly, for the design of biomembranes with defined properties, the interaction between amphiphilic amides and phospholipids in mixed monolayers has been studied.16 © 2012 American Chemical Society

Despite the multiple presence of the amide group in biological compounds, there are only a few model studies of unsubstituted fatty acid amide monolayers.17,18 However, systematic information was obtained about the main monolayer characteristics of various tailored amphiphiles, whose headgroup consists of an acid amide group and one or two hydroxyl groups separated by one or more methylene groups.19−29 The objective of the present work is to obtain first information about the influence of the interaction between NH2 and carbonyl oxygen in the amide group on the threshold for spontaneous clusterization. In previous papers,30−38 quantum chemical analysis of thermodynamic parameters of clusterization of substituted alkanes (alcohols, thioalcohols, amines, saturated and unsatured carboxylic acids, α-amino acids, and substituted melamines) were performed. The present work focuses on the calculation of structural and thermodynamic parameters of clusterization of unsubstituted aliphatic amides. Fatty acid amides with the general Received: August 27, 2012 Revised: November 17, 2012 Published: November 27, 2012 26358

dx.doi.org/10.1021/jp308479x | J. Phys. Chem. C 2012, 116, 26358−26376

The Journal of Physical Chemistry C

Article

4 Only the CH···HC interactions realized between two methylene groups of the alkyl chains arranged opposite to each other are taken into account, and the interactions between the alkyl groups arranged much farther away are neglected because of the decrease of interaction energy that is inversely proportional to r6; i.e. the CH···HC interactions are additive in pairs. 5 The coefficients found in the frameworks of additive scheme were used to obtain the thermodynamic parameter values of the cluster formation of large associates, including 2D monolayers. The detailed description of the procedure for the calculation of the thermodynamic parameters (enthalpy, entropy, Gibbs’ energy) of amphiphiles’ clusterization is reported elsewhere.45 The exploited model was successfully tested for 10 classes of amphiphilic compounds.30−38

composition CnH2n+1CONH2 (n = 6−16) were studied between 293 and 298 K.

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METHODS Calculation of structural and energetic parameters of clusterization of aliphatic amides CnH2n+1CONH2 (n = 6−16) at the air/water interface were carried out using the quantum chemical program package Mopac200039 in the framework of the semiempiric PM3 method. This method is parametrized with respect to the formation heats.40,41 Although the PM3 method overestimates the CH···HC interaction force between the alkyl chains of the amphiphilic molecules,42 it is capable of the correct description of the experimental data concerning the monolayer formation of different classes of amphiphiles.30−38 In addition, it was shown in the papers21,22 that the geometric parameters of the homochiral and racemic α-amino acids monolayers obtained in the framework of PM3 method are in good agreement with available experimental data.43 The facts suggested the use of the semiempiric quantum chemical PM3 method for calculations of the thermodynamic parameters of clusterization of aliphatic amides in the present work.

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RESULTS AND DISCUSSION Monomers. In the first stage of the study, the conformational analysis of aliphatic amide monomers was performed. The potential energy dependence of the monomer on the values of the two torsion angles, α = C2−C1−N−H1 and β = C3−C2−C1−N, was calculated. These angles correspond to the hydrogens of amino group located inside the hydrophilic part of the aliphatic amides and the general orientation of the head groups (see Figure 1). They were varied in the range 0−360° in

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MODEL In this study, the model used previously30−38 for the analysis of the thermodynamics of 2D clusterization of substituted alkanes at the air/water interface was implemented for the case of alkylamides. According to ref 44, the water phase retracts the functional group of the amphiphile and two to four methylene units adjoining to its hydrophilic part. At the same time, the hydrophobic part of the amphiphlic molecule is pushed off from the water surface and sticks into the gaseous phase. This particular complicated system cannot be described with the available calculation methods. In ref 32, an example of aliphatic alcohols, there are results of the use of COSMO model that account for the solvent presence in the system. These results show that the dimerization enthalpy of alcohols calculated in the framework of this model differs only slightly from that calculated in the vacuum. However, so far, the COSMO model has been incapable of assessment of the solvent impact on the entropy of the studied system. In this connection, the account of the water phase in our calculation model is indirect by its orientation and stretching effect. This allows for consideration of the amphiphilic molecules in linear conformation when all hydrogen atoms of the methylene groups of the alkyl chain are in the trans position. The tilt angle of the amphiphiles with respect to the interface depends on the volume of the hydrophilic part, and it is dependent on the Gibbs’ energy of the intermolecular interactions. The key points of the exploited model are the following: 1 The intermolecular CH···HC interactions between the methylene groups of alkyl chains of interacting amphiphiphile molecules provide the main contribution to the Gibbs’ energy of cluster formation. 2 The calculation of the thermodynamic parameters of the cluster formation of the considered types of amphiphiles was carried out in supramolecular approximation. 3 The additive scheme was constructed on the basis of the results of direct calculations. This scheme defines the values of the thermodynamic parameters of clusterization as total contribution of the CH···HC interactions and the interactions of the hydrophilic part of the amphiphilic molecules realized in the cluster.

Figure 1. Torsion angles of the functional groups of decylamide.

steps of 15°. There are four minima in the potential energy dependence for the monomer of tridecylamide on these torsion angles (see Figure 2). Additional optimization of the monomer

Figure 2. Potential energy surface for the monomer of tridecylamide. 26359



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structures in the vicinity of these minima confirmed that four stable conformations exist. They are characterized with the next values of the α and β angles: (165°, 78°), (165°, −84°), (−31°, 84°), and (−31°, −78°), respectively. Note that monomers 1 and 4 and monomers 2 and 3 are pairwise mirror-identical (see Figure 3 for nonylamide). Therefore, in the following, we consider only the structures of monomers 1 and 2.

planar and torsion angles that determine the location of the atoms of the functional group are compiled (see Figure 4).

Figure 4. Acetamide structure.

These parameters are compared with corresponding parameters obtained by ab initio calculations46−48 and available experimental data.49 The good agreement of the compared data allows the further application of the PM3 method for obtaining optimized structures of amide associates and the calculation of their thermodynamic parameters of formation and clusterization. Figure 3 shows that there are two intramolecular interactions between the atoms of the hydrophilic parts of amide. One of them is the same for both conformers: it is the interaction between one of hydrogen atoms of the amino group and the carbonyl oxygen (defined with a black arrow). The second intramolecular interaction is realized between the oxygen of the carbonyl group and the α-hydrogen atom of the methylene unit of the alkyl chain for monomer 1 and the β-hydrogen atom for monomer 2, respectively (defined with a dotted black arrow). The affinity of the latter interactions probably causes the proximity of the values of their thermodynamic parameters (within the calculating error). Table 2 compiles the enthalpy and Gibbs’ energy of formation and absolute entropy calculated for both conformations of monomers at 293 and 298 K (through the slash). Such choice of temperatures justifies the availability of the experimental data concerning the amide monolayer formation at 293 K, whereas the reference data concerning the thermodynamic parameters of amide formation are listed for standard conditions (298 K). In addition, calculations for other classes of amphiphiles were obtained at 298 K. It is to be noted that the correction for the free rotation of alkyl groups was not taken into account during the quantumchemical calculations, but it should be done to calculate entropy correctly. As shown previously in refs 32−35, the correction for the free rotation of methylene groups for different classes of amphiphiles is practically independent of the nature of the functional group. It was found to be 7.1 J/ (mol·K) for amines, 6.6 J/(mol·K) for alcohols, 7.0 J/(mol K) for alkylthioalcohols, 6.1 J/(mol·K) for carboxylic acids at 298 K. Therefore, for alkyl amides, the mean value of 6.7 J/(mol·K) was used. Note that it is impossible to calculate the correction for the free rotation of methylene groups at 293 K because the experimental data concerning the thermodynamic parameters of amphiphile formation are available only at 298 K. Therefore, the corrected values of absolute entropy of formation and free Gibbs’ energy are listed only for 298 K (see Table2, the values in brackets).

Figure 3. Geometric structure of aliphatic amide conformers (n = 9).

It should also be mentioned that there is a planar fragment N−C1−O−C2 (see Figure 1) in the functional amide group. It is caused by the p−π conjugation of the lone-electron pair of nitrogen atom and the π-electrons of the carbonyl oxygen atom. This is clearly seen from the data listed in Table 1 for the acetamide molecule. In Table 1, the values of bond lengths and Table 1. Selected Optimized Structural Data for Acetamide Monomer structural parameter

HF 6-31+G**46

MP2 6-31+G**46

PM3

r(C−O) r(C−C) r(C−N) r(N−H1) r(N−H2) r(C−H3) r(C−H4) r(C−H5) ∠CCO ∠NCO ∠H1NC ∠H2NC ∠H3NC ∠H4NC ∠H5NC τNCOC τH1NCO τH2NCO τH2CCO τH4CCO τH5CCO

1.201 1.512 1.355 0.994 0.991 1.080 1.084 1.086 122.2 122.0 118.4 122.5 108.8 112.5 108.7 181.4 2.0 178.7 27.6 149.6 −90.3

1.232 1.511 1.371 1.007 1.005 1.085 1.088 1.089 122.7 121.9 117.1 121.1 108.6 112.3 109.0 179.9 10.7 167.6 30.1 151.6 −87.8

1.223 1.504 1.422 0.994 0.996 1.098 1.098 1.098 124.56 117.52 115.44 114.00 111.53 110.93 111.36 176.03 18.97 152.86 5.23 125.42 −114.52

experiment49 1.220 1.519 1.380 1.022 1.022 1.124 123.0 121.9 118.5 120.0 109.8

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Table 2. Thermodynamic Parameters of the Formation of Amide Monomers system

monomer 1

C2H5CONH2 C3H7CONH2 C4H9CONH2 C5H11CONH2 C6H13CONH2 C7H15CONH2 C8H17CONH2 C9H19CONH2

−232.25/−231.78 −255.06/−254.48 −277.72/−277.04 −300.48/−299.70 −323.23/−322.35 −346.00/−345.03 −368.78/−367.70 −391.56/−390.38


325.04/326.64 357.26/359.20 389.05/391.33 421.08/423.70 452.73/455.70 484.76/488.07 516.23/519.88 548.07/552.06


(340.04) (379.30) (418.13) (457.20) (495.90) (534.97) (573.48) (612.36)

−131.42/−128.77 (−130.48) −123.97/−120.57 (−122.28) −116.25/−112.10 (−113.81) −108.71/−103.80 (−105.51) −101.03/−95.38 (−97.09) −93.50/−87.10 (−88.81) −85.80/−78.64 (−80.35) −78.21/−70.30 (−72.01)

monomer 2

system

ΔH0293,mon/ΔH0298,mon, kJ/mol −233.68/−233.21 C10H21CONH2 −256.25/−255.68 C11H23CONH2 −278.99/−278.32 C12H25CONH2 −301.71/−300.94 C13H27CONH2 −324.47/−323.59 C14H29CONH2 −347.23/−346.26 C15H31CONH2 −370.00/−368.93 C16H33CONH2 −392.78/−391.60 S0293,mon/S0298,mon, J/(mol·K) 320.05/321.65 (335.05) C10H21CONH2 352.04/353.98 (374.08) C11H23CONH2 384.23/386.51 (413.31) C12H25CONH2 416.19/418.81 (452.31) C13H27CONH2 448.20/451.17 (491.37) C14H29CONH2 480.19/483.50 (530.40) C15H31CONH2 511.73/515.38 (568.98) C16H33CONH2 543.42/547.41(607.71) ΔG0293,mon/ΔG0298,mon, kJ/mol −131.38/−128.71 (−130.42) C10H21CONH2 −123.63/−120.21 (−121.92) C11H23CONH2 −116.11/−111.94 (−113.65) C12H25CONH2 −108.50/−103.58 (−105.29) C13H27CONH2 −100.95/−95.27 (−96.98) C14H29CONH2 93.39/−86.96 (−88.67) C15H31CONH2 −85.71/−78.53 (−80.24) C16H33CONH2 −78.08/−70.14 (−71.85)

It should be mentioned that experimental data regarding the standard thermodynamic characteristics of the formation of alkylamides are scarce (only for the first five to six members of the homologous series).50,51 In addition, in the case of propylamide and butylamide, these data are available only for the crystalline phase, but, for instance, from the crystalline propylamide heat of formation (−338.2 kJ/mol)48 and its heat of sublimation (85.9 kJ/mol),51 the standard heat of formation of its gaseous form is easily calculated to be −252.3 kJ/mol. Correspondingly, the values of standard enthalpies for the formation of gaseous form for butylamide, pentanamide, hexanamide and octanamide were calculated to be −261.0, −290.2, −324.3, and −362.7 kJ/mol, respectively.50−52 On the basis of the calculated data summarized in Table 2, the correlation dependencies of the standard thermodynamic characteristics of the aliphatic amides with the alkyl chain length (n) were constructed (at T = 293 and 298 K). These dependencies are linear, similar to other classes of amphiphiless studied previously.30−38 The values of the slope for these dependencies, which characterize the contribution of the methylene groups of the alkyl chain, are equal to the enthalpy −22.978 (−22.67) for monomer 1 and −22.77 (−22.66) kJ/ mol and for monomer 2, for entropy 31.46 (31.80) and 30.50 (31.84) J/(mol·K), respectively. Here and below, the first values listed refer to 293 K, and the values in brackets correspond to 298 K. The absolute term that characterizes the contribution of the hydrophilic part of the molecule was found to be, for enthalpy, −186.65 (−186.13) for monomer 1 and −187.94 (−187.67) kJ/mol for monomer 2 and, for entropy, 263.67 (264.60) and 258.65 (259.57) J/(mol·K), respectively. Because the values of the slopes and absolute terms of the corresponding correlations are quite similar, it is possible to express these partial correlations in a general form:

monomer 1

monomer 2

−414.34/−413.06 −437.12/−435.73 −459.90/−458.42 −482.68/−481.10 −505.47/−503.78 −528.25/−526.46 −551.03/−549.15

−415.56/−414.28 −438.34/−436.96 −461.12/−459.64 −483.90/−482.32 −506.68/−505.00 −529.47/−527.68 −552.25/−550.37

579.26/583.60 610.60/615.28 641.10/646.12 673.10/678.45 703.63/709.33 735.36/741.40 764.93/771.31

(650.60) (688.98) (726.52) (765.55) (803.13) (841.90) (878.51)

574.62/578.95 606.04/610.71 636.31/641.32 668.20/673.55 699.25/704.94 730.55/736.58 760.94/767.31

(645.95) (684.41) (721.72) (760.65) (798.74) (837.08) (874.51)

−70.44/−61.78 −62.71/−53.29 −54.73/−44.56 −47.20/−36.27 −39.23/−27.55 −31.62/−19.18 −23.37/−10.17

(−63.49) (−55.00) (−46.27) (−37.98) (−29.26) (−20.89) (−11.88)

−70.30/−61.61 −62.59/−53.15 −54.55/−44.35 −46.98/−36.03 −39.17/−27.46 −31.43/−18.96 −23.42/−10.20

(−63.32) (−54.86) (−46.06) (−37.74) (−29.17) (−20.67) (−11.91)

0 ΔH293,mon = −(22.77 ± 0.00) ·n − (187.30 ± 0.27)

[S = 0.64 kJ/mol; N = 30]

(1)

0 S293,mon = (31.48 ± 0.11) ·n + (261.17 ± 1.10)

[S = 2.61 J/(mol · K); N = 30]

(2)

0 ΔH298,mon = −(22.67 ± 0.03) ·n − (187.03 ± 0.27)

[S = 0.64 kJ/mol; N = 30]

(3)

0 S298,mon = (31.82 ± 0.11) ·n + (262.08 ± 1.10)

[S = 2.62 J/(mol · K); N = 30]

(4)

where S is the standard deviation, and N is the sampling amount. The values of the slopes in eqs 3 and 4, which characterize the contributions from the methylene groups, agree well with the values calculated earlier for other classes of amphiphilic compounds at 298 K.30−38 The standard errors for the calculation of enthalpy, entropy, and Gibbs’ energy of the alkylamide formation do not exceed the corresponding values of the amphiphile classes previously studied. The correlation coefficients of the corresponding correlation dependencies exceed 0.9999. Dimers, Trimers, and Tetramers. The dimers were built from the monomer conformations thus obtained. The structures of these entities based on monomer 2 are illustrated in Figure 5. Here, the vector drawn through the centers of the nitrogen atom of the amino group and the carbon atom of the α-CH2 unit of the alkyl chain and directed from the carbon to the nitrogen atom was chosen as a direction of the orientation 26361



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Figure 5. Relative orientation of aliphatic amide monomers in the dimer: a, “parallel” (p); b, “serial” (s).

⎛ sin δ ⎞ t = arcsin⎜ ⎟, ⎝ cos θ1 ⎠

of the monomer functional groups in the dimer. According to this definition, the structures of dimers were subdivided into two classes, characterized by “parallel” (p) and “serial” (s) relative orientation of the head groups. For example, the definition “dimer 2,s” indicates that this dimer structure was build on the basis of monomer 2, and the hydrophilic head groups of the monomers are oriented “serially” in it (see Figure 5, b). To determine the tilt angles of alkylamide molecules with respect to the p and q directions of the cluster unit cell, the “parallel” and “serial” types of dimers with the “a” CH···HC interaction type (in Figure 6 marked with red arrows) were

⎛ sin φ ⎞ θ1 = arctg⎜ − ctg θ ⎟ ⎝ sin δ·sin θ ⎠

(5)

where δ is the tilt angle of surfactant molecules with respect to the p-axis of the cluster unit cell, φ is the tilt angle of surfactant molecules with respect to the q-axis of the cluster unit cell, and θ is the angle between the p and q directions of the cluster unit cell. The dependence of the dimerization Gibbs’ energy for the dimer 2,s structure on the value of the tilt angle of the alkyl chain with respect to the normal to the q direction is shown in Table 3. From the listed data, it can be seen that the minimal dimerization Gibbs’ energies correspond to dimer structures with φ2 equal to 11.3° and 20.5°. Additional optimization of these structures shows the existence of only one stable structure with φ2 = 20.5°. The presence of the second minimum of the dimerization Gibbs’ energy with φ2 = 36.4° corresponds to the dimer structure having one less CH···HC interaction than in the dimer of undecylamide shown in Figure 7. The loss of this CH···HC interaction causes an increase in the dimerization Gibbs’ energy and a lower preference of such structures in comparison with those having the maximum number of CH···HC interactions. It should be noted that the dimer 2,s structure has intermolecular interaction between the hydrogen of the amino group of one amide molecule and the oxygen of the carbonyl group of the other amide molecule (marked with a double-edged solid blue arrow in Figure 7). This interaction stipulates the orientation of the dimer at the angle φ2 = 20.5° with respect to the q direction. The presence of intermolecular hydrogen bonds N−H···OC realized in formamide dimers was proved in refs 47, 49, 53, 54. The dimerization of formamide was investigated by matrix isolation spectroscopy, static ab initio calculations, ab initio molecular dynamics, and DFT simulations. The comparison of the experimental matrix IR spectra with ab initio calculations has shown that two types of dimers are predominantly formed, depending on the dimer structure with two and one strong N−H···OC hydrogen bonds. The length of these hydrogen bonds was determined to be in the range of 1.94−1.98 Å in ref 48, 1.814−2.004 Å in ref 47, and 1.868−2.270 Å in ref 54. It is rather smaller than the N−H···OC bond length found to be 2.557 Å using the semiempirical PM3 method. The possibility of N−H···OC

Figure 6. Determination of the molecular tilt angle with respect to the normal to the q-direction.

constructed of two monomers. Applying the parallel shift of one molecule with respect to the other one in both the p and q directions, the dependencies of the dimerization Gibbs’ energy on the δ and φ angles were tabulated correspondingly. The minima of the dimerization Gibbs’ energy for these associates correspond to optimal δ and φ values. Using them, it is easy to calculate the value of the general tilt angle, t, of the alkyl chain with respect to the normal to the interface (see Figure 7):31 26362



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Figure 7. Orientation of the aliphatic amide molecule with respect to the air/water interface.

amide molecules in the monolayer with respect to the air/water interface to be t1 = 25° and t2 = 23° (see eq 5). We regard the amphiphile monolayers with regular structure of monomers entered in them. Therefore, the inclusion of data concerning small clusters with edge effects is unreasonable for further building of the additive scheme that allows calculation of thermodynamic parameters of clusterization for such films. The edge effects mean the appearance of such interactions between monomer molecules (among both their functional groups and alkyl chains) that are absent in 2D films. Note that they can be avoided in structures of larger rectangular clusters (tetramers, hexamers) because the increase in the monomer number in the cluster leads to a more ordered optimized structure because of the better regularity of interactions between the atom groups inside of this cluster. Therefore, the structures of dimer 1,p and other linear clusters with edge effects in the p direction are not included in the further construction of the additive scheme. The corresponding energetic increments of the interactions realized between functional groups of the amide molecules were obtained from the tetramers 2 having these interactions without the edge effect distortion. The structures of amide dimers described above and larger clusters are listed in Figure 8. Here and below, the cluster definition consists of its name (dimer, trimer, etc.); the number, which coincides with the number of corresponding basic monomer (1 or 2); and the descriptor of the headgroup orientation (p or s). Table 4 summarizes the calculated thermodynamic parameters of the clusterization of dimers. Trimers and tetramers of alkylamides are built on the basis of the two considered monomer conformations. However, we do not give the thermodynamic parameters for dimers and trimers with “parallel” orientation of the head groups because these structures are not included in the additive scheme because of the existent edge effects. Enthalpy, entropy and Gibbs’ free energy of clusterization are calculated from the expressions 0 0 Cl 0 0 Cl ΔHCl T,m = ΔHT − m·HT,mon, ΔST,m = ST − m·ST,mon, and ΔGT,m =

Table 3. Dependence of the Dimerization Gibbs’ Energy of Aliphatic Amides on the Molecular Tilt Angle (φ) with Respect to the Normal to the q-Direction of Monolayer Propagation tilt angle φ, °

ΔHdim 298 , kJ/mol

ΔSdim 298 , J/(mol·K)

ΔGdim 298 , kJ/mol

53.51 48.39 36.40 36.44 30.33 21.21 20.51 20.57 11.30 9.95 1.53

−67.07 −73.41 −81.38 −81.38 −90.50 −87.24 −88.06 −88.06 −87.28 −85.71 −86.99

−261.09 −294.53 −292.52 −292.45 −361.93 −315.69 −295.98 −296.12 −287.55 −311.13 −359.25

10.74 14.36 5.79 5.77 17.35 6.83 0.14 0.18 −1.59 7.01 20.07

hydrogen bond formation in the crystal structure of formamide is confirmed by neutron diffraction data,18 by data obtained in the framework of the SHELXS-97 program,55 and by GIXD results for nonadecylamide monolayers.56 Applying the procedure for the determination of the molecular tilt angle of amides with respect to the normal to the q direction of the cluster unit cell for the dimer 1,s structure shows that the minimum of the dimerization Gibbs’ energy corresponds to the value φ1 = 10°. The dimer 1,s structure has one less CH···HC interaction than dimer 2,s (for structures with an even number of methylene units in the alkyl chain). Minima of the dimerization Gibbs’ energy for “parallel” dimers based on the structures of monomers 1 and 2 correspond to values of δ1 = 23° and δ2 = 10°, respectively. In “parallel” dimers, the maximum number of the “a” CH···HC interaction type is realized (e.g., eight for heptadecylamide), and the intermolecular hydrogen bond between hydrogen of the amino group of one amide molecule and oxygen of the carbonyl group of the other amide molecule is absent. The values of the δ and φ angles define the general tilt angle of 26363



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Figure 8. Optimized geometric structure of aliphatic amide associates. Cl 0 0 ΔHCl T,m − T·ΔST,m, where ΔHT and ST are enthalpy and entropy of the clusters at a certain temperature, T; H0T,mon and S0T,mon are enthalpy and entropy of the corresponding monomers at the same temperature, T; and m is the number of monomers in a cluster. The data listed in Table 4 show the preferred formation of associates with mutual “serial” orientation of the hydrophilic head groups by Gibbs’ energy of clusterization. In addition, the structures built on the basis of monomer 2 have smaller values of Gibbs’ energy of clusterization that stipulates their greater energetic preference. This can be a result of the existence of hydrogen bonds between the hydrogen of the amino group of one amide molecule and the oxygen of the carbonyl group of the other molecule. For all homologous series of the calculated thermodynamic parameters of clusterization (enthalpy, entropy,

and Gibbs’ energy), the correlation dependencies on the number of intermolecular CH···HC interactions Ka were built. The parameters of correlation equations for the corresponding thermodynamic characteristics are listed in Table 5. From these data, one can see that the values of the slope that characterize the energetic contribution from the CH···HC interactions were found to be in the range −10.09 (−10.09) to 10.32 (−10.33) kJ/mol for enthalpy, −20.44 (−20.46) to −25.90 (−25.92) J/(mol·K) for entropy, and −2.73 (2.60) to −4.26 (−4.17) kJ/mol for Gibbs’ energy. Note that the slopes of correlation equations for alkylamides calculated at 298 K are quite close to those calculated for the types of amphiphiles studied previously.30−38 The increment in the clusterization enthalpy of the “parallel” oriented hydrophilic headgroup of aliphatic amides is statistically insignificant, in contrast with the “serially” oriented 26364



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Table 4. Thermodynamic Parameters of the Formation of Dimers, Trimers, and Tetramers of Aliphatic Amides in the Approximation of the PM3 Method Calculated at 293 K molecule

ΔHCl 293,m, kJ/mol

ΔSCl 293,m, J/(mol·K)

ΔGCl 293,m, kJ/mol

ΔHCl 293,m, kJ/mol

ΔSCl 293,m, J/(mol·K)

C6H13CONH2 C7H15CONH2 C8H17CONH2 C9H19CONH2 C10H21CONH2 C11H23CONH2

−30.33 −38.04 −40.15 −48.12 −50.48 −58.41

−184.45 −205.51 −209.16 −228.36 −237.01 −254.13

24.63 23.20 22.18 19.93 20.15 17.32

Dimer 1,s C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2

−60.84 −68.76 −71.22 −79.15 −81.62

−262.73 −279.96 −288.95 −306.16 −313.00

17.45 14.66 14.88 12.09 11.65


−27.96 −30.14 −38.03 −40.30 −48.25 −50.53

−150.00 −174.02 −179.10 −198.05 −205.06 −218.68

15.99 20.85 14.45 17.73 11.83 13.54

Dimer 2,p C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2

−58.22 −60.80 −68.53 −71.12 −78.89

−224.22 −238.92 −252.71 −266.59 −277.91

7.47 9.21 5.51 7.00 2.54


−36.34 −37.49 −46.63 −47.87 −56.97 −58.25

−168.61 −165.28 −195.93 −193.35 −221.14 −217.59

13.07 10.94 10.78 8.78 7.83 5.50

Dimer 2,s C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2

−67.33 −68.68 −77.71 −79.07 −88.09

−245.34 −245.59 −271.98 −270.01 −295.25

4.55 3.27 1.98 0.04 −1.58


−64.59 −80.19 −84.45 −100.46 −104.82 −121.02

−354.72 −395.57 −409.60 −445.91 −459.98 −494.33

39.34 35.71 35.57 30.19 29.95 23.82

Trimer 1,s C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2

−125.54 −141.70 −146.27 −162.46 −167.04

−506.81 −541.39 −559.29 −590.45 −606.90

22.96 16.93 17.60 10.54 10.78


−55.27 −58.86 −75.32 −79.12 −95.72 −99.71

−296.80 −338.02 −353.87 −383.37 −410.59 −433.61

31.69 40.18 28.36 33.21 24.58 27.33

Trimer 2,p C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2

−116.30 −120.36 −136.40 −140.92 −157.08

−459.14 −483.64 −505.41 −537.09 −558.69

18.23 21.35 11.69 16.45 6.62


−73.76 −75.71 −94.31 −96.43 −115.00 −117.24

−344.10 −324.88 −397.52 −387.87 −447.94 −438.94

27.06 19.48 22.16 17.22 16.25 11.37

Trimer 2,s C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2

−135.75 −138.05 −156.52 −158.85 −177.31

−496.14 −489.37 −548.05 −541.08 −595.34

9.62 5.33 4.05 −0.32 −2.87


−111.36 −130.46 −152.82 −171.42 −194.57 −213.05

−615.82 −662.85 −708.39 −738.05 −797.36 −824.75

69.07 63.75 54.74 44.83 39.06 28.60

Tetramer 1 C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2

−236.36 −254.75 −278.11 −296.48 −319.91

−883.00 −912.33 −971.05 −998.54 −1050.05

22.36 12.56 6.41 −3.91 −12.25


−126.39 −136.93 −167.92 −174.94 −209.26 −216.56

−571.76 −636.88 −662.24 −675.79 −744.45 −761.56

41.13 49.68 26.11 23.07 8.86 6.58

Tetramer 2 C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2

−250.95 −258.23 −292.68 −300.05 −334.43

−830.64 −848.77 −920.59 −934.96 −1004.07

−7.58 −9.54 −22.95 −26.10 −40.24

amides. Therefore, there are dashes at the corresponding places in Table 5. The increments of the interactions between head

molecule

ΔGCl 293,m, kJ/mol

groups in the clusterization entropy are approximately the same for both orientations of the head groups in the dimers built on 26365



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Table 5. Parameters of Correlation Equations for the Thermodynamic Characteristics of the Clusterization of Aliphatic Amides y = (a ± Δa)·Ka + (b ± Δb) (sampling number, N = 11) 293 K system

(a ± Δa)

(b ± Δb)

dimer 1,s dimer 2,s dimer 2,p trimer 1,s trimer 2,s trimer 2,p tetramer 1 tetramer 2

−10.16 −10.31 −10.09 −10.16 −10.32 −10.12 −10.41 −10.25

± ± ± ± ± ± ± ±

0.25 0.13 0.24 0.23 0.11 0.21 0.06 4.49

−9.00 ± 1.25 −6.05 ± 0.72


−25.33 −25.71 −23.41 −24.45 −25.90 −24.82 −21.53 −20.44

± ± ± ± ± ± ± ±

0.77 0.30 1.79 0.75 0.61 1.57 0.34 0.87

−132.14 −90.82 −93.40 −256.55 −182.46 −171.05 −402.37 −349.96

± ± ± ± ± ± ± ±

3.84 1.66 9.84 7.51 6.67 17.30 7.07 19.10


−2.74 −2.78 −3.23 −3.00 −2.73 −2.85 −4.11 −4.26

± ± ± ± ± ± ± ±

0.07 0.20 0.31 0.08 0.27 0.27 0.06 0.13

29.72 20.56 28.48 53.21 40.56 53.63 111.70 94.29

± ± ± ± ± ± ± ±

0.33 1.09 1.69 0.81 3.02 2.94 1.20 2.97

−21.96 ± 2.34 −12.90 ± 1.24 −6.19 ± 1.28 −8.25 ± 0.20

298 K R

ΔHCl T,m, kJ/mol 0.997 1.32 0.999 0.70 0.997 1.29 0.998 2.49 0.999 1.19 0.998 2.18 0.999 1.28 0.998 4.32 ΔSCl T,m, J/(mol·K) 0.996 4.09 0.999 1.60 0.975 9.48 0.996 7.99 0.998 6.42 0.982 16.67 0.999 7.07 0.992 18.40 ΔGCl T,m, kJ/mol 0.997 0.36 0.978 1.05 0.962 1.63 0.997 0.86 0.957 2.91 0.963 2.83 0.999 1.20 0.996 2.86

the basis of monomer 2. The enthalpy increments of the interactions of the “serially” oriented head groups of amide molecules in dimers based on the structure of monomer 1 are large by absolute value in comparison with those based on monomer 2. Additionally, the associate structures built on the basis of monomer 1 have one less CH···HC interaction than those built on the basis of monomer 2. That is why the formation of “serial” clusters based on monomer 2 is more preferred by the clusterization Gibbs’ energy. The slopes of the calculated regression coefficients of partial correlations for dimers, trimers, and tetramers of alkylamides are quite similar. Therefore, the partial correlations for all clusters considered can be generalized into one correlation: Cl ΔH293, m

R

S

−8.94 ± 1.25 −5.98 ± 0.72

0.997 0.999 0.997 0.998 0.999 0.998 0.999 0.998

1.32 0.70 1.29 2.49 1.19 2.18 1.28 4.33

−10.17 −10.31 10.09 −10.17 −10.33 −10.12 −10.42 −10.25

± ± ± ± ± ± ± ±

0.25 0.13 0.24 0.23 0.11 0.21 0.06 0.20

−25.35 −25.73 −23.43 −24.47 −25.92 −24.84 −21.55 −20.46

± ± ± ± ± ± ± ±

0.77 0.30 1.78 0.75 0.61 1.57 0.34 0.87

−133.92 −90.55 93.13 −256.06 −181.90 −170.50 −401.64 −349.17

± ± ± ± ± ± ± ±

3.84 1.66 9.85 7.51 6.67 17.31 7.07 19.13

0.996 0.999 0.975 0.996 0.998 0.982 0.999 0.992

4.09 1.60 9.49 7.99 6.42 16.67 7.07 18.43

−2.61 −2.65 −3.11 −2.88 −2.60 −2.72 −4.00 −4.17

± ± ± ± ± ± ± ±

0.07 0.20 0.31 0.08 0.28 0.27 0.06 0.14

30.37 21.01 28.99 54.49 41.47 54.48 113.71 96.03

± ± ± ± ± ± ± ±

0.33 1.10 1.73 0.81 3.06 3.02 1.23 3.02

0.997 0.975 0.957 0.996 0.952 0.957 0.999 0.995

0.35 1.06 1.67 0.86 2.95 2.91 1.23 2.91

−21.82 ± 2.34 −12.74 ± 1.24 −5.98 ± 1.28 −8.02 ± 4.50

+ (5.67 ± 0.54) ·n1,p − (6.38 ± 0.40) ·n2,s + (2.70 ± 0.40) ·n2,p , [N = 88; R = 0.999; S = 2.15 kJ/mol]

(8)

Cl ΔS298, m = − (22.30 ± 0.75) · K a − (139.94 ± 5.12) · n1,s

− (53.43 ± 6.80) ·n1,p − (93.39 ± 5.01) ·n2,s − (82.35 ± 5.01) ·n2,p , [N = 88; R = 0.999; S = 27.27 J/(mol · K)]

(9)

where Ka is the number of CH···HC interactions realized in the regarded associate. It can be obtained for all considered aggregates using equations for the calculation of these interactions for dimers as the elementary structural units of larger clusters. For dimers 1,s:

+ (4.97 ± 0.57) ·n1,p − (6.64 ± 0.42) ·n2,s + (2.44 ± 0.42) ·n2,p , [N = 88; R = 0.999; S = 2.30 kJ/mol]

(b ± Δb)

Cl ΔH298, m = − (10.29 ± 0.06) · K a − (9.93 ± 0.40) · n1,s

= −(10.25 ± 0.06) ·K a − (10.17 ± 0.43) ·n1,s

Ka =

(6)

{ n −2 1 }

(10)

For dimers 1,p; 2,p; and 2,s:

Cl ΔS293, m = − (22.20 ± 0.75) · K a − (140.54 ± 5.13) · n1,s

Ka =

− (54.97 ± 6.79) ·n1,p − (94.03 ± 5.02) ·n2,s − (82.99 ± 5.02) ·n2,p , [N = 88; R = 0.999; S = 27.37 J/(mol · K)]

(a ± Δa)

S

{ 2n }

(11)

where n is the number of methylene groups in the alkyl chain of aliphatic amides; braces denote the integer part of the number; ni,p and ni,s are the descriptors of “parallel”- and “serial”-oriented

(7) 26366



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Figure 9. Structure of the unit cell of the infinite 2D clusters of aliphatic amide: I, based on the monomer 1, II, based on the monomer 2; (a) view along the a axis; (b) view along the b axis.

functional head groups in the structure, with i denoting the number of the corresponding monomer used for construction of the regarded dimer. In the case that interaction between the functional groups of the head groups exists in the structure of the cluster, then the value of the corresponding descriptor is equal to the number of the interactions of this type. If this interaction is absent, this descriptor is zero. In the correlation equations of enthalpy and entropy of clusterization, the multiple regression coefficients are close to unity. The standard deviations for enthalpy and entropy of clusterization for alkylamides are commensurate with those for the corresponding thermodynamic characteristics of the types of amphiphile studied previously. Large and Infinite Clusters. The correlation eqs 6−9 allow the use of the found values of regression coefficients for building the additive scheme. This scheme enables the calculation of the thermodynamic parameter values of clusterization for the amide associates of any dimension up to infinite 2D films, and it expresses them as the sum of the

corresponding increments of intermolecular CH···HC interactions and interactions between the hydrophilic head groups. Before the construction of the additive scheme, the geometric parameters of the unit cells of amide monolayers built on the basis of the monomer 1 and 2 structures were considered. Optimization of the structures of small associates described above in the framework of the PM3 method results in the tetramers (see Figure 8), which can be considered as the unit cells of the corresponding monolayers. The geometric parameters of these tetramers were found to be a1 = 4.74 Ǻ , b1 = 4.26 Ǻ , and θ1 = 89° for the 2D film 1 based on the monomer 1 structure and a2 = 4.51 Ǻ , b2 = 4.74 Ǻ , and θ2 = 84° for the 2D film 2 based on the monomer 2 structure. Hence, the tilt angles of the molecules with respect to the normals to the p and q directions of the monolayer were δ1 = 23°, φ1 = 10° and δ2 = 10°, φ2 = 20.5° for the infinite 2D cluster 1 and 2, respectively (see Figure 9). The general molecular tilt angle with respect to the normal to the interface, t, was calculated to be 25° and 23° for the considered types of alkylamide monolayers. Note that 26367



Article

the t values calculated according to ref 31 agree satisfactorily with the experimentally obtained value of 18°.57 Figure 10 shows the fragment of the infinite 2D cluster 2. This 2D cluster 2, just as 2D cluster 1, involves two types of

ns = q·(p − 1),

n p = p ·(q − 1)

(12)

whereas the number of intermolecular CH···HC interactions vs alkyl chain length can be defined for associates built on the basis of monomers 1 and 2, respectively, ⎧n − 1 K a,1 = q·(p − 1)⎨ ⎩ 2 K a,2

} + p·(q − 1)⎧⎨⎩ 2n } ⎧n = [q·(p − 1) + p ·(q − 1)]·⎨ } ⎩2

and

(13)

where n is the number of methylene groups in the alkyl chain of aliphatic amides, and the braces denote the integer part of the number. To calculate the number of interactions described above per one monomer molecule of the infinite 2D cluster, one has to divide eqs 10 and 11 by the number of monomers in the cluster (m = p·q) and calculate the limits of the resulting expressions at an infinite number of molecules in the cluster. Therefore, for infinite 2D clusters 1 and 2 (p = ∞, q = ∞), eqs 10 and 11 become ns = n p = 1

Figure 10. Fragment of the geometric structure of the infinite 2D film 2.

(14)

The number of intermolecular CH···HC interactions per one amide molecule of the 2D films 1 and 2 correspondingly can be calculated using the next expressions:

intermolecular interactions between the hydrophilic head groups of aliphatic amides that were defined earlier as “parallel” and “serial” in the p and q directions, respectively. In the “serial” interactions of the amide head groups, a hydrogen bond is realized between the hydrogen of the amino group of one amide molecule and the oxygen of the carbonyl group of the other molecule, as proved in ref 57. The number of both “serial” and “parallel” interactions realized in the cluster can be determined using following expressions,

K a,1 = n − 1

and

⎧n K a,2 = 2·⎨ ⎩2

}

(15)

Introducing eqs 14 and 15 into the correlation equations for the enthalpy and entropy of clusterization 6−9, one obtains the expressions for the thermodynamic characteristics of alkylamide clusterization per one monomer molecule,

Figure 11. Dependence of the variation of clusterization Gibbs’ energy on the alkyl chain length for 2D film 1 of aliphatic amides; p and q are the numbers of monomer molecules, which determines the size of the 2D cluster. 26368



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Figure 12. Dependence of the variation of clusterization Gibbs’ energy on the alkyl chain length for 2D film 2 of aliphatic amides; p and q are the same as in Figure 11.

AiCl (T ), ∞ m

= Ui ·K a, i + Vi

CH···HC interactions per one amide molecule realized in the q direction of the monolayer propagation. It is seen from the dependencies of clusterization Gibbs’ energy per one monomer molecule (cf. Figure 11 and 12) that the spontaneous formation of the 2D film 1 is possible if the alkyl chain length has no less than 15 carbon atoms. The spontaneous clusterization threshold for the 2D film 2 is 14 methylene units in the alkyl chain. This prediction agrees well with the experimental data,17 which proved the existence of stable monolayers for C15H31CONH2 and their absence for C13H27CONH2. Cl The analysis of the ΔGi(T),∞ /m dependencies offers a possibility to make a prediction about the clusterization path of the regarded amide monolayers. Thus, the formation of 2D film 2 can be formed by the preferential formation of dimers 2,q and trimers 2,q, their further aggregation and linkage in tetramers 2 and larger associates having less energetically preferred interactions of hydrophilic head groups as in dimers 2,p. That means 2D films 2 are preferentially formed by linear associates. It may stipulate dendritic monolayer structures. In the case of 2D monolayer 1, the dimers of aliphatic amides will be preferentially associated in structures of tetramers 1 because their formation is more advantageous in comparison with trimer 1,p and 1,q structures (their formation is almost isoenergetic). This may stipulate closely packed monolayer structures. It should be mentioned that McConnel et al.58,59 developed an interesting theory for the description of shape and growth of amphiphilic domains. They proposed that the shape and size of domains are determined by a balance between line tension and dipole−dipole interaction. Our results do not contradict this theory because the exploited model is based on the calculations in supramolecular approximation. This approximation accounts all types of intermolecular interaction, including dipole−dipole interaction. In previous studies,30−38 quantum chemical calculations of thermodynamic parameters of amphiphiles clusterization were performed for 298 K. Therefore, the necessary coefficients of eq 16 for 298 K listed above can be used to compare the values of the spontaneous clusterization threshold for the homologous

(16)

where the values of the coefficients Ui and Vi depend on the particular thermodynamic characteristic AiCl(T),∞/m (enthalpy, entropy or Gibbs’ energy) on the structure of the monomer (descriptor i corresponds to its serial number) on which the 2D cluster is based and on the temperature. The values of the slope in eq 16 that characterize the increment of the intermolecular CH···HC interactions, Ui, per one monomer were found to be the same for 2D films 1 and 2: for enthalpy, −10.25 (−10.29) kJ/mol; for entropy, −22.20 (−22.30) J/(mol·K); and for Gibbs’ energy, −3.75 (−3.65) kJ/ mol. Here and below, the first values listed correspond to 293 K, and the values in brackets correspond to 298 K. The absolute term that characterizes the contribution of the functional groups' interaction per one monomer molecule for the 2D films 1 and 2, Vi, was found to be, for enthalpy, −5.20 (−4.26) and −4.20 (−3.68) kJ/mol, for entropy, −195.51 (−193.36) and −177.02 (−175.73) J/(mol·K); for Gibbs’ energy, 52.08 (53.36) and 47.67 (48,69) kJ/mol, respectively. For example, for the 2D film 2, the dependencies of thermodynamic parameters of clusterization at 293 K are ΔH2Cl(293) ∞ m

⎧n = −20.50·⎨ ⎩2

ΔS2Cl(293) ∞ m ΔG2Cl(293) ∞ m

} − 4.20, ⎧n = −44.40·⎨ } − 177.02, ⎩2 ⎧n = −7.50⎨ } − 47.67. ⎩2

The dependencies of ACl i(T),∞/m on the alkyl length at 293 K for the two considered types of infinite clusters are illustrated in Figures 11 and 12 for Gibbs’ energy of clusterization. It is clearly seen that two types of dependencies of clusterization of Gibbs’ energy exist: linear for 2D film 1 and stepwise for 2D film 2. It is stipulated by the different number of intermolecular 26369



Article

unchanged. Then, if the same superposition can be constructed in two different ways, each involving two entities (molecules, ions, radicals, clusters), it becomes possible to calculate the structure and properties of one of these entities, provided the structure and properties of the remaining three entities are known. This principle is graphically illustrated in Figure 13. The molecules 1, 2, 4, and 5 are the structures that involve the alkyl

amides with the results obtained previously for nine other homologous series of amphiphiles.30−38 The dependencies of enthalpy, entropy, and Gibbs’ energy of clusterization per one monomer of the cluster at 298 K are of the same type as those shown above at 293 K. Therefore, they are not listed here. However, as can be easily calculated according to eq 16, spontaneous clusterization of aliphatic amides in the structure of 2D film 2 at 298 K is possible for molecules having no less than 14 methylene units, as in the case of 293 K, whereas the formation of 2D film 1 is possible for molecules having no less than 16 carbon atoms at 298 K. It is one carbon atom more than is necessary for monolayer formation at 293 K. Thereby, among all classes of amphiphiles studied earlier, aliphatic amides have the same spontaneous clusterization threshold as carboxylic acids, α-amino acids, and thioalcohols (n = 14−15). It is interesting to compare the spontaneous clusterization thresholds for amphiphiles that differ only by one functional group, such as saturated carboxylic acids, amides or alcohols, and amines. The objective of this comparison is to define the relative influence of functional groups −OH and −NH2 on the clusterization thermodynamics of these amphiphilic compounds. As previously shown33 by using the PM3 method, the spontaneous clusterization threshold for amines is 18−19 carbon atoms in the alkyl chain,33 whereas for alcohols, it is 10−12 carbon atoms.32 Calculated values agree well with experimental data, which show the presence of stable monolayers for alcohols starting from dodecanol35 and for amines starting from hexadecylamine.17 This fact indicates that intermolecular interactions of the functional groups realized between amine molecules provides a larger destabilizing contribution to the Gibbs’ energy of clusterization than the interactions between alcohol molecules with analogous chain length. It is also proved by the fact that tetradecylamine is not capable of stable monolayer formation.32,33 On the other hand, the exchange of the hydroxyl group in carboxylic acids by the amino group does not lead to any significant shift in the spontaneous clusterization threshold to longer alkyl chains. It can be perhaps explained by the comparability in the increments of intermolecular hydrogen bonds O···H−O, which are realized between carboxylic acid molecules, and intermolecular hydrogen bonds O···H−N,55 which are realized between amide molecules. Description of Thermodynamic Parameters of Formation and Clusterization of Alkylamides in the Framework of Superposition-Additive Approach. Theoretical Reasons. The superposition−additive approach (SAA) is theoretically based on the postulate about the way in which atoms exist in molecules.60 According to this postulate, each atom in a molecule retains its individuality in various chemical combinations (i.e., in various molecules). This refers to transferability of atomic patterns. In addition, the atomic values, being summed over all atoms in the molecule, yield the molecular average so that the corresponding molecular characteristics are additive. The above presumption about the way in which atoms exist in molecules is the background for various additive schemes.60 The main idea of the superposition−additive approach is based on the transferability of atomic properties and the additivity of molecular properties. The essence of the procedure is the assumption that when two molecular graphs are virtually superimposed (atoms of one molecule coincide spatially with corresponding atoms of the other molecule), the properties of the constituent atoms remain

Figure 13. Generalized superposition−additive scheme for the calculation of thermodynamic parameters of monomers of substituted alkanes.

chain and the functional groups X, Y, and Z (these groups can be the same or different). Structure 3 is the result of the superposition of structures 1 and 2 and also of structures 4 and 5. Because these two superpositions lead to the same result, the properties of any of the four molecules could be expressed as the algebraic sum of the corresponding properties of three other molecules. Thus, for example, to calculate any thermodynamic parameter of molecule 4, one has to add the corresponding values for the molecules 1 and 2 and subtract the value of molecule 5. In ref 61, the superposition−additive approach was implemented for the description of the thermodynamic parameters of formation and clusterization of monosubstituted alkanes that possess amphiphilic structure and are capable of monolayer formation at the air/water interface. This approach allows reasonably accurate reproducing thermodynamic parameters of formation and clusterization of alkanes, fatty alcohols, carboxylic acids, thioalcohols, amines and cis-unsaturated carboxylic acids and parameters of their phase transition, as well. It should be mentioned that SAA enables the description of thermodynamic parameters of formation not only for monosubstituted alkanes but also for amphiphiles having two functional groups, for example, α-amino acids. Thus, in the framework of the regarded approach, the values of the thermodynamic parameters of formation of aliphatic α-amino acids could be expressed as the sum of the corresponding parameters of carboxylic acids and amines after subtraction of alkanes. As opposed to the mentioned above, it is impossible to apply this scheme to the case of α-amino acids clusterization. This is stipulated by the structural inequalities of α-amino acid monolayers and monolayers of amines, carboxylic acids, and alkanes. They have a different number of intermolecular CH···HC interactions per one monomer of the 2D cluster. Consequently, it leads to impossibility of their superimposition in the monolayers of the considered amphiphiles. As a result, the main requirement of superposition−additive approach (virtual superimposition of the considered molecular graphs) is not implemented. 26370



Article

The structure of alkylamide monolayers built on the basis of monomer 2 agrees reasonably well with the monolayer structures of homologous amines, carboxylic acids, and alcohols studied earlier. There are an equal number of intermolecular CH···HC interactions per one monomer of their 2D clusters. This ensures a maximal region of superimposition of the molecular graphs for the regarded compounds. In this connection, it is interesting to apply the regarded approach to the description of thermodynamic parameters of formation and clusterization of aliphatic amides because the increment of the functional amide group in the values of these parameters can be considered as a total increment of the functional groups of amines and carboxylic acids after subtraction of alcohols. As in the case of refs 60 and 61, the physicochemical characteristics involved in the superposition−additive approach can be either those calculated by the semiempirical quantumchemical PM3 method or those obtained from the experiment.50−52 Both options are utilized in the present work. The calculated results according to the superposition−additive schemes (SAS) for alkylamides are listed in corresponding tables. In these tables, the column “SAS Scheme No. (cal)” lists the values estimated by SAS using the corresponding parameters that were previously determined by PM3 calculations listed in the “Direct Calculation” column. In the “SAS Scheme No. (exp)” column, the values are shown that were estimated by SAS from the available experimental data50−52 listed in the “Experiment” column. In our previous study61 devoted to the application of the superposition−additive approach for the description of the thermodynamic parameters of formation and clusterization of substituted alkanes, we looked at different SASs, which exploited the values of the corresponding parameters referred both to one class of compounds and to several classes, as well (three in the case of α-amino acids). In the present study, we examine only the most interesting SAS, which exploits the data for the three surfactant classes carboxylic acids, amines, and alcohols, where X ≠ Y ≠ Z (see Figure 13). Calculation of Thermodynamic Parameters of Formation of Alkylamide Monomers Using the Superposition-Additive Schemes. It is known62,63 that it is possible to reasonably use the quite wide range of superposition−additive schemes. However, the best results can be obtained in the framework of schemes having maximal superimposition of the molecular graphs. Therefore, at first, we consider the scheme (see Figure 14) with maximal mutual overlap of the alkyl chains (CnH2n+1),

Figure 14. Superposition-additive scheme (SAS 1) for the calculation of the thermodynamic parameters of aliphatic amides monomers.

the ketonic CO group and the amine NH2 group. Note that the simplest superposition scheme for calculation of thermodynamic parameters of the alkylamide formation can be the following scheme: “amide = aldehyde + amine − alkane”. However, this scheme cannot be exploited because of the presence of p−π conjugation of the lone-electron pair of nitrogen atom and π-electrons of carbonyl oxygen atom in the hydrophilic headgroup of amide and its absence in aldehyde. At the same time, carboxylic acids have such conjugation between the lone-electron pair of the hydroxyl oxygen atom and πelectrons of carbonyl oxygen atom. As a result, the π-electronic system realized in the compounds described above provides planarity of the examined atomic groups. This enables maximal superimposition of the molecular graphs in the case of using the next scheme: “amide = carboxylic acid + amine − alcohol” due to the planar structure of the functional groups for the two classes of amphiphiles used in this scheme and the pyramidal structure of the two others. Consider now the methodology of the calculation in the framework of the superposition−additive scheme 1 in detail. To calculate the thermodynamic parameters of amide molecule, containing n carbon atoms in the alkyl chain, one should use the parameters of monomer molecules of three other examined classes of amphiphiles with the same number (n) of carbon atoms in their alkyl chains. For example, to calculate the thermodynamic parameter for octylamide, one should add the values of the corresponding parameter (enthalpy, entropy, or Gibbs’ energy) for octanoic acid and octylamine and subtract from the calculated sum the corresponding thermodynamic parameter of octanol. It was mentioned above that there are other superposition− additive schemes with smaller regions of molecular graphs overlapping (Cn−2H2n−5),

SAS 1: A(CnH 2n + 1[XZ]) = A(CnH 2n + 1[XY]) + A(CnH 2n + 1Z) − A(CnH 2n + 1Y)

(17)

where A is the thermodynamic parameter (absolute entropy, enthalpy, or Gibbs energy of the formation of the compound from elementary substances) at normal conditions (T = 298.15 K); n is the number of atoms in the alkyl chain; X, Y, and Z define schematically the structural fragments of the functional groups, e.g. [XY] = COOH for carboxylic acids, Y = OH for alcohols, Z = NH2 for amines, [XZ] = CONH2 for amides. This scheme can be illustrated graphically as follows. Here, the functional COOH group of carboxylic acids can be represented as a combination of the ketonic CO group and the hydroxyl OH group of alcohols, whereas the functional amide group CONH2 can be represented as a combination of

SAS 2: A(CnH 2n + 1[XZ]) = A(CnH 2n + 1[XY]) + A(Cn − 2H 2n − 5Z) − A(Cn − 2H 2n − 5Y)

(18)

SAS 3: A(CnH 2n + 1[XZ]) = A(Cn − 2H 2n − 5[XY]) + A(CnH 2n + 1Z) − A(Cn − 2H 2n − 5Y) 26371

(19)



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Table 6. Comparison of Formation Enthalpy of Amide Monomers Calculated via SAS 1 with the Experimental Data and Data Obtained in the Framework of the PM3 Methoda ΔH0298,mon, kJ/mol system CH3CONH2 C2H5CONH2 C3H7CONH2 C4H9CONH2 C5H11CONH2 C6H13CONH2 C7H15CONH2 C8H17CONH2 C9H19CONH2 C10H21CONH2 C11H23CONH2 C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2 a

SAS 1 (cal)

−336.56 −359.23 −381.91 −404.59 −427.26 −449.95 −472.62 −495.30 −517.97 −540.63

(−323.59) (−346.26) (−368.93) (−391.61) (−414.29) (−436.97) (−459.65) (−482.33) (−505.00) (−527.65)

direct calculation

−323.59 −346.26 −368.93 −391.60 −414.28 −436.96 −459.64 −482.32 −505.00 −527.68 −550.37

SAS 1 (exp) −243.0 −291.1 −307.5 −326.2 −353.0 −372.6 −394.8

(−211.0) (−259.1) (−275.5) (−294.2) (−321.0) (−340.6) (−362.8)

experiment −238.3 −252.3 −261.0 −290.2 −324.3 −362.7

Corrected values are listed in parentheses.

Figure 15. Generalized superposition−additive scheme (SAS 4) for the calculation of the thermodynamic parameters of clusters of substituted alkanes.

1.86 J/(mol·K), respectively, for entropy; and 0.59, 0.66, and 0.56 kJ/mol for Gibbs’ energy of formation. The standard deviations of the enthalpy of formation calculated by the SAS 1−SAS 3 from the experimental data including the corrected values are 3.33, 8.26, and 8.43 kJ/mol, respectively. Calculation of Thermodynamic Parameters of Formation and Clusterization of Alkylamide Aggregates Using SAA. As noted in ref 60 regarding the application of the proposed approach to van der Waals molecules and clusters, it should be kept in mind that, in contrast to the individual monomers, these systems also involve intermolecular CH···HC interactions, shown by red arrows in Figure 7. Thus, CH···HC interactions realized in the clusters of amphiphilic molecules with an odd number of carbon atoms in the monomer chains do not overlap with those realized in the clusters of amphiphilic molecules with an even number of carbon atoms in the monomer chains. Therefore, in this case, the schemes provided with the principle of the mutual molecular graphs overlapping would be correct. Molecular graph overlapping is possible if one uses thermodynamic properties of clusters with an odd (even) number of methylene units for the calculation of the corresponding parameters only for clusters having an odd (even) number of CH2 groups. All calculations were carried out for linear “parallel” structures of amide dimers as well as trimers and a tetramer with oblique structure (see Figure 8) optimized

The results of the calculation of thermodynamic parameters within SAS 1 are listed in Table 6. Note that the standard deviations of calculation of enthalpy, entropy, and Gibbs’ energy are almost the same for all schemes considered. As mentioned above, the experimental data regarding the standard thermodynamic characteristics of the formation of alkylamides are very scarce and are available only for enthalpy of formation, so there are results only for enthalpy as an example in Table 6. It should be mentioned that the superposition−additive approach cannot account for the intramolecular interaction between the oxygen of the carbonyl group and the amino group in the amide molecule when superimposing the molecular structures of amine, carboxylic acid, and alcohol. This causes a systematic error of the description of enthalpy, entropy, and Gibbs’ energy of the amide formation. This means the value for all examined schemes were 12.97 kJ/mol, 8.41 J/(mol·K), and 15.91 kJ/mol, respectively, in comparison with the data obtained by direct calculation using the PM3 method. For experimental data, this error was calculated to be 31.97 kJ/mol. The result of the mentioned errors significantly reduces the value of these standard deviations (the corrected values are listed in parentheses in Table 6). The standard deviations of the values calculated by the SAS 1−SAS 3 from the results of the PM3 calculations with including the corrected values are 0.02, 0.01, and 0.01 kJ/mol, respectively, for enthalpy; 1.90, 1.97, and 26372



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Table 7. Comparison of Enthalpy and Absolute Entropy of the Formation Per One Monomer Molecule of Amide Clusters Calculated by SAS 4 with Data Obtained in the Framework of the PM3 Methoda dimer system

SAS 4

trimer direct calculation

SAS 4

tetramer direct calculation

SAS 4

direct calculation

ΔH0298,m/m, kJ/mol C6H13CONH2 C7H15CONH2 C8H17CONH2 C9H19CONH2 C10H21CONH2 C11H23CONH2 C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2 standard deviation C6H13CONH2 C7H15CONH2 C8H17CONH2 C9H19CONH2 C10H21CONH2 C11H23CONH2 C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2 standard deviation a

−351.75 −375.80 −402.19 −426.15 −452.55 −476.66 −503.06 −527.15 −553.60 −576.99 11.01

377.09 392.38 417.25 443.81 470.59 487.24 511.57 535.06 560.87 595.26

(−362.76) (−386.81) (−413.20) (−437.17) (−463.56) (−487.67) (−514.08) (−538.17) (−564.61) (−588.00) (1.35)

(412.98) (428.28) (453.15) (479.71) (506.49) (523.14) (547.47) (570.96) (596.77) (631.16)

−337.54 −361.30 −387.91 −411.73 −438.38 −462.20 −488.73 −512.70 −539.25 −563.22 −589.79

376.28 396.59 425.92 448.47 476.51 501.45 529.29 554.16 578.65 603.34 628.41 35.90 (7.24)

−351.50 (−371.76) −375.47 (−395.73) −401.87 (−422.13) −425.84 (−446.10) −452.22 (−472.48) −476.33 (−496.60) −502.72 (−522.98) −526.84 (−547.10) −553.27 (−573.53) −576.69 (−596.95) 20.26 (3.32) S0298,m/m, J/(mol·K) 377.87 400.77 428.14 452.85 480.14 503.43 531.64 551.16 575.64 615.44

(361.31) (384.21) (411.57) (436.29) (463.58) (486.87) (515.08) (534.59) (559.08) (598.88)

−341.98 −365.84 −393.99 −417.94 −446.15 −470.16 −498.37 −522.41 −550.44 −574.63 −602.71

352.38 370.96 397.55 419.75 442.20 466.28 488.37 512.43 536.56 557.63 581.15 16.56 (7.29)

−367.27 −392.23 −422.91 −448.01 −478.72 −504.42 −534.36 −559.48 −590.17 −615.29 15.82

299.11 323.83 341.86 360.03 371.39 387.51 409.57 430.95 447.25 460.75

(−383.09) (−408.05) (−438.73) (−463.84) (−494.54) (−520.24) (−550.18) (−575.31) (−605.99) (−631.11) (2.98)

(342.81) (367.53) (385.56) (403.73) (415.09) (431.21) (453.27) (474.65) (490.95) (504.45)

−355.15 −380.46 −410.87 −435.30 −466.57 −491.07 −522.35 −546.85 −578.15 −602.68 −633.96

308.37 324.39 349.94 378.58 392.94 420.41 433.74 461.43 474.85 502.89 516.33 43.70 (10.95)


deviations of the thermodynamic parameters of the formation of amide associates are larger than the corresponding values for the monomer formation. This is caused by complication of investigated structures that consequently gives rise to a decrease in their order with respect to the monomer structure. In addition, as in the case of monomers, there are systematic errors of the description of the formation of enthalpy, entropy and Gibbs’ energy of amide associates. The result of these errors significantly reduces the value of the standard deviation (corrected values are listed in parentheses in Table 7). The results of the calculation of enthalpy, entropy, and Gibbs’ energy of clusterization per one monomer of the amide cluster according to SAS 4 are listed in Table 8. One can see that the calculated values of the thermodynamic parameters of clusterization have a systematic error. This is probably a result of incomplete molecular graphs overlapping of the structures involved in this scheme. The latter can be drawn by the impossibility to represent the intermolecular interactions of the hydrophilic head groups in the amide associates only as a simple combination of the corresponding interactions realized in the clusters of carboxylic acids, amines, and alcohols. The p−π system realized in the functional group of the amide molecule differs from that present in carboxylic acids, and it is absent in the molecules of amines and alcohols. The impact of such differences can be retraced if one compares the contributions of the functional group interactions with the clusterization Gibbs’ energy per one monomer molecule for all compounds involved in SAS 4. Thus, for alcohols, amines, carboxylic acids, and amides, the values of the examined contributions were 36.05, 44.50, 47.74, and 48.69 kJ/mol,

in the framework of the PM3 method. Note once again that we consider the amide associates based on the monomer 2 structure because these clusters have the same number of intermolecular CH···HC interactions as those in the corresponding structures of amines, carboxylic acids, and alcohols exploited in SAS. The SAS 4 with maximal molecular graphs overlapping was used for the calculation of the thermodynamic parameters of formation and clusterization of amide dimers and larger clusters, SAS 4: A(CnH 2n + 1[XZ])m /m = A(CnH 2n + 1[XY])m /m + A(Cn − 2H 2n − 5Z)m /m − A(Cn − 2H 2n − 5Y)m /m

(20)

where A is the thermodynamic parameter of formation or clusterization of associates, m is the number of monomers in a cluster, and n is the number of carbon atoms in the alkyl chain of the monomer. This scheme for the calculation of the thermodynamic parameters of formation (and clusterization) of associates is illustrated in Figure 15. As in the case of SAS 1, the thermodynamic parameters of the entities involved in SAS 4 should have the same alkyl chain length, n (to obtain maximal molecular graphs overlapping). According to SAS 4 described above, enthalpy and absolute entropy of the formation for alkylamide clusters and their standard errors from the results of the PM3 calculations were calculated (see Table 7). The listed data show that the 26373



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Table 8. Comparison of Enthalpy, Entropy and Gibbs’ Energy of Clusterization Per One Monomer Molecule of Amide Clusters Calculated by SAS 4 with Data Obtained in the Framework of the PM3 Methoda dimer system C6H13CONH2 C7H15CONH2 C8H17CONH2 C9H19CONH2 C10H21CONH2 C11H23CONH2 C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2 Standard deviation C6H13CONH2 C7H15CONH2 C8H17CONH2 C9H19CONH2 C10H21CONH2 C11H23CONH2 C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2 Standard deviation C6H13CONH2 C7H15CONH2 C8H17CONH2 C9H19CONH2 C10H21CONH2 C11H23CONH2 C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2 standard deviation a

SAS 4

−16.56 −20.32 −21.58 −25.45 −26.70 −30.64 −31.72 −35.83 −36.96

(−15.11) (−18.87) (−20.14) (−24.01) (−25.25) (−29.19) (−30.27) (−34.39) (−35.51)

tetramer direct calculation ΔHmcl/m, kJ/mol −13.95 −15.04 −18.98 −20.13 −24.10 −25.24 −29.09 −30.38 −34.25 −35.54 −39.42

1.45 (0.09)

−93.98 (−75.20) −102.32 (−83.54) −112.38 (−93.60) −119.34 (−100.56) −121.24 (−102.46) −139.04 (−120.26) −137.88 (−119.10) −155.22 (−136.44) −154.21 (−135.43)

−32.94 −41.21 −43.26 −51.65 −53.84 −62.54 −64.19 −72.26 −74.71

(−33.59) (−41.86) (−43.92) (−52.30) (−54.50) (−63.19) (−64.84) (−72.91) (−75.36)

direct calculation −31.55 −34.20 −41.94 −43.70 −52.29 −54.11 −62.72 −64.54 −73.15 −75.00 −83.60

0.65 (0.35) ΔSmcl/m, J/(mol·K) −74.89 −86.91 −89.45 −98.94 −102.44 −109.26 −112.03 −119.39 −126.29 −133.23 −138.90

18.78 (6.88)

11.45 (10.00) 10.17 (8.73) 11.91 (10.46) 10.11 (8.66) 9.42 (7.98) 10.79 (9.35) 9.37 (7.92) 10.42 (8.97) 8.99 (7.55)

SAS 4

−171.32 −182.15 −190.31 −209.76 −222.12 −245.29 −243.54 −264.95 −271.12

(−142.47) (−153.29) (−161.46) (−180.91) (−193.26) (−216.44) (−214.68) (−236.09) (−242.27)

−142.79 −159.10 −165.44 −168.83 −186.01 −190.29 −207.58 −212.12 −230.09 −233.69 −250.98

28.86 (8.87) ΔGmcl/m, kJ/mol 8.37 10.86 7.67 9.36 6.43 7.32 4.30 5.20 3.39 4.16 1.97

4.26 (2.04)

18.11 (8.58) 13.07 (3.54) 13.45 (3.91) 10.86 (1.32) 12.35 (2.81) 10.56 (1.03) 8.38 (−1.15) 6.69 (−2.84) 6.09 (−3.45)

11.00 13.21 7.36 6.61 3.14 2.60 −0.86 −1.32 −4.59 −5.36 −8.80

9.54 (2.40)


thermodynamic parameters of clusterization are listed in brackets in Table 8. As noted repeatedly earlier,32,33,64,65 the formation of the infinite 2D films is of most practical interest during the investigation of the clusterization processes at interfaces, so the final stage of this study considers the description of the thermodynamic parameters of clusterization of aliphatic amides in the framework of the superposition−additive approach. Remember one more time that, as in the case of small clusters for the calculation of thermodynamic parameters of clusterization per one monomer of monolayers, we use these parameters for structures having an equal number of carbon atoms (n) in the alkyl chain of the amphiphile involved. The calculated values of enthalpy, entropy, and Gibbs’ energy of clusterization per one monomer of the infinite amide clusters are listed in Table 9. Here, the “additive scheme” column contains the values of the examined parameters calculated

respectively. It is clearly seen that the contributions for the two last compounds (carboxylic acids and amides), having a close structure of the functional group, are quite approximate, whereas for the two other compounds (especially alcohol), the regarded contributions are sufficiently different. The increments of the intermolecular CH···HC interactions are practically the same for the different classes of amphiphiles,30−38 but the increments of the interactions realized between structurally different functional groups of amphiphiles are different. This causes the systematic errors of the description of the thermodynamic parameters of clusterization for associates of different dimensions up to infinite 2D films. The result of the systematic errors described above significantly improves the agreement between the values of enthalpy, entropy, and Gibbs’ energy of clusterization calculated per one monomer molecule using SAS 4 and the results of the direct calculation in the framework of the PM3 method. The corrected values of the 26374



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Table 9. Comparison of Enthalpy, Entropy and Gibbs’ Energy of Clusterization Per One Amide Molecule of 2D Films Calculated by SAS 4 with Data Calculated in the Framework of the Additive Schemea ΔHmcl/m, kJ/mol system C6H13CONH2 C7H15CONH2 C8H17CONH2 C9H19CONH2 C10H21CONH2 C11H23CONH2 C12H25CONH2 C13H27CONH2 C14H29CONH2 C15H31CONH2 C16H33CONH2 standard deviation a

SAS 4 −63.81 −84.65 −84.55 −105.39 −105.29 −126.13 −126.04 −146.88 −146.78 −167.62 1.30

(−65.11) (−85.95) (−85.85) (−106.69) (−106.60) (−127.44) (−127.34) (−148.18) (−148.08) (−168.92) (0.38)

ΔSmcl/m, J/(mol·K)

additive scheme −65.71 −65.71 −86.21 −86.21 −106.71 −106.71 −127.21 −127.21 −147.71 −147.71 −168.22

SAS 4 −326.02 −370.30 −373.31 −417.59 −420.59 −464.87 −467.88 −512.16 −515.16 −559.45 21.95

ΔGmcl/m, kJ/mol

additive scheme

(−304.07) (−348.36) (−351.36) (−395.64) (−398.65) (−442.93) (−445.93) (−490.22) (−493.22) (−537.50) (4.11)

−310.19 −310.19 −354.59 −354.59 −398.98 −398.98 −443.37 −443.37 −487.76 −487.76 −532.15

SAS 4 33.35 25.71 26.70 19.06 20.05 12.40 13.40 5.75 6.75 −0.90 9.86

(23.49) (15.85) (16.84) (9.20) (10.19) (2.55) (3.54) (−4.10) (−3.11) (−10.75) (1.27)

additive scheme 25.18 25.18 17.69 17.69 10.19 10.19 2.70 2.70 −4.80 −4.80 −12.30


The tilt angles of molecules in “serial” and “parallel” dimers with respect to the normal to the directions of the monolayer unit cell are found: φ1 = 10, φ2 = 20.5 and δ1 = 23°, δ2 = 10°, respectively, for structures based on monomers 1 and 2. The calculated values of these angles give rise to the general tilt angle of alkylamide molecules with respect to the normal to the interface t1 = 25° and t2 = 23°, agreeing satisfactorily with experimental data.57 The spontaneous clusterization threshold of aliphatic amides at the air/water interface is 14 carbon atoms in the alkyl chain at 293 K for monomer 1 and 15 carbon atoms for monomer 2. These values agree well with the available experimental data.16 The analysis of the dependencies of clusterization Gibbs’ energy per one monomer molecule of associates and 2D films is the basis for the postulation of different clusterization paths for the structures of monomers 1 and 2. Thus, 2D film 2 can be formed by the preferential development of linear “serial” clusters, their further aggregation and linkage to larger associates that have less energetically preferred interactions of the hydrophilic head groups, as in “parallel” dimers. That means that the clusterization of monomer 2 with preferential formation of linear associates may stipulate a dendritic structure of 2D film 2, whereas 2D film 1 can have denser packing because of the preferential formation of tetramers and larger two-dimensional amide associates, in comparison with the formation of linear associates. It is shown in the framework of the superposition−additive approach that enthalpy, entropy, and Gibbs’ energy of formation and clusterization of aliphatic amides can be obtained as a sum of the corresponding parameters for carboxylic acids and amines, subtracting alcohols.

previously according to the additive scheme. The data listed in Table 9 reveal that, as in the case of small amide associates, the thermodynamic parameters of clusterization per one monomer of 2D films have a systematic error. The structural differences between the functional groups of the amphiphiles involved in SAS 4 cause incomplete molecular graphs overlapping for the monolayers of these compounds. As seen from Table 9, these structural differences affect mostly the entropy of clusterization, and thus, they cause an insufficient agreement between the values of Gibbs’ energy obtained in the framework of SAS 4 and the additive scheme. The inclusion of the present systematic error reduces significantly the value of the standard deviation for the description of the thermodynamic parameters of clusterization per one amide molecule of the monolayers (corrected values are listed in parentheses in Table 9). Summarizing, different superposition−additive schemes have been applied to calculate the thermodynamic parameters of formation and clusterization for both monomers and clusters (dimers, trimers, tetramers) up to 2D films of amides. Enthalpy, entropy, and Gibbs’ energy of formation and clusterization of aliphatic amides can be obtained as a sum of corresponding parameters for carboxylic acids and amines after subtraction of alcohols.

■

CONCLUSION To summarize, the quantum chemical semiempirical PM3 method is employed to study the clusterization process thermodynamics of aliphatic amides at the air/water interface. The conformational analysis has shown that four conformations of the alkylamide monomer exist. They are pairwise mirroridentical. Therefore, enthalpy, entropy, and Gibbs’ energy of formation are calculated only for monomers 1 and 2, which are not mirror isomers of each other. These monomer structures are used for the construction of the amide clusters. The regression dependencies of the calculated thermodynamic parameters on the number of methylene groups in the alkyl chain of the amide are developed. The obtained regression dependencies are linear, whereas the contributions from one methylene group to the values of thermodynamic parameters of formation are shown to be quite equal to those calculated earlier for other classes of amphiphiles. Two types of dimers are built on the basis of chosen monomer conformations: with “parallel” and “serial” mutual orientation of the functional groups of monomer in the dimers.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

REFERENCES

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