Quantum Chemical Analysis of Thermodynamics of ... - ACS Publications

5374

J. Phys. Chem. C 2007, 111, 5374-5381

Quantum Chemical Analysis of Thermodynamics of 2D Cluster Formation of n-Thioalcohols at the Air/Water Interface Yu. B. Vysotsky,† E. A. Belyaeva,† V. B. Fainerman,‡ D. Vollhardt,*,§ and R. Miller§ Donetsk National Technical UniVersity, 58 Artema Str., 83000 Donetsk, Ukraine, Medical Physicochemical Centre, Donetsk Medical UniVersity, 83003 Donetsk, Ukraine, and Max Planck Institute of Colloids and Interfaces, D-14424 Potsdam/Golm, Germany ReceiVed: December 29, 2006; In Final Form: February 15, 2007

The semiempirical PM3 method is used to calculate the thermodynamic parameters of the formation of monomers, dimers, trimers, tetramers, and one of the possible hexamers of saturated thioalcohols with normal structure and alkyl chain lengths of 6-16 carbon atoms. The dependencies of the potential energy surfaces on the torsion angles for monomers and dimers of normal thioalcohols are calculated. The most stable conformations of monomers and dimers are determined and used to construct the structures of trimers, tetramers, and larger clusters. For various conformations of dimers, trimers, tetramers, and for the hexamer, the thermodynamic parameters of clusterization (enthalpy, entropy, and Gibbs energy) are calculated. It is found that these parameters are stepwise-dependent on the alkyl chain length. It is shown that a two-dimensional square-symmetric infinite cluster and clusters constructed on the basis of cyclic trimers are formed for alkyl chain lengths of 14-15 carbon atoms and above.

Introduction It is known that substances with amphiphilic structures, such as long-chain alcohols, acids, carbon acid salts, and so forth, exhibit surface-active properties in aqueous solutions and form adsorption layers or Langmuir monolayers at the interfaces.1-3 Adsorbing at interfaces, surfactants play an important role in wetting, dispersing, foaming, solubilizing, and a great number of other phenomena. The importance of Langmuir (insoluble) monolayers and Langmuir-Blodgett films is also very significant.4 These films are used to prevent the evaporation of liquids from reservoirs, in the preparation of polylayer coatings and microelectronic devices, in the preparation of solid nanoparticles using the chemical reactions, or in the photochemical reduction of metal salts. Adsorbed and Langmuir monolayers in which phase transitions of first or second order can take place are of special interest. In this regard, studies of intermolecular interactions at the gas/liquid interface are important. The formation of a new phase is governed by the action of various forces at the interface reaching from weak van der Waals forces up to strong covalent forces, cf. for example, ref 5. For hydrocarbon compounds or the compounds that contain alkyl chains, such as long-chain thioalcohols which are studied here, weaker interactions are more characteristic, which are due to both the formation of hydrogen bonds (if the electronegative atoms are present in the system) and the formation of hydrogenhydrogen bonds.6 Thioalcohols with the general chemical formula CnHn+1SH, similar to many other amphiphilic substances, are capable of the formation of two-dimensional monolayers at interfaces.7 However, attempts, made in a number of studies to form stable monolayers at the air/water interface failed because of the * Corresponding author. E-mail: [email protected]. † Donetsk National Technical University. ‡ Medical Physicochemical Centre. § Max Planck Institute of Colloids and Interfaces.

oxidation of the thioalcohols by the oxygen present in the air (see ref 8). Stable C18H37SH monolayers were only prepared when aqueous 5 × 10-4 M BaCl2 solution was used as the substrate.8 The surface pressure-area per molecule (π - A) isotherm of C18H37SH at 21 °C presented in ref 8 shows that for A > 20 Å2 the surface pressure of the monolayer becomes approximately zero. This fact indicates that, similar to what was shown earlier for the higher homologues of n-alcohols,9,10 the value of critical area per molecule, that is, the value at which the two-dimensional phase transition commences, is high, and, therefore, the Gibbs free energy of clusterization for C18H37SH is high. When the area per C18H37SH molecule becomes lower than 20 Å2, a rapid increase of surface pressure is observed. In the present study, we focus on the theoretical analysis of the behavior of thioalcohol monolayers at the air/water interface that is of prognostic interest, especially in comparison with the behavior of monolayers formed by long-chain n-alcohols or acids. Thus, this work is the continuation of previous papers,9-13 where the results of quantum chemical studies of intermolecular complexes formed at the air/water interface by a series of saturated and polyfluorinated alcohols and n-carboxylic acids were reported. In these publications, the applicability of the semiempirical PM3 method for the calculation of the thermodynamic parameters of such systems was demonstrated. Methods The geometric structures of thioalcohol monomers and dimers were optimized using the Mopac 2000 software package. The BFGS algorithm was employed, which is suitable for the calculation of large molecules. In the Mopac 2000 program module used for the entropy calculations, the vibration frequencies below 100 cm-1 were neglected. Because vibrations with such frequencies are observed experimentally for van der Waals molecules, and their proper account is important for the correct calculations of entropy values, the contributions from these

10.1021/jp069025w CCC: $37.00 © 2007 American Chemical Society Published on Web 03/21/2007

2D Cluster Formation of n-Thioalcohols

Figure 1. Dependence of the C16H31SH monomer formation enthalpy on the HSCC torsion angle.

vibrations were additionally calculated according to the method described in ref 9. Results and Discussion Monomers. At the first stage of the study, the conformational analysis of thioalcohol monomers was performed. For example, the dependence of potential energy on the HSCC torsion angle is shown in Figure 1. It is seen that three stable conformations exist: two symmetric global minima that correspond to the HSCC torsion angle values of 65° and 360° - 65° ) 295° (monomer 1) and one local minimum at 180 °C (monomer 2).

J. Phys. Chem. C, Vol. 111, No. 14, 2007 5375 These structures of monomers are stable because of the existence of hydrogen-hydrogen interactions between the hydrogen atom in the thiol group and either β-hydrogen atoms of the alkyl chain for monomer 1 or R-hydrogen atoms for monomer 2. The structures of these monomers and the structures of the dimers, trimers, and tetramers on the basis of these monomers are shown in Figure 2. The thermodynamic characteristics of the thioalcohol monomer’s formation from elementary substances were calculated using the AM1, MINDO/3, MNDO, and PM3 methods. Table 1 summarizes the calculated values of enthalpy, entropy, and Gibbs energy for monomer 1, which corresponds to a global minimum. In Table 1, the experimental data for the thioalcohol series with alkyl chain lengths from 3-12 carbon atoms are presented.14 It was found that the values calculated in the MNDO and PM3 parametrizations exhibit the best correspondence with the experimental data. The root-mean-square error in the calculation of enthalpy change for the AM1, MINDO/3, MNDO, and PM3 methods was 6.8, 11.2, 4.3, and 3.8 kJ/mol, respectively, for conformer 1 and 7.8, 12.4, 3.8, and 5.7 kJ/mol for conformer 2. Comparing the standard error obtained for the PM3 parametrization (5.7 and 3.8 kJ/mol) with that calculated earlier for n-alcohols (23.0 kJ/mol)13 and acids (5.9 kJ/mol),10 it is seen that the root-mean-square error of the calculated entropy change

Figure 2. Optimized geometrical structures of monomers, dimers, and larger clusters of thioalcohols.

5376 J. Phys. Chem. C, Vol. 111, No. 14, 2007

Vysotsky et al.

TABLE 1: Standard Thermodynamic Characteristics of Formation for Conformer 1 molecule C3H7SH C4H9SH C5H11SH C6H13SH C7H15SH C8H17SH C9H19SH C10H21SH C11H23SH C12H25SH C13H27SH C14H29SH C15H31SH C16H33SH

AM1 -75.30 -103.96 -133.25 -161.24 -189.02 -218.53 -247.17 -275.82 -304.47 -333.12 -361.77 -390.42 -419.07 -447.71

MINDO/3

MNDO

PM3

standard enthalpy ∆H2980, kJ/mol -116.37 -76.33 -143.04 -96.11 -169.30 -115.82 -195.51 -135.52 -221.72 -155.22 -247.93 -174.93 -274.13 -194.63 -300.32 -214.33 -326.54 -234.04 -352.74 -253.74 -377.33 -273.45 -405.12 -293.14 -431.35 -312.85 -457.50 -332.53

-63.90 -86.50 -109.15 -131.81 -154.48 -177.15 -199.83 -222.51 -243.90 -267.87 -290.55 -313.23 -335.91 -358.59

C3H7SH C4H9SH C5H11SH C6H13SH C7H15SH C8H17SH C9H19SH C10H21SH C11H23SH C12H25SH C13H27SH C14H29SH C15H31SH C16H33SH

326.91(345.00) 360.22(384.34) 393.71(423.86) 426.25(462.43) 456.45(498.66) 492.22(540.46) 524.39(578.66) 549.45(609.75) 588.97(655.30) 621.90(694.26) 653.71(732.10) 686.23(770.65) 717.74(808.19) 749.03(845.51)

standard entropy S2980, J/mol‚K 332.50(344.89) 322.59(341.43) 367.76(384.28) 356.00(381.12) 403.35(424.00) 389.07(420.47) 438.04(462.82) 422.04(459.72) 472.96(501.87) 454.68(498.64) 507.38(540.42) 487.64(537.88) 542.35(579.52) 519.55(576.07) 576.12(617.42) 552.07(614.87) 610.88(656.31) 583.40(652.48) 642.99(692.55) 615.74(691.10) 677.97(731.66) 647.47(729.11) 710.22(768.04) 678.94(766.86) 744.26(806.21) 708.84(803.04) 775.26(841.34) 740.92(841.40)

326.71(347.80) 359.60(387.72) 391.88(427.03) 424.37(466.55) 456.56(505.77) 488.90(545.14) 521.28(584.55) 552.78(623.08) 584.86(662.19) 617.46(701.82) 648.65(740.04) 680.50(778.92) 711.58(817.03) 743.95(856.43)

C3H7SH C4H9SH C5H11SH C6H13SH C7H15SH C8H17SH C9H19SH C10H21SH C11H23SH C12H25SH C13H27SH C14H29SH C15H31SH C16H33SH

-1.92(-7.32) 0.50(-6.68) 2.61(-6.37) 4.70(-6.08) 6.90(-5.68) 8.96(-5.41) 11.29(-4.89) 13.44(-4.53) 15.98(-3.79) 18.07(-3.49) 20.88(-2.48) 22.98(-2.18) 25.88(-1.07) 27.01(-1.74)

standard Gibbs energy ∆G2980, kJ/mol -45.49(-49.19) -1.89(-7.51) -41.62(-46.55) 9.03(1.54) ep37.76(-43.91) 20.13(10.77) -33.78(-41.16) 31.17(19.94) -29.81(-38.43) 42.30(29.20) -25.58(-35.43) 53.49(38.51) -21.55(-32.62) 64.90(48.06) -18.38(-30.69) 76.25(57.53) -12.94(-26.48) 87.63(67.05) -8.38(-23.15) 98.98(76.53) -3.82(-19.82) 110.82(86.50) 0.88(-16.35) 122.47(96.27) 5.42(-13.04) 134.10(106.03) 9.75(-9.94) 145.60(115.65)

10.44(4.15) 18.73(10.34) 27.02(16.54) 35.23(22.65) 43.50(28.83) 51.76(34.97) 60.21(41.34) 64.29(47.52) 77.09(54.04) 85.23(60.08) 93.92(66.68) 102.20(72.88) 110.99(79.53) 119.49(85.84)

for thioalcohols is much lower than the error obtained for n-alcohols and is comparable with that for carboxylic acids. At the same time, the error in the standard entropy calculations for the methods listed above was 10.1, 8.7, 10.1, and 9.9 J/(mol‚K) for conformer 1 and 11.4, 8.6, 10.3, and 11.6 J/(mol‚K) for conformer 2, respectively. Similar to our previous studies, the calculations disregarded the free rotation of methylene groups of the alkyl chain. The corresponding corrections in the AM1, MINDO/3, MNDO, and PM3 methods are 6.03, 4.13, 6.28, and 7.03 J/(mol‚K), respectively; the account for this fact resulted in the essential improvement of the correspondence between the calculated values and the experimental data. In particular, the root-mean-square error for the description of the experimental data for entropy was 2.8, 3.7, 2.3, and 1.5 J/(mol‚K) for conformer 1 and 4.3, 3.5, 2.4, and 2.8 J/(mol‚K) for conformer 2. The corrected values of ∆S2980 and ∆G2980 are shown in Table 1 in parentheses. The values of the thermodynamic parameters listed in Table 1 were used to obtain the regression dependencies of ∆H2980, ∆S2980, and ∆G2980 on the alkyl chain length. Similar to those obtained earlier for alcohols and acids, these dependencies are linear. The regression data parameters and standard

expt -67.5 -87.8 -109.8 -129.2 -149.5 -170.1 -190.8 -210.9 -232.5 -253.2

336.50 375.20 415.40 454.70 493.89 533.14 572.39 611.64 650.90 690.10

2.58 11.39 18.04 27.56 36.219 44.557 52.796 61.63 68.97 77.23

TABLE 2: Correlation Equations of the Type y ) (a ( ∆a)n + (b ( ∆b) for Thioalcohol Monomers (Number of Points ) 14); n is the Number of Methylene Units conformer

parameter

1

∆H2980 (kJ/mol) S2980 (J/mol‚K) ∆G2980 (kJ/mol) ∆H2980 (kJ/mol) S2980 (J/mol‚K) ∆G2980 (kJ/mol)

2

a ( ∆a

b ( ∆b

S

-22.68 ( 0.06 4.08 ( 0.59 0.87 39.07 ( 0.12 227.21 ( 1.20 1.76 6.28 ( 0.08 -15.23 ( 0.87 1.28 -22.67 ( 0.01 9.27 ( 0.03 0.04 39.09 ( 0.05 231.80 ( 0.53 0.78 6.28 ( 0.01 -11.40 ( 0.14 0.21

deviations are listed in Table 2. In all cases, the correlation coefficients were better than 0.999. Dimers, Trimers, and Tetramers. The initial structures of the thioalcohol dimers were obtained on the basis of the optimized structure of monomer 1 corresponding to the global minimum. The corresponding potential energy surfaces were built, and the conformational analysis was performed. Figure 3 illustrates the potential energy surface for the dimer of C16H33SH. It is seen that four minima can be distinguished at the potential energy surface. In the vicinity of these minima, additional total optimization of the geometric structure was


J. Phys. Chem. C, Vol. 111, No. 14, 2007 5377 The thermodynamic characteristics of clusterization were calculated according to the formulas

∆Hclm ) ∆H2980 - m∆H1 ) ∆S2980 - m∆S1 and ∆Gclm ) ∆Hclm - T∆Sclm

Figure 3. Potential energy surface for the C16H31SH dimer.

Figure 4. Dependence of the clusterization enthalpy on the alkyl chain length.

performed. The structures of four stable conformations of dimers are shown in Figure 2. It is seen that in three of these dimers an intermolecular hydrogen bond exists between the sulfur atom of the thiol group of one monomer and the hydrogen atom of the thiol group of the other monomer. Using the optimized structure of stable conformers of monomers and dimers as the basis, first the initial and then the optimized structures of trimers, tetramers, and more complicated clusters were determined. For these structures, the thermodynamic parameters of the formation were calculated. Table 3 summarizes standard enthalpies ∆Hclm, entropies ∆Sclm, and Gibbs energies ∆Gclm of the clusterization for dimers, trimers, and tetramers of n-thioalcohols (CnH2n+1SH) for n ) 6/16.

where ∆H1 and ∆S1 are the enthalpy and entropy of the corresponding monomer, ∆H2980 and ∆S2980 are the standard enthalpy and entropy of the formation of the corresponding clusters, and m is the number of monomers in the cluster. To calculate ∆Hclm and ∆Sclm, the thermodynamic characteristics of the monomers with the corresponding type of hydrogenhydrogen interactions were used. It should be noted that Table 3 does not list the thermodynamic characteristics for the tetramer that does not involve any intermolecular hydrogen bonds because the compounds of this series, being optimized, exhibit the tendency toward the formation of such bonds. This tendency could presumably be attributed to the instability of large clusters formed by entities with low alkyl chain lengths, bonded together by hydrogen-hydrogen interactions only. For the same reason, Table 3 does not list any data for trimers with alkyl chain lengths lower than nine carbon atoms, which do not possess hydrogen bonds. The dependencies of ∆Hclm, ∆Sclm, and ∆Gclm on the alkyl chain length were built. Similar to the cases of the long-chain n-alcohols and carboxylic acids, these dependencies are steplike. The correlation coefficients for ∆H dim exceed 0.996, whereas those for ∆S dim exceed 0.96. It should be noted that for all clusters considered the slopes are similar. Therefore, these correlations can be combined into a single one. It should be kept in mind, however, that the free terms of these correlations are different and depend on the mutual orientation, more precisely, on the interaction13 between the thiol groups in the cluster. For clusters with similar orientations of the SH groups, that is, dimer 1, trimer 1 and tetramer 1, or dimer 3 and trimer 2, the free terms in the correlation dependencies will be the same. Figure 4 shows the correlation dependencies of the clusterization enthalpy on the alkyl chain length for linear clusters with classic hydrogen bondings. The results of the corresponding direct calculations are presented by points. It is seen that the points coincide rather well with the corresponding step-like curves. The slopes are the same because the character of H-H interactions in these dimers is the same. Similar dependencies are also characteristic for clusterization entropies. The structure of the clusters is shown in Figure 5.

Figure 5. Structure of the pq cluster: (a) view from above; (b) view along p direction; (c) view along q direction.


Vysotsky et al.

TABLE 3: Standard Thermodynamic Characteristics of the Formation of Dimers, Trimers, and Tetramers of Thioalcohols Calculated by PM3 Parametrization molecule

∆Hmcl, kJ/mol

∆Smcl, J/mol‚K

∆Gmcl, kJ/mol

C6H13SH C7H15SH C8H17SH C9H19SH C10H21SH C11H23SH

-36.39 -38.48 -46.19 -48.40 -56.36 -58.19

-179.67 -180.32 -202.84 -199.65 -224.99 -218.38

17.15 15.26 14.26 11.10 10.69 6.89


-30.04 -32.00 -39.75 -42.02 -49.83 -54.82

-180.46 -183.67 -203.42 -206.81 -220.03 -236.43

23.74 22.74 20.87 19.61 15.74 15.63


-38.50 -40.61 -48.56 -50.93 -58.86 -61.31

-159.44 -165.98 -183.63 -190.03 -207.97 -213.51

9.02 8.86 6.16 5.70 3.11 2.31


-32.11 -33.98 -42.19 -44.35 -52.37 -57.29

-167.44 -178.60 -192.21 -201.32 -208.17 -222.24

17.78 19.24 15.09 15.64 9.67 8.94


-65.03 -68.48 -84.73 -88.70 -105.26 -113.11

-351.58 -363.10 -391.40 -409.90 -430.74 -446.34

39.74 39.72 31.91 33.45 23.10 19.90

C9H19SH C10H21SH C11H23SH C12H25SH

-81.63 -97.83 -106.19 -117.32

-380.67 -409.92 -421.45 -436.45

31.82 24.32 19.41 12.74


-97.46 -99.57 -125.90 -128.03 -154.39 -160.44

-433.23 -432.40 -481.83 -481.97 -528.49 -526.62

31.64 29.29 17.68 15.60 3.10 -3.51

C6H13SH C7H15SH C8H17SH C9H19SH C10H21SH

-95.85 -100.86 -126.33 -131.93 -152.54

-480.71 -510.15 -555.68 -580.17 -641.74

47.40 51.17 39.27 40.96 38.70


-119.65 -137.08 -160.68 -169.68 -202.04 -215.88

-572.49 -618.16 -637.12 -679.15 -727.33 -751.11

50.96 47.13 29.18 32.71 14.70 7.95

C6H13SH C7H15SH C8H17SH

-250.93 -274.66 -328.59

-1072.71 -1119.07 -1200.68

68.74 58.82 29.21

∆Hmcl, kJ/mol

∆Smcl, J/mol‚K

dimer 1 C12H25SH C13H27SH C14H29SH C15H31SH C16H33SH

-66.59 -69.10 -77.01 -79.44 -87.35

-241.79 -248.42 -266.08 -267.52 -284.14

5.46 4.93 2.29 0.28 -2.68


-60.14 -62.58 -70.46 -72.94 -80.86

-246.94 -251.45 -272.80 -271.32 -290.44

13.45 12.36 10.83 7.91 5.69


-69.23 -71.70 -79.22 -82.10 -89.56

-230.50 -234.65 -250.68 -252.90 -245.85

-0.54 -1.77 -4.52 -6.74 -16.30


-62.68 -65.10 -73.03 -75.50 -83.41

-230.46 -237.11 -249.85 -254.01 -265.75

6.00 5.56 1.42 0.19 -4.22

trimer 1 C12H25SH C13H27SH C14H29SH C15H31SH C16H33SH

-125.92 -129.89 -146.33 -150.58 -166.97

-468.96 -473.07 -502.83 -501.88 -534.05

13.83 11.09 3.51 -1.02 -7.82

trimer 2 C13H27SH C14H29SH C15H31SH C16H33SH

-123.08 -138.08 -143.88 -158.87

-465.26 -483.25 -505.07 -523.44

15.57 5.93 6.63 -2.89

trimer 3 C12H25SH C13H27SH C14H29SH C15H31SH C16H33SH

-182.92 -185.05 -211.36 -213.58 -239.89

-578.03 -571.25 -621.95 -612.17 -668.29

-10.66 -14.82 -26.02 -31.16 -40.74

tetramer 1 C11H23SH C12H25SH C13H27SH C14H29SH

-168.22 -187.86 -194.35 -218.95

-637.85 -668.40 -687.71 -721.16

21.86 11.33 10.59 -4.05

tetramer 2 C12H25SH C13H27SH C14H29SH C15H31SH C16H33SH

-243.47 -252.40 -285.10 -294.06 -325.94

-807.59 -824.75 -866.08 -878.13 -929.20

-2.81 -6.62 -27.00 -32.38 -49.04

hexamer 1 C9H19SH C10H21SH C16H33SH

-352.25 -406.27 -639.98

-1245.97 -1331.28 -1789.77

19.05 -9.54 -106.63

molecule

The clusters considered here involve at least four different types of interactions between the SH groups. The number of such interactions in the clusters is denoted as follows: nSH-SH

∆Gmcl, kJ/mol

is the number of classical hydrogen bonds in a cluster with sequential location of the SH bonds (dimer 4, trimer 1, tetramer 1); nS-S is the number of interactions between SH bonds located


J. Phys. Chem. C, Vol. 111, No. 14, 2007 5379

in parallel (dimer 3 and trimer 2); ntri is the number of hydrogen SH bonds for their relative location as in trimer 3; nlac is the number of lacunas formed due to the interaction of two trimer 3’s when combined into hexamer 1. Other types of interactions are also possible for different relative locations of the SH groups. However, only the interaction types listed above are essential for the description of large and infinite clusters. Each of these interaction types is characterized by its correlation parameter. For example, the correlation of standard enthalpy of clusterization on the number of corresponding interactions is

∆Hclm ) -(9.78 ( 0.10)ka - (4.35 ( 0.64)nSH-SH (3.05 ( 0.81)nS-S - (2.87 ( 0.67)ntri (R ) 0.9996, S ) 4.86 kJ/mol, n ) 78) (1) It is seen that the regression slope with respect to ka is close to that of the corresponding regressions for long-chain n-alcohols8-10 and n-carboxylic acids.11 Thus the H-H interaction parameters determined earlier for alcohols can also be used for the description of thermodynamic parameters of clusterization for other homologous series of long-chain amphiphilic compounds. Similar correlations are also valid for entropies:

∆Sclm)

-(17.75 ( 0.64)ka - (114.82 ( 3.94)nSH-SH (97.07 ( 4.98)nS-S - (86.31 ( 4.50)ntri (124.66 ( 21.78)nlac (R ) 0.998, S ) 29.58 J/(mol‚K), n ) 78) (2)

In this case, the regression slope for ka is almost the same as that found for n-alcohols (-18.4 ( 0.6 J/(mol‚K)).10-14 It should be noted that for thioalcohols the value of the standard deviation for the description of entropy is intermediate between those for n-alcohols (36.1 J/(mol‚K))8-10 and carboxylic acids (17.2 J/ (K‚mol)).11 Large and Infinite Clusters. It was noted above that the correlation slopes of enthalpy and entropy obtained for nalcohols are almost equal to those for thioalcohols. Therefore, it is possible to use the coefficients obtained for n-alcohols to construct the additive scheme of the thermodynamic characteristics for thioalcohols, similar to that in ref 13. In the present work, the thermodynamic parameters of large and infinite clusters, in particular, the clusters on the basis of the geometric structure of trimer 3, have been calculated using eqs 1 and 2. Figure 5 illustrates the structure of the linear cluster. Also, the notation used for its description is defined. It is seen that the clusters shown in Figure 5 involve SH-SH and S-S interactions and the a-type hydrogen-hydrogen bonds, see ref 12. From Figure 5, it is straightforward to determine the numbers of corresponding interactions:

ka ) [(p - 1)q + (q - 1)p]{n/2} nSH-SH ) (p - 1)q nS-S ) (q - 1)p

(3)

Here, similar to our earlier publication, the braces {...} denote the integer part of a number.12 Introducing these expressions into eqs 1 and 2, one can calculate the standard enthalpies and entropies of clusterization for any rectangular-shaped clusters, see Figure 5. To derive the expressions for infinite clusters, one should calculate the limiting values of ka, the numbers of classical

Figure 6. Dependence of the clusterization free energy on the alkyl chain length for rectangular clusters (pq).

hydrogen SH-SH bonds, and S-S interactions (SH bonds inthe cluster with their parallel alignment) per one monomer molecule for an infinite number of molecules in the cluster. Thus, for the linear infinite cluster shown in Figure 5 (p ) ∞, q ) 1) eq 3 becomes

ka∞ ) {n/2};

nSH-SH∞ ) 1;

nS-S∞ ) 0 (4)

Introducing these values into eqs 1 and 2, one obtains for infinite clusters the expression for the thermodynamic parameters of clusterization for one molecule. For example, for linear infinite cluster that involves classical hydrogen bonds (p ) ∞, q ) 1) eqs 1 and 2 become

∆Hcl∞/m ) -9.78{n/2} - 4.35 kJ/mol ∆Scl∞/m ) -17.75{n/2} - 114.82 J/(mol‚K)

(5)

For the two-dimensional infinite cluster shown in Figure 5, eq 3 becomes

ka∞ ) 2{n/2};

nSH-SH∞ ) 1;

nS-S∞ ) 1 (6)

which provide the expression for the free energy of clusterization:

∆Gcl∞/m ) -8.98{n/2} + 55.74 kJ/mol

(7)

Figure 6 illustrates the dependencies of the clusterization free energy for one molecule on the alkyl chain length for clusters shown in Figure 5. It is seen from Figure 6 that, similar to the thioalcohol dimers that involve both the classic hydrogen bonds and the S-S interactions, the clusters of higher dimension become stable for alkyl chain lengths of 14-15 and more. For n < 13, spontaneous clusterization is impossible in principle because the clusters, if formed, should decompose into monomers. It should be noted that thioalcohols are not only capable of forming infinite clusters shown in Figure 5 but they could also form large and infinite clusters on the basis of trimer 3. The geometrical structures of these compounds are shown in Figure 7 (view from above). It is seen from Figure 7 that, instead of SH-SH and S-S interactions, these clusters involve hydrogen SH bonds with their relative positions characteristic to trimer 3, the lacunas formed as the result of the interaction of two trimer 3’s due to the formation of hexamer 1, and the a-type hydrogen-hydrogen bonds. The number of


Vysotsky et al.

Figure 7. Geometric structures on the basis of trimer 3: (a) trimer 3; (b) hexamer 1; (c) the first layer of the infinite hexagonal cluster; (d) two internal layers of the infinite hexagonal cluster; (e)three internal layers of the infinite hexagonal cluster.

Figure 8. Dependence of the clusterization free energy on the alkyl chain length for clusters on the basis of trimer 3.

corresponding interactions can be determined easily from Figure 7

ka ) 6r{n/2} + 6r(3r - 1)n ntri ) 18r2 nlac ) 3(3r2- r)

(8)

where r is the number of layers. To determine the thermodynamic characteristics of clusterization to infinite clusters on the basis of trimer 3, the limits of corresponding values for the number of molecules in the cluster (m ) 18r 2) approaching infinity were calculated:

ka∞ ) n;

ntri∞ ) 1;

nlac∞ ) 0.5

(9)

Introducing these values into eqs 1 and 2, one obtains the dependencies of the enthalpy, entropy, and free energy of clusterization on the alkyl chain length, n:

∆Hcl∞/m ) -9.78n - 2.87 kJ/mol ∆Scl∞/m ) -17.75n - 148.64 J/(mol‚K) ∆Gcl∞/m ) -4.49n + 41.42 kJ/mol

(10)

The dependencies of the Gibbs energy of clusterization on the alkyl chain length are shown in Figure 8. It is seen that the spontaneous clusterization of structures that contain the triangular fragment becomes possible for alkyl chain lengths of 1213 carbon atoms and more. At this value of chain length, the formation of the trimer becomes possible. At the same time, it was noted above that the formation of dimers becomes thermodynamically favorable for n > 13. Because the probability of collision of three monomers (which is necessary for the direct formation of the trimer) is much lower than the probability of the collision of two monomers, it can be presumed

that clusterization of structures that contain the triangular fragment would commence, similar to the situation with rectangular clusters, for alkyl chain lengths of 14-15 and more. The dependencies shown in Figures 6 and 8 are step-like, similar to those found earlier for long-chain n-alcohols10 and carboxylic acids.13 Only for the infinite cluster on the basis of trimer 3, the dependence is linear, see Figure 8. This form of the dependencies is related to the fact that the free energy of clusterization is proportional to {n/2}, which results in the steplike character of the dependencies. However, for the clusters on the basis of trimer 3 it is seen from eqs 8-10 that a smooth transition from the step-like dependence to the linear one takes place as the number of molecules in the cluster approaches infinity. Conclusions In the framework of the semiempirical PM3 method, the thermodynamic parameters of the formation and the geometric structures of monomers, dimers, trimers, and tetramers of the homologous series of saturated n-thioalcohols are calculated. It is shown that the calculated values of formation enthalpies, standard entropies, and Gibbs energies for the formation of thioalcohols from elementary substances for the monomers agree well with the experimental data available. Therefore, this method can be applied for the description of the clusterization at the air/water interface. Similar to the long-chain n-alcohols and carboxylic acids studied earlier, the thermodynamic parameters of clusterization exhibit a step-like dependence on the alkyl chain length. It is shown that the slopes of the regressions calculated for the thioalcohols are rather similar to those obtained earlier for longchain n-alcohols and carboxylic acids. This fact can be regarded as an extra justification of the validity of the alcohol-based additive scheme for the calculation of the thermodynamic parameters of clusterization for other homologous series of unbranched amphiphiles. The additive scheme developed was used to calculate the thermodynamic parameters of a number of large and infinite clusters. It is shown that two-dimensional rectangular infinite clusters and clusters on the basis of trimer 3 are formed for alkyl chain lengths of 14-15 carbon atoms and more. This fact agrees with the scarce experimental data available7,8 and shows the potential prospects of systematic studies of thioalcohol monolayers. References and Notes (1) Rosen, M. J. Surfactants and Interfacial Phenomena; John Wiley & Sons: New York, 1978. (2) Schick, M. J. Nonionic Surfactants: Physical Chemistry, Surfactant Science Series 23; Marcel Dekker: New York, 1986.

2D Cluster Formation of n-Thioalcohols (3) Davies, J. T.; Rideal, E. K. Interfacial Phenomena; Academic Press: New York, 1963. (4) Organized Monolayers and Assemblies: Structure, Processes and Function; Mo¨bius, D., Miller, R., Eds.; Elsevier Science B. V.: Amsterdam, The Netherlands, 2002. (5) Kaplan, I. G. Theory of Molecular Interactions; Elsevier: Amsterdam, 1986. (6) Custelcean, R.; Jackson, J. E. Chem. ReV. B 2001, 101, 19631981. (7) Itaya, A.; Van der Auweraer, M.; De Schryver, F. C. Langmuir 1989, 5, 1123-1126. (8) Mingotaud, A.-F.; Mingotaud, C.; Patterson, L. K. Handbook of Monolayers; Academic Press: San Diego, CA, 1993; Vol. 1.

J. Phys. Chem. C, Vol. 111, No. 14, 2007 5381 (9) Vysotsky, Yu. B.; Bryantsev, V. S.; Fainerman, V. B.; Vollhardt, D.; Miller, R. J. Phys. Chem. B 2002, 106, 121-131. (10) Vysotsky, Yu. B.; Bryantsev, V. S.; Fainerman, V. B.; Vollhardt, D. J. Phys. Chem. B 2002, 106, 11285-11294. (11) Vysotsky, Yu. B.; Bryantsev, V. S.; Fainerman, V. B.; Vollhardt, D.; Miller, R. Colloids Surf., A 2002, 209, 1-14. (12) Vysotsky, Yu. B.; Bryantsev, V. S.; Fainerman, V. B.; Vollhardt, D.; Miller, R. Prog. Colloid Polym. Sci. 2002, 121, 72-75. (13) Vysotsky, Yu. B.; Muratov, D. V.; Boldyreva, F. L.; Fainerman, V. B.; Vollhardt, D.; Miller, R. J. Phys. Chem. B. 2006, 110, 4717-4730. (14) Daubert, T. E.; Danner, R. P.; Sibul, H. M.; Stebbins, C. C. Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation, Part 1 - Part 5; Taylor & Francis: PA, 1998.

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