Most stable configurations of polynuclear aromatic hydrocarbon molecules in pitches via molecular modelling

Carbon. Vol. 30, No. 7, pp. 1033-1040. Printed in Great Britain.

1992 Copyright

ooO8-6223192 $5.00 + .OO 0 1992 Pergamon Press Ltd.

MOST STABLE CONFIGURATIONS OF POLYNUCLEAR AROMATIC HYDROCARBON MOLECULES IN PITCHES VIA MOLECULAR MODELLING E. R. VORPAGELand J. G. LAWN Du Pont Fibers, Pioneering Research Laboratory, Experimental Station Wilmington, DE 19880-0302, U.S.A. (Received 27 January 1992; accepted in revisedform 23 March 1992)

Abstract-Molecular mechanics calculations were performed on a series of polynuclear aromatic hydrocarbon molecules in various geometric arrangements and combinations. Homologous aromatic hydrocarbons associate strongly face-to-face, in a parallel shifted stack arrangement with a displacement of about 4.7 A. Heteromerous aromatic hydrocarbons also prefer a shifted stack configuration oftwo or three molecules high. A third or fourth molecule added to a stack will prefer to orient perpendicular to the stack such that its face is against the edge of the stack. Methyl groups act to encourage stacking interactions between dissimilar aromatic hydrocarbons with the methyl groups preferring to be inside the stack and thus, having a minimal effect on edge-to-edge interactions between stacks. These results support the colloidal model for the behavior of pitches. Key Words-Mesophase

pitch, basic structural units, molecular modelling, molecular mechanics.

1. INTRODUCTION

In their pioneering work[ 11, Brooks and Taylor established that mesophase droplets formed within a pitch; discotic molecules were associated face-to-face with their edges to the surface of the droplet. Coalescence of the droplets led to formation of larger regions of extended order with a generally lamellar arrangement of the pitch molecules. Oberlin[2-51 identified the presence of basic structural units (BSU) in pitches; these consisted of small stacks of molecules less than 10 A in diameter. As the pitches are converted into graphite, the stacks become much longer, and exhibit a characteristic misorientation of & 30”. Recently Lafdi et al. have proposed that colloidal suspensions provide a better model for pitch behavior, and that the dominant association between molecules is edge-to-edge[6,7]. Advances in molecular modelling techniques and the speed of modern computers have made it possible to computationally investigate the preferred configurations for model compounds similar to pitch molecules. A molecular mechanics formalism similar to that used to calculate benzene dimer and benzene crystal was chosen for the analysis. Fortunately crystal structures are known for some molecules germane to those typically found in pitches, and will be referenced when appropriate. Table 1 shows the set of aromatic hydrocarbons used in this study: coronene, ovalene, and dodecacoronene representing the strictly peri-condensed molecules typically found in coal-tar pitches; anthracene, dibenzochrysene, and tetrabenzoovalene representing the cata-condensed molecules typically found in petroleum pitches. For reference, the diameter of the circular coronene molecule, measured between hydrogen atom nuclei, is 9.5 A. Similarly, ovalene is 9.2 A wide and 11.6 A long; dibenzochrysene is 7.1 A wide and 10.4 A long. The larger mole1033

ecules included in this study, tetrabenzoovalene (MW 546.64) and dodecabenzocoronene (MW 666.74) approach the 800 to 900 average molecular weight of fiber-forming mesophase pitches[ 111.

2. COMPUTATIONAL

METHODS

Molecular mechanics calculations were performed on a CAChe@ Worksystem[8] which implements Allinger’s standard MM2 force field[9]. In this

formalism, molecules are modelled using a ball and spring approximation for atoms and bonds, respectively. The force field includes bond stretching, angle bending, angle torsions, and nonbonded van der Waals terms. Electrostatic terms were not included in the original MM2 force field for aromatic hydrocarbons. Studies have shown[ IO] that nonbonded van der Waals potentials alone do not correctly account for the energetics of the benzene dimer, and electrostatic interactions between molecules are necessary to get the proper crystal geometryl[ 121 for benzene. Allinger[ 131 recommends the use of bond moments for the (&-H (0.6 Debye) and Csp~-Cspj (0.9 Debye) bonds with the sp2 carbon as the negative end of the dipole. Pettersson and Liljefors[ lo] recommend a charge of -0.15 on the sp2 carbon and +O. 15 on the attached hydrogen atom. If the bond length for an C&-H bond is 1.082 A, then this would be equivalent to a bond moment of 0.78 Debye. When a bond moment of 0.8 Debye was used in the CAChe@ Worksystem implementation of MM2, we could not reproduce the results of Pettersson et al.; a bond moment of 1.O Debye was necessary. This is most likely due to the way the CAChe@ Worksystem handles the electrostatic terms; the bond moments are converted to atomic charges and then handled as charge-charge interactions rather than as dipole-dipole interac-

1034

E. R. VORPAGELand J. G. LAWN Table 1. Aromatic hydrocarbons used in this study

Structure

Name and molecular formula Benzene

Mol. wt. (g/moJ)

wt. % carbon

wt. % hydrogen

78.11

92.26

7.74

178.23

94.34

5.66

276.35

95.62

4.38

300.37

95.97

4.03

398.46

96.46

3.54

546.64

96.68

3.32

666.74

97.28

2.72

C6Hs

Anthracene Cr4f-f~ Dibenzochrysene C&12

Coronene C24H12

Ovalene C32Hl4

Tetrabenzoovalene C42H16

Dodecabenzocoronene C54H18

Thus, electrostatic terms were added to the force field with bond moments of 1.O Debye for the C,,2-H bond and 1.3 Debye for the C,,,2-CsP3bond. All CsP2-CsP2and C&-H bonds had no dipole moments, consistent with the standard MM2 force field. All geometries were optimized using a conjugate gradient technique to a convergence of less than 0.0002 Kcal/mol for the energy and less than 0.06 Kcal/mol. A average gradient. This convergence criterion was the sole method used to determine when the structures were optimized. Second derivatives of the forces on the atoms with respect to energy were not calculated to determine whether the optimized structure was a true minimum or just a saddle point on the potential energy surface. Indeed, the edge-toedge configurations may all be saddle points and not true minima. They were included in this study for their heuristic value when making comparisons with other geometric arrangements. Intermolecular interaction energies were calculated by subtracting the sum of the optimized individual molecules from the total energy calculated for the particular configuration of interacting molecules involved in the cluster. Thus, they are relative to the molecules at infinite separation. Atoms in figures are displayed at 90% of their van der Waals radius. tions.

tion (IV). Small modifications to the perpendicular or coplanar configurations like V or VI do not significantly change the relative interaction energies and will not be mentioned again. Table 2 shows the results of molecular mechanics optimized structures of homologous dimers of the aromatic hydrocarbons in Table 1. The interaction energy (Kcal/mol) for each dimer is given relative to the molecules at infinite separation. Dimers of molecules with a smaller number of rings prefer a perpendicular configuration over the face-to-face. However, molecules with more than six rings prefer face-to-face in-

3. RESULTS There are numerous ways to orient two molecules like benzene in space. Pettersson and Liljefors[ lo]

described six. Larger aromatic hydrocarbons of different symmetries have even more geometrical arrangements. For the purpose of this paper, only four geometric arrangements (configurations) will be considered for the various molecules of interest. These are shown for benzene in Fig. 1 as the parallel stacked, or “face-to-face” configuration (I), the perpendicular or “T-shaped” configuration (II), the coplanar or “edge-to-edge” configuration (III), and the shifted parallel stacked or “shifted stack” configura-

IV Fig. 1. Optimized

V

VI geometric arrangements dimer.

of benzene

Configurations of molecules in pitches

1035

Table 2. Interaction energies (Kcal/mol) for four configurations of homologous aromatic hydrocarbon dimers relative to the molecules at infinite separation Hydrocarbon Benzene Anthracene Dibenzochrysene Coronene Ovalene Tetrabenzoovalene Dodecabenzocoronene

Face-to-face -0.6 -3.5 -7.8 -9.2 - 14.2 -21.8 -29.8

teractions over perpendicular. The edge-to-edge configuration is the least favored geometric arrangement while, with the exception ofbenzene, the shifted stack configuration is preferred overall. Calculated shifts between dimers range from 4.5 to 4.8 A, depending on the molecular shape. Coronene trimers were studied to test the molecular mechanics force field, to see if small clusters of molecules would lead to the stacking found in crystal structures. Figure 2 shows optimized configurations for three coronene trimers: a shifted stack (VII), a face-to-face arrangement with the center molecule shifted (VIII), and a shifted stack dimer with the third molecule perpendicular (IX). Their intermolecular interaction energies are -23.0, -21.8, and -22.3 Kcal/mol, respectively. The shifted stack arrangement found in the coronene crystal structure[ 141 is also predicted to be the best coronene trimer configuration, thus lending credence to the force field used in this study. Since pitches are composed of many different molecules, several combinations of aromatic hydrocarbons were studied to determine the preferred geo-

Shifted stack

Perpendicular

-2.9 -8.2 - Il.4 - 11.2 - 16.8 -26.2 -33.0

-3.0 -1.9 -8.4 -6.1 -8.7 - 12.5 -8.9

-0.4 -0.7 -0.5 -0.2 -0.3 -0.5 -0.1

metrical arrangements. Table 3 shows the interaction energies (KcaI/mol) of selected heteromerous (consisting of parts that differ) dimers in either the shifted stack or perpendicular configuration. Two configurations are possible for the perpendicular orientation depending on which molecule is at the trunk of the T. Figure 3 shows the computer-generated structures for coronene-ovalene (X, XI, XII) and coronene-dibenzochrysene (XIII, XIV, XV). Figure 4 shows four geometric arrangements of coronene-methylcoronene: two shifted stack configurations, one with the methyl group projecting away from the adjacent molecule (XVI) and the other with the methyl group interacting with the face of the adjacent molecule configurations (XVII), and two perpendicular (XVIII, XIX). Figure 5 shows three geometric ar-

XII Fig. 2. Optimized geometric arrangements for three configurations of coronene trimers: Shifted stack (VII), center displaced face-to-face (VIII), and shifted stack dimer with perpendicular (IX).

Edge-to-edge

XV

Fig. 3. Optimized geometric arrangements for selected heteromerous dimers of coronene-ovalene and coronene-dibenzochrysene.

1036

E.R. VORPAGEL andJ.G.

LAWN

Table 3. Interaction energies (Kcal/mol) for selected heteromerous aromatic hydrocarbon dimers relative to the molecules at infinite separation Shifted stack

Hydrocarbon Coronene-Dibenzochrysene Coronene-Ovalene Coronene-MethylCoronene Ovalene-MethylCoronene

-

Perpendicular (other C-H)

10.5 (XIII) 13.3 (X) 12.3 t(XVI1) 11.4 $(XVI) 14.3 T(XX)

Perpendicular (Coronene C-H)

- 8.0 (XIV) -8.3 (XI) -6.1 (XVIII)

-6.6 (XV) -6.7 (XII) -6.1 (XIX)

-8.3 (XXI)

-6.7 (XXII)

tMethyl group contacting adjacent ring (compare to - 11.2Kcal/mol for coronene dimer). *Methyl group projecting away from adjacent ring. (Configuration references in parentheses refer to Figs. 3,4, and 5.)

rangements of ovalene-methylcoronene (XX, XXI, XXII). Again a shifted stack configuration is preferred over a perpendicular arrangement. Trimers of coronene and ovalene can be arranged in several different ways. Figure 6 shows four geometric arrangements of two coronene molecules with one ovalene: a shifted stack with ovalene in the center (XXIII), a shifted stack with ovalene on one face (XXIV), a face-to-face arrangement with ovalene in the center, shifted (XXV), and a shifted stack dimer with ovalene perpendicular (XXVI). Figure 7 shows three geometric arrangements of two ovalene molecules with one coronene: a shifted stack with coronene on one face (XXVII), a face-to-face arrangement with coronene in the center, shifted (XXVIII), and a shifted stack dimer with the coronene perpendicular (XXIX). Their intermolecular interaction energies (Kcal/mol) are shown in Table 4. Preferred

configurations become a much more complex issue and will be discussed below. A few tetramers were also investigated to probe the nature of larger clusters. Figure 8 shows the optimized configurations of shifted stack coronene trimer with either perpendicular (XXX, XxX1, XxX11) or parallel stacked (XxX111, XXXIV, XXXV) geometric arrangements of ovalene, dibenzochrysene, and 6methyldibenzochrysene, respectively. Their intermolecular interaction energies (KcaI/mol) are shown in Table 5. Preferred geometrical arrangements become a matter of how many and what type of intermolecular interaction is present. To investigate the effect of alkyl substituents on aromatic hydrocarbon stacking, a series of geometrical arrangements of methylcoronene with either two coronene or two ovalene shifted stacks were calculated. Figure 9 shows four geometric arrangements with coronene: a shifted stack with methylcoronene in the center (XXXVI), a shifted stack with methyl-

Fig. 4. Optimized geometric arrangements of heteromerous dimers of coronene-methylcoronene.

Fig. 5. Optimized geometric of heteromer. ^ . arrangements . ous dimers ofovalene-methylcoronene.

1037

Configurations of molecules in pitches

Table 4. Interaction energies (Kcal/mol) for selected trimers of coronene and ovalene relative to the molecules at infinite seoaration Hydrocarbon cluster description

XXIV

Shifted stack coronene dimer: Ovalene center Shifted stack coronene dimer: Ovalene face Face-to-face coronene dimer: Ovalene center Shifted stack coronene dimer: Ovalene perpendicular Shifted stack ovalene dimer: Coronene face Face-to-face ovalene dimer: Coronene center Shifted stack ovalene dimer: Coronene perpendicular

Relative energy -28.2 (XXIII) -25.5 (XXIV) -27.4 (XXV) -23.6 (XXVI) -3I.o(xxvII) -26.2 (XXVIII) -31.7 (XXIX)

(Configuration references in parentheses refer to Figs. 6 and 7.)

xxv

XXVI

Fig. 6. Optimized geometric arrangements of selected trimers containing one ovalene and two coronene molecules.

on one face (XXXVII), a face-to-face arrangement with methylcoronene in the center, shifted (XXXVIII), and a shifted stack dimer with methylcoronene perpendicular (XxX1X). Figure 10 shows four geometric arrangements with ovalene: a face-to-face arrangement with methylcoronene in the

coronene

center, shifted, and the methyl group outside the stack (XL), a shifted stack with methylcoronene on one face (XLI), a face-to-face arrangement with methylcoronene in the center, shifted, and the methyl group inside the stack (XLII), and a shifted stack dimer with methylcoronene perpendicular (XLIII). Their intermolecular interaction energies (Kcal/mol) are shown in Table 6.

XXXIV

Fig. 7. Optimized geometric arrangements of selected trimers containing one coronene and two ovalene molecules.

-

Fig. 8. Optimized geometric arrangements of coronene trimer and single molecules of either ovalene, dibenzochrysene, or 6-methyldibenzochrysene.

E. R. VORPAGEL and J. G. LAVIN

1038

Table 5. Interaction energies (Kcal/mol) for trimers of coronene with selected heteromerous aromatic hydrocarbons relative to the molecules at infinite seoaration Hydrocarbon cluster description Ovalene perpendicular Ovalene face Dibenzochrysene perpendicular Dibenzochrysene face 6-Methyldibenzochrysene perpendicular 6-Methvldibenzochrvsene face

Relative energy - 38.6 -37.4 -36. I -34.0 -29.7

(XXX) (XXXIII) (XxX1) (XXXIV) (XxX11)

- 28.5 (XXXV)

(Configuration references in parentheses refer to Fig. 8.)

4. DISCUSSION

In general, the preferred interaction between homologous polynuclear aromatic hydrocarbons is that of parallel shifted stack, analogous to P-graphitelike crystal packing[ 141. This preferred geometrical arrangement is seen in coronene[ IS] and ovalene[ 161 crystal structures: the molecules are shifted by 4.70 A forming long columns of stacked molecules with an interplanar spacing of 3.46 A. These columns line up in parallel with their edges forming either a series of perpendicular or shifted coplanar interactions between adjacent columns (see Fig. 11). These preferred interactions are rather well reproduced with the molecular mechanics force field. Molecular shifts and interplanar spacings calculated for shifted stack dimers

Fig. 10. Optimized geometric arrangements of selected trimers containing one methylcoronene and two ovalene molecules.

and trimers are within 0.1 A of the values measured in crystal structures. For smaller hydrocarbons like benzene and anthracene, the intraplanar spacing in the shifted stack configuration is about 3.0 A. For larger hydrocarbons, intraplanar spacing in the shifted stack configuration is about 3.38 k 0.02 A. This compares well with the intraplanar spacing in graphite (experimen-

Table 6. Interaction energies (Kcal/mol) for selected trimers of methylcoronene with either ovalene or coronene relative to the molecules at infinite separation Hydrocarbon cluster description

XXXVIII

XXXIX

Fig. 9. Optimized geometric arrangements of selected trimers containing one methylcoronene and two coronene molecules.

Shifted stack coronene dimer: Methylcoronene center Shifted stack coronene dimer: Methylcoronene face Face-to-face coronene dimer: Methylcoronene center Shifted stack coronene dimer: Methylcoronene perpendicular Face-to-face ovalene dimer: Methylcoronene center out Shifted stack ovalene dimer: Methylcoronene face Face-to-face ovalene dimer: Methylcoronene center in Shifted stack ovalene dimer: Methylcoronene perpendicular

Relative energy -24.2 (XXXVI) -24.2 (XXXVII) -23.9 (XXXVIII) -22.5 (XxX1X) - 26.6 (XL) - 32.0 (XLI) -28.1 (XLII) -32.7 (XLIII)

(Configuration references in parentheses refer to Figs. 9 and 10.)

Configurations of

B Fig. I I. Coronene crystal structure: (A) interaction between four stacks, (B) perpendicular interactions between two stacks, (C) shifted coplanar interactions between stacks.

tal 3.354 A). Larger values for interlayer spacing found in other forms of graphitized carbon most likely result from an averaging of imperfections not present in this study of model compounds. In the perpendicular configurations, the distance between nearest hydrogen atoms in one hydrocarbon and the ring plane of the other hydrocarbon remained relatively constant at 2.56 * 0.03 A. In the edge-to-edge configurations, the nearest hydrogen atoms remained a constant 2.60 5 0.02 A apart. Dimers between different molecules show the same preference for a shifted stack configuration. The primary driving force behind the shifted stack arrangement is electrostatic in nature. The C-H bonds have a dipole moment associated with them (vide ir?f;a) and this tends to dictate the best geometrical arrangement. The lowest energy interaction has all the dipole moments arranged in the most favorable way. Table 3 reveals the nature of the perpendicular configuration: the stabilization energy for the perpendicular arrangements is proportional to the number of C-H bonds interacting with the plane ofthe other aromatic hydrocarbon. This is similar to the herringbone packing found in crystal structure with the molecular centroids shifted. This is very useful when trying to unravel the interaction energies between trimers and tetramers. For example, Fig. 2 shows three configurations for coronene trimer. We can understand the intermolecular interaction energies for these trimers by summing up the interaction energies for the dimers found in Table 2. A single shifted stack dimer is worth 11.2 Kcal/mol while a perpendicular dimer is worth 6.1 Kcal/mol. Thus, configurations

molecules

in pitches

1039

VII and VIII would each be expected to have a net interaction energy of -22.4 Kcal/mol while the perpendicular configuration (IX) with one shifted stack and two perpendicular interactions would have a total of - 23.4 Kcal/mol. These values are not exactly correct because they do not take into account all the interactions between stacks nor the fact that the perpendicular interaction energy is less when the region of interaction is near the circumference of the molecule. The additive nature of the intermolecular interactions can be used to understand the configurational preferences for the trimers between ovalene and coronene (Table 4). The preferred geometric arrangement between one ovalene and two coronene molecules is to have the ovalene in between the coronene molecules in a shifted stack configuration (XXIII in Fig. 6). A perpendicular ovalene (XXVI) has the least interaction energy. From Table 3, a single shifted stack dimer between ovalene and coronene is worth 13.3 Kcal/mol while a perpendicular dimer is worth 6.7 Kcal/mol. Thus the interaction energies for these two molecules can be approximated as -26.6 and -24.6 Kcal/mol, respectively (see Table 4): the right order. However, the preferred geometric arrangement between one coronene and two ovalene molecules has the coronene arranged perpendicular to the ovalene stack! Again the interaction energies can be approximated from the dimers to give the correct relative order. A similar explanation can be made for the relative interaction energies for tetramers listed in Table 5. When one of the aromatic hydrocarbons has a methyl substituent, configurations where the methyl group can interact with the face of an adjacent molecule become more stable relative to the unsubstituted hydrocarbon. The perpendicular interactions are not affected (assuming steric hindrance is avoided) and little effect is seen when the methyl group is outside the stack. This can be demonstrated by comparing dimers in Tables 2 and 3. Shifted stack coronene-methylcoronene dimer, with the methyl group inside the stack, has 1.1 Kcal/mol greater stabilization energy than coronene dimer. The perpendicular configurations have the same relative interaction energies. Likewise for ovalene-coronene and ovalene-methylcoronene dimers, 1.O Kcal/mol greater stabilization energy for the shifted stack configuration is observed. This increase in interaction energy is also seen in the trimers and tetramers. Methyl groups strengthen the shifted stack interaction between dissimilar aromatic hydrocarbons and have little effect on the perpendicular configurations. The molecules which make up pitches are far less regular and have a much greater size distribution than the model compounds considered here. However, their behavior in some respects can be understood by the model compounds. The observation that the larger aromatic hydrocarbons readily form shifted stacks of two or three high is explained by the great stability of the face-to-face association modified

1040

E. R. VORPAGELand J. G. LAVIN

by the dipolar nature of the C,-H bond.The preferred association of an additional molecule perpendicular to the stacked molecules supports the colloidal model proposed by Lafdi et a1.[6,7], although the existence of optical anisotropy in mesophase pitches must still be explained. Finally, the preferred “shifted stack” arrangement of the large molecules may help explain the misorientation of large stacks during graphitization. 5. CONCLUSION Homologous polynuclear aromatic hydrocarbon molecules associate strongly face-to-face, in a parallel shifted stack arrangement with a displacement of about 4.7 A. In the crystal, stacks of molecules associate edge-to-edge. Heteromerous polynuclear aromatic hydrocarbon molecules also prefer a shifted stack configuration of two or three molecules high. A third or fourth molecule added to a stack will prefer to orient perpendicular to the stack such that its face is against the edge of the stack. Methyl groups act to encourage stacking interactions between dissimilar aromatic hydrocarbons with the methyl groups preferring to be inside the stack and thus having a minimal effect on edge-to-edge interactions between stacks. These results support the colloidal model for the behavior of pitches.

Acknowledgement--The authors wish to acknowledge stimulating discussions on this topic with Dr. Agnes Oberlin.

REFERENCES J. D. Brooks and G. H. Taylor, Carbon 3, 185 (1965).

: : A. Oberlin. J. L. Boulmier. and B. Durand. Geochimica

et Cosmochimica Acta 38,‘641(1974). 3. D. Auguie et al., Carbon 18,337 (1979). 4. A. Oberlin and M. Oberlin, J. ofMicroscopy 132, 353 (1983). 5. J. N. Rouzaud and A. Oberlin, Carbon 27,5 17 (1989). 6. K. Lafdi, S. Bonnamy, and A. Oberlin, Carbon B,6 17 (1990). I. K. Lafdi, S. Bonnamy, and A. Oberlin, Carbon 29,83 1 (1991). 8. Available from CAChe Scientific (A Tektronix Comnanv). P.O. Box 500. Beverton. OR. 9. N. L.‘Allinger, J. Am. Chem. ioc. 99,8127 (1977). 10. I. Pettersson and T. Liljefors, J. Camp. Chem. 8, 1139 (1987). 11. U.S. Patent 4,209,500. 12. D. E. Williams, Acta Cryst. A30,7 1 (1974). 13. N. L. Allinger and J-H. Lii, J. Comp. Chem. 8, I 146 (1987). 14. J.A.R.P. Sarma and G. R. Desiraju, Act. Chem. Rex 19,222 (1986). 15. J. K. Fawcett and J. Trotter, Proc. Roy. Sot. London, Ser. A 289,366 (1965). 16. R. G. Haze11and G. S. Pawley, Z. Kristallogr. 137, 159 (1973).