REMARKS ON MOLECULAR STRUCTURE AND VAN DER WAALS F O R C E S EDWARD MACK, JR. Department of Chemistry, University of North Carolina, Chapel H i l l , North Carolina Received October 19, 19% I. STRUCTURE O F THE BENZENE RING
If we examine the structure of graphite as determined by x-ray analysis, and also the structure of crystals such as benzene, naphthalene, anthracene, diphenyl, etc., we are very much disturbed to find relatively large holes in the lattice. These empty spaces seem always to occur on both sides of the flat benzene ring. A chemist is naturally distinctly unhappy about this situation, because he would much prefer to have these empty places between the molecules and planes of molecules filled with pieces of impenetrable matter of some sort, and thus explain how it is that the structure is kept from collapsing to a more compact configuration. Assuming that such pieces or “bumps” of impenetrable matter do exist, one would like very much to know their size and shape. So in 1929-30, when I became interested in this question, I made a series of models, just as any other chemist would do, and tried to determine which one of the forms n-ould give the best explanation of the available data on the structure of crystals of aromatic compounds. Figure 1 shows how the conception developed. Models A and B were crude attemph to indicate the position of electron orbits perpendicular to the plane of the ring. Model C represented a crater-like elevation protruding above and below the ring, and was supposed to represent the impenetrable volume (in the additive sense of Kopp) of the oscillating double bonds (in the sense of Kekulk). Models D and E, with cone and dome, were supposed to take into account electron orbits across the ring (such as Pauling’s p-orbits). Of all of these forms, the “dome” model, E, was the most useful conception. K h e n it was mounted ( 5 ) over the hexagonal rings in the flat layers of graphite, and the “hard surface” of the impenetrable dome was arbitrarily assigned a radius of 1.84 A.U.: it was possible to account for the Presented a t the Symposium on Molecular Structure, held a t Princeton Vniversity, Princeton, New Jersey, December 31, 1936 t o January 2, 1937, under the auspices of the Division of Physical and Inorganic Chemistry of the American Chemical Society. 221
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EDWARD MACK, JR.
3.40 A.U. spacing between layer planes and for the type of superposition observed for the layers, and to give a satisfactory picture for the gliding of layers over one another. The dome of the benzene molecule was larger, as would be expected from its three-times larger electron content, arid had to be assigned a radius of 2.45 A.U. A further refinement in the picture of the dome in benzene is given in figure lF, showing regions of greater penetrability or of easier compression, around the base of the dome, between the carbon atoms. This feature appears in the molecule of tetraphenylmethane, as well as in the lattices of benzene, diphenyl, p-diphenylbenzene, and others. It is desired to emphasize particularly that the basis for this conception of the benzene ring dome was, and is, empirical. It is true that the quantum-mechanical calcdations in connection with benzene and other aromatic coinpounds by Huckel and especially by Pauling seem to support the idea. For instance, in a recent very beautiful paper, “The Diamagnetic Anisotropy of Aromatic illolecules,” Pauling (8) says : “The remaining six L electrons, which give to benzene its characteristic electronic structure
OH u’
A
B
C
D
E
F
FIG.1. Suggested shapes of space occupied by the “unsaturation” of the benzene ring
and properties, occupy orbital wave functions which are antisymmetric with respect to reflection in the plane of the nuclei. The probability distribution function for these electrons is large only in two ring-shaped regions, one above and one below the carbon hexagon. JJ7e may well expect that in these regions the potential function representing the interaction of a n electron with the nuclei and other electrons in the molecule would be approximately cylindrically symmetrical with respect to the hexagonal axis of the molecule, the electron, some distance above or below the plane of the nuclei, passing almost imperceptibly from the field of one carbon atom to that of the next.” This is support for the conception of some sort of organized electron cloud over the carbon hexagon, with a cylindrical and ring-like symmetry. Further, one does not have to suppose that the shape which such an impenetrable region presents to approaching neighbor molecules is exactly the same as the prolate ellipsoid of magnetic susceptibility found by Krishnan (2) and his collaborators. The fact that the calculations of Pauling (9) and Wheland in another paper show that 80 per cent of the resonance
MOLECULAR STRUCTURE AND VAX DER WAALS FORCES
223
energy of benzene comes from the Kekul6 structures alone, might be interpreted in itself as support for such a form as that of figure 1C; but the 20 per cent of the total resonance energy that comes from the three excited canonical structures with bonds across the ring suggests justification for capping or bridging the Kekul6 form to give an impenetrable dome, as in figure 1E. Khatever the final results of the quantum-mechanical calculations may be, it is probably true, as has been shown ( 5 ) in a previous paper, that the addition of such a dome to the ring or rings of the molecule involved is necessary and sufficient to account for the observed arrangement in the lattices of aromatic compounds, and to reproduce the unit cell dimen:'-1011s and space group. Recently I have been constructing models for many other crystals of this sort, but since it is practically impossible to describe adequately these complicated three-dimensional structures without three-dimensional representation, I prefer to exhibit these models at the Symposium, if there is time and opportunity. Once the usual habits followed by a few such molecules in establishing van der Waals contacts among themselves in the lattice have been clearly shown, it is not only likely that we can predict lattice structure without x-ray data, but also likely, when the number of hydrogen-to-hydrogen, hydrogen-to-dome, dome-to-dome contacts per molecule are counted, that we can assign proper values for van der Waals energies of separation to the various types of contact, and so construct on an additive basis a scheme for the explanation of heats of fusion and heats of sublimation and heats of solution, and also have the foundation for a prediction of solubility and of melting points. 11. FILMS AND SURFACE ENERGY
This conception of the size and shape of the benzene molecule gives us a satisfying explanation, as has already been shown ( 5 ) in a previous paper, of the surprisingly large area occupied by the phenol group (polar head) attached to a long, vertically oriented aliphatic chain, on a water surface. Figure 2 shows the setting. (The reader is looking down on the oil film.) The area, in the surface, occupied by the hydrocarbon chain is expected to be about 20 sq. A.C., but the benzene ring (OH group underneath, in the water) is found by Adam (1) and his collaborators to occupy an area of 24 sq. A.U. The arrangement shown is the closest possible pecking and involves the use of a dome and a hydrogen atom of exactly the same sizes as in the benzene crystal lattice. The area of the rectangular cell is 48 sq. A.U., and n i t h two molecules in the cell the predicted area of the phenol group is thus 23 sq. A.C. Langniuir (3) has pointed out that the hydrocarbons from hexane to
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EDWARD MACK, J R .
molten paraffin have substantially the same total surface energy, 46 to 48 ergs per cm.2, as do also the alcohols, inethyl alcohol, ethyl alcohol, etc., and has given as his reason for this “that the surface layer in both cases consists of CH3groups. With such substances as CH3N02,CH31,we find that the surface energy is much greater than that of the hydrocarbons. This is due to the fact that the volume of the I or the NOz js so great that the surface cannot be completely covered by the CH3radicals. The forcing apart of these groups increases the surface energy.’’ Now we are probably justified in supposing that the formation of this surface paved with methyl groups is equivalent to an evaporation of the methyl groups from the liquid, or in this case partial evaporation, since the methyl groups (probably spinning) are still in fairly good contact around their edges with surrounding methyl groups in the surface layer of hydrocarbons and alcohols; that is, the inethyl groups are only partially stripped
FIG.2. Suggested packing for polar heads (phenol groups) in oil film
of their van der Waals force contacts. From the data of heats of vaporization for the homologous straight-chain hydrocarbons it can readily be shown that the heat of vaporization for a mole of CH3a t room temperature is about 2000 cal. or 8.4 X 1O1O ergs, or about 14 X ergs for a n actual CH3group. There are approximately 5 X 1014methyl groups in 1 sq. cm. of such a surface (area of hydrocarbon chain section = about 20 sq. A.U.), and hence the surface energy would be about 70 ergs per cm.2if the methyl groups were in the completely evaporated condition. The fact that the surface energy is actually only 46 to 48 ergs per cm.2 may then be interpreted as a n indication that the methyl groups are, on the average, only about two-thirds evaporated. On the other hand, such liquid compounds as
p-chlorotoluene p-nitrotoluene
p-cresol
hfOLECULrlR STRCCTL-RE AiYD V A S DER WAALS FORCES
225
with niolecules “tilted up on edge” (to use Dr. Langmuir’s expression) and thuq oriented Jvith the methyl groups in the surface layer, show much larger surface energies, 67.3, 66.2, and 70.0 ergs per cm.*, respectively. It is not unlikely that t h e packing of the p-cresol molecules, for example, in the liquid surface resembles that of figure 2. If we modify the setting to the extent of substituting methyl groups (represented as heary circles) for the long hydrocarbon chains, we obtain figure 3. It will be seen that, eyen with the closest possible packing, the bulky domes of the benzene rings isolate the methyl groups from their neighbors, playing much the same r61e that Langmuir conceived for the I and KO2. In view of the extremely rapid decrease in intensity of r a n der TTaals forces with increasing distance (5th, 6th, or 7th power law), it may reasonably be supposed that the methyl groups are here practically completely stripped of van der Waals force contacts. Thus, from the calculation given in the preceding
DC
FIG.3. Suggested spacing for methyl groups in surface layer
paragraph, we would expect a surface energy of about 70 ergs per cm.2 (as actually observed for p-cresol) were it not for the smaller population of methyl groups per unit area. There are only about 4 X l O I 4 of these (as compared with about 5 X 1OI4 per cm.* in the case of the long-chain molecules), and the predicted surface energy for p-cresol would be about 4/5 X 70, or 56 ergs per cm.2 The difference between this and the observed 70 ergs per cm.2 is to be explained in terms of the slight stripping of van der JTaals contacts from the upper regions of the dome and from the two hydrogen atoms in ortho positions to the methyl group. Indeed, the relatively large surface energies of aromatic compounds of this general type, ranging from about 60 to about 90 ergs per depending on the nature and positions of the polar groups, can probably be satisfactorily accounted for by the isolation, in the surface layer, of the upper portions of the benzene molecules and the topmost group which it bears.
226
EDWARD MACK,
JR.
111. MELTING-POINT BEHAVIOR O F MOLECULES W I T H DOUBLE BONDS
Let us represent any typical organic molecule as a generalized brick-like form, figure 4. After a crystal lattice made up of such molecules has melted donm completely, it seems clear that the total heat of fusion divided by the total number of molecules, or the average heat of fusion per molecule, is necessarily the energy required to cause the molecule to break away from the van der Waals forces holding it rigidly in the lattice, around one-halj of the molecule’s mrfuce, namely a t the three faces, u , b, and c . This is triie no matter what the mechanism of the melting process may be. It is also probably true, furthmnore, that the melting does actually proceed in just this way, i.e., by a breaking away of every individual molecule a t its three faces, a, b, and c, first starting with the corner molecules in the crystal, and then proceeding regularly down the rows of molecules in the edges and faces of the crystal as new corners are produced. It is the exact identity of this repeated act of escape from the lattice that results in sharpness of melting point. ;\loreover, the escaping molecule must break away a!l a t once at its three faces (and not step-wise, first from a, then b, and finally c , as probably happens in the evaporation of a liquid molecule).
FIG.4. Brick-shaped molecule
There are some interesting instances, however, of a “step-wise” escape of a molecule from a crystal lattice, in a somewhat different sense. I n table 1 the melting point of stearic acid is given as 69.3”C. Inmeltingout of the lattice, this molecule escapes as a whole. But if a double bond is introduced, say between the sixth and seventh carbon atoms, as in A 6 ,‘-oleic acid, thus
C-C-C-C-C-C=C-C-C-C-C-C-C-C-C-C-C-COOH the situation becomes quite different. Around the double bond there is more room for rotation on bonds, and fewer van der Waals contacts t o hinder free rotation on bonds, than in a normal hydrocarbon section. As a result the chain is flexible on each side of the double bond, and the left-hand portion (strictly hydrocarbon portion) of the molecule melts off first, in a manner shown in figure 5, b or c. Then as the temperature continues to rise, the right-hand section, containing COOH, finally melts, when it has acquired sufficient kinetic energy to break the much larger van der Waals forces holding it rigidly in the lattice. Such a picture explains almost perfectly the observed melting points in H more table 1. In the case of substance 2 (A6ji-oleic acid), the C ~ H or
MOLECULAR STRUCTURE AKD VAN DER WAALS FORCES
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227
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EDWARD MACK, J R .
probably the CSHI1CH=C 5ection melts off firit, probably a t a temperature corresponding roughly to that of hexane or heptane, and then the H(CH2)l~COOHsection melts at a temperature of 33-34"C., corresponding closely t o the melting point 28.3"C. for undecoic acid (substance 7 in the table). Similarly, Ag~lo-oleic acid melt:, a t about 16'C., checking the nielting point of caprylic acid, 16.5"C.; and A12m13-oleicacid is a liquid a t room temperature, a5 one would cxpect from the fact that valeric acid melt? a t - 20°C. RIoleculc,q with two double bonds, like linoleic acid, would melt in three sections, and those with three double bonds, like linolenic, would melt in four sections. Furthermore, in these latter cases, we may expect that the melting point of the acid section will be much lower than usual because of the relatively violent kinetic disturbance to which the acid section would be subjected by the rest of the molecule, in the liquid phase. This theory of melting-point behavior in molecules containing double bonds was suggested to me by one of my former students, Dr. Sherman E. Smith, and it i:, presented here with his permission. The theory can readily be extended to give a very satisfying explanation of these curious
0
(=C-(->COOH,
aCOOH,
a.
HHFY-)COOH
b
C
FIG.5 . Step-nise melting of molecule
melting points, not only for other acids, but for the chain hydro carbons themselves, and for certain aromatic molecules, and probably for all molecules possessing regions of marked flexibility. It would be extremely interesting t o test this theory, for example in the case of the oleic acids, by using the technique of Raman (10) and Ramdas for examining the quality of the light scattered from a reflecting surface. By selecting the proper crystal face, allowing a beam of sunlight to fall upon it, and gradually warming up the crystal from low temperature, one could determine whether the surface does in fact become minutely "roughened" at a definite temperature somewhat above the normal melting point of the more fusible section of the molecule. This temperature would be somewhat above the normal melting point because the surface would be appreciably roughened only when the sections of the molecules were lifted out all over the face of the crystal rather than merely at the corners. IV. EXTERNAL AXD I N T E R S A L VAN D E R WAALS FORCES
3Iuch study has been made of what may be called external van der Waals forces between O ~ niolecule P and a neighbor molecule, but apparently little
229
MOLECULAR STRUCTURE AXD VAK DER WAALS FORCES
attention has been devoted to the play of similar internal force? among the atoms and groups of an individual molecule. h'evertheless this effect often is of great importance in controlling both physical and chemical properties. One consequence of it, which might be of interest and which ha. never been referred to before, as far as I know., is in connection with the heat of combustion. When, for example, hydrocarbon molecules are burned in oxygen, the carbon and hydrogen atoms must not only be separated from TABLE 2 Heats of combustion ( A H ) at R5OC. f o r gaseous hydrocarbons SUBSTANCE
INCREASE IN
AH
FORXOL.4
CH2
FOR
AH
calorrer
hlethane . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ethane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Propane , . . . . . . . . . . . . . . . . . . . . . . . , . . .
- 212,790
,
160,020 -372.810 157,760
~
-530.570
n-Butane . . . . . . . . . . , . . . . . . . . . . . . . . . .
-687:940
n-Pentane . . . . . . . . . . . . . . . . . . , . . . . . . . .
- 845.270
' ~
157,370 157,330 157,130
n-Hexane . . . . . . . . . . . . . . . . . . . . . . . . . . .
- 1.002,400
n-Heptane . . . . . . . . . . . . . . . . . . . . . . . . . .
- 1.159,400
%-Octane... . . . . . . . . . . . . . . . . . . . . . . . . , '
- 1,316,400
n-Konane.. . . . . . . . . . . . . . , . . . . . . . . . , . '
-1,173,400
n-Decane , . . . . . . . . . . . . . . . . , , , . , . , . , ,
-1.630.400
n-Undecane . . . , . . . . . . . . . . . . . , . . . , . . .
- 1,787,400
n-Dodecane . . . . . . . . . . . . . . . . . . . . . . . . . .
-1,944,400
157 000 ~
157,000 157,000 157,000
157,000 157,000
one another along their chemical bonds, but the hydrogen atoms m w t be also separated against internal van der TTaals forces, although the energy consumed in doing this would, of course, be small in comparison with the bond energies. Table 2 lists Roqsini's (11) latest published values for the heats of combustion of some straight-chain hydrocarbons (gaseous). It will be noted that the increase in AH per CH2 beconies constant after hexane. This we might well expect, since once the gaseous molecule has become long enough to be coiled into a complete loop, the number of van der Kaals internal contacts established by eyery further CH2 group would
23 0
E D W A R D MACK, J R .
be the same. Furthermore, it is readily to be seen, with the aid of a scaled three-dimensional model, that the improvement in internal contacting between hydrogen atoms beconies progressively less per CH,, beginning with methane and ending with hexane. Consequently, the energy required to rupture all such van der Waals contacts (about 400 cal. in the case of hydrogen-to-hydrogen) should most certainly be taken into account in the calculation of energies of formation and of bondenergies for these and other molecules. That such straight-chain molecules are actually folded up, or coiled up, in the gaseous state can hardly be doubted. Langmuir (4) has predicted a globular or droplet-molecule from a consideration of the tendency to reduce surface energy to a minimum in the molecule’s own surface, and one arrives at the same conclusion by adopting the procedure we are employing here, naniely by counting the much larger number of hydrogen-to-hydrogen contacts that can be made in the coiled form as compared x-ith the extended molecule. It has also been ihown by calculation of the collision areas (7) of the gaseous molecule> of n-heptane, n-octane, and n-nonane (from viscosity data) that the niolecules are coiled. ‘In the liquid state, however, the situation i. quite different. Therp, in contrast to the vapor state, the external van der Waals contacts must he reckoned with. I t can be demonstrated that the sum total of internal and external van der Kaals contacts (between hydrogen atoms) is much better with extended than with coiled molecules, mainly because of the better packing of the extended forms. On such a priori grounds, a t least, we have every reason to believe that these molecules spend most of their lives extended to full length. R e know, of course, that this is true in the crystalline state, and what little pertinent x-ray evidence there is for liquid hydrocarbons suggests also the extended shape. The argument is north following through into a t least one other setting, namely in a system of randomly arranged macro-length chain molecules, as in the substance rubber. Here the external forces would play a relatively uniniportarit r81e because of the criss-crossing, and because of the hindrances to adjustment of position that are imposed by the entanglement of the thread-like molecules. If the structure is such that internal forces can come into play and can implement foldings, by bond rotation, between groups favorably placed at regular intervals along the chain, then v-e would expect the appearance of the wrious types of elastic behavior (6) shown by rubber-like substances. REFEREXCES (1) A D ~ Mh:o c . lioy. s o c . London 103A, 676 (1923); A D . q BERRY, IND TAYLOR: Proc. Roy Soc. London 117A,3 2 (1928). (2) KRISHSIN:References cited by Pauliiig (8). (3) L A N G M U I R : Chem. >let. EIlg. 16, 169 (1916).
MOLECULAR STRUCTURE ABD TAT DER W A A L S FORCES
23 1
(4) LASGMUIR:Alexander’s Colloid Chemistry, Vol. I, pp. 523-45. The Chemical Catalog Co., Inc., New York (1926). (5) MACK:J. Am. Chem. Soc. 64,2141 (1932). (6) MACK:J. Am. Chem. SOC.66, 2757 (1934). (7) MELAVESA N D MACK:J. Am. Chem. SOC.64, 888 (1932). (8) PAULING: J. Chem. Physics 4,673 (1936). (9) PAULIXG AND ITHELAND: J. Chem. Physics 1,362 (1933). (IO) RAMAN A N D R.~MD.~s: Proc. Roy. Soc. London 108A,561 (1925) and later papers. (11) ROSSINI:Bur. Standards J. Research 13, 21 (1934).
