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I N D U S T R I A L A X D ENGINEERISG CHE-VIISTRY
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Dipole Moments’ Charles P. Smyth PRINCETOS UNIVERSITY, PRISCETON, N. J .
While the analysis of spectra makes possible the calculation of energy levels and, in simple cases, the distribution of mass in molecules, and x-ray analysis has been used mainly to show the grouping of atoms, molecules, or ions in solids, the measurement of dipole moments shows the distribution of electricity and, indirectly, the arrangement of the atoms in molecules. These measurements also provide a new and effective tool for the study of the many problems arising from the interaction of dipole forces. A group of atoms in a molecule. may be regarded as forming a dipole consisting of a positive charge and a negative charge of electricity very close together. The size of the dipole is measured by its electric moment, which is obtained from measurements of dielectric constant and is a vector. When two of these vectors of known size are placed in a molecule, the resultant moment may be used to calculate the angle between them, which gives
information concerning the arrangement of the atoms and their valence forces in the molecule. The molecules of benzene, diphenyl, and naphthalene are thus shown to consist of flat rings. When two dipoles in the same molecule are movable, the resultant moment may vary with temperature, providing a qualitative means of investigating the internal energy of the molecule. Isomers may sometimes be distinguished from one another by the differences between their moments. The orientation of dipole molecules relative to one another affects the apparent moment obtained from dielectric constant measurements so t h a t a means is provided of studying molecular orientation or association. Dipole molecules in a crystalline solid are found t o t u r n slowly in a n alternating electric field, showing a similarity between a crystalline solid and a very viscous liquid. The energy used in turning the molecule may be a n important factor in the power loss and the breakdown of insulators.
T IS a familiar fact that matter is made up of positive
moment p as in Figure 1 ( b ) . In this way, he obtained the expression for the polarization P:
I
and negative electricity. Studies of solutions and of electrical discharge in gases showed the independent existence of both positively and negatively charged atoms and molecules, which were termed “ions.” Less than twenty years ago x-rays showed that many crystalline substances, such as sodium chloride, are made up of positive and negative ions rather than of neutral molecules. However, sodium chloride vapor consists of molecules, each containing a positive sodium ion and a negative chloride ion. Because of the presence of these two mutually neutralizing charges, a molecule of this type was called “polar” and, in present parlance, it would also be spoken of as a dipole molecule. The molecule of a hydrocarbon, such as benzene or hexane, was supposed to contain no such definitely separated charges and was spoken of as non-polar. However, between these extremes lie substances which exhibit different degrees of polarity, the degree assigned depending upon the qualitative method employed in estimating it and often upon the attitude of the investigator. Debye’s introduction ( 2 ) of the idea of permanent dipoles into the theory of dielectrics not only made possible the quantitative representation of the variation of dielectric constant with temperature, but, what was far more important, led to a new means of feeling inside of the molecule and, in particular, of quantitatively determining its polarity. The relation of the dielectric constant of a substance to temperature and density had previously been explained by assuming the induction of a dipole in each molecule when it was placed in an electric field as shown in Figure 1 (a). As shown in this diagram, each molecule acquires a negative charge on the side toward the positive plate and an equal positive charge on the side toward the negative plate. The molecule may thus be regarded as forming an electric doublet or dipole. The magnitude of the dipole is measured by its electric moment, which is the product of either of the two equal charges by the distance between them. As this conception of the induced dipole was only partially successful in explaining the facts, Debye was led to assume that each molecule might contain a permanent dipole of 1
Received August 20, 1931
in which
e
=
dielectric constant
AM = molecular weight
d = density -V = number of molecules i n a gram-molecule = y
k T
6.06 x 1023 molecular polarizability, that is, the moment induced in a molecule by a field of unit strength = molecular gas constant = 1.372 X = absolute temperature =
Because of the permanent dipoles the molecules tend t o orient in the applied field with their axes in the direction of the field [Figure 1 ( b ) ] ,but this orientation is opposed by the thermal agitation of the molecules, which, of course, varies with the temperature so that the polarization is a function of the temperature. Obviously, when the molecules are not entirely free to orient in an applied field, the equation cannot be expected to apply. I n liquids the molecules are so close together that large doublets attract one another strongly, forming complexes or, a t least, restricting one another’s freedom of motion. If, however, the dipoles are sufficiently separated from one another by molecules without moments, such as those of benzene or heptane, they should behave much as in the gaseous condition. When, therefore, the dielectric constant and the density of a substance are measured a t different temperatures in the gaseous condition, or the determinations are carried out a t several concentrations in dilute solution and the polarizations calculated are extrapolated to infinite dilution, the results obtained should conform to Equation 1. As the molecular polarizability and the permanent moment are constants, b / T , showing that the Equation 1 may be written, P = a polarization should be a linear function of 1/T, or P T plotted against T should be a straight line. This has been found to be true for gases and for the polarizations of liquids calculated from measurements in dilute solution, as shown in Figure 2. The slope of each straight line is a and the vertical intercept b, from which the moment may be calculated.
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ISDUSTRIAL A N D ENGINEERING CHEMISTRY
November, 1931
The vertical intercept for hexane is zero; that is, the molecule has no moment. As the value of a is commonly not far from that of the molar refraction of the substance, the approximate value of b/T, and hence of the moment, is most often obtained by subtracting the molar refraction from the polarization. It is thus possible to determine the electric moment of the molecule of a substance by measuring the dielectric constant and density over a range of temperature in the gaseous condition or in dilute solutions in a nonpolar solvent, or by measuring a t one temperature only and subtracting the molar refraction from the polarization.
" 0 0 0 oo
(0)
Fiaure 1-Molecules
i b) of a Dielectric
Relation of Electric Moment to Molecular Structure
The relation of this electric moment t o the structure of the molecule will now be examined. The argon atom is supposed to consist of a positive nucleus with eighteen elertrons distributed about it. If this distribution is symmetrical, the center of gravity of the system of electrons is coincident with that of the positive nucleus, and the atom, therefore, has no permanent electric moment, which is found experimentally t o be the case. The chloride ion is supposed to resemble the argon atom in the number and arrangement of its electrons, but the nucleus has only seventeen instead of eighteen positive charges. If the center of gravity of the electrons lies in the positive nucleus, the system of charges may, as an approximation, be resolved into a single negative charge, 4.771 X 10-'8 e. s. u., located a t the nucleus. If, now, a hydrogen nucleus could, without distortion of the system, be attached to form a neutral hydrogen chloride molecule, a permanent dipole should be formed. The moment of this dipole would be the product of the single electronic charge by the distance between the nuclei, which is calculated from infra-red spectra (1) as 1.27 X 10-8 cm.; that is, p = 4.774 X 10-'0 X 1.27 X 10-8 = 6.06 X 10-'8 e. s. u. This is far larger than the value 1.03 X lo-'* obtained by application of the Debye equation to measurements of the dielectric constant of gaseous hydrogen chloride, because the positive hydrogen nucleus draws the electrons of the chloride ion toward it, thus greatly diminishing the length of the dipole into which the system of charges has been resolved. Present knowledge of atomic structure is not yet sufficient to permit of the precise calculation of this attraction, but, from the polarizability of the molecule ( I I ) , it is possible to calculate that the distortion is of the right magnitude to account for the difference between the value of the moment calculated from the molecular structure and that obtained from experimental data. The axis of the dipole will evidently lie on the imaginary line joining the hydrogen to the chlorine nucleus. Dipoles and Structure of Aromatic Compounds
BENZENES-The dipole is a particularly effective tool in the study of the structure of aromatic compounds. The benzene molecule is found to have approximately zero mo. ment; that is, it is electrically symmetrical. The replace-
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ment of a hydrogen by a chlorine atom to form chlorobenzene destroys the symmetry and gives rise to an electric moment of 1.52 x 10-'8 e. s. u. This moment is due mainly to a dipole which should have its axis in the imaginary line between the chlorine nucleus and that of the benzene carbon to which the latter is joined. I n other words, it marks the direction of the external valence of the benzene carbon. If a second dipole is introduced into the molecule by the substitution of another chlorine, the moment of the molecule is the resultant of two moments, 1.52 X lo-'* each, and depends, evidently, upon the angle between these moments. The angle between these two vectors may thus be calculated. It was shown some years ago (13) that, of the commonly discussed formulas for benzene, only the flat hexagon of KekulB would give angles between the dipoles corresponding to the observed resultant moments. This regular hexagon would, of course, give an angle of 60" between the dipoles in o-dichlorobenzene, as shown in Figure 3, 120" between their axes in m-dichlorobenzene, and 180" in p-dichlorobenzene. In Table I are shown the observed values in romparison with those calculated on the basis of these angles between the two moments of 1.52 X each. Table I-Moments
(X
1018)
COXPOUND
of Disubstituted Benzenes, Naphthalenes, and Diphenyls OBSD CALCD. 2.25 2.63 1.48 1.52 0 6 03 3.76 0 0
::;:!
0 5,l 0
Figure 2 - P -
0 6 ih 3 9 0
i!, 2 1 86 0
4.5 0
T-T Curves for Ethyl Bromide, Chlorobenzene, Chloroform, and Hexane
The values of the nitro compounds shown in Table I resemble those of the chloro in the agreement between observed and calculated. The observed values for the nieta and para oompounds are close to the calculated, while the observed values for the ortho compounds are distinctly lower than the calculated. This discrepancy was originally attributed to the effect of repulsion between the two groups attached in the ortho position. Such repulsion would widen the angle between the two dipoles and thus reduce the resultant moment. I n the case of o-dichlorobenzene, the angle between the dipoles would have to be widened from 60" to nearly 90" in order to account for the difference between
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 23, No. 11
the observed and calculated values. I n the light of present knowledge of the dimensions of the molecule and of the atoms involved, i t now seems improbable that the mutual repulsion of the chlorines could cause so great a widening of the angle. Smallwood and Herzfeld (9), by a necessarily arbitrary method, have recently calculated the lowering of the moment of each dipole by the inductive effect of the other as well as the inductive action of the dipole upon the rest of the molecule. This effect of induction can be made to account satisfactorily for the considerable differences between the observed and calculated moments of the ortho tom-
as in the corresponding para-disubstituted benzenes. Any bending of the bond between the two rings would give a finite resultant moment to the molecule. The 2,2'-substituted compounds show a behavior typical of many molecules. If the two rings lay in the same plane and the two substituents were on the same side of the m o l e cule to give a cis-form, the moment should be the same &s that calculated for the corresponding ortho-disubstituted benzene. If, on the other hand, the substituents lay on opposite sides to give a trans-form, their dipoles should o p pose one another and give zero moment. Such relations have been found for the acetylene dihalides, in which the double bond fixes the two halves of the molecule relative to one another so that the trans-form is found to have zero moment and the cis-form a large moment. However, in the 2,2'-disubstituted diphenyls the two halves of the molecule are free to rotate around the single C-C bond joining them, so that the value of the resultant moment may lie anywhere between that for the &-arrangement and zero. Williams (24) has developed an expression for the mean effective moment of molecules of the type of ethylene dichloride, in which two dipoles are rotating relative to one another. Unfortunately, the equation does not apply satisfactorily to these small molecules because of the close proximity of the dipoles to one another, but it does give good results in the case of the 2,2'-disubstituted diphenyls. The expression for the resultant moment is p = 1.41 m sin 8, in which m is the moment of each of the two individual dipoles and 8 is the angle which the axis of the dipole makes with the 4,4' line-in this case, 60". The agreement between the observed and calculated values in Table I is all that could be expected.
pounds and the small differences found in the case of the meta compounds, I n this way, close agreement has been obtained between the observed and calculated moments of a large number of disubstituted benzenes. Even the first few dipole determinations on substituted benzenes led to the belief in a plane hexagonal structure for the benzene molecule a t a time when x-ray measurements were interpreted as indicating a puckered ring. It is interesting to note that recent x-ray studies (4, 5 ) point to the plane hexagonal ring as correct. NAPHTHALENES-The extension of the dipole method to the study of more complex ring structures is shown in Table I. The approximately zero moment found for the naphthalene molecule indicates a symmetrical structure. If it consists, as represented in Figure 4, of two plane hexagons sharing an edge, the substituted naphthalenes can be treated in the same way as the benzenes. It is evident, then, that like dipoles in the 1 and 5 positions should oppose and cancel one another, giving zero moment as found in 1,bdinitronaphthalene; in the 1 and 8 positions they should point in the same direction, so that the resultant moment should be double that of a-nitronaphthalene, which is 3.6 X This calculated value, 7.2 X agrees well with the observed. These results thus conform to a plane hexagon for each half of the molecule, and unpublished results for molecules with substituents in the 2, 3, 6, and 7 positions agree with this and further indicate that the two hexagons lie in the same plane. DIPHmYLs-since the results indicate that the benzene ring is a plane hexagon with the external valences lying in the plane, the two rings in diphenyl should lie as shown in the diagram, with the possibility of the rotation of either ring about the line joining the 4 and 4' positions. That there is no bending of the rings out of this line is shown by the zero moments of the 4,4'-dichloro- and 4,4'-dinitrodiphenyl, in which the doublets oppose and cancel one another
Variation of Moment with Temperature
In the ethylene dihalides, the dipoles are so close together that there is a considerable potential energy between them. As this energy is a minimum when the dipoles are as far away from one another as possible, the positions in which the dipoles are on opposite sides of the molecule and opposing one another are more probable. The moments observed for these compounds are, therefore, considerably lower than the calculated. Meyer (6) has calculated that increase in the energy of rotation within the molecule should overcome the effect of this mutual potential energy of the doublets and should tend to make all positions of rotation equally probable. This would cause an increase in moment with rising temperature, which has been observed by Meyer for ethylene chloride and confirmed in the present author's laboratories for the chloride, the bromide, and the chlorobromide, a 100' C. rise in temperature causing an increase in moment of about 30 per cent. The temperatures used for these substances have not been sufficiently high to permit of approach to the limiting values of the moments, which are all that the simple equation can give. However, by lengthening the carbon chain between the halogen dipoles and so reducing their mutual potential energies it has been possible to reach the limiting value calculated by the equation for the dibromide. Thus the dipole provides a t least a qualitative means of investigating the internal energies of certain types of molecules. Dipole Moments as a Measure of Polarity
It has been seen how, by putting dipoles a t different points in molecules, the spatial arrangement of the atoms and of the valences joining them can be observed. The moment may be regarded as a quantitative measure of the polarity of the molecule as a whole, but it is not always possible to determine the polarity of a single bond. I n simple
November, 1931
INDUSTRIAL A N D ENGINEERING CHEMISTRY
cases where this can be done, the polarity corresponds but very roughly to that deduced from chemical behavior. For example, it has not been possible to correlate the small differences in moment observed among n-butyl, tert-butyl, and triphenylmethyl chlorides and alcohols with the great differences in chemical behavior (12). It is evident that many of the supposed differences in polarity which have been regarded by some organic chemists as determining factors in chemical behavior are too small to be detected by means of electric moments. One cannot but wonder if these very minute polarities have real physical significance and are not merely convenient means for systematizing present knowledge. Possibly the dipole moment is too blunt a tool to penetrate their intricacies. Identification by Determination of Moment Since it is now understood how the moment of a molecule depends upon the positions of its groups relative to one another, the determination of moment may sometimes be used as a method of analysis. Thus, the moment will often tell the location of groups in an aromatic compound or will distinguish between’ cis- and trans-forms ( 7 ) . However, its use is certainly not to be advocated as a general method of analysis, for its interpretation is difficult in the case of complex compounds and more easily obtainable physical constants are usually to be had for simple substances. Orientation of Dipole Molecules Just as the positions of dipoles in the same molecule relative to one another affect the resultant moment of the molecule, so the orientations of dipole molecules relative i to one another affect the apparent moments calculated for the molecules. If the dipole molecules are sufficiently close together to bring about this mutual orientation, the effect is apparent in the polarization as previously stated, thus providing a m e a n s for the study of molecular orientation or association. The change of polarization and, hence, of association with change of concentration in solution or in the v a p o r s t a t e can be followed. It is thus possible to determine not only the e x t e n t of the intermoFigure 4-Structures of Disubsti- l e c u l a r action, as in the tuted Compounds case of f r e e z i n g - p o i n t I-Benzenes I I-Naph thalenes measurements, but also 111-Diphenyls the amroximate directions in which the molecules must orient relative to one another. It has thus been shown that there are a t least two types of association occurring in the alcohols. Dipoles in Solids and in Insulators
If dipole molecules are rigidly fixed in the solid state, they are unable to orient in an externally applied field, and the dipoles, therefore, make no contribution to the polarization. This means a sharp drop in the dielectric constant of a polar liquid upon solidification. Thus, the dielectric constant of water is ordinarily reported as about 80 and that of ice as about 3. However, Errera (3) has found that, when
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the dielectric constant is measured with a very slowly alternating field a t temperatures just below the melting point, the dielectric constant of the crystalline solid is but’ little lower than that of the liquid, a result which has been confirmed in the present author’s laboratory. This means that molecules in the solid can turn as in the liquid, though more slowly. As the temperature is lowered, or as the frequency of the alternating current is increased, the dielectric constant decreases until it no longer contains any contribution from the dipoles. I n the absence of dipoles the dielectric constant shows little variation with temperature and frequency. The long rod-like molecules of heptyl bromide show no variation of dielectric constant with temperature and frequency. It would appear that they are so packed in the solid that they cannot turn over, while smaller, more compact molecules can turn. These investigations are being continued. Dipole studies thus give information concerning the solid state. They indicate a certain similarity between a crystalline solid and a very viscous liquid, in which the dielectric constant varies with temperature and frequency, that is, shows anomalous dispersion. This anomalous dispersion involves the absorption of energy and consequent heating of the material. It appears, in this way, to play an important part in the power loss and the possible breakdown of commercial insulating materials. Certainly the dielectric properties of these materials are greatly influenced by the polar character of their molecules. As the commercial insulating materials which have been extensively investigated are mixtures of complex and variable composition, the application of dipole theory to the important phenomena involved in insulation is in a primitive state, but the electrical engineer is beginning to take cognizance of the dipole. Conclusion
It has been shown how the observed electric moments of molecules follow logically from considerations of atomic and molecular structure, and a few typical examples have been used to illustrate the value of the moment in giving information concerning molecular structure. At a time when the physicist maintained that valence forces were not localized or directed, electric moments indicated the contrary and gave rough information concerning the angles a t which valences acted. It is interesting to note that the most recent calculations with wave mechanics concerning valences (8) are in accord with these indications of the dipole moments, which are now being employed in further investigations of valence angles. The dipole moment is thus seen as a new tool to be used by the physical chemist in his investigations of the structure of matter and of the problems of molecular forces and energies, by the organic chemist in his studies of structure and the resulting chemical behavior, and by the industrial chemist in the development of commercial insulation. [For a detailed treatment of the subject matter of this Daner . . reference (IO).] Literature Cited Czernr, 2. Phrsik, 45, 476 (1927). Debye, Physik. 2.. 13, 97 (1912). Errera. J . fihys. radium, [a] 6 , 304 (1924). Hendricks. Chem. Rn’icws. 1, 431 (1930). Lonsrlale. Proc. Roy. SOC.(London), 1438, 494 (1929). Meyer, 2. Chysik. Chem., BE, 27 (19301. Miiller and Seck. PhysiR. 2.. 31, 815 (1930). Pailling, J . Am. Chem. Soc., 53, 1367 (1931). Smallwood and Herzfeld, Ibid., 62, 1919 (1930). Smyth. “Dielectric Constant and Molecular Structure.” Catalog, h‘ew York. 1931. Smyth. Phil. Mag.,11, 530 (1924). Smyth and Dornte, J. A m . Chem. Soc., 53, 545 (1931). Smyth and Morgan, Ibid., ID, 1030 (1927). Williams, 2. Physik. Chem., A138, 75 (1828).
Chemicsli
