0
MODELS ILLUSTRATING THE PRINCIPLES OF OPTICAL ACTIVITY CARL R. NOLLER Stanford University, California
T o PARAPHRASE a statement credited to Prof. T. M. Lowry,' the real theory of optical rotatory power is revealed to the mathematician, but is concealed from the chemist. Nevertheless it seems desirable that the chemist should have some concept of the nature of optical rotation if only to satisfy his ego. The writer has tried to obtain a physical picture of the phenomena involved and has constructed a series of models to illustrate them. The present paper is an attempt to transmit to teachers of organic chemistry, as painlessly as possible, any insight that he has acquired, so that they in turn may be able to impart it to the average may be caused by longitudinal vibrations or transverse student. The author realizes that his knowledge is vibrations. In a longitudinal vibration such as a sound superficial, but hopes that any shortcomings of the wave, the vibrations are parallel to the direction of present article will stimulate some better qualified per- propagation and are symmetrical around the direction son to present the true picture in words of one syllable of propagation. In a transverse vibration, such as an .ocean wave, the vibrations are perpendicular to the and without mathematical equations. Three general types of theory currently are discussed, direction of propagation, and there is a lack of symnamely, the coupled oscillator theories of Born and of metry. Ordinary light does not show a lack of symKuhn, the polarizability theory of Kirkwood, and the metry, but it can be converted into a wave lacking one-electron or single oscillator theory of Kauzmann; symmetry by polarization. Hence ordinary light must Walter, and Eyring.= All of these theories have been be a transverse vibration in all planes perpendicular to expressed in terms of quantum mechanics, but the the direction of propagation. According to Maxwell's electromagnetic theory of coupled oscillator theories can be explained by classical light, there are two vector quantities associated with a mechanics. Perhaps because of this circumstance the writer is of the opinion that the coupled oscillator theory ray of light, the electric induction and the magnetic inof Kuhn is most capable of providing a physical picture duction. They are mutually perpendicular, and both are perpendicular t ? the direction of propagation of the of the phenomenon. Before discussing optical activity, it will be desirable light. Atoms consist of negative electrons and positive to review some of the properties of light. Wave motion nuclei, and if light is electromagnetic in character, it would he expected to react with them. S i c e for diamagnetic substances the magnetic permeability differs 'BORN,M., Pmc.Roy. Soc. ( L a d a ) , [A]130, 86 (1935). from 1 by the effect of the magnetic vector of a For an extensive review and biblioeraohv see W. J. KAUZMANN, J. E. WALTER,AWD H. EYRING, Chem. Rev., 26, light may be disregarded and the whole effectattributed 339-407 (1940). to the eiectric vector. This electric field will cause a relative di~~lacement'of the negative and positive particles of the atonis mith the production of dipoles. Since the electric vector of the light is vibrating, it will start vibrations in the dipole which will reemit the absorbed energy. If the frequency of the light is the same as that of the particle, the energy of the light will be converted completely into heat, and the spectrum of the particle will show an absorption band a t this frequency. If, however, the frequency of the light is diierent from that of the induced vibration, the particle will r e b i t light of a different frequency; that is, the light will be scattered, The diqpinution in energy of the incident lieht caused bv the scatterine slows ddwn the lieht rav. ", causing refrarkon. The v e k y of light in any mari.I ' ~ o u b h~ ~ f m o t i obyn terial medium is equal to the velocit~in a vacuum dicd~it.
-
603
-
Model 1
vided by the refractive index. The ease with which the electrons are dis~lacedfrom the nucleus is known as the polarizability of'the atbm. The polarizabiiity will be greater, the greater the number of valence electrons and the farther away they are from the nucleus. Hence the atomic refractions increase in the order hydrogen < carbon < chlorine < bromine < iodine. Because of the greater mobility of electrons in a double bond than in a single bond, the refractivity of the double bond is the greiter. Although light is vibrating in all planes perpendicular to the direction of propagation, each of the electric vectors may be considered to be the resultant of two components a t right angles t o each other. When light passes through any crystal, except one belonging to the cubic system, in any direction, except that of the optic axis, the velocity of the component of light vibrating in one plane is different from the velocity of the component vibrating in the other plane. The result is double refraction and the separation of the light into its two components. I n the case of crystals belonging to the hexagonal or tetragonal system one component is refracted even when the incidence of the light is perpendicular to the face of the crystal, and is known as the extraordinary ray because it does not obey the ordinary laws of refraction. The other component obeys the laws of refraction and is known as the ordinary ray. Double refraction of a calcite crystal is illustrated diagrammatically in Fig. 1. The operation of the Nicol prism, the. common device used to separate these'two rays and produce plane polarized light, is too well known to need review here. The propagation of plane polarized light may be
represented by Fig. 2 which shows the instantaneous magnitude of the electric vectors throughout a given distance. The behavior of the vectors during propagation of the wave may be visualized by moving the boundary of the sine wave along the direction of propagation. Each electric vector maintains a fixed position and direction, but varies continuously in magnitude from zero t o +l t o zero to - 1to zero. Model 1represents two sine waves of equal amplitude a t right angles to each other, but the wave in the horizontal plane is 90" out of phase with that in the vertical plane. The resultant of the two plane waves, obtained by adding the vectors a t all points along the axis of the ray, is a left-handed spiral lookmg toward the source of the light, and represents the propagation of circularly polarized light. If the spiral is moved without rotation in the direction of propagation of light, the electric vectors of the circularly polarized beam will not change in amplitude, but will rotate in a clockwise or right-handed direction. If the sine wave in the horizontal plane had been out of phase with that in the vertical plane by 90° in the opposite direction, the spiral would have turned clockwise and the resultant electric vectors of the circularly polarized ray would have rotated in a connterclockwise direction. Model 2 illustrates what happens when d and 1 circularly polarized rays travel in phase with the same velocity. By omitting the spirals, one can see that the sine waves in the horizontal plane cancel each other while those in the vertical plane reinforce each other. Hence the resultant is a plane polarized wave of twice the amplitude of the circularly polarized waves. To snm-
602
JOURNAL OF CHEMICAL EDUCATION
marize, circularly polarized light may be considered to consist of two components of plane polarized light a t right angles to each other and 90° out of phase, while plane polarized light may be considered to consist of two waves of circularly polarized light thatare in phase but of the opposite sign. Fresnel was the fint to postulate that the rotation of plane polarized light in passing through an optically active medium is due to circular double refraction; that is, one circularly polarized component of the plane polarized wave travels slower than the other. Since the velocity of light is equal to the frequency times the wave length, and since the frequency always remains constant, a decrease in velocity requires a decrease in wave length. This decrease in wave length of the retarded circularly polarized wave has been greatly exagerated in Model 3 where it has just half the wave length of the faster circularly polarized beam. If all the components of the waves in Model 3 are added vectorially, Model 4 is obtained. It can be seen that it is a plane polarized wave that is continuously rotated as it passes throueh the medium. It is of interest that. usine the D line of sodium, the difference in refractive index for d and 1 circularly polarized light in the case of a compound having a specific rotation of 100" is about 3 X lo-'. The refractive index for the D line of ordinary light for most liquids is 1.3 to 1.7, that is, the difference from the refractive index in vacuum is 0.3 to 0.7. Hence optical activity is the result of an optical disturbance that is less than one hundred thousandth of that causing ordinary refraction. Granting that the rotation of the plane of polarization of plane polarized light is caused by the fact that
-
Model 3
Model 4
one of its circularly polarized components is retarded more .than the other, the important question to the chemist is why a molecule whose mirror image is not superimposable will cause a differencein velocity of the d and 1 circularly polarized components. For simplicity we may consider the behavior of a molecule having a single asymmetric carbon atom (Figure 3). The vibrations of the electrons in an atom or group excited by the plane polarized light would set up induced vibrations of electrons in the other atoms or arouws - . of the atoms. While the vibrations in the molecule as a whole would be quite complex, the behavior can be visualized readily if we assume that the vectors of the induced vibrations of any two groups will be parallel with the line joining the centers of the groups. Hence the resultant R , of the vibrations of one pair will be perpendicular to the resultant R, of the other pair and separated by a distance Z, as illustrated in Figure 3. Kuhn has pointed out that this behavior is that of two oscillators, A and B, separated by a distance, Z, whose vibrations are at right angles to each other, and which are coupled in such a way that any vibrations set up in
DECEMBER, 1047
603
quirement for optical activity is that two like molecules cannot be orientable in such a way that they are mirror images of each other or in other words that the mirror image of a molecule cannot be superimposable. CONSTRUCTION OF MODELS
The sine waves were constructed by bending 3/32 in. brass or copper-plated iron welding rod into loops of the proper shape and size, and soldering them to a brass rod in. in diameter and 25 in. long. The loops of the basic sine waves were 6 in. wide aC the base and 4 in. high. For the resultant plane polarized wave of Model 2, they were 6 in. wide and 8 in. high. For the retarded wave of Model 3, they were 3 in. wide and 4 in. high. Holes were bored in the horizontal supporting rods a t the proper place and angle to facilitate placing and soldering the loops. The spirals of Models 1and 5 were bent to the proper shape and afExed after the supporting loops or rods were in place. Vectors were added t o two of the loops of Model 1 t o demonstrate more clearly that the spiral was the resultant of the two plane waves. Model 4 was constructed in an entirely different manner. Forty-eight brass sleeves, '/z in. long, 3/s in. Firu.. 4. Mechanism of Model 3 external diameter, and %6 in. internal diameter, were bored and threaded through one side wall at the center one will induce simultaneous. vibrations in the other. so that a 3/3z-in.threaded brass rod could be screwed Model 5 illustrates how this system can lead to optical perpendicularly into the sleeve. The sleeves were activity. The action of the model may be clearer if strung on a a/a-in. brass rod threaded a t both ends. considered along with the diagram shown in Figure 4. Nuts on the ends held the sleeves loosely in place. The electric vector of either d or 1 circularly polarized light sets up an oscillation in A, and the energy of the vector of the d or 1 wave is diminished by the vector quantity a, or a,, thus slowing down or refracting the wave. The oscillation of A, however, produces a simultaneous oscillation in B, the energy of this oscillation being designated by the vector a', or a', which is at right angles to ad or a,. At the same time, however, oscillator B is being acted on by the electric vectors d' or 1' which, because of the time lag caused by the distance Z , are out of phase with the vectors d or 1 by 90°, if Z is chosen equal to one-quarter wave length. Moreover, the direction of vector 1' will be opposed to that of vector d'. The vector quantities corresponding t o the action of d' or 1' on B will be b,' orb;. The coupled vector a'& or a', will be added t o the vector b,' t o give the resultant vector r, but will be subtracted from vector b,' t o give the resultant vector r,. Therefore the d circularly polarizes component will be slowed down t o a greater extent (rJ than the d component (r,), and the plane of the plane polarized light will be rotated to the left. In Model 5 and Figure 4 the distance, Z, was chosen as one quarter wave length merely t o show more readily the effects of the vectors on each other. This distance is several thousand times larger. than that between coupled oscillators in a molecule, but the effect will be the same. If two atoms or groups are alike, the random orientation of the molecules will provide each molecule with a mirror image so that any rotatory effects of the individual molecules would-cancel. Therefore the only reModel 5
v8
-
604
Threaded 8/32-in. brass rods of the proper length were screwed into the sleeves, adjusted to the proper angle, and the sleeve set to the center bar by tightening the rod. A single full lobe of the curve requires one rod 8 in. long, and two rods each 7a/8, 5s/8, and 3 in. long. Each base of the lobe will end a t a l/z-in. sleeve without a rod where the curve passes through zero. The length of the rods and the angle of each was determined originally by taking the vector sum of all of the components of Model 3 a t half-inch intervals along the horizontal rod. It is believed that in constructing a similar model it: would be sufficientto set the central 8-in. rod of each lobe a t angles of 120' to those of the adjacent lobes and to adjust the angles of the other rods
JOURNAL OF CHEMICAL EDUCATION
by eye to give a smooth surface. When all of the rods were set, holes were bored a t the proper angle through the horizontal rod and sleeve where the curve passes through zero. A soft 14-gage copper wire was soldered 'to the ends of each rod and passed through the holes in the horizontal rod to outline the shape of the curve. In all of the models the fundamental sine waves were painted with red, white, or yellow enamel in order to give them contrast. A curve resulting from the combination of a red and a yellow sine wave was painted orange and one from a red and a white sine wave was painted pink. The author wishes to acknowledge the valuable assistance of Mr. Adriaan Jansse in constructing the models.
