A SIMPLE METHOD FOR MEASURING ROTATORY DISPERSIOK BY ISAAC BENCOWITZ
Introduction The importance of ,rotatory dispersion has been well recognized both by physicist and chemist. While the general apparatus for polarimetric measurements has considerably improved and is available in every well-appointed laboratory, the measurement of rotatory dispersion has been confined to very few laboratories. This is due to the fact that this field of work is still one of the most difficult in experimental physics. The chief difficulty lies in the lack of light sources of sufficient purity and intensity for polarimetric measurements. The increase in the intensity of a nearly monochromatic source of light is usually accompanied by a decrease in its homogeneity, while accurate polarimetry demands both intensity and homogeneity. Furthermore, in dispersion work where several hundred readings are taken in a single day, it is very essential that the source of light should be steady, free from flickering or “running.” Flames, therefore, even if they were of sufficient homogeneity cannot be employed in extensive measurements. Metallic arcs suffer from the same disadvantage. Even the best rotating arcs do not provide a steady source of illumination. When either flames or arcs are used, very elaborate spectroscopic apparatus must be employed to purify the light, and it is physically impossible for one man to make measurements and keep the sources adjusted simultaneously. The enclosed arc is the only source of light suitable for polarimetric work. Unfortunately, we are confined, a t present, to the mercury arc, giving only two lines of sufficient intensity and homogeneity for dispersion measurement. Cadmium gives a spectrum which in conjunction with the mercury arc is ideal for dispersion measurements. It has four intense lines sufficiently apart in the spectroscope scale to make elaborate monochromators unnecessary. These four lines together with the two mercury lines cover practically the entire range of the visible spectrum. Unfortunately, the difficulty of producing a cadmium lamp which burns steadily and gives out light of high intensity has been so great, that the four cadmium lines have been used only very occasionally in optical experiments. Lowry and Adamsl used a quartz cadmium vapor lamp for dispersion measurements. It was later improved by Sand2, but it still required the continuous use of a pump and frequent refilling. Bates3 succeeded in building an enclosed cadmium quartz lamp devoid of all the inconveniences of the arcs of previous workers. He used a mixture of metallic gallium and cad~~~
Lowry and Adams: Trans. Faraday SOC., 10, 103 (19x4). * S a n d : Proc. Phys. SOC.,28, 94 (1915l, Bates: U. S. Bureau of Standards, Sci. Paper, 371, 16 (1920)
1164
ISAAC BENCOWITZ
mium. Gallium, however, is costly and difficult to obtain. The construction of the lamp is still far from a simple process.1 These considerations make enclosed cadmium quartz lamps unavailable for chemical laboratories, and as long as we are confined to the mercury arc as the sole source of light for dispersion measurement, this important approach to many physico-chemical problems will remain inaccessible. It has been our aim to develop a method so simple as to make the measurement of rotatory dispersion generally available for ordinary routine measurements of the laboratory. The method described below does away with the necessity of a cadmium quartz lamp, and other expensive apparatus. Moreover, it enables us to employ practically any line in the visible spectrum and as many as are needed. I t was recognized a t the outset that many applications of rotatory dispersions require the highest degree of accuracy. For most chemical inveqtigations, on the other hand, the purity of the substances studied is such thst the highest precision is unnecessary. I n such cases, especially where only the visible range of the spectrum is desired, an accuracy of 0.02 of a degree is sufficient. Continuous Spectrum as a Source The continuous spectrum of the sun was the first source of light employed in polarimetric work.2 Lippich3 employed an artificial continuous spectrum in conjunction with a direct-vision spectroscope. He passed the light through a spectroscope the eye-piece of which was replaced by a narrow slit, which served as a source of light for the polarimeter. The chief source of error inherent in the use of a continuous spectrum is the effect of stray light. I n addition, the ordinary methods of calibrating a spectroscope are unsatisfactory, These methods, besides being cumbersome, require additional apparatus, which is rather expensive and is often not available even in the best chemical laboratories. >\Toreover,most spectroscopes used in conjunction with polarimeters will not “stay” calibrated. This necessitates frequent recalibration. The most fundamental objection, however, lies in the fact that the wave length of the optical center of a patch of continuous spectrum is not the wave length obtained by the calibration of the prism with a monochromatic source. Moreover, the optical center of gravity of a patch of continuous spectrum varies with the intensity of the source of power and the width of both the slit a t the collimator and at the telescope ends. On the other hand, a continuous spectrum employed as a source of light in rotatory dispersion measurements offers several important advantages. I t provides a steady source of light which requires hardly any care. Its position 1 The Cooper Hewitt Company, however, has lately succeeded in building a cadmiumgallium arc for us, the construction of which took them almost a year and was posslble only because of their untiring effort and interest in the success of the undertaking. * Brach: Ann. Chim. Phys., 34, 119-121(1852). 3 Sitzungsber. Akad. Kiss. W e n , 91 11, I970 (1885).
A SINPLE METHOD FOR MEASCRISG ROTATORY DISPERSION
116j
relative to the optical axis of the apparatus is not disturbed; any desired intensity may be obtained; and any wave length of the spectrum is attainable, It is because of these obvious advantages of a continuous spectrum on the one hand, and the enormous difficulties encountered in the use of other sources of illumination, on the other hand, that we have attempted to develop a method based on the use of a continuous spectrum. The considerations of the following section suggest such a method. Theoretical Considerations The method for measuring rotatory dispersions developed in this paper is based on the following considerations: A beam of white light passing through a narrow slit of the collimator and incident upon a prism is dispersed into a continuous spectrum. If the eyepiece a t the telescope end of the spectroscope is replaced with another slit similar to that a t the collimator end, we are enabled to isolate a narrow patch of light of the continuous spectruni. Let the opening of the slit be such that the patch of light transmitted consists of several TvaTYe lengths, XI, XS, XS.
. . .
XK.
The telescope-end slit then serves as a source of light for the polarimeter. The patch of light, having been polarized, is t'hen rotated by an optically active medium placed in its path between the polarizer and the analyzer. The rotation of the planes of polarization by an optically active substance is different for different wave lengths, and the section of spectrum incident upon the polarimeter will be further resolved before it reaches the analyzer. The extent of this resolution will depend upon the dispersion curve of the optically active substance, and the total magnitude of the rotation. If the width of the slit is such that the difference aI - CYK is considerable, the illuminated portion of the field will not be totally extinguished, but as the analyzer is rotated a dark band will appear and disappear intermittently. The setting of the analyzer corresponding to the various dark bands will give the rotations al,a?, . . . ak of the plane of polarization of the wavelengths XI,XZ, . . . X k respectively. If, on the other hand, the width of the slit is made narrow so that AX is small, the intermittent dark bands will not appear when viewed a t the analyzer-end. But the difference between a1and ak may still. be too large and the patch of light will not be completely extinguished. However, AX can be made still smaller by closing the slit further so that the magnitude of the difference of the total rotation is reduced sufficiently to obtain perfect extinction. The width of the illuminated band due to the difference between a1 and f f k even when perfect extinction is obtained may still be considerable and the average rotation recorded by the annlyc.ei' will lie somewhere between cy1 and ak. This mean rotation, aC,will depend upon the distribution of the energy intensities among XI,A?, . . . Xk. It is possible, at least) abstractly, to find a monochromatic source of wave length X, such that when polarized its plane of polarization will be rotated by the given optical substance to the same extent as that of the nonhomogeneous patch of light. That is, if a0 is the rotation of a non-homogene-
I 166
ISAAC BENCOTVITZ
ous source and a , the rotation of the corresponding monochromatic source: then X, = .A, We define A, as the wave length of the “polarimetric” optical mean of the pat’ch of light of continuous spectrum consisting of XI, X?, , . . Xk such that A, = .A, I t is a theoretical wave length of a monochromatic source that would give a rotation equivalent to that of the ent,ire band XI, A,. . . . Xk. It is not necessarily identical with the optical center of gravity determined spectroscopically, i.e. one dependent upon the distribution of energy and maw length. The optical mean as defined here depends upon the inherent characteristics of optical activity. The value of the “polarimetric” optical mean, A,, as defined above can be obtained by means of any optically active substance w!iose disper-’ hion curve is known, simply by measuring the rotation of the plane of polarization of the patch of light and determining from the dispersion curve the corresponding .X, Or given a definite X, the corresponding a,”is obtained from the dispersion curve or available tables for the standard substance. The prism of the spectroscope is then moved until the patch of light illuminating the polarimeter is such that the standard substance rotates its plane of polarization to the extent of a. = a,. The optical mean of that patch of light is then A, = .A, We thus establish a correspondence between definite patches of light in terms of monochromatic sources. Any substance, the rotatory dispersion curve of which is known, can be employed as a standard. However, the question arises, will the polarimetric optical mean determined by any one substance be identical with that determined by another, the dispersion curve of which is different? A cursory analysis of the characteristics of polarimetry as well as of the results given in Table I seem to indicate an affirmative reply. The width of the illuminated band to be extinguished by the analyzer will depend upon the magnitude of the difference between the terminal wave lengths of the patch of light incident upon the polarimeter and the difference between the corresponding rotations of al and ak. The differences between A, and A k is kept constant by maintaining the same width of the slit, and is, therefore, independent, of the optical substances employed. The difference of the total rotations al and ak,on the other hand, will depend upon the dispersion curve of the substance and the magnitude of the rotations. However, the rotation a0 recorded by the analyzer is the mean of al, as, . . . ak and for patches of light sufficiently narrow to give complete extinction, the mean will be independent of the width of‘ the band at - (Yk. The value of A, determined by one substance will, therefore, be identical with that determined by another substance and independent of their respective dispersion curves. This conclusionmay not be rigorous but that it is valid within the precision justified by the purity of most optically active substances is established by the data given below. Quartz is an ideal substance to be employed as a standard. Its dispersion curve1 and its temperature coefficient2 have been accurately determined. The 1 T.M. Lowry: Phil. Trans., 2 1 2 4 261-297; Lowry and Coode-Adams: 226 A, 391-466 (1927).
*U.S. Bureau of Standards Circular, No. 44, 1 8 (1918).
.4 SIMPLE METHOD FOR MEASURING ROTATORY DISPERSIOS
I 167
fact that quartz test plates are employed in saccharimetry makes it possible to procure them in various thicknesses and convenient form. The plates are rigidly enclosed in metallic frames adjusted to fit the polarimeter. The United States Bureau of Standards is equipped to calibrate the thickness of the plates as well as their optical rotation for several wave lengths.
Experimental Procedure and Results ,A Schmidt and Haensch polarimeter provided with a direct-vision spectroscope was employed in all measurements. A quartz mercury arc served as a source of monochromatic light and a small electric bulb with a horizontal tungsten filament was used as the source of non-homogeneous light. This lamp was mounted on brackets attached to the spectroscope so that when the direct vision prism was rotated the lamp remained focused. A quartz test plate supplied by Bausch and Lomb and calibrated in the Bureau of Standards was employed as a standard. The solutions were kept 0.01 by in jacketed tubes and the temperature was maintained at 3 j"C means of a rapid stream of water from a t,hermostatic bath. The polarimeter was first tested by means of the quartz plate for the mercury green line, 5461 A, and the mercury violet, 4358. The average of twenty readings checked with the values of the Bureau of Standards to within + o O . 0 1 ~which is well within the error of the apparatus. The values in Table I were obtained in the following manner. A solution of an optically active substance was placed in the polarimeter, and the rotation of the plane of polarization of the Hg-green, j461, with the mercury arc as a source of light was determined. These values are recorded under a , in column z . The mercury arc was then replaced by the incandescent lamp and a narrow patch of its continuous spectrum was focused upon the analyzer. The quartz plate was then placed in the polarimeter, and the prism of the spectroscope adjusted so that the optical center X, of the patch of light passing through the slit of the telescope-end was equivalent to 5461. That is, the prism was moved until the plane of polarization of the patch of light was rotated by means of the quartz plate to the same extent aQ as that given by the Bureau of Standards for monochromatic green of 5461 A. The quartz plate was then replaced by the solution and its rotation determined. These values are given in Table I, column 3. In determining the value of aq,the zero point of the apparatus was added to the required reading of the quartz plate and the temperature correction was applied. In the case of the solution, the zero point of the tube was determined before filling and subtracted from the reading. The above procedure was repeated with mercury violet, 4358 A, the results of which are given in columns 5 and 6 and for mercury yellow in columns 8 and 9. In the latter case, the optical centers of both the mercury arc and the continuous spectrum were found by means of the quartz plate. Solutions of various concentrations giving a total rotation from 50.00' to 3.00' were employed.
I 168
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ISAAC BESCOWITZ
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A SIMPLE METHOD FOR MEASURIXG ROTATORY DISPERSIOS
169
The differences between the rotation of a non-homogeneous patch of light ac, and that of a monochromatic source of light am,are given in columns 4, 7
and I O . The close agreement between the two is remarkable in view of the fact that the dispersion curves of the three substances employed are different. The dispersion curves of the pentacetates of a-Mannose and P-Mannose are accurately expressed' by one term of Drude's equation cy = Z
K x 2 -x2, ~
. The
dispersion curve of tartaric acid, on the other hand, is reproduced by2 cy = Ki
K2
x2-x:
x2-x;
while that of quartz is given by
a =
Ki h2_x:+
xz-x:+F' K?
KB
In obtaining the data given in Table I, only the ordinary precautions of routine measurements were observed. KO attempts were made at more painstaking accuracy; otherwise the agreement might have been much closer. Experimental Procedure in Measurements of Rotatory Dispersion
The details of the following method are a description of the procedure used in obtaining the data published elsewhere. The following wave lengths were chosen: Li, 6708 red; Cd, 6438 red; Zn, 6364 red; Cu, 5790 yellow; Hg, j j o o yellow; Hg, 5461 green; TI, 5351 green; Cd, 5086 green; Cd, 4800 blue; Hg, 43 59 violet. The rotations, a ~LYCd, ~ ., . . L Y H ~ of- the ~ ~ plane ~ ~ ~ of polarization of the corresponding wave lengths by our quartz plate were calculated from the known thickness of the plate and the datagiven by Lowry. With the incandescent lamp as a source, the prism of the spectroscope was rotated until the patch of light passing through the slit of the telescope-end was red and the zero point of the empty tube for the red region of the spectrum was determined. Similarly, the zero point of the empty tube was determined for the green, blue and violet regions. I t was found by preliminary measurements that the zero point of the tube did not vary much for wave lengths within each region. The zero point of the tube having been determined, the tube was filled with the solution and allowed to come to the temperature equilibrium. Meanwhile, the quartz plate was placed in the polarimeter and the prism of the spectroscope moved until the patch of light passing through the quartz plate plus the zero was such that its rotation by the plate was equal to that of q,, point of the apparatus for red. The tube with the solution was then put in place of the quartz plate and the rotation of the same patch of light by the solution was measured. The quartz plate was again substituted and the setting of the spectroscope checked. Whenever the two readings did not agree, the spectroscope was reset and the readings with the solution repeated. As a rule, the spectroscope seldom needed resetting. This procedure was repeated for the ten wave lengths. At least fifteen readings were taken for each 1
P. A. Levene and I. Bencowitz: J. Biol. Chem., 72,627; 74, 153 (1927)
* T. SI.Lowry and P. C. Austin: Phil. Trans., 212 A, 249-308 (1922).
~
1170
ISAAC BEXCOWITZ
setting. To check the readings as well as to determine whether any change in the concentration took place during the measurements, the entire procedure was repeated from Li red to Hg violet. Rarely did the average of the two sets of readings differ by more than i o O . 0 2 , notwithstanding the fact that often as long as six hours elapsed between the two sets of readings. Conclusion The procedure described in this paper provides a means for measuring rotatory dispersions which requires no cadmium quartz lamp or other expensive apparatus. The technique is simple and with a little experience it is possible to make a complete determination for ten wave lengths in five hours. It is accurate to within o.ozo and the purity of most optically active substances does not justify higher precision. This method likewise enables us to employ any wave length the rotation of which in quartz is known. I take this opportunity of thanking Dr. P. A. Levene for suggesting the problem and for much valuable advice. summary
A simple substitution method of measuring rotatory dispersion is described. The Laboratm'es of the RockefeUer Institute for Medical Research,
Neur Ymk.
