~~
Measurement of Optical Rotation by an Absorption Method SIR: In the study of optical rotary dispersion ( I ) for the elucidation of the structure of complex molecules, commercial spectropolarimeters (e.g., Cary Model 60) record the degree of optical rotation as a function of wavelength. An attachment made by Perkin-Elmer that uses a concept discussed by Crumpler, Dyre, and Spell (2) is also available. It employs a polarizer and an analyzer maintained at an angle 4 = 45 O and the degree of rotation is related to absorbance through a fairly complex function. It would be of interest if such measurements could be made with a conventional dual beam spectrometer (e.g., Cary Model 15) by the addition of fixed polarizers in the sample compartment. The approach and the preliminary results using inexpensive Tiffen polarizers (Tiffen Optical Co., Roslyn Heights, L. I., N. Y.)mounted in the entrance and exit of the light beam to the cell compartment of the Cary 15 will be discussed here. The intensity of light I transmitted through polarizers oriented at an angle 9 is given by
Z = Io ki COS'
".-
0
ce I' 0 1
andwith9 = ~ 1 2 ,
where I" is the entering light intensity and kl is a proportionality constant. If the polarizers are exactly crossed, the light intensity transmitted would be extremely low depending upon the quality of the polarizers. If one uses polarizers which allow a low, but finite transmittance of light, the intensity I , is written as:
AA
Zi
=
I" (ki COS' 4
+ kz)
(2)
where kz is a constant for the light level. In our case the polarizers had about 0.1 % transmittance at cross polarization. If a solution containing an optically active nonabsorbing compound is now placed between the analyzer and the polarizer, the net transmitted light is affected by the optical rotation fa. Because the polarizers were crossed initially, the transmitted intensity is increased as follows : Zz =
Po (ki COS' (4
f a)
+ kz)
(3)
40'
30
( O'I~I'
Figure 1. High concentration region. Exponential of absorbance change us. square of concentration for sucrose solution
(1)
c$
20
IO
=
log
kl sin2 a
+ kz
(7)
k2
and combining constants and simplifying :
AA
=
log ( k gsin2 a
+ 1)
(8)
At small angles of rotation, sin a equals a , and the constant k3 can now be adjusted to include the conversion factor from degrees to radians. Also, a = [a]IC where [a]is the specific rotation, I is the length in decimeters, and c is the concentration in grams per milliliter. Substituting these terms in Equation 8, the relationship expressed in exponential form is
loAA= (ka sin2 a
+ 1)
or 1
+ 1)GE
eAA= (ka sin2
(9)
which can be approximated by
In terms of absorbance, Equation 2 can be written as A1 = -log (ki
COS'
4
+ kz)
(4)
where AI is the absorbance with the reference solution, namely, the solvent such as water, between the polarizer and the analyzer. Likewise, Equation 3 becomes
Az = -log (ki COS' (4 f a )
+ kz)
(5)
Here a plot of exponential of the change in absorbance is approximately a linear function of the square of the concentration of the optically active compound. For a small change in absorbance, Equation lQ.maybe expanded in a power series as follows :
where A2 is with the solution containing an optically active compound. Thus the change in the absorbance due to rotation alone is and absorbance approximated as
AA (1) Carl Djerassi, "Optical Rotatory Dispersion," McQraw-Hill, New York, 1960. (2) T. B. Crumpler, W. H. Dyre, and A. Spell, ANAL.CHEM., 27,
1645 (1955).
kc2
by omitting the higher order terms. Hence, AA is proportional to the square of the concentration. Equations 10 and 12 are verified experimentally in Figures 1 and 2 for sucrose solutions. For evaluating the specific rotation, the constant k must be known and can be determined from the experimental VOL. 39, NO. 14, DECEMBER 1967
* 1897
:iI26
130
I34
138
142
REFRACTIVE INDEX
0
2
4
6
8
1
Figure 2. Low concentration region. Abaorbance change GS. square of concentration for sucrose solution
plots of Figures 1 and 2. The value of k3 is fixed for a given set of polarizers under defined conditions as is evident from Equations 1 and 2. As k is not fixed and is dependent upon the specific rotation of the sample, the value of k s can be calculated knowing the specific rotation of sucrose. This can now be used for evaluating the specific rotation of unknown solutions using Equation 10 or 12. For example, the values of specific rotation at 589.3 rnp for sugars (after mutarotation) glucose and fructose were determined to be 52.5” and 91.2” using the value of k 3 from Figures 1 and 2. These results are. in fair agreement with the literature values (3) of 52.51 O and 89.2 O , respectively. The experimental value for fructose may be high due to an impure sample. The transmitted light intensity and, consequently, the absorbance is affected by changes in the reflectivity of light between the cell walls and the sample solution. The refractive index of the solution which determines the reflectivity is concentration dependent. Assuming that the solvent is water, the change in absorbance was found to be less than unit for a change of refractive index from 1.33 to 1.52 as can be seen in Figure 4. This change in absorbance is the same order of magnitude as our experimental error. (3) “Handbook of Chemistry and Physics,” The Chemical Rubber Publishing Co., Cleveland, 1962, p. 1784.
e
ANALYTICAL CHEMISTRY
I50
0
cZx1o4( $ / m ~ * )
189%
146
nb
Figure 3. Effect of refractive index of solution on absorbance change
The above discussions are valid at all wavelengths. If the optically active sample absorbs light, a modified approach can be used. With the polarizers mounted only in the sample compartment, the absorbance of solvent as a function of wavelength in matched cells should be taken. The rotatory dispersion curve can be obtained then by replacing the solvent by the sample solution in both cells and repeating the scan. This method is seriously limited by the low signal to noise ratio when highly absorbing solutions are used. ACKNOWLEDGMENT
The authors thank A. Abu Shumays of Cary Instruments for his valuable suggestions. S. SRINIVASAN VAKULA THEODORE KUWANA
Department of Chemistry Case Western Reserve University Cleveland, Ohio 44106 RECEIVED for review July 7, 1967. Accepted September 20, 1967. Work supported by Grant GIM 14036 from the Research Grant Branch of National Institutes of General Medical Sciences and by NSF Grant No. GP 6479.
