tems with triplet state energies between 5ooo and 12,000 cm.+ would help distinguish several rare earths with resonance fluorescence transitions in the near-infrared region. Using the present chelate systems, fluorescence studies in this wavelength region are in preparation and it is anticipated that the spectrum strippiug program discussed here will be a powerful tool in the analysis of the closely spaced and overlapping emission lines of this rare earth group.
LITERATURE CITED
(1)Alberti, G., Massucci, M. A., ANAL. CEEM.38, 214 (1966). (2) Bauer, H., Blanc, J., Ram, D. L., J . Am. Chem. Soe. 86, 5125 (1964). (31 Bhaumik. M. L.. J . Chem. Phw. ‘ b, 3711 (lk). (4) Bhaumik. M. L., El-Sayed, . M. A., . Ibid., 42, 787 (1965’). (5)Bhaumik, M. L., Fletcher, P. C., Nugent, L. J., Lee, S. M., Higa, S., Telk, C. L., Weinberg, M., J . Phys. Chem.68,1490 (1964). (6) Crosby, G . A., Whan, R. E., Alire, R. M., J . Chem. Phys. 34,743 (1961). (7) Crosby, G.A., Whan, R. E., Freeman, .T. J .. .r. 66. 2493 (19621. --, - . -Phvs. Chem. (8j-Dieke, G. H., Cross‘white,’ H. M., Appl. Opt. 2,675 (1963). (9) Drushel, H. V., Sommers, A. L., Cox, R. C., ANAL. CEEM. 35, 2167 ( 1963). (10) Fassel, V. A., Heidel, R. H., ANAL. CHEM. 26, 11% (1954). (11) Filipescu, N., Sager, W. F., Serafin, F. A., J . Phys. Chem.68,3324 (1964). (12) Freeman, J. J., Crosby, G . A., J . Phys. Chem. 67,2717 (1963). (13)Lem icki, A., SameLson, H., Brecher, C., J . $hem. Phys. 41, 1214 (1964) (14) Lott, P. F., J . Chem. Educ. 41,A327 (1964). ’
-0.-
ACKNOWLEDGMENT
The authors express appreciation to Dale D. Grosvenor and his s t d of the Oklahoma State University Computer Center for their advice and assistance. The plotting subroutine was written by E. J. Kobetich, Kansas State University. Acetonitrile purified in a GLC prep column was kindly furnished us by Continental Oil Co. during the early stages of this project.
(15) Melby, L.R., Rose,N. J., Abramson, E., Caris. J. C., J . Am. Chem. Soc. 86, 5ii7 (1964). (16) Muller, R. H.,ANAL. CHEM. 37, (13),93A (1965). (17) Schimitschek, E. J., Nehrich, R. B., Trias, J. A., J . Chem. Phys. 42, 788 (1965). (18)Stanley, Elizabeth C., MS Thesis, Oklahoma State University, May 1966. (19) Vickery, R. C.,“Analytical Chemistry of the Rare Earths,” Pergamon Press New York, 1961. (20) Whan, R. E., Crosby, G. A., J . Mol. Spectr. 8, 315 (1962). (21) Winston, H.,Marsh, 0. J., Suzuki, C. K.. Telk. C. L.. J . Chem. Phus. 39. 267 (i963).‘ (22) Woyski, M. M., Harris, R. E., Kolthoff, I. M., Elving, P. J. (eds.), “Treatise on Analytical Chemistry,” Part 11, Vol. 8, pp. 1-146, Interscience, New York, 1963. (23) Yariv, A., Gordon, J.P.,Proc. I E E E , pp. 4-29, January 1963. “
I
RECEIVEDfor review April 1, 1966. Accepted July 5, 1966. This work waa supported, in part, by the Oklahoma State University Research Foundation and by an NSF Summer Fellowship for Teaching Assitants, 1964.
Occurrence of Bias in the Spectropolarimeter AUGUSTE L. ROUY and BENJAMlN CARROLL Chemishy Department, Rutgers-The State University, Newark, N. 1.
A spectropolarimeter may exhibit a bias when the phase shift in an amplifier is coupled with a synchronously rectified signal that is not strictly of a simple harmonic form. Highly absorbing samples and especially samples that scatter appreciable radiation may overburden an amplifier and cause the phase shift. The bias i s usually levo although under certain conditions it may become dextro. Bias effects which have been reported as large as a few hundred millidegrees may be fully accounted for on the basis of the present treatment. The general case of bias is considered and some specific examples are examined.
S
INVESTIGAMRS have observed a bias in the readout of the spectropolarimeter (4, 6, 8). The reported optical activity data of other investigators have been challenged on this account (4, 6, 7, 10,12). The bias is exhibited frequently with solutions of high optical density, say above 2 or 3 and at much lower optical density for turbid solutions. Although the bias may be reproducible, the bias effects of absorption and scattering are not entirely additive so that controls for such systems may
EVEBAL
not be reliable (4, 6). Thus results in the literature for some systems having rotations in the range of 10-l to lo-* degree may be in serious error. A n explanation of this effect is attempted here. The bias appears to be frequently of a levo character. For example Resnik and Yamaoka (8) found that a clear solution of pot,assium dichromate which is neither optically active nor fluorescent yielded an apparent levo rotation of more than a hundred millidegrees. Hayatsu showed that spurious optical rotations up to 180 millidegrees could be obtained on a number of commercial spectropolarimeters when appreciable scattered light was present. In previous publications (2, 9) we have considered the limitations of the spectropolarimeter, and have shown that they may attain a sensitivity of about a millidegree in the absence of absorption or scattering and a lower sensitivity as the transmittance of the sample is decressed. The special effects due to scattering have also been discussed (3, 11). In all this work only the optics of the polarimeters were treated; the combined effects of the optics and the electronics were not considered. The possible existence of a bias in the spectropolarimeters was brought to our attention by E. Anders (1). This
phenomenon appears to be of a general character and may be explained as a coupled effect of the optics and electronics of the instrument. The order of magnitude of the bias is deduced for a few cases and is compared with experimental values. ORIGIN OF THE BIAS
Assuming that the optics of the polarimeter is aligned properly, the origin of the bias appears to be in the phase &it introduced by the amplifier when it is overloaded (6). It has been shown that the phaw shift alone will not produce the bias (10)unless it is coupled with the signal resulting from the process of synchronous rectification. Again if the signal is strictly of simple harmonic form, no bias will result. The point in absorption and scattering at which the bias will appear in an instrument will depend then upon its amplifier and the character of the oscillating signal intercepted by the phototransducer. TREATMENT OF THE GENERAL CASE
The oscillating signal arises from the oscillation of one of the polarizing el+ ments; either a magneto-optic (Faraday) effect or some kind of mechanical linkage is used for this purpose (8). Figure 1 is a diagram indicating the VOL 38, NO. 10, SEPTEMBER 1966
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following elements: a light source, an oscillating polarizing prism making extreme angles of €0 and -eo about its optic axis, a sample having an optical activity a and an analyzer whose optic axis is orthogonal to the mean position of the polarizer axis in the absence of sample. The position of the analyzer is rotated by the same angle and direction as that of the sample to maintain the null point position. In this method of measuring a, synchronous rectification is used, where one half cycle mean signal is compared with the consecutive other half cycle mean signal. The sign of the difference is that of the optical rotation imposed by the sample. Consider now the periodic oscillation of the polarizer about a fixed direction normal to the analyzer axis. The light energy emerging from the analyzer becomes a periodic function of the time. Regardless of the method used to achieve the oscillation, be it that of a mechano-optic linkage or a magnetooptic method, the instantaneous angular position of the linearly polarized amplitude can be defined exactly by a Fourier series of appropriate harmonic termbi.e.
+
= a0
+ a1 sin (ut u2 sin (2wt
$1)
+
- qb2)
+ ...
(1)
In the ideal case the value of e is described by the simple harmonic term alsin (ut - 41). However additional harmonic terms may be present including the term, &. The latter term may be caused by the stray light, imperfections in the polarizing elements, etc. I n the case of the magneto-optic type of polarimeter, the term may also include the hysteresis term of the Faraday cell, as well &s its birefringence related to the temperature gradient of the cell. Crystallographic defects in the polarizing elements may cause light leakage of the order of 10 to 40 niillipercent of the light entering the sample. Consider the expression for the polarized amplitude, A , projected onto the analyzer axis for an orthogonal system in the absence of the optical activity of the sample. The value of its projection, A is given as A = A . c o s ( ~ + ~ ) = -Aosine
(2)
where is a periodic function of the time, Periodically the value of e takes on the same values at the time interval, 2’. The instantaneous energy emerging from the analyzer takes the form
f(t).
(3) The presence of optical activity, a, of the sample (omitting the absorption 1368
ANALYTICAL CHEMISTRY
J Figure 1. Vector diagram illustrating optical components in the spectropolarimeter I , light source; P, polarizer oscillating between two positions PI ond Pz; cg, peak angular dirtancea from orthogonal axis OY; a, optical activity of sample; PI’ and P2’, vectors indicoting the linearly polarized axis direction which arcillotes between the angular positions €0 a and M f a; A,, analyzer axis1 E, and Et, indicative of output energies when analyzer oxis is parallel to x direction; and El’ and €2‘. indicative of output energies when analyzer axis is rotated b y angle @ = a to restore the null point so that €1’ = Ez’
*
-
factor for the present) changes Equation 3 to A 2
E = 0 sin2 (e 2
+ a)
and
E“
(4)
when the axis of the analyzer remains normal to the mean angular position of the polarizer axis. The common characteristic for all the polarimeters using the periodic angular oscillation of the polarized light amplitude is the null point. I t is achieved by rotating the analyzer to an angular position fl equal in magnitude and sign to the optical rotat
2
(28)
Because
AE+
0 as the null point is approached, it can be shown that Equation 28 leads to an invariant levo bias, this being
"'(;>['-2sin'(;)] r and
(34)
It can be seen that Equation 39 can lead to a positive or negative bias depending upon whether the ratio
where
-
Ao'
e-tzc(Al 2
AE =
+ A*)
[l (36)
In the absence of sample, a = O and so that the polarimeter attains
cp = 0
the balancing position -2hco
such that
4
x ;- 2eOro x
than
z/a.
Suppose the phsse of the second harmonic in the magneto optical signal, +, is taken as zero then = 0 and the bias becomes A& =
h'
=
-
Zo sin cp
6
or
h = pki n l $
is larger or smaller
- 2&(3]
[I 1
2 sin'
(:)I
Equation 40 indicates that the bias, , tends toward large values which may be either positive or negative when cp is in the neighborhood of 9 0 ' . Taking A@ as a measure of a small departure A&
(37)
Upon the introduction of sample which has no optical activity but has &cient absorbance to cause the phase shift, cp, to appear the new equilibrium point, h' leads to the equation
of
from
2
(a b e i i negative), Equa-
tion 40 becomes
scattering are not additive. The nonadditivity phenomenon may be deduced from the above treatment. Clearly the phase shift of the amplifier will be altered when its burden is increased by the addition of scattering effects to the effects of absorption. Zt is questionable whether controls which exhibit scattering are meaningful when the amplifier is exhibiting a phase &it although the bias effects may be reproduced precisely. One should consider that constituting a control to duplicate the scattering properties of a sample implies duplicating the size and shape of the scattering particles, a task that is not easily accomplished. Generally the present polarimeters are restricted to solutions having optical densities of about three or less and also exhibiting little scattering. This is due to the orthogonal arrangement of the optics employed. This problem has been discussed previously (2, 9) and the advantages of possible non-orthogonal instruments for highly absorbing and scattering samples have been considered. LITERATURE CITED
2 1 2elo ;[3sin
(I$
+ @) - sin+] = 0
or
One may consider (0-10-~ degree or larger since 4 is of the order of one degree. Taking A+ as f0.1" yields a dextro bias of lo2 millidegrees and a levo bias of the stme magnitude for A+ = -0.1'. DISCUSSION
The bias may be written as
hB*=h'-h=rosinI$ x
The above analysis of the bias phenomenon indicates the necessity of checking the limitations of spectropolarimeter when used with solutions that over-burden the amplifier. An estimate of the region of reliability of the instrument under Severe conditions of absorption and scattering may be obtsined by using calibrated neutral density filters and frosted glass screens. Hayatsu has found that the bias effects produced by absorption and by
( 1 ) Anders, E., Fermi Institute for Nu-
clear Studies University of Chicago,
private communication, 1965.
(2) Carroll, B., Blei, I., Science 142, 200 (1963). (3) Carroll, B., Quigley, T. J., J . A p p l .
Polymer Sn'. 9, 1905 (1965).
(4) Hayatsu, R., Science (In press). (5) Hayatsu, R., Science 149, 443 (1965). (6) Malmstadt, H..V., Enke,. G., G;:
Toren, "Electronics for Scientlsts, W. A. Benjamin he., New York, 1962. (7) Nagy, B., Science 150, 1846 (1965). (8) b n i k , R. A., Yamaoka, K., Biopolymers (In press). (9) b u y , A. L., Carroll, B., ANAL. CHEM. 33, 594 (1961). (IO) b u y , A. L., Carroll,. B.,. Nature (In pr&) (11) b u y , A. L. Carroll, B., Quigley, T. J., ANAL.CHEM.35, 627 (1963). (12) Urey, H. C., Science 151, 157 (1966). RECEIVEDfor review April 21, 1966. Accepted July 15, 1966. Supported by NASA Grant NsG550.
VOL 38, NO. 10, SEPTEMBER 1966
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