The addition of 1 or 2 drops of 10% sodium chloride solution to the standards before digestion with chloric acid enhances reproducibility. While the role of sodium chloride is not precisely known, it seems reasonable that some pyrophosphate may be formed in its absence. yaturally occurring sodium chloride should have a similar protectire influence.
T'olumetric flasks must be stoppered immediately after adding hydrazine sulfate, because exposure to air leads t o erroneous results. LITERATURE CITED
(1) Bloor, IT. R., J . Bzol. Chem. 17, 3T7 ( 1914).
(2) Boltz, D. F., Mellon, AI. G., CHELI.19, 873 (194T).
h . 4 ~ .
(3) F i s k C. H., Subbarow, I-., J. B d . Chem. 66,375 (1925). (4) Youngburg, G. E., Youngburg, LI. V., J. Lab. Clin. Pled. 16, 158 (1930). ( 5 ) Zak, B., Willard, H. H., Myers, G. B., Boyle, A. J., BXAL.CHEM.24, 1345
(1952). RECEIVEDfor review July 25, 1957. -4ccrpted January 14, 1958. Granbin.4id, Michigan Heart Association and the Xational Institutes of Health, Division of Neurological Diseases and Blindness.
The Rouy Method for Photoelectric Polarimetry BENJAMIN CARROLL, HAROLD B. TILLEM, and ELI S. FREEMAN Chemistry Department, Rufgers, The State University, Newark, N . J.
F A set of adapters, each employing two Polaroid plates, can convert the photoelectric colorimeter to a highly sensitive polarimeter. The theory and experimental results for this method are given. When the phase angle between the polarizer and analyzer for the two adapters is the same but opposite in sign, the sensitivity will increase as the phase angle approaches 90'. Reproducible rotations of 10.001 have been attained.
R
publications ( I , 2, 6) have indicated several advantages of photoelectric polarimetry over visual polarimetry. All experimental rrork published in photoelectric polarimetry making use of polaroids has been based on the use of a single set of polaroids with their optical axes crossed usually a t an angle e = 45". Keston and Laspalluto (3) reported a method in which polaroids were employed a t angles larger than 6' = 45". Rouy (4) has pointed out that two sets of polaroids, each set having the same fixed angle but opposite in sign and having the phase angle greater than 45", considerably enhance the sensitivity of the photoelectric polarimeter. Because an increased sensitivity as high as lo2 over previous instruments of this type has been observed, the theory, apparatus, and experimental data for this method are considered. ECEXT
THEORY OF METHOD
Measurements are taken x i t h a set of adapters, constructed to hold the cuvette containing the optically active solution. One adapter has the axes of its front and rear Polaroid plates crossed at e, the other a t - e. This is illustrated in the vector diagram Figure 1. K h e n a sample having a n optical activity, a, is placed bet\\-een the polarizer and analyzer, the polarized amplitudes, Opl and OPn, will have corresponding
+
emerging amplitude projections :
o x = oP: COS (e + OX= OP:COS (-e +
(1)
CY)
(2)
CY)
The corresponding light energies which are proportional to the square of the vector projections on the common axis, OA, are given by Equations 3 and 4.
-
+ (-0 +
E1 = OP:' cos2 (e ~
OF':*
E2
COS'
(3)
cy)
0 4 $ $ + + LAnalyzer A Axis
(4)
CY)
Sources of extinction such as light absorption or scattering will alter Equations 3 and 4 by the same factor. One method of preventing this factor from affecting polarimetric determinations, is making use of a polarimetric scale such as R, where
Substitution of Equations 3 and 4 in Equation 5 leads to
R =
sin 2 e sin 2cy
+
1
COS
(6)
2 e COS 2CY
Equation 6 may be derired as follows: substitution of Equations 3 and 4 in Equation 5 and making use of the relationship that
op:= op: yields R =
cos2 ( - e c0sy-e
+
CY)
- cos2 (e
+
cy)
Because
(e
COS^
Eb
CY)
+ + cosye + 00
+ a ) = ~ / ~+[ i
COS
2(e
(5a)
5' Figure 1. Effect of placing sample with optical activity, a, between polarizer and analyzer
COS
2(-e
+ cos =28 cos CY + sin 28 sin 2 c ~ CY)
may be used in Equation 5b. Upon simplification, Equation 6 is obtained. The latter equation may be put into the form of a series which may be used for experimental purposes, by using sin 28
+
COS
=
2e =
substitution in Equation 5a results in R= 1 1
+ cos 2 ( - e + - 1 + cos 2 ( - e + + 1 + CY) CY)
2 ( e M COS 2(e cy)
COS
+
(5b) COS
2(6
+
CY)
=
cos 28 cos CY
- sin 28 sin 2a:
e
+ tan2 0
1 - tan2 e 1 tan20
+
and similar expressions for sin 2 a and cos 2 a . Substitution of these in Equation 6 yields
R
= 2
tan
e tan
[l
The identities,
2 tan 1
+ tan2 0 tan2
CY
CY]
(6a)
The latter equation may be expanded in a series VOL. 30, NO. 6, JUNE 1958
1099
I.
Table
Cornpa rison of Polorimeter Scales
Angular Scale (Degrees) 0.0
1.0
1.5 2.0 3.0 5.0
R
=
["-I +
[$
x
t
1001,
r0Dev.
0.0000 0,0871 0.1732 0,257'4 0.3389 0.4904 0.7344
0.5
220
tan 6 = 5,0 'R' Scale, Ea E1 -1
0.0 0.2
0.7
1.7
2.9 6.4
15.9
2 tan 6 tan a [ l - tan2 e tan2 tan48 tan4 - . . . ]
+
(Gb)
Because tan 0 may be written as tan e
= 9
+
+
2/15e6
Figure 2.
+...
C.
and a similar series may be written for tan CY, substitution of a series for tan e tan cy in Equation 6b finally results in
A. 6. 6,.
R
=
2(1
2a a - 2 (1
- l/a* +
where a
1
2/15U4)d a b
a3 a 3
- ...
A
(7)
= tan 6
Equation 7 permits the evaluation of the optical activitp from a knowledge of the phase angle, 8, and the value of R. A set of values based on Equation 7 for tan e = 5 is compared n i t h the angular scale (Table I). To estimate the departure of the 'R' scale from linearity, an ideal photoelectric scale may be defined as
R* = 2(tan e ) a
=
2 tan e
It appears from Equation 9 that the sensitivity of the photoelectric polarimeter may be increased almost without limit by having e approach 2 x . Honever, this increase in sensitivity is accompanied by a decrease in the range of the photoelectric polarimeter and by an increasing loss of linearity between optical activity and response of the instrument. 4 n empirical approach to the Rouy method, employing a calibrating substance and avoiding the use of Equation 7 to determine optical activity, may be more desirable. Thus reliance on the absolute values of e, the wave length of
1100
ANALYlICAL CHEMISTRY
the light, the path length of the sample, etc., can be circumvented. Equation 7 is useful for extrapolating to dilute solution. The optical activity is usually a linear function of the conb centration-Le., 01
=
[QIC
Substituting in Equation 7 and dividing by C yields
R / C = 2 ~ [ a-] 2 (1
-;,a>
C2
Per cent concentration of sucrose W a v e length of filtered light, mp Wide pass-bond high transmission filter having range of 400 to 600 mp Same filter, R measured directly on meter of colorimeter which contains no amplifier
a3[a]3C*
+ ...
,
.
(10)
(8)
The third column of Table 1is a measure of the per cent deviation of the 'R' scale. For rotations of 1' or less, the nonlinearity of the photoelectric scale, R , is less than 1%. For larger angles the departures from linearity are appreciable, but they may be evaluated by Equation 7 . Equation 7 also estimates the sensitivity of the Rouy method, because for small rotations da
Linear relationship between R/C and
A plot of R/C vs. C2should be linear over an appreciable range of concentration, the extrapolated value leading to the determination of [a], the specific rotation at infinite dilution. EXPERIMENTAL PROCEDURE
The sugars, sucrose, maltose, and dextrose were dried for several hours a t 105" C. Solutions of known concentrations were prepared and checoked with a visual polarimeter to *0.01 . Apparatus. Two arrangements were employed in taking photoelectric measurements. I n one case a Weston colorimeter was used with its wide pass-band high transmittance filter having a range of about 400 to 600 mp. The standard 1-cm. cuvette holder of the instrument was faced with polaroids having their optical axes crossed a t arc tan 5. The output of the photocell was sufficient to activate the meter of the colorimeter directly. As it was essential to use amplification with the narrow pass-band filters of the Weston instrument, the Inductronic direct current Amplifier Model 1411 mas employed. The output of the amplifier was fed to a Weston Model 322 microammeter. The latter arrangement permitted the use of a set of adapters hav-
ing polaroids crossed at an angle, arc tan 30. The filters had a range of about 30 my a t half intensity, except the 4 1 5 m p filter which had about twice the band width of the other filters. Procedure. The colorimeter was set a t a transmittance of 50% or higher with the solvent in t h e path betn-een the analyzer and polarizer of one adapter. The solvent was replaced by t h e optically active solution and t h e transmission taken as El. The analyzer was then rotated from a n angle of +e to -6 by changing to the other adapter of the set. The instrument was reset a t its previous transmittance value using the solvent, and the reading for the sample was taken as EB. Vhen the highest precision \vas desired, a series of about six readings was taken in rapid succession for each adapter. A 1-em. path was used in all cases. RESULTS
The specific rotations were calculated for a 10% sucrose solution using Equation 7 and compared nith those in the International Critical Tables (Table 11). Contributing causes for the deviation of the ratio of the observed to the literature value may be ascribed to uncertainty in the absolute value of the path length of the sample, nave lengths of light, and the angle between the optical axes of the polarizer and analyzer. As the only variable in the different resdings is the nave length of the filtered light, it may be assumed that this factor is the main cause for the variations. The fair agreement between the literature and laboratory values proves the validity of the Rouy method. The average value for the data in Table 11, 0.9i5,is identical with a sirni1ar ratio that Crumpler and coworkers
observed for some 26 optically active solutions. I n the latter work, a single filter (590 mp) having a band width of 30 mp was used. The consistently low values for the optical rotation observed in the colorimeter may be due to the fact that the maximum transmittance of a filter in colorimetry does not correspond to the peak in polarimetry. A further test of the validity of this method is provided by the data in Figure 2 . Here the ratio (RIG') is plotted against C2, where C is the concentration of the optically active substance. The linear relationship over a 20% concentration range of sucrose is in accordance with Equation 10. Xithin the experimental error, the slopes of the lines in Figure 2 are in keeping 17-ith this equation. For accurate measurements a calibrating substance having about the same rotatory dispersion properties as the sample is desirable. Such a procedure has the additional advantage of permitting the use of a wide pass-band filter. Table I11 gives the results for maltose and dextrose using sucrose as a calibrating substance. The uncertainty of the average value for a 107, maltose and 10% dextrose solution indicates that a precision having an upper limit of about = t 5 X degree is obtainable with polaroids crossed a t 45'. The results for the mide pass-band filter are as reliable as those for the regular fil-
Table II. Calculated Values of Specific Rotation Compared to literature Values"
Wave Length, Filter 640 580 520 445 415
Calcd. [a]Lit. ' 0,970 0.972 1.008 0.951 (0.848) Av. 0.975 Based on Equation 7 and experimental R values for a single concentration (1070) of sucrose.
Table 111.
as a Standard" tz.n e = 5
[CY]
ters; the use of such a filter obviated the need for the amplifier. A set of adapters having 0 = arc tan 30 was used in subsequent measurements with the same solutions. Rotations of +1 X lop3could be observed, thus permitting the analysis of a 1% sucrose solution in a 1-cm. cuvette with a precision to better than i 2 % . Further investigation as to the upper practical limit of sensitivity for this method is planned. ACKNOWLEDGMENT
The authors wish to express their a p preciation to A. Rouy for valuable discussions and for constructing the adapters used in this Iyork.
Relative Specific Rotation
of Maltose and Dextrose Using Sucrose
Obsd. av.
2.100 2.081 2.072 2.070 2.085 2.063 2.073 2.078
Lit. 589
2.080
640 580 520 445 4:1 B
BO
f.0.004
0.792 0.776 0.809 0.819 0.815 0.796 0.783 0.799
f . 0 ,008
0.793
Lit. av. 447 to 656 2.07 0.791 Based on a single concentration (10%) of maltose and dextrose. b \Tide passband high transmission filter Bo,no amplifier used. LITERATURE CITED
(1) Crumpler, T. B., Dyre, W. H., Spell, il., ANAL.C H E ~27, . 1645 (1955). 121 Heller. W.. in Weissberaer, A,, ('Physical ' Methods of Orianic Che&stry," Vol. I, Part 11, Interscience, NPW - . .. Ynrk. - - -- I 1949. (3) Keston, A,, Laspalluto, J., Proc. Fed. SOC.Exatl. Biol. 12, 229 (1953). ( 4 ) Rouy, A.,'private communication. (5) Saltaman, R. S., Abro ast, J. F., OSborn, R. H., .$SAL. '%EM. 27; 1446 \ -
!
I
(1955). RECEIVEDfor review July 19, 1957. Accepted January 15, 1958.
Identification of Sod um Phosphates with an X-Ray Focusing Camera D. E. C. CORBRIDGE' and F. R. TROMANS Research Department, Albrighf & Wilson (Mfg. ), ltd., Oldbury, Birmingham, England
b X-ray powder diffraction data, recorded with a Guinier-type focusing camera, are presented for 60 crystalline sodium phosphates. The greater resolution and increased definition of the diffraction lines compared with those obtained with the usual DebyeScherrer type camera, offer several advantages for the identification and analysis of this class of compound. of the sodium phosphates have considerable industrial application in water treatment, food and textile processing, and the manufacture of detergent and pharmaceutical products. X-ray powder diffraction ANY
Present address, Research Department, Unilever, Ltd., Port Sunlight, Cheshire, England.
photographs recorded by the focused beam technique (5) are particularly valuable for the identification and analysis of the great variety of crystalline phosphates which are known to exist. In addition to the usual advantages of the x-ray method-e.g., speed, sensitivity to crystalline form, and smallness of sample required-focusing cameras provide a greater wealth of diffraction data than the more widely used parallel beam method (6). Focusing camera patterns are presented for 60 well characterized sodium phosphates. The ASTM Index ( I ) contains about 20 cards relating to different sodium phosphates, but several of these are in error owing to the presence of impurities, or to false identity of material.
APPARATUS AND TECHNIQUE
The photographs were recorded on a four-tier Sonius focusing camera similar in design to that described by de WOH ( 1 1 ) (Figure 1, A ) . Exposures were for 2 hours on Ilford G film using CuK a radiation a t 50 k v . ; 18 ma. were obtained from a Kenton Yictor Raymax unit with a vertically mounted filament. Samples were finely powdered in a small mortar and dusted into thin layers between adhesive Sellotape. Sample thickness and exposure were adjusted to enable the weaker diffraction lines to be recorded. MATERIALS
The purity of the materials Tc'as believed to be greater than 99%, except where otherwise indicated. Crystalline impurities if present to the extent of less than 1%, were not expected to give VOL. 30, NO. 6, JUNE 1958
1101
