m/e 165-though mechanistically important peaks have been deduced. The alternative procedure of using high resolution data yields essentially the same type of inlamation; the elemental compositions of ions are obtained directly rather than by inference, but hydrogens cannot be structurally distinguished. In the case of structure elucidation of unknown molecules, maximum information will result from the use of both high resolution and labeled TMS derivatives.
ACKNOWLEDGMENT
We are grateful to Pamela Crain for technical assistance. RECEIVED for Review September 6, 1967. Accepted October 26,1967. Research supported by the Robert A. Welch Foundation (4-125) and the National Institutes of Health (GM 13901). A. M. Lawson is indebted to the Robert A. Welch Foundation for a Postdoctoral Fellowship.
A Differential Interference Refractometer E. M. Thorndike Lamont Geological Observatory, Columbia University, Palisades, N . Y., 10964, and Queens College, Flushing, N . Y., 11367
A. P. Marion Queens College, Flushing, N . Y. 11367
MEASUREMENTS OF REFRACTIVE INDEX have been employed in the analysis of liquids and gases for many years. For liquids, wide use has been made of the Abbe and dipping refractometers in which the refractive index is determined from the known refractive index of a glass prism and an angle which can be related to the critical angle at the surface between the liquid and the prism. In precision instruments of this type, the accuracy is approximately three in the fifth decimal place. The Rayleigh, Jamin, and Mach-Zehnder interference refractometers have been used primarily for gases and only to a lesser extent for liquids. Kinder ( I ) has recently developed a refractometer using an interferometer of the Michelson type. In all of these interference refractometers, the difference between the refractive indices of an unknown gas or liquid and a standard is determined by measuring the difference in the wavelength of light in the two media. With care, an increment in refractive index in the seventh or eighth decimal place can be measured, but long light paths and very good temperature control are essential for the higher accuracy. The instrument described in this article is of the interference type and is designed for use with liquids. It has an accuracy in excess of the Abbe and dipping refractometers but, in its present form, less than that obtained with many interference refractometers, the accuracy being approximately one in the sixth decimal place. It is of simple design and provides versatility and freedom from compensating plate and zero-order fringe problems. DESIGN AND THEORY
The instrument is a Michelson-type interferometer with arms of equal length arranged so that the light paths through the cells for the known and unknown liquids are parallel and adjacent, The cells are of the same overall length and have glass end-plates and flexible bellows for side walls. Each is divided into two parts by a transverse, movable glass plate mounted on a common carrier and driven in a direction parallel to the light paths by a calibrated screw. The cells are (1) W. Kinder, Oprik, 24, 323 (1966-67).
236
ANALYTICAL CHEMISTRY
equipped with holes for filling and are crossconnected by tubes so that one liquid can flow freely between SIand Sz and a second liquid between ULand Uz(Figure 1). It can be assumed that the cells SIand SZhave been filled with a standard liquid of refractive index n, and the cells .VI and Uzwith an unknown whose refractive index is nu, and that the interferometer has been adjusted to give straightline fringes with monochromatic light having a wavelength, X,in a vacuum. If the center partitions of the cells are moved a distance, d, toward the observer, the number of waves in the path 1 (through S1 and Vl) will be increased by 2dnu/X and decreased by 2dn,/X giving a net increase of 2d (nu - n,)/X. In a similar manner, the net decrease in the number of waves in path 2 (through cells UZand SZ)is 2d (nu - n,)/X. Thus, the number of interference fringes, X,that move across the field is given by the equation X = 4d (nu - n,)/X and the difference in refractive index between the unknown and known is An = nu n, = XX/4d. (1)
-
Thus, it becomes possible to determine the difference in refractive index for any wavelength by counting fringes and measuring the corresponding displacement of the center partition. In principle, the standard can be any fluid, air for example, but with a liquid as unknown, the number of fringes crossing the field of view may be large and require automatic counting. In practice, the method is particularly attractive when n , and n, are approximately the same so that the number of fringes to be counted is small. A feeling for the performance of the instrument can be obtained by considering an example with light in the visible region of the spectrum and a displacement of the movable plates of 1 cm. Then, substituting in Equation 1 , An 10 - 5 X and, assuming that the number of fringes can be estimated to 0.1 fringe which experimentation shows is not difficult, differences in refractive index of one in the sixth decimal place are detectable. If the number of fringes to be counted is limited to 100 or less, the difference between the known and unknown refractive indices must not exceed Obviously, the number of fringes to be counted can always be lowered by reducing the displacement but this may introduce difficulties in obtaining the required accuracy.
-
1
CELL
LIGHT SOURCE
Ab
BEIH SPLITTER H I
2
/'[/MIRROR
H4_--
'I
OBSERVER
Figure 1. Schematic diagram of interference refractometer
CONSTRUCTION AND ADJUSTMENT
The refractometer was constructed largely of parts that were available in the laboratory. While this procedure does not yield an ideal, well-designed instrument, it fills an intermediate step in the development of such apparatus and is adequate to demonstrate the capabilities of the method. The instrument shown in Figure 2 and described below, is optically and mechanically equivalent to the original model but includes simplifications planned for the model currently under construction. The base of the interferometer is an aluminum plate 38 cm x 46 cm x 2.5 cm in which a hole 13 cm X 34 cm is cut to accept the water bath containing the cells for the known and unknown liquids. The interferometer mirrors are mounted on this base with flexure plates which permit adjustment of the directions of their normals. The focussing mechanism of a microscope provides motion in the line of sight for M2. This is adjusted to make the lengths of paths 1 and 2 equal. The end mirrors, M I and M,, are positioned so that their normals are parallel to the direction of travel of the carriage, to which the movable dividing plates of the cells are attached, and to the base plate. The beam splitter, Ma, and the mirror, M4, are adjusted so that their normals are parallel to the base plate and make angles of 45' with those from M I and Mz. A small telescope with a Gauss eyepiece is useful in making these adjustments. The final adjustment of the interferometer is made by observing the point of a needle placed in front of a mercury arc source, first with light traversing path 1 and then path 2. The end mirrors are rotated about horizontal and vertical axes until the needle points appear to coincide. (Weaker images formed by reflections from the glass surfaces of M 3 and M 4 are ignored.) Fringes should now appear. They can be made to have any desired orientation and width by tilting MI and M2 slightly. The end mirror,
M,, is now moved slowly in the line of sight until the fringes are extremely sharp and straight. The two light paths are now essentially equal. The appearance of fringes with a white-light source can be used to give assurance that the paths are exactly equal, but this adjustment is not necessary. A sturdy aluminum tank serves as mounting for the end plates of the cells and for the mechanism for driving their center dividers and also holds the water for maintaining constant, known temperature for the liquids in the cells. The sides and bottom of the tank are 1.2 cm thick and the ends 2.5 cm thick. Angle brackets, positioning pins, and machine screws maintain the tank in a definite position relative to the interferometer base but allow its removal for refilling the cells. Four plates of optical glass, 2.5 cm in diameter and 5 mm thick, are mounted in polyvinyl chloride holders which are fastened to the walls of the tank. Two glass plates, 5.7 cm in diameter and 6 mm thick, are mounted in a brass plate that is attached to the movable carriage of a micrometer slide (Gaertner Model M-301). The ends of four bellows (6.9-cm 0.d. and 2.5-cm i.d.) made of polyvinyl chloride (obtained from Gagne Associates, Binghamton, N. Y.)are sealed to the glass plates by pressure transmitted by O-rings in such a way that the rings are not in contact with the liquids in the cells. The cells are cross-connected with polyvinyl chloride tubes and the same type of tubing is used to provide means for filling and emptying the cells. The tank and mountings for the cells are made with normal instrument shop care but, in terms of the wavelength of light, the cells do not have equal lengths and the glass surfaces are not necessarily plane or parallel. Therefore, when the cells are filled with distilled water and the tank is mounted in the interferometer, the pattern of interference fringes will be altered and the end mirrors must be readjusted. With the glass plates used, no adjustment of the end mirrors gave fringes that were straight and evenly spaced. It would be clearly an advantage to have glass plates with surfaces of better quality, preferably plane to 0.1 wavelength. Then evenly-spaced, straight fringes could be obtained by adjustment of the end mirrors. The entire refractometer rests on a massive metal base and is enclosed by a shield to protect it from air currents which might produce temperature fluctuations. The air inside the shield is circulated by a small fan and cooled and dried by passing it over coils of copper tubing through which cold water flows. This is necessary to prevent condensation on the cell windows when working at low temperatures. Water from a constant-temperature bath is pumped through the tank around the cells to maintain constant temperature in the cells. The light source and filters, as well as the observing telescope, are mounted outside the shield. A shaft from the micrometer slide that drives the dividing plates extends through the shield so the plates can be moved from outside. MEASUREMENTS ON SODIUM CHLORIDE SOLUTIONS
Aqueous solutions of sodium chloride with molarities of 0.1168, 0.2628, 0.3504, 0.4545, and 0.5548 were prepared from dried, reagent-grade sodium chloride and distilled water. Hypodermic syringes were used to flush the cells with distilled water between runs until free of chloride and then several times with the solution to be measured. A few readings were taken, a fresh sample of solution was introduced without rinsing, and another set of data was obtained. Good agreement was interpreted as an indication that the wash water had been removed and that the system was ready for further investigation. VOL 40, NO. 1, JANUARY 1968
8
237
bn/MzI02
I
I 0
KRUIS
0 GRUNWALD a n d I E R K O W I T Z X
THIS WORK
I
Figure 2. Interference refractometer The difference between the refractive indices of each solution and distilled water, An, was determined at a number of temperatures ranging from 10" to 45" C for four wavelengths: 6563 A (hydrogen), 5893 A (sodium), 5461 A (mercury), and 4358 A (mercury). This involves counting the number of fringes passing the cross hairs of the observing telescope and noting the corresponding displacement of the divider plates. Substitution in Equation 1 gives the difference in the refractive indices. This quantity divided by the molarity, &/M, gives a convenient quantity with which to work. An inspection of the data shows that the temperature dependence of AnIM for any wavelength can be represented reasonably well over the range of temperature used by the equation
(An/Wt
=
(An/M>o [1
- at
+ Pt21
(2)
The three quantities: (An/M)o, a, and /3 were calculated by least squares for each concentration for each of the four wavelengths. Values of (An/M) at 25" C obtained by substituting the values in Equation 2 are given in Table I. For most concentrations, the observations are grouped near 25' C, so that values of (An/M) at this temperature have good experimental basis although values of a and /3 are uncertain. However, for the concentration
I
I
I
I
I
I
I
010
20
30
40
,50
60
.70
MOLARITY
Figure 3. Change in refractive index per mole of dissolved sodium chloride against molarity 0.3504M, the values of a and /3 are probably accurate to 10%. The average values for the four wavelengths used are d = 4.9 X 10-3and/3 = 5.5 x 10-j. In order to compare these results with those of Kruis ( 2 ) and of Grunwald and Berkowitz (3), values of (An/M) at 25" C and wavelength 5461 A were obtained from Kruis' results by graphical interpolation, and the value at the highest concentration used by Grunwald and Berkowitz was calculated from their data. Figure 3 shows these values together with those obtained in this work. The agreement is within the limits set by the uncertainties in the measurements of a and X. CONCLUSIONS
It is clear from this work that a differential interference refractometer employing variable lengths for the cells containing the known and unknown fluids is relatively simple to construct and operate. The interpretation of the observations is extremely direct involving no compensator or use of "zero order" fringe. It appears that the accuracy obtainable for relatively large values of An is determined primarily by that for dand X but for very small values of An uniformity of temperature is of great importance. ACKNOWLEDGMENT
The major part of the construction was done by D. A. Veit. The observations were made by F. H. Wirth. We are grateful for this assistance.
Table 1. ( A n / M ) at 25" C as a Function of Wavelength and Molarity Wavelength, A Molarity 0.1168 0.2628 0.3504 0.4545 0.5548
238
6563
1.008 X 0.995 0.989 0.981 0.982
5893
5461
4358
1.015 x 10-2 1.025 x 10-2 1.064 x 10-2 1.004 1.012 1.052 0.999 1.008 1.047 0.991 1.OOO 1.036 0,990 1.OOO 1.038
ANALYTICAL CHEMISTRY
RECEIVED for review August 31, 1967. Accepted October 24, 1967. This work was supported by the U. S. Department of the Navy, Office of Naval Research, contract Nonr 266 (48). Lamont Contribution No. 1130. (2) A. Kruis, 2. Physik. Chem. ( L e i p i g ) , B 34, 13 (1936). (3) E. Grunwald and B. J. Berkowitz, ANAL.CHEM., 29, 124 (1957).
