Anomalies in Extinction Coefficient Measurements LIONEL S. GOLDRING’, ROL-AND C. HAWESZ, GEORGE H. HARE, ARNOLD 0. BECKMdN, AND
MICHAEL E. STICKNEY Beckman Instruments, Inc., South Pasadena, Calif., and The Massachusetts Institute of Technology, Cambridge, Mass. Numerous unexplained departures from absorption theory in photoelectric spectrophotometry have been reported. The possible causes for such anomalies were studied. Physical reasons are proposed for results found in the literature, which may quantitatively account for the departures observed. Experiments that illustrate the precision attainable w-ith the Beckman quartz spectrophotometer, when the proper precautions are taken, are described. It is now possible to show what experimental conditions are necessary in order to limit the precision and accuracy obtainable by means of photoelectric spectrophotometry solely by the performance of the instrument, and under what conditions the instrunlent may give its best performance.
S
struments, Inc., bulletin (3). In particular the term “absorbancy” is substituted for the more loosely defined “optical density.”
I S C E Vandenbelt, Forsyth, and Garrett (30) called attention to them in 1945, anomalies in extinction values with varying concentration, or departures from the Bouguer-Beer law observed in measurements made with the Beckman quartz spectrophotometer, have attracted the interest of spectroscopists (8, 11, $3). It has fiequently been assumed that instrumental nonlinearities are responsible for the observations. This has resulted in part from lack of agreement regarding the magnitude of the departures, and additionally from the extremely discorda n t results reported in collaborative studies of instrument pelformance by users interested in the analytical employment of absolute extinction coefficients (11,12,15, 22, 31). These findings have led to grave misgivings regarding the advisability of employing standard extinction values for analytical puiposes, of the suitability of the Beckman instrument for the determination of extinction values, and even of the application of spectrophotometric methods in general for such purposes. I t is the purpose of this report to review the known causes of such findings, to call attention to certain easily overlooked causes, and to present data indicating that, for a carefully analyzed system, these causes can account quantitatively for the anomalies. In addition, experimental results are included which indicate the order of both precision and accuracy achievable with meticulous attention to details of technique. Hardy and Young (17) have stated that the absorption la\\ is invaiiably follox\ ed by a sample containing a single absorbing molecular species, if flalvless technique and proper interpretation are employed. That this is not necessarily true is well knovin to infrared spectroscopists who have worked with gas samples exhibiting pressure broadening. Here intermolecular energy transfer a t higher concentrations causes a modification of the contour of absorption bands, resulting in true changes in monochromatic extinction coefficients with concentration (26). Even obvious causes for apparent anomalies are briefly mentioned here, in order to make this summary as complete as possible and to afford an opportunity to particularize in some instances regarding the instrumental and chemical systems. Chemical and photochemical problems are considered first, instrumental ones second, and technique factors last. While the literature on the last is not reviewed, special mention may be made of the excellent summary by Abbott ( 1 ) . Terminology used follom standards suggested by the Committee on Colorimetry of the Optical Society of America (27), of the Xational Bureau of Standards, and of the American Society for Testing Materials. It is descrihed in detail in a Beckman In-
CHEMICAL AND PHOTOCHEMICAL F4CTORS
General. In all that follows, it is assumed that the present concern is with dilute solutions and with optically absorbing chemical species which uiidergo no alteration by dissociation or by reaction (other than adsorption) with any constituent of sample, solvent, dissolved gas, or container. It is, of course, also assumed that the cleanliness of the apparatus is beyond question, that apparatus weight and volumetric calibrations have been verified, and that chemical manipulations of tested reliability are employed. Turbidity. This may be of importance (8)for the determination of absolute extinctions, since significant turbidity may easily escape casual observation, and may vary with time and temperature or w ith otherwise apparently insignificant details of technique. I t is usually not troublesome in the study of absorption law anomalies because solvent turbidity effects \?ill be included in usual cell corrections, while slight turbidity in a concentrated absorbing solution will merely introduce a small error in its extinction coefficient, without affecting the relation between dilution and apparent absorption. However, because of the ready growth of microorganisms in distilled water and many other common chemical solutions, turbidity must be especially guarded against in such studies when working with aggregating, peptizing, or coagulating agents-for example, chromate ion. Common laboratory dust can, however, easily cause erratic errors of 0.001 to 0.002 in absorbancy, especially in very short path length cells where it preferentially settles in cell windows. Trouble from these sources may generally be discovered by centrifuging samples. Suspected results should be carefully verified using several lots of reagents and solvents. Fluorescence and Molecular Scattering. Because of the optical inefficiencies of these processes they are generally insignificant. A check should be made if working in a wave-length region such as the short wave-length limit of a phototube or near the transmission limit of the absorption cell wall material, where instrumental efficiency may also be low-. Freedom from fluorescence errors may be checked by a filter test, such as for stray light. Solvent Absorption. This is of no concern if it is Blight, because it will be included in cell corrections. All batches of solvents including water should be checked for transmission before use, and occasionally during storage. Photochemical Reactions. These may be of importance, in ultraviolet work especially, and should be guarded against by watching for changes in extinction values with time after sample
1 Present address, Nuclear Derelopment Associates, Inc., White Plains, N. Y. * Present address, Applied Physics Corp., Pasadena, Calif.
869
ANALYTICAL CHEMISTRY
870 preparation and after exposure to the radiant beam in the instrument. Adsorption on Glassware and Cell Walls. This is of especial concern when working with very dilute solutions. It is easily tested for by filling an initially dry absorption cell repeatedly with the solution and measuring absorbancy after each filling. Solvent Evaporation. No comment is required, except to note that if stoppered cells are employed for a prolonged sequence of measurements it may be necessary to keep the sample compartment cover slightly warm to avoid condensation of a droplet on the stopper. A gooseneck desk lamp serves conveniently. IN STRUM ENTA L FACTORS
Although the general design features of the Beckman quartz spectrophotometer have been described (7), it seems worth while to describe briefly likely sources of instrumental difficulties, the precautions taken to minimize them in design and manufacture, performance achieved, and valid tests which the user may make to ensure that his instrument is in good working order. Wave-Length Accuracy, Temperature Coe5cient, and H y s t e r e sis. Each instrument is checked against mercury emission lines a t the wave lengths and to within the tolerances shown in Table I. Typical temperature coefficients (chiefly due to the effect of temperature on the refractive index of quartz) are 0.1 mp per degree centigrade a t 546.1 mp, and 0.003 mp per degree centigrade at 253.6. Hysteresis of motion is about 0.5 mp a t 546.1, hence wave-length positions should always be approached from the same (longer wave length) direction.
Table I.
Wave-Length Check Points and Tolerances (ita Millimicrons)
Wave Length 222.47 237.83 239.94 248.27 253.6 265.2 275.3 280.35 289.36 296.7 302.15 312.6
Tolerance, =t
0.1 0.1 0.1 0.1
0.1 0.1 0.12 0.12 0.15 0.15 0.15 0.2
Wave Length
313.2 334.1 365.0 404.7 407.8 435.8 491.6 546.1 577.0 579.1 690.8 1014.
Tolerance, rt
0.2 0.2 0.2 0.4 0.4 0.4 0.5 0.2 0.6 0.6
2.0 +9 -3
A study of the wavelength accuracy and other characteristics of the instrument has been reported by Gibson and Balcom ( l a ) . Instruments should occasionally be checked for wave-length &curacy against emission lines of a low pressure mercury, hydrogen, or other gas discharge lamp, or against flame emission lines. A convenient adjustment is provided ( 2 ) to compensate for any slight shift in wave length due to age or handling. An extremely important factor, often overlooked by users inexperienced in spectroscopy, is that the “background response” (the resultant of spectral variations in phototube sensitivity, lamp emissivity, and over-all optical transmission efficiency), in combination with practical limitations on spectral band width, sometimes result in substantial differencesbetween the effective central wave length of the spectral interval and the nominal value. & a result of all these factors the available wavelength accuracy is not great enough to permit the uncritical use of published extinction coefficients and wavelength values for instrument calibration, when working near the limits of the operating range of a particular phototube or lampfilter combination, unless the change of extinction coefficientwith wave length is very slight. The same is true in any wavelength region if the absorption bands are steep-sided, particularly if measurements must be taken on the sides of the bands (18). A convenient check on the difficulties to be expected is to determine whether appreciable differences in measurements result
from doubling the slit width. It should be warned that this test may not give information applicable to more than the one instrument, near phototube operation limits because of variations in spectral sensitivity between phototubes of the same type. For instance, commercial tolerances on 8 5 surface phototubes permit about thirty-fold differences in sensitivity between 600 and TOO mp. A way of avoiding these problems is to use the monochromator merely to isolate emission lines from a low-pressure gas discharge, as described by Tunnicliff (68). However, this practice leads to problems of its own, as emphasized by Kortum (23),and discussed in some detail under “stray light” belonv. Resolution. Effects Due to Finite Spectral Band Width. Many different definitions exist for band width. Hogness, Zscheile, and Sidwell (10)employed the “half intensity band width” determined by measurements on a monochromatic emission line. When employing a heterochromatic source the half intensity band width is equivalent to the “effective band width” (16),and includes one half of the total wavelength range of the spectral region isolated, or “spectral slit width.” This half-spectral range includes wave lengths usually contributing about three fourths of the total energy (exactly three fourths, if background response and dispersion are unchanged over the spectral region isolated). Because a finite (and often substantial) spectral interval must be accepted in order to obtain sufficient radiant energy to give good accuracy of measurement, two distinct and significant types of departure from simple theory occur. A mathematical derivation of some pertinent relationships is given below. The largest effect of finite spectral band width is on absolute extinction coefficients, which may readily differ by several per cent from the true value a t the nominal wave length. Examples are computed below. This is especially troublesome in spectral regions where background response changes rapidly with wave length or operation conditions-for instance, near 325 mp with the tungsten lamp, where lamp emissivity is very sensitive to voltage variations. Absorption law anomalies may also, in part, be accounted for by the effect of finite spectral band width. At low absorbancies it is, however, a minor factor as compared with others to be described. A good test of the difficulties to be anticipated is again afforded by making measurements a t several slit widths. Extrapolating the data to zero slit width will of course provide values unaffected by limitations of resolution, unless unusual spectral d e tail is present. Because of the relatively unfavorable operating conditions in the 600- to 625-mp region where the two phototubes may be used interchangeably, this source of trouble has caused many users to have misgivings about the reliability of the instrument. In this region the phototubes have opposite sensitivity slopes, and that of the ultraviolet-sensitive tube is very steep. Absorption Cell Imperfections. Beam Deviation Effects, Wall Scattering, Reflections. Unfortunately, phototubes with uniformly sensitive cathode surfaces do not exist. When tested with an image of a small area source of light focused on the cathode, variations of several fold are frequently found rn the spot is moved about. I n this respect the red, 5-2 (cesium oxide) surface appears usually to be inferior to the ultraviolet, 5-5 (cesium antimony). The envelope surfaces of both phototubes are roughened by sandblasting to diffuse partially the beam. Such treatment is not itself uniform, and the resulting surface is very sensitive to contamination by oil, fingerprints, etc. hiore effective diffusing screens or the use of integrating sphere beam diffusers entail severe loss of efficiency, requiring much wider spectral bands, which present their own problems. The choice made in the instrument design requires the user to be somewhat more painstaking in measuring and computing cell corrections and in preparing reflection samples or solid transmittance samples, but it affords numerous compensating advantages.
V O L U M E 25, NO. 6, J U N E 1 9 5 3
871
Because of these facts it will be obvious that cell corrections must be determined for each particular set of operating conditions (8) when highest accuracy is required, and that measurements on solid samples containing striae or surface imperfections or samples having differences in transmission or reflection over the beam area must be viewed with skepticism or repeated on various sample areas to determine the effective average values. Also standardization against an air path or against samples of different refractive index (at the wave length of measurement) from the unknown is a hazardous procedure. Accessories should be carefully inspected to determine that they meet exacting requirements in respect to cell placement precision, negligible or uniform beam masking, etc.
taken to avoid it, the beam passes repeatedly through the cell, being reflected back on itself by the rearward cell walls and returned again by the front faces, the exit beam lens, the outer faces of the slit jaws, and possibly by other suitably disposed surfaces in the cell compartment. As will be shown in the experimental part, it is not unlikely that this cause is responsible for a substantial part of the reported anomalies. Variations in reflection efficiencies as well as differing cell geometry, including varying cell path lengths, may help explain the differences between their magnitudes. A theoretical treatment of the effect is given in the mathematical section of this paper, while a typical predicted extinction us. absorbancy curve is shown in Figure 1. The figure also shows recalculated curves obtained experimentally for potassium chrw mate by Vandenbelt (50) and by Kortum (23). The values of the former are brought into agreement with the theoretical curve a t A = 1 by assuming the correct extinction coefficient is 4782, and stray light is 0.03%. The Kortum data is that of curve D of his Figure 52, taken with the Halle-Muller double monochromator. and brought into agreement a t A = 1.06 by assuming a n E value of 4413 (436 mp). Kortiim attributed the observations to residual stray light. It is believed that multiple reflections offer a better explanation.
TO BE SUBTRACTED FROM ABSORBANCY READINGS (IN PERCENT OF READINGS) CURVE C IXSTRAY LIGHT, ABSORE&O WITH @*OK 1
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