solvent selection, and for the actual measurement. It is possible to run the pure compound, estimate a heat of decomposition, check two or three solvents for applicability and reactivity, and make the measurement in the chosen solvent on a sample of approximately five milligrams. Samples purified by thin layer chromatography are large enough to be used. The method is, therefore, well suited to the study of the first product obtained by the organic chemist. For example, considerable information can be obtained about a potential explosive before a dangerous amount of the compound has been prepared. A thermal phenomenon, the effect of temperature on reaction rate (activation energy), is studied by a thermal method. Most other determinations involve gasometric determinations of the rates with the implicit assumption, not always valid, that the reaction rate is proportional to the gas evolution rate. The estimation is rapid. Commercial equipment is available. The procedure presented is certainly not definitive; however, the authors
believe that reasonable results will be obtained when the method is used within its limitations.
ACKNOWLEDGMENT
The authors thank S. K. Yasuda and M. J. Naranjo of this laboratory for preparative and analytical thin layer chromatographic work.
LITERATURE CITED
(1) Barrall, E. M. 11, Porter, R. S., Johnson, J. F., ANAL.CHEY.36, 2172 (1964).
(2) Borchardt, H. J., Daniels, F., J. Am. Chem. SOC.79, 41 (1957). (3) “Chemistry of the Solid State,” Garner, W. E., ed., Butterworths, London, 1955. (4) Johnston, J., Atomic Weapons Research Establishment, Aldermaston, Berkshire, England; private communication, 1961. (5) Kissinger, H. E., ANAL.CHEM.29, 1702 (1957). (6) Krein, G., Ezplosivstofe 13, 205 (1965).
(7) Lind, C. D., U. S. Naval Ordnance Test Station, ChinaLake, Calif.; private communication, 1961. (8) Novozhilov, B. V., Dokl. Akad. Kauk SSSR 154, 106 (1963). (9) O’Neill, M. J., ANAL. CHEM. 36, 1238 (1964). (10) Rabovskii, B. G., Kogan, V. hl., Furman, A. A., Zh. Fiz. Khim. 38, 1574 (1964). (11) Reed, R. L., Weber, L., Gottfried, B. S., Ind. Eng. Chem., Fundamentals 4, 38 (1965). (12) Rideal, E. K., Robertson, A. J. B., Proc. Roy. Soc. (London) Ser. A 195, 135 (1948). (13) Robertson, A. J. B., J . SOC.Chem. Ind. (London) 61, 221 (1948). (14) Robertson, A. J. B., Trans. Faraday SOC.45,85 (1949). (15) Smothers, W. J., Chiang, Y., “Differential Thermal Analysis: Theory and Practice,” Chemical Publ. Co., New York. 1958. (16) Watson: E. S., O’Neill, hL J., Justin, J., Brenner, ?I AKAL. ., CHEW 36, 1233 (1964). RECEIVEDfor review October 4, 1965. Accepted December 29, 1965. This study of reaction kinetics was performed under the auspices of the U. S. Atomic Energy Commission.
New Concept in Precision Photometric Analysis Using a Radioisotopic Light Source HARLEY H. ROSS Analytical Chemistry Division, Oak Ridge National laboratory, Oak Ridge, Tenn.
A new experimental approach is presented for making high precision photometric measurements. The theoretical interpretation of the proposed system is based on the unusual properties of a beta-activated radioisotopic light source. In addition to high precision, other advantages of the technique include increased stability, controlled sensitivity, simplicity, low power requirements, and direct digital results. Five colorimetric systems were investigated and the results are shown to agree with a simple mathematical model. The available high precision of the system enables absorption photometry to be effectively extended to the analysis of large amounts of material.
A
LTHOUGH ABSORPTION
PHOTOMETRY
is one of the most valuable techniques available to analytical chemists, its use is generally restricted to the analysis of trace materials. This is easy to understand, if one recognizes that the precision of measurement with conventional photometric instruments cannot compete with that obtained by standard gravimetric and titrimetric 414
ANALYTICAL CHEMISTRY
procedures. I n an attempt to overcome this shortcoming, a variety of refinements have been devised to augment both the sensitivity and precision of the technique. For example, photometric instruments have been developed to a high degree of reliability by the use of stabilized power supplies for light sources and other electronics, low-noise amplifiers, dual monochromators with improved baffling, photomultiplier-tubedetectors, and dual-beam instrumentation. Conversely, to extend the sensitivity of the photometric method, a number of special measurement procedures have been developed; these techniques are discussed and summarized by Boltz and Schenk (1). This high degree of sophistication in experiment and instrument design has greatly extended the usefulness of absorption photometry, but little has been done to develop a n alternate physical basis of measurement to extend even further the upper limits of sensitivity and precision. An excellent article by Muller discusses this problem with considerable insight
(4)*
The research presented here represents a unique theoretical and experimental approach for making precise
photometric measurements. The high degree of available precision enables absorption photometry to be effectively extended to the analysis of macro amounts of material. Additionally, the unusual design of the proposed instrument system carries with it a number of advantages equally as important as the improved precision. Colorimetric systems are used to illustrate the basic principles involved and the results are shown to be in agreement with a simple mathematical representation of the system. THEORETICAL
Conventional color photometer systems typically consist of four basic sub-systems: the continuously-emitting light source and power supply, the radiant energy discriminator (filters or monochromator), an analog detector and associated electronics, and a read-out device (meter or strip-chart recorder). Advanced instruments include additional refinements, which are too well known to delineate here. h block diagram of a proposed new photometer system is shown in Figure 1. I n this scheme, significant changes in
R A ~ ~ o i S o T o P ~R,C LIGHT ---)I
SAMPLE
System. An exact analytical description of the system is difficult t o
AMPLIFIER
+
DISCRIMINATORS
SOURCE
POWER SUPPLY
H I G H SPEED SCALER
Figure 1. Block diagram of radioisotopic source photometer system
design are made in three of the four subsystems noted above. These are the light source, the detection system, and the read-out device. No filter or monochromator is indicated in the proposed system because such a device was not used in this investigation; however, there are only limited difficulties in introducing this component into the proposed scheme. The properties and characteristics of the individual components are discussed below. Radioisotopic Light Source. The light source for the proposed system consists of two distinct components, a scintillating material and a small amount of a fi-emitting radioisotope. The scintillating material can be either liquid or solid, organic or inorganic; the isotope can be mixed with, deposited on, or located in the vicinity of the scintillator. Interactions of the scintillator with the emitted 0 particles caused the scintillator to be excited with the subsequent emission of visible light. Under the influence of B excitation, the light source possesses two important characteristics necessary for its use in this application. First, the visible light output from the source consists of a train of individual and discrete pulses rather than the continuous emission observed with a conventional light source. Second, the intensity of these pulses is not constant but varies from zero to some maximum value; the intensity of any given pulse depends on the energy of the fi particle causing it. These two properties of the source are essential for operation of the proposed system. A mathematical description of the source emission characteristics is given in a following section. Detector and Associated Electronics. The detector for the system is a conventional photomultiplier tube. The face size of the tube depends on the geometry of the sample transmission system. High gain and low noise are desirable but not mandatory. The tube should have maximum spectral sensitivity a t about 430 mp. The linear amplifier is a type generally used in radiation detection. The amplifier should have a minimum bandwidth of 1 mc. and upper and lower discriminators with a stability of 0.2% of the full output of the amplifier. Of
course, the signal-to-noise ratio should be as high as possible. Read-Out Device. The read-out device in the proposed system is a high speed scaler. This should have a minimum pulse acceptance rate of lo4 per second without pile-up losses and its sensitivity should be high enough to permit triggering directly by the linear amplifier. A common power supply is used to furnish high-voltage to the photomultiplier tube and low voltage to the amplifier and scaler. All of these electronic units are commercially available.
I
tained with scintillation detectors are not well characterized mathematically. However, a n approximate mathematical model can be developed involving only two rather obvious and simple assumptions. I n the following operations, a general solution will be shown for a hypothetical system. Specific experimental examples will be described later. As noted previously, light pulses from 8 scintillator excited by a p emitting source are not of constant intensity. If one plots the intensity of these pulses (in terms of electronic pulse height, P) us. counts or pulses per unit time, a pulse height spectrum is obtained. It has been shown (2) that many 0emitting nuclides, when observed under specific conditions, exhibit a pulse height distribution that follows an exponential function over a large portion of the spectrum. An example of this is shown
.-
PULSE HEIGHT
Po PULSE HEIGHT
D
PULSE HEIGHT Figure 2.
PULSE HEIGHT Beta pulse-height distributions VOL. 38, NO. 3, MARCH 1966
e
415
in Figure 2A. Note that deviations from exponential behavior occur only a t the extremes of the distribution. Assume first that the distribution is completely exponential over its entire range. This is a reasonable assumption because the following analysis will not consider the low pulse height end of the spectrum and the error introduced in the high pulse height end of the spectrum is small because of the exponential nature of the distribution. If the assumed distribution is plotted on a semi-log graph, a straight line results and an intercept with the pulse height coordinate can be found for any arbitrary value of total count. I n the case shown (Figure 2 A ) , a pulse height, Po, is the intercept for a total count of ten. Note, however, that any total count-Le., 100 or 1-could have been used to define the intercept. The illustrated pulse height distribution is experimentally obtained by observing the pulses from a beta-activated scintillating sample directly. If a second spectrum of the sample is taken under similar conditions with a weakly absorbing colored filter placed between the scintillating source and the detector, a beta spectrum shift is observed. That is, the intensity of each pulse from the source is reduced by partial absorption in the filter, and because observed electronic pulse height is directly proportional to light pulse intensity, a spectrum shift is required. Filters of increasing opacity will cause increasing shifts in the distribution. The result is a family of distributions illustrated in Figure 2B. The pulse height intercept ( P ) of each of these distributions can be found by use of a Stern-Volmer equation ( 7 ) :
where
P = intercept of filtered sample Po = intercept of directly observed sample (at any value of total count) K = a constant A = effective absorbance of the filter If instead of a filter, a colored solution is used as the absorber, the BeerLambert relationship, A = abc, can be substituted into Equation 1 to give:
where effective molar absorptivity of the color species b = path length of the solution c = molarity of the absorbing species a
=
The constants K and a can be combined to give : 416
ANALYTICAL CHEMISTRY
I
I
I
I
8
Figure 3. tion
p = - PO kbc
+1
Computer plot
(3)
it is now necessary to introduce the second assumption used in the analysis. The enlarged portion of Figure 2B shows that, although spectrum shifts are observed in the system, the distributions tend to intersect each other in a very restricted area. This behavior has been reported previously (5). The second assumption then is to consider the intersection of these distributions to occur a t a single point. ;"Jon,, since no use is made of the portions of the spectra to the left of the assumed intersection point, it is possible to change the coordinate system so that the intersection point becomes zero pulse height-Le., the ordinate of Figure 2B assumes the position of the dashed line. To an observer, it now appears that the family of shifted curves rotates about a point on the total count axis. Figure 2C shows a modified pulse height distribution having the displaced ordinate described above. Interest is now directed from the whole distribution to just a small portion of the spectrum. Discriminators may be introduced into the detection system so that only a segment of the pulse height distribution is observed. These discriminators, d l and dz, are adjusted on the pulse height scale to the positions indicated in Figure 2C. If the detector-counter system is allowed to count only those pulses falling between d1 and d2, the observed count (after some fixed time) corresponds to the shaded area in the figure denoted by ro. If a colored solution is introduced between the source and detector, the expected shift is observed as shown in Figure 2 0 . The pulses occurring between dl and d2 are represented by the lightly shaded area, r,. The heavily shaded area in this figure is the area lost because of the shift. With these effects established, it is now possible to show a relationship
of log ( r o / r e )vs. concentra-
between r,, T , , and c, the concentration of the absorbing species. Consider Equation 3 when k and 6 are equal to unity. Then:
P
= P,/c
+1
(4)
Assign the arbitrary value of 10 to Po. Values of c can be assumed from zero to any positive number and the resulting P from each incremental change can be calculated from Equation 4. From the calculated values of P and from the known y-intercept of 106 for each spectrum, the equation of each generated distribution can be defined. These equations can then be used to calculate the area under the distribution between any two arbitary discriminator levels ( r , when P = Po,rEwhen P < P o ) using the equation: Area
=
106 l ; e - ' d P
(5)
These calculations were carried out using a simple computer program. The arbitrarily chosen values of c were plotted against the computed values of log ( r o / r c ) . The value of dl m s taken to be equal to two and dz equal to three. The resulting graph is shown in Figure 3. The straight line result indicates that the concentration of a colored species in solution can be determined by the displacement it causes in a beta pulse-height spectrum. The linearity of the plot shown in Figure 3 can be evaluated from the deviations of the individual points shown. The average slope of the line computed a t each point is 0.90 with a standard deviation of 0.01; this error is well within the range of the deviation> caused by the assumptions used in the treatment. To better illustrate the series of computations performed, a computer calculation flow-diagram is shown in Figure 4.
Pc IPc = Po WHEN C = O
DISTRIBUTION
)
1 START
VALUES OF
I
- -- - 4C log
Figure 4.
=
log (r,/rJ
=
kbc
'o/'c e------'
I
Computer flow diagram
In practice, photometric measurements using this new instrumental system are made in the following way. The instrument is suitably calibrated to evaluate k for a particular colored system. A reagent blank is placed between the source and detector and a count (r,) is taken for some fixed period of time between two pre-determined discriminator levels. The blank is replaced by a colored sample and the count repeated ( r J . Using the following equation, the concentration of the colored species can be calculated :
R
TO EACH ASSUMED VALUE OFC
(6)
EXPERIMENTAL
Reagents. All of t h e general laboratory chemicals and solvents used in this study were reagent grade. Colorimetric reagents and scintillation materials were the best commercially available quality. The p-emitting isotope, Cl36, was obtained in high specific activity from the Isotopes Division of ORNL and was supplied as hydrochloric acid having an approximate concentration of 300 ,uCi./ml. Distilled water further treated by passage through a mixed-bed ion exchange column was used throughout the investigation.
Apparatus. A11 volumetric glassware was individually calibrated; weight burets were employed for dilutions of t h e standard metal solutions and a calibrated set of weights was taken as the standard reference point for all mass and volume determinations. Fluorescence measurements were made with a Cary spectrophotometer, Model 14, using the fluorescence attachment and ultraviolet excitation. The scintillation detection system was constucted by combining portions of two commercial instruments, a Packard TriCarb liquid scintillation spectrometer (Model 314) and a Radiation Counter Laboratories 256-channel analyzer. The sample housing, photomultiplier tube detector, and pre-amplifier of the TriCarb were connected to the linear amplifier input of the RCL analyzer. All components of the analyzer were used except the high voltage section; detector voltage was supplied by the Tri-Carb unit. A special source-sample holder was fabricated to fit the sample shield of the Tri-Carb. Preparation of Radioisotopic Light Source. As noted in the theoretical section, a number of different types of scintillators can be used for the proposed application. A liquid scintillator source with internal excitation was selected because of the antici-
where
ro = count of the blank r, = count of the sample R = displacement factor k = absorption constant for the system b = solution path length c = molarity of the absorbing species
Of course, the units of' k must be compatible with those of b and c. Accuracy of Measurement. The digital nature of the proposed system allows statistical calculations to be made that will predict the maximum accuracy expected in a particular measurement. If one assumes that chemical manipulations of a sample contribute no error, themaximum accuracy is reflected in the counting statistics of the ratio (ro/rc). Using the standard equation for the counting statistics of a ratio, in terms of r, and r,, error
Figure 5.
Table 1.
Fluorescence spectrum of
liquid scintillator
Calculated Error in R (log r e / r c ) for Assumed Values of ra and rc
=
(9
107
the error results shown in Table I can be computed. From the table, it can be seen that the instrumental error can be made as small as desired, if sufficient counts are taken for the measurement. ;Is the total accumulated count of ro and rc approaches infinity, the error approaches zero. It is also true that at any fixed value of r,, the error in R decreases as the ratio of (r,/r,) increases.
8 x
106
6 X lo6 4. X lo6 2 X lo6
1.250 1.667 2.500
n . oonfi
n nw,Q
n nwi
n
0.2219 0.3979 0.6990
0.2221 0.3981 0.6991
0,090 0.050 0.014
2nfi
5.000
0.0007 0.0010 0.0018
106
8 x 106 6 X 10' 4 x 105 2 X 106
1.250 1.667 2.500 5.000
0.0013 0.0017 0.0026 0.0051
0.0969 0.2219 0.3979 0.6990
0.0974 0.2224 0.3984 0.6994
0.516 0.225 0.126 0.057
lo5
8 6 4 2
X lo4 X lo4 X lo4 X lo4
1.250 1.667 2.500 5.000
0.0040 0.0053 0.0080 0.0159
0.0969 0.2219 0.3979 0.6990
0.0983 0.2233 0.3993 0.7003
1.44 0.631 0.352 0.186
VOL. 38, NO. 3, MARCH 1966
417
Table II. Average Slope ( c / R ) and Standard Deviation of Slope Calculated at Each Individual Point for Various Colored Systems
Ion species Fe+Z(batho) Fe+2 (ortho)
No. of observations 17 18 20 20 14
Ni+2
CrZOT-2
c u +z
pated ease of preparation. First, a scintillator solution was prepared by combining 700 ml. of p-dioxane, 200 ml. of absolute ethanol, 100 gm. of naphthalene] 7 gm. of PPO (2,5-Diphenyloxale), and 0.4 gm. of dimethyl POPOP (1,4-bis-2-(4-methyl-5-phenyloxazoly1)-benzene). After dissolution of the solid materials, the solution was purged for 30 minutes with dry argon. The resulting scintillation mixture exhibited the fluoresence spectrum shown in Figure 5. Although this spectrum was obtained using ultraviolet excitation (366 mF), the same distribution occurs if p particles are used as the energy source; the emission of the solution is characteristic of the solutes
Table 111. Determination of Iron in National Bureau of Standards Steel Sample l O l c
Sample wt'., mg. 11.43
Aliquot
Iron found, %
1 2 1 2 1 2 1 2 1 2 1 2
70.52 70.57 70.49 9.88 70.56 70.66 12.88 70.60 70.33 10.99 70.34 70.19 11.0, 70.24 12.2, 70.48 70.43 Av. 70.45% Rel. std. dev. 0.21oj, NBS value 70.66%. yodev. from NBS value 0.30%. Table IV. Determination of Iron in National Bureau of Standards Sample 161
Sample wt., mg. 47.72
55.56
Aliquot 1 2 3 4 5 6 1 2 3 4 5 6
Av. Rel. std. dev.
Iron found, % 14.97 15.01 15.03 14.96 14.97 14.97 15.04 15.03 14.99 14.98 15.04 15.02 15.00% 0.20%
NBS value 15.01%. yo dev. from NBS value 0.07%.
418
ANALYTICAL CHEMISTRY
Std. dev. of
Av. slope 2 7 . 3 pg./ml./R 4 2 . 3 pg./ml./R 3 8 . 0 mg./ml./R 161 pg./ml./R 142 ml./ml./R
slope, % 0.37 0.47 0.53 0.90 2.10
used and is not a function of the type of energy excitation. Two milliliters of the scintillator solution were pipetted into a standard 1-cm. quartz absorption cell having provision for a glass-stoppered top. Three microliters (= 9 pCi.) of the chlorine-36 tracer solution were added to 100 pl. of absolute ethanol; this solution was transferred into the absorption cell and mixed with the liquid scintillator. The resulting light source is small, stable, and completely self contained. The pulse-height distribution of the source was determined using the counting equipment described previously. Over 85% of the experimental spectrum was found to follow a n exponential function with an average error of 0.02%; this error is within the limits of the counting statistics of the measurement. Fabrication of Source-Sample Holder. The sample holder furnished with the Packard Tri-Carb counting instrument is designed only for counting liquid scintillation samples. Therefore, it was necessary to design and fabricate a new holder, which was made of aluminum and anodized a flat black. The unit was designed t o hold two standard 1-cm. absorption cells, one the radioisotopic light source, the other the sample t o be analyzed. The separation between the two cells is fixed a t 1 mm. Procedure. After integration of the light source, source-sample holder, and electronics into a working system, a general scheme was developed t o check the validity of the theoretical interpretation. Very simply, this involved the preparation of a series of solutions of different concentration, reaction of these solutions with a colorimetric reagent if necessary] measurement of each solution, and, finally, analysis of the data using Equation 6. A series of iron determinations was also made on a National Bureau of Standards steel sample and a nickelchromium casting alloy. Standard master solutions of iron, nickel, and copper were prepared by dissolution of high purity samples of each metal in a n appropriate acid and then diluting to a known volume. Primary standard potassium dichromate was dissolved directly in 0.1N sulfuric acid t o prepare the master chromium solution. Using a weight buret, a set of twenty dilutions was made for each master solution. The nickel, copper, and chromium solutions, requiring no further treatment] were measured directly; iron solutions were reacted with either 1,lo-phenanthroline (ortho)
or 4,7-diphenyl-l,lO-phenanthroline (batho) using conventional colorimetric procedures (6). The colored solutions were measured in 1-cm. quartz cells using a reagent blank to determine r,. The time of measurement was adjusted to give a total count of a t least 106 for the blank and 5 X 105 for each sample. Upper and lower discriminator points were taken to give about a 13% span of the entire spectrum starting 20% above the zero pulse-height level. The same instrumental procedure was used to determine the amount of iron in KBS steel sample lOlc and casting alloy sample 161. Six samples of steel, each weighing about 10 mg., were dissolved in hydrochloric acid. These were carefully diluted to yield solutions containing about 0.5 pg. of iron per milliliter. Aliquots of the diluted solutions were taken and, after buffering with sodium acetate and reducing with hydroxalamine hydrochloride, were reacted with orthophenanthroline to produce the color. Finally, the solutions were diluted and measured. The master iron solution was used as the comparison standard. The casting alloy was treated similarly. RESULTS
Solution Standards. The R us. c plots for the various solutions investigated are shown in Figure 6 and numerical results are presented in Table 11. These graphs show excellent linearity with all lines intersecting a t the origin. The predicted instrumental error when r, equals 106 and r, equals 5 x lo5 would be approximately 0.2oj,. I n the studies of iron, nickel, and chromium, the standard deviation of the slope calculated a t each point is in good agreement with this value. Copper solutions agreed well a t low concentrations, but deviations started to occur a t a concentration of about 6 mg./nil. The results for the standard deviation of the slope (Table 11) are higher than expected on the basis of counting statistics alone. This is explained by noting that dilution errors and true deviations from the theoretical treatment are combined with the counting error to produce the observed standard deviation. To test the counting and dilution errors separately] two additional sets of experiments were performed. First, a single sample of dichromate solution was measured 20 different times. The observed error, 0.18%, was due only to counting statistics because no dilutions were made and only a single concentration was employed. Then, a series of 20 identical dilutions was made from one concentration of dichromate standard solution. The observed measurement error for this experiment was 0.45% indicating that dilution results in a 0.27y0 (0.45 - 0.18) error. Therefore, the experimental deviations observed in the copper and chromium systems apparently
,375,
I
I
'3
I
IRON ,ug./ml. ( as bathophenanthroline complex)
IRON kg./ml. (as orthophenanthroline complex) I
I
I
* 5 7 3 * /*
/'?
CHROMIUM, pg./ml. ( a s dichromate)
NICKEL, mg./ml. ( a s nitrate)
