has been suggested as a possible cause. Resolution loss is illustrated in Figure 2. Another significant feature of this figure is that the regions from channel 780 to 805 and 830 to 850 contain more counts at higher dead times, and seem to indicate that counts lost from the center of the peak (channels 805 to 830) may appear at the sides of the peak. Referring again to Table 11, the 412-keV peak is 54 channels wide when counted without C O C O , as determined by the derivative method, and 81 channels wide when counted with W o . Recently, preamplifiers with pole-zero corrections have become available, and resolution change with count rate is greatly reduced by this device. This correction has recently been added to our electronics, and it is planned to repeat the presently described experiments to re-evaluate the peak area measurement problem. SELECI'ION OF PEAK BOUNDARIES FOR ACCURATE RESULTS
From the foregoing, it is clear that accurate results can only he obtained if peak boundaries are properly chosen. The blanket imposition of a predetermined W on the calculation may not result in accurate peak area calculation. One way in which accurate results may be obtained is to use the derivative method. If it is necessary to obtain the most accurate results, it might then be appropriate to apply to Covell's method, choosing A I consistent with the W values provided by the derivative method. Results obtained in this
way, from the derivative method and the Covell method, should agree reasonably well, otherwise there is cause for concernabout theaccuracy oftheresults. The proper selection of W is very important. If W is chosen too small, resolution loss may result in low peak areas. If W is too large, unnecessarily large errors may be obtained. Further, choice of W must exclude effects of nearby peaks; this is done automatically by the derivative method. A great advantage of the derivative method is that it requires no subjective judgment. Of course, there is subjective judgment built into the computer program, but this affects all results in largely the same way and should cancel out in comparison of areas from standards and unknowns. One word of caution is needed here: in applying the smoothing technique to a spectrum, it is important to follow the guidelines in reference (4). ACKNOWLEDGMENT
The author thanks R. E. Wainerdi of Texas A & M University for suggesting the problem, and for many helpful discussions. RECEIVED for review November 3, 1967. Accepted May 9, 1968. Work supported by the Texas A & M University Research Council and the Texas Eneineerine Exoeriment Station.
The Anti-Quench Shift in Liquid Scintillation Counting B. E. Gordon and R. M. Curtis Shell Deuelopment Co., Emeryuille, Calg. An i n c r e a s e in efficiency (anti-quench shift) h a s b e e n observed in liquid scintillation counting of s a m p l e s containing optically diffusing white m a t e r i a l s o r surfaces. Theoretical calculations a n d e x p e r i m e n t s s u p port t h e hypothesis t h a t t h e e n h a n c e d efficiency results from a reduction in t h e a m o u n t of light lost t h r o u g h total internal reflection. The effect is equivalent to a s h i f t in pulse height s p e c t r u m a n d can b e allowed for by t h e usual m e t h o d s of efficiency calibration except for t h e external s t a n d a r d total count method which is not satisfactory.
IN some recent publications (I, 2) the application of liquid scintillation counting to the determination of radiotracers on white fabric was described. In the first of these involving sulfur-35, carbon-14, or tritium, it was pointed out that the presence of fabric in the scintillation via! had no effect on the carbon-14 efficiency up to 0.5 gram weight. In fact, the tritium efficiency even showed a slight increase in the presence of the fabric. This effect posed no analytical problem so long as a single isotope was present and counting was at, or close to, balance point conditions. In the second report (Z), however, involving double labelling with tritium and carbon14, balance point was not preserved in order to get good isotopic separation and the effect was quite marked. This (1) B. E. Gordon, W. T. Shehs, D. H. Lee, and R. U. Bonnar.
J. Am. Oi/Chem. Soc., 43,525 (1966). (2) B. E. Gordon, W. T. Shebs, and R. U. Bonnar, ibid., 44, 711 (1967).
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ANALYTICAL CHEMISTRY
Figure 1. Vials with and without fab:ic sample
report describes the effect, its cause, and discusses its analytical significance. The Effect. The system initially under study is illustrated in Figure 1 which contrasts a clear and fabric-containing via!. The scintillator is 20 ml of toluene containing the usual scintillation cocktail of 2,s-diphenyloxazole (PPO) (6 grams/ liter) and 1,4-bis[2-(4-methyl-5-phenyloxazoyl)]-benzene (dimethyl POPOP) (0.1 gram/liter). The fabric is 0.5 gram of white cotton but the effect has been noticed with other white fabrics. It seems reasonable from an examination of Figure 1 that, because scintillation counting depends upon the emission
IO
8
6
'b X
k 4
2
1
0
0
I
80
I
160
I
I
1 I 240 320 400 Window Setting, Arbitrary Units
I
480
560
Figure 2. Shift in tritium spectra with different diffusers
of photons from the vial, the fabric might decrease counting efficiency. That this is not so is shown in Table I, which presents the effect of increasing fabric weight on the count rate of a sample of toluene-14C dissolved in the scintillator. Thus, with up to 0.5 gram of cloth no effect was noticed. This surprising lack of interference was also noted in liquid scintillation systems containing gelling agents-such as Cab0-sil-which render the solution nearly opaque. When an attempt was made to apply this to a doublylabelled (carbon-I4 and tritium) system in the presence of fabric the situation was quite different. In this analysis an automatic method of standardization was required because of the great number of samples to be counted each day (100200). The external method of standardization was selected because it is well suited to double isotope analysis on a threechannel spectrometer, the Packard Model 3003 Tri-Carb. After determining the proper instrument settings for good isotope discrimination at reasonable sensitivity using clear toluene solutions containing 14C-toluene and tritiated toluene as standards, the efficiencies for both isotopes in both channels were obtained without and with fabric present. The external standard count rate was also obtained. The results are shown in Table 11. The effect of fabric is not insignificant. Furthermore, it is consistent with an increase in gain, in effect an anti-quench shift, The lower efficiency of carbon-I4 in the tritium channel is due to the same effect-Le., lower energy carbon-I4 pulses are being amplified out of the tritium channel. There is also a large effect in the external standard count rate. The effect is more pronounced the larger the number of pulses of amplitude lower than the lower window for that channel. This gain shift can only be caused by increased photon collection per disintegration resulting in an increased pulse height. A plot of the tritium spectrum with and without fabric is shown in Figure 2. Included also is the spectrum of clear toluene scintillator in a vial sandblasted on the outside to roughen the surface. As can be seen, the fabric-containing and sandblasted vials have almost identical spectra, both of which show a shift to higher pulse height compared to the clear vial. In fact, this shift can be virtually duplicated by an increase in amplifier gain.
To determine whether the anti-quench shift was present with different vial treatments, a group of vials were prepared by sandblasting to make roughened inside surface, outside surface, and roughened strips inside and outside. A photograph of the vials is shown in Figure 3. As shown in this figure, inside roughening disappears in the presence of toluene indicating that the refractive indices of glass and toluene are close. These treated vials were then filled with scintillation solution plus a constant amount of tritiated toluene in each and all were counted under normal conditions for tritium. The efficiencies are shown in Table 111. As expected, inside roughening has no effect, outside has the maximum. Evidently, once all the photons are collected that can be, the introduction of fabric only reduces the efficiency, probably
Table I. Effect of Fabric Weight on Count Rate of Carbon-14
Grams of cloth
cpm 12,200 12,500 12,200 12,100 12,400 10,700
0.0 0.1
0.2 0.3 0.5 1.0
Table 11. Effect of Cotton Fabric on Efficiency
Fabric
Ext. std. channel," cpm
SH SH
No
...
4C
No
14 c
Yes
Isotope
1
226Ra
Yes
...
...
...
102,000 Yes 118,000 a Channel settings: External std., gain m; tritium, gain = 8l%, window gain = 11%, window = 200-1000. az6Ra
No
EA: in tritium channel 27.4 30.3 13.2 10.9
Efficiency in 14C channela 0.19 0.42
...
...
= =
57.4 60.2
...
.*.
2%, window = 30050-800; carbon-14,
VOL. 40, NO. 10, AUGUST 1968
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Figure 4. Spherical vessel
Figure 3. Appearance of vials varyingly sandblasted
Angular region of total reffection for source S (shaded) and area of total transmission (inner circle) because of a small absorption effect. Outside strips are nearly as effective as a completely sandblasted surface, for reasons which will be covered below. The Cause. Schwerdtel (3) recently pointed out that the greater counting efficiency obtained when using polyethylene vials compared to glass was due not to the greater transmission of polyethylene for the scintillation photons, but rather to the greater scattering ability of the opalescent plastic. H e invoked the theory of Shurcliff and Jones ( 4 ) which states that in cells of high symmetry the totally reflected quanta move along within the cell by reflection from the cell wall at the same angle until they are absorbed. Using this theory, the following discussion includes the three types of vials of interest; clear, sandblasted, and fabric-containing. Clear Vial. Internal reflection occurs when the light generated within the solvent is incident on the exterior surface of the glass at an angle greater than the critical angle. Theglassand solvent (usually toluene) havea similar refractive index and can be considered optically homogeneous as is shown in Figure 3. With a refractive index of -1.5 the critical angle is obtained by sin7o
R.I. air = I R.I. glass 1.5 ~
and y o = 42" for the case of the scintillation vial. Thus all scintillation photons incident at an angle greater than 42" will be trapped. For the fraction of trapped light to be appreciable the condition of high internal symmetry must exist so that the photon will continue reflections at the same angle until absorbed by the solvent or solutes. If the symmetry (3) E. Schwerdtel, Int. J. Appl. Radialion and Isotopes, 17, 419 (1966). (4) W. A. Shurcliff and R. C. Jones, J. Opf. Soc. Am., 39, 912 (1949).
Table 111. ENect of Various Vial Treatments on Tritium Efficiency Efficiency, Treatment Clear 39.5 Clear plus fabric 44.8 Sandblasted inside 40.0 Sandblasted outside 46.0 Sandblasted outside plus fabric 43.2 Sandblasted outside strips 45.3
z
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Figure 5. Coordinates for cylinder
is not perfect then a competition will exist between scattering events for a photon that, ultimately, results either in deflection at an angle which allows transmission, or in absorption. Figure 4 presents schematically the situation for a symmetrical vessel. Once a photon enters the area of total transmission it cannot strike the wall at an angle greater than the critical angle. Shurcliff and Jones (4) have developed the general case for a sphere and a rectangular parallelepiped. For application to liquid scintillation counting the case for a cylinder is developed below first for infinite and then for finite height. The result is expressible in terms of elliptic integrals and is thus somewhat more complex than previously considered geometries. Quite recently Rosenstingl, er a[ (5) have calculated the yield from the end of a cylinder. Their treatment is more realistic than our idealized model, but unfortunately is limited to end-on geometry rather than the type of geometry considered here. Consider in Figure 5 an infinite cylinder of unit radius with 0 on the axis and P the point of light emission. The line OP of length h is normal to the cylinder axis. Erect cylindrical coordinates (r,O,z) centered at P with the z axis parallel to the original cylinder. M is the point of intersection with the cylinder of a ray from P so that line PM has a length m. Then if y is the angle between line P M a n d the cylinder normal at M it is found that ( 5 ) E. Rosenstingl,
L. Commanay, and A. Godeau, Nucl. Inst. and
Methods, 58.61 (1968). ANALYTICAL CHEMISTRY
P
cosy =
toss dl - h2sin26
(1)
where cos@ = r/m. Following Shurcliff and Jones, if the
“
ir-
critical angle for total internal reflection is yo, then C
=
cosyo, S
=
sin y o = l/n
O
T
0,8
where n is the index of refraction. We assume a constant value of n interior to the cylinder. If a unit sphere is now centered at P, the locus of points on this sphere for which y = y G is given by
C
=
rq l
- h2 sin28
(2)
There are, by symmetry, two such closed curves on the spherical surface and within one hemisphere only the light originating from P within the solid angle defined by Equation 2 can leave the cylinder. This solid angle is equal to the area on the surface of the unit sphere. Again by symmetry it is sufficient to consider one octant of the sphere. The area of interest within the range 0 8 n/2 and 0 r 1 is given by
<
4 and exit from the wall. Thus, while a counting vial has reflecting surfaces at each end (liner in cap and metal support under bottom), these are of little significance because they cannot return a photon in such a way as to be detected. The theoretical model for a vial thus becomes the infinite cylinder with a predicted loss of light from internal reflection of 55 % at n = 1.5. An indication of the variation of the trapping fraction with n is provided by the two estimates G = 50z a t n = 1.4and G = 6 0 Z a t n = 1.6. The detailed geometry of a counting vial departs markedly from the idealized model represented by a n infinite cylinder. The lack of perfect symmetry will result in a trapping fraction much smaller than that calculated and in only a superficial resemblance to Curve B of Figure 6. A few measurements have been made by blackening selected portions of a vial with paper or paint that illustrate this difference. When the aluminum foil liner in the cap is replaced by black paper there is, as predicted, no significant change in counting rate. But when the exterior bottom of the vial is similarly covered there is a drop of several per cent in count rate. The exterior bottom surface of a vial is relatively flat except for a thickening or lip in the form of a ring at the circumference. Apparently photons which exit through the bottom are diffusely scattered by the metal base on which the vial rests and a portion of these photons can pass through this ring to be counted. Black paint on the ring has about the same effect on counting rate as complete covering of the bottom.
Table IV. Test of Total Reflection Theory Count rate Millimeters from wall Clear Sandblasted Clear f fabric 0 5 8 12. 5a a
25357 27498 27124 27688
26539 27392 27628 27691
/
27445 27547 27518 27472
Figure 7. symmetry
The structure at the base of the vial and other departures from the model symmetry, all of which tend to decrease the trapping fraction, suggest that the photon loss indicated by Curve B of Figure 6 is too high. Attempts to modify &he degree of internal reflection will obviously be most effective near h = 1 and the experiments described below indicate that the modification possible is much less than the 75z predicted by this curve. Thus Curve B must be lowered and one consequence of this is that out to h = 0.6 or 0.7 there will be relatively little internal reflection loss. Sandblasted Vial. There is no observed effect from sandblasting the interior of the vial. This is as expected because the refractive indexes of toluene and glass are sufficiently close t o produce a nearly homogeneous system. Exterior roughening decreases the fraction of trapped light by the mechanism illustrated in Figure 7. Here the effect of a scratch (magnified) on two photons, SI and SP,in the area of total reflection is shown. SIhas begun the path around the vial which normally would lead to total absorption. Deflection a t the scratch causes the photon to enter the area of total transmission from which it must strike the wall at an angle smaller than the critical angle. S2 encounters the scratch immediately and since it now strikes the wall a t an angle much less than 42' it is transmitted. Sandblasting obviously does not produce a perfectly diffuse surface nor completely destroy the symmetry of the vial. But it does reduce the loss of photons effectively. It should be noted that a totally reflected photon always intersecting the wall at the same angle will not strike at the same position each time. Therefore, the introduction of a strip of asymmetry should have nearly the same effect as total roughening. Thus strip roughening (Table 111) shows almost the same effect as total roughening. If the theory of Shurcliff and Jones is correct, then a light source present in the center of the vial should show little or no difference between clear and sandblasted vial while one at, or near, the wall should show the maximum difference. Such a light source was prepared by the method of Dobbs (8) by fusing barium carbonate-l4C into a thin glass needle. This was mounted in a slot cut in the cap of a scintillation vial so that it could be moved radially from the center to the edge, Carbon-14 (hSx = 0.155 MeV) has a range of about 0.3 mm in toluene and thus the needle became a line source of light of about 1.5-mm diameter (needle diameter was about
Center (8) H.
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ANALYTICAL CHEMISTRY
Elimination of circular
E.Dobbs, Nature, 200, 1283 (1963).
Figure 8. Comparison of clear and fabric calibration curves using channels ratio method
1 mm). This was placed in a vial and count rates were obtained at various positions from the center t o the wall. This was done for three vials; clear, roughened, and fabriccontaining. The results are shown in Table IV. The data support the theory. At the center there is no difference in count rate among the three. At the wall there is about a n 8 % difference between the clear and fabric and 4 % between the clear and frosted. Statistical uncertainties in the count rate are far smaller than the differences because multiple counts were made. The calculations suggest that the region of noticeable internal reflection begins about 0.65 radius from the center. Thus one would expect the count rate in the clear vial to start to fall off at about 4 m m from the wall. It would not be noticed until closer to the wall than this because of statistical uncertainty and the size of the needle, but it is clear that no effect exists 5 mm from the wall. The ratio of count rates at the center and wall for the clear vial provides a measure of the change required in the cylinder curve of Figure 6 for application to a vial. Cloth-Lined Interior. While this was the situation which originated this work, it is also of concern to those attempting liquid scintillation counting of paper chromatographic strips and possibly of opalescent gels (Cab-o-sil, Triton X-loo/ toluene). It may seem surprising that cloth (cotton, Dacron, etc.), with a refractive index not substantially different from that of toluene or glass, should be a far better diffuser of light than a sandblasted vial interior. However, reference t o Figure 1 shows that the apparent refractive index of the fabric is quite different from the solution. For the cloth t o be so effective it must be both a poor absorber (good reflector) and an excellent diffuser. The latter property depends on a large difference in index of refraction between solvent and cloth. This large difference evidently is due t o entrained air bubbles and voids in the individual fibers that are not penetrated by the solvent. Consider a scintillation within the bulk fabric. The photons must penetrate the cloth to be counted. There is little likelihood of directly penetrating a strand of cloth considering the number of fibers per strand and the relatively good reflectivity of the white fiber. Thus the interstices provide the main avenue of exit. These openings amount t o
about 10% of the cloth area (for cotton), as determined by direct transmission measurements, SO that about 10 reflections are required before the photon leaves the cloth. Because there is very little light loss during this sequence of scattering events (to within 1 based on Table IV), the loss of light by absorption is no more than -0.1% per scattering event, Thus the cloth must be truly “white” for this t o occur. With increasing amounts of cloth (see Table I) there is a n increasing number of scattering events before transmission can occur and loss by absorption becomes significant. Light which leaves the fabric at less than the critical angle leaves the vial. Light which leaves the fabric at greater than the critical angle is reflected back into the cloth where it is scattered and a certain fraction of this light again leaves the vial. Thus the cloth serves to rescatter trapped photons until they are able t o leave the vial. Because most of the photons generated within the vial are scattered at least once by the cloth, this cloth becomes, in effect, the photon source. The observed count rate should then be independent of the point of origin of photons if the origin is interior t o the cloth, and this is verified in the last column of Table IV. It might be anticipated that in the course of multiple scattering by the cloth a larger fraction of light would be lost through the ends of the vial, but this is denied within the accuracy of the counting statistics by the last line of Table IV. With a cloth-lined vial, multiple scattering is a n essential mechanism leading t o the observed count rates. This is possible becaus? of the low absorbance of the solution for photons of -4500 A wavelength. Assuming an absorbance of about 10-4 liter/ mole the mean free path of a photon is about 3 meters which is sufficient for scattering to be the predominant effect. The Significance. With more stable, sensitive, and lower background liquid scintillation counters the tendency even for single isotope analyses is not to count in balance point but t o include as much of the entire spectrum as is possible, The anti-quench shift arising from an opalescent vial then may significantly increase efficiency compared to that of a clear unquenched vial. Therefore, one must determine this new counting efficiency. While the internal standard method does work, it is rapidly being replaced by the more convenient methods of external standardization and channels ratio. VOL. 40, NO. 10, AUGUST 1968
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t-
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L? Figure 10. Comparison of clear and fabric Calibration curves using external standard ratio
5
2
30
;
1.2
0
'
Frorted/Clear
0 Cloth/Clear
1.1
'
0 0
0.8
Loo I
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ANALYTICAL CHEMISTRY
I
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1
1
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1
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1
The channels ratio method seems to be entirely adequate for such samples as shown in Figure 8 for tritium. CC14 is the quenching agent for all samples. Here the unquenched fabric-containing samples simply appear higher on the efficiency curve than the unquenched clear samples. External standardization is a more recent development in liquid scintillation counting and because of convenience may become the most widely used method of standardization. Two methods of using the external standard count are in use: the total count and the channels ratio. The total count approach is not applicable to samples with the anti-quench shift as shown in Figure 9. The fabric-containing vials yield a curve clearly displaced from the clear vials. However, the use of channels ratio for the external standard yields a single calibration curve for both fabric and clear standards as shown in Figure 10. The lower values for nylon are due to a very slight yellowish color which increases photon absorption during multiple scattering. The anti-quench shift not only appears in any samples which make the scintillator opalescent but also when the vial changes from a clear to a slightly opalescent appearance. This is quite common in counters using freezers operated at low temperatures. Removing the vial--e.g., for internal standard addition-and replacing it causes a temporary increase in count rate caused by moisture condensation on the outer surface. One must then allow sufficient time for the condensate to evaporate from the vial surface to the colder parts of the instrument before beginning counting. Failure to take this into account--e.g., if one makes a rapid recountmay lead to significant errors. A final word about the fact that this effect has not been previously reported as a problem in liquid scintillation count-
ing, First, the most widely used method of standardization, the internal standard method, corrects for the shift. Second, it is clear that the channel width has an effect on whether there is an increase, decrease, or no change in counting efficiency. Figure 11 shows the effect of the window width on the ratio of counting efficiency of the treated to the clear vial. As can be seen at window widths of 50-600 to 50-800, the usual balance point operation, no effect is noticed. At narrower window widths in lower energies the efficiency of the treated vials is lower than the clear vial because pulses have been amplified beyond the upper discriminator. CONCLUSIONS
The presence of any diffusing material in a liquid scintillation vial or any roughening of the vial outer surface causes an increase in pulse height per disintegration. This is due to increased photon collection by the photomultiplier arising from a reduction in the number of totally reflected photons. This increased efficiency in counting must be taken into account for accurate analysis. The internal standard method, the channels ratio method of Baillie (9), or the external standard channels ratio method can be used to determine the disintegration rate of clear and heterogeneous samples containing cloth or gelling agents. The external standard total count method cannot be so used. The effect is of particular importance in double label analysis because the spillover coefficients undergo significant changes when such a diffuser is present. RECEIVED for review March 11, 1968. Accepted May 22, 1968. (9) L. A. Baillie, Int. J. Appl. Radiation and Isotopes, 8, 1 (1960).
VOL. 40, NO. 10, AUGUST 1968
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