from a gelatinous precipitate to an opalescent colloidal solution is evident a t the concentrated level. As yet, there is no good explanation for this behavior. The precision of determinations can be varied over a limited range by proper adjustments of relative amount of sample, titrant strength, or titration speed. The precision of a determination which is the difference of two end-point interpolations necessarily suffers in comparison with one in which only one end point is located. Thus, free acid determinations are possible with relative precision of 1-3YG and those of the cations from 2-10%. The latter determination can become almost meaningless in cases of mixtures of cations whose hydroxide solubilities are fairly close together. This titration does not offer a better method of determination over other methods now available for hydrolyzable cations with the exception of beryllium. I t does afford anapproach to a rapid semiquantitative estimation in the case of one simple cation and a qualitative and semi quantitative identification in the case of mixtures of certain cations.
Presently available reagent grade lithium chloride shows great variation in quality from various vendors and between batches from the same vendor. Material from the most reliable commercial source thus far still contains a small amount of hydrolyzable cation which can be removed by combined solvent extraction and ion exchange treatment. There is also some residual basic material which can be neutralized or adjusted for as a reagent blank. The effect of reagent blanks can be minimized by titrating a t higher concentrations. Ten molar lithium chloride is used in many chemical operations a t this laboratory, and analytical work thus far indicates that this is a good level a t which to operate from the standpoints of nonaqueous behavior, fluidity, and solubility parameters. The glass calomel electrode pair gives excellent response to changes taking place during these titrations. A high alkali glass electrode (such as Beckman 40495) gives better all around performance in the high salt solutions and is recommended in preference to the ordinary glass electrode. There is loss
in sensitivity with time: however, this degradation is very slow. Sulfates and phosphates form insoluble lithium salts. The former causes no interference with either free acid or cation determination, but the latter is a definite interference which cannot be tolerated. Hydroxyl will not displace fluoride; therefore, any fluoride present will detract from the total equivalents of cations. Carbonates are also relatively insoluble in this medium, and titrations at high pH levels can be carried out with little danger of carbon dioxide pickup and dissolution interfering with the end point break. LITERATURE CITED
( 1 ) Critchfield, F. E., Johnson, J. B., ANAL.CHEM.30, 1247 (1958). ( 2 ) Zbid., 31, 570 (1959). (3) Hogfeldt, E., Leifer, L., Acta Chem. Scand. 17, 338 (1963).
RECEIVEDfor review August 28, 1964. Accepted September 21, 1964. 12th Anachem Meeting, Detroit, SIich., October 1964. Research sponsored by the C . S. Atomic Energy Commission under contract with the Union Carbide Corp.
Correction of Quenching in Liquid Scintillation Counting of Homogeneous Samples Containing Both Carbon-14 and Tritium by Extrapolation Method C. T. PENG Radioacfivity Research Center and School of Pharmacy, University of California, Son Francisco, Calif.
b An extrapolation method for quenching correction in doubly labeled samples is described. The samples are integral-counted at different concentrations in a two-channel liquid scintillation spectrometer which is adjusted to afford the counts of C14 in the first channel and CL4and H3 in the second channel. Degrees of quenching in these two channels are shown to b e a simple and a composite exponential function of the sample concentration, respectively. In addition, attenuation of background counts by quenching in each sample can b e estimated from a correlation curve. Merits of integral vs. differential counting of doubly labeled samples are also discussed.
H
samples containing both carbon-14 and tritium can be counted in a two-channel liquid scintillation spectrometer. Because of the difference in their beta disintegration energy, it is possible to adjust the OMOGENEOUS
2456
ANALYTICAL CHEMISTRY
pulse height amplification and the acceptance slit appropriate to each channel so that channel 1 contains counts due to C14 in the sample and channel 2 contains counts of both isotopes. From a predetermined ratio of count rates or counting efficiencies observed in channels 2 and 1 with a given, nonquenched sample containing C14alone, the count rate due to H3 in an unquenched sample containing both isotopes can be computed by subtracting the counts in channel 1 multiplied by this ratio from the observed total counts in channel 2. The screening and the discriminator-ratio methods described by Okita et al. (6) and reexamined by Kabara et al. (6') are essentially of this principle. I n the presence of chemical and/or color quenching, the ratio of C14 counting efficiencies in the two channels will be altered from sample to sample. Failure to adjust for this deviation will invalidate the results obtained. The extent of quenching in the sample
can be measured by the use of internal standards of C14 and H3. Such a procedure, however, involves additional manipulations and counting of each sample following the addition of each internal standard, and, therefore, it is prone to error. This report describes a method in which the sample containing both C14 and H3 is counted at two different concentrations and from the observed counts in the two channels, quenching in the sample is corrected by the extrapolation method ( 7 ) . EXPERIMENTAL
The counting instrument usedin this study was a TriCarb liquid scintillation spectrometer, Model 314E, manufactured by Packard Instrument Co., Inc., La Grange, Ill. I n this instrument, the lower and the upper discriminator levels and the gain control of the pulse height amplification of each of the two channels can be individually adjusted. The settings used for this study for the integral mode of counting were 0100-toProcedure.
infinite window width, gain 10 (10074 of the maximum) for channel 2 and 0700-to-infinite window width, gain 5 for channel 1; for the differential mode of counting, 0100-to-0300 window width, gain 10 for channel 2 and 0500-to-1000 window width, gain 3 for channel 1. The voltage dial setting was 5-900 or 1070 volts. The samples were counted in Wheaton low-potassium glass vials to which was added 10 nil. of a mixed liquid scintillator consisting of 5 nil. of 0.3y0 of P P O (2,5-diphenyloxaeole) in toluene arid 5 nil. of a purified dioxane solution containing 7 grams of PPO, 0.05 gram of POPOI-’ [2,2’-p-phenylenebis(5phenylosazole)], and 50 grams of nalihthalene per liter. The use of the inixed scintillator was found advantageous because of the improved solvent and fluorescence characteristics. -111 the samples were repeatedly counted to a statistical precision of less t’han i1% standard deviation and the background counts of all samples were measured over 30-minute periods. Toluene-C’4 and t,ritiated toluene were used to “spike” all the samples, which were counted before and aft,er each addition. The chemicals used as qumchers were of reagent grade. The volume of the internal standard was less than 0.10 nil. and that of quencher, 0.25 nil. S o significant change in counting efficiency accompanying this volume increase in the counting sample yill result ( 7 ) . RESULTS AND DISCUSSION
Quenching Correction. I t has been pointed out ( 7 , 8 ) that by the integral mode of counting the apparent specific activity, Sa.defined as the observed
count rate per unit sample concentration, S / C , of a homogeneous counting sample containing a single isotope, is an exponential function of the sample concentration, C, and can be expressed as follom-s:
Sa= So exp(-qC)
(1)
where So is the specific activity of the sample in the absence of quenching and p, the quenching constant. q = 0.6931 CliZ,where Cl,2is the sample concentration that will reduce the count to half its initial value by quenching. (The term “apparent specific activity,” defined here, is applied to quenched samples only, and the term “specific activity” similarly defined is applied to unquenched samples. The latter when divided by counting efficiency gives absolute specific activity which is expressed as disintegrations rate per unit sample concentration.) I n homogeneous samples containing double labels, such as C14 and H3, the count rate per unit sample concentration observed in channel 1 by integral mode of counting will be entirely due to C14 and will obey Equation 1; thuq
Sal = Solexp(-plC)
(14
The count rate per unit sample concentration observed in channel 2 by the same mode of counting can be shown to be a composite exponential function of the concentration of the sample as follows :
Sa,= RSpl exp(-ql’C)
+
802exp(--qzC)
C-14
(2)
+ CI-3
C-14
n-3
10
20
30
PHENYL
40
SO
60
70
80
90
I00
ISOTHIOCYANATE, p L
Figure 1 , Composite quenching curve and its components for homogeneous samples in channel 2 Theoreticol values r e p r e s e n t e d b y lines; observed volues, b y individual points
where S o t is the apparent t’otal specific activity of the sample containing two isotopes; Sol and SOZare the specific activities of C14 in channel 1 and H3 in channel 2 , respectively, for the sample in the absence of quenching; ql’ and pz represent the respective quenching constants for C14 in channel 1 and H3 in channel 2 ; and R is the ratio of the count rates or counting efficiencies of an unquenched sample of C14 in the two channels. The product, RSolrepresents the unquenched specific activity of C14 in channel 2 . Rearranging Equation 2, we obtain
So2exp(-q2C)
=
Sa,RSol exp(-q,’C)
(3)
= sa2
where Sa2 is the apparent specific activity of H3 in the doubly labeled sample. The validit,y of Equation 2 on which the present method is based is substantiated by ample experimental results. An illustrative example given here consists of a composite quenching curve shown in Figure 1, obtained with a series of saml)les containing known counts of C14 and H 3 to which various amounts of phenyl isothiocyanate, a strong quencher, were added. This quenching curve can be resolved by means of Equation 2 into tLvo component activities, one for C14 and the other for H3, both of which are in good agreement with the observed values of the added activities. Because of the difference in E,,, of the two isotopes, the counting efficiency for H 3 is more adversely affected by quenching than that of C14 at a given concentration of the quencher, as manifested by the steeper slope of the quenching curve of the former as compared to that of the latter. The reliability of the above extrapolation method would depend upon, among other factors, the constancy of R , a linear dependency of ql’ upon q,, and the ratio of the two isotopes in the sample. Using samples cont’aining C14 ranging from 1.78 X 106 to 44.3 d.p.ni., the R value was found by the integral mode of counting to be consistently constant, yielding a value of 3.104 + 0.0728 (std. dev.) for t,he particular instrument settings used for this study. At ext’reniely low levels of sample counts t’he R value may deviate more from the mean, owing to the fact that counts accumulated in both channels within a preset time period are not sufficiently numerous to ensure good counting statistics. On the other hand, a t extremely high levels of sample counts, summation of light pulses may occur and may alter the nornial pulse height distribution in the two channels to affect the R value. When quenched samples containing C14 were counted, the channels ratio VOL. 36, NO. 13, DECEMBER 1964
2457
Table I.
Accuracy of Assay on Variation of Isotope Ratio in Homogeneous Samples
Ratio :
Counts addeda Counts founda H3 c14 H3 C'4 Relative error, % CI4 (d.p.m.) (channel 2) (channel 1) (channel 2) (channel 1) H3 C'4 0.13 7.15 2,857 9,632 9,644 0.64 3 662 0 81 1.92 3,688 16,335 3,691* 16,653 1 82 1.62 551 185 182 6 . 42c 541 1.41 973 2 22 991 14,019 32 1 13,706 64.2 26,399 975 27,759 997 4.90 2 20 Average of 5 observations at 1-minute intervals. Identical sample but counted at high voltage setting of 6-900 or 1140 volts. c Counted for 10-minute periods t o achieve statistical precision but expressed as average counts accumulated per 1-minute interval. H3 (d.p.m.)
~
Q
d CHj
on
L7 Od-N=C.S
c/ci 2 (CHANNEL 11
Figure 2. Relationship between channels ratio of variably quenched samples and C/Clp2
was found to increase with the degree of quenching in the sample. Figure 2 shows the plots of channels ratios us. C,'Clla values of various quenchers in integral counting. The C,:C1,2 describes an equal state of quenching in the saniple. The value of channels ratio for color quenchers deviates more from a straight, line a t high C/Cl,, values than that for the chemical quenchers because at high color concentrations, transmission of light is more adversely affected than would be predicted by Equation 1. Below C/Cl/2 = l-i.e.3 in the region of less than 50% quenching-all the plots are linear and converge to the channels ratio of an unquenched sample. Since the channels ratio is very sensitive to the presence of small amounts of quenchers, plots of this kind may be useful in ascertaining the validity of the R value obtained otherwise. The nature of the dependency of ql' upon yl was ascertained by plotting Cli2 values obtained from quenching curves of samples containing known activities of C14 and various concentrations of quenchers: acetic acid, acetone, h1)iezon wax in toluene, carbon tetrac,hloride, S,S-dimethylformaniide, ferric chloride in ethanol, methanolic hyaniine hydroxide, ethanolic iodine solution, and methanol. h linear relationshil) over a range involving apl)rosimately two orders of magnitude of Cl12values were obtained. The C1!2 values of the mild quenchers, methanol and S,S'-dimethylforniainide, showed deviations from linearity at high CUZ values iirobably owing to uncertainties in their evaluation. This deviation does not significantly alter the accuracy of assay.
The accuracy of assay using the extraliolation method depends upon the ratio of the two isotopes in the sample. Table I s h o w the results of assay on 2458
ANALYTICAL CHEMISTRY
samples with isotope ratios varying from 0.64 to 64.2. The per cent differences observed between added and found sample counts of the two isotopes are within the experimental error. Since the counts of H3 in the sample are obtained by difference, it is probable that, the accuracy of the assay for low levels of H3 in samples containing high levels of activity of C14 will be adversely affected; the converse, however, is not necessarily true. Application. For routine assay of biological and chemical specimens containing both C'4 and H3, the homogeneous counting samples are prepared a t sample concentrat,ions differing from each other by a factor of 2 . From the count rates observed in channel 1 on these two samples, the activity of C14 in the absence of quenching t a n be obtained from Equation l a . This value, when divided by the counting efficiency, gives the absolute specific activity of C'4. In channel 2 the observed counts can be resolved into those due to C14:which is represented by RSol exp(-ql'C) in Equation 2 , and those due to H3. So, is known from the above; R is determined wit,h a known, nonquenched sample of C14; yl' is linearly dependent upon q1 and was found to be 7.1 times larger in value for the instrument settings used in this study. Therefore, the apparent specific activity of H3 in channel 2 can be determined by subtract,ion of the apparent specific activity of C14, calculated by the above expression, from the observed apparent total sllecific activity to give Sa2in Equation 3 . From the equation and the counting efficiency of H3, the absolute specific activity of H3 in the sample in the absence of quenching can be obtained. I n mildly quenched samples, exp (-ql'C) approaches 1, and the apparent specific activity of C14 may be represented by RS,,. If a 2% error in this value is tolerable, 0.1 nil. of the sample with a Glia of 0.35 nil. or larger can be assayed wit,hout the use of the exponential correction factor. When strong quenchers are assayed,
however, a series of samples containing increasing increments of t,he st,rong quencher should be used to give a quenching curve from which correct values of Sal in channel 1 and Soz in channel 2 can be extrapolated. The presence of a minute amount, of a strong quencher in the sample causes a drastic reduction of the observable count; and, in many such cases, only the initial portion of the quenching curve is linear and usable for extrapolation purpose ( 9 ) . For this reason, in routine assay, selection of sample concentration should be limited to the region where Equation 1 applies. Frequently this represents a concentrat,ion less than C,, (7). Estimation of Loss of Background Counts Due to Quenching. Although the loss of background counts by quenching is not determinable in each individual sample, it can be approximated by the following method. The energy spectrum of background radiation differs from that, of CI4 or H3. Under given conditions when the counts of C14 in a sample are quenched to half the initial value, the background counts would presumably and probably be quenched to some reproducible degree which may constitute a given fraction of the background counts, irrespective of the chemical naturr of the quencher. Results of counting a number of background samples containing chemical and/or color quenchers indicat,e that the loss of background counts in samples containing half concentrations of quenchers is comparable. Figure 3 shows the plot's of the ratio of C/Cli9 against quenching loss of background counts per 10 minutes in channels 1 and 2, respectively. Since more counts were accumulated in channel 2 , less scattering of the points occurred. h correlat,ion curve obtained from these points can be used for t,he q)proximation of loss of background counts by quenching a t any given sample concentration. I n practice, the correction is carried out by a method of iteration or successive approximation. The gross samiile counts in channel 1 are plotted
IO9 CHANNEL 2 5
CHANNEL 1 102
9
0
*
S
A ACETIC ACID 0 ACETONE A APIEZON WAX v c Cl4 0 DIMETHYLFORMAMIDE 0 FoClj
IO'
CH30H
I2
5
X PICRIC ACID 0 O-N=C=S
L I
Figure 3.
Loss of background counts by quenching
v5.
equal quenching states,
C/C,,,of various quenchers after subtraction of the unquenched background counts according to Equation l a . From the quenching curve obtained, the Cirglis estimated, and the correslionding C/IClIP value a t each sami)le concentration is calculated. l'he latter is used to determine the number of background counts lost by quencbhing from a predetermined curve for the particular instrument settings used such as the ones shown in Figure 3. The corrected background counts are then subtracted from the gross sample counts to yield the net sample counts, which are replotted to give more accurate CIr2 and C/ICIIBvalues. This procebs of approximation is repeated until a stable C;CI,, is reached. The C/CIII value thus obtained for channel 1 is used to approximate the quenched background counts of channel 2 from a similar correlation curve. The ahove method for quenching correction of background counts is generally alqilicable to chemical- and color-quenched samples containing C14 using one correlation curve. Based on the nn1)irical relationship between the counting eficiency and the background counts of quenched samples, Scales (10) described a method for correction of background counts lost due t o quenching from a precalibrated correlation curve. However, this approach requires a c o r d a t i o n curve for each type of quencher encountered. The present
method employing plots of C/C, 2 us. background counts lost because of quenching has apparently eliminated this disparity. Fleishman and Glazunov ( 2 ) , using an external CoM standard, obtained a single correlation curve relating background count rate to counting efficiency for quenched samples. Merits of Integral us. Differential Counting. T h e application of the extrapolation method for correction of quenching in either qingly or doubly labeled samples is limited only to
Table 11.
Reproducibility of Channels Ratio in Differential and Integral Countings at Low Sample Counts
Gross
Mode of counting Differential
integral counting-i.e., counting all the pulses above a bias setting. However, for samples containing single ipotopes, the differential mode of counting is preferred. This mode of counting uses an upper discriminat,or in pulse height analysis to exclude large light pulses from cosmic radiation a,4 a means to reduce t,he background counts and consequently increases the figure-ofmerit value, S 2 / B , In dual labeled samples, the use of upper discriminator introduces serious limitations. For instance, the channels ratio of C14 obtained on an identical set of unquenched samples containing varying levels of activity is more consistently constant by integral counting than by differential counting with a standard deviation of 2.35 and 9.677,, respectively. The large deviation in the case of differential mode of counting is apparently caused at low sample counts by the unusually large individual deviations from the mean. An illustrative example is given in Table 11. The R value for differential counting was decreased from 5.50 t o 2.24 when the counting time was increased from 10 to 50 minutes, although the mean value was 1.82; whereas the integral counting value showed a relatively small change from 2.92 to 3.22 against a mean value of 3.10. The discrepancy in the deviation of the channels ratios from the mean values in the two modes of counting may be attributed to t,he difference in the proportion of the background count rate in samples of low c,ounts. I n the integral mode of counting, the relative magnitudes of the counts accumulated in the two channels parallel that of the respective background counts. I n contrast, in t,he differential mode of counting, the smaller net sample count rate in channel 2 is obtained by a difference between two large numbers-vis., the gross sample count rate and the background count
Channel no. 1
2 1
sample5 counts per 10 min. 283 336
Backgrounda Net sample counts per counts per 10 min. 10 min. 69 214 297 39 204 177 579 517
Channels ratio 5 . 5 0 ( 2 24)c
381 2.92fi3.22) 2 1096 Bverage cahannels ratiod Differential counting 1 822 i 0 17@ ( 1 9 671;) 3 104 i 0 0728 ( f 2 3 5 7 , ) Integral counting a Average of 5 observations Obtained as quotient of counts between channels 1 and 2 in differential counting and between channels 2 and 1 in integral counting e Channels ratio obtained by counting same sample for 50-minute intervals This v a l w of R instead of 5 *50Ras used to calculate mean Cf d Obtained from 12 samples ranging from 44 3 to 1 78 X 1(J6d p m Cf
Integral
assuming equal weights
(if
12 samples
VOL. 36, NO. 13, DECEMBER 1964
2459
rate-which is accompanied by inherently large statistical fluctuations. The use of an upper discriminator also excludes the fraction of light pulses from C14 whose amplitude exceeds the limit set by the discriminator. As the concentration of the quencher is increased, the amplitude of the light pulse is attenuated and will fall within the preset acceptance slit, thus causing an enchancement of t,he count rate of the sample. This monotonical increase is continued until a maximum is reached beyond which further increase of the concentration of the quencher causes the counting rate to decrease in an exponential manner. The initial increase followed by subsequent decrease of the counts in the preset acceptance slit, cannot be treated quantitatively by Equation 1. Figure 4 shows the pulse height distribution of background counts. The significance of the counts observed with empty well, empty vial, and solvent, has been described ( 7 ) . The increase in background counting rate from 0100-to1000 window to 0100-to-infinite window was about 18yO-i.e., from 93 to 113 c.p.m.-and the increase from 0700-to1000 to 0700-to-infinite window was approximately fivefold-Le., from 5 to 23 c.p.m. for this particular instrument used. At low sample counts, as shown in Table 111, the P/’B value for channel 1 vias 2 to 4 times in favor of differential counting, whereas the S 2 / B value for channel 2 for the identical sample was several orders of magnitude larger for integral counting. I n counting samples containing single isotopes, the S2,’B value can be used as a guide for selection of instrument settings, but in double isot,ope counting, the manipulated gain of Sz/B value for C14 in channel 1 in the differential mode of counting is usually accompanied by a loss in channel 2 , since S z / B for t,he latter is maximized for counting tritium. I n achieving over-all accuracy, under given condit,ions, the integral mode of counting appears to be t,he method of choice for counting doubly labeled compounds. In addition, the use of integral mode of counting would also satisfy the condition
b E M P T V WELL .EMPTY
>lode of counting Differential
Channel no.
Sample
1
no. a
2
a
1
2
e SCINTILLATIONSOLUT~ON
DISCRIMINATOR
SETTINGS
Figure 4. Pulse height distribution of background counts
- _ _ - Channel
1 Channel 2
of wide-channel counting, which, according to Bush (1) and Herberg (4) yields minimum errors for samples of all levels of activity. Generalization. A generalization of the extrapolation method described above can be made for quenching correction in homogeneous samples containing three isotopes such as H3, C14, and P32. The spectrometer can be adjusted to perform a three-channel operation by the integral mode of counting, in which channel 1 contains only the counts of P32, channel 2 , of both P3? and C14, and channel 3, of all three isot,opes. Accordingly, the following three equations may be formulated:
Sa’” =
R13801
Rd02
exp(-ql”C)
exp(-qz’C)
+ + SO3
Sa’’ = R12S01 exp(-ql’C)
+
exp (- q3C)
SOZ exp(-qzC) Sa’
=
Solexp(-qlC)
where R12,R13, and Rz3indicate channels ratio between channels 1 and 2 , 1 and 3,
b
b a b
a b
Ket samplela Background,” counts per counts per 10 min. 10 min. 214 69 243 63 39 297 149 287 177 204 310 213 517 579 940 608
Average of 5 observations. b S * / B represents (net sample count rate)2/(background count rate)
a
2460
VIAL
0 SOLVENT
Comparison of Figures of Merit of Differential and Integral Countings
Table 111.
Integral
I
ANALYTICAL CHEMISTRY
SZb B 667 936 5 71 154 45 1 462 1400
and 2 and 3, respectively. The threechannel operation can be completed by one counting in a three-channel spectrometer or by two successive countings of channels 1 and 2 , 2 and 3 in a twochannel spectrometer. The success of this procedure for counting multilabeled samples would depend upon the linearity, gain, and dynamic range of the preamplifier and the amplifier in the spectrometer. A high gain in the amplifiers is necessary for generation of pulses of large amplitude which, as a matter of fact, can stand attenuation by quenching better than pulses of small amplitude. When operated a t a full gain, the amplifiers should yield, after initial amplification by the multiplier phototube, undistorted pulses from H3 ass well as from P32. Since scintillation pulse height is a power function of E,,, of the radionuclide as inferred from Figure 4 of ( 7 ) , amplifiers with high gains would afford less overlapping of the average pulse heights or the energy spectra of the isotopes. To obtain maximum separation of the isotopes between channels, the pulse amplitudes of P32 in channel 1, C14 in channel 2, and H3 in channel 3 should be made comparable. This may be accomplished by adjusting the gain control and the lower discriminator level until the C1)z values in the three channels on three given set,s of samples, containing, separately, P3*,C14, or H3 and identical amounts of a quencher, are approximately equal. Such an arrangement for equal ClIz values in all three channels is valuable in detecting any abnormalities which may occur in the routine assay procedure. Vnder ordinary conditions, t,he quenching correction for P32 in channel 3 will probably be minimal, and the expression R13&1 exp(-qI’‘C) may be replaced with R13S01. Since P32yields pulses of relatively large amplitude as compared to those of H3 or C l 4 ? the probability is exceedingly small of their being attenuated below the bias setting and lost as counts. Simultaneous liquid scintillation counting of P32,C14,and H3compounds in a two-channel spectrometer with quenching correction by internal standards was reported by Wu ( 2 1 ) . Extrapolation t‘s. Internal Standard Method. The merits of these two methods may now be compared. For routine assay, the extrapolation method uses two points for extrapolation to obtain the specific activity of the sample in the absence of quenching, irrespective of whether the sample is singly, doubly, or triply labeled. The advantages of this method are many; the errors due to manipulation are minimal; the counting can be completed without interruption, thus eliminating any fluctuations in instru-
ment stability; the samples can be recoverrd alter rcunting for further investigative use, if necesary; arid the l( air ( i f calcwlation lends itself easily to i)rograniniing and machine coml)utatic 11.
I n contrast, the internal standard niethod also uses two points, one for the unqurncnhed standard and the other for the same standard but quenched, to determine the estent of quenching which is tht’n used for quenching correction in t h r sample. For singly labeled and not too severely quenched samples, this nic~thtrd is ,straightfornard and reliable. l-Io\\-c~\~ci., to ensure the ~ a l i d i t yof the methcd, the count rate of the quenched stantlaid should equal or esreed the c w n t rate of the sample (9). This i ~ ~ p i i , e i n c ~was n t verified 1 y Herberg ( 3 ) i’roni a cwnsideration c,f counting statihtici of *ingle iroto1:es. I n doubly 01’ I riply labeled samples, several
internal standards would have to be added to each sample for quenching correction, resulting in nianipulational errors which are random and unrelated. In addition, the loss of the sample for recount and for further investigative use, and the probability of instrument instability over long intervals of time between successive countings, should be considered. I n severely quenched samples, the use of internal standard for quenching correction may not be justified. LITERATURE CITED
Bush, E. T., ANAL. CHEM.36, 1082 (1964). (2) Fleishman, D. G., Glazunov, V. T-., Pribory i Tekhn. Eksperl‘m. 7, No. 3 , 55 (1962). ( 3 ) Herberg, R . J., ANAL.CHEM.35, 786 (1963). (4) Ibid., 36, 1079 (1964). (5) Kabara, J. J., Spafford, ?;. R., bIcKendry, 1J. A , , Freeman, S . L., (1)
in “Advances in Tracer Methodology,” S. Rothchild, ed., Yol. 1, p. 76, Plenum
Press, New York, 1963. (6) Okita, G . T., Kabara, J. J., Richardson, F., LeRoy, G. V., Sucleonics 15, So. 6, 111 (1957). (7) Peng, C. T., ANAL.CHEM.32, 1292 (1960). (8) Peng, C. T., in “Liquid Scintillation Counting,” C. G. Bell, Jr., F. N, Hayes, eds., p. 198, Pergamon, New York, 1958. (9) Peng, C. T., “Organic Scintillation Detectors,” G. H. Daub, F. N. Hayes, and E. Sullivan, eds., U. S. Government Printing Ofice, Washington, 11. C., TID7612, 260 (1960). (10) Scales, B., ilnal. Biochem. 5 , 489 (1963). (11) m u , I and requires accurate standard
