The use of thymol-sulfuric acid appears t o have an advantage over tryptophan for quantitative work with biological samples, in that protein has less influence on the absorption curve.
LITERATURE CITED
(1) Alonzo, L. P., Bruna, J . JI., Laboratorzo 15, 301 (1953). ( 2 ) Schmor, J., Klzn. Vochschr. 33, 449 (1955). ( 3 ) Shetlar, M. R., Foster, J. Y.,Everett,
M. R., Proc. Soc. Exptl. Biol. X e d . 67, 125 (1948). (4) Udransky, L., Hoppe-Seyler's 2. phys201. Chem. 12, 355 (1888). RECEIVED for review July 16, 1956. Accepted October 22, 1956.
Estimating Total Absolute Activity of Small Radioactive Precipitates on Filter Paper PAUL
T. WAGNER, LOUIS R. POLLACK,
and CLARENCE G. DONAHOE, Jr.
Industrial laboratory, Mare Island Naval Shipyard, Vallejo, Calif.
b The total absolute activity of a small amount of a radioactive precipitate on filter paper, containing a simple, low-energy beta emitter, is estimated from the counts obtained from both sides of the paper. By means of a chart based on exponential precipitate distribution, a relationship between the two counting rates and the total activity (counts per minute) is obtained. This relationship is dependent upon the product of the absorption coefficient and the thickness of the paper (including precipitate). For purposes of counting, a close geometry is stipulated-e.g., a windowless flow counter. Total activity is converted to total absolute activity (d.p.m.1 by multiplying by a geometrical factor. This factor is the ratio of 4n to the solid angle subtended by the sensitive volume of the counter based on average precipitate position, including a correction factor for radiations absorbed by the walls of the counter. For radiocarbon precipitates, an accuracy within 10% of the absolute value is expected.
W
a small amount of a precipitate containing a simple, lowenergy beta emitter is filtered on paper, the material becomes embedded within the paper and the activity appearing at the surface is reduced by absorption of radiations by the paper and precipitate. This article shows that the total activity (activity which would have been observed in the absence of any absorption losses) can be obtained from the ratios of the observed activities of the top and the bottom of the paper. ,4 chart showing this relationship (Figure 1) is based on exponential precipitate distribution and close-geometry conditions of counting. As shown by Suttle and Libby ( 5 ) , activities obtained under close-geometry conditions can HEK
conveniently be converted to absolute activities. CLOSE-GEOMETRY AND ABSOLUTE ACTIVITY
For close-geometry conditions, the absolute specific radioactivity was shonm to be related to the observed activity of either an infinite or a finite thickness of precipitate (6). This relationship is based on the values for the absorption coefficient, the surface area of the sample, and the factor G. G is the ratio of 4r to the solid angle subtended by the sensitive volunie of the counter from the point source on the precipitate being considered. These same arguments apply also to closegeometry placement of filter paper samples in end-window positions, as well as to the cylindrical placement used by Suttle and Libby in their screen-n-all counter. I n this case the filter paper with precipitate represents a finite sample thickness. I n end-window placement. the geometrical factor, G, can be considered from a standpoint of average precipitate position, with a correction for the radiation absorbed by the walls of the counter. To convert total activity counts per minute as obtained from Figure 1,to total absolute activity (disintegrations per minute), we need only to multiply the total activity obtained by the value of G. I n a 2n counter, G would be expected to be only slightly greater than 2. EXPONENTIAL DISTRIBUTION
I n a filtered precipitate the particles tend to be concentrated on top of the paper, the concentration (expressed as activity per unit thickness of paper) decreasing with increasing depth. Such a distribution of particles can readily be envisaged as exponential. This mathematical relationship satisfies a large number of precipitate distributions, while a given proportionality
constant will define a particular distribution. I n an exponential distribution of precipitate:
- dc dl
E
kc
and c = c0ebk1
where c
(1)
activity per unit thickness at depth 1 which would be observed if there were no absorption of beta rays co = activity per unit thickness at zero depth k = proportionality constant, sq. cm. per mg. 1 = depth within filter paper, mg. per sq. cm. =
If we consider a sample of filtered precipitate with an exponential distribution, the total activity can be considered to be the sum of the activities of an infinite number of infinitesimally thin layers. Using Equation 1, the total activity, z , is as follows:
where g
=
total thickness of paper with precipitate, mg per sq. em.
Kunierous authors (1-5) have shown the applicability of self-absorption equations relating measured activity to total activity in solid radioactive samples. These relationships are based on exponential beta-ray absorption for homogeneous samples where the activity from the top is measured. For exponential precipitate distribution, and exponential absorption of beta rays, the measured activity, 2, from the top side of filter paper becomes:
VOL. 29,
NO. 3, MARCH 1957
405
011 top of the paper, T. y = z y = and the nieasured activity on top is the total activity. Real Conditions. For real piecipitates k is neither zero nor infinite; but from Equations 3 and 4 we obtain an equation for the activity ratio, x, y, 3s a function of k .
Iiijei eM0,
where p = absorption coefficient for beta rays in filter paper with precipitate, sq. cm. per mg.
As the distance measured from the bottoni is g - I , the measured actiT-ity, y, on the bottoni side is:
Sindarly, by combining Equations 2 , 3. and -1 we obtain an equation for i
CO (e-ku
p - k
-
e-pu)
(4)
Limiting Conditions. I n the preceding equations k can vary from zero to infinity. By substituting these two values of k , we obtain equations for activity ratios a t the limiting conditions. Equation 2 can be expanded:
’
y:
1 - e-(@
+ k)u + ( e - r o
-
Similar tables can be prepared for other pg values; and the activity ratios can be used to plot z/y as a function of z ’y. Thus, a value of z/y can be obtained for any measured ratio of z,’y. APPROXIMATE RELATIONSHIP
Although an assumed eyponential distribution appears to be a reasonable type of precipitate distribution for obtaining an estimate of the total activity, setting u p a table for each of the various thicknesses and absorption coefficients encountered might become somen-hat laborious. A simpler method of calculation would be more attractive.
e-’g)
(9) By substituting arbitrary values of k , o t h e ~than zero or infinity, in Equations 8 and 9 we can obtain values of x/’y and z y and construct a table showing these relationships for a given p g value. Table I s h o w some k values and the
Table I.
Tabulation for Equation (pg =
k
D 0 2 0 3
0 5
0 7
1 0
1 6 2 0
-
As k 0, we approach the liniiting equations: i
= cog
y =
corresponding z/y and z/y ratios for pg = 2.24 ( p = 0.28 for radiocarbon and g = 8 for a typical filter paper).
3 0 5 0 10 0 I
2 (1 - e - P o ) CI
and r = y
Combining equations for z and y : z- = -
y
PS
1 - e - ~
(5)
Suhstituting 2 = y, and rearranging, result in an equation for self-absorption similar to the one given by Cook and Duncan ( 2 ): z =g
PX
1 - e-w
Thus, when k +. 0, the ratio of x/y 1, the precipitate is distributed uniforinly throughout the paper, and the well-known equations for self-absorption become applicable. -4s IC m , Equations 2, 3, and 4 yield the following liniiting relationships : =
-
X
-
Y
=
elro
z - = elro
Y
(7)
and
z = x Thus, when k -* m , the entire precipitate is in a n infinitesimally thin
406
ANALYTICAL CHEMISTRY
Plotted points are from Table 1
2.24) ZiY
ZlY
1 1 71
2 17 3 19 4 17 5 30 6 60 7 09 7 79
8 40 8 88
9 39
2 51 .~ ~
3 35 3 85
4 90 5 82 6 78 7 75 8 08 8 52 8 87 9 13 9 39
9
Assuming a generalized exponential distribution of precipitate, we can construct an approximating curve through two particular points. The obvious points of choice are the limiting onesLe., those corresponding to k = 0 and k = m . Plotting z/y as ordinate and x/y as abscissa, me determine from Equations 5 , 6, and 7 that the two points are (1, pg/l-e-@g) and (erg! erg); but in order to connect these points by a curve i t is necessary to have a n equation which expresses z ’ y as a function of x/y. The characteristics of filter paper are such that a usable precipitate will approximate a distribution that behaves as if all of the precipitate were concentrated in a thin layer. I n an equation based on a hypothetical thinlayer precipitate in which the precipitate position is such that the measured x,’y ratio is satisfied,
x
= ze-r
y = ze-dg
- 1)
Multiplying these two equations and rearranging. we can write:
This equation holds only for thinlayer concentrations of precipitates; however, when the x/y ratio of a real precipitate approaches its maximum, e@g, the precipitate concentration approaches a thin-layer concentration and the equation holds for that particular 2/11 ratio. For other x/y ratios Equation 10 is a n approximation, the degree of uncertainty in z/y increasing with decreasing x/y values. The desired relationship between z/y and s l y , satisfying the two fixed points, is non- indicated by the form of Equation 10. However, in order to satisfy both limiting conditions, k = 0 and k = a , x/y niust have some degree of independence from the exponent. The required conditions are satisfied by tlie equation:
A solution for b can be found by substituting the value of z/y when x y is unity. From Equations 5 and 11.
-2 -_ y
”
1-e-PO
= epgh
Then,
Equations 10 and 11 are identical when pg = 0; as
However, as pg # 0, b is slightly less
than 1/2. and Equation 11 gives z y values somewhat lower than Equation 10, which is as espected. Equations 11 and 12 can be combined to give an equation nhich niay be plotted to give a straight line on logarithniic paper, through the two previously fixed points:
DISCUSSION
Agreement between Equation 9. exponential distribution equation. and Equation 13, logarithmic equation, can be seen from the curve in Figure 1. The points on the curve for pg = 2.24 were obtained from Equation 9. The curve itself was constructed by drawing a straight line between the points (1, pg/l--e-pQ) and (erg, epe). Similar curves were constructed by this method for pg values of 1.5, 2.0, 2.5, 3.0, 3.5. 4.0, and 4.5, The dotted line in Figure 1 represents the curve 17-hen z ’y = x/y-Le., tlie z l y ratios one would get if x = z. The use of these curves is illustrated by a n example: The absorption coefficient for beta rays from carbon-14 in filter paper is 0.28 sq. em. per nig. The absorption coefficient of the piecipitate alone is 0.29 sq. em. per nig. Consequently. the absorption coefficient for a small amount of precipitate in filter paper is assigned the value of 0.28, the same as for the paper alone. The thickness of the paper containing the precipitate is 8 nig. per sq. em.; this gives a value of 2.24 for pg. If the top side of the paper has a measuied activity of 120 counts per minute and the bottom side a n activity of 40> r ’ y equals 3. From the curve in Figure 1. when pg equals 2.24, an x’y ratio of 3 gives a z y ratio of about 4.8. Since y is 40, z = (4.8) (40) = 192 counts pel minute. This represents the total activity of the precipitate, which is greater by 60% than the activity which one mould have obtained by taking the top measurement as representative of the total activity. I n the example cited, the relatively low 5 y ratio ( niax. = 9.4) niay be iiidicative of a slight loss of precipitate. For an exponential distribution of precipitate, the value of k , as obtained from Table I, is 0.36. The fraction of precipitate lost n-ould then be e-“, 01 0.025-i.e., about 2.5yGof the precipitate has not been retained b y the filter paper. The delivations in this article assume thin-layer concentrations of precipitate in which self-absorption coriections ale
negligible. A real precipitate, however, may have an appreciable thickness of precipitate concentrated above the paper. If the precipitate is sufficiently large to be removable, i t can be counted independently, and the paper counted on both sides for total remaining activity. If it is not of sufficient thickness to be removable, it may be of interest to know how thick it can be nithout introducing serious errors. TKO examples are given, and the total activities based on these distributions are compared to the total activities ohtained by the use of Figure 1. If we consider distributions in which all of the precipitate is on top, the bottom of the precipitate (or top of tlie paper) will have the same activity as the top of the precipitate, x. Activity a t the bottom of the paper will be reduced by the thickness of the filter paper. Then, X
-
Y
where
g, = g2 =
9 =
= eroz
thickness of paper, mg. per sq. cm. thickness of precipitate, mg. per sq. cm. 91
+ g2
I n a n exaggerated example, if the thickness of a radiocarbon-tagged piecipitate is the same as the thickness of the filter paper, and all the precipitate is concentrated on top, a thickness of 8 for the precipitate and 8 for the paper gives a total thickness of 16 mg. per sq. cm. with .u = 0.28, pgl = 2.24. pg2 = 2.24, and pg = 4.48. From Equations 14 and 15, the x/y ratio is calculated to be 9.4, and the z/y ratio 23.6. From Figure 1, if x/y is 9.4. z y is 20.0; and the curre gives a value differing by about 15% from the value based on the hypothetical distribution. Smaller precipitates, of the size Kith {Thich this article deals, Jvould range up to 15 mg. For a planchet 1 inch in diameter, this is equivalent to about 3 nig. per sq. em. Taking a typical value of 2 mg. per sq. em. for the precipitate. g is 10 nig. per sq. em, and hg becomes 2.80. I n this example xly is calculated to be 9.4 and d y 12.3. By interpolation between pg = 2.5 and pg = 3.0 in Figure 1, z,’y is found to be 11.7. These z ‘y values differ by only about 5%. The examples cited are indicative of deviations from the curves if a precipitate of appreciable thickness is coneeiitiated solely on top of the paper. Experimentally, this is the unusual case, as shown by the x,‘y ratios. I n general, any variation of piecipitate distiibution from the assumed distribution for the curve in Figure 1 will introduce niinor uncertainties in the results. Although the true distribution is not VOL. 2 9 , NO. 3, MARCH 1957
407
known, the deviation of the results from the correct results, while not calculable, will generally be less than in the extreme example cited. The magnitude of the z/y uncertainty for a given precipitate distribution is also influenced by the nature of the beta rays, weaker beta rays introducing a greater degree of uncertainty. On the other hand, rather pronounced shifts in precipitate distribution from a n assumed distribution cause only minor deviations in results. From this it is evident that, even though a precipitate distribution differs from that represented by the curves in Figure 1, the results obtained are not expected to differ by much from the results that would have been obtained if the true distribution had been known. A z’y value obtained for a precipitate containing radiocarbon, for example, is expected to differ by less than 10% from the true value. CONCLUSION
The proposed method a l l o w estiniation of the total activity of precipitates on filter paper from the measured ac-
tivities of both sides of the paper. The absorption coefficient, p, for the beta rays and the thickness, g, for the paper with precipitate must be known. Close-geometry conditions of counting must be used, in which the filter paper is close to the counter. A family of curves parametric in pg (Figuie 1) serve to define z/y as a function of z/y, where z is the total activity and z and y are the measured activities from the top and bottom of the filter paper, respectively. Total activity, z, can be converted to absolute total activity (d.p.m.) by multiplying by the geometrical factor of the counting setup. This is the ratio of 4 8 to the solid angle subtended by the sensitive volume of the counter, based on average precipitate position and corrected for radiations absorbed by the walls of the counter. For an efficient flow counter this factor is expected to be approximately equal to 2. I n the case of small radiocarbon-tagged precipitates, the total absolute activities obtained by means of Figure 1 are expected to differ by less than 10% from the absolute values.
ACKNOWLEDGMENT
The assistance of H. G. Isbell and L. 8. Turcios in the preparation of this manuscript has been invaluable. The authors 11-ish to thank the Bureau of Ships, United States S a v y Department, for permission to publish this material; but all opinions expressed are solely those of the authors. and do not necessarily reflect the official views of the S a v y Department. LITERATURE CITED
(1) Aten, A. W., Jr., Sucleonics 6, S o . 1, 71 (1950). (2) Cook, G. B., Duncan, J. F., “Modern Radiochemical Practice,” Oxford University Press, London, 1952. (3) Schii-eitzer, G. K., Stein, B. R., Sitcleonics 7, S o . 3, 65 (1950). (4) Solomon, A . K., Gould, R G., .infinsen, C. B., Phys. Reo. i 2 , 1097 (1947). (5) Suttle, A . D., Jr., Libby, K. F., r i ~ aCHEU. ~ . 27, 921 (1955). RECEIVEDfor revieiv June 3, 1956. Accepted Sovember 17, 1956.
Application of Thermal Diffusion to Separation of Aliphatic Alcohols and Fatty Acids from Their Mixtures C. W. BLESSIN, C. B. KRETSCHMER, and RICHARD WIEBE Northern Ufilizafion Research Branch, Agriculfural Research Service,
b Although separation of mixtures by thermal diffusion is often very effective -for instance, in mixtures of paraffin hydrocarbons-very little or no separation was found in alcohols and fatty acids. This failure is attributed to hydrogen bonding, which obscures structural differences and prevents their separation.
I
N CONNECTIOS with the possible ap-
plication of thermal diffusion to the analysis of complex mixtures of fatty acids and their derivatives, such as those encountered in vegetable-oil technology, binary mixtures of the lower aliphatic alcohols and fatty acids were studied. APPARATUS AND PROCEDURE
The stainless steel thermal diffusion column used in this n-ork was similar in
408
ANALYTICAL CHEMISTRY
U. S.
Deparfment of Agriculture, Peoria, 111.
design to the one described by Jones and Rlilberger (4). The fractionating section vias 6 feet in length, with an annular space of 0.0115 in. and an annular volume of 22.5 ml. The inner surface was n-atercooled, while the outer one n-as heated electrically. I n older to check the efficiency of the column, the separation of a series of binaiy paraffin hydrocalbon niiutures n a s studied (Table I). -4s \\as to be expected from n-paraffin hydrocarbon mixtures, sepaiation increased viith incieasing differences of the molecular weights between the two components of the mixture. The per cent separation is givcn for a -%hour run in each case and is close to the equilibrium value for this column. RESULTS
I n Table I the density values are quoted from API Research Project 44 ( I ) . The values of final composition listed were determined from experi-
mental plots of refractive index us. volume fraction, which in most cases !yere nearly straight lines. Alcohol Mixtures. No such regulaiity was found with binary mixtures of t h r lower aliphatic alcohols. The
0
20
40 60 80 HOURS OF OPERATION
100
Figure 1. Effect of time on separation of 50 volume mixture of propionic acid in butyric acid
yo
