dicated to be a problem in continuous crystal size distribution analysis. Such analyses are always based on a finite segment of size, but the distribution being measured is continuous and contains large numbers of particles below the lowest size scanned by the Coulter Counter. Some account of the excessive spurious counts that are expected in the lowest size channels has to be made to avoid erroneous conclusions.
W
6.
5. 4 -
3 Q Botch Mode 0 Continuous Mode
10-6
WEIGHED
2
3
4
5
7
10-1
PARTICLE CONCENTRATION IN
SAMPLE, gm/ml
Figure 6. Check of particle mass calculated from population counts
and directly weighed mates of minimum secondary coincidence error. Corrected counts were obtained simply by subtracting the intercepts from the corresponding observed number at any total particle concentration. The mass of particles calculated from corrected counts was plotted in Figure 5. The corrected points show a better agreement with the lower solid line (weighed) than the uncorrected points. It is clear from Figure 5 that most of the error was due to the secondary effect. In plotting the corrected mass, the 3% or so mass that remained below the threshold of channel 13 was ignored. Significant error in material balance can result from errors such as the existence of spurious counts, as evidenced in Figure 5. A material balance check on the population counts therefore is important. The mass obtained from counting (Equation 1)is plotted vs. the expected mass (from weighing) in Figure 6 for various narrow-size particles using both the batch and continuous modes of counting. Considering the smallness of the numbers, the agreement is satisfactory. No consistent bias was observed in the results of the mass balance experiments.
CONCLUSIONS It has been demonstrated in the present work that the Model T Coulter Counters are accurate in the population mode. Spurious counts, however, existed for particles at the low-size end of the distribution below the threshold size of the measurement spectrum. Secondary coincidence error is in-
NOMENCLATURE K , = volumetric shape factor = mid-channel size, pm m, = calculated mass, g m, = weighedmass, g N = total true number of particles n = total observed number of particles Ani = average number in channel i t = time, min V = volume of stock suspension, ml Y = volume of suspension used for counting, ml a = sensing volume of an aperture, ml p = density of particles, g/cm3 r = average retention time, minutes LITERATURE CITED (1) R. L. Eckhoff, J. Scl. Instrum., 2, 973 (1969). (2) T. Allen, "Particle Size Measurement", second ed., John Wlley & Sons, New York, 1975. (3) A. D. Randolph, and K. Rajagopal, i d . Eng. Chem., Fundam., 9, 165 (1970). (4) L. G. Bauer, M. A. Larson, and V. J. Dallons, Chem. Eng. Scl., 29, 1253 (1974). (5) M. D. Cise and A. D. Randolph, AiChESymp. Ser., 68, No. 121, 42 (1972). (6) M. A. Larson and A. D. Randolph, CEP Symp. Series, 65, No. 95, l(1969). (7) A. D. Randolph and S.K. Sikdar, Paper A5-3, Reprlnts Vol. 1, GVC/ AIChE-Jolnt Meeting, Munlch, 1974. (8) W. D. Cooper and G. D. Parfitt, Kolloid-2. Z.Polym., 22 (2), 160 (1967). (9) M. D. Cise. Ph.D. Dissertation, Department of Chemical Engineerlng, University of Arizona, Tucson, A r k , 1971. (IO) "lnstructlon and Servlce Manual for the Model T Coulter Counter". Coulter Electronics, Inc., Hialeah, Fla., 1969. (11) S.K. Slkdar and A. D. Randolph, Paper presented at the 77th National AlChE Meeting, Pittsburgh, Pa., 1974. (12) L. H. Princen, Rev. Sci. Instrum., 37, 1416-1418 (1966). (13) I. C. Edmundson, Nature(London),212, Dec. 24 (1966). (14) M. Wales and J. N. Wilson, Rev. Sci. Instrum., 32, 1132 (1961). (15) R. H. Berg, "Sensing Zone Methods in Fine Particle Size Analysls", Reprint from Mater. Stand., 5, No. 3 (1965) (16) H. E. Kubltschek, Rev. Sci. instrum., 33, 576 (1962) (17) "Reference Manual for the Coulter Counter Model TA 11". Coulter Electronics, Inc., Hialeah, Fla., 1975. (18) L. H. Prlncen and W. F. Kwolek, Rev. Sci. instrum., 36, 646 (1965). (19) H. Bader, H. R. Gordon, and 0. B. Brown, Rev. Sci. Instrum., 43, I O , 1407 (1972).
RECEIVED for review May 9,1975. Accepted April 21,1976. The authors gratefully acknowledge the financial support rendered by the National Science Foundation through Grant GK-36517X.
I CORRESPONDENCE
I
Trace Determination of Vacor Rodenticide by Pulse Polarography Sir: During the summer of 1975, Vacor, a single dose quick-kill rodenticide, was introduced into the United States market ( 1 ) .It is expected to be widely used in both urban and rural areas for rodent control. The specificity of Vacor for rodents has been called info question because of a series of human poisoning incidents in Korea which are linked cir1418
ANALYTICAL CHEMISTRY, VOL. 48, NO. 9, AUGUST 1976
cumstantially to the ingestion of Vacor (2).In response, Vacor has been relabeled to display more prominently the "warning." We have developed a pulse polarographic method for the determination of RH787 (l-(3-pyridylmethyl)-3-(4-nitropheny1)urea) ( 3 ) ,
0-c 'N
0
HS~ H c NH
-
~ 0,
N
the active ingredient in Vacor, which is based on the reduction of the nitro moiety. The data reported were obtained with a Princeton Applied Research Corporation Model 174 Polarographic Analyzer and a dropping mercury electrode with flow rate of 2.892 mgh. Tetrabutylammonium salts as supporting electrolytes produce a well defined wave for RH787. Tetrabutylammonium bisulfate [TBA(HS04)] was the electrolyte of choice since the anion is employed in the bisulfatelsulfate buffer a t pH 2.0, and the background currents are the least bothersome of those examined. The RH787 wave in 0.1 M TBA(HS03, pH 2.0, occurs at Ell2 = -535 f 5 mV vs. SCE in the normal pulse polarographic (NPP) mode and a calculated potential E = E,, f AE/2 of -536 f 2 mV in the differential pulse polarographic (DPP) mode, where AE is the pulse amplitude. The NPP sensitivity is 30.6 C! 1.6 pAImM at a drop time of 1 s, while the dc sensitivity is 9.8 pA/mM. The sensitivity ratio, 3.1, can be compared with the theoretical ratio for diffusion controlled reactions for these conditions, 3.0 ( 4 ) .The DPP response a t 1-s drop time and various pulse amplitudes is AE: 100 mV, 155.6 f 1.1fiA/mM; 50,76.6 f 1.3; 25,36.6 f 0.5. The sensitivity is approximately linear with pulse amplitude, which is to be expected for an irreversible process. The calibration curves for all modes are linear in the range 1.5-20 fiM RH787 with zero intercepts within experimental error. Figure 1shows differential pulse polarograms of RH787 standards; the sensitivity calculated from these data is 236 f 36 pAImM. The 15%relative standard deviation is primarily due to difficulty in estimating the background current which depends on the analyte concentration. From the data of Figure 1,the detection limit calculated according to the equation dl = st/m, where s is the pooled standard deviation of the current residuals, t the one-sided t statistic at 95% confidence, and m the slope of the unweighted least squares calibration curve is 2 X loV8M (17 ng in 3 ml). Using this procedure, recoveries of 98 f 11%and 109 f 9% were obtained for 3.0 and 1.5 mg RH787 spikes in human liver samples which were homogenized with water and extracted several times with tetrahydrofuran (THF). One gram of a commercially formulated Vacor place pack-reported to contain 2% RH787 active ingredient-was extracted 3 times with THF. Analysis of the extract by DPP was not complicated by any interferences and showed the RH787 content to be 1.7%. The reduction of RH787 was also compared with the reduction of p-nitroaniline (PNA) which undergoes a 6 e- reduction ( 5 ) .The N P P and dc diffusion limited currents of RH787 are 0.64 of the PNA currents which indicates a 4 ereduction for RH787. This is consistent with the known 4 ereductions of nitro groups to hydroxylamines (6).Under the conditions we have examined, the Ell2 for PNA and RH787 differ by about 30 mV. Polarograms in any mode of mixtures of the two substances show no resolution. Because preliminary results of metabolism studies in dogs suggest p-nitroaniline is a metabolite of RH787 (7),distinguishing between these two compounds is of some interest. One approach is to determine PNA in mixtures by a method which depends on the amine functionality. This can be done by modification of the method of Bandelin and Kemp (8) which involves diazotizing the amine and coupling with N (1-napthy1amine)ethylenediamineto produce an azo dye with Amax 550 f 5 nm. Addition of an unknown containing 3-64 NaNOz formed the fig PNA in 5 ml 10%H2SO4 to 25 ~ 1 0 . 1 % diazonium salt. After 12 min, the latter was coupled by adding
V Figure 1. Differential pulse polarograms of RH787 in 0.1 M tetrabutylammonium bisulfate (pH 2.0)
(0,2.5, 5, IO, 15, 35, 64) X IO-* M RH787; v: 2 mV/s; A€: -100 mV; f: 2s
25 fi1 2 mM N - (1-napthy1amine)ethylenediamine.After 30 min, the absorbance was measured at 550 nm with an apparent molar absorptivity of 24 500. The response was linear over the range 2 to 47 X loe5 F PNA with a detection limit at the 95% F. confidence level of 2.5 X Alternatively RH787 and PNA can be separated by thin layer chromatography (TLC) prior to polarographic analysis. We have used a modification of an unpublished Rohm and Haas TLC method. T H F solutions of PNA and RH787 were streaked on a Brinkmann 2 mm X 20 cm X 20 cm precoated silica gel 60 F-254 plate which was developed using 65:35 acetone:benzene eluent. The Rf values of 0.10 for RH787 and 0.47 for PNA were determined by viewing in short and long wave uv radiation. The fluorescing material was found not to interfere with polarograms of T H F extract of the scraped plates. The two compounds can also be distinguished using gas liquid chromatography. A 0.64-cm. i.d., 1.8-m long glass column packed with 5% OV-210 on 80/100 mesh Gas Chrom Q (Analab, Inc.) was operated isothermally a t 175 "C (injection port 235 "C, detector 240 "C) with nitrogen carrier gas at 90 mllmin. Under these conditions, PNA elutes in a sharp symmetrical peak well before RH787. The RH787 peak is too' broad to be suitable for analytical purposes. More complete discussions of the electrochemistry of RH787 and its determination in complex matrices will appear in future papers.
ACKNOWLEDGMENT The authors are grateful for the standard grade RH787 provided by W. D. Weir, Rohm and Haas, Philadelphia, Pa. LITERATURE CITED (1) Chem. Ena. News, 24 March 1975, p 8. (2) Chem. En& News, 14 July 1975, p 8. (3) W. D.Weir, US. Patent 3829419 (1974); Chem. Abstr., 81, 1207099 (1974). (4) E. P. Parry and R. A. Osteryoung, Anal. Chem., 37, 1634 (1965). (5) A. J. Fry, "Synthetic Organic Electrochemistry", Harper and Row, New York, N.Y.. 1972. I) 228. (6) Ref.'5, p 225.
ANALYTICAL CHEMISTRY, VOL. 48, NO. 9, AUGUST 1976
1419
(7) M. C. Seidel, Rohm and Haas Research Laboratories, Spring House, Pa. 19477, unpublished results. (8) F. J. Bandelin and C. R . Kemp, lnd. Eng. Chem., Anal. Ed., 18, 470 ( 1946).
Jeffrey W. Whittaker Janet Osteryoung* Department of Microbiology Institute of Rural Environmental Health Colorado State University Fort Collins, Colo. 80523
RECEIVEDfor review March 8,1976. Accepted April 26,1976. This study was supported through a contract with the Epidemiologic Studies Program, Human Effects Monitoring Branch, Technical Services Division, Office of Pesticide Programs, U.S. Environmental Protection Agency, Washington, D.C., 20460. The mention of trade names or commercial products does not constitute endorsement or recommendation for use by the Environmental Protection Agency. The views expressed herein are those of the investigators and do not necessarily reflect the official viewpoint of the Environmental Protection Agency.
Similarity Measures for Binary Coded Mass Spectral Data Sir: In a series of studies ( 1 4 ,Grotch has presented a case for the use of binary coded mass spectral data in file search systems for spectrum identification. The principal advantages of binary encoding of spectral data are the resulting economies in requisite storage and reductions in search times. Early in this series of studies ( 2 ) ,it was found that simple similarity/ dissimilarity measures such as the AND/XOR of binary coded vectors were not satisfactory. Intuitive conceptions of the matching process were invoked to explain the failings of these simple measures. Thus, it was argued that the deficiency of an XOR dissimilarity measure is due to its weighting a 0/0 match equally with a 1/1 match whereas intuitively one might expect a 1/1 match to have greater significance. In consequence, a dissimilarity measure of the form given by Equation 1was proposed: D = XOR
- FAND
(1)
Several different values for the parameter I.L have been considered ( 2 , 3 )with a value p = 2 being generally found to be optimal. This finding has been confirmed in the most recent of these studies which was primarily concerned with the possibility of using different weighting factors for each binary channel ( 5 ) . The essential limitation of simple similarity/dissimilarity measures such as AND or XOR is that they do not take into account the information provided by the sizes of the binary vectors. This can be illustrated through the examples of Table I. As shown there, the simple AND measure of similarity and XOR measure of dissimilarity give non-intuitive results if the lengths of the vectors differ substantially. Thus, it is essential to use normalized similarity measures which reflect the influence of the length of the vectors (i.e., the number of 1’s set in the binary vector). Several normalized similarity measures have been devised and evaluated in the context of more conventional “Information Retrieval” systems. The following list of some of the more commonly used measures is taken from van Rijsbergen (6):
(IAl represents the length of vector A). Table I1 gives the values of these similarity coefficients for some of the binary vectors of Table I. It can be seen that these normalized similarity measures do reflect intuitive assessments of the closeness of the binary vectors. It is interesting to note that the dissimilarity measure proposed by Grotch is, in fact, an indirect method of partially compensating for the influence of vector lengths on an XOR dissimilarity measure. For by using the relation:
IAl
MI+ P I
D(A,B) = IA XOR BI - MIAAND BI = (1+ ~ / 2 ) l AXOR BI - (F/~)(IAI+ IBI or with 1.1 = 2: D (A,B) = 21 A XOR BI
VPim-
When D = XOR - 2 AND, this normalized dissimilarity coefficient is closely related to the ‘Overlap’ measure of similarity. The following analysis establishes the form of the relationship: Let IAl
’
IBI
D,,, corresponds to the case where A and B have no bits in common. Then:
IAANDBI = O [ A XORBI = IAl IB(
+
so
Dmax = IAl (3)
Overlap coefficient:
(4) 1420
- (IAI + IBJ)
(This reformulation of the dissimilarity measure would simplify the computational process for it shows that it is only necessary to calculate the XOR of the vectors rather than to compute both XOR and AND.). In his most recent paper, Grotch has defined a normalized variation of his dissimilarity coefficient ( 5 ) :
(2)
Cosine coefficient:
IA AND BI
+ 21A ANDBI
= [ A XORBI
this dissimilarity coefficient can be rewritten:
Dice’s coefficient:
21A ANDBI
+ IBI
ANALYTICAL CHEMISTRY, VOL. 48, NO. 9, AUGUST 1976
+ IB(
For Dmin,the only bits that differ correspond to the extra bits set in the longer binary vector A . So:
