338
ANALYTICAL CHEMISTRY
method as the independent variable and the per cent phosphorus pentoxide by the colorimetric method as the dependent variable. A straight line through the points should have a slope of unity, an intercept of zero, and all points on the line, if correlation is perfect. The actual slope of the least squares line did not differ significantly from unity and the intercept did not differ significantly from zero, both a t the 99.701, confidence level. As a measure of the deviation of the points from the line, the correlation coefficient, r , was 0.9988. Although the independent variable was not measured without error, statistical tests did not divulge any bias in its measurement. Data were also available to compare phosphorus pentoxide determinations by the volumetric method on the same sample in two different laboratories. The same technique was applied and the results may be summarized in the value of r, which vas 0.9991. Thus, evidence exists to show the colorimetric method is no less precise than the volumetric method. Variation in the colorimetric determination of phosphorus pentoxide was the same as for the volumetric method, a relative 2% of the phosphorus pentoxide determined. Phosphorus pentoxide determinations from samples in solution can be made in about one eighth the time required by the volumetric method. CONCLUSION
The ammonium phosphomolybdovanadate colorimetric determination of phosphorus pentoxide provides a quick and accurate method for routine determination of phosphorus pentoxide
in phosphatic fertilizer materials. By use of a properly aged color reagent solution, a standard calibration graph of scale reading against phosphorus pentoxide content can be prepared which is satisfactory for the determination of phosphorus pentoxide in the wide variety of phosphatic materials normally encountered by the fertilizer industry, and which does not require frequent recalibration. ACKNOWLEDGMENT
This work was supported by the Engineering Experiment Station and the Institute for Atomic Research of Iowa State College. The statistical analysis was made by J. P. Mills. LITERATURE CITED (1) Assoc.
Offic.Agr. Chemists, “Official and Tentative Methods of
Analysis,” 6th ed., pp. 20-5, 1945. Barton, C. J., ANAL.CHEM., 20,1068-73 (1948). Epps, E. A , , Jr., I b i d . , 22, 1062-3 (1950). Hanson, W. C., J . Sci. Food Agr., 1, 172-3 (1950). Kitson, R. E., and Mellon, b9. G., IND.E n . CHEM.,ASAL. ED., 16, 379-83 (1944). ( 6 ) Koenig, R. A., and Johnson, C. R., Ibid., 14, 155 (1942). (7) Maksimova, N. V., and Koglovsky, hI. T., J . Anal. Chem. (U.S.S.R.), 2, 353-8 (1947); abstracted in Analyst, 74, 73 (1949). (8) hlisson, G., Chem. Ztg., 32, 633 (1908). (9) Murray, W. M., Jr., and Ashley, S. E. Q., ISD.ENG.CHEM., ASAL.ED.,10, 1 (1938). (10) Willard, H. H., and Center, E. J., I b i d . , 13, 81 (1941). (2) (3) (4) (5)
R E C E I ~ Efor D review August 28, 1952,
.4ccepted September 29. 1952.
Determination of Benzene, Cyclohexane, and Methylcyclopentane by Mass Spectrometer SEYIIZOUR MEYERSON Research Department, Standard Oil Co. (Indiana), Whiting, 2nd.
HE current interest in benzene from petroleum has created Ta demand for a rapid and accurate means of determining benzene and the benzene-forming naphthenes-cyclohexane and methylcyclopentane-in naphthas. A specific method that would allow direct determination of all three hydrocarbons simultaneously would be especially valuable. Benzene alone can be determined by ultraviolet or infrared absorption, but mass spectrometry ( 6 ) possesses the advantage of speed. Both benzene and the naphthenes can be determined from the refractive indices of closely distilled, narrow-boiling fractions, provided the azeotropic behavior of these hydrocarbons is understood ( 6 ) . The method is S~OR-, however, and mass spectrometry offers a more rapid way of determining these compounds. The mass spectrometer has been employed for several years for the complete analysis of hydrocarbon mixtures in the Cs to Cg range (2, 11). Such an analysis requires careful distillation into narrow-boiling fractions and the solution of sets of relatively large numbers of simultaneous equations. For present purposes, it appeared probable that substantial time could be saved by utilizing a procedure for the determination of only the desired components. Such a procedure is feasible provided the contributions of other components to the peak heights used in the calculation can be eliminated or closely estimated, and provided means are available for introducing samples into the spectrometer in constant and reproducible quantities. These problems are overcome in a procedure that has been developed for the simultaneous determination of benzene, cyclohexane, and methylcyclopentane. Benzene is determined directly from the peak a t m / e 78, where contributions from other aromatics are small and contributions from nonaroniatics are negligible.
Cyclohexane and niethylcyclopentane are determined from the peaks a t m / e 84 and 69. Any other hydrocarbons that may make appreciable contributions to these peaks must be regarded as sources of interference. I n Table I are shown the errors in cyclohexane and methylcyclopentane content that would result from the presence, in 1% concentration, of each of several hydrocarbons. Olefins as a class contribute heavily to these pedm and must be excluded. Seven-carbon naphthenes also cause serious interference but can be largely removed by distillation. Hexanes and heptanes cause little difficulty; most of the Z-methylhesane, the only significant interfering member of this group, can be removed by distillation. Higher-boiling hydrocarbons contribute to peaks a t loiyer mass numbers and are presumed to interfere; these can be completely removed by distillation. Small amounts of 7-carbon naphthenes that may distill in the c6 cut can be corrected for in the calculations. When warranted, approximate corrections for paraffins can be made from the data in Table I if information is available on the paraffin distribution in the particular naphtha. For example, a c6 fraction of a virgin naphtha containing no benzene and no naphthenes would be expected to show 0.2 to 0.5y0cyclohexane itnd 1 to ZYOmethylcyclopentane. SEPARATION FROM INTERFERING HYDROCARBONS
If the olefin-free sample contains no 7-carbon riaphthenes, 2-methylhexane, or higher-boiling material, it can be analyzed directly by the mass spectrometer. Otherwise, i t must be fractionally distilled under conditions that remove the interfering hydrocarbons, yet retain all the desired compounds.
339
V O L U M E 25, NO. 2, F E B R U A R Y 1 9 5 3 Table I. Interference by Hydrocarbons i n Determination of Cyclohexane and 1Iethylcyclopentane by Mass Spectrometer (Errors in cyclohexane and methylcyclopentane determinations t h a t would result from failure t o correct for contributions from each of the listed compounds present a t a concentration of 17"by volume) Boiling Volume % Contribution t o Point, CycloMethylhexane cyclopentane Interfering Hydrocarbon F. ( 7 ) Olefins 1.2 3-Methyl-1 - p e n t e m 128.8 0.05 0.2 129.2 4-Methyl-1 -pentene 0.09 1-Hexene 146.4 0.1 0.2 2-Ethyl-1-butene 148.9 0.09 1.3 2.3 2-Methyl-2-pentenr 153.0 -0.05 cis-3-Hexene 153.7 0.4 0.3 1.6 154.0 0.1 trans-3-Rlethyl-Z-pentpne 154.2 0.4 trans-2-Hexene 0.2 0.4 154.6 0.3 trans-3-Hexene cis-2-Hexene 0.2 I555 0.4 cis-3-~Iethyl-2-pentrne 158.9 1.6 0.1 Saphthenes Cyclopentane 120.7 0.05 -0.01 190.1 1,l-Dimethylcyclopentane -0.2 1.2 195.4 /rans-l,3-Dimethylcyclopentane -0.1 0.5 197.1 -0.1 0.6 cis-l,3-Dimethylcyclopentane 0.6 197.4 -0.1 trans-l,2-Dimethylcyclopentane 211.1 -0.1 cis-I ,2-Dimethylcyclopentane 0.6 0.6 213.7 -0.04 3Iethylcyclohexane 218.2 Ethylcyclopentane -0 4 1.8 Paraffins 2,3-Dimethylbutane 0.02 136.4 -0.005 2-Methylpentane 140.5 0.02 -0.OOB 3-hlethvl~entane 145.9 0.02 -0.004 n-Hexan& -0.002 155.7 0.01 -0.005 2.2-Dimethylpentane 174.6 0.02 0.07 2,4-Dimethylpentane 176.9 -0.005 2,2,3-Trimethylbutanc 0.08 177. 6 -0.008 3,3-Dimethylpentane 0.04 186.9 0.006 194.1 2-Methylhexane -0.03 0.1
m / e 60, because loner peaks are not used, and carried through m / e 100, to permit reading the aromatic peaks a t m / e 91 and 92 and the 7-carbon-naphthene peak a t m / e 98 as a rough check on the fractionation. Before recording the spectrum of a succeeding sample, the instrument is flushed for 2 minutes with a portion of the sample to be run next and is pumped for 4 minutes. Because instrument sensitivity may drift from day to day, it is necessary to calibrate daily for these samples. For calibration, a synthetic benzene-cyclohexane mixture containing about 50% of each component is used. The spectrum obtained from this run provides sensitivities for both compounds as well as a check on the cyclohexane pattern. So long as the calibration pattern remains constant, methylcyclopentane sensitivity is directly proportional to that of cyclohexane; daily values for methylcyclopentane sensitivity can therefore be calculated. COMPUTATION
Benzene IS determined in both the 130" to 183" F. fraction iind the residue directly from the peak a t mle 78. I n a sample free of dimethylcyclopentanes, cyclohexane and methylcyclopentane contents can be calculated by the solution of a matrix of the pattern coefficients a t m/e 84 and 69. HoiTever, when fractional distillation has been employed to remove the 7-carbon naphthenes, a few per cent of dimethylcyclopentanes may have distilled in the 130" to 183" F. fraction and must be corrected for.
HANDLE
Table 11. Operating Condit ions for Fractional Distillation Charge, ml. Throughpiit, ml./hr. Product rate, ml./hr. Up t o 130' F. 130Oto 165' F. 165' t o 183" F. Reflux ratio Distillation time, Iir.
-
d
200 500
2.5 10 2.5 200/1 and 50/1 2 5 t o 30
Adequate distillations have been obtained with a Hyper-Cal column 120 cm. long and 2.5 cm. in diameter, operated under the conditions shown in Table 11. The initial cut point of 130" F. is low enough to preclude loss of benzene but high enough to eliminate the more volatile components. The upper cut point of 183" F. is the midpoint between the boiling point of cyclohexane and that of 1,l-dimethylcyclopentane,the lowest-boiling compound presenting serious interference. I n practice, all or part of the benzene and cyclohexane distills as the 1 to 1 azeotrope boiling a t 171.9' F. ( 6 ) , and a portion of either the azeotrope or any significant excess of one component usually remains in the residue boiling above 183" F. Because benzene can be determined in the residue by mass spectrometer with little or no interference from other components, it is convenient to assure distillation of all the cyclohexane as the azeotrope by adding a knoivn amount of benzene, to determine the total benzene content, and to correct for the amount added. The residue is fractionallv distilled, if necessary, to eliminate higher aromatics that may interfere, EQUIPMENT AND OPERATING PROCEDURE
The instrument used in this work is the Consolidated Ilodel 21-102 mass spectrometer, similar to the earlier model described by \\-ashburn (13). ildmission of the sample to the mass spectrometer is made through the metal inlet system by means of a mercury orifice ( 4 ) , as diagramed in Figure 1. The helium line n as removed from the valve block, and the mercury-orifice outlet tube was coupled to the block a t the opening thus provided. The constant-volume pipet used to introduce a knon-n quantity of sample is a calibrated 0.001-ml. "capillary dipper" of the type described by Charlet (5) and by Purdy and Harris (81.. I n order to meter the samples a t low pressure so as to minimize adsorption effects and deviations from the gas lam, the inlet system is equipped with an oil-mercury manometer ( 1 2 ) having a multiplying factor of 10.8. I n obtaining the spectrum of a sample, the scan is started a t
y
TO MULTIPLYING
MANOMETER
TO EXPANSION CtiA MBER
TO 8AROMETRIC LEG
VALVE BLOCK
ii
'I' t TO P V W
Figure 1. Liquid Introduction System In setting up a correction for any i-carbon naphthenes present, cis-l,2-dimethylcyclopentane,methylcyclohexane, and ethylcyclopentane are assumed absent because of high boiling point. The four dimethylcyclopentanes that require consideration are the 1,l-; trans-1,3-; cas-l,3-; and trans-l,2-isoniers. If the peak a t m/e 83 is used as the base peak, these four compounds eyhibit nearly identical pattern coefficients at m/e 84 and the first three have nearly identical coefficients a t m / e 69. These coefficients, calculated from National Bureau of Standards spectra ( 1 ) are shown in Table 111. The inclusion of the average pattern coefficients in the matrit: used to calculate cyclohexane and methylcyclopentane contents adequately corrects for the effects of the dimethylcyclopentanes. The average pattern provides a measure of the contributions of the four lower-boiling, 7-carbon naphthenes a t m / e 84; a t m / e 69, it provides a measure of the contributions of the first three compounds and of about 50% of the contribution of trans-lJ2-dimethylcyclopentane, which is the highest boiling and presumably the least abundant of the four isomers.
340
ANALYTICAL CHEMISTRY
Table 111. Mass-Spectral Patterns of the Lower-Boiling Dimethylcyclopentanes A.P.I. Spectrum Hydrocarbon No. 1,l-Dimethylcyclopentane 185 trans-l,3-Dimethylcyclopentane 189 cis-l,3-Dimethylcyclopentane 188 trans-l,2-Dimethylcyclopentane 187 Average a Average of first three pattern coefficients only.
Pattern Coefficients at n / e 69 83 84 127.0 100.0 6.44 118.0 100.0 6.59 129.0 100.0 6.01 226.0 100.0 6,59 125.0a 100.0 6.4
Once the hydrocarbon patterns under given operating conditions have been established, inverse equations calculated from the matrix are set u p to facilitate the rapid computation of results. For example, from the typical matrix
_-84 Cyclohexane Dimethylcyclopentane Rlethylcyclopentane
d e 83 6.23 100.0 2.32
100.0 6.4 39.3
-
69 33.8 125.0 100.0
130' to 183' F. fraction of an unknown sample showed the follom-ing results in volume per cent: benzene: 13.2, 13.4; cyclohexane: 3.2, 3.1 ; methylcyclopentane: 18.9, 18.5. These results are typical for samples of this type and are comparable with those obtainable in analyzing gaseous samples. A further check of the accuracy of the method is afforded by a comparison of analytical results obtained by mass spectrometer and by other means on the same sample. Table I V shows comparative results for three samples analyzed by mass spectrometer and ultraviolet absorption, and for three samples analyzed by mass spectrometer and refractive index calculations. The methods are in good agreement. Reproducibility and accuracy of the method are highly dependent upon the ability to introduce reproducible quantities of liquid sample into the instrument. Extensive experience with the capillary dipper, used in conjunction with the mercury orifice, indicates that this device can be relied upon provided the dipper is cleaned carefully after each use. Table V shows pressure readings obtained on the multiplying manometer upon repeated admissions of three different samples from a single dipper.
are derived the inverses
+
A'A = 1.12216 Psc 0.49344 P83 - 0.45245 Pea N B = 1.15105 Peg - 0.30061 Psa - 1.41957 Pg:
where ~ Y A= number of scale divisions due to cyclohexane a t m / e 84; X B = number of scale divisions due to methylcyclopentane a t m / e 69; and P = number of scale divisions of peak height a t the indicated m l e . The volume concentration of a component in the liquid phase is obtained by dividing the number of scale divisions due to that component a t its base peak by its volume sensitivity. The mole per cent-or volume concentration in the expansion chamber after vaporization-of a component is calculated from its partial pressure, which is obtained by dividing the number of scale divisions due to the component a t its base peak by its pressure sensitivity. Typical sensitivities for the three components iiivolved in the computation are: Yolume 18.9 6.19 3.57
Benzene Cyclohexane Met hylcyclopentane
Pressure 43.0 16.9 10.2
Table IV. Comparison of Results by Various Methods of Analysis
Component Benzene Cyclohexane hIethylcyclopentane Total
(All results expressed in volume 7a) Sample ~Method 1 2 3 4 5 Mass Spectrometer 29.5 27.7 8.0 1.8 26.0 27.1 7 9 Ultraviolet 29.7 Refractive index i : 8 2s:z ii.'o ii.'6 i:o io o 7.1 Mass spectrometer .. ,. 10.1 7.7 Refractive index ..
Refractive index
6 1.3
i:s
8.0 8.6
14.3 14.1 17.2 36.2 24.5 28.9 36.1 24 4 28.1 54: 8 53:4 2 6 : 2 48.0 5 7 . 6 38.2 .. . . 4 8 . 0 57.3 38.3
Table V. Replicate Sample Pressures from Single Dipper
n
Over-All Time Sample Elapsed, Hours 1 8 2 8 3 months 3 Four determinations
Manometer him. 27 8 27 8 20 2 20 2 25 8 26 2
Readings Oil 27 8 27 8 20 2 20 2 26 2 26 04
1
DISCUSSION
Reproducibility and accuracy of analyses of this type arc similar to those obtained by mass spectrometric analysis of gaseous hydrocarbon mixtures (IO,14). As possible sources of error, consideration must be given to instrumental interference, adsorption on the walls of the inlet system, and volume effec'ts on mixing. The reproducibility and accuracy obtainable under optimum conditions are illustrated by repeated analyses over a11 8-hour period of a known benzene-cyclohexane synthetic mixture containing 49.84 volume % benzene and 50.16 volume % cyclohexane. The results of these analyses were: Benzene Cyclohexane Total
49.76 50.17 99.93
49.88 50.07 99.95
49.88 50.07 99.95
49.88 50.17 100.05
The average deviation of the benzene contents from the average, 49.85, is 0.045; the average deviation of the cyclohexane contents from the average, 50.12, is 0.050. The average benzene and cyclohexane contents found differ from the k n o w (sontents by 0.01 and 0.04%, respectively. Another benzene-cyclohexane synthetic mixture, containing about 50% of each component and analyzed eight times over a 12-month period, showed the following benzene contents: 47.4 47.1 47.3 47.5 46.8 48.1 48.1 47.7 The average deviation of these values from the average, 47.5, s 0.35. Duplicate analyses carried out a month apart on the
Such effects as instrumental "interference" (16) can be minimized by reducing the sample pressure in the ionization chamber. [On several occasions when an ionization chamber developed e\cessive interference, this effect was much more marked between benzene and cyclohexane than between gaseous hydrocarbons. Thus, when the spectrometer exhibited 2 to 4% interference between ethane and n-butane, the corresponding values for benzene and cyclohexane, measured a t m / e 78 and 84, were as much :tb 407,.] This can be conveniently accomplished by closing the valve between the mercury orifice and the manometer prior to admitting the sample to the 2000-ml. expansion chamber. The volume relationships are such that this procedure results in a reduction of about 65% in sample pressure in the spectrometer. This reduction in sample pressure has been observed to cause a change in the ratio of the cyclohexane peaks a t m/e 69 and 84, which, though small, is significant and reproducible. The mole per cent benzene in a 50 to 50 benzene-cyclohexane mixture, calculated from calibrations that make use of manometer readings, is consistently lower by about 0.5% than the value calculated from the volume per cent and mole volume. This effect is believed to result from the preferential adsorption of benzene on the walls of the inlet system. The volumes of mixtures of benzene with cyclohexane ( 9 ) or with other nonaromatics (6) do not exactly equal the sums of the volumes of the individual components. Disregard of this characteristic undoubtedly introduceq error into an analytical procedure
341
V O L U M E 25, NO. 2, F E B R U A R Y 1 9 5 3 that utilizes a fixed volume rather thsn a fixed weight of sample. The data required to correct for such effects are not available. Nevertheless, in the analysis of synthetic benzene-cyclohexane mixtures, the sums of the concentrations found do not differ significantly from 100.0%. ACKNOWLEDGMENT
The assistance of E. H. Harclerode and N. G. Foster in establishing operating conditions for the required fractionation is gratefully acknowledged. LlTERATURE CITED ( 1 ) Am. Petroleum Inst., Research Project 44, “Catalog of Mass
Spectral Data,” Pittsburgh, Pa., Carnegie Institute of Technology, 1947-. (2) Brown, R. A,, Taylor, R. C., Melpolder, F. W., and Young, W.S., ANAL.CHEM., 2 0 , 5 (1948). (3) Charlet, E. M . , Consolidated Engineering Corp., Pasadena, Calif., Muss Spectrometer Group Rept. 72 (19.50). ( 4 ) Ibid., 74 (1950).
(5) Lumpkin, H. E., and Thomas, B. W., ANAL.CHEM.,23, 1738 (1951). (6) Marschner, R. F., and Cropper, W. P., Ind. Eng. Chem., 38, 262 (1946). (7) Satl. Bur. Standards, “Selected Values of Properties of Hydrocarbons,” Washington, D. C., Government Printing O 5 c e , 1947. (8) Purdy, K. M., and Harris, R. J., ANAL.CHEM.,22, 1337 (1950). (9) Scatchard, G., Wood, S.E., and Mochel, J. M., J . Phys. Chem., 43, 119 (1939). (10) Starr, C. E., Jr., and Lane, T., ANAL.CHEM., 21, 572 (1949). (11 1’ Thomas, B. W.. Consolidated Engineering Corp., Pasadena, Calif., Mass Spectrometer Group E&. 88 (1951)(12) Union Oil Co. of California,Ibid., 18, (1945). (13) Washburn, H. W., Wiley, H. F., and Rock, S. M., IND. ENQ. CHEM.,ANAL.ED.,15, 541 (1943). (14) Washburn, H. W., Wiley, H. F., Rock, S. M., and Berry, C. E., Ibid., 17, 74 (1945). (15) Wiley, H. F., “Operation and Maintenance of the Consolidated Engineering Corp. Mass Spectrometer,” Vol. I, pp. 69-71, Pasadena, Calif., Consolidated Engineering Corp., 1946. RECEIVED for review March 14, 1952. Accepted October 4, 1952. Presented before t h e Pittsburgh conference on -4nalytical Chemistry and A p plied Spectroscopy, March 6, 1952.
Ultraviolet Spectrophotometric Determination of Nitrites With 4-Arninobenzenesulfonic Acid J. M. PAPPENHAGEN‘ WITH M. G. MELLON, Purdue University, Lafayette, Ind.
HE Griess method ( 2 ) for the colorimetric determination of Tnitrites has been used for many years. An investigation of the color reaction was made by Rider ( 5 ) ,who determined the optimum conditions for diazotization of 4-aminobenzenesulfonic acid with nitrites and subsequent coupling of the diazo compound with 1-aminonaphthalene hydrochloride. The versatility of this method is shown by its acceptance as the standard method for the determination of nitrites in water and sewage ( 1 ). 1 Present address, Department of Chemistry, Kenyon College, Gambier. Ohio.
I n the hope of developing an alternate absorptiometric method, it seemed of interest to investigate the ultraviolet absorption spectra of 4aminobenzenesulfonic acid and its diazo compound. The spectral curves of these systems, obtained with a Cary recording spectrophotometer, &re shown in Figure 1. In addition, the spectrum of the diazo compound versus a 4-aminobenzenesulfonic acid blank is included. The nature of the increased absorption of the diazo compound, relative to that for the acid itself, indicated a possible method for the determination of nitrites. This paper presents the results of the investigation. APPARATUS AND REAGENTS
220
250
- 280 Wavelength, m p
310
3
Figure 1. Transmittance of 4-Aminobenzenesulfonic Acid and 4-Sulfobenzenediazonium Chloride pH 1.4
1-cm. cells
0.1 mp band width
0.4 p.p.m. nitrite nitrogen
A Beckman hlodel D U spectrophotometer, with matched I-cm. cells, was used for absorbance measurements. An investigation of the spectral curve of the diazo compound versus a reagent blank showed the wave length of maximum absorption to be 270 mp. Using this wave length for all quantitative measurements, the instrument was aperated a t a constant spectral band width of 1.8 mb. A stock nitrite solution was standardized according to directions given by Kolthoff and Sandell ( 3 ) . Approximately 1 gram of reagent grade sodium nitrite v a s placed in a 100-ml. volumetric flask and diluted to volume with distilled water. An excess of standard potassium permanganate solution was added to portions of this solution, and then potassium iodide. The iodine liberated by the excess permanganate solution was titrated with standard thiosulfate solution. Appropriate amounts of the standardized solution were diluted to 1 liter, and a few drops of chloroform were added as a preservative. The solution should be slightly basic, and a few milligrams of sodium hydroxide per liter may be added. The 4-aminobenzenesulfonic acid reagent was prepared by placing 0.60 gram of recrystallized material in about 50 ml. of distilled water. The solution was warmed to aid dissolution, cooled, and diluted to 100 ml. with water. An acid solution suitable for pH adjustment contained 20 ml. of reagent grade concentrated hydrochloric acid diluted to 100 ml. with water. All other chemicals were of reagent grade, and distilled water was used for all solutions and dilutions. Unless otherwise stated, all absorbance measurements were made versus a reagent blank. EFFECT OF SOLUTlON VARIABLES
In order to specify operating details for a recommended procedure, the effect of possible variable factors was studied.
