Computer Program to Draw Absorption Profiles in Atomic Absorption Spectrometry C. L. Chakrabarti,’.?Rajendra
and Mohan Katyal?
Carleton Unicersity, Ottawa, Ontario KIS 5B6, Canada
THESTUDY of absorption profiles (1-3) in atomic absorption spectrometry is important not only from the point of view of the analyst who seeks to locate the position for maximum absorbance in a flame but also for others (1-3) who study the relationship of flame profiles to various parameters of the flame-metal system producing free atoms. Most of the absorption profiles of flame-metal systems were drawn manually in the past (1-3). The manual drawing is laborious, tedious, time-consuming, and subject to errors inherent in human judgment and also to those due to variations that are normally found between replicate drawings drawn at different times, and those due to personal fatigue. Since these absorption profiles are often used for the purpose of comparison (1-3), they should be free of all personal errors mentioned above. The computer program described in this paper replaces manual plotting of absorption profiles by computerplotting, and is therefore free of all personal errors inherent in manual plotting. Also the error in the manual method of curve fitting is much greater than that of the least squares method of curve fitting used in this computer program. Another major advantage of this computer program is the enormous saving of time and labor. EXPERIMENTAL
The computer program employs Fortran IV for use with an IBM 360165 computer in conjunction with the off line MILGO DPS-6 digital plotting system. The program consists of a main routine in which the experimental data are systematically read, and with the help of subroutine POLFIT proper curve fitting is done. Subroutine PAL is used to generate the data required for plotting. The main program punches out these data which are then fed in the second program used exclusively for plotting. The system hardware consists of the plotter with a 3 0 4 . X 30-in. horizontal plotting surface and a nine-track magnetic tape unit. The system software is stored in IBM 360/65 system library. When mounted on the DPS-6 tape unit, the magnetic tape containing plotter control codes and data to be plotted, drives the plotter to produce the required absorption profiles as line segments. RESULTS AND DISCUSSION
In the experiment there are three variables-namely, absorbance, horizontal traverse, and height above the burnertop. For a given height above the burner-top, the experimental data consist of the dependent variable absorbance 2s. the independent variable horizontal traverse. Table I shows a typical set of experimental readings for various values of All correspondence to be addressed to this author.
* Department of Chemistry.
Department of Mechanical Engineering. ( I ) C. S. Ram and A. N. Hambly, ANAL.CHEM., 37,879 (1965). (2) A. N. Hambly and C. S. Rann, in “Flame Emission and Atomic Absorption Spectrometry,” Vol. I , Theory, J. A. Dean and T. C. Rains, Ed., Marcel Dekker, New York, N. Y., 1969, p 241. (3) C. L. Chakrabarti, M. Katyal, and D. E. Willis, Specrrochin?. .Icto,
1704
25B,629 (1970). e
1.0
~
0.8
W
0 0.6
t
-
V. 2
i 0.4
s 0.2I
I
0
2 .o
1.0
HORIZONTAL
I
I
1.0
4 1)
3.0
TRAVERSE in
mm
X
Figure 1. Plot of absorbance as a function of horizontal traverse with V , height above the burner-top in mm, as a parameter, and using strontium as chloride in an aqueous solution and the strontium 4607.3 line
A
height above the burner-top. A d o t of the same experimental readings is shown in Figure 1, in which the independent variable horizontal traverse has been plotted as X coordinate and the dependent variable absorbance has been plotted as Y coordinate, for various values of V , height above the burnertop. Input Data. The program reads Y for various values of V at fixed values of X. This is continued till data for all values of X are read in. Subroutine POLFIT. It is required to fit the suitable curve in X and Y for each value of V. Subroutine POLFIT generates an approximate polynomial equation by the method of least squares. The method of least squares has been well covered in text-books, and so will not be described in this paper. The equation so derived contains as many terms as are necessary to bring the standard error or the order of the polynomial equation within the specified ranges. The method of least squares is based on the assumption that a set of experimental data can be fitted in the curve of the type Y = a. alX u2X? a.Xn. Y = a0 alX is treated as a first approximation. The coefficients and the standard error of the dependent variable Y are computed. This is compared with the predetermined maximum permissible limit of error. If the standard error is greater than the specified maximum error, the process is repeated, adding a term anXn,where n = 2, 3, 15, until the standard error or the order of the polynomial equation is within the specified ranges ( i x . , within either the maximum permissible limit of error or the order of the polynomial equation). In this case, it was experimentally found that the absorption profiles have maxima (each profile one maximum), which are at the center of the profiles and therefore they fit a second order equation, and so, the second order best represents the required polynomial. Hence, the maximum order of the required polynomial equation was specified as 2. The standard error of this second order polynomial will depend upon the deiviation of each datum and the total number of observations. UIX The curve thus generated was of the type Y = a0 a2X2.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
+
+
+
+
+
+
+
12
10
9
S
4
2 -4
Figure 2A. Computer-plotted absorption profile of strontium as chloride in an aqueous solution. Sr 4607.3 A line used
Table I. Height above burnertop, mm
-3
-e
-1
1
0
e
3
Figure 2B. Computer-plotted absorption profile of strontium as strontium titanium oxalate in an aqueous solution. S r 4607.3 A line used
Typical Set of Experimental Readings
Absorbance values at various points of horizontal traverse. The horizontal traverse shown below in the first horizontal __ column _ _ ~ _are _ _distances ~ in mm from _ _ _the _ _optic ~ axis taken in a direction perpendicular to the optic axis __ 1 1.5 2 2.5 3 3.5 4 4.5 5.0
2 4 6
0.400 0.392 0,350 0.324 0.271 0.235
8 10
12
0.675 0.615 0.510 0.430 0.360 0.290
0.843 0.728 0.621 0.495 0,425 0.324
0.950 0 , 7.70 0.640 0.490 0.400 0.315
1 .00
0.784 0.633 0.442 0,350 0.271
0.870 0.640 0.570 0.375 0.280
0.225
0,675 0.510 0.390 0.300 0.210 0.176
0.500
0.360 0.280 0,225 0.140 0.125
0,204 0.198 0.156 0.134 0,095 0.075
Table 11. Coefficients as Found for the Curve for Which V = 8; Also, the Observed and Calculated Values of Y and the Difference of These ORDER 2
TOLERANCE 0.4999999OE-02
ORDER
COEFFICIENT 0.14848244E 00 0.26193827E 00 -. 54100681E-01
0 1
2
STANDARD ERROR 0.31261 314E-01
NO. OF PTS 9
X
OBS Y
CALC Y
DIFF
0 . IOOOOOOOE 01 0.15000000E 01
0.32399994E 00 0.42999995E 00 0.49499995E 00 0,48999995E 00 0.44199997E 00 0.37500000E 00 0.29999995E 00 0.22499996E 00 0.13399994E 00
0.35632002E 00 0.41966331E 00 0.45595628E 00 0.46519887E 00 0.44739115E 00 0.40253234E 00 0.33062381E 00 0.23166561E 00 0.10565662E 00
-. 323200828-01
0.20000000E 01 0.25000000E 01 0.30000000E 01 0.35000000E 01 0.40000000E 01 0.45000000E 01 0.50000000E 01
0.10336637E-01 0.39043665E-01 0.24801075E-01 -. 5391 1805E-02 - . 27532339E-01 -. 30623853E-01 -. 66656470E-02 0.2834332OE-01
ANALYTICAL CHEMISTRY, VOL. 43, NO. 12. OCTOBER 1971
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Table 111. Values of Two Roots (Maximum and Minimum) for Various Values of Absorbance, Y ,for the Curve for Which V = 8 MAXIMUM MINIMUM ROOT R1 ROOT R2 ABSORBANCE Y 0 50202E 01 -0 17851E 00 0 lOOOOE 00 0 46363E 01 0 20539E 00 0 2M)OOE 00 0 41701E 01 0 67161E 00 0 30000E 00 0 35215E 01 0 13202E 01 0 40000E 00 0 IOOOOE 03 0 lOOOOE 03 0 50000E 00 0 lOOOOE 03 0 lOOOOE 03 0 60000E 00 0 lOOOOE 03 0 lOOOOE 03 0 70000E 00 0 lOOOOE 03 0 IOOOOE 03 0 80000E 00 0 lOOOOE 03 0 lOOOOE 03 0 90000E 00 0 lOOOOE 03 0 lOOOOE 03 0 IOOOOE 01
Computer calculates the coefficients ao, al, and a? for each curve. Table I1 shows the coefficients as found for the curve for which V = 8 (say). The printout also shows the observed and calculated values of Y and the difference of these. Subroutine PAL. Once the coefficients of the curves are known, for any given value of Y,two roots of the equation can be found as follows:
Y is varied from 0.1 to 1.0 absorbance unit. It may be noted that either both the roots will be real or imaginary. Whenever 4a4ao - Y) > u l * , the roots will be imaginary. Subroutine PAL thus finds all the roots of various curves for various absorbance values. To facilitate the programming, whenever 4 4 a o - Y ) > al*, the imaginary roots are = some constant = 100 (say), Later, these written as R1,* imaginary roots will be ignored in plotting. Table I11 shows TabIe IV. NEGATIVE X -0 321304E 01 -0 311012E 01 -0 300350E 01 -0 255799E 01 -0 253746E 01 -0 228598E 01 -0 245604E 01 -0 259914E 01 -0 261960E 01 -0 232152E 01 -0 234650E 01 -0 214873E 01 -0 190515E 01 -0 215338E 01 -0 205546E 01 -0 213741E 01 -0 200208E 01 -0 150479E 01 -0 174477E 01 -0 190378E 01 -0 184381E 01 -0 135455E 01 -0 163419E 01 -0 167061E 01 -0 737007E 00 -0 130402E 01 -0 147724E 01 -0 831997E 00 -0 125441E 01 -0 982260E 00 -0 596773E 00
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the values of two roots (maximum and minimum) for various values of Y for the curve for which V = 8 (say). It may be noted that imaginary roots have been printed above as 100 (ix., 0.10000E 03). Ignoring imaginary roots, the main program then collects all the real roots of various curves for a given value of Y . Table IV presents the computer output for plotting absorption profiles by the computer-plotter. Table IV shows that the total number of curves that give the set of real roots decreases as Y is increased. Also, at Y = 0.1, there are 6 curves giving real roots, whereas at Y = 0.8, there is only one curve giving real roots. At Y = 0.9 and 1.0, there is no real root in this particular case. Figure 2A has been plotted using the values shown in Table IV (which have been obtained from Tables 1-111). The Tables for Figure 2B have not been shown. Output. The output of the main program is taken as a set of punched data cards for the next program. which is exclusively used for plotting. Output cards are punched so that for a given Y all the minimum and maximum roots of various curves are punched separately. Plotting Program. This program sets up the plotting codes and data for the tape using the punched output data cards of the first program. This program sets up a 4-sided set of rectangular axes at a prescribed location on the plotting board surface. The scale and size of the plot are specified. Scale ticks, numbers, and specified titles of the axes are then drawn. Using supplied punched data, the plotter then draws the absorption profiles as line segments for the various absorbance values. The final results of the program are shown as Figure 2 A and 2B, (which are absorption profiles for two different chemical compounds) which were plotted and labeled by the computer (all the writings on the Figures were done entirely by the computer). The advantages of the compnter-plotting
Computer Output for Plotting Absorption Profiles by the Computer-Plotter POSITIVE X 0 189365E 01 0 197043E 01 0 219520E 01 0 219648E 01 0 226852E 01 0 228599E 01 0 113664E 01 0 145944E 01 0 181130E 01 0 196001E 01 0 207744E 01 0 214874E 01 0 765456E 00 0 134508E 01 0 169395E 01 0 186846E 01 0 200209E 01 0 696486E 00 0 138326E 01 0 163483E 01 0 184381E 01 0 993036E 00 0 136524E 01 0 167062E 01 0 375498E 00 0 103508E 01 0 147724E 01 0 563051E 00 0 125441E 01 0 982266E 00 0 596781E 00
ABSORBANCE Y COORDINATES 0 600000E 01 0 600000E 01 0 500000E 01 0 500000E 01 0 400000E 01 0 400000E 01 0 300000E 01 0 300000E 01 0 200000E 01 0 200000E 01 0 lOOOOOE 01 0 IOOOOOE 01 0 600000E 01 0 600000E 01 0 500000E 01 0 500000E 01 0 400000E 01 0 400000E 01 0 300000E 01 0 300000E 01 0 200000E 01 0 200000E 01 0 IOOOOOE 01 0 I OOOOOE 01 0 500000E 01 0 500000E 01 0 400000E 01 0 400000E 01 0 300000E 01 0 300000E 01 0 200000E 01 0 2OOOOOE 01 0 IOOOE 01 0 lOOOOOE 01 0 400000E 01 0 JOOOOOE 01 0 300000E 01 0 300000E 01 0 200000E 01 0 200000E 01 0 IOOOOOE 01 0 lO00OOE 01 0 300000E 01 0 300000E 01 0 200000E 01 0 200000E 01 0 lOOO00E 01 0 IOOOOOF 01 0 300000E 01 0 300000E 01 0 2OOOOOE 01 0 200000E 01 0 lOOOOOE 01 0 IOOOOOE 01 0 200000E 01 0 2OOOOOE 01 0 lO00OOE 01 0 lOO0OOE 01 0 lOOOOOE 01 0 lOOOOOE 01 0 lo000OE 01 0 lOODO0E 01
ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
NO. OF CURVES 1
2
3 4 5 6 1 2 3 4
5 6 1
2 3
4 5 1
2 3
4 1 2 3 1
2 3 1
2 1 1
of absorption profiles are as follows. The computer program can be used for routine drawing of absorption profiles by using directly the absorbance values to produce absorption profiles. The manual drawing of curves as in Figure 1 is completely eliminated, saving time and labor. There is a n enormous saving of time and labor-this is one of the most important advantages; this advantage becomes particularly important when one has to draw a large number of absorption profiles as in the case of references (1-3). The chances of personal errors due to the experimenter’s judgment being a t fault, personal idiosyncrasies, personal fatigue, and other personal factors, normal variations among replicate manual drawings due to human limitations, etc., are all eliminated by the computer-plotting, whereas manual drawings are subject to all these personal errors. Also, in curve-fitting, the manual method which uses one’s best judgment produces
much more error than the method of least squares. Since the absorption profiles are often used for the purpose of comparison, they should be free of all personal errors, or at least the errors should be constant, in order that the comparison is valid. In the manual method, the magnitude and the direction of personal errors change with time, the nature, and quantity of work, making the total error in the manual method variable. Compared to this, the computer program plots the absorption profiles free of all personal errors, thus enabling valid comparisons of different absorption profiles. RECEIVED for review April 12, 1971. Accepted June 25, 1971. The authors are indebted to the National Research Council of Canada for financial support of this research project.
Simplified Wet Ash Procedure for Total Phosphorus Analysis of Organophosphonates in Biological Samples Donald S. Kirkpatrick and Stephen H. Bishop Department of BiochcmLstry, Baylor College of Medicine, Houston, Texas 77025 WET ASH METHODS capable of digesting difliculii:,, hydrolyzable phosphorus compounds in the presence of lares amounts of organic material and inorganic cations inc!u;ie refluxin,: in concerltrated perchloric acid or in concenrrakd sulfuric acid with hydroger. peroxide. These methods suffer from difficulty in controlling acid loss due to reflux (without the use of special glassware such as Kjeldahl flasks), due to oxidation of the sample material, and due to neutralization by cation residue. Because al! standard orthophosphate determinations using the phosphomolybdate blue complex are sensitive to acid concentration ( I ) , the amount of acid in the residue after digestion must be adjusted before the subsequent orthophosphate determination. Here we report the composition of a nitric, perchloric, sulfuric acid mixture and time-temperature operating conditions for wet-ashing samples containing 0.040 gram of organic material and 0.6 meq of inorganic cation. The procedure yields a uniform amount of acid in the residue after digestion in test tubes. Orthophosphate (1-50 nmole) can be determined by Bartlett’s ultramicro method ( 2 ) o n the digested residue without adjustment of acid concentration. Recovery of total phosphorus from a n organophosphate and four phosphonates ranges from 95 to 101 %. Relative standard deviation for replicates averages 1.7 %. EXPERIMENTAL
Reagents. 2-Aminoethylphosphonic acid (AEP) was synthesized as described by Kosolapoff (S), and purified by chromatography o n Dowex-50-(H+)-8%. A. F. Isbell, Department of Chemistry, Agricultural and Mechanical College ( 1 ) 0 . Lindberg and L. Emster, “Methods of Biochemical Analysis,’’ D. Glick, Ed., Vol. 111, Interscience Publishers, Inc., New York, N . Y . , 1956, p 1. (2) G. R. Bartlett, J . Biol. Chem., 234, 466 (1959). (3) G. M. Kosolapoff, J . Amer. G e m . SOC.,67, 2112 (1947).
of Texas, Collegt Station, Texas generously supplied N . methyl-AEP and N,N-dimethyl-AEP. 2-Amino-3-phosphonopropionic acid (2A3PPA) was purchased from Calbiochem, Los Angeles, Calif. Phosphoserine was purchased from Sigma Chemical Company, St. Louis, Mo. Orthophosphate standard was prepared from Baker Certified Aminonaphthol sulPrimary Standard KH?POI (99.9 fonic acid (ANS) was purchased from Eastman Organic Chemicals, Rochester, N. Y ., and recrystallized. Concenvacuum distilled) was purchased trated perchloric acid (70 from G. Frederick Smith Chemical Company, Columbus, Ohio. All other chemicals used were analytical reagent grade. Deionized water was used throughout the procedure. Digestion mixture was prepared by stirring 98 ml of concentrated sulfuric acid into 230 ml of wafer. After cooling, 1200 ml of concentrated nitric acid and 120 ml of concentrated perchloric acid were added and the volume was adjusted to 1800 ml with water. This reagent could be stored for at least two months in a used hard glass sulfuric acid reagent bottle without increase in background due to silicate. Ammonium molybdate reagent was 1.18% solution in water. ANS reagent was 0.1 ANS in aqueous NaHSOs (0.548M), N a p S 0 3(0.159M) as described by Bartlett ( 2 ) . Equipment. TUBEHEATER.Test tubes (18 X 150 mm) were heated in a thermostatically controlled aluminum block electric tube heater (Warner-Chilcott Laboratories Instrument Division) loaned by T. E. Nelson of this Department. Temperature was monitored by a thermometer immersed in a tube containing DC-560 silicone oil. SPECTROPHOTOMETER. The Gilford Model 240 Spectrophotometer was used with cuvettes having 1.OO-cm light path and 1.5-ml capacity (Pyrocell No. 1007). Total Phosphorus Determination. DIGESTION PROCEDURE. In each digestion tube is placed a sample containing 1-50 nmole of phosphorus in the presence of less than 0.040 gram of organic material and less than 0.6 meq of cations. Digestion mixture (1.5 ml) is dispensed into a blank tube, a tube containing AEP standard (50 nmole), and each sample tube. The tubes are placed in the heating block for 1.5 hours at
z).
z,
ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
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