value). The derived reactivity ratio for butene, i.e., the reciprocal of the slope, 0.51, is quite reasonable in comparison with the literature value of 0.50 (28) reported for a related catalyst system, Et3A1/TiC13. However, much more data would be required for a satisfactory measure of this parameter. These materials were then used in the heated cell infrared method of Tosi et al. (8). The absorbances were recorded together with those obtained for a number of blends of polybutene and polypropylene homopolymers. The blends and the standards generate two different lines (Equations 4 and 5 respectively) which, by t test, have significantly different slopes ( t = 2.10; t0.06, 16 = 2.12). Thus, calibrated standards are necessary to carry out the method accurately. Presumably, this is the reason that blends were not used in earlier work on the infrared methods.
y(absorbance ratio) = 1.015~(molar ratio P/B) + 0.244 (4) y = 0.798~ + 0.240 (5) Coincidentally, the line generated in our work is not statistically different from that obtained by Tosi, et al. (81, (Equation 6) whereas that for the blends is strikingly so.
y = 0.705~ + 0.244
(6)
where t for slopes of Equations 5 and 6 = 0.89, to.o5,33 = 2.04, t for slopes of 4 and 6 = 4.49, to.001, 35 = 3.60.
CONCLUSION 13C NMR is a simple and effective method for determination of propylene incorporation into butene-propylene copolymers. Standards calibrated by this method are suitable for use in simpler plant methods, e.g., IR or DSC. ACKNOWLEDGMENT We thank Henry P. Katstra who painstakingly made the infrared measurements, Walter T. Young who prepared the copolymers, and Robert L. Lichter for useful discussions.
LITERATURE CITED (1) J. C. Verdler and A. Guyot, Macromol. Chem., 175, 1543 (1974). (2) E. W. Neumann and H. G. Nadeau, Anal. Chem., 35, 1454 (1963). (3) E. M. Barrall, R. S. Porter, and J. F. Johnson, J. Chromafogr.,11, 177 (1963). (4) E. M. Barrall, R. S. Porter, and J. F. Johnson, J . Appl. folym. Sci., 9, 3061 (1965). (5) A. Turner Jones, J. folym. Scl., folym. Left. Ed., 3, 591 (1965). (6) D. F. Slonaker, R. L. Combs, and H. W. Coover, Jr., J . Macromol. Scl., Chem., 1, 539 (1967). (7) T. Huff, C. J. Bushman, and J. W. Cavender, J. Appl. folyrn. Scl., 8 , 825 (1964). (8) C. Tosl, M. P. Lachl, and A. Pinto, Macromol. Chem., 120, 225 (1968). (9) N. J. Wegemer, J. Appl. Polym. Scl., 14, 573 (1970). (10) J. Lomonte, J. Polymer Sci., Polym. Left. Ed., I , 645 (1963). (11) J. E. Brown, M. Tryon, and J. Mandel, Anal. Chem., 35, 2172 (1963). (12) A. Valvassorl and G. Sartorl, Chlm. Ind. (Mian),44, 1091 (1962); Chem. Absfr., 57, 16824f (1962). (13) G. Natta, Q. Mazzantl, A. Valvassorl, and G. Pajaro, Chlm. Ind. (Milan), 30, 733 (1957); Chem. Abstr., 52, 3729c (1958). (14) L. P. Lindeman and J. Q. Adams, Anal. Chem., 43, 1245 (1971). (15) D. M. Grant and E. G. Paul, J. Am. Chem. Soc., 86, 2984 (1964). (18) C. J. Carman, A. R. Tarpley, Jr., and J. H. Goldstein, Macromolecules, 8, 719 (1973). (17) J. G. Murray, J. Zymonas, E. R. Santee, Jr., and H. J. Harwood, folym. Prepr., Am. Chem. Soc., Div. folym. Chem., 14, 1157 (1973). (18) L. F. Johnson, F. Heatley, and F. A. Bovey, Mscromkuks, 3, 175 (1970). (19) I. D. Rubin, “Poly(l-Butene),” Gordon and Breach, New York, 1968, Chap. 8. (20) C. A. Lukach and H. M. Spurlln In “Copolymerization,” Vol. 18 of “High Polymers”, 0. E. Ham, Ed., Intersclence, New York, 1964, Chap. I V A. (21) A. Zambelli, P. Locatelll, G. Bajo, and F. A. Bovey, Macromolecules, 8, 6819 (1975). (22) A. Zambelil, D. E. Dorman, A. I. R. Brewster, and F. A. Bovey, Macromolecules, 6, 925 (1973). (23) J. R. Lyerla, Jr., and G. C. Levy in “Topics In NMR Spectroscopy”, Vol. 1, G. C. Levy, Ed., Wlley, New York, 1974, p 79. (24) J. Schaefer and D. F. S. Natusch, Macromolecules, 5, 416 (1972). (25) J. Schaefer, Macromolecules, 5, 427 (1972). (26) Identity of NOE for methlne and methylene protons at 35 ‘C has been reported for three homopolymers by J. Schaefer, Macromolecules, 8, 882 (1073). (27) J. Schaefer In “Topics In NMR Spectroscopy,” Vol. 1, G. Levy, Ed., Wliey, New York, 1974, p 149. (26) I. Hyashl and K. Ono, Kobunshl Kagaku, 22, 446 (1965); Chem. Absfr., 64, 21740 (1966).
RECEIVED for review October 15,1976. Accepted May 20,1977. The funds for the spectrometer were provided in part by NSF Grant No. GP 37025.
Computerized Curve-Fitting to Determine the Equivalence Point in Spectrophotometric Titrations Scott R. Goode Department of Chemistry, University of South Carolina, Columbia, South Carolina 29208
A nonllnear least-squares curve-fit Is used to determlne the equivalence polnt In spectrophotometrlctltratlons. Tltratlon curves, wlth a maximum absorbance of 0.4 to 0.8, are calculated under condltlons of dllferent equlllbrlum constants, and slgnal-to-noise ratios and then flt to a two-parameter model. The equlvalence polnt found Is wlthln 2 % of the true value as long as the noise Is less than 0.008 absorbance unlt, even when the tltratlon curve Is sufflclently smooth to show no change in slope at the equlvalence polnt. More favorable condltlons yleld an equlvalence polnt wlthln a few tenths of a percent of the true value.
Volumetric methods are among the most widely-used techniques of chemical analysis. Their popularity is a consequence of their precision, accuracy, and simplicity. The 1408
ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
analytical result (location of the equivalence point) is based on a rapid concentration change; thus only relative concentrations need be measured. This makes titrations inherently more accurate than methods which require an absolute knowledge of concentration. The titration curve is a plot of some signal, proportional to analyte concentration as a function of the amount of titrant added. Titration curves have two general forms, sigmoidal and segmented ( I ) . An example of the former is the classical, sigmoid-shaped curve which resulta when pH is plotted during the titration of an acid with a base. The segmented curve is obtained when a parameter which is related linearly to analyte concentration, e.g. absorbance, is corrected for dilution and plotted as a function of titrant added. The accuracy and precision of the chemical analysis are directly related to the error in locating the equivalence point. When a sigmoidal titration curve is obtained, the inflection
point (maximum slope) is generally used to describe the equivalence point. The inflection point, however, does not always coincide with the equivalence point (2,3) because of dilution effects. The segmented curves, however, do not exhibit this inaccuracy, and the intersection of the two segments coincides with the equivalence point. This communication will describe several methods to determine the equivalence point of segmented titration curves. The methods include two different computerized curve-fitting procedures and a derivative method. These techniques are applied under conditions with different equilibrium constants and signal-to-noise ratios. The results are compared critically and the methods are analyzed as to their potential utility in a fully-automated titrator. LOCATION O F T H E EQUIVALENCE P O I N T BY COMPUTERIZED CURVE-FITTING Nonlinear Curve-fits. The most commonly used model is used to fit experimental data to a linear model. An exact equation is available to calculate the slope and intercept which best describe the data (4). The “best” fit is the one which minimizes the sum of the squares of the residual (calculated minus experimental). The least-squares fit is not limited to linear equations; a more complex equation can be fit to experimental data, but now an exact solution is generally unavailable, and a numerical one must be used. Parameters are varied in an iterative fashion such that the sum of the squares of the residuals is minimized. Anfalt and Jagner (5) suggested that multiparametric curve-fitting should produce the most accurate equivalence point, but did not implement this idea, primarily because of the complexity. Both sigmoidal and segmented curves are tractable to multiparametric curve-fitting. Gran developed a relatively simple method to linearize the sigmoid-shaped titration curve (6). Gran plots exhibit curvature near the equivalence point when the analyte is present in small concentrations or the equilibrium constant of the titration is small. Several researchers (7-9) have proposed functions which show less curvature. Barry and Meites (10)used a 3-parameter fit to determine pK,, the analyte concentration, and activity coefficient in the titration of acetate ion with strong acid. The precision in determining the equivalence point varied between 0.05% to 11% as the concentration of the acetate decreased from 0.002 M to 0.00016 M. They were even able to determine the equivalence point under conditions when an inflection point didn’t exist. The authors later included the concentration of the acid as an additional unknown (11)and found that the accuracy was improved by a factor of five when compared to titrating with standardized acid and determining the inflection point. Meloun and Cermak (12) performed a 5-parameter fit to a linearized function of a titration which employed a metallochromic indicator. A precision of 0.2% was obtained under favorable conditions. Several investigators (13,14)have used nonlinear least-squares fits to data obtained with ionspecific electrodes. Isbell et al. (14) found less error in the curve-fit than in any of the derivative or Gran methods. McCullough and Meites (15)performed a multiparameter fit to a segmented titration curve. They chose to exclude Keq from the adjustable parameters and therefore rejected points in the region of curvature, as well as other outliers. In general, they concluded that it was difficult to produce an accurate and precise value of the equivalence point in a system with instrumental or systematic errors. Fitting t h e Data to a Linear Equation. Several authors have determined the best slope and intercept of the two linear segments by a least-squares fit. These data are used to calculate the intersection points. Carr and Onisicki (16)
determined that the precision of determining the equivalence point was independent of the angle between the segmenta, but dependent on the difference in slope. They added random noise to simulate a real chemical measurement. An amperometric titration curve was analyzed by Coenegracht and Duisenberg (17).The data were corrected for dilution, but some curvature resulted due to the finite equilibrium constant of the reaction. The precision of the location of the equivalence point was 1%when equilibrium constant-concentration product, KJ!, was 100. A linear least-squares fit was applied to the segments of a spectrophotometric titration by Rosenthal et al. (18). They examined the influence of the equilibrium constant and measurement error on the precision of the equivalence point. As the curvature increased (K, decreases), less of the titration curve fits a linear model, and fewer data points can be used. The noise rejection is obviously poorer under these circumstances, and the precision is about 2% for KeqC= 20. GENERATION O F TITRATION CURVES Titration curves are generated by numerical computation, The general reaction is
S+T+P where S is the sample, T the titrant, and P is the product. The equilibrium is described by an equilibrium constant TDl
K,,
=-
LL J
[SI [TI The titration curve is a plot of absorbance as a function of volume of titrant. The absorption of light is due only to the product so one may conclude
A = eb[P]
(2)
At any point along the titration curve
(3) (4) where Cs and CT are the analytical concentrations of the sample and titrant. Equations 1-4 may be combined and solved for absorbance
+ + 1 - d(a + p + 1)* - 4ap)
eb[ff p
A=
P=
2Keq
vT
Keq
vS
+
vT
(5)
(7)
where V , is the volume of the sample as placed in the titration vessel, and VT is the volume of titrant added a t any point. Titration curves are generated by computation of Equation 5 by a FORTRAN program on an IBM 370/168. Several different conditions, as shown in Table I, were used for the computations. Plots of all curves were performed on a Calcomp flat-bed plotter, interfaced to the computer. In general, 10 mL of 0.01 M sample was titrated with 0.1 M titrant. Two very dissimilar curves, Figures 1and 2, resulted when the equilibrium constants were 100 and lolo, respectively. All curves would have a maximum value of one absorbance unit if the reaction were complete and dilution effeds were negligible. Inclusion of Noise. There are two major sources of noise in an experimental spectrophotometric titration curve. The spectrophotometric measurement is inherently imprecise, due ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
1409
Table I. Parameters Used for Titration Curves Equilibrium constant K,, = lo2 and 10'' Concentration of sample C s = 0.01 M Volume of sample V s = 10.0 mL Concentration of titrant CT = 0.10M Equivalence point V,, = 1.00 mL Molar absorptivity e = 100 L-mol-' cm-' Path length b = 1.00 cm Range of titrant 0 to 2.00 mL 0.001 mL and 0.100 mL Titrant aliquot Uncertainty in absorbance 0, 0.001,0.002,0.004,0.008, 0.016 absorbance units Uncertainty in volume 0, or 0.004to 0.012 mL (see text)
Table 11. Precision and Accuracy of Titrant Deliverya Volume Volume Standard read, mL delivered, mL deviation, mL 0.100 0.089 0.004 0.200 0.300 0.500 0.700 1.000 1.500 2.000
0.194 0.295 0.497 0.701 1.002 1.499 2.000b
0.008 0.008
0.009 0.010 0.011 0.012 0.012
a Buret stopped and read every 0.01 mL. to 2.000.
Normalized
0
3,
VoI ume
Volume 25
0'.50
0'.75
1'.00
1'.25
1'.50
1'.75
21.00
VOLUME OF T I T R R N T . N L
Figure 1. Spectrophotometric titration curve. Keq= lo2, 0.004 absorbance unit of noise. Includes uncertainty in volume. Equivalence point = 1.000 mL. (0)Experimental points. (-) Computer-generated
C I
n
fit Volume
Flgure 3. (A) Titration Curve. (B) First derivative plot. (C) Second derivative plot
4
00
0 25
0 50
0' 75
1'00
I ' 25
1'50
1'75
2'00
~ ~ L U UOF E TITRRN',ML
Figure 2. Spectrophotometric titration curve. Keq= IO'', 0.004 absorbance unit of noise. Includes uncertainty in volume. Equivalence point = 1.000 mL. (0)Experimental points. (-) Computer-generated fit
to several reasons (19). The other major source of noise is the imprecision in the volume measurement. Each is treated below. Spectrophotometric Noise. Ingle and Crouch (19) have shown that the noise sources in a spectrophotometer fall into three major groups. The optimum situation occurs when the dominant noise is source-flicker. This is, indeed, the major noise source in most high-quality modern spectrophotometers except in situations where the light level is low, such as found when small slit widths or when unfavorable wavelengths must be used. This noise is seen as an uncertainty in the absorbance measurement, e.g., 0.30 f 0.001 absorbance unit, where the magnitude of the uncertainty is independent of the absorbance. The smallest amount of noise included in the calculations is probably more than would be present in a typical spectrophotometer (20, 21). 1410
ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
The IBM-furnished subroutine RANDU (22)is used to add a constant amount of noise to the titration curve. Titration curves are calculated and noise of 0.001,0.002, 0.004,0.008, and 0.016 absorbance unit are added to each absorbance value. The noise is random, with a mean of zero and a standard deviation of 0,001, 0.002, etc. Volume Noise. Uncertainty in the volume delivery is more difficult to include. A Radiometer ABU-13 automatic buret (London Company, Westlake, Ohio) was filled with vacuum pump diffusion fluid; aliquots were dispensed and weighed. The buret dispensed 0.100 mL increments, so the data, shown in Table I1 are the precision of delivering volumes from 0.000 to 0.100, 0.100 to 0.200 mL, etc. These reflect the actual precision obtained in a titration, where an aliquot is delivered, a measurement is made, and another aliquot delivered. The precision in operating between two fixed points is better. The delivery of 1.OOO d has a relative standard deviation of 0.17% if the buret is always started at 0.0 and stopped at 1.000 mL. Noise corresponding to the values shown in Table I1 is added to the volume axis, also using RANDU. EXPERIMENTAL Ten to twelve titration curves are generated for each different set of experimental conditions. These are stored on magnetic tape for ease of accessibility. Each curve is different, as the noise added is truly random, but with known variance. The titration curves are analyzed by three procedures. The equivalence point is determined by a derivative method, an extrapolation method, and a nonlinear curve-fit. The accuracy and precision of each method is reported below. RESULTS Derivative Method. A representation of the titration curve, first, and second derivative are shown in Figure 3. The
m
0
-1
1'
% 00
0'25
0'50
0'75
1'00
VCLUME OF T I T S R N T .
'25
WL
1'50
1'75
2
oc
Second derivative plot. Keq = 10". No noise in absorbance measurement Figure 4.
" 1
%'33
0'.25
C'.S0
3'.75
VOLUME
Figure 5.
of-noise
l'.OC
'C
Second derivative plot.
1'.25
TITRFYT.
I'.5C
1'.75
2.3i
NL
K,,-., = lo'', 0.001 absorbance unit
71
fil ?I OC.'?
C'.25
3'.50
c'.75
I'.OO
1.25
V S L L N E OF T I T R R N T . ' P i
Flgure 6.
Second derivative plot.
".OC
K,, = lo'', 0.004 absorbance unit
of noise
second derivative of the titration curve is calculated using the Savitsky-Golay algorithm (23). This method includes a 23-point smooth to improve noise immunity. Titration curves consisted of 2000 points, spaced 0.001 mL apart. This small interval is necessary because the numerical derivative is inherently digital. Thus to obtain a precision of 0.1% , at least 1000 points are needed prior to the equivalence point. Figures 4, 5 , and 6 show the second derivative obtained when 0, 0.001, and 0.004 absorbance unit of noise when K,, = 1O1O are added to a titration curve obtained. The titration curve with the most noise (0.004 absorbance unit) is shown in Figure 7. One can see that the derivative method cannot be used under conditions of moderate noise. When the equilibrium constant is small, the titration curve
Flgure 7.
Titration curve.
Kea = IO'', 0.004
absorbance unit of noise
shows no inflection point, as illustrated in Figure 1. The second derivative has no maximum, and cannot be used to determine the equivalence point. Under favorable conditions the numerical derivative method always gives the correct answer if there is little or no noise present. Before the derivative is calculated, it is little trouble to have the computer correct for dilution, hence removing the inaccuracy present in an analog or graphical treatment (1). Computation of the derivative has a more fundamental limitation. It requires at least 1000 points to obtain an accuracy of 0.1%. This requirement tends to make the derivative method unwieldy. Extrapolation Method. The two segments of the titration curve may be corrected for dilution, and fit to two linear equations. The intersection point is calculated to determine the equivalence point. The results of such a study indicate that serious systematic errors arise when the equilibrium constant is small, i.e., Figure 1cannot be represented as two linear segments. The interval between data points becomes increasingly important as more points are needed if noise is to be rejected. When the equilibrium constant is small, however, only a fraction of the titration curve is described by a linear equation. These results agree with previous reports (17, 18). Nonlinear Least-Squares Fit. The titration is a function of seven parameters: Keq,E , b, Cs, CT,Vs, and V,. Of these seven, four are known to the experimenter: the path length, b; the volume of sample, Vs;the concentration of the titrant, CT; and the volume of titrant added, V,. The other parameters are described below. Concentration of Sample. The sample concentration, CT, is not known, and is to be determined by the titration. Molar Absorptivity. The molar absorptivity will, in general, not be known. The value is dependent on ionic strength, hence the sample matrix. The nonlinear curve-fit treats E as an unknown. Equilibrium Constant. The value of the equilibrium constant also is not generally known. The value of the equilibrium constant, however, does not affect the location of the equivalence point, but merely the amount of curvature in the titration curve. Uncertainty in K,, can influence the accuracy and precision in calculating the end point, but the equilibrium constant can be determined from the titration of a known amount of sample. Typical results for the determination of K,, and the errors introduced by uncertainty in K,, are shown in a later section. Even though K,, is generally treated as a known quantity, a three-parameter fit can be employed with Kq as one of the unknowns. Computational Algorithm. The nonlinear regression of Dye and Nicely (24) is used. This algorithm allows the variables, both independent and dependent, to be weighted in accord ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
1411
Table 111. Accuracy and Precision of Nonlinear Curve-Fit
Standard deviation of absorbance 0.001 0.002 0.004 0.008
0.016
Equilibrium constant = 10’’ No imprecision in volume Includes imprecision in volumea Equivalence Standard deviation Equivalence Standard deviation point, mLb of equivalence point, mL point, mL* of equivalence point, mL 1.000 0.001 0.996 0.003 1.000 0.001 1.003 0.999 1.002
0.003 0.006
0.997
0.003
0.01
Equilibrium constant = 10’ 0.001
1.000
0.002
1.005 0.998 0.981
0.004 0.008
0.016 a
See Table I1 and text.
0.014 0.016 0.042 0.054 0.17
0.92
1.01
87
0.92
114
1.05
0.04 0.05 0.04
a Noise is 0.004 absorbance unit; data include impreciCorrect value, 1.000 mL. sion in volume delivery.
to their experimental variances. This feature was used in all trials. Twenty data points are fit into Equation 5. The program adjusts t and Cs to minimize the sum of the squares of the differences between the absorbance calculated from t and CS, and the experimental value. The nonlinear least-squares fit requires an initial estimate of the variables fitted, E and Cs. The program may not converge if the estimates are poor. Initial Estimates. The value of the equilibrium constant was found to influence the latitude of the initial estimates. When the curve is smooth (K,, = 100, Figure 1) any value within a factor of 10 of the correct Cs and t allowed the program to converge to proper values. The worst case required 31 iterations, or approximately 3 seconds of CPU time. The sharper curve (K, = 1O1O, Figure 2) required estimates within a factor of two to converge. Obviously, one can provide better estimates from the sharper curve. Accuracy and Precision. The results of the curve-fit are shown in Table 111. If the noise is 0.004 absorbance unit, or less, the accuracy is better than 0.5% when K,, = 1O1O, and 5% when K,, = 100. The precision is remarkable, especially considering the adverse noise included in the experimental curves. Figures 1and 2 show the experimental points and the theoretical best fit generated by the computer. Influence of Equilibrium Constant. When the concentration of the sample, Cs, is known, one may perform a curve-fit to determine K,, and E. Theoretical data for K,, = 100, noise of 0.004 absorbance unit, and noise in the volume delivery were used to obtain an experimental Keq. The value of K,, ranged from 87 to 114, with a mean of 102, and a standard deviation of 10. Since K , is now known, these values are used to calculate the concentration of the sample in other titration curves. These results are also included in Table IV. The incorrect values of K, influence location of the calculated equivalence point, but the maximum error is only 8%. These results are quite good considering the magnitude of the noise, lack of knowledge about the chemical system, and small concentration-equilibrium constant product (CSK,, = 1). 1412
0.025
0.983
0.038
Correct value, 1.000 mL.
Table IV. Influence of Keq on Curve-Fita Calculated Keq equivalence point, mLb Standard deviation, mL 102
0.996
ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
CONCLUSIONS The nonlinear least-squares fit to a spectrophotometric titration curve is shown to be a superior method to obtain the equivalence point of a spectrophotometric titration. The precision and accuracy vary, according to the amount of noise. If a titration with a large equilibrium constant, and less than 0.004 unit of noise is performed, the equivalence point can be determined to within a few tenths of a percent, and will generally be limited by the precision to which the volume is measured. When the equilibrium constant is small, the curve-fit may be the only method which is capable of extracting the location of the equivalence point. A titration curve obtained when the equilibrium constant is 100 will provide an answer accurate within 5% as long as the noise is less than 0.01 absorbance unit. The derivative method and the extrapolation of linear segments do not product acceptable results when the equilibrium constant is small. Additionally, the derivative method also required too many data points to be a good, generalpurpose method of locating the equilibrium point. The nonlinear least-squares fit does require a large computer, but on-line data acquisition is not necessary. The titration curve, 20 pairs of numbers in the cases illustrated here, may be transmitted to a larger computer for analysis a t a slightly later time. The data link may be high speed dedicated lines, if the titration data must be analyzed within seconds, or punched cards if overnight computation is acceptable. One major application of this work is to analyze titration curves obtained under adverse conditions such as low equilibrium constant, poor signal-to-noise ratio, perhaps due to the spectral region involved, and low concentrations of anal*. The nonlinear least-squares fit is seen to provide a good value for the equivalence point under conditions when other techniques fail completely. ACKNOWLEDGMENT The author thanks Jethro Matthews, Don Schermer, and David Otto for their help. LITERATURE CITED (1) L. Meites and J. A. Goldman, Anal. Cbim. Acta, 30, 28 (1964). (2) L. Meites and J. A. Goldman, Anal. Cbim. Acta, 29, 472 (1963); 31, 297 (1964). (3) L. Meites and J. A. Goldman, Anal. Chim. Acta, 30, 18 (1964). (4) D. G. Peters, J. M. Hayes, and G. M. Hieftje, “Chemical Separations and Measurements”. W. B. Saunders, Philadelphia, Pa., 1974, p 32 ff. (5) T. Anfalt and D. Jagner, Anal. Cblm. Acta, 57, 165 (1971). (6) G. Gran, Ana/yst(London), 77, 661 (1952). (7) F. Ingman and E. Still, Talanta, 13, 1431 (1966). (8) A. Johansson, Anamst (London), 95, 535 (1970).
D. Midgley and C. McCollurn, Talanta, 21, 273 (1974). D. M. Barry and L. Meites, Anal. Chim. Acta, 88, 432 (1974). D. M. Barry and L. Meites, Anal. Chim. Acta, 89, 143 (1974). M. Meloun and J. Cerrnak, Talanta, 23, 15 (1976). ~,M. J. D. Brand and G. A. Rechnitz, Anal. Chem., 42, 1172 (1970). i141 A. F. Isbell. R. L. Pecsok. R. H. Davies. and J. H. Purnell, Anal. Chem., ~, 45, 2383 (1973). (15) J. G. McCullough and L. Meites, Anal. Chem., 47, 1081 (1975). (16) P. W. Carr and S. Onisicki, Anal. Lett., 4, 893 (1971). (17) P. M. J. Coenegracht and A. J. M. Duisenberg, Anal. Chim. Acta, 7 8 , 183 (19751. \--.-,-
(18) D. Rosenthal, G. Jones, and R. Megargle, Anal. Chlm. Acta, 53, 141 (1971). (19) J. D. Ingle, and S. R. Crouch, Anal. Chem., 44, 1375 (1972).
(20) L. D. Rothrnan, S. R. Crouch, and J. D. Ingle, Anal. Chem., 47. 1226 (1975). (21) J. D. Ingle, Anal. Chim. Acta, 88, 131 (1977). (22) “Systern/360 Sclentific Subroutine Package,” Version 111, GH20-0205-4, 5th ed., IBM Corporation, White Plalns, N.Y., 1970, p 77. (23) A. Savitsky and M. Golay, Anal. Chem, 27, 1627 (1964). (24) J. L. Dye and V. A. Nicely, J. Chem. Educ., 48. 433 (1971).
RECEIVED for review February 14, 1977. Accepted June 1, 1977. Acknowledgement is made to the Donors of The Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research.
High Solids Sample Introduction for Flame Atomic Absorption Analysis R. C. Fry’ and M. B. Denton” Department of Chemistry, University of Arizona, Tucson, Arizona 8572 7
Studies are presented describing direct, clog-free productlon of hlgh density flnely dlspersed aerosols from highly complex samples through use of a speclai nebulizer design based on principles first developed by R. S. Babington. Appllcatlon of thls technlque to sample lntroductlon for atomic absorption spectrometry is described for matrices of combined hlgh suspended solids content, Increased vlscoslty, and elevated salt concentration. Cu and Zn are determined In whole blood, urine, seawater, evaporated milk concentrate, and tomato sauce with mlnimal sample preparation.
Increasingly large numbers of environmental and clinical samples being submitted to analytical laboratories for determination of trace metal constituents make the development of “preparation free” methods of analysis extremely important from the standpoint of cost per analysis, speed, convenience, and freedom from reagent contamination. Atomic absorption spectrometry has been widely applied to samples of complex nature directly ( I ) , and indirectly through the use of digestion (2) and extraction procedures (3). Although such digestion or separation procedures tend to be time consuming and may frequently lead to volatilization loss (2) or sample contamination, existing methods often require these steps for a wide variety of samples. The complexity of untreated matrices that may be introduced directly is often limited by nonatomic absorption and vaporization interferences in the case of flameless sampling devices, and by clogging of the capillary orifice and burner slot in the case of conventional burnernebulizer systems. Although less sensitive than flameless atomizers, conventional burner-nebulizers have proven to be generally more convenient to operate, lower in cost, capable of introducing a larger number of samples per unit time into the absorption cell, and less susceptible to interferences (4,5). These advantages have established the continued use of the capillary pneumatic nebulizer as a principal sample introduction device for analytical atomic spectroscopy. Culver (6) has discussed ‘Present address, Department of Chemistry, Kansas State University, Manhattan, K a n . 66506.
the relative merits of carbon rod and flame techniques and concludes that, although flameless atomizers provide an alternative to nebulizer-burner atomization cells when greater sensitivity and smaller sample size is required, the more convenient flame system should be used whenever possible. Improvement in nebulizer design to allow more complex sampling is therefore highly relevant and desirable. Development and subsequent characterization of a unique nebulization principle by R. S. Babington (7) have resulted in the ability to generate high density, finely dispersed aerosols directly from a variety of extremely complex materials including fuel oil, paints, food products, etc. Possibilities for improved freeze-drying systems, oil burners for home heating, insecticide fogging, etc., applications have been outlined (8). A nebulizer based on this principle has been marketed by Owens-Illinois (Toledo, Ohio) and more recently by McGaw Respiratory Therapy (Irvine, Calif.) under the trade names of “HYDROSPHERE” and “MAXI-COOL” for the production of aerosols utilized in respiratory inhalation therapy. This Babington nebulizer has been reported to produce a dense aerosol with a droplet distribution (following considerable aerosol refinement) of median mass diameter at 3.6 km with 95% of all refined droplets being below 5 pm in diameter (9). In view of the spectrochemical importance of droplet size discussed by Alkemade (IO), it is apparent that this nebulization principle offers great promise as an approach to sample introduction in flame spectrochemical analysis. A major difference between the Babington nebulization technique and the conventional capillary pneumatic nebulizer arises from the fact that the conventional nebulizer requires the sample to pass through a small ( ~ 0 . 3 6mm) capillary orifice. In contrast, the Babington nebulizer requires that only gases pass through an orifice; the relatively unrestricted (2.38 mm) sample flow of this system provides the basis for high solids sampling and represents the primary advantage of Babington nebulization as applied to spectrochemical analysis. The upper limit on salt and solids content as well as viscosity of a slurry that may be directly sampled by this technique is determined by the ability of the material to pass through a pumping system. This paper deals with the application of a specially developed nebulizer based on the Babington principle in combination with high solids slot burners to provide direct atomic absorption analysis of highly complex ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
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