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Anal. Chem. 1988, 6 0 , 365-369
for the smaller diameters where these forces are weaker I ' ' 7 1 higher than crossflow forces. All of these observations are consistent I
N
/ i
3.0;
0
/ I
(gravity)
t
B
/
F
(flow)
1
0 0
10
20
30
40
50
60
DIAMETER, d (pm) Flgure 3. Plot of transverse drMng forces due to gravity and crossflow
as a function of particle diameter for the conditions used in Figure 1 (particle density = 1.05 g/mL, Ap = 0.05 g/mL, viscosity = 0.93 cP). inant force above 30-rm diameter. It is apparent that very substantial increases in the crossflow rate would be necessary to match the effects of gravity, particularly if the sample consisted of high-density particles. The 1.95 mL/min crossflow used here is already relatively high and requires a pressure drop of about 50 psi to maintain. Without significant changes in the frit and membrane materials that must be permeated by the crossflow, intolerably high pressure drops would be required to maintain the high crossflow velocities needed to compete with gravity in the large particle range. The plots in Figure 3 explain the results shown in Figure 2. Since the greater the net driving force, the further the particles are driven toward the wall and the lower the resulting R value, R is inversely correlated with the net force. Thus the R curve for combined gravity and crossflow is always lower than the curves corresponding to the individual forces. The crossflow and one-gravity curves cross a t approximately the same diameter that the force curves of Figure 3 cross. The one-gravity curve is lower than the crossflow curve for the larger diameters where gravitational forces are greater and
with the inverse relationship assumed between R and the net force. We should add that there is some uncertainty in the mechanism of separation of the larger particles, particularly with crossflow acting alone. The small difference in crossflow forces between, for example, the 30.1- and 49.4-pm particles compared to the large difference in gravitational forces, without a concomitant increase in resolution, suggests that the lift forces dominate the separation effects. However, it is possible, particularly for the weak crossflow case, that separation occurs as a result of the different transit times of particles from their initial (relaxed) positions near the accumulation wall to their steady-state positions part way across the channel. If the large particles are driven faster to their equilibrium positions by the lift forces, they would experience a higher average velocity within the channel than smaller particles that may ultimately reach the same equilibrium position. This question should be resolved by ongoing studies directed a t the better understanding of lift forces in FFF channels.
LITERATURE CITED (1) Giddings, J. C. Anal. Chem. 1981, 5 3 , 1170A. (2) Giddlngs, J. C. Sep. Sci. Techno/. 1984, 79, 831. (3) Giddings, J. C. In Chemical Separations: Navratil, J. D., King, C. J., Eds.; Litarvan: Denver, CO, 1986; p 3. (4) Giddings, J. C.; Chen, X.; Wahlund, K.-G.; Myers, M. N. Anal. Chem. 1987, 59, 1957. (5) Segre, G.; Silberberg, A. Nature (London) 1981, 789, 209. (6) Segre, G.; Silberberg, A. J. Fhid Mech. 1982, 74, 115. (7) Segre, G.; Silberberg, A. J. Fluid Mech. 1962, 74, 136. (8) Saffman, P. G., J. Fluid Mech. 1985, 22, 385. (9) Cox, R. 0.; Brenner, H. Chem. Eng. Sci. 1988, 2 3 , 147. (IO) Ho, B. P.: Leal, L. G. J. Fluid Mech. 1974, 6 5 , 365. (11) Vasseur, P.; Cox, R. G. J. Fluid Mech. 1978, 7 6 , 385. (12) Cox, R. 0.: Hsu, S. K. Jnt. J. Mulfbhase Flow 1977, 3 , 201. (13) Leal, L. G. Annu. Rev. FluidMech. 1980, 72, 435.
RECEIVED for review August 5, 1987. Accepted October 14, 1987. This work was supported by Grant No. CHE-8218503 from the National Science Foundation.
Hydropyrolytic-Ion Chromatographic Determination of Fluoride in Coal and Geological Materials Vincent B. Conrad* and W. D. Brownlee Consolidation Coal Company, Research and Development Department, 4000 Brownsville Road, Library, Pennsylvania 15129 A hydropyrolytk-kn chromatographk method was developed for the analysis of fluoride in coal, ash, and geological materials. The hydropyroiytlc extractlon employs humldlfled alr and Moosto promote the evolution of fluoride In a 1050 OC tube furnace. The fluoride Is captured In a weak solution of NaHCO, and determined by ion chromatography (IC). The I C determlnatlon utllizes a column swltchlng technlque to resolve F- from the void volume and CI- interferences. Short-term precision of the hydropyroiytic-IC determlnatlon Is approxlmately 5 %. The F- determinatlon Is linear from the detection llmlt of 1-500 ng. Results obtained for a coal and rock standard differ from the certHled values by 6.8% and 0.5 %, respectively. The fluoride concentrations of 15 geologlcai standard reference materials are compared to reported results and to results measured by an ion seiectlve electrode method.
Fluoride has been identified as an ecologically important trace element. Despite its environmental significance, there have been few reports establishing accurate methods for the determination of fluoride in coal, ash, and other geological materials. The fluoride contents of coals range from 0.001 to 0.048 w t % (1). The source of this fluoride has been identified largely as the intrinsically insoluble minerals, fluorapatite and fluorospar (2-4). Coal samples have been prepared for F- determination by combusting the coal in an oxygen bomb (5). This technique is laborious and produces results that are difficult to duplicate. Determinations of F in coal ash and other noncarbonaceous geological materials normally require that the sample be decomposed by alkali fusion (3, 6 ) or by acid dissolution (7). These techniques are time-consuming and are often inaccurate
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1
9
Flgure 1. Apparatus for hydropyrolysis of geological samples: (1) combustion boat, (2) quartz combustion tube, (3)tube furnace, (4) compressed air, (5) regulator, (6) flowmeter, (7) humidifier (deionized water), (8)Graham condenser, (9) receiving flask (0.0015 M NaHCO,), (10) separatory funnel (0.0015 M NaHCO,), (11) heating tape, (12)
power regulator. because of the inconsistent F- content of the digesting media. T h e F content of geological materials has been measured by spectrophotometric means (8, 9) and by more sensitive potentiometric methods (4,6). Both of these techniques can provide accurate results if problems caused by interferences (7, 9), complexation (7,IO),and ionic strength variations (11) are avoided. Hydropyrolysis has been used to prepare coal and other geological samples for F- determination by ion-selective electrode (12) and ion chromatography (13, 14). This decomposition technique is rapid and precise and produces a solution that is relatively free of interference and complexation effects. Ion chromatographic detection is both very sensitive and selective. However, interferences caused by ionic species eluting with the void volume and by chloride are often experienced when a typical (0.003 M NaHC0,-0.0024 M Na2C03)eluent is used (12,15). A weaker eluent can be used to improve the resolution of the fluoride peak; however, the retention times of and other strongly retained anions become prohibitively long. The hydropyrolytic technique described herein is used to prepare a relatively interference-free solution for ion chromatographic analysis. Ion chromatography employing a 0.0015 M NaHC03 eluent is used to rapidly determine F- in the presence of void volume and chloride interferences while eliminating strongly retained species with a column switching technique.
EXPERIMENTAL SECTION Hydropyrolytic Apparatus a n d Procedure. The hydropyrolytic apparatus is shown in Figure 1. Coal and ash samples are hydropyrolyzed in the following manner. Approximately 0.25 g of -325 mesh sample is weighed into a combustion boat (LECO Corp., St. Joseph, MI). Blank analyses of new and used combustion boats show no evidence of F- contamination. Rock samples are mixed with 0.035-0.070 g of MOO, to promote the extraction of F.The sample is placed into a quartz tube inside of a 1050 "C tube furnace (Model 54232, Lindberg, Watertown, WI). Ash samples are immediately heated to 1050 "C for 15 min whereas coal samples aie dried and oxidized for 5 min in the cooler end zone of the quartz tube before being moved to the 1050 "C center. Compressed air flowing a t 2.5 L/min is humidified (0.4 mL of water/L of air) by passing it through a 500-mL roundbottom flask containing 400 mL of boiling deionized water. The water-laden air sweeps the volatile fluoride species through the quartz tube into a Graham condenser. Fluoride is collected in 65 mL of 0.0015 M NaHC03, the ion chromatograph eluent. When the hydropyrolysis is complete, the Graham condenser is rinsed with 50 mL of 0.0015 M NaHCO, and the resulting solution is diluted to 200 mL with 0.0015 M NaHC03. Ion Chromatographic Apparatus. A 1pg/mL F- standard is prepared daily from a 1000 gg/mL stock solution (Dionex).
Injection of the 1 pg/mL F- standard with a 100-pL sample loop provides a 100 qg F- calibration. Hydropyrolyzed samples are diluted to fall within the 1-500 qg of F- linear range. A Dionex Model 16 ion chromatograph equipped with three, 3 x 250 mm AS-3 anion separator columns and a fiber suppressor is used to determine P in the sample solutions. The eluent pump provides a 2.15 mL/min flow of 0.0015 M NaHCO, a t 500-600 psi. The suppressor regeneration reservoir is pressurized with helium at 2-3 psi to maintain a constant flow (-3 mL/min) of 0.025 N HZSO4 through the fiber suppressor. The chromatograms are recorded and stored on an Hitachi D-2000 Chromato-Integrator. The resolution of the commercial ion chromatograph using a typical eluent and a single AS-3 anion separator column is not sufficient for quantitation of F- in many coal and ash samples. Samples containing high concentrations of alkali and alkaline elements often exhibit a nonretained peak that elutes with the void volume. This peak is caused by cations that are not eliminated by the suppressor and it is therefore more dominant on nonsuppressed systems (16). Use of a suppressor column and preparation of the sample by hydropyrolysis minimize this peak, but the interference is still significant at low F- concentrations. High concentrations of chloride can also interfere with the Fdetermination. Resolution of the F- from these potential interferents can be accomplished by decreasing the eluent strength. However, strongly retained species such as NO,- and S042-are then retained for more than an hour. The 700 psi back pressure limitation of the Dionex Model 16 severely limits the selection of alternative columns. No columns were found that could provide adequate resolution while providing a rapid F- analysis in the presence of NO3- and SO4*-. Consequently, the Dionex Model 16 was modified to permit the rapid determination of F- with a weak eluent while eliminating the more strongly retained species by means of a column switching technique. The determination of P is begun by loading the 100-pLsample loop with a Luer lock syringe. Initially, the eluent is flowing through anion columns 3 and 2 (Figure 2a). Column 3 is used to balance the back pressure, thereby preventing the appearance of system peaks during the switching procedure. The sample is injected by reversing the positions of the load/inject and separator valves. This action diverts the eluent through the sample loop (Figure 2b). The sample plug is carried through the manual regeneration valve and onto anion column 1. The purpose of this first anion column is to separate the Ffrom all other anions present in the sample. Four minutes after the injection, fluoride, the most weakly retained anion, elutes from column 1and passes onto anion column 2. The load/inject and separator valves are then reversed to change the eluent flow through anion columns 3 and 2 (Figure 2c). The fluoride elutes through anion column 2 where it is further resolved from potential interferents, through the suppressor column, and into a conductivity cell where it is detected. While the F- is eluting through anion column 2, the manual regeneration valve is reversed and the autoregeneration switch is activated to start the regeneration of column 1 (Figure 2c). The strong eluent 0.02 M NaHCO, passes through anion column 1, quickly cleansing it of strongly retained anions such as NO; and Sod2-.After 1 min, autoregeneration valve 1 automatically switches to the weak eluent reservoir, 0.0015 M NaHCO, (Figure 2d). The weak eluent is pumped through column 1 for 5 min to reequilibrate it before another sample is injected. Ion Selective Electrode Procedure. A Corning fluoride ion selective electrode and an Orion single-junction Ag/AgCl reference electrode were used in conjunction with a Fisher Model 750 Acumet selective ion analyzer to measure the concentration of fluoride. Standards covering the range 0.5-5 yg/mL were prepared daily from a Dionex 1000 pg/mL standard. Total ionic strength buffer (TISB) was prepared by dissolving 5 g of cyclohexylenedinitrilotetraaceticacid, 10 g of potassium nitrate, and 125 g of ammonium acetate in 480 mL of deionized water. The pH was adjusted to 6.5 with glacial acetic acid and the solution was diluted to a final volume of 500 mL. Geological samples were hydropyrolyzed as described in the previous section, with the following exceptions. The scrubbing solution, which was 50 mL of 0.025 M NaOH instead of 0.0015
ANALYTICAL CHEMISTRY, VOL. 60, NO. 4, FEBRUARY 15, 1988
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M NaHC03,was diluted to a final volume of 100 mL rather than 200 mL. The pH of a 20-mL aliquot of the hydropyrolyzed sample was adjusted to 6.0 with 5.0 N H2S04and finally to pH 5.0-5.2 with 0.5 N HaO,. The resulting solution was gently heated for 10 min to drive off C02 (5). After the solution cooled, 5 mL of the TISB was added and the solution potential was measured with a fluoride ion selective electrode utilizing the method of standard additions.
RESULTS AND DISCUSSION Air Flow Rate, Temperature, Burn Time, Fluxes, and Sample Size. A number of the hydropyrolytic parameters were optimized to obtain a complete F- extraction of the geological sample. Humidification of the air flow caused a significant increase in the F- recovery. This indicated that hydrolysis of the volatile fluoride species was part of the mechanism by which the fluoride was extracted and recovered (14, 17,18). The air flow rate was optimized by varying the flow from 0.90 to 3.7 L/min while maintaining a constant temperature of 1050 OC and a burn time of 15 min. The F- recovery for a typical coal sample reached a maximum at flow rates greater than 2 L/min (Figure 3, top). The P recovery for a phosphate rock standard followed a similar trend. Temperature profiles for the hydropyrolysis of a coal and
a phosphate rock standard showed that maximum F recovery was achieved a t temperatures exceeding 1050 "C regardless of the air flow rate or burn time (Figure 3, center). However, extraction efficiencies approaching 100% were only achieved when an air flow rate greater than 2 L/min and a burn time of 15 min were employed. The time required for complete P extraction was examined a t 1050 "C and an air flow rate of 2.5 L/min. Under these conditions the sample must remain in the hot zone of the combustion tube for a t least 15 min (Figure 3, bottom). Addition of fluxes such as Si02 (12), Vz05(14, 15), and Moo3did not significantly increase the F- recovery for coal and ash samples if the optimum hydropyrolytic conditions were used. However, low F- recoveries were obtained when various rock standards were analyzed under these conditions. Consequently, the utility of two fluxes Si02and Mooa was examined. In a hydropyrolytic system, metal fluorides are thought to react with silica and water to form volatile H2SiFs (19). SiO, has been added to geological samples to promote this reaction (20). No advantage was noted when SiO, was used as a flux. A constant 70% P recovery was obtained when 0 4 . 5 g of S O 2 was added to USGS Diabase Rock W-2. Failure of Si02to act as a P promoter indicates that the F extraction efficiency
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Table I. Concentration of Fluoride in 15 Geological Standard Reference Materials concn,
IC NBS Coal 163213 NBS Coal 1635 SARM Coal 20 BCR Coal 40 USGS Devonian Ohio Shale SDO-1 NBS Fly Ash 1633 NBS Fly Ash 1633a BCR Fly Ash 38 NBS Phosphate Rock 120b NBS Portland Cement 633 NBS River Sediment 1645 NBS Estuarine Sediment 1646 USGS Granite Rock G-2 USGS Andesite Rock AGV-1 USGS Diabase Rock W-2
58.4 41.9 140 119 741 202 81 548 38200 570 1470 490 1370 433 176
ISE 80 85 142 128 163 55 496 39600 525 1568 433 1511 407 123
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reported
method"
ref
20, 42 148 111.4 f 8.5 794 10, 20 110, 70, 87, 23
ISE IC ISE, SP IC US, AAS SSMS, PIGME, US, OS
22, 23 24 25 14 19 26, 26, 27, 28
NAA, IENA, IC, ISE
ISE IC, ISE
19 29 30, 19
OS, SP, CO, ISE, NAA OS, SP, CO, ISE SSMS, US
31, 32 31, 32 33
38400 f 1100 800 900, 1740 1260 f 90 420 f 50 164, 198
ISE, ion-selective electrode; IC, ion chromatography;SP, spectrophotometry; AAS, flame atomic absorption spectrometry; SSMS, spark source mass spectrometry; PIGME, proton induced y-ray emission spectrometry; NAA, neutron activation analysis; IENA, instrumental epithermal neutron activation; OS, optical spectrographic analysis; CO, colorimetric analysis; US, unspecified. is independent of the SiOz content of the geological sample. Reactions of FeF, and CrF3with metal oxides such as MooB at elevated temperatures have been shown to yield Fe203or Cr,03 and the metal fluoride (21). Complete fluoride exchange does not always occur in reactions with higher valence metal oxides and oxyfluorides are formed. Molybdenum fluorides and molybdenum oxyfluorides are very volatile compounds. Therefore, it was postulated that Moo3 could be used to promote the extraction of fluoride from geological samples that contain refractory fluorides such as fluorite and fluoroapatite. The addition of 0.035 g of Moo3 to the rock standards enhanced the F recovery by 1040%,resulting in quantitative F- recovery for these samples. With the exception of NBS Phosphate Rock Standard 120b, the F- recovery was independent of MOO, concentration at weights greater than 0.035 g (sample/flux ratio = 7.2). NBS 120b required 0.070 g of MOO, for complete F- recovery. The relationship between sample size and F extraction was investigated for several typical coal and ash samples. In all cases the F recovery was independent of sample weight when less than 1 g of sample was used. The extraction efficiency occasionally decreased with larger sample size and the magnitude of the decrease was very sample dependent. The addition of MOO, to larger samples did not increase the extraction efficiency. The loss at large sample weights appeared to be greater for samples with high sulfur concentrations and might have been caused by depletion of the scrubbing solution. Detection Limits and Linearity. Detection limits were determined by successively hydropyrolyzing and analyzing five blanks. The detection limit was defined as the minimum concentration of F that was found to differ significantly from the blank at the 99% confidence level. The ion chromatographic detection limit was determined to be 1 ng of F-. Addition of MOO, to the rock samples degraded the detection limit to 5 ng of F-. The increased variability in the blank was caused by condensation of the MOO, in the combustion tube and its revolatilization during the hydropyrolysis of subsequent samples. The calibration curve was found to be linear from the detection limit to 500 ng of F-. This range was found to be satisfactory for the majority of samples. When samples with an extremely high F- concentration were encountered, accuracy was preserved by hydropyrolyzing less sample or by diluting the scrubbing solution. Precision and Accuracy. The precision obtained for five successive digestions and determinations of F- in two typical
HYDROPYROLYTIC PARAMETERS
I
10
16
PO
26
BURN TIL[B (min)
Flgure 3. Dependence of fluoride recovery on (top)air flow, (center) temperature, and (bottom)burn time for (0)BCR Coal 40 and (A)NBS Phosphate Rock 120b.
samples, BCR Coal Standard 40 and USGS Diabase Rock W-2 was examined. The short-term relative standard deviation (RSD) of the F determinations was 4.9% for the coal standard and 5.3% for the rock standard. Short-term precision for five successive injections of a 0.5 gg/mL standard is 0.7%. This reflects the precision of the chromatographic determination and indicates that the RSD of the hydropyrolytic digestion is approximately 4%. A thorough evaluation of the accuracy of this method is difficult due to the lack of certified fluoride standard reference materials. Analysis of two certified standards, BCR Coal 40
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Anal. Chem. 1988, 6 0 , 369-371
and NBS Phosphate Rock 120b, yielded results that differ from the reported values by 6.8% and 0.5%, respectively. Table I lists the F- results that were obtained for 15 geological standard reference materials representing a variety of matrices. The hydropyrolytic-ion chromatographic results are generally in agreement with those reported even though the reported results often represent noncertified, literature, average, or magnitude values. Comparison with an Ion-Selective Electrode. The Fcontent of the 15 hydropyrolyzed reference materials was redetermined by an ion-selective electrode (ISE) to further verify the F- results obtained by the hydropyrolytic-ion chromatographic method. Fluoride concentrations listed in Table I are in general agreement (&lo%) with those determined by ion chromatography. In three instances, NBS Fly Ash 1633, NBS Portland Cement 633, and NBS River Sediment 1645, the F- concentrations determined by ISE are in better agreement with the hydropyrolytic-ion chromatographic results than with previously reported data. Good agreeement between the two methods is also obtained for BCR Fly Ash 38 and NBS Estuarine Sediment 1646 for which no reported F- concentrations were found. Poor agreement is obtained for samples containing less than 100 ppm P such as NBS Coals 163213 and 1635 and NBS Fly Ash 1633a. This disparity can be partially attributed to the poor precision of the ion-selective electrode (9.8% RSD) compared to the precision of the ion chromatograph (0.7% RSD) a t 0.5 ppm F-, the hydropyrolyzed concentration of F- from a 100 ppm sample. Imprecise determination of the F- concentration of the sample and standard addition spikes can severely alter the slope of the standard additions regression, thereby affecting the accuracy of F- determinations below 100 ppm.
CONCLUSION The data presented in this report show that a hydropyrolytic procedure can be used to quantitatively extract Ffrom geological samples. The F- content of the relatively interference-free extract can be determined either by ion chromatography or by an ion-selective electrode. However, ion chromatography is preferred when maximum selectivity and/or sensitivity is required.
ACKNOWLEDGMENT The authors thank F. G. Walthall of the United States Geological Survey and R. K. Leininger of the Indiana State Geological Survey for providing several of the rock standards
and G. A. Witt for performing many of the analyses. Registry No. F-,16984-48-8;Moo3, 1313-27-5.
LITERATURE CITED 8iological Effects of Atmosphere Pollutants-Fluorides ; National Academy of Sciences, National Research Council: Washington, DC, 1971; 295 pp. Gluskoter, H. J.; Pierand, L. H.; Pfefferkorn, H. W. J. Sediment. Petrol. 1970, 40, 1363-1366. Crossley, H. E. J. SOC. Chem. Ind., London 1944, 6 3 , 289-292. Thomas, J., Jr.; Giuskoter, H. J. Anal. Chem. 1974, 4 6 , 1321-1323. Annu. Book ASTM Stand. Part 26, D 3761-79. Troii, G.; Farzeneh, A,; Cammann, K. Chem. Geol. 1977, 2 0 , 295-305. Edmond, C. R. Anal. Chem. 1989, 41, 1327-1328. Gimeno Adeiantado, J. V.; Peris Martinez, V.; Checa Moreno, A.; Bosch Reig, F. Talanta 1985, 3 2 , 224-226. Leon-Gonzaiez, M. E.; Santos-Delgado, M. J.; Polo-Diez, L. M. Anal. Chim. Acta 1985. 778, 331-335. Butler, J. N. Ion-Selective Electrodes, NBS Spec. Publ.; Durst, R. A,. Ed.; National Bureau of Standards: Washington, DC, 1969; Chapter 5. Nicholson, K.; Duff, E. J. Anal. Lett. 1981, 74, 887-912. Ganiiang, G.; Bing, Y.; Yang, L. fuel 1984, 63, 1552-1555. Coerdt. W.; Mainka, E. Fresenius’ Z . Anal. Chem. 1985, 320, 503-506. Evans, K. L.; Tarter, J. G.; Moore, C. B. Anal. Chem. 1981, 5 3 , 925-928. Chakraborti, D.; Hiilman, D. C. J.; Zinagro. R. A.; Irgoiic, K. J. fresen/us’ Z . Anal. Chem. 1984, 319, 556-559. Hili, R. A. HRC CC, J. Hlgh Resolut. Chromatogr. Chromatogr. Commun. 1983, 6 , 275-276. Warf, J. C.; Cline, W. D.; Tevebaugh, R. D. Anal. Chem. 1954, 2 6 , 342-346. Whitehead. D.; Thomas, J. E. Anal. Chem. 1985, 5 7 , 2421-2423. Farzaneh, A.; Troll, G. Geochem. J . 1977, 1 7 , 177-181, Bock, R. A Handbook of Decomposition Methods in Analytical Chemistry; International Textbook Co., 1979. Cabeklu, N. C.; Leng, B.; Moss, J. H. J. fluorine Chem. 1975, 6 , 357-366. Giadney, E. S.;Burns, C. E.; Perrin, D. R.; Roelandts, I.; Gills, T. E. 1982 Compliatlon of Elemental Concentration Data for NBS Biological, Geological, and Environmental Standard Reference Materials ; NBS Publication 260-68, 231 pp. Dickinson Laboratorles Inc., El Paso, TX, private communicatlon. Gcdbeer, W. C.; Swaine, D. J. fuel 1987, 66, 794-798. Gonska. H.; Griepink, B.; Colombo, A.; Muntau, H. The Certification of the Contents of Arsenic, Cadmium, Chromium, Cobalt, Fluorine , Manganese, Mercury, Nickel, Lead, and Zinc in a Coal; Commission of the European Communities Report EUR 9473 EN, Brussels, Luxembourg, 1984. Clayton, E.; Dale, L. S. Anal. Lett. 1985, 18, 1533-1538. Bird, J. R.; Clayton. E. Nucl. Instrum. Meth. Phys Res. 1983, 218, 505-528. Bettineili, M. Analyst (London) 1983, 708, 404-407. National Bureau of Standards Certlficate of Analysis, SRM 633, Portland Cement, Washington, DC. 1983. National Bureau of Standards Certificate of Analysis, SRM 1645, River Sediment, Washington, DC, 1982.
RECEIVED for review May 4,1987. Accepted October 1,1987.
CORRESPONDENCE Procedure for Increasing the Accuracy of the Initial Data Point Slope Estimation by Least-Squares Polynomial Filters Sir: The least-squares polynomial filter for estimating the smoothed value and derivative of an initial point in the data set has potential applications in initial rate estimation in reaction kinetics (1,2),thermal lens measurements (3), and decay measurements (4)and has been applied by Harris et al. (5,6)to increase the precision in determining initial light intensities in thermal lens absorption measurements. Even though the Savitzky-Golay procedure (7), or its modified version (B), is excellent in smoothing and differentiation of
most of the data points, they do not allow initial-point smoothing and slope calculation since these procedures utilize a polynomial fit to a segment of data points to estimate the midpoint of the segment. However, a procedure has been described by Harris et al. (9,lO)in which a polynomial fit to a segment of data to estimate the initial point and its derivative has been utilized. In this paper accuracy of the initial point slope calculation by polynomial filters has been examined and a procedure for
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