I

I

Figure 1. Analytical calibration CUNB of signal, x, vs. concentration, c

The unknown Signal. xu, is re@& 10 an w h o m con(amat1m. cu, tJwcu$ the equation x = mc +

i. where rn io the slop and I is Uw lnteroept ot me line

The ability to quantify a trace ele- ment or molecule in chemical and bio- logical matrices using specific analyti- cal methods is often viewed in terms of the limit of detection. This limit of detection is a number, expressed in units of concentration (or amount), that describes the lowest concentra. tion level (or amount) of the element that an analyst can determine to be statistically different from an analyti- cal blank (I). Although this definition

approaches (1-13). In spite of the fact that the International Union of Pure and Applied Chemistry (IUPAC) adopted a model for the limit of detec- tion calculations in 1975 (I), and the ACS Subcommittee on Environmental Analytical Chemistry reaffirmed this standard in 1980 (2), acceptance of this model by the general analytical community has been slow. The result of this slow acceptance bas led to a great deal of uncertainty when limits

examine the statistical meaning of limit of detection values in a format consistent with the IUPAC definition. It is not intended to be a comprehen- sive review of the various methods of calculating limit of detection values. For a more complete review, the read- er is referred to the excellent articles by Kaiser ( 3 4 , Boumans (7-9). Cur- rie(lO),Glaseret al. IiI),aswellas available textbooks (12,13J. Rather, this HEPOHT is intended to be a sim-

seems rather straightforward. signifi- cant problems have been encountered in expressing these values because of the various approaches to the term “statistically different.” The calculat- ed limit of detection for an element can easily vary an order of magnitude through the use of different statistical

of detection are used a s~a basis for comparison between various analytical procedures, methods. or analytical in- strumenffi. Unless the limits of detec- tion are calculated in a consistent manner, the comparison may be meaningless.

ple and general discussion on methods for calculating limits of detection; it is geared to the analyst who does not have a rigorous knowledge of statis- tics. In this examination, the signifi. cance of the limit of detection values will be emphasized, and the possible problems encnuntered when using It is the purpose of this REPORT to

7 1 2 ~ ANALYTICAL CHEMISTRY, VOL. 55. NO. 7, JUNE 1 9 8 ~ 000%2700/83/035 1-7 12ASO 1.50/0 Q 1983 American Chemical Society

Gary L. Long J. D. Winefordner Department of Chemism University of Flwida Galmville. FIB. 32611

limit of detection values obtained from non-IUPAC methods as a basis for comparing methods and instru- menta will be discussed. Also, two methods will be introduced that per- mit measurement errors in the analyt- ical sensitivity to be included in the limit of detection calculation. These two methods as well as the IUPAC method will be evaluated for their ability to incorporate these errors into the numerical limit of detection.

Definition The IUPAC definition, adopted in

1975, states that “the limit of detec- tion, expressed as a concentration CL (or amount, qL), is derived from the smallest measure, XL, that can be de-

Flgure 2. Normal distribution curve for a measured x variable me pink shaded wet. 01. represents me pobabll- hvmt XE 3 (,A + k(r)OrxL a(& + 3%)

tected with reasonable certainty for a given analytical procedure” (I). This concept is further clarified by the ACS definition, which states “the limit of detection is the lowest concentration of an analyte that an analytical pro- cess can reliably detect” (2). To un- derstand what a reasonably certain measure or a reliable detection is, the method of measurement as well as the errors (including noises) agsociated with the measurement must be well understood.

Measurements Generally, most analytical methods

require the construction of analytical calibration curves for the determina- tion of unknowns. These cuwes are

generally plots of signal, x, vs. analyte concentration, c, and are represented as in Figure 1. The relationship be- tween x and c can be obtained by per- forming a linear regression analysis on the data. This analytical calibration relationship cnn be expressed as

x = m c + i

where m is the slope or analytical sen- sitivity and i is the intercept. When an unknown sample containing the ana- lyte is subjected to the analytical pro- cedure, a value, xu, can be measured. This value may then be inserted into Equation 1 to determine the concen- tration of the unknown, cu. However, the ability to solve accurately for h~ is dependent upon how well the m and i

ANALYTiCAL CHEMISTRY. VOL. 55. NO. 7, JUNE 1983 713,.

values are known. As long as the cali- bration curve is obtained in the linear response region of the method, the more points obtained in the construc- tion of the calibration curve the better defined them value will be. Also, if points are sampled near the origin, the i value may be better defined. How- ever, if the m and i values are not well- defined because of nonlinearity in the calibration curve or a poor choice of calibration curve ranges, the result of the unknown determination, eu, may he subject to considerable error.

Statistics The amount of error associated with

a measurement of x can be statistical- ly estimated. Most measurements are subject to error that follows a normal distribution. If a sufficiently large number of observations is made, plot- ting the measured responses would produce a curve similar to that shown in Figure 2. The mean value of the re- sponses, p, occurs a t the center of the curve. The curve is symmetric around p and extends outward in units of standard deviation, u. Since this curve includes all x values that could be ob- tained from the procedure for the sample, the area under the curve can be expressed in terms of probability, P (i.e., there is a 100% chance, P = 1, that a measured x value would fall somewhere under the curve).

probability can he measured to esti- mate the chance that a newly mea- sured x value, XE, would he a certain number of standard deviation units .away from the mean response, p. In Figure 2, XE is shown to the right of p and can be measured to be ku away from p. By dissecting the curve with a line drawn a t this x value, the area to the right of the line, a, is the prohabil- ity that XE 3 ( p + ku). This chance, which is represented by the pink shad- ed area, can be determined from

The relationship between area and

where the XE value is ku away from p, (Le., (XE - p) /u = k).

This illustration can also be used to aid in the explanation of the smallest detectable signal, XL, in the IUPAC definition. When the determination of a limit of detection is performed, blank measurements, XB, are normally taken. The question, however, is "how well are these XB values known?" A mean value of the blank responses, XB, can he calculated as

ng XBi

and the standard deviation as

(3)

I --

I-

Figure 3. Analytical calibration curve of signal, x, vs. concentration, c, show- ing the relationship of ks. to the limit of detection, q

nB (XBj - XBB)'

(4)

for nB Observations. Because a finite small number of blank readings is nor- mally taken, e.g., nB = 20 or greater, SB must be used instead of OB. If a sample of this size is used, SB can be considered to he a reasonable indica- tor of OB. If the random error follows a normal distribution, a plot of these re- sponses (frequency of occurrence vs. XB values) would resemble Figure 2. The probability that the smallest dis- cernible analytical signal, XL. can be measured and not be a random fluctu- ation of the blank is dependent upon how many standard deviation units XL is from XB. If XL is 3SB away from XB, the area to the right of XL is no less than 0.0013. Thus, there is a 0.13% chance that a signal measured a t XL or greater would be the result of a ran- dom fluctuation of the blank signal. This small chance of error can then fulfill the reouirement of a reasonablv

j-1 Sgz =

(ne - 1)

certain signal. In defining CL, IUPAC states that

XL = XB + kSB

where k is a numerical factor chosen in accordance with the confidence level desired. The CL is a function of XL and therefore

( 5 )

where m is the analytical sensitivity. Because the mean blank reading, XB, is not always 0, the signal must be background corrected. By substituting Equation 5 into Equation 6, Equation 7 is obtained

This definition of e~ can be illustrated

as shown in Figure 3. The limit of de- tection is found by relating ksB to a concentration value by dividing by the slope of the calibration curve line ob- tained from the linear regression anal- ysis. However, the value obtained can only be a true reflection of the limit of detection when m is well-de- fined and i is essentially 0.

level of 99.86% that XL Z (FB + 3se) for a measurement based on the error of the blank signal following a normal distribution. I t must he emphasized that if XB does not follow a normal distribution, then the probability that XL 2 (XB + 3.38) would he lOO(1 - lkz) , or 89% according to Tschebyscheffs inequality (5) . Hence, values of k < 3 should not be used for limit of detection calculations.

Other Approaches

es to calculating CL values are similar to the IUPAC model in that SB and k factors are involved. However, it is be- cause of these terms that trouble may he encountered when CL values are used as a basis for the comparison be- tween procedures, methods, or instru- ments. The most widely debated of the two factors has been the choice of a value fork. Kaiser was perhaps the first to stress the use of k = 3 for cL values ( 3 , 4 ) . This value has also been agreed upon by other authors (9,13), by IUPAC ( I , 14), and by the ACS (2). A value of 2 for k had been initially suggested (8) hut this value corre- sponds to a 97.7% confidence level for normal distribution and 75% for a nonnormal distribution of measure-

The use of k = 3 allows a confidence

The majority of the other approach-

-. ment error.

Although the use of k = 3 instead of k = 2 s l igky increases the CL value, it is clear that e~ values must differ by a factor of three for the values to be sig- nificantly different. Nevertheless, fac- tors of less than three have been com- monly used for comparison purposes. In order to minimize confusion, IUPAC suggested that XL values be re- ported in all literature with their k value, x~(k-8) . I t would be extremely useful to go one step further and in- clude the k values when CL values are reported, CL(~=S) . This change would be beneficial because CL values are more commonly reported than XL values.

A problem encountered in the com- parative use of CL values is the use of the standard deviation of the mean, sg ( 1 1 ) . the pooled standard deviation, sp (7,12), or the relative standard devia- tion (RSD) (7 ,9 ) . Although each of these standard deviation expressions is important and has its place in ana- lytical chemistry, the use or misuse of these expressions in CL calculations may result in significant deviation

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In many ICP determinations, the RSD has been measured to be 0.01 (as determined by emission flicker noise). Unfortunately, many ICP m values in papers and current manufacturers’ bulletins have been calculated with k = 2. Inserting these values into Equation 13 yields

Figure 4. Normal distribution C U N ~ S for the blank observation. %(pink line), the llmit of detection. x (blue line), and the limit of identification, xI (purple line) M e all standard deviations follow a m I dlswibutim and are equal

from the IUPAC model. The standard deviation of the mean (or the standard error), sg, is ex- pressed by

This value is calculated by dividing the standard deviation of the blank measures, 88 , by the square root of the number of blank Observations, nB. Usually when ss values are used, the k factor is replaced by a t distribution value. Even though the t values reflect the problem of defining a standard de- viation for a finite number of ohserva- tions, 3SB > t. SB/(nB)’/2 for a = 0.005 and five observations (four degrees of freedom). This inequality greatly in- creases as ne increases. If a large num- ber of observations are taken on the blank, say 30, the use of the t and will reduce the value of CL by a factor of six from the IUPAC model.

The use of the pooled standard de. viation includes the number of blank measurements as well as sample mea- surements. Generally, the pooled stan dard deviation, SP, is expressed as

where 8s is the standard deviation of a sample measurement and ng is the number of sample obnervations. If e = SB, then Equation 9 reduces to

For ns = 1, sp is essentially the same as SB. However, if ns and ne are both large, sp < SB. Again, the use of a largt number of observations as mentioned above would cause a sirmifieant reduc- tion in the IUPAC model.

value as eompared to the

Another common practice involves the use of the RSD, which is def ied as

This relationship is useful in ex- pressing the “concentrational limit of determination,” CD (7). Here, the mea- sure XD corresponding to CD is defined

XD = ko SB (12)

as

where SB is the standard deviation of the blank (not the RSD), and kD is a confidence factor that is defined by the reciprocal of the magnitude of the RSD value. For a maximum allowed RSD of5%, kD = 20 and for a RSD of lG%, kD = 10.

Another limiting expression involv- ing RSD values involves the rearrang- ing of Equation 7 (9). If the back- ground signal is included in the nu- merator and denominator of Equation 7, then

A problem that may be encountered with thii approach is that the RSD for some spectrometric detection systems may be >0.01. Before using this meth- od, an analyst should reconfirm the validity of RSD 4 0.01. Failure to measure and correct for high RSD val- ues could result in erroneous ues. An attempt to compare an ICP q, value obtained from this method and an IUPAC value for the same anal- ysis procedure would be meaningless.

A well-based but seldom used con- cept in the calculation of detection limits is the limit of identification, 9. as described by Boumans (7) or the limit of guarantee for purity, cc, de- scribed by Kaiser (3). These concepts are essentially the same and are based on the idea that the lowest statistical- ly discernible signal should be

val-

XI = XL + 381 where 81 is the error associated with the measurements at the XI level, or

if 81 = SB. This concept is illustrated in

Table 1. Statlstlcal Expresslons for the Slope and Intercept

n

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Figure 4. When measurements are made for a sample, the x values ob- tained should follow normal distribu- tion around a mean value. If a sample were measured to have a mean a t the XL value, the distribution of these x values around XL would resemble the blue line in Figure 4.One-half of the time the measurement would fall below the XL value and could not be considered a true signal according to the IUPAC definition. To avoid this high probability, the limit of XI is set at 3sr away from XL. This level is cbo- sen so the areas a and 0 are equal. If SI = SB then this level is 3SB away from XL or 6 s ~ away from ZB. By using k = 3, the area of the XI distribution curve below XL, (3, is no less than 0.0013. Thus, there is a 0.13% chance that an x value measured a t XI would fall below the XL limit and not be con- sidered as a true signal.

This idea of further statistically separating the blank measurements distributions and true signal distribu- tions has been proposed by the ACS Subcommittee on Environmental An- alytical Chemistry and has been termed the limit of quantitation (2). Since the numerical significance of the analyte concentration increases as the analyte signal increases above XL, a minimum criterion, representing the ability to quantify the sample, can be established reasonably far way from ZB. This criterion, called the limit of quantification (LOQ), is 1Ou away from i i ~ . For limit of detection work, u = ss. Samples that are measured as having a signal, x, where x > 1 0 8 ~ are termed tobe in the region of quantita- tion while samples where 3SB Q x Q 1OSB are termed to be in the region of detection.

By setting the quantitation level as loss or the identification limit as ~ S B , a much higher probability is afforded that the sample signal is not just a random fluctuation of the blank. However, when making comparisons using LOQ or CI to IUPAC CL values, the analyst must bear in mind the dif- ference in the kfactors for each limit.

Methods Involving Analytical Sensiilviiy Error

The previous models for calculating detection limits consider the error in the blank measurements. These mod- els also consider the analytical sensi- tivity, m, as a well-defined value. In practice, however, m may have signifi- cant error due to nonlinearity in the calibration curve, or measurement er- rors.

The following proposed detection limit approaches include errors associ- ated with measurements of the analyt- ical sensitivity. The first method, a graphical approach, includes the stan- ' . " '

Figure 5. Analytical calibration curve of signal, x. vs. concentration, c, show- ing graphical approach to limit of detec- tion calculation While dashed lines are Uw limit of emor bars. cL is obtalned ham xc if no m w occurs in slope. ca is obtained tmm xc if slope error is significant

dard deviation of the slope, s,, in the CL expression. The second method, a propagation of errors approach, con- siders the standard deviation of the concentration, sE. This value is calcu- lated by including the standard devia- tions of the blank, slope, and intercept in the equation. The statistical expres- sions for these values are listed in Table I.

Although these models require ad- ditional calculations, most linear re- gression analyses are performed using calculators or microcomputers. With additional programming, these calcu- lations can be easily performed, allow- ing more accurate determinations of CL values to be made. These values may also be used for a truer compara- tive look at the ability of an analytical method or instrument to quantify trace elements (or compounds) in a sample.

Graphical Approach To obtain a more reliable CL value,

the m value should be expressed as a confidence interval m f t,s,, where 8, is the standard deviation of the slope and t, is a t distribution value chosen for the desired confidence level, a, and the degrees of freedom, u. The insertion of this interval into Equation 7 produces

The effect of the inclusion of the con- fidence interval can best be seen by referring to Figure 5. The error bars (confidence interval) generated around the regression line are indicat- ed as white dashed lines. Because of error in the slope, three concentration

710A ANALYTICAL CHEMISTRY, VOL. 55, NO. 7. JUNE 1983

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values are found for a given XL value. When tasm = 0, (as in Equation 7), the value of CL is obtained. However, the reduced analytical sensitivity yields a value, CR, to the right of CL. If m >> tasm, then the CR will not be sta- tistically different from CL. For the sit- uation when tasm is not sufficiently small as compared to m, a CR may be aubstantially larger than CL, There- fore, only the larger value should be used in reporting a limit of detection.

An important consideration in the me of this model is the choice of a t value. The recommended k value of 3 involves a 99.87% confidence level, Therefore, the t should reflect a simi- ar level. An a = 0.0005 results in a :onfidence level of 99.9% for a two- ;ailed t distribution. The degrees of ieedom, u, are n - 2 for a linear re- :ression model. The n value used 5hould be the number of points used ;o prepare the calibration curve, i.e., ?ach point consists of a mean measure md a concentration value.

Propagation of Errors Approach In the second approach used to

evaluate CL, the error in the intercept term, i, as well as the error in m are considered. To include these errors, Equation 1 must be rearranged to

From Equation 18, any value of x can be related to a concentration using the m and i values obtained from the lin- ear regression model. The i term is usually neglected in most cases and sssumed to be 0 because the analytical measures are background subtracted. But in most linear regression analyses, i # 0. If a true reflection of the error in the determined concentration is sought, the error in m and i must be included in Equation 7.

The contribution of each term to the total error may be found by taking the first derivative of c with respect to each term:

+ - sm2 (19) (3 Taking the designated derivatives and the square root gives

+ (- %)2sm2]1/2 (20)

and finally combining like terms yields [... + s i2 + ( q 2 s m j 1 / 2

s, = (21) m

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0.05 5

Equation 21 allows the determination of standard deviation in a c value cal- culated from any x value.

In the case of limits of detection, the EL value is actually a confidence value expression of how well the blank is known. If Equation 7 is reconsid- ered, it can be written as

CL = ks, (22)

where the S B h term describes the error in terms of c (if c - a), Equa- tion 21 could now be used to evaluate se where x is the blank signal, jte, and SB is substituted for 9.. By measuring ZB. SB, and calculating m, i, s,, and si, the value of s, can be determined.

In most determinations, the data are background corrected, that is, XB = 0. Substituting the above mea- sured and calculated values in Equa- tions 21 and 22, the expression for CL is further simplified to

-

In the event that no significant error occurred in the slope, Equation 21 reduces to

(24) k[se2 + ~ i * ] ’ ’ ~

m CL =

If the error in the intercept, si, is suffi- ciently small, Equation 23 reduces to Equation 7, which is the IUPAC defi- nition of the limit of detection.

Evaluation of Approaches The IUPAC, graphical, and propa-

gation of errors models will be applied to four different sets of experimental data to show the effect of certain ex- perimental conditions on the estima- tion of CL values (Table 11). The data in Table I1 have been taken from a re- cent paper on ICP-excited ICP fluo- rescence detection limits ( I 5 ) . The four sets of typical experimental con- ditions are: A, Ca(I1) fluorescence data which have well-defined m and i values; B, Ca(I1) fluorescence data where SB is essentially the same as in A, but the calibration curve data are taken far away from CL resulting in a

poorly defined i value and a well.de. fined m value; C, Cu(1) fluorescence data where there is nonlinearity in the calibration curve resulting in ill-de- fined m and i values; and D, Co(II) fluorescence data where extreme non- linearity in the calibration curve re- sults in severe errors in both m and i values. The limit of detection values, CL(L=~) , for the three methods are tab- ulated in Table 111. Here the C L ( ~ = 3)

values are reported only to one signifi- cant figure, as all CL values should be. The subscript numbers representing the second significant digit in cases A and B are included only for compara- tive purposes.

For case A, the IUPAC model and the graphical approach agree well. Only the propagation of errors model shows a significantly higher C L ( ~ = 3) value; this deviation is the result of the error associated with the intercept value.

The values obtained in case B em- phasize the problem of an ill-defined, nonzero intercept. This problem is the direct result of constructing calibra- tion curves for detection limits when the lowest point of the calibration curve data is considerably removed from the CL(k = 3) value. Only the propagation of errors model accounts for this error, while the other two methods indicate an erroneously low CL(k = 3) value. Although there are no set guidelines for constructing calibra- tion curves, the third approach clearly illustrates the problem of sampling too far away from the limit of detec- tion.

In some instances, calibration curves may not be linear. Although the linear regression procedure will fi t a line through the data, the resulting m value is by no means a “true” repre- sentation of the analytical sensitivity a t all concentrations. Nonlinear cali- bration curves generally produce sig- nificant sm, si, and i values. Case C represents such conditions. The IUPAC model results in a CL(k = 3, of 0.03 ppm. Repeating the CL calcula- tion using the graphical approach re- sults in a value of 0.3 ppm. Finally al- lowing m and i errors to be included results in a CL(k 3) of 5 ppm for the propagation of errors method. The propagation of errors value is 170 times the IUPAC CL(k = 3) value.

further emphasized by considering case D. Here, the errors associated with m and i are greater; however, the large value of sm results in a special problem with the graphical approach. If t,s, > m, then the concentration value for the limit of detection can even be negative. Such negative values are the direct result of the graphical model not being statistically valid. Al- though the graphical model is easier to

The problem of nonlinearity can be

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P ~ I ~ P

724A ANALYTICAL CHEMISTRY. VOL

use than the propagation of errors ap- proach, the former may give erroneous results as seen in Case D. Thus, the graphical method could be used only for approximating CL values. The de- tection limit using the propagation of errors approach is calculated to be 6 ppm. Correspondingly. the detection limit for the IUPAC model is 0.5 ppm, differing hy a factor of 12 between the two methods.

Conclusions Based on the above considerations,

the graphical approach to CI, should not be used. The IUPAC approach i s valid only if the major source of error is in the blank, i.e., SR* >> si* or sm2. Therefore, the IUPAC approach in most cases gives artificially low values of CL. The propagation of errors ap- proach i s certainly the most liberal ap- proach and will give values of CL con- sistent with the reliability of the blank measures and the signal measures of the standards.

limits of detection using the IUPAC approach with k = 3 ( c L , ~ 3,). The use of the propagation of errors ap- proach is also recommended because errors in the analyte measurements can be incorporated into the CL value. By adopting these approaches, mean- ingful comparisons of analytical meth- ods and instruments based on CL val- ues can be made.

We recommend that analysts report

References (1) “Nomenclature. symbols. units and

their usage in spectrochemical analysis- 11,” Spectroehim. Acto R l97R, 33fl,242.

(2) “Guidelines for Data Acquisition and Data Quality Evaluation in Environmen- tal Chemistry.” Anal. Chcm. 19RO. 52, 2242.

(3) Kaiser. H. “Two Papers on the Limit of Detection of a Complete Analytical Pro- cedure”; Hafner: New York, 1969.

(4) Kaiser, H. Anal. Chem. 1970.42, (2). 24 A.

( 5 ) Kaiser. H. Anal. Chem. 1970.42, (4). 26 A.

(6) Kaiser, H. Speetroehim. Acta R 1978. 33R. 551.

(7) Houmans. P.W.J.M. Speetrochim. Acta R 1978,33R,625.

(8) Bournan!, P.W.J.M.; deBoer, F. J. Sperlroehrm. Acto R 1972.27R. 391.

(9) Houmans. P.W.J.M. “Lines Coinci- dence Tables for Inductively Coupled Plasma Atomic Emission Spectrometry”; Pergamon: Oxford. 1980.

(10) Currie. L. A. Nurl. Imtrum. Methods 1972,100,387.

(11) Glaser, J. A,; Fwrst. D. L.; McKee, C. D.; Quave, S. A.; Budde, W. L. Enui- Ion. Sri. Teehnol. l9Rl. 1.5, 1426.

(12) Peters, D. G.; Hayes. J. M.; Hieftje, C. M. “Chemical Separation and Mea- surements”; Saunderr: Philadelphia, 1974; Chapter 2.

(13) Winefordner. J. D. “Trace Analysis: Spectroscopic Methods for Elements”; Wiley: New York. 1976; Chapter 1.

(14) “Nomenclature. symbols, units, and their usage in spectrochemical analysis- III.”Spcctrochim. Acto R 1978.33fl. 248.

(15) Kosinski, M. A.; Uchida, H.; Wine- fordner, J. D. Anal. Chem. 1983,5.5.688.

Thiswork wassupported by AF-AFOSR. F49620-M-C.W05.

James D. Winefordner (1. ) is a gradu- ate research professor in chemistry a t the University of Florida. His re- interests include diagnostical mea- surements of flames and plasmas; laser-excited luminescence, pho- toacoustic and photoionization of molecules in gases and liquids; laser- excited fluorescence of a t o m in flames and plasmas; development of trace analytical methods for atoms and molecules based upon lumines- cence, chemiluminescence. pho- toacoustic, and ionization methods; specialized methods for molecules based upon synchronous lumines- cence, room-temperature phospho- rimetry, energy transfer lumines- cence. and time resolution; deuelop-

NO. 7. JUNE 1983

ment of new instrumental methods based upon new optical and detection approaches; and applications of ana- lytical techniques.

Gary L. Long is a postdoctoral asso- ciate in the department of chemistry a t the Uniuersity of Florida. He re- ceived his RS in chemistry from Wake Forest University in 1978 and his PhD in anolytical chemistry from North Carolina State University in 1982. His research interests include ICP-excited ICP fluorescence spec- trometry, laser-excited flame fluores- cence spectrometry, and the investi- gation of chemical and physical inter- ferences in flame and plasma spectro- metric analyses.